Abstract: Measurements of the spatial dependence of fuel mixture fraction are made for a non-premixed jet flame in a combustion chamber with imposed acoustic oscillations at frequencies of 22-55 Hz. As part of a set of studies on combustion instabilities and the dynamical behavior of combustion systems, this work is intended to provide a basic understanding of the characteristics of mixing under imposed acoustic oscillations. Infrared laser absorption and phase-resolved acetone PLIF are used to measure the fuel mixture fraction throughout the flow field. The degree of fuel/air mixing is then calculated from the measurements in terms of unmixedness factor, in both temporal and spatial respects. Results show that the acoustic excitation causes oscillations in fuel/air mixing at the driving frequency, which results in oscillatory flame behavior in the flame region. The unmixedness factors for the reacting flow cases exhibit greater overall magnitudes than the cold flow cases, which means that mixing becomes less effective in the presence of flame. Also the degree of mixing decreases with increasing frequency for reacting cases, while, for the cold flows, the mixing tends to be enhanced with frequency.

ID: CaltechAUTHORS:20110208-092444615

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Abstract: Fuel-air mixing behavior under the influence of imposed acoustic oscillations has been studied by investigating the response of the fuel mixture fraction field. The distribution of local fuel mixture fraction inside the mixing zone, which is expected to evolve into the local equivalence ratio in the flame zone, is closely coupled to unstable and oscillatory flame behavior. The Experiment was performed with an aerodynamically-stabilized non-premixed burner. In this study, acoustic oscillations were imposed at 22, 27, 32, 37, and 55Hz. Phase-resolved acetone PLIF was used to image the flow field of both isothermal and reacting flow cases and this data along with the derived quantities of temporal and spatial unmixedness were employed for analysis. The behavior of the unmixedness factor is compared with the previous measurements of oscillations in the flame zone. This comparison shows that local oscillations (of order millimeters or smaller) in fuel/air mixing are closely related to the oscillatory behavior of the flame. For each driving frequency, the mixture fraction oscillates at that frequency but with a slight phase difference between it and the pressure field/flame intensity, indicating that the fuel mixture fraction oscillation are likely the major reason for oscillatory behaviors of this category of flames and combustor geometry.

ID: CaltechAUTHORS:20110125-074002108

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Abstract: For understanding the fundamental properties of unsteady motions in combustion chambers, and for applications of active feedback control, reduced-order models occupy a uniquely important position. A framework exists for transforming the representation of general behavior by a set of infinite-dimensional partial differential equations to a finite set of nonlinear second-order ordinary differential equations in time. The procedure rests on an expansion of the pressure and velocity fields in modal or basis functions, followed by spatial averaging to give the set of second-order equations in time. Nonlinear gasdynamics is accounted for explicitly, but all other contributing processes require modeling. Reduced-order models of the global behavior of the chamber dynamics, most importantly of the pressure, are obtained simply by truncating the modal expansion to the desired number of terms. Central to the procedures is a criterion for deciding how many modes must be retained to give accurate results. Addressing that problem is the principal purpose of this paper. Our analysis shows that, in case of longitudinal modes, a first mode instability problem requires a minimum of four modes in the modal truncation whereas, for a second mode instability, one needs to retain at least the first eight modes. A second important problem concerns the conditions under which a linearly stable system becomes unstable to sufficiently large disturbances. Previous work has given a partial answer, suggesting that nonlinear gasdynamics alone cannot produce pulsed or 'triggered' true nonlinear instabilities; that suggestion is now theoretically established. Also, a certain form of the nonlinear energy addition by combustion processes is known to lead to stable limit cycles in a linearly stable system. A second form of nonlinear combustion dynamics with a new velocity coupling function that naturally displays a threshold character is shown here also to produce triggered limit cycle behavior.

Publication: Combustion Science and Technology Vol.: 177 No.: 2 ISSN: 0010-2202

ID: CaltechAUTHORS:20110207-072124993

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Abstract: Measurements of fuel mixture fraction are made for a jet flame in an acoustic chamber. Acoustic forcing creates a spatially-uniform, temporally-varying pressure field which results in oscillatory behavior in the flame . Forcing is at 22,27, 32, 37, and 55 Hz. To asses the oscillatory behavior, previous work included chemiluminescence, OH PUF, nitric oxide PUF imaging, and fuel mixture fraction measurements by infrared laser absorption. While these results illuminated what was happening to the flame chemistry, they did not provide a complete explanation as to why these things were happening. In this work, the fuel mixture fraction is measured through PUF of acetone, which is introduced into the fuel stream as a marker. This technique enables a high degree of spatial resolution of fuel/air mixture value. Both non-reacting and reacting cases were measured and comparisons are drawn with the results from the previous work. It is found that structure in the mixture fraction oscillations is a major contributor to the magnitude of the flame oscillations.

ID: CaltechAUTHORS:20110208-083707180

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Abstract: Thermoacoustic instability appears when unsteady heat release is favourably coupled with acoustic pressure perturbations. The important technical applications involving thermoacoustics are combustion instability in rocket motors and low-pollutant lean flames; noisy industrial burners; pulsed combustors; and thermoacoustic engines. The simplest device for studying thermoacoustic instability is a Rijke tube. In this work, a series of experiments is carried out to determine the nonlinear behavior of the transition to instability and the excited regimes for an electrically driven Rijke tube. A hysteresis effect in the stability boundary is observed. A mathematical theory involving heat transfer, acoustics, and thermoacoustic interactions is developed to predict the transition to instability and limit-cycle properties.

Publication: Electronic Journal Technical Acoustics Vol.: 12 No.: 12 ISSN: 1819-2408

ID: CaltechAUTHORS:20101130-144132487

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Abstract: A horizontal Rijke tube with an electric heat source is a system convenient for studying the fundamental principles of thermoacoustic instabilities both experimentally and theoretically. Given the long history of the device, there is a surprising lack of accurate data defining its behavior. In this work, the main system parameters are varied in a quasi-steady fashion in order to find stability boundaries accurately. The chief purposes of this study are to obtain precise values of the system parameters at the transition to instability with specified uncertainties and to determine how well the experimental results can be explained with existing theory. Measurement errors are reported, and the influence of experimental procedures on the results is discussed. A form of hysteresis effect at stability boundaries has been observed. Mathematical modelling is based on a thermal analysis determining the temperature of the heater and the temperature field in the air inside the tube, which, consequently, affects acoustical mode shapes. Solutions of the linearized wave equation for a non-uniform medium, including losses and a heat source term, determine the stability properties of the eigen modes. Calculated results are compared with experimental data and with results of the modelling based on the common assumption of a constant temperature in the tube. The mathematical model developed here can be applied to designing thermal devices with low Mach number flows, where thermoacoustic issue is a concern.

Publication: Journal of Sound and Vibration Vol.: 264 No.: 3 ISSN: 0022-460X

ID: CaltechAUTHORS:20101118-102239874

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Abstract: Vigorous burning of vortices, formed behind flame stabilizers, can drive significant pressure oscillations inside premixed-type combustors. The goal of this work is to derive a reduced-order model for interaction among vortex shedding, chamber acoustics, and combustion process. A dump combustor is considered a general system configuration. Formation of vortices at the sudden expansion in a chamber is affected by the oscillatory flow. A new quasi-steady model is proposed for determining the moment of vortex separation. Vortex burning is assumed to be localized in space and time. A "kicked" oscillator model is utilized for deriving the appropriate dynamical system. The moment of burning and the corresponding vortex location are dependent on the chamber geometry, velocity field, and characteristic chemical and hydrodynamic times. If Rayleigh's criterion is satisfied, acoustic waves can develop in the chamber. Model and experimental results are compared for a chosen configuration. A study of model performance for a realistic system is carried out by variation of parameters where the mean flow velocity and the number of modes are treated as variables.

Publication: Combustion Science and Technology Vol.: 175 No.: 6 ISSN: 0010-2202

ID: CaltechAUTHORS:20101117-101453870

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Abstract: Artificial cavitation, or ventilation, is produced by releasing gas into liquid flow. One objective of creating such a multiphase flow is to reduce frictional and sometimes wave resistance of a marine vehicle completely or partially immersed in the water. In this paper, flows around surface ships moving along the water-air boundary are considered. It is favorable to achieve a negative cavitation number in the developed cavitating flow under the vessel's bottom in order to generate additional lift. Cavities formed in the flow have limiting parameters that are affected by propulsive and lifting devices. Methods for calculating these influences and results of a parametric study are reported.

Publication: Ocean Engineering Vol.: 30 No.: 9 ISSN: 0029-8018

ID: CaltechAUTHORS:20101124-105231088

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Abstract: Perhaps the most curious aspect of the Wright Brothers' program to invent and commercialize the airplane is their decision in 1900 to use their novel canard configuration, and to persist with that geometry until 1910 despite the known deficiency that the aircraft were unstable in pitch. The reasons for their initial choice are well-known. Several studies in the part twenty years have proven beyond doubt that the Wrights did not intentionally make their canards unstable. The pitch instability of their machine was an unwitting byproduct of their design chosen partly out of fear of the conventional design and partly (they reasoned) for more positive control. With their great emphasis on control, the Wrights were able to develop a successful aircraft, albeit difficult to fly additionally because the 1903 aircraft also possessed a fast spiral instability. A canard design is not necessarily unstable, but owing chiefly to their airfoil, and an unfortunate fore-and-aft mass distribution, the Wright canards were all unstable. Though easier to fly, their 1909 aircraft was more unstable than the famous 1903 Flyer and the Brothers did not have a stable design until they finally adopted a conventional aft horizontal tail in 1910. Successful control of the canard aircraft depended heavily on large damping-in-pitch. The purpose of this paper is to apply modern analysis of flight mechanics to trace the detailed flying characteristics of their powered aircraft from 1903 to 1910 when they finally gave up the canard. Its a story in which technology, stubborness and commercialization are intimately mingled; we are concerned here only with the technology.

No.: AIAA-2003-0097
ID: CaltechAUTHORS:20101118-085016796

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Abstract: Various techniques have been employed by investigators to measure the response of flames to unsteady changes, but there has been no systematic study of the relative benefits and drawbacks of these competing techniques. The goal of this work is to characterize the performance of two different measurement techniques applied in three ways and to examine the differing insights they offer for the response of a flame in a periodic acoustic field. The burner configuration consists of a jet flame in a partial enclosure that stabilizes the flame approximately 8 cm above the jet exit. This burner is installed in an acoustic chamber that has actively-controlled, frequency-selectable, acoustic forcing. Flame response data for different frequencies obtained with chemiluminescence, OR PLIF, and NO PLIF measurement techniques is the basis for this work. Analysis of the data shows the complexity of the measurement required to achieve a given level of understanding of the flame's behavior. The usefulness of these techniques in flame response measurements individually and taken in combination is discussed, with examples.

ID: CaltechAUTHORS:20101118-080941990

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Abstract: The California Institute of Technology's Combustion Acoustics Facility is used to measure the changes in the creation of NO in a partially premixed jet flame due to acoustic forcing at frequencies ranging from 22 to 55 Hz. The facility generates a quarter-wave mode so that the test flame is in a region where the acoustic velocity is nearly zero. This facility and a similar burner have been previously used to measure the phase-resolved response of the OH field. In this experiment, phase-resolved NO planar laserinduced fluorescence (PLIF) measurements are recorded. The location and phase coupling of the NO field are analyzed, and the production and transport of NO are compared with previously reported OH field measurements. The NO levels increase for frequencies that exhibit stronger acoustic coupling to the flame. The NO concentration field variations lead (in phase space) the OH field variations. This is probably a result of the greater NO sensitivity to temperature (which itself is closely coupled to the chamber pressure).

No.: AIAA-2002-0195
ID: CaltechAUTHORS:20101117-112555177

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Abstract: Transient behavior of combustion systems has long been a subject of both fundamental and practical concerns. Extreme cases of very rapid changes include the ignition of reacting mixtures and detonation. At the other extreme is a wide range of quasi-steady changes of behavior, for example adjustments of the operating point of a combustion chamber. Between the limiting cases of 'infinitely fast' and 'infinitesimally slow' lie important fundamental problems of time-dependent behavior and a wide array of practical applications. Among the latter are combustion instabilities and their active control, a primary motivation for the work reported in this paper. Owing to the complicated chemistry, chemical kinetics and flow dynamics of actual combustion systems, numerical simulations of their behavior remains in a relatively primitive state. Even as that situation continually improves, it is an essential part of the field that methods of measuring true dynamical behavior be developed to provide results having both fine spatial resolution and accuracy in time. This paper is a progress report of recent research carried out in the Jet Propulsion Center of the California Institute of Technology.

ID: CaltechAUTHORS:20110208-081441006

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Abstract: The California Institute of Technology's Combustion Acoustics Facility is used to measure the response of a partially premixed jet flame to acoustic forcing at frequencies ranging from 22 Hz to 55 Hz. The facility generates bulk acoustic modes that simulate unstable combustor conditions. This same facility and burner has been previously used to measure the phase-resolved response of the OH PLIF field. In this experiment, phase-resolved chemiluminescence measurements are recorded and analyzed. Flame base oscillations are quantified and compared for two different burner configurations. The chemiluminescence also shows that frequencies that exhibit stronger acoustic coupling to the flame tend to have decreased luminosity in the flame stabilization zone, while frequencies with weaker coupling tend to produce greater luminosity at the base of the flame.

No.: AIAA-2002-0194
ID: CaltechAUTHORS:20101115-105224925

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Abstract: The California Institute of Technology's Combustion Acoustics Facility is used to measure the changes in the creation of NO in a partially premixed jet flame due to acoustic forcing at frequencies ranging from 22 to 55 Hz. The facility generates bulk acoustic modes that simulate unstable combustor conditions in the absence of velocity fluctuations. This facility and a similar burner have been previously used to measure the phase-resolved response of the OH field. In this experiment, phase-resolved NO planar laser-induced fluorescence (PLIF) measurements are recorded. The location and phase coupling of the NO field are analyzed, and the production and transport of NO are compared with previously reported OH field measurements. The NO levels increase for frequencies that exhibit stronger acoustic coupling to the flame. The NO concentration variations with the phase of the chamber pressure lead the OH field variations. This is probably a result of the greater NO sensitivity to temperature.

Publication: Proceedings of the Combustion Institute Vol.: 29 No.: 1 ISSN: 1540-7489

ID: CaltechAUTHORS:20101118-082923771

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Abstract: Active control of longitudinal pressure oscillations in a combustion chamber is studied theoretically by means of a low order model obtained by systematic reduction from a complete representation. The formulation is based on the derivation of a generalized wave equation that accommodates the effects of mean flow, combustion, noise and control action. By using spatial averaging, the equations describing the dynamics of the chamber are reduced to a set of coupled ordinary differential equations, representing the motions of a system of coupled oscillators. The form of the resulting equations is particularly convenient for model reduction and for introducing feedback control terms, while retaining all physical processes. The oscillator equations are then rewritten in state-space form. Simulations are carried out to investigate in a unified fashion various aspects of the problem. These include the influences of noise, parameter uncertainties, unmodeled modes and a single timedelay. A criterion is derived that guarantees stability of the controlled closed-loop system in the presence of those quantities. The particular controller used here is based on a standard LQR design, but any design technique can be used as long as the stability criterion is fulfilled.

No.: 2000-3124
ID: CaltechAUTHORS:20101115-085253275

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Abstract: Combustion instabilities exist as consequences of interactions among three classes of phenomena: chemistry and chemical dynamics; combustion dynamics; and combustor dynamics. These dynamical processes take place simultaneously in widely different spatial scales characterized by lengths roughly in the ratios (10^(-3) - 10^(-6)):1:(10^3-10^6). However, due to the wide differences in the associated characteristic velocities, the corresponding time scales are all close. The instabilities in question are observed as oscillations having a time scale in the range of natural acoustic oscillations. The apparent dominance of that single macroscopic time scale must not be permitted to obscure the fact that the relevant physical processes occur on three disparate length scales. Hence, understanding combustion instabilities at the practical level of design and successful operation is ultimately based on understanding three distinct sorts of dynamics.

No.: AIAA-2000-3178
ID: CaltechAUTHORS:20101115-083329034

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Abstract: A modified Price-Boggs-Derr model is applied to compute the linear and non-linear combustion response properties of monopropellant ammonium perchlorate. The kinetics constants were changed to achieve good agreement with response function data as well as with steady-state data. The numerical method was first validated by comparing computations using the Levine & Culick boundary condition in the limit of small perturbations with the exact mathematical solution for linear response. Then, using the AP model for the boundary condition, various linear and non-linear computations were performed. Supplemental mathematical analyses relate the AP model to the basic two parameters of the classical theory and show the key factors determining the nature of the combustion response.

No.: AIAA-2000-3694
ID: CaltechAUTHORS:20101115-101901737

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Abstract: A technique has been devised which can provide insight into the local dynamic response of a flame to an acoustic field. In the experiments, a test chamber is acoustically excited by a pair of low frequency drivers. The response of the flame is visualized by planar laser-induced fluorescence (PLIF) of the hydroxyl (OH) radical, which is a good indicator for heat release in the flame. The resulting images are phase-locked and averaged to yield a qualitative picture of the fluctuation of the heat release. This is correlated with a pressure transducer near the flame, which allows stability to be evaluated using Rayleigh's criterion. Results indicate that the drive frequency and burner configuration have a pronounced effect on the response of the flame. Drive frequencies ranging from 22 Hz to 55 Hz are applied to the jet mixed burner, supplied with a premixed 50/50 mixture of methane and carbon dioxide at a Reynolds number of 20,000. The burner is operated in two configurations; with an aerodynamically stabilized flame, and with a flame stabilized by two protruding bluff-bodies. Results indicate that in general, the bluff-body stabilized flame is less sensitive to chamber acoustic excitation

No.: AIAA-2000-3123
ID: CaltechAUTHORS:20101115-074125126

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Abstract: Considerable data exists suggesting that the response functions for many solid propellants tend to have higher values, in some ranges of frequencies, than predicted by the conventional QSHOD theory. It is a familiar idea that such behavior is associated with dynamical processes possessing characteristic times shorter than that of the thermal wave in the condensed phase. The QSHOD theory, and most of its variants, contains only the dynamics of that process, which normally has a characteristic frequency in the range of a few hundred hertz. Two previous works seeking to correct this deficiency (T'ien, 1972; Lazima and Clavin, 1992) have focused their attention on including the dynamics of the thermal wave in the gas phase. Both include effects of diffusion that complicate the analysis although the second achieves some simplification by applying the ideas of 'activation energy asymptotics'. While their results differ in detail, both works show influences at frequencies higher than those near the broad peak of the response due to the thennal wave. Recent theoretical work and simulations show that a combustion response function based on simple pressure coupling is not enough to explain the characteristics of the instability observed experimentally. Namely, differences in the shape of the response function fail to reproduce the differences observed experimentally in the characteristics of the limit cycle reached by combustion chambers with propellants of different chemical (or physical) composition. On the other hand, velocity coupling in the combustion response seems a promising mechanism able to predict the changes in the unstable modes observed experimentally and to produce considerable effect on the shape of the resulting limit cycle. The Baum and Levine model is used as a starting point in the investigation of velocity coupling. Other models, in which the mass burning rate is modified by some function of the velocity, are also investigated through direct time-simulation and by the use of a continuation method. Modeling of particle damping at high frequency constitutes a serious consideration in the modeling of the interaction of combustion dynamics and chamber acoustics. The effect of particle size distribution is analyzed by considering an experimental particle size distribution. The ultimate goal of this work is to find a link between the global dynamics of the combustion chamber and small changes in the combustion dynamics, caused by differences in propellant chemical composition or physical characteristics (for example, particle size and distribution). Response functions are shown for realistic ranges of the chief parameters characterizing the dynamics of the propellant. The results are also incorporated in the dynamical analysis of a small rocket motor to illustrate the consequences of the combustion dynamics for the stability and nonlinear behavior of unsteady motions in a motor.

No.: AIAA-2000-3187
ID: CaltechAUTHORS:20101115-094319661

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Abstract: The chief purpose of this paper is to investigate the influences of noise, more generally stochastic sources of any sort, on linear and nonlinear unsteady motions in combustion chambers. To be definite, our primary applications here relate to combustion instabilities in solid propellant rockets, particularly linear stability. Two aspects are especially relevant to practical applications: the direct effects of noise on stability; and extraction of information about stability margin from noisy pressure records taken for stable motors. However, the formulation and results are relevant to combustors generally. A fundamental issue is the distinction between and relative importance of self-excited (linearly unstable) oscillations on the one hand and forced oscillation on the other. This has been a controversial and occasionally misunderstood topic for many years. The essential ideas can be clarified unambiguously within the context of global dynamics treated here. We are not so concerned with the details of data processing as with the physical interpretation of the results.

ID: CaltechAUTHORS:20101118-105039121

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Abstract: Most of the previous work on periodic limit cycles in linearly unstable combustors has been carried out for the case of purely longitudinal classical modes whose natural frequencies are integral multiples of the fundamental. The contrary situation of transverse modes in a cylindrical chamber has led to unexpectedly high amplitudes in the periodic limit cycles, the reasons for which have not been thoroughly understood. Some results reported here serve to clarify the two chief consequences of nonlinear coupling between modes: the first is obvious, for the nonlinear coupling causes excitation of higher modes, and hence energy transfer, when, say, the first mode is unstable; the second has long been known, namely that the coupling must also cause shifts of the frequencies from their linear non-integral values to the integral values required for a periodic limit cycle, but part of the significance of this property has been unclear. In particular, the necessity for the frequency shifts reduces the efficiency at which energy is transfered between modes and leads to higher amplitude oscillations. Our analysis shows that the larger are the differences of the linear frequencies from perfect integral values, the larger are the amplitudes in the limit cycle. These conclusions suggest a way to reduce the amplitudes of transverse oscillations, and examples are presented showing this possibility.

Publication: Combustion Science and Technology Vol.: 144 No.: 1-6 ISSN: 0010-2202

ID: CaltechAUTHORS:20101118-135546896

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Abstract: A non-steady model for the combustion of ammonium perchlorate composite propellants has been developed in order to be incorporated into a comprehensive gasdynamics model of solid rocket motor flow fields. The model including the heterogeneous combustion and turbulence mechanisms is applied to nonlinear combustion instability analyses. This paper describes the essential mechanisms and features of the model and discusses the methodology of non-steady calculations of the combustion instabilities of solid rocket motors.

No.: AIAA-99-2804
ID: CaltechAUTHORS:20101118-132511549

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Abstract: This paper is a report of work in progress, part of the Caltech MURI Program: Novel Energetic Materials to Stabilize Rocket Motors. The primary technical objective of the MURI Program is to understand the connections between propellant composition and chemistry, and the dynamical behavior observed in solid propellant rocket motors. Here we are concerned with the theoretical framework in which chamber dynamics are investigated; and certain aspects of combustion dynamics represented by the response function which is ultimately the macroscopic realization of the propellant chemistry and combustion. Some results are given to illustrate possible influences of the frequency spectrum of the response function on linear and nonlinear motions in a solid rocket. A simple model is described which is extended eventually to provide a way to model phenomenologically some of the observed characteristics of the combustion dynamics of a burning solid propellant.

No.: 98-3704
ID: CaltechAUTHORS:20101118-144631059

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Abstract: A numerical analysis of unsteady motions in solid rocket motors with a nozzle has been conducted. The formulation treats the complete conservation equations for the gas phase and the one-dimensional equations in the radial direction for the condensed phase. A fully coupled implicit scheme based on a dual time-stepping integration algorithm has been adopted to solve the governing equations and associated boundary conditions. After obtaining a steady state solution, periodic pressure oscillations are imposed at the head end to simulate acoustic oscillations of a traveling-wave motion in the combustion chamber. The amplitude of the pressure oscillation is 1.0 % of the mean pressure and the frequency is 1790 Hz, corresponding to the twice of the fundamental frequency of the chamber. Magnitude and phase of pressure and axial velocity fluctuations are influenced by the upstream reflecting wave from the nozzle wall. Axial velocity near surface region oscillates in phase advance manner with reference to the acoustic pressure. Large vorticity fluctuations are observed in near surface region. The mass-flow-rate at the nozzle exit periodically oscillates with a time delay compared to the imposed pressure oscillations at the head end.

No.: 98-0253
ID: CaltechAUTHORS:20101118-141630231

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Abstract: Dynamics of laminar flames in closed tubes is studied by means of two-dimensional numerical simulations taking into account thermal conduction, fuel diffusion, viscosity and chemical kinetics. Development of the hydrodynamic instability of a flame front is investigated for flames with the chemical reactions of the first and the third order. We found that for a flame with the first order reaction the hydrodynamic instability is strongly reduced or even suppressed in sufficiently short tubes. Unlike this, in the case of a flame of the third order reaction the instability is enhanced due to significant increase of the normal velocity of the planar flame under confinement. The instability development for flames of both the first and the third order reaction is strongly affected by acoustic waves generated by the flame in a closed chamber. Particularly, a weak shock colliding with the flame front may lead to a temporary stabilization of the flame instability. On the contrary, when flame comes to the end of the tube the acoustic waves may cause significant increase of the flame instability. We studied a possibility of the detonation ignition ahead of the flame front as well. We found that the detonation can be ignited at the far end of the tube by the weak shocks and sound waves generated by the flame in a closed tube. Triggering of the detonation ahead of the flame propagating in a closed tube is related to the knock problem in spark-ignition engines.

Publication: Combustion Science and Technology Vol.: 136 No.: 1-6 ISSN: 0010-2202

ID: CaltechAUTHORS:20101201-074308292

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Abstract: A numerical analysis of unsteady motions in solid rocket motors has been conducted. A fully coupled implicit scheme based on a dual time-stepping integration algorithm has been adopted to solve the governing equations and associated boundary conditions. A narrow pressure pulse is imposed at the head end to simulate unsteady acoustic oscillations in the combustion chamber. Pressure increases when the front of the pulse reaches near the nozzle area. Self-generated oscillations with frequency of standing wave propagates upstream in the combustion chamber. Investigation of transient response of gas-phase dynamics to traveling pressure wave and its effects on propellant combustion reveals several aspects: Combustion responses have a strong relationship with vorticity fluctuations in case of high turbulent intensity on the propellant surface. Temperature fluctuations of the propellant surface in the head end region seem to be very unstable and independent of the pressure wave. Surface temperature without turbulence effect looks more sensitive to temperature fluctuations in the primary flame zone. Stability of surface temperature is strongly related to turbulent intensity on the propellant surface.

Vol.: 2 No.: 662
ID: CaltechAUTHORS:20110128-075156436

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Abstract: Hysteretic behaviour, as found in the dump combustor facility at GALCIT, allows nonlinear active control of the instability, demonstrated recently by Knoop et al. (1996). As in that work, pulses of secondary fuel, based on a simple on/off control law, have been successfully used to drive the transition between the two modes present in the hysteretic region, thereby reducing the amplitude of the pressure oscillations with minimal use of fuel. In order to clarify the origin of the phenomenon, high speed shadowgraph images of the flowfield during the transition between 'unstable' and stable burning have been taken, showing distinctive features that may help in modeling the observed behaviour. A preliminary parametric study (type of injector, duration of pulses, type of secondary flow) has also been conducted, showing that the transition can be obtained over a broad range of conditions.

Publication: Combustion Science and Technology Vol.: 126 No.: 1-6 ISSN: 0010-2202

ID: CaltechAUTHORS:20101118-151443293

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Abstract: A numerical analysis of unsteady motions in solid rocket motors has been conducted. The formulation considers a 2-D axisymmetric combustion chamber and a choke nozzle, and treats the complete conservation equations accounting for turbulence closure and finiterate chemical kinetics in the gas phase and subsurface reactions. A fully coupled implicit scheme based on a dual time-stepping integration algorithm has been adopted to solve the governing equations and associated boundary conditions. Results of the steady-state calculations indicate that the distributions of pressure in the motor and Mach number in the nozzle are one-dimensional along the axial direction. Vorticity contours show similar pattern to those of Mach number in the combustion chamber. The nozzle has an influence on the flow and temperature fields in the combustion chamber. A narrow pressure pulse is imposed at the head end to simulate unsteady acoustic oscillations in the combustion chamber. When the front of the pulse reaches near the nozzle throat, pressure near the nozzle throat increases and blocks the hot gas flow from passing through the nozzle throat. Self-generated oscillations have similar frequencies to those of standing waves of the combustion chamber. Large vorticity fluctuations are observed in near surface region. The luminous flame zone responds to low-frequency pressure wave rather than highfrequency one. Temperature fluctuations in the primary flame zone of the head end oscillates independently of the imposed pressure oscillations while temperature fluctuations in downstream region show pressure-dependent oscillations.

ID: CaltechAUTHORS:20101119-074948591

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Abstract: A study of propagation of a wide-band acoustic signal in a granular medium is reported. Experimental data on the propagation of pulses with an amplitude up to 3 MPa and characteristic length about 1 µs through a sample of cobalt-manganese nodules are compared with a computer model of the process. An anomalous sig'rfal absorption in the high-frequency range observed with relatively weak sounding pulses is explained under the assumption of a fractal sample structure on a certain scale. When the signal amplitude increases, the ahsorption assumes a normal power form which is evidence of substance structural changes.

Publication: Acoustical Physics Vol.: 43 No.: 5 ISSN: 1063-7710

ID: CaltechAUTHORS:20101209-142543898

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Abstract: Formal analysis of combustion instabilities has been based on expansion of the equations of motion in two small parameters, March numbers characterizing the average and fluctuating flows. The procedure is reviewed and extended in this note explain how new terms involving nonlinear mean flow/acoustic interactions may be incorporated. As a further example of the ordering procedure, the reasoning is given to show why coupling of modes, linear in the average March number, cannot legitimately be retained when the equations have been expanded only to first order in Mach number.

Publication: Combustion Science and Technology Vol.: 126 No.: 1 ISSN: 0010-2202

ID: CaltechAUTHORS:20101118-150130234

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Abstract: Experimental results for instabilities in dump combustors have long shown the presence of some sort of hysteresis, in the vicinity of the stability boundary defined by flow speed and mixture ratio. This note reports measurements of the precise character of hysteresis loops found when the mixture ratio is varied with flow speed held constant. The upper branch represents relatively high amplitude limit cycles and the lower branch contains low level oscillations possibly driven by stochastic sources within the chamber. Existence of the hysteresis loops suggests the possibility of causing a transition from the upper unstable branch to the lower stable branch. This has been accomplished by injecting short pulses of secondary fuel either in the boundary layer upstream of the dump plane or in the recirculation zone. Only a single pulse is required if its flow rate and width are suitably chosen. These results demonstrate the feasibility of a novel method of active control of combustion instabilities if hysteresis is present, apparently the first example of true nonlinear control of combustor dynamics. The main advantage is the small amount of secondary fuel required. More generally, this work illustrates the value, for active control, of understanding the dynamics of the uncontrolled system.

Publication: Combustion Science and Technology Vol.: 123 No.: 1-6 ISSN: 0010-2202

ID: CaltechAUTHORS:20101119-150022314

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Abstract: The results given in this paper constitute a continuation of progress with nonlinear analysis of coherent oscillations in combustion chambers. We are currently focusing attention on two general problems of nonlinear behavior important to practical applications: the conditions under which a linearly unstable system will execute stable periodic limit cycles; and the conditions under which a linearly stable system is unstable to a sufficiently large disturbance. The first of these is often called 'soft' excitation, or supercritical bifurcation; the second is called 'hard' excitation, 'triggering,' or subcritical bifurcation and is the focus of this paper. Previous works extending over more than a decade have established beyond serious doubt (although no formal proof exists) that nonlinear gasdynamics alone does not contain subcritical bifurcations. The present work has shown that nonlinear combustion alone also does not contain subcritical bifurcations, but the combination of nonlinear gasdynamics and combustion does. Some examples are given for simple models of nonlinear combustion of a solid propellant but the broad conclusion just mentioned is valid for any combustion system. Although flows in combustors contain considerable noise, arising from several kinds of sources, there is sound basis for treating organized oscillations as distinct motions. That has been an essential assumption incorporated in virtually all treatments of combustion instabilities. However, certain characteristics of the organized or deterministic motions seem to have the nature of stochastic processes. For example, the amplitudes in limit cycles always exhibit a random character and even the occurrence of instabilities seems occasionally to possess some statistical features. Analysis of nonlinear coherent motions in the presence of stochastic sources is therefore an important part of the theory. We report here a few results of power spectral densities of acoustic amplitudes in the presence of a subcritical bifurcation associated with nonlinear combustion and gasdynamics.

Publication: International Journal of Energetic Materials and Chemical Propulsion Vol.: 4 No.: 1+6 ISSN: 2150-766X

ID: CaltechAUTHORS:20101119-151322582

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Abstract: Instabilities of motions in a combustion chamber are consequences of the coupled dynamics of combustion processes and of the flow in the chamber. The extreme complexities of the problem always require approximations of various sorts to make progress in understanding the mechanisms and behavior of combustion instabilities. This paper covers recent progress in the subject, mainly summarizing efforts in two areas: approximate analysis based on a form of Galerkin's method, particularly useful for understanding the global linear and nonlinear dynamics of combustion instabilities and numerical simulations intended to accommodate as fully as possible fundamental chemical processes in both the condensed and gaseous phases. One purpose of current work is to bring closer together these approaches to produce more comprehensive and detailed realistic results applicable to the interpretation of observations and for design of new rockets for both space and military applications. Particularly important are the goals of determining the connections between chemical composition and instabilities; and the influences of geometry on nonlinear behavior.

Vol.: 2
ID: CaltechAUTHORS:20101119-113430324

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Abstract: A one dimensional acoustic model was used to predict the resonant modes of the Caltech pulsed combustion facility. The model accurately predicted pressure FFTs found through experiments for the 2.5 and 7.6 cm duct height configurations. Heat addition locations were found to have only marginal effects on shifting the location of the facility's acoustic modes. A detailed experimental analysis of the reacting vortex structures shed from a rearward facing step was also performed using high speed shadowgraph and CCD cinematography. Premixed vortical combustion was found to have two ignition mechanisms depending on the prior status within the combustor. In the first, burning was initiated at the surface and proceeded toward the center while in the second ignition was initiated near the center and the flame propagated outward. Time delays measured from the start of vortex shedding to subsequent ignition or to the corresponding maximum burning intensity were found to vary inversely with combustor pressure during injection (shedding) and with combustor pressure during burning. Reducing the height of the combustor increased interactions between the burning vortex and the wall, inhibited vortex growth, and produced longer axial burning regions and higher overall straining throughout the structure's cycle. Vortex straining was defined in two ways: first, based on the growth rate of the core diameter of the structure and second, based on the effective length of the streamline separating hot combustion products and cold reactants. Straining provided a sufficient delay mechanism to shift vortex shedding from 237 to 188 Hz for the 5.1 cm case.

Vol.: 306
ID: CaltechAUTHORS:20110208-095101547

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Abstract: The purpose of this paper is to give a broad overview of the field of combustion instabilities in propulsion systems. Virtually all of the material included here has appeared elsewhere, either in primary research reports or in reviews. None of the propulsion systems are covered in great detail, but sufficiently to establish the fundamental point that while there are obvious practical differences among the systems, for understanding and treating combustion instabilities, much is to be gained by treating the various phenomena within a common framework. In that context, the systems are distinguished chiefly by geometry and the kinds of propellants used. On that basis, a general framework can be constructed to serve both practical and theoretical purposes.

Vol.: 306
ID: CaltechAUTHORS:20110128-112158907

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Abstract: Chiefly for improved efficiency, the trend to increasing use of gas turbine engines in stationary powerplants has been firmly established. The requirement for minimum NOx production has motivated operation as close as practically possible near the lean flammability limit, to reduce flame temperatures and consequently reduce formation of nitrogen oxides via the Zeldovich thermal mechanism. However, experience has shown that under these conditions, stability of the chamber is compromised, often leading to the presence of sustained oscillations in the combustor. That possibility raises the problem of the influence of oscillatory motions on the production of nitrogen oxides. Numerically calculating these influences for a complex geometry gas turbine combustor is too computationally expensive at this ?me. Nonlinear analytical methods making use of these influences are a promising direction for simplei ways to design and develop operational gas turbine combustors. However, this analysis needs results on which to base unsteady models of the interaction between nonlinear oscillations and species production within a gas turbine combustor. In this paper, two methods are explored briefly as an initial step. The first is based on a configuration of perfectly stirred and plug flow reactors to approximate the flow in a combustion chamber. A complete representation of the chemical processes is accommodated, but the geometry is simplified. The second is a full numerical simulation for a realistic geometry, but at this stage the chemistry is simplified.

ID: CaltechAUTHORS:20101119-141141495

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Abstract: A shock traveling in air interacts with a laminar jet of helium flowing normal to the direction of shock propagation. Planar laser Rayleigh scattering is used to study the deformation and motion of the originally circular jet cross-section. The velocity of the jet before the shock interaction is much less than the velocities generated by the shock wave. Thus, the helium jet serves to create a cylindrical bubble of a lighter density gas imbedded in a heavier one. Four different shock Mach numbers (1.066, 1.14, 1.5, and 2.0) are studied. Two different jet/air density ratios are examined by using pure helium in the jet in one case, and a mixture of airlhelium in the other. After the shock interaction, a vortex pair forms from the baroclinically generated vorticity. The experiments measure the velocity of the helium relative to the surrounding air, the spacing between the vortex cores, and the circulation of the vortices. Experiments viewing the reflected shock interaction are also performed. Excellent agreement is found with previous computational studies.

ID: CaltechAUTHORS:20110204-100414048

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Abstract: A decoupled adaptive scheme is proposed for the trajectory control of robots. Under moderate constraints, the scheme is stable and robust in the presence of feedback delay and signal hold due to digital computation in the control loop. The design procedure involves a search for compensators with the aim of minimizing a quadratic performance index in order to minimize the maximum tracking error. Stability analysis of the proposed control law (the selected compensators) then provides stability bounds of disturbances, control and adaptation gains, and desired trajectories and their time-derivatives. The region of attraction is local due to unmodelled dynamics.

Publication: International Journal of Control Vol.: 61 No.: 2 ISSN: 0020-7179

ID: CaltechAUTHORS:20101122-080359296

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Abstract: N/A

No.: 169
ID: CaltechAUTHORS:20101122-074028101

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Abstract: N/A

ID: CaltechAUTHORS:20101119-084519588

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Abstract: A pulsed or "triggered" instability occurs when pressure oscillations develop in a linearly stable combustion system after being subjected to a sufficiently large disturbance. Such true nonlinear instabilities usually occur as subcritical bifurcations in dynamical systems theory. Understanding which nonlinear processes can lead to subcritical bi~urcations is the focus of this work. Earlier work with the approximate analysis used here has shown convincingly that nonlinear acoustics alone does not contain the phenomenon of pulsed instabilities; evidently some other nonlinear contribution must also be included. An extensive experimental and numerical investigation conducted by Baum and Levine strongly suggests that nonlinear combustion is required. Using models of pressure and velocity coupling, the current work studies the effect of nonlinear combustion on the behavior of the system.

No.: AIAA-95-2430
ID: CaltechAUTHORS:20101119-133446852

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Abstract: Two important approximations have been incorporated in much or the work with approximate analysis or unsteady motions in combustion chambers: 1) truncation of the series expansion to a finite number or modes, and 2) time-averaging. A major purpose or the present analysis is to investigate the limitations or those approximations. A continuation method Is used to determine the limit cycle behavior or the time-dependent amplitudes or the longitudinal acoustic modes in a combustion chamber. The results show that time-averaging works well only when the system Is slightly unstable. In addition, the stability boundaries predicted by the twomode approximation are shown to be artifacts of the truncation of the system. Systems of two, four. and six modes are analyzed and show that more modes are needed to analyze more unstable systems. For the six-mode approximation with an unstable second-mode, two birurcations are found to exist: 1) a pitchfork bifurcation leading to a new branch of limit cycles, and 2) a torus bifurcation leading to quasiperiodic motions.

Publication: Journal of Propulsion and Power Vol.: 10 No.: 4 ISSN: 0748-4658

ID: CaltechAUTHORS:20101124-101555564

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Abstract: A review is given of data that describe the mass flux of gas in large buoyant diffusion flames, with the aim of developing a rational picture for this process as well as a correlation of the data. A brief review of flame-height scaling parameters is followed by a discussion of measurement techniques, the previous work on far-field and fire-plume models, and a description of an effort to develop a rational entrainment model.

Vol.: 4
ID: CaltechAUTHORS:20101123-144201485

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Abstract: The essentially nonoscillatory (ENO) shock-capturing scheme for the solution of hyperbolic equations is extended to solve a system of coupled conservation equations governing two-dimensional, time-dependent, compressible chemically reacing flow with full chemistry. The thermodynamic properties of the mixture are modeled accurately, and stiff kinetic terms are separated from the fluid motion by a fractional step algorithm. The methodology is used to study the concept of shock-induced mixing and combustion, a process by which the interaction of a shock wave with a jet of low-density hydrogen fuel enhances mixing through streamwise vorticity generation. Test cases with and without chemical reaction are explored here. Our results indicate that, in the temperature range examined, vorticity generation as well as the distribution of atomic species do not change significantly with the introduction of a chemical reaction and subsequent heat release. The actual diffusion of hydrogen is also relatively unaffected by the reaction process. This suggests that the fluid mechanics of this problem may be successfully decoupled from the combustion processes, and that computation of the mixing problem (without combustion chemistry) can elucidate much of the important physical features of the flow.

Publication: Theoretical and Computational Fluid Dynamics Vol.: 6 No.: 2-3 ISSN: 0935-4964

ID: CaltechAUTHORS:20101123-142807198

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Abstract: The steady motion of a symmetric, finite core size, counterrotating vortex pair is characterized by circulation r, a velocity V, and a spacing 2x_∞. In the classical limit of a point vortex, the normalized velocity, vx_∞/r, is 1/(4π). The effect of finite core size is to reduce the normalized velocity below the value for a point vortex. The flow is governed by a single geometrical parameter R/x_∞, the ratio of effective vortex size to vortex half-spacing. Perturbation analysis is used to derive general, closed-form analytical solutions for the complete velocity field, the vortex pair velocity, and the boundary shape for a continuum of values of R/x_∞. Both uniform and piecewise constant density cases are treated. These solutions illustrate the different orders at which the solution deviates from the point vortex pair. For example, the vortex shape becomes noncircular at order (R/x_∞)^2, but the normalized velocity does not change until order (R/x_∞)^5. For the uniform density case, calculation of specific values of vortex pair velocity, aspect ratio, and gap ratio shows good agreement with previous numerical results.

Publication: SIAM Journal on Applied Mathematics Vol.: 54 No.: 1 ISSN: 0036-1399

ID: CaltechAUTHORS:20101123-110851054

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Abstract: Bifurcation theory has been used to study Ihe nonlinear dynamics of the F-14. An 8 degree-of-freedom model that does not include the control system present in operational F-14's has been analyzed. The aerodynamic model, supplied by NASA, includes nonlinearlties as functions of the angles of attack and sideslip, the rotation rate about the velocity vector, and the elevator deflection. A continuation method has been used to calculate the steady states of the F -14 as continuous functions of the elevator deflection. Bifurcations of these steady states have been used to predict the onset of wing rock, spiral divergence, and jump phenomena that cause the aircraft to enter a spin. A simple feedback control system was designed to eliminate the wing rock and spiral divergence instabilities. The predictions were verified with numerical simulations.

Publication: Journal of Aircraft Vol.: 31 No.: 1 ISSN: 0021-8669

ID: CaltechAUTHORS:20101123-102858346

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Abstract: N/A

Publication: AIAA Journal Vol.: 32 No.: 1 ISSN: 0001-1452

ID: CaltechAUTHORS:20101123-094949189

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Abstract: In this article, a robust adaptive control scheme for robotic manipulators is designed based on the concept of performance index and Lyapunov's second method. Compensators are selected for a given feedback system by using a quadratic performance index. Then the stability of the system is proven based on Lyapunov's method, where a Lyapunov function and its time-derivative are derived from the selected compensators. In the process of stabilization, stability bounds are obtained for disturbances, control gains, adaptation gains, and desired trajectories, in the presence of feedback delay due to digital computation and first-order hold in the control loop.

Publication: Journal of Robotic Systems Vol.: 11 No.: 4 ISSN: 0741-2223

ID: CaltechAUTHORS:20101123-141347474

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Abstract: To promote efficient performance of very high speed air-breathing propulsion systems, the combustor Mach number must be of the order of six for a flight Mach number of 18. Because of this high gas speed through the combustor, mixing rates of hydrogen fuel with air must be very rapid in order to allow a combustor of reasonable length. It is proposed to enhance the rate of mixing and combustion of hydrogen and air, and thereby reduce combustor length, through the introduction of streamwise vorticity generated by the interaction of a weak oblique shock wave with the density gradient between air and a cylindrical jet of hydrogen. Because of the high Mach number flow in the combustor, the oblique shock traverses the jet at a small angle with respect to the free stream direction, and the principle of slender body theory allows one conceptually to replace the three-dimensional steady flow with a two-dimensional unsteady flow. As a consequence, two-dimensional time-dependent computational studies and an extensive experimental shock tube investigation were employed to assess mixing rates for the steady flow in the combustor. The results indicated that under realistic conditions, adequate mixing could be accomplished within 1 ms, a rate that was technologically interesting. Encouraged by these experiments, a “practical” injector, utilizing shock-enhanced mixing, was designed for a combustor having a free stream Mach number of 6.0. A detailed aerodynamic and mixing investigation was carried out in the Mach 6 High Reynolds Number Tunnel at the NASA-Langley Research Center. The results confirmed both the details and the overall effectiveness of the shock-enhanced mixing concept.

Publication: Symposium (International) on Combustion Vol.: 25 No.: 1 ISSN: 0082-0784

ID: CaltechAUTHORS:20101123-150925263

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Abstract: The second order nonlinear longitudinal acoustics in a cylindrical combustion chamber are studied for the case of an unstable second mode. A modal analysis is undertaken and a continuation method is used to determine the limit cycle behavior of the time dependent amplitudes of the acoustic modes as functions of the linear stability of the unstable acoustic mode. It is shown that if an insufficient number of modes are included in the truncated system, bifurcations of the primary limit cycle occur. The energy in the limit cycles is analyzed and the bifurcations are shown to occur as a means of increasing the amount of energy transfer out of the unstable acoustic mode and into the stable acoustic modes through the nonlinear terms.

No.: 94-3190
ID: CaltechAUTHORS:20101123-135307146

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Abstract: [No abstract]

Publication: Journal of Fluids Engineering Vol.: 115 No.: 4 ISSN: 0098-2202

ID: CaltechAUTHORS:20101123-134419710

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Abstract: Airfoil theory for unsteady motion has been developed extensively assuming the undisturbed medium to be of uniform density, a restriction accurate for motion in the atmosphere, Glauert (1929), Burgers (1935), Theodorsen (1935), Kussner (1936), Karman and Sears (1938), Kinney and Sears (1975). In some instances, notably for airfoils comprising fan, compressor and turbine blade rows, the undisturbed medium may carry density variations or "spots," resulting from non-uniformaties in temperature or composition, of a size comparable to the blade chord. This condition existsfor turbine blades, Marble (1975), Giles and Krouthen (1988), immediately downstream of the main burner of a gas turbine engine where the density fluctuations of the order of 50 percent may occur. Disturbances of a somewhat smaller magnitude arise from the ingestion of hot boundary layers into fans, Wortman (1975), and exhaust into hovercraft. Because these regions of non-uniform density convect with the moving medium, the airfoil experiences a time varying load and moment which we propose to calculate.

Publication: Journal of Fluids Engineering Vol.: 115 No.: 4 ISSN: 0098-2202

ID: CaltechAUTHORS:20101123-132225533

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Abstract: Families of two-dimensional, unsteady shock-induced vortical flows are simulated numerically. The flows consist of one or more regions of light gas, surrounded by heavy gas, being overtaken by a normal shock wave. The interaction of the density gradient at each light/heavy interface with the pressure gradient from the shock wave generates vorticity. This causes the light gas regions to roll up into one or more counter-rotating vortex pairs, which stir and mix the light and heavy gases. The mixing is characterized by an asymptotic stretching rate. The effects of shock strength, light/heavy gas density ratio, and geometry on the mixing are investigated. These two-dimensional, unsteady flows are analogous to three-dimensional, steady flows that may be used in SCRAMJET combustors demanding rapid and efficient mixing of fuel and oxidizer. For such applications, 1) the fuel injectors should be elongated in the direction of the shock; 2) multiple smaller injectors are preferable to a single larger injector; 3) injectors should be arranged in groups of closely spaced pairs, rather than uniformly; and 4) multiple shock waves should be utilized, if possible.

Publication: AIAA Journal Vol.: 31 No.: 5 ISSN: 0001-1452

ID: CaltechAUTHORS:20101123-081927940

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Abstract: The spectra of pressure oscillations in combustion chambers often contain large peaks at frequencies corresponding to chamber acoustic modes. Pulsed combustors are designed to operate with fixed amplitude oscillations but in many systems the oscillations have undesirable consequences. An understanding of the nonlinear mechanisms responsible for the limiting-amplitude behavior is therefore desired. This paper is divided into two parts. First, characterization of the oscillations in terms of attractors in mathematical phase space has been performed on pressure signals measured in a laboratory combustor of premixed gases. The results for one set of operating conditions show a quasiperiodic attractor of dimension two over an order of magnitude of scales. Next, the nonlinear combustion response to oscillations of a single acoustic mode are used to model autonomous or 'self-excited' behavior. Two simple models of nonlinear combustion processes observed in the laboratory combustor result in unstable oscillations that reach limiting-amplitudes. With the variation of model parameters, the periodic limit cycles undergo subharmonic bifurcations and transition to chaos.

Publication: Combustion Science and Technology Vol.: 89 No.: 1-4 ISSN: 0010-2202

ID: CaltechAUTHORS:20101122-111659876

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Abstract: Two important approximations have been incorporated in much of the work with approximate analysis of unsteady motions in combustion chambers: truncation of the series expansion to a finite number of modes, and time averaging. A major purpose of the analysis reported in this paper has been to investigate the limitations of those approximations. In particular two fundamental problems of nonlinear behavior are discussed: the conditions under which stable limit cycles of a linearly unstable system may exist; and conditions under which bifurcations of the limit cycle may occur. A continuation method is used to determine the limit cycle behavior of the equations representing the time dependent amplitudes of the longitudinal acoustic modes in a cylindrical combustion chamber. The system includes all linear processes and second-order nonlinear gas dynamics. The results presented show that time averaging works well only when the system is, in some sense, only slightly unstable. In addition, the stability boundaries predicted by the two-mode approximation are shown to be artifacts of the truncation of the system. Systems of two, four, and six modes are analyzed and show that more modes are needed to analyze more unstable systems. For the six-mode approximation with an unstable second mode two bifurcations are found to exist. A pitchfork bifurcation causes a new branch of limit cycles to exist in which the odd acoustic modes are excited. This new branch of limit cycles then undergoes a torus bifurcation that causes the system to exhibit stable quasi-periodic motions.

No.: 93-0114
ID: CaltechAUTHORS:20101122-100414304

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Abstract: The Wing-In-Ground craft (WIG), a vehicle flying in the ground effect, is a promising transportation means of the near future. This paper describes mathematical modeling of WIG motion in all regimes, such as planing, take-off, transition to flight, and flight itself. The model, which includes nonlinear hydroaerodynamics, serves as a base for simulation of motion. The theory developed here enhances the process of designing WIG vehicles; its advantages and disadvantages are discussed. The results of numerical modeling are compared with experimental data obtained for planing and flight regimes of motion. The model is applied for studying emergency problems in WIG operation.

No.: AIAA 2003-600
ID: CaltechAUTHORS:20101210-094204604

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Abstract: N/A

ID: CaltechAUTHORS:20110207-085016646

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Abstract: Experiments have been carried out in which a cylindrical volume of a heavy gas is impulsively accelerated by a weak shock wave. A laminar jet of sulphur hexafluoride (SF_6) is used to produce the heavy gas cylinder. Planar laser induced fluorescence (PLIF) is used to visualize the flow. In viewing the PLIF images it is discovered that the vorticity that early on resides on the boundary between the two gasses, separates from the cylinder to form a pair of vortices. Subsequently these vortices wrap the heavy gas around them. This process is quite different from what is observed when the cylinder is lighter than its surroundings. Similar experiments with helium (part 1 of this series) showed that a small amount light gas stays with the vorticity, eventually becoming part of the vortex cores. A simple model capable of explaining these differences is presented. In addition, the displacement of the jet cross section is measured and agrees reasonably well with previous experimental and computational results.

ID: CaltechAUTHORS:20101129-083502142

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Abstract: Numerical solutions of viscous, swirling flows through circular pipes of constant radius and circular pipes with throats have been obtained. Solutions were computed for several values of vortex circulation, Reynolds number and throat/inlet area ratio, under the assumptions of steady flow, rotational symmetry and frictionless flow at the pipe wall. When the Reynolds number is sufficiently large, vortex breakdown occurs abruptly with increased circulation as a result of the existence of non-unique solutions. Solution paths for Reynolds numbers exceeding approximately 1000 are characterized by an ensemble of three inviscid flow types: columnar (for pipes of constant radius), soliton and wavetrain. Flows that are quasi-cylindrical and which do not exhibit vortex breakdown exist below a critical circulation, dependent on the Reynolds number and the throat/inlet area ratio. Wavetrain solutions are observed over a small range of circulation below the critical circulation, while above the critical value, wave solutions with large regions of reversed flow are found that are primarily solitary in nature. The quasi-cylindrical (QC) equations first fail near the critical value, in support of Hall's theory of vortex breakdown (1967). However, the QC equations are not found to be effective in predicting the spatial position of the breakdown structure.

Publication: Journal of Fluid Mechanics Vol.: 242ISSN: 0022-1120

ID: CaltechAUTHORS:20101129-102843529

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Abstract: This investigation was concerned with the nuxmg which occurs after the unsteady interaction of a shock wave with a laminar jet of helium. The jet of helium was injected normal to the direction of the propagation of the shock. The primary diagnostic, planar Rayleigh scattering, had sufficient spatial and temporal resolution to resolve the smallest diffusion scales present and allowed helium mole fractions to be measured in twodimensional planes normal to the original jet flow direction. The amount of molecular mixing was evaluated with a mass distribution function at increasing times after the shock interaction. The total masses of helium contained in regions where the molar concentration of helium was at least 30% and 50% were also calculated. The shock Mach number was varied, and the effect of a reflected shock was studied. It was found that shock interactions can significantly increase the mixing between the air and helium. A rough collapse of the mixing data occurs when time is normalized by the jet radius divided by the change in velocity of the air behind the shock. An increase in the enhancement of mixing occurred after the interaction with the reflected shock.

No.: 92-3546
ID: CaltechAUTHORS:20101129-084947901

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Abstract: This paper is concerned with some aspects of non-linear behavior of unsteady motions in combustion chambers. The emphasis is on conditions under which organized oscillations having discrete frequencies may exist in the presence of random motions. In order to treat the two types of motions together, and particularly to investigate coupling between noise and combustion instabilities, the unsteady field is represented as a synthesis of acoustic modes having time-varying amplitudes. Each of the amplitudes are written as the sum of two parts, one associated with the random field and the remainder representing the organized oscillations. After spatial averaging, the general problem is reduced to solution of a set of second-order ordinary differential equations whose structure depends on the sorts of nonlinear processes accounted for. This formulation accommodates any physical process; in particular, terms are included to represent noise sources, although only limited modeling is discussed. Our results suggest that random sources of noise have only small effects on combustion instabilities and seem not to be a cause of unstable motions. However, the coupling between the two sorts of unsteady motions may be important as an essential process in a proposed scheme for noise control. It is now a familiar observation that many nonlinear deterministic systems are capable of exhibiting apparently random motions called 'chaos.' This is a particularly interesting possibility for systems which also executed non-deterministic random motions. In combustion chambers, a nonlinear deterministic system (acoustical motions) exists in the presence of noise produced by flow separation, turbulent motions, and energy released by combustion processes. The last part of the paper is directed to the matter of discovering whether or not chaotic motions exist in combustion systems. Analysis has not progressed sufficiently far to answer the question. We report here recent results of processing data taken in one combustor to determine the dimensions of any attractors in the motions. No evidence has been found for chaos in the strict sense, but the method seems to be an important means of investigating the nonlinear behavior of combustion systems.

No.: 512
ID: CaltechAUTHORS:20110121-134650696

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Abstract: The performance of a particular class of fuel injectors for scramjet engine applications is addressed. The contoured wall injectors were aimed at augmenting mixing through axial vorticity production arising from interaction of the fueVair interface with an oblique shock. Helium was used to simulate hydrogen fuel and was injected at Mach 1.7 into a Mach 6 airstream. The effects of incoming boundary layer height. injector spacing, and injectant to freestream pressure and velocity ratios were investigated. Results from threedimensional flow field surveys and Navier-Stokes simulations are presented. Performance was judged in terms of mixing, loss generation and jet penetration. Injector performance was strongly dependent on the displacement effect of the hypersonic boundary layer which acted to modify the effective wall geometry. The impact of the boundary layer varied with injector array spacing. Widely-spaced arrays were more resilient to the detrimental effects of large boundary layers. Strong dependence on injectant to free stream pressure ratio was also displayed. Pressure ratios near unity were most conducive to losseffective mixing and strong jet penetration. Effects due to variation in mean shear associated with non-unity velocity ratios were found to be secondary within the small range of values tested.

No.: AIAA 92-0625
ID: CaltechAUTHORS:20101130-132815278

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Abstract: Experiments have been carried out to quantify the mixing induced by the interaction of a weak shock wave with a cylindrical volume of a gas (helium) that is lighter than its surroundings (air). In these experiments a round laminar jet was used to produce the light-gas cylinder, and planar laser-induced fluorescence (PLIF), utilizing a fluorescent tracer (biacetyl) mixed with the helium, was used to visualize the flow. These techniques provide a higher quality of flow visualization than that obtained in previous investigations. In addition, the PLIF technique could be used for the measurement of species concentration. The distortion of the helium cylinder produced by the passing shock wave was found to be similar to that displayed by images from previous experimental and computational investigations. The downstream displacement of several points on the boundary of the light-gas cylinder are measured and agree reasonably well with the results of earlier experimental and theoretical studies as well. Because the mixing process causes the helium originally contained within the cylinder to be dispersed into the surrounding air, the PLIF image area inside the contour at one half the maximum concentration of the fluorescent tracer decreases as the two gases mixed. The change in this area is used as a measure of the mixing rate, and it is found that the time rate of change of this area divided by the area of the initial jet is approximately - 0.7 X 10^3 S^(-1).

Publication: Journal of Fluid Mechanics Vol.: 234ISSN: 0022-1120

ID: CaltechAUTHORS:20101130-112755754

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Abstract: Interaction of a shock wave with a jet of light gas surrounded by an ambient heavy gas generates vorticity around the perimeter of the jet. This rolls the jet into a pair of counterrotating, finite-core size vortices. The canonical problem is the two-dimensional, unsteady interaction in a finite channel. The dynamics of the vortex pair are controlled by the incident shock strength, the light/heavy gas density ratio, and the channel spacing. Analytical expressions are derived which describe the strength and motion of the vortex pair as a function of these parameters. Numerical simulations shQw good agreement with these models. Various perturbations on the single jet flow are investigated with the goal of destabilizing the vortex pair and further enhancing the mixing. Single jet shape perturbations are relatively ineffective. However, an array of jets can dramatically increase the mixing. Another effective method is to form a reflected shock. Finally, an analogy to the corresponding three-dimensional, steady flows is demonstrated both qualitatively and quantitatively. This allows an understanding of the dynamics and mixing of the two imensional, unsteady flows to be directly applied to three-dimensional, steady flows typical of SCRAMJET designs.

No.: AIAA-92-0316
ID: CaltechAUTHORS:20101130-135036760

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Abstract: Sustaining a diffusion flame requires sufficient concentrations of fuel and oxidizer to maintain the combustion reaction. When the quantity of oxygen in the environment falls below a minimum value, combustion processes will be extinguished. An experimental technique is described which was used to determine the oxygen concentration in a vitiated environment of combustion products mixed with air which only just supports a large-scale diffusion flame. Measurements were taken of limiting oxygen concentrations and chemical species produced in fires near this flammability limit for methane (natural gas) and ethylene fuels. As limiting conditions were approached, radiation from soot in the reaction zone became imperceptible, leaving only a weakly luminous blue flame. Even with significant reductions in both the flame height and luminosity at these conditions, the fire completely consumed the fuel and generated no measurable amounts of products of incomplete combustion. A comparison of limiting oxygen concentrations and limiting flame temperatures for these experiments with the results of other investigations shows reasonably good agreement despite widely varying experimental techniques.

Publication: Fire Safety Journal Vol.: 19 No.: 2-3 ISSN: 0379-7112

ID: CaltechAUTHORS:20101130-111539300

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Abstract: N/A

No.: 143
ID: CaltechAUTHORS:20110125-152359532

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Abstract: A class of contoured wall fuel injectors was designed to enable shock-enhancement of hypervelocity mixing for supersonic combustion ramjet applications. Previous studies of these geometries left unresolved questions concerning the relative importance of various axial vorticity sources in mixing the injectant with the freestream. The present study is a numerical simulation of two generic fuel injectors which is aimed at elucidating the relative roles of axial vorticity sources including: baroclinic torque through shock-impingement, cross-stream shear, turning of boundary layer vorticity, shock curvature, and diffusive flux. Both the magnitude of the circulation, and the location of vorticity with respect to the mixing interface were considered. Baroclinic torque and cross-stream shear were found to be most important in convectively mixing the injectant with the freestream, with the former providing for deposition of vorticity directly on the fue1/air interface.

No.: 92-3550
ID: CaltechAUTHORS:20101122-094355204

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Abstract: An experimental and computational investigation of a contoured wall fuel injector is presented. The injector was aimed at enabling shock-enhanced mixing for the supersonic combustion ramjet engines currently envisioned for applications on hypersonic vehicles. Three-dimensional flow field surveys, and temporally resolved planar Rayleigh scattering measurements are presented for Mach 1.7 helium injection into Mach 6 air. These experimental data are compared directly with a three-dimensional Navier-Stokes simulation of the flow about the injector array. Two dominant axial vorticity sources are identified and characterized. The axial vorticity produced strong convective mixing of the injectant with the freestream. Shock-impingement was particularly effective as it assured seeding of baroclinic vorticity directly on the helium/air interface. The vorticity coalesced into a counter-rotating vortex pair of a sense which produced migration of the helium away from the wall. The influences of spatial averaging on the representation of the flow field as well as the importance of the fluctuating component of the flow in producing molecularly-mixed fluid are addressed.

No.: AIAA 91-2265
ID: CaltechAUTHORS:20101130-101649129

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Abstract: Classification of the long-term dynamical behavior of pressure oscillations in a laboratory combustion chamber has been performed using methods of modern dynamical systems theory. The method involves the construction of a phase-space representation from a single pressure record or time series using the time-delay embedding method. The pointwise correlation dimension of the resulting attractor in phase-space provides a lower bound on the number of modes that participate in the oscillations. The results show that the oscillations are quasiperiodic with a dimension near two over an order of magnitude of amplitudes. Quasiperiodicity is a result of the incommensurate frequencies of the system acoustic modes. A model for the dynamics is constructed by converting the governing equations to a kicked-oscillator model. When compared with the experimental data, the model results have similar pressure and velocity spectra and the attractor dimension verifies that quasiperiodic oscillations are present.

No.: AIAA 91-2082
ID: CaltechAUTHORS:20101130-100452033

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Abstract: Organized oscillations excited and sustained by high densities of energy release in combustion chambers have long caused serious problems in development of propulsion systems. The amplitudes often become sufficiently large to cause unacceptable structural vibrations. Because the oscillations are self-excited, they reach limiting amplitudes (limit cycles) only because of the action of nonlinear processes. Traditionally, satisfactory behavior has been achieved through a combination of trial-and-error design and testing, with control always involving passive means: geometrical modifications, changes of propellant composition, or devices to enhance dissipation of acoustic energy. Active control has been applied only to small-scale laboratory devices, but the limited success suggests the possibility of serious applications to full-scale propulsion systems. Realization of that potential rests on further experimental work, combined with deeper understanding of the mechanisms causing the oscillations and of the physical behavior of the systems. Effective design of active control systems will require faithful modeling of the relevant processes over broad frequency ranges covering the spectra of natural modes. This paper will cover the general character of the linear and nonlinear behavior of combustion systems, with special attention to acoustics and the mechanisms of excitation. The discussion is intended to supplement the paper by Doyle et al. concerned primarily with controls issues and the observed behavior of simple laboratory devices.

ID: CaltechAUTHORS:20101130-075321569

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Abstract: The mechanisms responsible for driving and damping of pressure oscillations in a laboratory combustor have been investigated. The chamber contains a turbulent methane/hydrogen/air premixed flame stabilized behind a rearward-facing step. Shadowgraph cinematography reveals the shedding of large vortices from the step at frequencies of the system acoustic modes. Variations in the fuel equivalence ratio and the mean flow speed result in a wide variety of nonlinear dynamical behavior. Typically, large cycle-to-cycle variations are observed such that energy may be added or subtracted over one cycle of oscillation but zero net energy change occurs many cycles of oscillation. A quantitative version of Rayleigh's Criterion is constructed by using the cross-spectral-density of the measured flame radiation and pressure. The results under one set of operating conditions show that large driving near the flameholder is balanced by equally large damping further downstream. A second set of conditions results in large energy addition to an acoustic mode balanced by attenuation at the mode subharmonic.

Publication: Combustion Science and Technology Vol.: 77 No.: 4-6 ISSN: 0010-2202

ID: CaltechAUTHORS:20101130-110248831

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Abstract: A fire burning in an enclosure with restricted ventilation will result in the accumulation of a layer of warm products of combustion mixed with entrained air adjacent to the ceiling. For many conditions, the depth of this layer will extend to occupy a significant fraction of the volume of the room. Eventually, the interface between this vitiated ceiling layer and the uncontaminated environment below will position itself so that a large portion of the combustion processes occur in this vitiated layer. A description is given here of experimental work concerning the rates of formation of product species and heat release in a turbulent, buoyant natural gas diffusion flame burning in this two-layered configuration. The enclosure was modeled by placing a hood above a burner so that it accumulated the plume gases, and the unsteady development of the ceiling layer was modeled by the direct addition of air into the upper portion of the hood. Measurements of the composition of these gases allowed the computation of stoichiometries and heat release rates. These investigations showed that the species produced in the flame depend primarily on the stoichiometry of the gases present in the ceiling layer and weakly on the temperature of the layer, but are independent of the fuel-air ratio of the mass transported into the layer by the plume. Heat release rates in the fires were compared to a theoretical limit based on a stoichiometric reaction of fuel and air with excess components left unchanged by the combustion.

Publication: Combustion and Flame Vol.: 83 No.: 3-4 ISSN: 0010-2180

ID: CaltechAUTHORS:20101130-104848579

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Abstract: Experiments concerning properties of large diffusion flames burning steadily in a vitiated atmosphere under conditions similar to those which may arise in a room fire are described. The effects of vitiation on the products of combustion and flame lengths, and the extinction limits are described for natural gas and ethylene diffusion flames stabilized on 8.9-, 19- and 50-cm pool-type burners. As vitiation was increased and the flame extinction limit was approached, the flame length increased slightly. Close to the limit, radiation from soot in the flame became imperceptible, leaving only a weakly luminous blue flame. Even with significant reductions in both the flame height and luminosity near the limit conditions, the hydrocarbon fuels were completely oxidized in the flame to water and carbon dioxide and no measurable concentrations of products of incomplete combustion were produced. A. comparison of limiting oxygen concentrations and limiting flame temperatures for these experiments with the results of other investigations shows reasonably good agreement despite widely varying experimental techniques. These results are contrasted with those obtained in the unsteady situation which arises when a large buoyant diffusion flame burns in an enclosed space such that the upper part of the flame is in a strongly vitiated layer composed of a mixture of air and products of combustion, and the lower part in fresh air.

Vol.: 3
ID: CaltechAUTHORS:20101130-083327723

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Abstract: In 1878, Lord Rayleigh formulated his criterion to explain several examples of acoustic waves excited and maintained by heat addition. It is a qualitative explanation successfully capturing the essence of the phenomena but not providing a basis for quantitative predictions. The widespread appeal of Rayleigh's criterion merits placing this important result on a more rigorous basis. To do so requires careful formulation grounded in the theory of small amplitude motions in a compressible fluid. In this chapter, we review the construction of an approximate analysis and establish the equivalence of Rayleigh's criterion and the condition for linear stability of small amplitude motions. Thus Rayleigh's criterion is formulated explicitly in the context of an analysis applicable to any combustion chamber. Some results are discussed for both linear and nonlinear motions. Recent experimental results discussed by others suggest that the criterion may offer a practical means for investigating the causes of instabilities in propulsion systems.

ID: CaltechAUTHORS:20110127-073132186

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Abstract: Conditions of high energy densities and low losses in combustion chambers encourage the excitation and sustenance of organized unsteady motions generically called combustion instabilities. The fluctuations, common in propulsion systems, often reach sufficient amplitudes to cause excessive rates of heat transfer to exposed surfaces and unacceptable structural vibrations, causing failure in extreme cases. In many cases, to avoid the occurrence of instabilities, combustion chambers are operated below their maximum performance. Considerable effort has been spent, for more than four decades, on experimental and analytical programs devoted to solving problems of combustion instabilities. Much of the work has been required to measure quantities which, because of the complex processes involved, cannot be predicted accurately from first principles. Analytical work has been concerned largely with linear behavior, the chief purpose being to predict stability of small disturbances in combustion chambers. Many useful results have been obtained, serving in practice to help design experiments, correlate data, and predict the stability of new systems. However, linear behavior is only a small part of the general problem. A combustion chamber is an isolated system so far as its stability is concerned, and unstable disturbances evolve as 'self-excited' motions. Hence their amplitudes will grow indefinitely unless nonlinear processes are effective. Complete understanding of observed behavior will therefore be reached only by treating nonlinear behavior. In the recent past, increased attention has been paid to nonlinear combustion instabilities. It is particularly important for practical purposes to explain the existence of limit cycles and the occurrence of unstable motions in linearly stable systems exposed to large initial disturbances. These matters are far from closed, and although substantial progress has been accomplished, little impact has been made on the development of new systems. The chief purpose of this paper is to provide a brief review of work on nonlinear combustion instabilities, largely in the framework of an approximate analysis. Some connections will be made with the modern theory of nonlinear dynamical systems, including very recent and incomplete attempts by others to assess the possible chaotic behavior observed in laboratory tests.

No.: 90-3927
ID: CaltechAUTHORS:20101129-112004053

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Abstract: Dynamical systems theory has been used to study the nonlinear dynamics of the F-14. An eight degree of freedom model that does not include the control system present in operational F-14's has been analyzed. The aerodynamic model, supplied by NASA, includes nonlinearities as functions of the angles of attack and sideslip, the rotation rate, and the elevator deflection. A continuation method has been used to calculate the steady states of the F-14 as continuous functions of the control surface deflections. Bifurcations of these steady states have been used to predict the onset of wing rock, spiral divergence, and jump phenomena which cause the aircraft to enter a spin. A simple feedback control system was designed to eliminate the wing rock and spiral divergence instabilities. The predictions were verified with numerical simulations.

No.: AIAA-90-0221
ID: CaltechAUTHORS:20101130-140634171

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Abstract: Nonlinear pressure oscillations in combustion chambers have been studied using an approximate analysis which treats the unsteady motions as a collection of coupled nonlinear oscillators, each corresponding to an acoustic mode of the chamber. Based on spatial and temporal averaging of the conservation equations, the formulation provides a convenient means for analyzing the nonlinear behavior of acoustic wave motions. The work addresses the linear and nonlinear characteristics of transverse acoustic waves in a cylindrical chamber, with attention focused on the conditions for the existence and stability of limit cycles. As a result of the special structure of the equations, both general and precise conclusions can be reached. Explicit results are given for the special cases of two and three standing modes. Spinning wave motions will be treated in a subsequent paper.

Publication: Combustion Science and Technology Vol.: 72 No.: 1-3 ISSN: 0010-2202

ID: CaltechAUTHORS:20101129-110317027

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Abstract: The possibility that shock enhanced mixing can substantially increase the rate of mixing between coflowing streams of hydrogen and air has been studied in experimental and computational investigations. Early numerical computations indicated that the steady interaction between a weak shock in air with a coflowing hydrogen jet can be well approximated by the two-dimensional time-dependent interaction between a weak shock and an initially circular region filled with hydrogen imbedded in air. An experimental investigation of the latter process has been carned out in the Caltech 17 Inch Shock Tube in experiments in which the laser induced fluorescence of byacetyl dye is used as a tracer for the motion of the helium gas after shock waves have passed across the helium cylinder. The flow field has also been studied using an Euler code computation of the flow field. Both investigations show that the shock impinging process causes the light gas cylinder to split into two parts. One of these mixes rapidly with air and the other forms a stably stratified vortex pair which mixes more slowly; about 60% of the light gas mixes rapidly with the ambient fluid. The geometry of the flow field and the mixing process and scaling parameters are discussed here. The success of this program encouraged the exploration of a low drag injection system in which the basic concept of shock generated streamwise vorticity could be incorporated in an injector for a Scramjet combustor at Mach numbers between 5 and 8. The results of a substantial computational program and a description of the wind tunnel model and preliminary experimental results obtained in the High Reynolds Number Mach 6 Tunnel at NASA Langley Research Center are given here.

No.: AIAA 90-1981
ID: CaltechAUTHORS:20101209-134118457

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Abstract: Based on spatial and temporal averaging of the conservation equations, an approximate analysis provides a convenient vehicle for analyzing the nonlinear behavior of unsteady motions in combustion chambers. Recent work has been concerned with the conditions for existence and stability of limit cycles, and in particular their dependence on the order of nonlinear terms contained in the equations of motion. It seems to be generally true that if only nonlinear gasdynamic terms to second order are accounted for, a stable nontrivial limit cycle is unique. This implies that no initial disturbance will cause a linearly stable system to execute a limit cycle, a result contrary to prior experience with, for example, solid propellant rocket motors. In this paper, we study some conditions under which true nonlinear instabilities may be found, with special attention focused on the effect of nonlinear gasdynamics. Our results indicate that third-order terms in the acoustic motions do not lead to triggering to either a stable or an unstable limit cycle; they only modify the stability domain of the system. However, the interactions between mean flow and nonlinear acoustic waves may trigger a linearly stable system to an unstable limit cycle. The influence of nonlinear combustion response may have quite different consequences and will be discussed in Part II of this work.

Publication: Combustion Science and Technology Vol.: 72 No.: 4-6 ISSN: 0010-2202

ID: CaltechAUTHORS:20101130-073713187

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Abstract: Mechanisms for generation of axial vorticity by swirling flows in rectangular nozzles have been investigated experimentally and computationally. A detailed experimental investigation is described that demonstrates the formation of axial vortices in the nozzle is dependant on the vorticity distribution at the turbine exhaust. Further, mechanisms providing for the formation of axial vortices are identified. A parallel computational investigation was carried out that not only confirmed the relationship between the turbine exhaust vorticity and the vortex patterns formed in the nozzle, but also provided details of the flowfield between the turbine discharge and the nozzle exit. On the basis of this more detailed understanding, it is now possible to "tailor" the vortex distribution at the nozzle exit by design of the turbine discharge and the intervening passage.

Publication: Journal of Propulsion and Power Vol.: 5 No.: 3 ISSN: 0748-4658

ID: CaltechAUTHORS:20101203-094947244

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Abstract: The behavior of unsteady pressure fluctuations in combustion chambers is examined. An approximate method used in the derivation of the amplitude equations is based on the spatial and time domain averaging of the conservation equations, and follows the analytical framework introduced by Culick (1976a,b). The first order perturbation terms retained in the analysis correspond to linear contributions from the combustion processes, gas/particle interactions, mean flow and boundary conditions, as well as second order nonlinear gas dynamics terms. Further simplification of these equations is obtained by an appropriate change of variables. Following this step, the analysis based on two longitudinal modes is reduced to the solution of a three-dimensional system of nonlinear equations. This enables derivation of exact results for the existence, stability and the amplitude of the limit cycle, in the general case of frequency shifted periodic oscillations. Consideration is also given to the transfer of energy within the spectrum of the acoustic modes. In agreement with experimental observations, it is shown analytically that the preferred direction of energy transfer is from the lower to the higher acoustic modes. Validation of the results is accomplished by comparison with numerical results obtained when higher numbers of modes are treated. Finally, it is shown that combustion instabilities can be treated analytically using the center manifold theory.

Publication: Combustion Science and Technology Vol.: 65 No.: 1-3 ISSN: 0010-2202

ID: CaltechAUTHORS:20101203-081753345

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Abstract: This paper consists of two parts summarizing two portions of the ONR/NAVAIR Research Option. The option began in 1983 and continued for five years, involving 11 organizations. Simultaneously, similar or related programs supported by other agencies or institutions were being carried out in several other places. Results of those programs have been briefly summarized in five papers collected in a document to be published by C.P.L.A. This paper contains two of the five papers in that document. Here we cover the subjects of approximate analyses and stability; and large-scale structures and passive control. The first is concerned chiefly with an analytical framework constructed on the basis of observations; it is intended to provide a means of correlating and interpreting data, and predicting the stability of motions in a combustion chamber. The second is a summary of recent experimental work directed to understanding the flows in dump combustors of the sort used in modern ramjet engines. Much relevant material is not included here, but may be found in the remaining papers of the document cited above. For completeness, we note briefly the substance of those reports. In their summary "Spray Combustion Processes in Ramjet Combustion Instability," Bowman (Stanford), Law (University of California, Davis) and Sirignano (University of California, Irvine) review several aspects of spray combustion relevant to combustion instabilities. The objectives of the works were: (1) to determine the effect of spray characteristics on the energy release pattern in a dump combustor and the subsequent effects on combustion instability; (2) to gain a fundamental understanding of the coupling of the spray vaporization process with an unsteady flow field; and (3) to investigate methods for controlling and enhancing spray vaporization rates in liquid-fueled ramjets. During the past five years considerable progress has been made in applying methods of computational fluid dynamics to the flow in a dump combustor including consequences of energy release due to combustion processes. Jou has summarized work done at Flow Research, Inc. and at the Naval Research Laboratory in his paper "A Summary Report on Large-Eddy Simulations of Pressure Oscillations in a Ramjet Combustor." The serious effects of combustion instabilities on the inlets of ramjet engines were discovered in the late 1970's in experimental work at the Aeropropulsion Laboratory, Wright Field, the Naval Weapons Center and the Marquardt Company. The most thorough laboratory work on the unsteady behavior of inlets has been accomplished at the McDonnell-Douglas Research Laboratory by Sajben who has reviewed the subject in his paper "The Role of Inlet in Ramjet Pressure Oscillations."

ID: CaltechAUTHORS:20101203-091515515

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Abstract: An analytical analysis has been developed to investigate the behavior of unsteady transverse pressure oscillations in combustion chambers. The model extends the previous analysis for the second-order standing wave motions and accommodates spinning oscillations and third-order nonlinearities. The influences of various parameters and initial conditions on the limit cycles and triggering of pressure oscillations are discussed. Results indicate that the existence of spinning oscillations depends strongly on the number of modes included in the analysis and on the initial conditions. The third-order acoustics has little influence on the triggering of instability. It only modifies the characteristics of limiting amplitudes.

No.: AIAA-88-0152
ID: CaltechAUTHORS:20101203-144226944

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Abstract: Dynamical systems theory has been used to study nonlinear aircraft dynamics. A six degree of freedom model that neglects gravity has been analyzed. The aerodynamical model, supplied by NASA, is for a generic swept wing fighter and includes nonlinearities as functions of the angle of attack. A continuation method was use to calculate the steady states of the aircraft, and bifurcations of these steady states, as functions of the control deflections. Bifurcations were used to predict jump phenomena and the onset of periodic motion for roll coupling instabilities and high angle of attack maneuvers. The predictions were verified with numerical simulations.

No.: AIAA-88-4372
ID: CaltechAUTHORS:20101203-102240185

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Abstract: This is a summary of a lecture intended primarily as a progress report of the Los Angeles AIAA Section Wright Flyer Project. Begun in late 1978, the project is devoted chiefly to construction of two replicas of the 1903 Wright 'Flyer.' The first, now being covered, is an exact replica intended for full-scale wind tunnel tests. The second will be a flying replica, incorporating minimal modifications to produce a less unstable aircraft. Partly in preparation for the second aircraft, considerable attention has been given to the aerodynamics, stability, and control of the 1903 'Flyer.' Wind tunnel tests have been conducted with a 1/6 flexible model, and a 1/8 scale steel model tested at full-scale Reynolds numbers. The data have provided basis for analyzing both the closed-loop and open-loop performance of the aircraft. Another aspect of the Project has been concerned with the history of early aeronautics, especially as related to the Wright Brothers' work. Thus a significant portion of the lecture is given to aeronautical history both before and after 1903, to provide a better appreciation for the Wrights' achievements and a clearer perspective of their work in the context of aeronautical progress.

No.: AIAA 88-0094
ID: CaltechAUTHORS:20101220-104426212

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Abstract: Combustion of reactants in a confined volume favors excitation of unsteady motions over a broad range of frequencies. A relatively small conversion of the energy released will produce both random fluctuations or noise, and, under many circumstances, organized oscillations generically called combustion instabilities. Owing to the high energy densities and low losses in combustion chambers designed for propulsion systems, the likelihood of combustion instabilities is high. The accompanying heat transfer to exposed surfaces, and structural vibrations are often unacceptable, causing failure in extreme cases. This paper is a brief review of combustion instabilities in liquid-fueled propulsion systems-rockets, ramjets, and thrust augmentors-with emphasis on work accomplished during the past decade. To provide a common framework for discussing the wide range of works, a theory of two-phase flow is reviewed as the basis for an approximate analysis of combustion instabilities. The analysis is directed primarily to treatment of linear stability; it is sufficiently general to accommodate all processes occurring in actual systems. A new result has been obtained for an extended form of Rayleigh's criterion and its relation to the growth constant for unstable waves. The chief mechanisms for combustion instabilities in liquid-fueled systems are reviewed, followed by a summary of the common methods of analysis and applications to the three classes of propulsion systems. Control of instabilities by passive and active means is examined briefly.

ID: CaltechAUTHORS:20110204-151853189

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Abstract: Active control of longitudinal pressure oscillations in combustion chambers has been studied theoretically using a digital state-feedback control technique. The formulation is based on a generalized wave equation which accommodates various influences on combustion, mean flow, unsteady motions, and contol actions. After a procedure equivalent to the Galerkin method, a system of ordinary differential equation governing the amplitude of each oscillatory mode is derived, serving as a basis for the controller design. The control actions is provided by a finite number of point acutators, with the instantaneous chamber conditions monitored by a few sensors. Several important control aspects such as sampling period, locations of sensors and controllers, controllability and observabi1ity have been investigated. As a specific example, the case involving two controlled and two residual (uncontrolled) modes is studied. The control and observation spillover phenomena due to the residual modes are clearly demonstrated.

No.: AIAA-88-2944
ID: CaltechAUTHORS:20101202-115230138

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Abstract: The structure of a diffusion flame embedded in a flow field parallel to the flame is studied under conditions where this external flow imposes an adverse pressure gradient. It is convenient to think of the physical problem as a flame lying along the flow direction of a divergent channel. The mathematical problem is reduced to a set of ordinary differential equations by (i) employing the Howarth transformation to eliminate the variable density and (ii) introducing a similarity solution somewhat in the manner of the Falkner-Skan treatment of boundary layer flows. Because the low-density gas near the flame responds more readily to the pressure gradient than does the higher density gas, a reverse flow develops in the low density region which severely affects both the structure of the flame and the fuel consumption rate. For a flame with unit stoichiometry, the reverse flow eventually leads to extinction of the flame by separating the two shear layers that bound the fuel and oxidizer streams. For stoichiometry corresponding to methane-air, the flame situates itself near the oxidizer side of the reverse flow and has no tendency toward extinguishment.

Publication: Symposium International on Combustion Vol.: 21 No.: 1 ISSN: 0082-0784

ID: CaltechAUTHORS:20101202-142309487

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Abstract: A research effort directed at analytically and experimentally investigating Electron-Cyclotron-Resonance (ECR) plasma acceleration is outlined. In addition, relevant past research is reviewed. Also, the prospects for application of ECR plasma acceleration to spacecraft propulsion are described. It is shown that previously unexplained losses in converting microwave power to directed kinetic power via ECR plasma acceleration can be understood in terms of diffusion of energized plasma to the physical walls of the accelerator. It is also argued that line radiation losses due to electron-ion and electron-atom inelastic collisions should be less than estimated in past research. Based on this new understanding, the expectation now exists that very efficient ECR plasma accelerators can be designed for application to high specific impulse spacecraft propulsion.

No.: AIAA 87-1407
ID: CaltechAUTHORS:20101202-102106634

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Abstract: A one-dimensional analytical model is presented for calculating the longitudinal acoustic modes of idealized "dump-type" ramjet engines. The model contains the matching required to place an oscillating flame sheet in the interior of a combustion chamber with mean flow. The linear coupling of the acoustic and entropy waves at the inlet shock, flame sheet, and exit nozzle along with acoustic admittances at the inlet and exit are combined to determine the stability of the system as well as the acoustic modes. Since the acoustic and entropy waves travel at different velocities, the geometry is a critical factor in determining stability. Typical values of the admittances will produce damped solutions when the entropy is neglected, but, as the ratio of the entropy to acoustic fluctuations is increased, the coupling can either feed acoustic energy into or out of different modes independently. This transfer of energy has a destabilizing or stabilizing effect on the acoustic modes of the system depending upon the phase of the energy transfer.

No.: AIAA-87-1872
ID: CaltechAUTHORS:20101202-105114390

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Abstract: A novel diagnostic technique, which makes use of laser light scattered by soot particles, was used in an effort to identify the flame sheets within a natural gas diffusion flame. Soot particles, inherently created and consumed in the flame, were used as the scattering medium, which obviated the need for externally supplied seed material. Since no foreign material was added to the flame, the current technique can be considered truly nonintrusive. The soot distribution within a large buoyant natural gas diffusion flame is argued to be a reasonable marker of the flame sheets. Measurements made in 47.4-190 kW natural gas flames stabilized on a 0.5 m diameter burner show that the flame sheets are highly wrinkled and convoluted surfaces. The flame sheets are distributed fairly uniformly within the instantaneous volume of the flame, based on images of the associated soot, and the instantaneous flame volume is devoid of soot for 40-60% of the time. When soot is present, it is observed as thin sheets which become narrower in regions where the average strain rate is estimated to be greater.

Publication: Combustion and Flame Vol.: 67 No.: 1 ISSN: 0010-2180

ID: CaltechAUTHORS:20101201-103241003

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Abstract: The mechanism by which longitudinal modes of a dump combustor are excited has been investigated. The unsteady combustion is a result of the shedding of large scale vortical structures from the flameholder. Driving and damping as determined by Rayleigh's criterion were investigated by using the cross-spectrum and phase of the fluctuating pressure and radiation intensity signals at various locations in the combustor. Thus, the excitation of a particular mode was found to depend on the pressure mode shape and the magnitude and phase of the velocity fluctuation at the flameholder. Fluid mechanical mixing and the chemical reaction rate of the fuel also effect the distribution of heat release and hence the locations of driving and damping. Finally, a mechanism for existence of the limit cycle is discussed.

No.: AIAA-87-0220
ID: CaltechAUTHORS:20101202-073712764

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Abstract: N/A

Publication: Combustion Science and Technology Vol.: 56 No.: 4-6 ISSN: 0010-2202

ID: CaltechAUTHORS:20101202-151716445

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Abstract: In August 1908, Wilbur Wright gave the first public demonstration of the Wright airplane, at Le Mans, France. Two weeks later Orville was the first to fly publicly a powered man-carrying aircraft in the United States, at Fort Myer, Virginia. Those astonishing flights were the beginnings of the Wrights' programs to fulfill the requirements of contracts the Brothers had made with the French and U.S. governments. At the time nobody else had a practical aircraft fully controllable and capable of being maneuvered at the pilot's command.

ID: CaltechAUTHORS:20110204-135939767

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Abstract: The high thrust to weight ratios now possible for military aircraft have made thrust vector pitch control more attractive and versatile than aerodynamic surface pitch control. Use of a rectangular nozzle is a natural consequence because articulation and sealing problems are less formidable than for conventional circular ones. The rectangular nozzle offers the additional possibility that the exhaust may mix rapidly with the ambient air and thereby reduce the radiative signature of the exhaust. A detailed experimental investigation is described, which demonstrates that the formation of axial vortices in the nozzle is dependent on the vorticity distribution at the turbine exhaust. Further, three mechanisms which provide for the formation of axial vortices are identified. A parallel computational investigation was carried out which not only confirmed the relationship between the turbine exhaust vorticity and the vortex pattern formed in the nozzle but also provided details of the flow field between the turbine discharge and the nozzle exit. On the basis of this more detailed understanding, it is now possible to tailor the vortex distribution at the nozzle exit by design of the turbine discharge and the intervening passage.

No.: AIAA-87-2108
ID: CaltechAUTHORS:20101203-145603258

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Abstract: In air breathing propulsion systems for flight at Mach numbers 7 to 20, it is generally accepted that the combustion processes will be carried out at supersonic velocities with respect to the engine. The resulting brief residence time places a premium on rapid mixing of the fuel and air. To address this issue we &re investigating a mechanism for enhancing the rate of mixing between air and hydrogen fuel over rates that are expected in shear layers and jets. The mechanism rests upon the strong vorticity induced at the interface between a light and heavy gas by an intense pressure gradient. The specific phenomenon under investigation is the rapid mixing induced by interaction of a weak oblique shock with a cylindrical jet of hydrogen embedded in air. The status of our investigations is described in three parts: a) shock tube investigation of the distortion and mixing induced by shock waves impinging on cylindric of hydrogen embedded in air, b) the molecular mixing and chemical reaction in large vortices, periodically formed in a channel, and c) two-dimensional non-steady and three-dimensional steady numerical studies of shock interaction with cylindrical volumes of hydrogen in air.

No.: AIAA-87-1880
ID: CaltechAUTHORS:20101201-110408219

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Abstract: The ballistic Mars hopper is proposed as an alternative mobility concept for unmanned exploration of the martian surface. In the ballistic Mars hopper concept, oxygen and carbon monoxide produced from the martian atmosphere are used as propellants in a rocket propulsion system for an unmanned vehicle on suborbital trajectories between landing sights separated by distances of up to 1000 km. This mobility concept is seen as uniquely capable of allowing both intensive and extensive exploration of the planet using only a single landed vehicle massing approximately 2000 kg. The technical challenges associated with In-Situ Propellant Production (ISPP) on the surface of Mars are reviewed. A rocket propulsion subsystem capable of using oxygen and carbon monoxide as propellants is described. Finally, results of mission analysis and a hopper landing hazard simulation are reported. It is concluded that an attractive Mars hopper can be developed based on relatively near-term technology.

No.: AIAA-87-1901
ID: CaltechAUTHORS:20101202-113823336

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Abstract: An analytical analysis has been developed to investigate the behavior of unsteady motions in combustion chambers. The model accommodates the third-order nonlinear acoustics and a second-order combustion response. Ths influences of various linear and nonlinear parameters on the limit cycles and triggering of pressure osoillations are disoussed in detail. Results indicate that the third-order acoustics has little influence on the triggering of instability. It only affects the limiting amplitudes and the stability domains of limit cycles. The nonlinear combustion response plays an essential role in determining the characteristics of triggering.

No.: AIAA-87-1873
ID: CaltechAUTHORS:20101203-142326424

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Abstract: The structure of a strained premixed laminar flame is examined. The flame is formed in the vicinity of a stagnation point established by the counterflow of fresh mixture and hot combustion products. This ideal configuration analyzed by Libby and Williams [18] with activation energy asymptotics is here examined numerically. This allows an exact description of flame and flow structure and a calculation of the mass rate of reaction per unit flame area for the whole range of strain rates. Previous results obtained for intermediate and high strain rates are confirmed. However, for low strain rates the mass rate of reaction per unit flame area differs from that determined with large activation energy asymptotics. The present calculations also provide the exact value of the strain rate (or Damkiihler number) for which the partial extinction regime appears. If the strain rate is increased beyond that value the flame front develops on the hot side of the stagnation point. The reactive front first moves away from the stagnation point and then moves back toward that point for the very large values of the strain rate.

Publication: Combustion and Flame Vol.: 64 No.: 2 ISSN: 0010-2180

ID: CaltechAUTHORS:20101203-093502119

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Abstract: Longitudinal combustion instabilities in liquid-fueled ramjet engines have been investigated with attention focused on determination of the acoustic mode structures. Detailed pressure measurements, including both amplitude and phase, were made at ten positions spanning the length of the engine. The experimental data have been analyzed using two linear acoustic models. Four distinct modes were observed for various inlet/combustor combinations. These results help identify the mechanisms exciting low-frequency pressure oscillations in ramjet engines.

Publication: Journal of Propulsion and Power Vol.: 2 No.: 2 ISSN: 0748-4658

ID: CaltechAUTHORS:20101201-085332901

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Abstract: A new approach for linear analysis of the stability of jets with arbitrary mean velocity profiles is presented. This method is based on utilizing Green function technique a to transform the Rayleigh equation into an integral equation form. The integral equation is then solved numerically using a type of finite element approximation to determine the eigenvectors and complex wave numbers of various instability modes. In order to demonstrate this method's capability of handling arbitrary jet mean velocity profiles, a comparison is made to the elliptic jet case where generally good agreement 1s apparent. A brief discussion on how the effects of compressibility and temperature variation in flows car be incorporated within the formalism is presented.

No.: AIAA-86-0542
ID: CaltechAUTHORS:20101122-083110170

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Abstract: Several fluid dynamic processes which play important roles in the development of accidental fires in structures are discussed. They include a review of information concerning the characteristic flow regimes of fire plumes and the properties of the flow in these regimes, and a brief review of flow through openings and in ceiling jets. Factors which lead to the development of thermal stratification in ceiling layers are also discussed.

Publication: Fire Safety Science Vol.: 1
ID: CaltechAUTHORS:20101206-115227793

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Abstract: Pressure oscillations in ramjet engines have been studied using an approximate method which treats the flow fields in the inlet and the combustor separately. The acoustic fields in the combustor are expressed as syntheses of coupled nonlinear oscillators corresponding to the acoustic modes of the chamber. The influences of the inlet flow appear in the admittance function at the inlet /combustor interface, providing the necessary boundary condition for calculation of the combustor flow. A general framework dealing with nonlinear multi-degree-of-freedom system has also been constructed to study the time evolution of each mode. Both linear and nonlinear stabilities are treated. The results obtained serve as a basis for investigating the existence and stabilities of limit cycles for acoustic modes. As a specific example, the analysis is applied to a problem of nonlinear transverse oscillations in ramjet engines.

Vol.: 1 No.: AIAA-1986-1
ID: CaltechAUTHORS:20110126-104752906

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Abstract: Unsteady motions in combustion chambers have previously been treated with an approximate analysis in which an acoustic field is represented as a collection of coupled nonlinear oscillators constructed in one-to-one correspondence to the acoustic modes. Two parameters characterize the linear behavior of each oscillator; a single parameter arises from the nonlinear acoustics carried out to second order in small fluctuations. The formal results are used here as the basis for studying the existence and stability of limit cycles for longitudinal modes. Owing to the special structure of the equations, explicit and precise conclusions can be reached. Existence and stability depend only on the parameters defining the linear motions. The nonlinear gasdynamics influence the amplitudes of motion in the limit cycle. At least one of the acoustic modes must be linearly unstable to produce a nontrivial limit cycle. Generally, energy flows both up and down among the modes, but there are exceptional cases when limit cycles exist only if the fundamental mode is unstable. Explicit results are given for the special cases of two and three modes; the analysis is extendible to any number of modes.

Publication: Combustion Science and Technology Vol.: 46 No.: 3-6 ISSN: 0010-2202

ID: CaltechAUTHORS:20101201-083223351

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Abstract: The time dependent interaction of a laminar diffusion flame with a single plane vortex and with a stretched line vortex is examined with the aim of determining the flame configuration and the augmentation to the reactant consumption rate resulting from the interaction. Elements of the resulting curved flame sheets behave essentially as isolated flames until the neighboring flame sheets become so closely spaced that they interact and consume the intervening reactant. This process creates a core of combustion products with external isolated flame surfaces. The augmentation of the reactant consumption rate results both from the local straining of the flame in its own plane and from the overall increase in flame surface area. Three examples are treated in detail. The first is the plane problem in which an initially straight flame is distorted by a vortex. In the second, the situation is similar except that the problem is expanded to three dimensions and the vortex line is being stretched along its own axis. Finally, the effects of the density change resulting from the heat release are examined.

Publication: Combustion Science and Technology Vol.: 45 No.: 1-2 ISSN: 0010-2202

ID: CaltechAUTHORS:20101201-080248569

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Abstract: Undesirable sound generation in the combustion chambers of solid propellant rocket motors previously has been attributed to vortex shedding from obstructions that are uncovered as the propellant burns back. An experimental investigation of the phenomenon has re-conf irmed this observation and extended the understanding of the mechanism by which the process is self-sustaining. A pair of aluminum baffles within a lucite duct through which air is drawn models the important aspects which enable the sound generation mechanism to operate. The baffles form an edgetone system which interacts with the longitudinal acoustic modes of the chamber. Pure acoustic tones occur spontaneously, at frequencies equal to the acoustic resonances, when the spacing between the baffles satisfies certain criteria. Flow visualization using smoke and a strobe light triggered by the pressure oscillation indicates that vortex shedding occurs at the upstream baffle in phase with the acoustic velocity oscillation there. Based on the results of the present experiments and others reported in the literature, a mechanism is postulated which explains the observed behavior. It is suggested that pressures induced on the downstream baffle by the vortices convected past by the freestream drive the acoustic resonance. In turn, the acoustic velocity at the upstream baffle serves as the perturbation triggering the formation of vortices in the shear layer growing from the separation point at that location. The amplitude is limited by the nonlinearity in the growth of the vortices in the shear layer. A lIodel based on the proposed mechanism is formulated and written as a computer program. The results predict the behavior of the experilllental apparatus well, confirming that the postulated mechanism is correct.

No.: 86-000183
ID: CaltechAUTHORS:20101207-081629419

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Abstract: The Los Angeles Chapter of the American Institute of Aero and Astronautics is building two replicas of the 1903 Wright Flyer airplane; one to wind-tunnel test and display, and a modified one to fly. As part of this project the aerodynamic characteristics of the Flyer are being analyzed by modern wind-tunnel and analytical techniques. Tnis paper describes the Wright Flyer Project, and compares key results from small-scale wind-tunnel tests and from vortex-lattice computations for this multi-biplane canard configuration. Analyses of the stability and control properties are summarized and their implications for closed-loop control by a pilot are derived using quasilinear pilot-vehicle analysis and illustrated by simulation time histories. It is concluded that, although the Wrights were very knowledgeable and ingenious with respect to aircraft controls and their interactions (e.g., the good effects of their wing-warp-to-rudder linkage are validated), they were largely ignorant of dynamic stability considerations. The paper shows that the 1903 Flyer was readily controllable about all axes but was intrinsically unstable in pitch and roll, and it could barely be stabilized by a skilled pilot.

No.: WF 84/09-1
ID: CaltechAUTHORS:20101207-140100221

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Abstract: A finite difference scheme with a shock-fitting algorithm has been used to investigate unsteady inviscid now with a shock in an inlet diffuser. The flowfield consists of three different regions: the supersonic and the subsonic regions, and a region containing both air and liquid fuel droplets, separated by a normal shock wave and a fuel injection system. The analysis is based on a two-phase, quasi-one-dimensional model. The response of a shock wave to various disturbances has been studied, including large-amplitude periodic oscillations and pulse perturbations.

Publication: Journal of Propulsion and Power Vol.: 1 No.: 3 ISSN: 0748-4658

ID: CaltechAUTHORS:20110125-143851324

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Abstract: This paper summarizes work accomplished during the past five years on analysis of stability related to recent experimental results on combustion instabilities in dump combustors. The primary purpose is to provide the information in a form useful to those concerned with design and development of operational systems. Thus most substantial details are omitted; the material is presented in a qualitative fashion.

ID: CaltechAUTHORS:20110207-100340630

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Abstract: The acoustic/vortical interaction in a twodimensional free shear layer has been studied. The flowfield is represented by division into two parts: the vortical and the compressible flows. Each field is treated separately and linked with the other through the Bernoulli enthalpy. Acoustic waves are identified as unsteady compressible motions free of vorticity. Calculations have been carried out for the flowfields with and without externally imposed disturbances. Preliminary results reported here indicate that the motion of large coherent flow structures contributes significantly to sound generation. In particular, the formation of large structure and subsequent pairing appear globally as a quadrupole source.

No.: AIAA 85-0043
ID: CaltechAUTHORS:20101208-072047856

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Abstract: The determination of an internal feedback mechanism which leads to combustion instability inside a small scale laboratory combustor is presented in this paper. During combustion instability, the experimental findings show that a large vortical structure is formed at an acoustic resonant mode of the system. The subsequent unsteady burning, within the vortex as it is convected downstream, feeds energy into the acoustic field and sustains the large resonant oscillations. These vortices are formed when the acoustic velocity fluctuation at the flameholder is a large fraction of the mean flow velocity. The propagation of these vortices is not a strong function of the mean flow speed and appears to be dependent upon the frequency of the instability. Continued existence of large vortical structures which characterize unstable operation depends upon the fuel-air ratio, system acoustics, and fuel type.

No.: AIAA-85-1248
ID: CaltechAUTHORS:20101206-101510045

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Abstract: A simple diffusion flame with fast chemical kinetics is initiated along the horizontal axis between a fuel occupying the upper half-plane and an oxidizer below. Simultaneously a vortex of circulation T is established at the origin. As time progresses the flame is extended and "wound up" by the vortex flow field and the viscous core of the vortex spreads, converting the motion in the core to a solid-body rotation. The kinematics of the flame extension and distortion is described and the effect of the local-flow field upon local-flame structure is analyzed in detail. It is shown that the combustion field consists of a totally reacted core region, whose radius is time dependent, and an external flame region consisting of a pair of spiral arms extending off at large radii toward their original positions on the horizontal axis. The growth of the reacted core, and the reactant-consumption rate augmentation by the vortex field in both core and outer-flame regions were determined for values of the Reynolds number (T/2πv) between 1 and 10^3 and for a wide range of Schmidt numbers (v / D) covering both gas and liquid reactions. For large values of Reynolds number the radius r _* of the reactant grows much more rapidly than the viscous core so that only the nearly inviscid portion of the flow is involved. The more accurate condition for this behavior is that R(Sc)^(1/2)>50 and, under this restriction, the similarity rule for the core radius growth is shown to be r _*(T^(2/3)D^(1/3)t)^(1/2)=0.5092+O(D/T)^(1/2) In this case also the reactant consumption rate becomes independent of time and, for the complete diffusion flame in the vortex field, the augmentation of reactant-consumption rate due to the vortex field satisfies Augmented consumption rate == 1. 2327 ,-1.4527(D/T)^(1/6) + O(D/T)^(1/2) T^(2/3) D^(1/3) Both of these similarity rules are, as is appropriate for high Reynolds number, independent of kinematic viscosity.

ID: CaltechAUTHORS:20101207-085326836

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Abstract: Natural gas diffusion flames stabilized on 0.10, 0.19 and 0.50 m. diameter porous bed burners have been studied for heat release rates ranging from 10 to 200 kW. Flame heights were measured from video tape recordings and by eye averaged techniques. The dependence of flame height on a dimensionless heat addition parameter shows a transition for values of the parameter around unity. For flames taller than three burner diameters, the initial diameter of the fire does not affect the length of the flame whereas for short flames, initial geometry becomes important. Another prominent feature of these flames is the presence of large scale axisymmetric structures which are formed close to the burner surface with more or less regular frequency and which rise through the flame region. These structures are responsible for the fluctuations of the flame top and strongly influence the geometry of the flame.

Publication: Symposium (International) on Combustion : [papers] Vol.: 20 No.: 1 ISSN: 0082-0784

ID: CaltechAUTHORS:20101206-110336671

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Abstract: This paper describes entrainment measurements made in fire plumes with a new technique. Measurements were in plumes rising from natural gas diffusion flames stabilized on 0.10, 0.19 and 0.50 m diameter burners and the heat release rates ranged from 10 to 200 kW. The heights examined ranged from elevations starting very close to the burner surface to distances about five times the average flame heights. Experiments indicate the presence of three regions: a region close to the burner surface where plume entrainment rates are independent of the fuel flow (or heat release) rates; a far field region above the flame top, where a simple point source model correlates the data reasonably well; and an intermediate region where entrainment appears to be similar to that of a turbulent plume.

Publication: Combustion Science and Technology Vol.: 39 No.: 1 ISSN: 0010-2202

ID: CaltechAUTHORS:20101206-091030426

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No.: AFRPL-TR-79-84
ID: CaltechAUTHORS:20101208-091246752

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Abstract: Pressure oscillations in a side-dump ramjet engine have been studied, using a one-dimensional numerical analysis. The engine is treated in two parts; the inlet section, including a region of two-phase flow downstream of fuel injection, and a dump combustor. Each region is treated separately and matched with the other. Following calculation of the mean flow field, the oscillatory characteristics of the engine are determined by its reponse to a disturbance imposed on the mean fiow. Results have shown favorable comparison with experimental data obtained at the Naval Weapons Center, China Lake.

No.: AIAA-1984-365
ID: CaltechAUTHORS:20101209-115108188

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Abstract: The frequency response of a normal shock in a diverging channel is calculated for application to problems of pressure oscillations in ramjet engines. Two limits of a linearized analysis arc discussed: one represents isentropic flow on both sides of a shock wave; the other may be a crude appr'l'I;imation to the influence of flow separation induced hy the wave. Numerical results arc given, and the influences of the shock wave on oscillations in the engine are discus,ed.

Publication: AIAA Journal Vol.: 21 No.: 10 ISSN: 0001-1452

ID: CaltechAUTHORS:20101208-111845159

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Abstract: Measurements of pressure losses and heat transfer rates were made for an unconventional crossflow heat exchanger with tubes of lenticular cross section so spaced to reduce variation in the velocity of the fluid outside the tubes, thus reducing separation and drag. The results of these experiments are reported for various tube spacing and demonstrate that the performance of the lenticular tube heat exchanger is superior to that of conventional circular tubes by 20 percent at Reynolds numbers of 20,000 to 50,000.

Publication: Journal of Heat Transfer Vol.: 105 No.: 3 ISSN: 0022-1481

ID: CaltechAUTHORS:20101209-111159133

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Abstract: In this paper, we discuss two problems. First, using a second order expansion in the pressure amplitude, some analytical results on the existence, stability and amplitude of limit cycles for pressure oscillations in combusticm chambers are presented. A stable limit cycle seems to be unique. The conditions for existence and stability are found to be dependent only on the linear parameters. The nonlinear parameter affects only the wave amplitude. The imaginary parts of the linear responses, to pressure oscillations, of the different processes in the chamber play an important role in the stability of the limit cycle. They also affect the direction of flow of energy among modes. In the absence of the imaginary parts, in order for an infinitesimal perturbation in the flow to reach a finite amplitude, the lowest mode must be unstable while the highest must be stable; thus energy flows from the lowest mode to the highest one. The same case exists when the imaginary parts are non-zero, but in addition, the contrary situation is possible. There are conditions under which an infinitesimal perturbation may reach a finite amplitude if the lowest mode is stable while the highest is unstable. Thus energy can flow "backward" from the highest mode to the lowest one. It is also shown that the imaginary parts increase the final wave amplitude. Second, the triggering of pressure oscillations in solid propellant rockets is discussed. In order to explain the triggering of the oscillations to a nontrivial stable: limit cycle, the treatment of two modes and the inclusion in the combustion response of either a second order nonlinear velocity coupling or a third order nonlinear pressure coupling seem to be sufficient.

No.: AIAA-1983-576
ID: CaltechAUTHORS:20101209-094958257

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Abstract: The general problem of flame stabilization on bluff objects centers about the determination of the maximum stream velocity at which stable combustion may be achieved for various flame holder geometries, gas mixtures and conditions of the approaching combustible stream. Since the process involves both gas dynamic problems and chemical kinetic problems of great complexity, the most reasonable approach is one of similarity, that is, to determine under what conditions the behavior of one flame holder is similar to the behavior of another one. Because a very large number of physical and chemical variables is involved in a combustion problem, similarity conditions can be formulated most easily after experimental investigations have indicated which parameters or groups exert little influence on the mechanism and hence may be neglected. The experiments described in this paper were conducted with the object of clarifying the role of the more important parameters in the flame holding mechanism. The results indicate that a relatively simple formulation of the similarity conditions may be obtained in which the fluid mechanical parameters and chemical parameters are effectively separated.

ID: CaltechAUTHORS:20110203-125953778

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Abstract: Pressure oscillations in ramjet engines are studied. within quasi one-dimensional linear acoustics. The flow field in the dump combustor is approximated by division into three parts: a flow of reactants, a region containing combustion products, and a recirculation zone, separated by a flame sheet and a dividing streamline. The three zones are matched by considering kinematic and conservation relations. Acoustic fields in the inlet section and in the combustion chamber are coupled to provide an analytical equation for the complex wave number characterizing the linear stability. The calculated results are compared with the experimental data reported by the Naval Weapons Center. Reasonable agreements are obtained.

No.: AIAA 83-0574
ID: CaltechAUTHORS:20101207-145019986

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Abstract: An experimental investigation has been carried out for acoustic oscillations sustained by flow through a duct containing two baffles. Pure acoustic tones corresponding to longitudinal resonant modes of the duct are produced when certain flow and geometrical conditions are satisfied. The conditions are such as to ensure close coincidence between the frequency of vortex shedding from the forward baffle, and a natural frequency of the duct. Flow visualization has shown that under these conditions a stable vortex structure exists between the baffles, containing at all times an integral number of vortices.

Publication: Journal of Sound and Vibration Vol.: 84 No.: 2 ISSN: 0022-460X

ID: CaltechAUTHORS:20101209-093924977

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Abstract: Measurements of the rate of ambient air entrainment by axisymmetric diffusion flames suggest that entrainment occurs at a wrinkled laminar flame front in the lower regions of visible flame (Ref. 1). Entrainment of such flames requires a solution of the axisymmetric steady laminar diffusion flame which does not yield a self-similar solution. If one then considers the simple case of steady plane diffusion flame in semi-infinite fuel and oxidizer media separated by a flame sheet, an exact similarity solution can be obtained from equations of motion, energy and species conservation equations. This solution can also incorporate the differences in fuel and oxidizer densities resulting from either molecular weight differences or the temperature differences of oxidizer and fuel media. This problem was treated by G. C. Fleming and F. E. Marble to investigate the stability of such a flame front to periodic disturbances (Ref. 2). Inspired by their study, we chose to develop an integral solution to the same problem by appropriate selection of velocity, temperature and species profiles.

ID: CaltechAUTHORS:20110131-072412068

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Abstract: This paper describes an experimental investigation of interactions between acoustic waves and a non-uniform steady flow field. Data have been obtained for a resonance tube having a vent at the center in the lateral boundary, an average flow being introduced at the ends. Experiments have been done for both circular and slot vents, over ranges of both frequency and Mach number. According to the one-dimensional linear stability analysis, the interactions between the longitudinal acoustic field and the mean flow in the vicinity of the vent cause a net transfer of acoustic energy from the average flow to the acoustic field. This result has been verified by the experiments reported here. The gain of energy measured is less than that deduced from a one-dimensional analysis.

Publication: Journal of Sound and Vibration Vol.: 75 No.: 4 ISSN: 0022-460X

ID: CaltechAUTHORS:20101209-102019799

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Abstract: A new technique for measurement of mass flow rates in buoyant fire plumes is described. The characteristics of 10 - 200 k W methane diffusion flames stabilized on porous-bed-burners of 0.10 - 0.50 m dia. are described. A transition in the dependence of flame height on heat input and burner size was observed when the flame height was about four times the burner diameter. The mass flow rates in the buoyant plumes produced by the fires were measured for a range of elevations starting just below the time-averaged top of the flame and extending to six times this flame height. The mass flow rates in this region of the plume were correlated by the use of a simple plume model. Atmospheric and forced disturbances in the air being entrained increased the entrainment rate of the plume.

Publication: Fire Safety Journal Vol.: 3 No.: 3 ISSN: 0379-7112

ID: CaltechAUTHORS:20101208-105713788

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Abstract: Two problems crucial to the stability of longitudinal acoustic waves in solid rocket motors are examined experimentally. The first is the dissipation of energy associated with an average flow inward at the lateral boundary. Measurements reported here, though subject to considerable experimental error, show that the actual losses are much larger than predicted by the approximate one dimensional analysis. The second problem is the attenuation of waves accompanying reflection by the nonuniform flow in a choked exhaust nozzle. Empahsis in this work has been on technique, to provide data relatively easily and inexpensively. It appears that good results can be obtained in a routine manner using small supersonic wind tunnel operated as an open cycle. At least for Mach numbers up to 0.04 at the nozzle entrance, difficulties with signal/noise are satisfactorily overcome with a tracking filter.

No.: NTRS: 2005-10-10
ID: CaltechAUTHORS:20101208-114247352

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Abstract: A model which completely describes the Cu/CuCI double pulse laser is presented. The dissociation discharge pulse and afterglow are simulated and the results are used as initial conditions for an analysis of the pumping discharge pulse and laser pulse. Experimental behavior including the minimum, optimum, and maximum delays between pulses, and the dependence of laser pulse energy on dissociation energy are satisfactorily reproduced. An optimum tube temperature is calculated, and the dependence of laser pulse energy on tube temperature (i.e., CuCI vapor pressure) is explained for the first time.

Publication: Journal of Applied Physics Vol.: 51 No.: 6 ISSN: 0021-8979

ID: CaltechAUTHORS:20101208-101900961

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Abstract: A description is given of a model which predicts the motion of combustion products and fresh air caused by a fire located in one room of a two-room structure. The gas in each room is assumed to be divided into two homogeneous layers, a layer next to the ceiling which contains hot combustion products and one next to the floor which contains fresh air. The model predicts the motion of the interface separating these layers and the density of the hot layers as a function of time and an arbitrarily specified fire heat release rate.

Publication: Fire and Materials Vol.: 4 No.: 1 ISSN: 1099-1018

ID: CaltechAUTHORS:20101206-103041848

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Abstract: The coherent flame model is applied to the methane-air turbulent diffusion flame with the objective of describing the production of nitric oxide. The example of a circular jet of methane discharging into a stationary air atmosphere is used to illustrate application of the model. In the model, the chemical reactions take place in laminar flame elements which are lengthened by the turbulent fluid motion and shortened when adjacent flame segments consume intervening reactant. The rates with which methane and air are consumed and nitric oxide generated in the strained laminar flame are computed numerically in an independent calculation. The model predicts nitric oxide levels of approximately 80 parts per million at the end of the flame generated by a 30.5 cm (1 foot) diameter jet of methane issuing at 3.05 x 10^3 cm/sec (100 ft/sec). The model also predicts that this level varies directly with the fuel jet diameter and inversely with the jet velocity. A possibly important nitric oxide production mechanism, neglected in the present analysis, can be treated in a proposed extension to the model.

No.: EPA-600/7-80-018
ID: CaltechAUTHORS:20101209-090337380

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Abstract: Pressure oscillations in ramjet engines are approximated as one-dimensional motions and treated within linear acoustics. The exhaust nozzle is represented by the admittance function for a short choked nozzle. New results have been obtained for the quasi-steady response of a normal shock wave in the diffuser. Acoustic fields in the inlet region and in the combustion chamber are matched to provide an analytical expression of the criterion for linear stability. Combustion processes are accommodated but not treated in detail. As examples, data are discussed for two liquid-fueled engines, one having axial dump and one having side dumps.

No.: AIAA 80-1192
ID: CaltechAUTHORS:20101209-074709263

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Abstract: Large solid propellant rocket motors are conveniently assembled with segmented grains. The interfaces of the grains are coated with inert, slow-burning material. As the propellant burns radially during a firing, the inert material is exposed in the form of annular rings oriented normal to the axis of the chamber. The flow through a ring will produce periodic shedding of vortices over a broad range of conditions.

Publication: Journal of Sound and Vibration Vol.: 64 No.: 3 ISSN: 0022-460X

ID: CaltechAUTHORS:20101213-084217131

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Abstract: The transient response of large burners depends primarily upon fluid mechanical adjustment rather than in time delays associated with transient chemical response. Examples of this behavior are the non-steady behavior of burners in utility boilers, and the low-frequency response of after burners in aircraft gas turbines. The non-steady behavior of a flame stabilized by a single-flame holder at the center of a long two-dimensional duct is investigated analytically when it is excited by periodic acoustic disturbances that approach the flame zone from either the upstream or downstream direction. The flame zone itself is considered acoustically compact. The problem is treated by an integral technique in which relevant equations are integrated across high-density and low-density portions of the gas separately; the two fields are then coupled across the thin flame front, the determination of its shape being part of the solution. Transmission and reflection coefficients were calculated for a range of flame velocities, burner inlet flow velocities, combustion temperature ratio and imposed acoustic frequency. The results showed that a considerably stronger pressure wave passed upstream of the flame than downstream, in the sense that could be expected from the different acoustic impedences of the hot and cold gas. Of most significance, however, was the very large (active) response of the burner at certain characteristic frequencies which corresponded to well-defined values of ωL/u_o where L is the length of the flame zone and u_o is the flow velocity upstream of the burner. It is indicated that these energetic response modes result from vorticity shed from the distorted flame which induces a propagating wave along the flame front.

Publication: Symposium (International) on Combustion Vol.: 17 No.: 1 ISSN: 0082-0784

ID: CaltechAUTHORS:20110121-130330771

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Abstract: [No abstract]

Publication: Annual Review of Fluid Mechanics Vol.: 11ISSN: 0066-4189

ID: CaltechAUTHORS:20101207-103410790

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Abstract: The Wright brothers' "Flyer" of 1903 was not just a lucky effort by two bicycle mechanics from Dayton but the outcome of an intensive program of research, engineering and testing

Publication: Scientific American Vol.: 241 No.: 1 ISSN: 0036-8733

ID: CaltechAUTHORS:20101213-074304929

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Abstract: Electron-density measurements have been made in a CuCl/Ne discharge using a CO2 laser interferometer. A local maximum followed by a local minimum in electron density have been found to move a higher tube temperature with higher buffer pressure. Extrema in Cu/CuCl double-pulsed laser energy may be correlated with the extrema in electron density. An analysis based on rate equations yields qualitative agreement with measured laser-pulse energies. The results support the idea that ionization of copper is primarily responsible for the decrease of laser output as the tube temperature is increased.

Publication: Applied Physics Letters Vol.: 33 No.: 8 ISSN: 0003-6951

ID: CaltechAUTHORS:KUSapl78

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Abstract: A consistent set of continuum-like equations which describe, under certain limitations, the flow of bubbly gas-liquid mixtures is applied in the solution of a few problems that bear on technological issues of nuclear reactor safety. The solutions of these problems illustrate the significance of the ratio between the viscous relaxation time of the bubbles and the characteristic time of the flow, in scaling experimental results. The choked flow of a bubbly mixture through a contraction in a one-dimensional duct is treated. It is found that in many cases the ratio of the contraction residence time to the viscous relaxation time is small, indicating the motion of the bubbles will be dictated largely by the dynamic forces on them. The one-dimensional equations are solved approximately for small values of this ratio. A rudimentary experiment on choked bubbly flow through a contraction was conducted using a contraction with gradual changes in area, making the experimental situation amenable to a one-dimensional analysis. Distributions of pressure and mass flow rates of liquid and gas were measured. The results compare favorably with theoretical calculations. The rise through a liquid of a uniform cloud of bubbles is also analyzed. Self-preserving wave solutions of the non-linear equations are found to exist and have the form of transitions between a region of high void fraction below and a region of lower void fraction above. These waves are unstable to small disturbances in response to which they will steepen, developing into clumps of bubbles above which are regions of low void fraction. The fact that the bubbles in these clumps may coalesce presents a mechanism for a change in flow regime from bubbly to some other, perhaps slug or annular flow. The effect of bubble-bubble interactions i.n impeding the formation of these clumps i.s speculated upon. Finally, the flow of a bubbly mixture over a wavy wall is analyzed. The solution illustrates some of the important deviations from one-dimensional flow and shows the manner in which phase separation tends to make use of the strict one-dimensional flow assumption more limited than in single phase flow. The solution is incomplete in the sense that the effect of interactions between bubbles and solid boundaries is lacking.

ID: CaltechAUTHORS:20151111-133341240

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Abstract: A simple analytical model has been developed to determine the time required for a room to fill with products of combustion from a small fire. The room is assumed to be closed except for small openings at either the floor or ceiling level and the assumption is made that the leak is large enough to allow the transient pressure term in the energy equation to be neglected. Products of combustion are assumed to occupy a layer next to the ceiling and the model predicts the growth of the thickness and the mean density of this layer as a function of time. The analysis shows that times required to fill a typical room are small. For example, a typical bedroom fills with products from a 20 kW fire in several minutes. The time required to fill a room and the mean density of ceiling layer are determined in terms of fire size, room geometry, leak position, fire elevation and geometry.

Publication: Fire and Materials Vol.: 2 No.: 2 ISSN: 0308-0501

ID: CaltechAUTHORS:20101210-114840222

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Abstract: A computer model which treats the fluid dynamic aspects of a transient fire in a two-room structure is described. In the model, the gas in each room is divided into two regions of uniform density: A ceiling layer which contains hot products of combustion, and a layer next to the floor which contains uncontaminated air. The fire plume entrains this fresh air, mixes it with hot combustion products and transports it to the ceiling layer. Flow through openings is described by a calculation similar to that used for orifice flows. Fire growth, heat transfer to the walls, and other important features of a fire are described by ad hoc selection of parameters. The thickness and temperature of the ceiling layers and the rate of flow of hot and cold air through opening are calculated as a function of the time by numerical integration of ordinary differential equations derived from the conservation laws of mass and energy. A number of examples are presented to illustrate the use of the program and some general scaling rules for the initial stages of a room fire.

ID: CaltechAUTHORS:20110121-143711174

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Abstract: N/A

ID: CaltechAUTHORS:20101210-141234875

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Abstract: A one-dimensional thermal theory is applied to a low-pressure, laminar, premixed, CS_2/O_2 flame. The spatial distribution of the species concentrations and rate of production of carbon monoxide are calculated. The flame speed is calculated as a function of the initial O_2/CS_2 ratio at a pressure of 1 kPa.

Publication: Combustion and Flame Vol.: 33 No.: 2 ISSN: 0010-2180

ID: CaltechAUTHORS:20101210-120127838

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Abstract: The theory relating to the interaction of entropy fluctuations ('hot spots'), as well as vorticity and pressure, with blade rows is described. A basic feature of the model is that the blade rows have blades of sufficiently short chord that this is negligible in comparison with the wavelength of the disturbances. For the interaction of entropy with a blade row to be important, it is essential that the steady pressure change across the blade row should be large, although all unsteady perturbations are assumed small. A number of idealized examples have been calculated, beginning with isolated blade rows, progressing to single and then to several turbine stages. Finally, the model has been used to predict the low-frequency rearward-radiated acoustic power from a commercial turbojet engine. Following several assumptions, together with considerable empirical data, the correct trend and level are predicted, suggesting the mechanism to be important at low jet velocities.

Publication: Proceedings of the Royal Society A: Mathematical, physical, and engineering sciences Vol.: 357 No.: 1690 ISSN: 1364-5021

ID: CaltechAUTHORS:20101213-114306465

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Abstract: The non-steady flow generated by convection of gas containing non-uniform temperature regions or "entropy spots" through a nozzle is examined analytically as a source of acoustic disturbance. The first portion of the investigation treats the "compact nozzle", the case where all wave lengths are much longer than the nozzle. Strengths of transmitted and reflected one-dimensional waves are given for supersonic and subsonic nozzles and for one configuration of supersonic nozzle with normal shock at the outlet. In addition to a wave reflected from the nozzle inlet, the supersonic nozzle discharges two waves, one facing upstream and the other facing downstream. For reasonable values of the nozzle inlet Mach number, the pressure amplitude of each wave increases directly as the discharge Mach number. The acoustic perturbations from a supercritical nozzle of finite length, in which the undisturbed gas velocity increases linearly through the nozzle, are analyzed for several inlet and discharge Mach number values and over a wide frequency range. The results, which agree with the compact analysis for low frequency, deviate considerably as the frequency rises, achieving pressure fluctuation levels of several times the compact values. It is shown that this result originates in a phase shift between the two waves emitted downstream and that the pressure fluctuations for moderate frequencies may be approximated from the compact analysis with an appropriate phase shift. In all cases, the pressure fluctuations caused by a 2% fluctuation in absolute inlet temperature are large enough to require consideration in acoustic analysis of nozzles or turbine blade channels.

Publication: Journal of Sound and Vibration Vol.: 55 No.: 2 ISSN: 0022-460X

ID: CaltechAUTHORS:20101214-073952475

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Abstract: There is abundant evidence to show that the exhaust noise from gas turbines contains components which exceed the jet mixing noise at low jet velocities. This paper describes results of a theory developed to calculate the acoustic power produced by tempetature fluctuations from the combustor entering the turbine. With the turbine Mach numbers and flow directions at blade mid-height, and a typical value for the fluctuation in temperature, as parameters it has been possible to predict the acoustic power due to this mechanism for three different engines. In all three cases the agreement with measurements of acoustic power at low jet velocities is very good. Similarly, based on a measured spectrum of the temperature fluctuation, the prediction of the acoustic power spectrum agrees quite well with that measured.

Publication: Journal of Sound and Vibration Vol.: 54 No.: 2 ISSN: 0022-460X

ID: CaltechAUTHORS:20101214-073031680

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Abstract: The rate of vibrational population of carbon monoxide in a steady CS_2/O_2 flame has been determined from CO overtone emission. A steady-state analysis indicates that, for a flame, the fifteenth vibrational level has the largest rate of population.

Publication: Journal of Chemical Physics Vol.: 67 No.: 5 ISSN: 0021-9606

ID: CaltechAUTHORS:20101213-112042239

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Abstract: The one-dimensional response of a subsonic nozzle flow to small pressure and entropy disturbances is calculated. The response is expressed in terms of transmitted acoustic waves (which propagate from the nozzle in the same direction as the disturbance wave) and reflected acoustic waves (which propagate from the nozzle in the direction opposite to that of the disturbance wave) for three independent disturbances: a downstreampropagating acoustic wave impinging upon the nozzle inlet, an upstream-propagating wave impinging upon the nozzle exit, and an entropy wave convecting through the nozzle. The solution for high frequency disturbances is discussed and used with the compact (long wavelength disturbance) solution to normalize several numerical calculations. The normalization shows that the transmitted waves created by the two acoustic disturbances may be represented by the same function offrequency for a given inlet and exit nozzle Mach number. The same is seen to be true for the reflected waves created by the two acoustic disturbances. The normalization allows results for a wide range of nozzle Mach number distributions and disturbance frequencies to be presented concisely.

Publication: Journal of Sound and Vibration Vol.: 52 No.: 2 ISSN: 0022-460X

ID: CaltechAUTHORS:20101213-104516314

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Abstract: A description of the turbulent diffusion flame is proposed in which the flame structure is composed of a distribution of laminar diffusion flame elements, whose thickness is small in comparison with the large eddies. These elements retain their identity during the flame development; they are strained in their own plane by the gas motion, a process that not only extends their surface area, but also establishes the rate at which a flame element consumes the reactants. Where this flame stretching process has produced a high flame surface density, the flame area per unit volume, adjacent flame elements may consume the intervening reactant, thereby annihilating both flame segments. This is the flame shortening mechanism which, in balance with the flame stretching process, establishes the local level of the flame density. The consumption rate of reactant is then given simply by the product of the local flame density and the reactang consumption rate per unit area of flame surface. The proposed description permits a rather complete separation of the turbulent flow structure, on one hand, and the flame structure, on the other, and in this manner permits the treatment of reactions with complex chemistry with a minimum of added labor. The structure of the strained laminar diffusion flame may be determined by analysis, numerical computation, and by experiment without significant change to the model.

No.: TRW-29314-6001-RU-00
ID: CaltechAUTHORS:20101210-105056861

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Abstract: The flame speed for a low speed premixed CS_2/O_2 flame has been experimentally determined as a function of O_2/CS_2 ratio. The data, which are given in Fig. 1, were taken for lean flames at 1 kPa, under conditions which are similar to those found in flame lasers.

Publication: Combustion and Flame Vol.: 30 No.: 1 ISSN: 0010-2180

ID: CaltechAUTHORS:20101210-102405671

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Abstract: N/A

Publication: Combustion Science and Technology Vol.: 15 No.: 3 ISSN: 0010-2202

ID: CaltechAUTHORS:20101214-075406344

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Abstract: The response functions of composite propellants are theoretically derived, including explicitly the pressure-dependent degradation term in the condensed phase, hypothesizing that the overall rate-limiting reactions are in the relatively low temperature condensed phase. The method of "inner" and "outer" expansions with the reduced activation energy as the singular perturbation parameter has been employed. The results cover subsurface reactions with and without surface reactions, adiabatic and uniform-combustion models for the quasisteady gas phase processes. The response functions display several experimentally observed features like dependence on mean pressure and the instability behavior of some "zero-n" propellants.

Publication: Combustion Science and Technology Vol.: 15 No.: 5 ISSN: 0010-2202

ID: CaltechAUTHORS:20101213-105529799

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Abstract: The electron temperature as a function of laser tube temperature of a copper vapor laser utilizing copper chloride as a lasant has been obtained by measuring the microwave incoherent radiation from the plasma in the laser tube. An unexpected increase of electron temperature at higher laser tube temperature may be due mainly to Penning ionization of the Cu atom by the metastable state of He or Ne buffer gases. The results obtained in this work provide part of the basis for understanding the behavior of the laser output as a function of tube temperature.

Publication: Journal of Applied Physics Vol.: 47 No.: 10 ISSN: 0021-8979

ID: CaltechAUTHORS:SOVjap76

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Abstract: The approximate analysis developed in Part I of Ihis work is apllied to severa1 specific problems. One purpose is to illustrate the use of the formalism, and second is to demostrate the validity of the method by comparing results with numerical solutions, obtained elsewhere, for the "exact" equations. A simple problem is treated first, the decay of a standing wave in a box containing a mixture of gas and suspended particles; one example of the steepening of an initially sinusoidal wave in pure gas is included. Viscous losses on an inert surface are treated essentially according to classical linear theory; recent experimental results are used as the basis for incorporating approximately the influence of nonlinear heat transfer in unsteady flow. All of the preceding results are combined in calculations of two examples of unstable motions in a solid propellant rocket motor and in a T-burner.

Publication: Acta Astronautica Vol.: 3 No.: 9-10 ISSN: 0094-5765

ID: CaltechAUTHORS:20101217-103254887

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Abstract: The effect of duct Mach number upon the acoustic reflection coefficient at the inlet of a duct with mean flow is investigated. An analysis, which models the duct inlet as a very short, one-dimensional nozzle over which the mean flow is accelerated from rest, gives good agreement with some recent experimental results. Discrepancies between the analysis and the experimental results are discussed in terms of radiation losses at the inlet and real fluid-flow effects within the duct.

Publication: Journal of the Acoustical Society of America Vol.: 59 No.: 6 ISSN: 0001-4966

ID: CaltechAUTHORS:20101217-092218676

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Abstract: Some aspects of the noise generated internally by a turbojet engine are considered analytically and experimentally. The emphasis is placed on the interaction of pressure fluctuations and entropy fluctuations, produced by the combustion process in the engine, with gradients in the mean flow through the turbine blades or the exhaust nozzle. The results are directly applicable to the problem of excess noise in aircraft powerplants and suggest that the phenomenon described is the dominant mechanism. The one-dimensional interaction of pressure fluctuations and entropy fluctuations with a subsonic nozzle is solved analytically. The acoustic waves produced by each of three independent disturbances are investigated. These disturbances, which interact with the nozzle to augment the acoustic radiation, are (i) pressure waves incident from upstream, (ii) pressure waves incident from downstream, and (iii) entropy waves convected with the stream. It is found that results for a large number of physically interesting nozzles may be presented in a concise manner. Some of the second-order effects which result from the area variations in a nozzle are investigated analytically. The interaction of an entropy wave with a small area variation is investigated and the two-dimensional duct modes, which propagate away from the nozzle, are calculated. An experiment is described in which one-dimensional acoustic waves and entropy waves are made to interact with a subsonic nozzle. The response of the nozzle to these disturbances is measured and compared with the response as calculated by the analytical model. The interaction of two-dimensional entropy waves with a subsonic nozzle and with a supersonic nozzle is investigated experimentally. The results are explained in terms of an analysis of the acoustic waves and entropy waves produced by a region of arbitrary heat addition in a duct with flow.

ID: CaltechAUTHORS:20151111-164208663

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Abstract: The noise field produced by the passage of pressure and entropy fluctuations through a supersonic nozzle has been investigated in an experimental program. Magnitude and phase information for the disturbances produced within the nozzle are presented and are compared with numerical calculations.

Publication: Journal of Engineering for Power Vol.: 98 No.: 1 ISSN: 0022-0825

ID: CaltechAUTHORS:20101217-080309933

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Abstract: This paper is concerned with the general problem of the nonlinear growth and limiting amplitude of acoustic waves in a combustion chamber. The analysis is intended to provide a formal framework within which practical problems can be treated with a minimum of effort and expense. There are broadly three parts. First, the general conservation equations are expanded in two small parameters, one characterizing the mean flow field and one measuring the amplitude of oscillations, and then combined to yield a nonlinear inhomogeneous wave equation. Second, the unsteady pressure and velocity fields are expressed as syntheses of the normal modes of the chamber, but with unknown time-varying amplitudes. This procedure yields a representation of a general unsteady field as a system of coupled nonlinear oscillators. Finally, the system of nonlinear equations is treated by the method of averaging to produce a set of coupled nonlinear first order differential equations for the amplitudes and phases of the modes. These must be solved numerically, but results can be obtained quite inexpensively. Subject to the approximations used, the analysis is applicable to any combustion chamber. The most interesting applications are probably to solid rockets, liquid rockets, or thrust augmentors on jet engines. The discussion of this report is oriented towards solid propellant rockets.

Publication: Acta Astronautica Vol.: 3 No.: 9 ISSN: 0094-5765

ID: CaltechAUTHORS:20101217-100432116

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Abstract: The purpose of this paper is to describe briefly and in a general way several schemes used to calculate the motion of smoke through a structure or part of a structure involved in a fire. Calculations of this type are required if we are to understand the spread fire through the structure and if we are to learn how to write building codes and other regulations which can provide the best possible protection for building occupants. For example, one of aims of designers of high rise buildings is the incorporation in their designs of regions where people can be protected from contact with cornbustion products without the requirement that they be able to escape from the building. Another aim is to restrict combustion products to the floor of the fire origin at least and, if possible, to a part of that floor. Finally, consider the simpler problem posed by the requirement that a ceiling or wall of a burning home be opened to change the flow of smoke such that firemen can approach the fire. To obtain a solution of each of these problems, we must be able to calculate the effects of smoke control measures (active or passive) on the gas motion.

ID: CaltechAUTHORS:20110203-141659911

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Abstract: This paper summarizes recent work on the approximation to nonlinear pressure oscillations using two modes. A large part of the effort has been concerned with the consequences of gasdynamic nonlinearities of second order in the fluctuations. It appears that the two-mode approximation is valid over a broad range of the linear parameters that govern the global qualitative behavior, particularly if the lower mode is the unstable mode. Exact solutions have been found for the existence and stability of limit cycles, allowing meaningful comparison with numerical solutions obtained with larger numbers of modes considered. The nonlinear analysis to second order does not contain "triggering" - nonlinear instability of a linearly stable system - because the nonlinear processes order terms involving the mean flow speed, or DC shifts in the amplitudes of oscillation do produce triggering.

ID: CaltechAUTHORS:20110207-102353008

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Abstract: The structure of open turbulent jet flames is experimentally studied in the context of their noise emission characteristics. The differences between premixed and (co-flow) non-premixed flames are explored. Recent experiments repeated in an anechoic chamber complement earlier results obtained in a hard-walled bay. The reactants (methane and enriched air) are burned in the premixed, or non-premixed, mode after a length of pipe flow (ℓ/D> 150). The thick-walled tubes anchor the flames to the tip at all of the velocities employed (maximum velocity, well over 300 ft/sec), thus eliminating uncertainties associated with external flameholders. The time-averaged appearance of the flames is obtained with still photographs (1160 sec). The detailed structures are revealed through high-speed (≈ 2500 frames/sec) motion pictures. The acoustic outputs of the flames are mapped with a condenser microphone. The recorded data are played back to obtain the amplitude, waveshapes, directionalities, and frequency spectra of the noise. Profound differences are found between the premixed and non-premixed flames in their structures and noise characteristics.

No.: AIAA 75-523
ID: CaltechAUTHORS:20101216-111045073

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Abstract: The problem oflinearized three-dimensional motions in a non-uniform flowfield is re-examined. Several modifications of the general analysis are effected: The influence of particulate matter is acounted for, to zeroth order, and certain boundary processes treated in earher one-dimensional computations are incorporated in an analysis applicable to any geometry. All processes occurring in combustion chambers are accommodated. As a specific example, the results are applied to a problem of linear stability in solid propellant rocket motors.

Publication: Combustion Science and Technology Vol.: 10 No.: 3 ISSN: 0010-2202

ID: CaltechAUTHORS:20101216-154702705

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Abstract: Several steady state and time-dependent solutions to the compressible conservation laws describing direct one-step near-equilibrium irreversible exothermic burning of initially unmixed gaseous reactants, with Lewis-Semenov number unity, are presented. The quantitative investigation first establishes the Burke-Schumann thin-flame solution using the Shvab-Zeldovich formulation. Real flames do not have the indefinitely thin reaction zone associated with the Burke-Schumann solution. Singular perturbation analysis is used to provide a modification of the thin-flame solution which includes a more realistic reaction zone of small but finite thickness. The particular geometry emphasized is the un bounded counterflow such that there exists a spatially constant rate of strain along the flame. While the solutions for diffusion flames under a finite tangential strain rate may be of interest in and of themselves for laminar flow, the problems are motivated by the authors' belief that they are pertinent to the study of diffusion-flame burning in transitional and turbulent shear flows.

Publication: SIAM Journal on Applied Mathematics Vol.: 28 No.: 2 ISSN: 0036-1399

ID: CaltechAUTHORS:20101216-133642630

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Abstract: A cloud of small water droplets in saturated air attenuates acoustic disturbances by viscous drag, heat transfer, and vapor exchange with the ambient gas. The viscous and heat transfer phenomena attenuate at frequencies above 104 Hz for I-J.l droplets. The processes associated with phase exchange attenuate at a much lower frequency that may he controlled by choice of the liquid mass fraction. The strength of this attenuation is proportional to the mass of water vapor in the air, a factor controlled by air temperature. For plane waves, the attenuation magnitude e~ceeds 5 db!m ~t a temperature of 25°C with a cloud of 0.7 J.l radius droplets constituting 1 % of the gas mass. ThiS attenuation mcreases to more than 7 dbjm at frequencies above 1000 Hz where viscous and heat transfer mechanisms contribute significantly. The attenuation of higher order duct modes is strongly increased over the above values, similarly to the attenuation by duct lining. When the droplet cloud occupies only a fraction of the duct height close to the walls, the droplet clond may be up to twice as elfective as the uniform cloud, and a significant saving is possible in the water required to saturate the air and furnish the water droplets.

Publication: AIAA Journal Vol.: 13 No.: 5 ISSN: 0001-1452

ID: CaltechAUTHORS:20101216-132206855

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Abstract: This report summarizes a theoretical investigation of the current problems of nitramine (composite) propellant combustion. This study has, as its distinctive feature, a detailed examination of the condensed-phase processes in the combustion of nitramine propellants. As a consequence of a recently developed model for the combustion of ammonium perchlorate (AP)/ composite propellants, it is hypothesized that the condensed-phase degradation of the nitramine oxidizer particles to a vaporizable state is the overall rate-limiting step. It is also assumed that the gas-phase details are secondary in importance and need be studied only to the extent of supplying the correct boundary conditions on the condensed-phase/vapor-phase heat transfer. Because of our imprecise understanding of the gas-phase processes in the presence of combustion, several plausible models are considered for the gas phase. It is found that all of the gas -phas e models considered lead to predictions sufficiently clos e to experimental trends for us to conclude that the precise details of gas -phase processes are not of critical importance in determining propellant combustion behavior. More to the point, we are led to believe that a thorough examination of the condensed-phase details may be sufficient in itself not only to interpret most of the available data on experimental regression rate vs. pressure of nitramine propellants but also to aid in the formulation of propellants to suit our needs.

No.: AIAA 75-239
ID: CaltechAUTHORS:20101216-143236750

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Abstract: The larger number of problems that qualify as unsteady aerodynamics relate to non-uniform motion of surfaces -- such as pitching of airfoils -- or the correspondingly non-uniform motion of a fluid about a surface -- such as a gust passing over an airfoil. Experiment and analysis concerning these problems aims to determine the non-steady forces or surface stresses on the object. These may be thought of as "kinematically" non-steady problems. Another class of problems presents itself when the undisturbed gas stream temperature (or density) is non-steady although the velocity and pressure are steady; such non-uniformities are associated with entropy variations from point to point of the stream. In a locally adiabatic flow these entropy variations are transported with the stream, and when a fixed boundary -- such as an airfoil -- is encountered, the flow field undergoes a non-steady change because the density variations alter the pressure field -- or the stresses at the boundaries. This happens in spite of the fact that the undisturbed free -stream velocity field and the surface boundaries of the flow are independent of time. A gas turbine blade, for example, will experience a time-dependent load simply because of temperature fluctuations in the combustion products flowing over it, although the angle of attack is independent of time. We shall call these "thermodynamically" unsteady flows in contrast with the more familiar kinematically unsteady flows.

ID: CaltechAUTHORS:20110208-105530510

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Abstract: At the present time, there are three general analytical techniques available to study problems of unsteady motions in rocket motors: linear stability analysis; approximate nonlinear analysis, founded on examining the behavior of coupled normal modes; and numerical calculations based on the conservation equations for one-dimensional flows. The last two yield the linear results as a limit. It is the main purpose of this paper to check the accuracy of the approximate analysis against the numerical analysis for some special cases. The results provide some justification for using the approximate analysis to study three dimensional problems.

No.: AIAA 74-201
ID: CaltechAUTHORS:20101216-103529506

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Abstract: There is evidence to show that the exhaust noise from gas turbines contains components which exceed the jet mixing noise at low jet velocities. This paper describes a theory developed to calculate the acoustic power produced by temperature fluctuations from the combustor entering the turbine. Using the turbine Mach numbers and flow directions at blade mid-height, and taking a typical value for the fluctuation in temperature, it has been possible to predict the acoustic power due to this mechanism for three different engines. In all three cases the agreement with measurements of acoustic power at low jet velocities is very good. Using a measured spectrum of the temperature fluctuation the prediction of the acoustic power spectrum agrees quite well with that measured.

ID: CaltechAUTHORS:20110207-081618338

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Abstract: Two independent methods were used to measure the rate of heat transfer from a hot gas to the walls of a cylindrical combustion chamber in which large-amplitude combustion-driven oscillations accompanied a mean flow. The results obtained from the two methods were in good agreement and indicated a definite increase in the heat transfer in the presence of oscillations. The increase was found to vary approximately as the square root of the oscillation amplitude and as the fourth root of the frequency. A correlation in terms of dimensionless variables was obtained using the thickness of the acoustic boundary layer as the appropriate length scale.

Publication: Combustion Science and Technology Vol.: 9 No.: 1/2 ISSN: 0010-2202

ID: CaltechAUTHORS:20101216-110120321

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Abstract: An actuator disc analysis is used to calculate the pressure fluctuations produced by the convection of temperature fluctuations (entropy waves) into one or more rows of blades. The perturbations in pressure and temperature must be small, but the mean flow deflection and acceleration are generally large. The calculations indicate that the small temperature fluctuations produced by combustion chambers are sufficient to produce large amounts of acoustic power. Although designed primarily to calculate the effect of entropy waves, the method is more general and is able to predict the pressure and vorticity waves generated by upstream or downstream going pressure waves or by vorticity waves impinging on blade rows.

No.: 57
ID: CaltechAUTHORS:20110126-092110939

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Abstract: This work is aimed at experimentally exploring the effects of minor compositional variables upon the combustion behavior of composite solid propellants. More specifically, it is intended to determine the influence, if any, of ingredients that improve the mechanical properties upon the oscillatory combustion characteristics. Tests are carried out in the familiar Crawford bomb, a low-pressure L^* burner, and a high-pressure T-burner. Two families of propellants are investigated; each family consists of two propellants with a minor compositional variation between them. In the family that shows a decreasing (steady state) pressure index (n) with increasing pressures, all of the combustion characteristics are found to be very similar although the mechanical properties are widely different. In the other family, which shows an increasing n with increasing pressures, unmistakable differences are found between the two propellants in the low-pressure L ^* instability behavior (along with the differences in the mechanical properties), while the other combustion characteristics are almost identical. The results are interpreted to be consistent with a theory that highlights the importance of condensed phase heat-transfer effects.

Publication: Combustion Science and Technology Vol.: 8 No.: 4 ISSN: 0010-2202

ID: CaltechAUTHORS:20101216-101742743

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Abstract: The problem of nonmetallized AP/composite propellant combustion is studied with the aim of coherently interpreting apparently diverse experimental data. Three fundamental hypotheses are introduced: the extent of propellant degradation at the vaporization step has to be specified through a scientific criterion; condensed phase degradation of AP to vaporizable fragments is the overall rate-limiting reaction; the rate of combustion in the gas phase is controlled by diffusive-mixing processes. Theoretical predictions of the regression rates of AP are seen to match well with experimental observations (both hot-plate pyrolysis and single-crystal deflagration). Theoretical curves of regression rate are presented for a typical composite propellant. The gas phase processes are discussed qualitatively. It is seen through analyses that either of the two familiar models for the gas phase (flame sheet approximation and uniform combustion) describes the general behavior adequately, hence de-emphasizing the role of gas phase details in propellant combustion.

Publication: Combustion Science and Technology Vol.: 8 No.: 3 ISSN: 0010-2202

ID: CaltechAUTHORS:20101214-142422277

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Abstract: Some theoretical studies on the time-independent and oscillatory combustion of nonmetallized ammonium perchlorate (AP)/composite propellants are presented. A coherent and unified interpretation was made of the voluminous data available from experiments related to propellant combustion. Three fundamental hypotheses are introduced: the extent of propellant degradation at the vaporization step has to be specified through a scientific criterion; the condensed-phase degradation reaction of ammonium perchlorate to a vaporizable state is the overall rate-limiting step; gas-phase combustion rate is controlled by the mixing rate of fuel and oxidizer vapors. In the treatment of oscillatory combustion, the assumption of quasi-steady fluctuations in the gas phase is used to supplement these hypotheses.

Publication: JPL Quarterly Technical Review Vol.: 3 No.: 2
ID: CaltechAUTHORS:20101214-114320657

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Abstract: The problem of linearized one-dimensional motions in a non-uniform flow field is re-examined. Earlier work is clarified, and some assumptions previously used are relaxed. The formalism accommodates all processes occurring in combustion chambers, including sources of mass, momentum, and energy at the lateral boundary. The work is intended partly to provide some results required for subsequent analyses of linear and nonlinear three-dimensional unsteady motions.

Publication: Combustion Science and Technology Vol.: 7 No.: 4 ISSN: 0010-2202

ID: CaltechAUTHORS:20101214-143437599

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Abstract: A study is presented of the radiation of acoustic modes from the end of a duct immersed in a uniformly moving medium. It is shown that the uniform flow has roughly the same effect as an increase in frequency at constant mode number: the number of lobes of the radiation pattern increases, and the radiation maximum is slightly displaced towards the duct axis. When the mode is near cut-off the forward radiation for an inlet is enhanced. The acoustic radiation characteristics of ducts with soft or absorbing walls and hard, perfectly-reflecting walls are then compared. It is shown, and this is of technological interest, that the side radiation from the end of an acoustically soft duct is greatly reduced for lower-order modes.

Publication: Journal of Sound and Vibration Vol.: 28 No.: 1 ISSN: 0022-460X

ID: CaltechAUTHORS:20101214-111254699

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Abstract: Combustion and NO formation are investigated in the turbulent mixing region between parallel fuel and oxidant streams. Chemical reactions are divided into two classes: (i) the fast, diffusion-limited combustion reaction, and (ii) the relatively slow, rate-limited NO formation. For the fast reaction, the turbulent mixing zone contains fuel, oxidant, and reaction products. The formation of NO is calculated separately as a trace species, since it has negligible effect on the flowfield. Transport of momentum, enthalpy, and chemical species is calculated, using a mixing-length theory. Because NO generation is highly temperature sensitive, the history of combustion product gases, subsequent to their formation, is decisive in determining the total NO production. Upper and lower bounds on NO production are obtained by considering that: (i) the combustion products remain undiluted and intact in the form of eddies as the turbulent field transports them throughout the mixing layer, and (ii) the combustion products are locally mixed with cool oxidizer or fuel. These yield upper and lower limits, respectively. The time-averaged velocity, temperature, and concentrations of fuel, oxidant, products, and NO distributions, are illustrated. Molecular mixing of turbulent eddies is shown to have a great influence on the amount of NO formed, although its effect on the time-averaged fluid properties is negligible. For a sample problem, the NO concentration obtained by assuming complete local molecular mixing is nearly an order-of-magnitude lower than the value predicted for no mixing.

Publication: Symposium (International) on Combustion Vol.: 14 No.: 1 ISSN: 0082-0784

ID: CaltechAUTHORS:20101214-141112621

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Abstract: Acoustic transmission and reflection is analyzed for plane waves propagating from a hot moving medium, impinging on a plane shear discontinuity into a cold stationary region. It is shown that incident waves originating in the hot region and propagating in the flow direction are transmitted into the cold region at almost right angles to the interface. The result is employed to examine the strong side radiation of internal noise transmitted through the exhaust duct of a turbojet engine.

Publication: Journal of Sound and Vibration Vol.: 24 No.: 1 ISSN: 0022-460X

ID: CaltechAUTHORS:20101214-090746220

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Abstract: The behavior of small spheres in non-steady translational flow has been studied experimentally' for values of Reynolds nunber from 0 to 3000. The aim of the work was to improve our quantitative understanding of particle transport in turbulent gaseous media, a process of extreme importance in powerplants and energy transfer mechanisms. Particles, subjected to strong sinusoidal oscillations parallel to the direction of steady translation, were found to have changes in average drag coefficient depending upon their translational Reynolds number, the frequency and amplitude of the oscillations. When the Reynolds number based on the sphere diameter was les s than 200, the synunetric translational oscillation had negligible effect on the aver age particle dr ago For Reynolds numbers exceeding 300, the effective drag coefficient was significantly increased in a particular frequency range. For example, an increase in drag coefficient of 25 per cent was observed at a Reynolds nwnber of 3000 when the amplitude of the oscillation was 2 per cent of the sphere diazneter and the disturbance frequency was approximately the Strouhal frequency. The occurrence of the maximum effect at frequencies between one and two times the Stroubal frequency strongly suggests non-linear interaction between wake vortex shedding and the oscillation in translational motions. Flow visualization studies support this suggestion.

No.: ARL 72-0017
ID: CaltechAUTHORS:20101220-154423061

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Abstract: Unstable motions must be anticipated as a possible problem in solid-propellant rocket motors; the characteristics of an instability depend primarily on the geometry of the motor and composition of the propellant. It is the purpose of this paper to review mainly the current state of analyses of combustion instability in solid-propellant rocket motors, but appropriate measurements and observations are cited. The work discussed has become increasingly important, both for the interpretation of laboratory data and for predicting the transient behavior of disturbances in full-scale motors. Two central questions are addressed: linear stability and nonlinear behavior. Several classes of problems are discussed as special cases of a general approach to the analysis of combustion instability. Application to motors, and particularly the limitations presently understood, are stressed.

No.: AIAA 72-1049
ID: CaltechAUTHORS:20101214-091516347

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Abstract: Due to non-linear loss or gain of energy, unstable oscillations in combustion chambers cannot grow indefinitely. Very often the limiting amplitudes are sufficiently low that the wave motions appear to be sinusoidal without discontinuities. The analysis presented here is based on the idea that the gasdynamics throughout most of the volume can be handled in a linear fashion. Non-linear behavior is associated with localized energy losses, such as wall losses and particle attenuation, or with the interaction between the oscillations and the combustion processes which sustain the motions. The formal procedure describes the non-linear growth and decay of an acoustic mode whose spatial structure does not change with time. Integration of the conservation equations over the volume of the chamber produces a single non-linear ordinary differential equation for the time-dependent amplitude of the mode. The equation can be solved easily by standard techniques, producing very simple results for the non-linear growth rate, decay rate, and limiting amplitude. Most of the treatment is developed for unstable motions in solid propellant rocket chambers. Other combustion chambers can be represented as special cases of the general description.

Publication: Combustion Science and Technology Vol.: 3 No.: 1 ISSN: 0010-2202

ID: CaltechAUTHORS:20101214-084430395

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Abstract: The phenomenon of transient condensation onto, or evaporation from, a liquid sheet in contact with its pure vapor is treated from a kinetic theory viewpoint. The Maxwell moment method is used to formulate the detailed transient problem. A steady surface mass flux rate exists for times large in comparison with the collision time, that is, in the continuum regime, and explicit formulas are given for this limit. The complete gasdynamic field, however, is nonsteady for all times. The calculations are carried out utilizing four moments, and the effects of incorporating additional moments are negligible. Finally, the analysis is extended to incorporate imperfect mass and temperature accommodation. Examination of the transient solution and a matched asymptotic "quasisteady" solution shows that the gasdynamic field consists of a diffusion process near the liquid surface coupled through an expansion or compression wave to the constant far field state.

Publication: Physics of Fluids Vol.: 14 No.: 3 ISSN: 1070-6631

ID: CaltechAUTHORS:20101220-151620237

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Abstract: Of the various unstable motions observed in solid propellant rocket chambers, the most troublesome currently are those involving oscillatory motions parallel to the axis. Such instabilities are found to arise particularly in larger rockets using propellants which contain aluminum. The problem is formulated here in one-dimensional form and solved for the case of small amplitude standing waves. Both pressure and velocity coupling may be accommodated, although the proper description of the response function for velocity coupling is not yet known. In addition to several special cases, the stability boundary is discussed for a straight chamber having variable cross section. The influences of the mean flow field, the nozzle, particulate matter, and motions of the solid propellant grain are taken into account.

Publication: Combustion Science and Technology Vol.: 2 No.: 4 ISSN: 0010-2202

ID: CaltechAUTHORS:20101220-152647813

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Abstract: The process of acoustic attenuation in a condensing medium is investigated using a continuumlike formulation that allows for the phase-exchange process. The liquid phase is assumed sufficiently disperse so that the field may be treated as a continuum. The elementary relaxation processes associated with droplet velocity, temperature, and vapor pressure equilibration are equally important in determining the attenuation when vapor, liquid, and inert gas mass fractions are of the same order. When the liquid mass fraction is small, however, a strong attenuation band appears at low frequencies. This attenuation process involves a coupled relaxation process in which heat transfer and vaporization processes combine to change the temperature of the relatively large gas mass. This attenuation band (i) centers on a frequency that is proportional to the concentration of liquid, and (ii) has a maximum value that varies directly as the concentration of condensible vapor and roughly as the square of the latent heat of vaporization. When the concentrations of liquid and condensible vapor are both small, the low-frequency attenuation band is nearly isolated and may be described in a convenient analytical manner.

Publication: Physics of Fluids Vol.: 13 No.: 11 ISSN: 0031-9171

ID: CaltechAUTHORS:MARpof70

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Abstract: The two-dimensional theory of airfoils with arbitrarily strong inlet flow into the upper surface was examined with the aim of developing a thin-airfoil theory which is valid for this condition. Such a theory has, in fact, been developed and reduces uniformly to the conventional thin-wing theory when the inlet flow vanishes. The integrals associated with the arbitrary shape, corresponding to the familiar Munk integrals, are somewhat more complex but not so as to make calculations difficult. To examine the limit for very high ratios of inlet to free-stream velocity, the theory of the Joukowski airfoil was extended to incorporate an arbitrary inlet on the upper surface. Because this calculation is exact, phenomena observed in the limit cannot be attributed to the linearized calculation. These results showed that airfoil theory, in the conventional sense, breaks down at very large ratios of inlet to free-stream velocity. This occurs where the strong induced field of the inlet dominates the free-stream flow so overwhelmingly that the flow no longer leaves the trailing edge but flows toward it. Then the trailing edge becomes, in fact a leading edge and the Kutta condition is physically inapplicable. For the example in this work, this breakdown occurred at a ratio of inlet to free-stream velocity of about 10. This phenomena suggests that for ratios in excess of the critical value, the flow separates from the trailing edge and the circulation is dominated by conditions at the edges of the inlet.

ID: CaltechAUTHORS:20110208-150155345

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Abstract: This review deals with a certain restricted portion of the mechanics of heterogeneous media. The volume fraction of the solid-particle or droplet cloud is considered to be so small that the interaction between individual particles may be neglected or highly simplified. This limitation applies to the individual flow fields about the particles as well as to collisions, and to heat and mass transfer as well as to momentum exchange between phases. Under this circumstance, the problem of detailed transport processes between particles and gas may be treated independently of the complete dynamical problem, and this aspect, being a study of its own, will be suppressed to a considerable extent here. There are problems, such as the impact of particles on walls, the concentration separation in boundary layers or pipe flow, in which the distortion of the particle flow field due to a solid wall or another particle is the central physical issue. These problems therefore lie outside the scope of the review. On the other hand, the structure of shock waves, sound attenuation, and many flow-field problems can be treated within our present restrictions. The basic equations and exchange processes will be introduced first, together with the physical parameters that indicate the relative importance of the particle cloud and the limitations of the dusty-gas concept. Then several different problems will be discussed that lead to some of the significant results in the field and illustrate analytical techniques that have proven useful.

Publication: Annual Review of Fluid Mechanics Vol.: 2ISSN: 0066-4189

ID: CaltechAUTHORS:20101220-141547545

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Abstract: Because of its inherent complexity and detail, as well as its rather tenuous relationship to existing combustion theory, the propagation of uncontrolled fires in large buildings remains one of the unsolved problems facing our cities. On October 13, 1969 (see Appendix), a fire in a Los Angeles apartment claimed the lives of eight people and sent more than a score to the hospital for various degrees of burn and smoke inhalation. As the fire developed, flames spread quickly up the main stairwell, blocking exits from apartment units, forcing some to jump from upper floors. Within a matter of minutes, all three floors were so involved in fire that normal escape was impossible. Our lack of quantitative knowledge about the propagation of building fire has a more widespread effect than such disasters. It is a major factor in preserving archaic and inappropriate building codes; it places a severe limit on architectural innovation because fire hazards in novel structures cannot be evaluated quantitatively. This is a truly serious restriction in an era where low-cost multiple dwellings are in urgent need.

ID: CaltechAUTHORS:20110203-131719678

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Abstract: Interactions are considered between a moving, alkali-metal seeded, dense plasma and a metallic electrode whose surface properties are influenced by the absorption of seed particles. The plasma behavior is governed by a set of differential equations, which are coupled to the surface through the boundary conditions. These conditions are obtained by utilizing the particle desorption rate expressions of Levine and Gyftopoulos. The solution of the problem yields the state of the surface as well as the spatial distribution of plasma properties. In particular, electrode voltage drops are predicted, which indicate whether the electrode operates in a thermionic or arc mode. The method has been applied to a potassiwn-seeded argon plasma in contact with a tungsten electrode in a stagnation flow geometry. The results show that the plasma - surface interaction may lead to large electrode currents at moderate voltage drops. These currents can be up to an order of magnitude greater than what the random electron current would be at the surface under conditions of perfect thermodynamic equilibrium at the surface temperature. R.esults of a comparable experiment show reasonably good agreement with the theory.

ID: CaltechAUTHORS:20101220-133221838

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Abstract: A calculation of the burning rate for a composite solid propellant is based on a model in which the distribution of combustion in the gas phase is specified. The formulation of the problem can accommodate an arbitrary distribution, but only the simplest case of uniform combustion is treated here. An inverse numerical computation is carried out, as the magnitude of the reaction rate, and its dependence on pressure, are calculated for several specified burning rates. Simultaneously, flame stand-off distances and thicknesses are determined as part of the solution. The numerical results for those characteristics of the flame appear to be comparable to observed values. However, the principal value of this treatment of the problem is due to the ease with which one can study and understand the influence of the various physical properties and combustion characteristics.

Publication: Combustion Science and Technology Vol.: 1 No.: 3 ISSN: 0010-2202

ID: CaltechAUTHORS:20101221-134757282

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Abstract: The mean velocity and pressure fields in a turbulent boundary layer on a Hat plate at M∞ = 2.6 are investigated for ratios of mass-How per unit area injected at the wall to that at the edge of the boundary layer (Λ_e) between 0 and 0.03. Two-dimensionality is demonstrated, and a similar How approached with linear growth of momentum and displacement thicknesses. A Howarth-Dorodnitsyn transformation for the normal coordinate is found to bring the data into good agreement with incompressible results for the same value of Λ_e. At the highest injection rate, the transformed velocity profiles agree well with incompressible turbulent mixing layer results. Finally, the induced side forces are found to be comparable to those obtained by equivalent injection through a slot.

Publication: AIAA Journal Vol.: 7 No.: 9 ISSN: 0001-1452

ID: CaltechAUTHORS:20101221-080701462

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Publication: AIAA Journal Vol.: 7 No.: 7 ISSN: 0001-1452

ID: CaltechAUTHORS:20101221-094400998

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Abstract: It has long been a cherished hope of some people that measurements of unsteady burning in the laboratory should be applicable to the very important practical problem of instabilities in a rocket chamber. In this Note, we wish to describe what appears to be the first experimental verification of this idea.

Publication: AIAA Journal Vol.: 7 No.: 6 ISSN: 0001-1452

ID: CaltechAUTHORS:20101221-083201081

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Abstract: An exact similarity solution is given for the flow of a fluid-particle suspension over an infinitely large disk rotating at a constant velocity. Numerical solutions of the resulting ordinary differential equations provide velocity distributions for both fluid and solid phases and density distributions for the solid. The boundary-layer thicknesses of the particle cloud and the fluid are found to be approximately equal. In addition to its intrinsic value as a solution to a physical problem, the results provide a convenient basis for judging the accuracy of approximate techniques.

Publication: Physics of Fluids Vol.: 12 No.: 1 ISSN: 1070-6631

ID: CaltechAUTHORS:20101221-112626068

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Abstract: An Elementary Calculation of the Combustion of Solid Propellants. The problem of the burning of a solid propellant is treated in an approximate manner by prescribing the spatial distribution of energy rdease in the gas phase. Adoption of this inverse approach converts the usual non-linear problem to a linear eigenvalue problem which is easily solvable. Results for concentrated combustion (a flame front) and special cases of distributed energy release are given. Qualitative aspects such as flame stand-off distance, flame thickness, and various components of heat transfer within the combustion region are clearly shown. Examination of the influence of energy loss by radiation from the solid-gas interface gives satisfactory agreement with previous computations based on the non-linear formulation. An application to the problem of unsteady burning, and the response to pressure fluctuations is discussed briefly. The ease with which useful results can be obtained seems to justify the imperfect nature of the analysis.

Publication: Astronautica Acta Vol.: 14 No.: 2 ISSN: 0004-6205

ID: CaltechAUTHORS:20101221-102902637

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Abstract: Experimental data has been obtained from two T-burners and an L^* burner over a range of frequencies from 10 cps to 8000 cps and from 25 psia to 1000 psia. From these data the response of the propellants to a pressure perturbation has been calculated and has been found to be consistent between burners. The results have been interpreted as a response function surface with burning rate and frequencies as independent variables. The data indicates that for a given pressure level the response function has a peak value at a frequency that increases as pressure increases. The magnitude of this peak height varies with pressure so that there is a localized peak in the response function surface for a given propellant. The results are in qualitative agreement with theoretical studies in that the models also predict a maximum value in the response function. However, they also predict that this magnitude should be approximately a constant and not dependent on the pressure and frequency to the extent observed in the present study. The results obtained for an aluminized propellant indicate that presence of metal in the combustion zone greatly influences both the magnitude of the response function peak as well as its location.

Publication: Symposium (International) on Combustion Vol.: 12 No.: 1 ISSN: 0082-0784

ID: CaltechAUTHORS:20101221-114030246

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Abstract: An experimental study was made of the disintegration of a liquid sheet due to gravity force. The influence of surface tension, viscosity, and density of liquids on the phenomenon of disintegration was found. Conditions of liquid sheet breaking into streams, as well as the frequency of appearance of streams and the mean diameter of droplets independent of properties of the liquid, were found experimentally.

Vol.: 4
ID: CaltechAUTHORS:20110208-113026851

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Abstract: Experimental and theoretical studies have been made of the electrothennal waves occurring in a nonequilibrium electrical discharge in a potassium-seeded argon plasma. The studies presented in this paper refer to discharges in transverse gas flow and magnetic field. The behavior of these discharges as determined by photographs, photomultiplier measurements, and voltage probes is discussed and the results interpreted in terms of a steady, one-dimensional theory. A single discharge was found to operate in one of three modes-the shorted, transition, or normal mode-depending on the length of the ionization transient. An extension of the one-dimensional theory to the inlet problem predicts the approximate length of this transient and thus provides criteria for the existence of each mode. The normal mode was studied in a duct with a series of circuits discharging in parallel across a gas flow. Here, a regular set of steady, one-dimensional streamers was found in the center of the duct between hot boundary regions along each electrode wall. The properties of the one-dimensional streamers are shown to agree in detail with values predicted from the one-dimensional theory. A scheme is then presented for calculation of the effective conductivity of a duct using the amplitude of conductivity fluctuations predicted by this theory.

Publication: AIAA Journal Vol.: 7 No.: 8 ISSN: 0001-1452

ID: CaltechAUTHORS:20101221-100324714

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Abstract: Some Gasdynamic Problems in the Flow of Condensing Vapors. The general problem of the flow of a wet vapor, with or without an inert diluent is formulated under the assumption that the liquid phase is finely divided and dispersed throughout the gaseous component in droplets whose radii are nearly constant in any local region. The processes of momentum transfer, heat transfer between phases are assumed to take place according to Stokes law and Nusselt number of unity, respectively. The mass transfer process is treated as diffusion governed in the presence of an inert diluent and kinetic governed for two phases of a pure substance. The physical understanding of such problems, in contrast with those of conventional gas dynamics, rests largely in the role played by the relaxation times or equilibration lengths associated with these three processes. Consequently, both simple and coupled relaxation processes are examined rather carefully by specific examples. Subsequently, the problem of near-equilibrium flow in a nozzle with phase change is solved under the small-slip approximation. The structure of the normal shock in a pure substance is investigated and reveals three rather distinct zones: the gasdynamic shock, the vapor relaxation zone, and the thermal and velocity equilibration zone. The three-dimensional steady flow of the two-phase condensing continuum is formulated according to first order perturbation theory, and the structure of waves in such supersonic flow is examined. Finally, the attenuation of sound in fogs is formulated and solved accounting for the important effects of phase change as well as the viscous damping and heat transfer which have been included in previous analyses.

Publication: Astronautica Acta Vol.: 14 No.: 6 ISSN: 0004-6205

ID: CaltechAUTHORS:20101221-140000406

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Publication: AIAA Journal Vol.: 6 No.: 12 ISSN: 0001-1452

ID: CaltechAUTHORS:20101223-101546101

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Abstract: The paper describes a study concerning the sonic injection of a gaseous jet through a transverse slot nozzle in a wall into an external flow which is uniform outside of a turbulent boundary layer. An analytic model of the flowfield has been constructed in which conservation of momentum is applied to a control volume at the jet nozzle exit. A series of flat-plate experiments was conducted with normal, sonic jets at external flow Mach numbers of 2.61, 3.50, and 4.54. Pressure data near separation and the plateau were in agreement with existing correlations. Comparisons of the trends predicted by the analysis with two-dimensional force data from these experiments and from other sources showed good agreement. Values of amplification factor, the upstream interaction force plus the jet thrust divided by the vacuum thrust of a sonic jet, of 2.9 to 3.2 were measured. The amplification factor is relatively insensitive to variations in external flow Mach number and variations in injectant gas properties. A correlation of data obtained from experiments with finite-span slots demonstrates that the effective jet penetration height and the slot span are the important characteristic dimensions of such flowfields.

Publication: AIAA Journal Vol.: 6 No.: 2 ISSN: 0001-1452

ID: CaltechAUTHORS:20101222-095858065

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Abstract: The mean velocity and pressure fields in a turbulent boundary layer on a flat plate at M_∞ = 2.6 are investigated for ratios of mass flow per unit area injected at the wall to that at the edge of the boundary layer Λ_e) between 0 and 0.03. Two dimensionality is demonstrated, and a similar flow established with linear growth of momentum and displacement thicknesses. A Howarth-Dorodnitsyn transformation for the normal coordinate is found to bring the data into good agreement with incompressible results for the same value of Λ_e. At the highest injection rate, the velocity profiles agree well with turbulent mixing-layer results. However, unlike mixing layers, the maximum rate of mass entrainment is the same as for the incompressible case. Finally,the induced side forces are found to be comparable to those obtained by equivalent inje ction thr ough a slot.

No.: 68-129
ID: CaltechAUTHORS:20101223-075127801

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Abstract: A chemical kinetic model describing photochemical reactions that are likely to be important in "cold" argon ahead of a strong shock wave is examined on a quantitative basis. The model includes the propagation of resonance radiation far from the shock front in the wings of the resonance absorption line, partial trapping of the absorbed resonance radiation, subsequent photoionization of excited atoms, photoionization of ground state argon, and certain recombination and deexcitation processes. Specific consideration is given to shock tube geometry, the occurrence of both nonequilibrium and equilibrium regions of variable lengths behind the pressure discontinuity, and the (experimentally) known shock tube wall reflectivity. Theoretical predictions of electron and excited atom concentrations ahead of the shock wave are presented for typical shock tube operating conditions.

No.: AIAA 68-666
ID: CaltechAUTHORS:20101223-071151029

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Abstract: The governing equations of condensation phenomena controlled by heat transfer on large droplets in a pure vapor are derived. Using the isentropic expansion as the first approximation, the equations are integrated by means of the perturbation method. This method is illustrated by presenting an example. The problem is an important one in the field of steam turbine engineering, although the condensation problem is of more general interest.

Publication: International Journal of Heat and Mass Transfer Vol.: 10 No.: 12 ISSN: 0017-9310

ID: CaltechAUTHORS:20101222-091908271

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Abstract: Steady, one-dimensional current streamers have been observed in nonequilibrium plasma subjected to crossed E and B fields. Their half-width and amplitude agree with a nonlinear model of electrothermal waves.

Publication: Physics of Fluids Vol.: 10 No.: 9 ISSN: 0031-9171

ID: CaltechAUTHORS:ZUKpof67

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Abstract: The small slip approxitnation to the theory of two-phase flow in rocket nozzles is reviewed to show that the inaccuracies associated with drag and heat transfer laws, and those associated with the fundamental approximation, are independent and that the former may be removed algebraic1y. Selected applications ofthe approximate theory are discussed to indicate that these stress the nature of the dependence of the results upon the relevant physical parameters and the possible consequence of scaling laws, rather than numerical accuracy too often limited by inaccurate initial data. It is suggested that approximate analytical results may offer much more assistance to the rocket engineer than has yet been used to advantage.

No.: AFRPL-TR-67-223, Vol. 2
ID: CaltechAUTHORS:20101222-101345306

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Abstract: Calculation of the Admittance Function for a Burning Surface. A thorough analysis of pressure oscillations in a solid propellant rocket requires specification of the response of the burning solid. Indeed, for the case of small amplitude waves, this is the most crucial aspect of the problem; unfortunately, it is also poorly understood. The admittance function is merely a convenient expression of the response which contains the primary mechanism for driving waves. In the work reported here, the usual one-dimensional approximation is made, and three main regions are distinguished: the solid phase being heated, the solid phase involving decomposition (a thin region near the surface), and the gas phase. The problem reduces simply to the solution of appropriate ordinary differential equations and satisfaction of boundary conditions, which include matching at interfaces. The most significant differences from previous work are incorporation of a decomposition region and the treatment of the gas phase. A greatly simplified analysis of the latter leads essentially to the same results found elsewhere, but with substantially less labor. Only a quasistatic analysis, valid for frequencies less than a few thousand cycles per second, is covered, but it can be extended to higher frequencies. Laboratory measurements have shown that the response consists generally of a single peak in the range of frequency for which the quasi static approximation appears to be accurate. The qualitative aspects of such peaks, and their connection with 'self-excited' oscillations, are discussed. In particular, the influence of decomposition and pressure sensitivity of the various chemical reactions is examined. Limited numerical results are included. Eventually, the aim of calculations is principally to gain some understanding of the unsteady combustion process and to aid in classifying propellants. The regions involved in the burning are separately characterized by a small number of dimensionless groups. It appears that the effects represented by these parameters may be distinguished in the response function; one may therefore be able, by use of experimental results, to determine at least qualitative connections between the response to pressure oscillations and changes of composition. In this regard, observations made in both T -burners and L * burners should prove useful.

Publication: Astronautica Acta Vol.: 13 No.: 3 ISSN: 0004-6205

ID: CaltechAUTHORS:20101222-075221402

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Abstract: Droplet Agglomeration in Rocket Nozzles Caused by Particle Slip and Collision. The development of the particle mass spectrum in a rocket nozzle is investigated under the assumption that droplet growth by collision and agglomeration is the dominant mechanism subsequent to initial appearance of particles in the rocket chamber. Collisions are calculated on the basis oflinearized particle slip theory and a spectral integral equation is derived describing the development of particle mass spectrum during the flow process along the nozzle. This agglomeration process continues until the droplet temperature falls below the freezing point of the material. A solution is obtained for the approximate growth in the average particle size during the expansion process. The results show that, according to this model, the particle size is strongly dependent on the initial pressure in the rocket chamber and is independent of nozzle geometry. These results suggest that the collision-agglomeration process is at least one of the critical factors that accounts for the size of solid particles in rocket exhausts.

Publication: Astronautica Acta Vol.: 13 No.: 2 ISSN: 0004-6205

ID: CaltechAUTHORS:20101222-073250075

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Abstract: Flow Induced by the Impulsive Motion of an Immite Flat Plate in a Dusty Gas. The problem of flow induced by an infinite flat plate suddenly set into motion parallel to its own plane in an incompressible dusty gas is of considerable physical interest in its own right as well as because of its close relation to the non-linear, steady (constant-pressure) laminar boundary layer. Its solution provides complete and exact information about modifications of the boundary layer growth and skin friction due to particle-fluid interaction. Moreover, it provides a basis for judging the accuracy of approximations which have been employed in more complex problems of viscous fluid-particle motion. The uncoupled thermal Rayleigh problem for small relative temperature differences is directly inferred and this answers questions about the modifications of the surface heat transfer rate and about the possibility of similarity with the velocity boundary layer. Similarity is possible when, in addition to a Prandtl number of unity, the streamwise relaxation processes are also similar.

Publication: Astronautica Acta Vol.: 13 No.: 4 ISSN: 0004-6205

ID: CaltechAUTHORS:20101222-112413026

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Abstract: A review of experiments concerned with the description of the steady flowfield produced by the separation of a turbulent boundary layer ahead of a forward-facing step is presented. The Mach number is restricted to the supersonic range and only two-dimensional flows are investigated. The dependence of the induced pressure field at the wall on Reynolds number, Mach number, and step height is considered. It is shown that the pressure rise in the separation region expressed in normalized form is independent of Mach number and Reynolds number and that the scale for the separation phenomena is the boundary-layer thickness. In addition, it was found that the plateau pressure rise is independent of Reynolds number for the turbulent regime and that the induced side force increases linearly with Mach number.

Publication: AIAA Journal Vol.: 5 No.: 10 ISSN: 0001-1452

ID: CaltechAUTHORS:20101222-080455403

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Publication: AIAA Journal Vol.: 4 No.: 12 ISSN: 0001-1452

ID: CaltechAUTHORS:20110104-074418915

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Abstract: Particles in a plasma can appreciably change the electron density from the value it would assume if the particles were not present. The case of pure particle ionization, in which there is only thermionic emission from the particles and no gas ionization, is first considered. It is established that the potential and the charge distributions can be divided into a strong shielding regime, in which most of the free electrons are packed close to the particle surfaces in regions of high potential, and its direct opposite, a weak shielding regime. In both regimes, the free-electron content of the plasma is most readily altered by variations in the particle size, rather than in the work function or particle temperature. The suppression of one form of ionization by the other when both particle and gas contribution to the electron density are comparable is next investigated. In the case of gaseous ionization enhancement it is shown that, if the thermionically emitting particles are hotter than the gas, the electron temperature will also be higher than that of the gas and the gaseous ionization thereby enhanced. Lastly, it is shown that in some transient situations, the particles are able to control the time rate of change of the electron density.

Publication: Physics of Fluids Vol.: 9 No.: 12 ISSN: 1070-6631

ID: CaltechAUTHORS:20101221-150859236

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Abstract: An experimental investigation of the initial phase of shock produced ionization in argon, krypton, and xenon has been conducted in order to elucidate the atom-atom ionization reaction and to determine the atom-atom ionization cross sections. A high-purity shock tube was employed to heat these gases to temperatures in the range from 5000° to 9000°K at neutral particle densities of 4.4 X 10^(17), 7.0 X 10^(17), and 13.3 X 10^(17) cm^(-3), and impurity levels of approximately 10^(-6) A K-band (24-GHz) microwave system situated so that the microwave-beam propagation direction was normal to the shock tube, monitored the ionization relaxation process occurring immediately after the passage of the shock front. Electron density was calculated from the microwave data using a plane-wave-plane-plasma slab interaction theory corrected for near field effects associated with the coupling of the microwave energy to the plasma. These data, adjusted to compensate for the effects of shock attenuation, verified that the dominant electron-generation process involve a two-step, atom-atom ionization reaction, the first step (excitation to the first excited states) being rate determining. The quadratic dependence on neutral density associated with this reaction was experimentally demonstrated (with an uncertainty of ± 15%). The cross section, characterized as having a constant slope from threshold (first excited energy level), represented as the cross-sectional slope constant C, was found to be equal to 1.2 X 10^(-19)±15% cm^2/eV, 1.4 X 10^(-19)±15% cm^2/eV, and 1.8 X 10^(-20)±15% cm^2/eV for argon, krypton, and xenon, respectively. The electron-atom elastic momentum-exchange cross sections derived from the microwave data correlated quite well with Maxwell-averaged beam data, the agreement for the case of argon being ±20%; krypton, ±30%; and xenon, within a factor of 2.

Publication: Journal of Chemical Physics Vol.: 45 No.: 5 ISSN: 0021-9606

ID: CaltechAUTHORS:20110103-110108976

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Abstract: The atom-atom ionization process occurring in high-purity argon-xenon mixtures has been investigated by means of a conventional shock tube employing a microwave probe to monitor the electron-generation rate. All tests were conducted at approximately atmospheric pressure and at temperatures in the range between 5000° and 9000°K, corresponding to a neutral-particle density of 7.0 X 10^(17) cm^(-3). The cross-sectional slope constant for xenon ionized by collision with an argon atom is 1.8 X 10^(-20) cm^2/eV±20%, that is, equal to that for xenon ionized by collision with another xenon atom. The data for the reaction of argon ionizing xenon are consistent with an activation energy of 8.315 eV, that is, of the xenon-xenon, atom-atom ionization process. No data were obtained for xenon ionizing argon. Good correlation was obtained between the cross sections for electron elastic momentum exchange derived from the microwave experiment and those obtained from beam experiments. The argon-xenon ionization cross section implies that, for atom-atom processes in the noble gases at pressures ~ 1 atm and temperatures ~2/3 eV, the ionization cross section is independent of the electronic structure of the projectile atom.

Publication: Journal of Chemical Physics Vol.: 45 No.: 5 ISSN: 0021-9606

ID: CaltechAUTHORS:20110103-113055359

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Abstract: The flow induced in an incompressible dusty gas by an infinite flat plate oscillating in its own plane is studied. The differential equation describing this problem is given; its form exhibits the relaxation from a frozen-diffusion process (corresponding to a clean gas) to an equilibrium-diffusion process (corresponding to a single heavier gas). The gas velocity profile, shear stress on the plate and the particle velocity profile are obtained exactly and are discussed in terms of the parameters of the problem. The essential feature is the inhibition of viscous diffusion in the gas by the particle-gas velocity relaxation. Mechanical energy dissipation is discussed.

Publication: Physics of Fluids Vol.: 9 No.: 9 ISSN: 1070-6631

ID: CaltechAUTHORS:20110104-072935743

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Abstract: New data are presented which provide direct experimental confirmation of the validity of a physical model which has been widely employed to predict the electrical conductivity of dense, two-temperature, seeded plasmas. Experimental measurements of electron temperature, and ionization and recombination rates are presented for partially ionized plasmas of potassium-seeded argon. Experimental conditions were chosen to cover those ranges of interest in connection with proposed magnetohydrodynamic energy conversion devices for which nonequilibrium electrical conductivity measurements have been previously reported, e.g., translational atom temperatures of about 2000°K, total atom densities near 10^(18)/cm^3, potassium densities of about 10^(16)/cm^3, electron densities from 10^(13)/cm^3 to 10^(15)/cm^3, and electron temperatures from 2200 to 3500°K. Measured values of electron-electron-ion recombination coefficients for potassium show good agreement with theoretical values based upon the Gryzinski classical inelastic-collision cross-section expressions. Observed ionization rates and relaxation characteristics appear to be adequately explained by a similar formulation for the ionization process.

Publication: Physics of Fluids Vol.: 9 No.: 4 ISSN: 1070-6631

ID: CaltechAUTHORS:20110103-093330751

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Abstract: The electrohydrodynamic phenomena associated with the motion of a charged particle in a plasma are investigated. It is shown that the type of disturbance produced in the plasma depends significantly on the speed of the particle, i.e., whether it is subsonic, transonic, or supersonic. In the subsonic case, the electrohydrodynamic drag experienced by the particle is caused by an unsymmetric wake formed by the screening electrons. In the supersonic case, electron screening is confined to the Mach cone. Ahead of the Mach cone, the plasma behaves as if it were an incompressible fluid. The electrohydrodynamic drag in this case has a logarithmic nature.

Publication: Physics of Fluids Vol.: 9 No.: 3 ISSN: 1070-6631

ID: CaltechAUTHORS:20110103-092229516

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Abstract: Acoustic Oscillations in Solid Propellant Rocket Chambers. Among the various kinds of periodic motions observed in rocket combustion chambers, the most common and simplest to analyze are those related to classical acoustic modes. If the amplitudes are small, the main perturbations of the familiar standing or travelling waves in a closed chamber are proportional to the Mach number of the mean flow. The correct equations describing the problem are here obtained from the general equations of motion by a limit process which will also provide equations for studying waves of finite amplitude. Subsequently, a single non-homogeneous wave equation is deduced, and solved by an iteration· perturbation procedure. The principal result is a simple formula for the complex frequency showing explicitly the effects of burning, suspended particles in the gases, the exhaust nozzle, and viscous wall forces as well as the mean flow itself. The last is particularly interesting since, owing primarily to the flow inward from the burning surface, the mean flow, if it is irrotational, never acts to damp modes which do not involve axial oscillations. As a particular application, the extensive data taken by BROWNLEE and MARBLE are interpreted to the extent that the linear analysis permits. A stability boundary was obtained from 250 firings of small cylindrical rockets, the principal variables being initial port diameter and length. The propellant did not contain metal particles, and it appears that the observations cannot be explained by the supposition that viscous damping associated with particles in the product gases was the main source of energy loss. Apparently dissipation at the head end, such as that associated with tangential wall shear forces, was an important loss. On the other hand, there is little doubt that if the combustion produces particles, the consequent dissipation is adequate to damp small amplitude waves.

Publication: Astronautica Acta Vol.: 12 No.: 2 ISSN: 0004-6205

ID: CaltechAUTHORS:20110103-101232276

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Abstract: During the process of withdrawing fluids from tanks, surface distortion and subsequent gas ingestion have been observed in situations where no liquid rotation was present. The distortion takes the form of a depression of the liquid surface over the outlet, which leads to ingestion of gas in the outlet line before all of the liquid has drained from the tank. This phenomenon becomes more important as the fluid flow rate is increased. The flow of fluids from tanks, under conditions that lead to gas ingestion, has been studied with emphasis on a theoretical solution, e.g., Abramson et al. and Saad and Oliver. However, no results applicable to the problem studied here have been obtained, and to the authors' knowledge, no comprehensive experimental study of the ingestion phenomenon has been undertaken prior to this work. This paper describes the results of such an investigation for flat-bottomed, right cylindric tanks with right cylindric outlets located on the tank centerline. The work discussed here deals primarily with the determination of the maximum height of the liquid surface when the surface distortion reaches the outlet. This distance is called the "gas ingestion" height, h. This note extends the experimental work and correlation of Ref. 3. A more complete description of the theoretical work is presented in Ref. 3.

Publication: Journal of Spacecraft and Rockets Vol.: 3 No.: 11 ISSN: 0022-4650

ID: CaltechAUTHORS:20110104-080049601

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Abstract: An experimental study has been made of the motion oflong bubbles in closed tubes. The influence of viscosity and surface tension on the bubble velocity is clarified. A correlation of bubble velocities in vertical tubes is suggested and is shown to be useful for the whole range of parameters investigated. In addition, the effect of tube inclination angle on bubble velocity is presented, and certain features of the flow are described qualitatively.

Publication: Journal of Fluid Mechanics Vol.: 25 No.: 4 ISSN: 0022-1120

ID: CaltechAUTHORS:20110103-104138242

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Abstract: Experimentally determined values of electrical conductivity and electron temperature have been measured in a non-equilibrium seeded plasma. These results are in good agreement over a wide range of parameters with values calculated from a two-temperature model of the plasma. There is no doubt that the two-temperature model is valid over a wide range of gas temperatures, seed concentrations, and current densities for the argon-potassium and helium-potassium plasmas. However, the model does not give an accurate description of the plasma when the current density is below about 0.4 amp/cm^2; in this range the omission of the influence of atom-atom excitation and the influence of non-equilibrium excited state populations may explain the discrepancy between experiment and theory. In addition, the electron-elecron-ion collisional recombination rate for potassium has been measured in the argon-potassium system. The range of electron temperatures investigated was between 1900° K to 3000° K with electron densities between 3X10^(13) and 4x10^(14)/cm^3. The measured values show a scatter of 60 per cent about theoretical values calculated from present recombination-rate theory employing the Gryzinski classical collision cross sections.

ID: CaltechAUTHORS:20110204-143621068

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Publication: AIAA Journal Vol.: 4 No.: 6 ISSN: 0001-1452

ID: CaltechAUTHORS:20110103-100121099

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Publication: AIAA Journal Vol.: 4 No.: 8 ISSN: 0001-1452

ID: CaltechAUTHORS:20110103-102744600

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Abstract: The apparent spectral absorption coefficients of the H_20 infrared bands in the vicinity of 2·7 µ were measured in a shock tube behind reflected shock waves in an Ar-H_20 mixture. By interrupting an infrared beam at a 60 kc rate and projecting this beam across the shock tube to a monochromator, it was possible to measure simultaneously both emission and absorption of H_20 at 1000°K. The spectral absorption coefficients obtained from emission measurements averaged 9·8 per cent higher than absorption coefficients obtained from absorption measurements, probably due to experimental errors (smaller than usually encountered in shock tube measurements). At 1933°K experimental difficulties precluded simultaneous measurement of infrared emission and absorption, so measurements were restricted to emission. The apparent absorption coefficients were integrated to give the integrated absorption coefficients for the collection of bands near 2·7 µ. Integrated absorption coefficients were 49·8 cm^(-2) atm^(-1), 54·7 cm^(-2) atm^(-1), and 31·6 cm^(-2) atm^(-1) for absorption at 1000°K, emission at 1000°K, and emission at 1933°K, respectively. The two values at 1000°K were in good agreement with those of Goldstein, who made no measurements above this temperature.

Publication: Journal of Quantitative Spectroscopy and Radiative Transfer Vol.: 5 No.: 1 ISSN: 0022-4073

ID: CaltechAUTHORS:20110103-085202868

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Abstract: In a previous paper, the authors presented experimental values of electrical conductivity measured in a plasma composed of argon gas seeded with potassium vapor. The measurements were made at atmospheric pressure with a neutral gas temperature of 2000° ± 100°K and with a number of values of seed concentration in the range 0.2 to 0.8 mole %. The effect of nonequilibrium heating of the electron gas-excited potassium system was investigated for a range of current densities between 0.8 and 80 amp/cm^2. These data were in good agreement with values of the conductivity calculated by a scheme, outlined in Ref. 1, which included the effects of energy loss from the system, composed of the electron gas and the electronically excited states of potassium due to radiation from the excited potassium atoms. In addition, the pulsed technique used to measure the conductivity in response to a step function application of the electric field made possible the determination of the relaxation times for the ionization process.

Publication: AIAA Journal Vol.: 3 No.: 2 ISSN: 0001-1452

ID: CaltechAUTHORS:20101223-112858217

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Abstract: The flow field around the injection port for secondary injection of a gas normal to a supersonic stream has been studied in a series of wind-tunnel experiments. The experiments were conducted at freestream Mach numbers of 1.38 to 4.54. Gaseous nitrogen, argon, and helium were used as injectants. New information concerning pressure fields, concentration fields, and shock shapes was obtained. A scale parameter has been calculated, based on a simple, inviscid model of the flow field. This scale parameter gives a good general correlation of the data. Use of this scale parameter allows prediction of a simple scaling law for the side forces generated by secondary injection. This side-force scaling law is in approximate agreement with existing rocket motor test results.

Publication: AIAA Journal Vol.: 2 No.: 10 ISSN: 0001-1452

ID: CaltechAUTHORS:20110105-094540345

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Abstract: A theory is developed for the one-dimensional flow of a gas, containing solid particles of two different sizes, in which the effect of particle collisions is accounted for as well as the interaction between the particles and the gas. It is assumed that the particles behave as smooth elastic spheres, that they follow the Stokes drag law and exchange heat with the gas at a Nusselt number of unity. It is shown that there exists a range of parameters which provides that (i) the viscous flow fields about each particle do not interfere during collision, and (ii) the random velocities imparted by one collision are damped before either particle suffers another collision. Using the assumption of small particle slip, the one-dimensional flow problem is solved explicitly up to first order terms in the small slip. It is found, of course, that the tendency of collisions is to cause the two particle-slip speeds to have more nearly the same value than they would in the absence of interparticle collision. It appears that, although the physical assumptions restrict the magnitude of the interparticle forces, the model does provide the proper limit for very strong particle interaction and can conceivably be applied in this range also without gross error.

Publication: Physics of Fluids Vol.: 7 No.: 8 ISSN: 1070-6631

ID: CaltechAUTHORS:MARpof64

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Abstract: The spectral absorption coefficients of liquid water have been measured between 2200 and 3000 cm^(-1) and between 3700 and 7600 cm^(-1) at temperatures of 27, 89, 159, and 209°C. The integrated intensities for the entire spectral regions extending from 4600 to 5900 cm^(-1) and from 5900 to 7600 cm^(-1) have also been determined at each of the specified temperatures. Following Buijs and Choppin, the experimental data have been used, in a highly simplified analysis, for the determination of hydrogen bonding in liquid water on the assumption that water consists of clusters containing only zero, one or two hydrogen bonds per molecule. We have also indicated briefly a more complete analysis of the experimental measurements in which the full range of results on spectral absorption coefficients as a continuous function of frequency is properly utilized.

Publication: Journal of Quantitative Spectroscopy and Radiative Transfer Vol.: 4 No.: 3 ISSN: 0022-4073

ID: CaltechAUTHORS:20110105-081524276

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Abstract: N/A

Publication: Zeitschrift für Angewandte Mathematick und Physik Vol.: 15 No.: 2 ISSN: 0044-2275

ID: CaltechAUTHORS:20110104-142506543

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Abstract: The integrated intensities and spectral absorption coefficients of water vapor in the 1·38 µ, 1·87 µ, 2·7 µ and 6·3 µ spectral regions have been measured at temperatures up to 1000°K. The experiments were performed in a specially designed, high-temperature absorption cell using self-broadening to remove the rotational fine structure.

Publication: Journal of Quantitative Spectroscopy and Radiative Transfer Vol.: 4 No.: 2 ISSN: 0022-4073

ID: CaltechAUTHORS:20110104-134624109

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Abstract: No abstract is available for this article.

Publication: Journal of Quantitative Spectroscopy and Radiative Transfer Vol.: 4 No.: 2 ISSN: 0022-4073

ID: CaltechAUTHORS:20110104-140209282

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Abstract: The rate of ionization behind strong shock waves in argon, krypton, and xenon, is observed by a transverse microwave probe, over a range of electron densities low enough that atom-atom inelastic collisions are the rate-determining mechanism. Shocks of Mach number 7.0 to 10.0 propagate down a 2-in. sq. aluminum shock tube into ambient gases at pressures of 3.0 to 17.0 mm. Hg., heating them abruptly to atomic temperatures of 5500°K to 9600°K. The subsequent relaxation toward ionization equilibrium is examined in its early stages by the reflection, transmission, and phase shifts of a 24.0 Gc/sec (1.25 cm) transverse microwave beam propagating between two rectangular horns abreast a glass test section. The data yield effective activation energies of 11.9 ± 0.5 eV for argon, 10.4 ± 0.5 eV for krypton, and 8.6 ± 0.5 eV for xenon. These coincide, within experimental error, with the first excitation potentials, rather than the ionization potentials of the gases, indicating that in this range ionization proceeds via a two-step process involving the first excited electronic states of which the excitation step is rate controlling.

Publication: Physics of Fluids Vol.: 7 No.: 2 ISSN: 1070-6631

ID: CaltechAUTHORS:20110104-121347304

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Abstract: An approxhnate procedure is described for the theoretical calculation of the spectral absorption coefficient produced by bound-free and free-free transitions in plasmas containing polyelectronic atoms and ions. Our method of calculation is based on the assumption that only two ionized species make important contributions to the opacity and that these two ionic constituents are present in equal concentrations. The approximate formulas are shown to yield results that are in good accord with estimates based on detailed numerical computations for nitrogen.

Publication: AIAA Journal Vol.: 2 No.: 9 ISSN: 0001-1452

ID: CaltechAUTHORS:20110105-092119084

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Abstract: Measurements of conductivity have been made in a plasma composed of argon seeded with potassium vapor. The gas temperature was 2000°K; the pressure, 1 atm; and the potassium concentration was between 0.22 and 0.80 mole-percent. Conductivity values, calculated from a two-temperature model in which the energy dependence of the cross sections and radiation losses from the plasma are taken into account, agree well with experimental values. Measured values of the plasma temperature appear to be about 10% less than predicted values. Relaxation times for the conductivity in response to a step function change in the electric field were proportional to (n_e0l/σ_0E^2) and were a few tens of microseconds for a field strength in the range 3 to 10 v/cm. The ionization rate appeared to be limited primarily by the heating rate for the plasma, and the short relaxation times suggest that ionization occurs by a multistep process. Analysis of conductivity and light intensity data obtained during the transient period indicates that the electron temperature approaches its final value during the first few microseconds.

Publication: AIAA Journal Vol.: 2 No.: 8 ISSN: 0001-1452

ID: CaltechAUTHORS:20110105-090038619

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Abstract: The similarity groups for multicomponent, reacting gas mixtures with radiative energy transport are derived (Section I). The resulting relations are used to consider the feasibility if scaling for flow processes with radiative energy transport under highly simplified conditions (Sections 2 and 3). Next the scaling parameters are derived for radiant energy emission from isobaric and isothermal gases for arbitrary opacities and various spectral line and molecular band models (Section 4). Scaling parameters for radiant energy emission from isobaric but non-isothermal systems are discussed for arbitrary opacities and various spectral line and molecular band models under the restrictions imposed on the allowed temperature profiles for dispersion and Doppler lines by the Eddington-Barbier approximation (Section 5). Finally, we consider the radiative scaling properties for representative temperature profiles for both collision-broadened and Doppler-broadened line profiles on the basis if exact numerical calculations that we have performed for a rotational spectral line belonging to a molecular vibration-rotation band. (Section 6). It appears that simple scaling rules generally constitute a fair approximation for dispersion lines in non-isothermal systems but that corresponding relations apply to lines with Doppler contour only in the transparent gas regime.

ID: CaltechAUTHORS:20110127-120321921

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Abstract: The flow of a gas-particle mixture through a rocket nozzle is analyzed under the approximation that the particle slip velocity is small compared with the average mixture velocity, using one-dimensional gasdynamics, the Stokes drag law, and corresponding approximations for the heat transfer between solid and gas phase. The variational problem defining the pressure distribution giving the minimum impulse loss due to particle lag is formulated and solved for nozzles of prescribed mass flow, length, and of given exit pressure or area. The throat section of the optimum nozzle is considerably elongated and more gradual than that of the conventional nozzle. The velocity and temperature lags were much lower (about 1/3) in the throat region than those for the conventional nozzle. The impulse loss of the optimum nozzle was, however, reduced only about 30% below that of the conventional nozzle. It is concluded that contouring of the nozzle to improve gas-particle flow performance will result in only very modest gains. As a direct consequence, the impulse losses calculated herein for optimum nozzles can be used as a rough but convenient approximation for the impulse losses in conventional nozzles having the same area ratio or pressure ratio.

Publication: AIAA Journal Vol.: 1 No.: 12 ISSN: 0001-1452

ID: CaltechAUTHORS:20110104-120110913

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Publication: AIAA Journal Vol.: 1 No.: 11 ISSN: 0001-1452

ID: CaltechAUTHORS:20110104-112109595

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Abstract: Gas discharge rates through a de Laval nozzle from a closed chamber have been measured for Ar, He, and CO_2. The effective desorption rates from vessels containing sand and silica gel have also been determined at various temperatures by measuring the time rate of pressure decay in the chamber. The experimental data have been used, in conjunction with a theoretical expression for diffusion controlled desorption rates, to estimate heats of desorption from silica gel. Results have been obtained that are in approximate agreement with estimates made by other investigators using more conventional procedures.

Publication: Physics of Fluids Vol.: 6 No.: 11 ISSN: 1070-6631

ID: CaltechAUTHORS:20110104-113444432

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Abstract: Experimental measurements of the population temperature behind the reflected shock in a shock tube are presented. Emission from two wave length intervals of the OH^2∑ → ^2Π electronic band system was measured photoelectrically, the signals observed being generated by a narrow core of hot gas in the reflected shock region looking axially up the tube. The ratio of the rate of increase of intensity, per unit increase of optical depth, in the two spectral regions is a unique function of the temperature for a transparent gas. The linearity of the signal increase with time represents an experimental verification of the transparency and equilibrium of the test gas. In the temperature range of 3300-4300°K (M_s ~ 4), the measured spectroscopic temperature was in good agreement with the calculated equilibrium temperature, the estimated accuracy of the spectroscopic temperature being ± 75°K. A relaxation time of about 25 µsec was observed for the (2,2) and (3,3) vibration bands to reach statistical equilibrium with the lower (0,0) and (1,1) vibrational levels in the ^2∑ state from which the emission occurred.

Publication: Journal of Quantitative Spectroscopy and Radiative Transfer Vol.: 3 No.: 3 ISSN: 0022-4073

ID: CaltechAUTHORS:20110104-104430745

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Abstract: N/A

Publication: Journal of Quantitative Spectroscopy and Radiative Transfer Vol.: 3 No.: 3 ISSN: 0022-4073

ID: CaltechAUTHORS:20110104-110939383

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Abstract: The problem of determining the stability of high-frequency pressure oscillations in rocket combustion chambers is treated explicitly as a perturbation of the classical acoustics problem. On the basis of previous experimental results, the energy addition hy combustion is emphasized, and an analysis is developed for tbe stability of stationary pressure waves in chammers using either liquid or gaseous propellants. The formulation is for the three-dimensional case; computations are carried out in detail for a cylindrical chamber in which the mean velocity is parallel to the axis and varies only with axial position. The principal result is a formula for the imaginary part of the complex frequency associated with each of the natural modes of the chamber. This yields a single dimensionless group as a measure of the stability of individual chamber modes. Because of the present lack of sufficiently detailed experimental evidence, quantitative interpretation seems impossible, but qualitative agreement with observations can be demonstrated.

Publication: AIAA Journal Vol.: 1 No.: 5 ISSN: 0001-1452

ID: CaltechAUTHORS:20110104-082306038

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Abstract: N/A

Publication: Journal of Physical Chemistry Vol.: 67 No.: 3 ISSN: 0022-3654

ID: CaltechAUTHORS:20110106-105613945

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Abstract: Combustion chemistry is one of the oldest branches of chemical science. Among its pioneers must be counted Lavoisier, Bunsen, and others whose names belong among those of the founders of chemical science. That this close connection between combustion science and chemistry continues is well illustrated by the work of C. N. Hinshelwood and N. N. Semenov in elucidating chain reaction mechanisms, for which they shared the 1956 Nobel Prize. This work was at least partly motivated by difficulties in solving a classical problem in combustion science, viz., measurement of explosion limits for premixed gases in closed vessels.

Publication: Chemical and Engineering News Vol.: 41 No.: 2 ISSN: 0009-2347

ID: CaltechAUTHORS:20110106-080122631

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Abstract: N/A

Publication: Journal of Quantitative Spectroscopy and Radiative Transfer Vol.: 3 No.: 1 ISSN: 0022-4073

ID: CaltechAUTHORS:20110106-102523673

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Abstract: The geometrical interchange factors for radiative energy transfer have been evaluated for various conical configurations. A representative calculation has been carried out for the radiant energy transfer to a centrally located area element at the plane of intersection between two coaxial cones.

Publication: Journal of Quantitative Spectroscopy and Radiative Transfer Vol.: 3 No.: 1 ISSN: 0022-4073

ID: CaltechAUTHORS:20110106-133056508

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Publication: AIAA Journal Vol.: 1 No.: 6 ISSN: 0001-1452

ID: CaltechAUTHORS:20110104-093958992

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Abstract: N/A

ID: CaltechAUTHORS:20110208-103139308

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Abstract: Representative theoretical and experimental studies relating to the determination of gaseous radiation from isothermal systems are discussed. The following recently concluded studies are described: f-number measurements for OH behind shock fronts; a method for the direct determination of radiative and collisional life times of vibrationally excited, molecules; emissivity calculations for CO_2; emissivity calculations for a hydrogen plasma at temperatures up to about 10,000°K.

ID: CaltechAUTHORS:20110204-080105852

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Publication: Astronautics Vol.: 6 No.: 11 ISSN: 0097-7152

ID: CaltechAUTHORS:20110204-072536822

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Abstract: N/A

Publication: Review of Scientific Instruments Vol.: 33 No.: 10 ISSN: 0034-6748

ID: CaltechAUTHORS:20110106-152408147

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Abstract: The spectral absorption coefficients in electronic band systems of diatomic emitters have been computed in the past by models that may be described as 'the just overlapping line model' and a model 'utilizing a smeared out rotational structure'. Although the basic relations are obtained by utilizing somewhat different physical arguments, the resulting equations are, in fact, identical. Spectral absorption coefficients have been calculated for the NO γ-bands at 2000ºK by using the approximate theoretical relations. The calculated results are in good agreement with estimates derived by numerical calculations in which, however, the absorption coefficient data were averaged over intervals of 2000 cm^(-1).

Publication: Journal of Quantitative Spectroscopy and Radiative Transfer Vol.: 2 No.: 3 ISSN: 0022-4073

ID: CaltechAUTHORS:20110111-140517033

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Abstract: N/A

Publication: Journal of Quantitative Spectroscopy and Radiative Transfer Vol.: 2 No.: 3 ISSN: 0022-4073

ID: CaltechAUTHORS:20110106-131913150

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Abstract: The measurement of free-electron densities and collision frequencies in ionized-gas flows by a probing transverse microwave beam is described. Interpretation of the observed reflection and transmission coefficients and their phases is developed on the basis of an idealized plane wave-plane slab model, for which typical results are displayed. Application of the device and technique to a specific experiment—the buildup of ionization behind a strong shock in argon—is outlined. Effects of various departures of the microwave radiation patterns and flow configurations from the slab assumptions are discussed and examples evaluated.

Publication: Physics of Fluids Vol.: 5 No.: 6 ISSN: 0031-9171

ID: CaltechAUTHORS:JAHpof62

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Abstract: Quantitative spectroscopic experiments in shock tubes such as f-number measurements [for example (1)] require an absolute calibration of the optical system, monochromator, and detector. This is very often done for ultraviolet transitions around 3000-3500A with a tungsten strip filament lamp for which emissivities are known (2).

Publication: Applied Spectroscopy Vol.: 16 No.: 5 ISSN: 0003-7028

ID: CaltechAUTHORS:20110106-135634209

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Abstract: The heat of dissociation of N_2O_4 has been determined from measurements of the temperature dependence of the integrated absorption of NO_2 and N_2O_4 vibration-rotation bands. Results have been obtained that are in acceptable accord with the earlier estimate of Giauque and Kemp.

Publication: Journal of Chemical Physics Vol.: 36 No.: 1 ISSN: 0021-9606

ID: CaltechAUTHORS:20110111-133201065

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Abstract: The integrated intensities as a function of temperature have been measured for one NO_2 and for four N_2O_4 combination bands in the spectral region from 1 to 5µ. The temperature was varied from 50 to 100°C for the gas-phase studies and from 25 to 100°C for the liquid-phase experiments. In the spectral region from 5 to 15µ, integrated intensities at 25°C were measured for one NO_2 and for three N_2O_4 fundamental bands. Saturated vapors were used in all experiments; the optical depth was varied by using a series of spacers in a specially designed infrared absorption cell capable of handling both liquid and gas. Measured intensities for N_2O_4 combination bands in the liquid and gas phases were compared and found to differ by less than 16 per cent for three out of four combination bands studied; for the fourth band, the observed difference was about 50 per cent. Results for all of the combination bands investigated indicate that the integrated intensities vary approximately as l/T in the temperature range under consideration.

Publication: Journal of Quantitative Spectroscopy and Radiative Transfer Vol.: 2 No.: 1 ISSN: 0022-4073

ID: CaltechAUTHORS:20110111-134738438

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Abstract: Approximate relations are derived for determining under what conditions in two-phase flow heterogeneous two-body processes are expected to proceed as rapidly as the homogeneous three-body recombination reaction.

Publication: Astronautica Acta Vol.: 8 No.: 4 ISSN: 0004-6205

ID: CaltechAUTHORS:20110106-153626736

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Abstract: A perturbation analysis of the velocity and temperature lags in two-phase flow in rocket nozzles is developed and applied to the calculation of specific impulse and other performance characteristics of nozzles of arbitrary shape. Within the limitations of the one-dimensional flow approximation, the analysis is valid for distributions of particle diameters that are in a practical range.

ID: CaltechAUTHORS:20110121-101804833

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Abstract: N/A

Vol.: 3:1
ID: CaltechAUTHORS:20110125-105124057

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Abstract: A high‐speed valve has been designed for opening a deLaval nozzle in times less than 10^(−3) sec.

Publication: Review of Scientific Instruments Vol.: 32 No.: 11 ISSN: 0034-6748

ID: CaltechAUTHORS:20110111-104401338

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Abstract: The principles involved in the construction of a detector based on the use of an infrared maser (i.e., an iraser) are described for diatomic molecules. The use of iraser detectors holds promise for increasing detector sensitivity over more conventional detector devices for a selected number of diatomic emitters, namely, for molecules with relatively distant rotational line spacing such as HCl or HF. The iraser device may also be used as a multi-wavelength, coherent infrared source

Publication: Journal of Quantitative Spectroscopy and Radiative Transfer Vol.: 1 No.: 2 ISSN: 0022-4073

ID: CaltechAUTHORS:20110111-105512909

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Abstract: The nuclear rocket is potentially capable of much higher specific impulse than any chemically fueled rocket, because of the high energy content per unit mass of the fissionable material. While a part of this potential can be realized by use of a low molecular weight propellant heated by solid fuel plates, it seems clear that the full potential can be realized only if the fissionable material can be retained in gaseous form, and its fission energy transferred directly to the propellant.

Publication: Journal of the Aerospace Sciences Vol.: 28 No.: 9 ISSN: 0001-4966

ID: CaltechAUTHORS:20110111-103208503

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Abstract: One of the problems that must be faced in the development of direct-current plasma accelerators is that of boundary-layer growth on the electrode surfaces. These surfaces must be maintained at a somewhat lower temperature than is desirable in the bulk of the gas flow. The associated reduction in electrical conductivity near the electrode surface, together with the continuous current through the boundary layer, may result in greatly augmented Joule heating near the surface, and increased heat transfer. This phenomenon is treated within the framework of boundary layer theory. It is found that similar solutions for the thermal and viscous boundary layers exist for a certain class of accelerated flows in which the velocity varies as a power of the streamwise coordinate. The solutions show that the heat-transfer rate at Mach numbers near unity may be as much as ten times that which would be expected for a normal boundary layer. At higher Mach numbers, the similarity is not precisely valid; however, the analysis indicates qualitatively that a stagnation enthalpy overshoot may occur in the high-temperature portion of the boundary layer as a result of the electromagnetic acceleration.

Publication: Journal of the Aerospace Sciences Vol.: 28 No.: 8 ISSN: 0001-4966

ID: CaltechAUTHORS:20110111-095750483

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Abstract: N/A

Publication: Journal of the Optical Society of America Vol.: 51 No.: 4 ISSN: 0030-3941

ID: CaltechAUTHORS:20110106-072930687

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Abstract: Recent analytical work by Bray indicates that single element, chemically reacting systems, e.g., H_2 ⇋ 2H, may suddenly freeze their composition at some point in a high speed nozzle and then remain at fixed composition throughout the remainder of the expansion. This sudden freezing or "quenching" phenomenon was also apparent in some theoretical calculations reported by Hall et al. and has been verified experimentally by Wegener. It is the purpose of this note to show qualitatively how Bray's sudden-freezing criterion is related to engine size by the scale factor for geometrically similar engines having n on equilibrium nozzle flows and in which a propellant system is used for which Bray's analysis is valid.

Publication: ARS Journal Vol.: 31 No.: 3 ISSN: 0097-4056

ID: CaltechAUTHORS:20110111-082616427

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Abstract: Solutions are obtained for the propagation of plane electromagnetic waves parallel to a gradient of free electron density, in the form of complex Airy functions. Reflection and transmission coefficients are derived for normal incidence on a linear "ramp" of electron density connecting a uniform dielectric gas with a uniform ionized gas, as functions of ramp length and propagation exponent of the latter. Machine evaluations of typical cases of physical interest are displayed and discussed. Similar study is made of two‐stage ramps of variable proportions, intended as second approximations to smooth profile transition zones. In each case, the reflection and transmission coefficients are found to depend strongly on ramp width over a range of several tenths of a wavelength, then to oscillate mildly toward the asymptotic values predicted from a WKB‐type approximation. The results are less sensitive to the detailed shape of the electron density profile. Propagation through a finite slab of ionized gas bounded on each side by such linear transition zones is formulated and evaluated for typical cases. Asymptotic approximations for the linear ramp problem are found to be inadequate to cover the entire range of interest. The neglect of variation in collision frequency through the transition is discussed and justified for a broad class of equilibrium profiles.

Publication: Journal of Applied Physics Vol.: 32 No.: 1 ISSN: 0021-8979

ID: CaltechAUTHORS:20110105-113557287

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Publication: Symposium (International) on Combustion Vol.: 8 No.: 1 ISSN: 0082-0784

ID: CaltechAUTHORS:20110110-112613040

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Abstract: The discrepancies in the stability limits based on the characteristic time τ_0, which were observed when burner families of different geometry were compared in Section III, have been explained by use of the residence time concept. Thus, the present experiments with burners of varying geometry have clearly shown that the residence time in the mixing zone is the proper correlation parameter for the stability limits. This parameter is not affected by the great variation the flow field encounters when the slot ratio is changed over a wide range. The experiment also has shown that the most satisfactory correlation is obtained by use of a residence time for the material in the inner part of the mixing zone. The small slot-ratio burner shows several interesting similarities with the can-type combustion chamber. The primary similarity lies in the structure of the mixing zone, because there is good reason to believe that the mixing zone in the can burner also is covered by a flow of fresh mixture for only a short distance. Hence, the successful correlation of stability limits for small slot-ratio burners, shown here, strongly suggests that the mechanism of governing importance for flame stabilization in can burners is the same as that for bluff-body flame stabilization.

Publication: Symposium (International) on Combustion Vol.: 8 No.: 1 ISSN: 0082-0784

ID: CaltechAUTHORS:20110124-110529826

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Abstract: N/A

Publication: Symposium (International) on Combustion Vol.: 8 No.: 1 ISSN: 0082-0784

ID: CaltechAUTHORS:20110110-095214561

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Abstract: N/A

Publication: Symposium (International) on Combustion Vol.: 8 No.: 1 ISSN: 0082-0784

ID: CaltechAUTHORS:20110110-115025686

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Abstract: The Theory of Steady, One-dimensional, Laminar Flame Propagation for One-step Chemical Reactions. The present status of the theory of one-dimensional, steady, laminar flame propagation for one-step chemical reactions is reviewed with particular emphasis on methods of solution and on the physical processes that dominate observable results.

Publication: Astronautica Acta Vol.: 7 No.: 2-3 ISSN: 0004-6205

ID: CaltechAUTHORS:20110111-093335267

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ID: CaltechAUTHORS:20110204-094751496

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Publication: Annual Review of Physical Chemistry Vol.: 11ISSN: 0066-426X

ID: CaltechAUTHORS:20110105-105940018

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Publication: Physics Today Vol.: 13 No.: 7 ISSN: 0031-9228

ID: CaltechAUTHORS:20110105-102637019

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Abstract: N/A

Publication: Journal of the Optical Society of America Vol.: 50 No.: 6 ISSN: 0030-3941

ID: CaltechAUTHORS:20110111-150128667

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Abstract: A simplified combustion model, which is motivated by available performance studies on the diverging rocket reactor, has been used as basis for an engine performance evaluation. Comparison with conventional rocket configurations shows that an upper performance limit for the diverging reactor is comparable with performance estimates for engines using an adiabatic work cycle. Development of the diverging reactor for engine applications may, however, offer some advantages for very hot, high-energy, propellant systems.

ID: CaltechAUTHORS:20110112-101905761

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Abstract: N/A

Publication: Journal of Chemical Physics Vol.: 32 No.: 2 ISSN: 0021-9606

ID: CaltechAUTHORS:20110111-143329050

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Publication: Journal of Chemical Physics Vol.: 32 No.: 2 ISSN: 0021-9606

ID: CaltechAUTHORS:20110111-142123659

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Abstract: One of the problems that must be faced in the development of plasma accelerators is the growth of boundary layers upon the accelerator walls. The boundary-layer effects may be important not only from a heat-transfer standpoint, but because of the displacement effect on the main flow. For the steady-flow accelerator utilizing crossed electric and magnetic fields, such as that discussed by Resler and Sears, a very interesting situation may develop upon the walls that are perpendicular to the current flow. Since the wall must generally be cool, there is a tendency for the plasma conductivity near the wall to be lower than that in the relatively hot free stream. Consequently, the Joule heating associated with the continuous current will be highest in the neighborhood of the wall. This increased heating may produce an abnormal thermal boundary layer and, quite possibly, a severe heat-transfer condition.

Publication: Journal of the Aerospace Sciences Vol.: 27 No.: 2 ISSN: 1936-9999

ID: CaltechAUTHORS:20110112-113100379

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Abstract: In the course of investigating boundary-layer flow in continuous plasma accelerators with crossed electric and magnetic fields, it was found advantageous to have at hand simple closed-form solutions for the magneto-gas dynamic flow in the duct which could serve as free-stream conditions for the boundary layers. Nontrivial solutions of this sort are not available at present. and in fact, as in the work of Resler and Sears, the variation of conditions along the flow axis must be obtained through numerical integration. Consequently, some simple solutions of magneto-gasdynamic channel flow were sought, possessing sufficient algebraic simplicity to serve as free-stream boundary conditions for analytic investigations of the boundary layer in a physically reasonable accelerator. In particular, since the cooling of the accelerator tube is likely to be an important physical problem because of the high gas temperatures required to provide sufficient gaseous conductivity, channel flow with constant temperature appears interesting. Some simple algebraic solutions for the case of a constant temperature plasma are developed in the following paragraphs.

Publication: Journal of the Aerospace Sciences Vol.: 27 No.: 1 ISSN: 1936-9999

ID: CaltechAUTHORS:20110113-074847570

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Abstract: Unstable combustion in solid propellant rocket motors is characterized by high frequency chamber pressure oscillations, often accompanied by changes in the mean burning rate. Experiments with casebonded, cylindrically perforated motors using a polysulfide, ammoniumperchlorate propellant were reproducible as a result of careful manufacturing control and extended propellant curing time. In these motors the oscillations were in the fundamental standing tangential mode and were accompanied by increases in the average burning rate. At sufficiently high pressure levels all firings were stable. Reduction of the operating level led to mild instability. A sufficient further reduction produced a sudden change to maximum instability. Continued reduction in pressure level from this point resulted in a gradual decrease in the degree of instability but it could not be experimentally verified that a low pressure stable region existed. The levels at which these events took place were frequency dependent and generally increased as the tangential frequency was reduced. At a given operating leve1, the instability became less severe when the grain length was reduced below a critical value. Increasing the length above the critical value did not affect the level at which the motors became stable. The pressure levels for stability and for maximum instability moved to lower values with decreases in the propellant grain temperature in a manner not entirely accounted for by the effect of grain temperature on burning rate. Stable, mildly unstable and severely unstable operation was observed throughout the range -80°F to 180°F. The maximum instability decreased with grain temperature.

No.: 1
ID: CaltechAUTHORS:20110111-110838368

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ID: CaltechAUTHORS:20110204-101842249

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Abstract: N/A

Publication: Journal of the Aerospace Sciences Vol.: 27 No.: 7 ISSN: 0001-4966

ID: CaltechAUTHORS:20110112-095904098

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Abstract: The theory of three-dimensional flow in axial turbomachines was extended to include the effects of variable hub and tip radii such as occur in the entrance stages of conventional axial flow compressors. and, to a larger extent, in mixed flow compressors. The problem is simplified by assuming an infinite number of infinitely thin blades in each blade row, so that axially symmetric fluid motion results. The effect of variable hub and tip radii of the annulus walls is investigated when the tangential velocities are small but arbitrary, and when they are large but of special form. The combined effect of heavily loaded inlet guide vanes and variable hub radius is also investigated for the case in which the inlet guide vanes impart a motion very nearly of the solid body type. The boundary conditions for the variable hub radius require linearization, thus restricting the magnitude of perturbation to be induced by the wall. Finally, the effect of a loaded blade row placed behind the inlet guide vane is determined. The local axial and tangential velocities induced by the variable wall radius were found to be of the same general magnitude as the velocities induced by a normal rotor or stator blade row. Although the forms of the solutions are somewhat complex for routine application in turbomachine design. a sufficiently simple approximate result is obtained for one case and it is indicated how the method of approximation may be extended.

ID: CaltechAUTHORS:20151109-120157425

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Abstract: In his excellent analysis of electrical measurements in shock tube flows, Hollyer(1) has demonstrated certain pitfalls in the application of conventional Langmuir probe techniques to the evaluation of charge densities in the moving stream of hot gas confined within the tube walls. The purpose of this note is to describe somewhat similar experiments which illustrate other eccentricities in probe behavior under these conditions.

Publication: Physics of Fluids Vol.: 2 No.: 4 ISSN: 1070-6631

ID: CaltechAUTHORS:JAHpof59

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Abstract: An experimental study has been carried out for the purpose of verifying theoretical predictions concerning the relations between total absorptivities and total emissivities for transparent gases. The experimental conditions have been designed in such a way as to permit a direct check of theoretical relations derived for (a) nonoverlapping dispersion lines and (b) spectral lines with sufficient pressure broadening to permit neglect of the rotational fine structure. A comparison between the emissivities derived from absorptivity measurements and emissivities calculated from the spectroscopic constants of CO shows a good agreement (within 20% for most of the temperature range). The apparatus for the measurement of total gas absorptivities is described. Results for total absorptivities of carbon monoxide measured at temperatures between 300 and 500°K are given and total emissivities have been calculated in the temperature range of 300 to 1600°K. The range of total gas pressure is 0 to 515 psia.

Publication: Journal of Applied Physics Vol.: 30 No.: 6 ISSN: 0021-8979

ID: CaltechAUTHORS:20110113-104239681

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Abstract: The equations for conservation of mass, momentum, and energy are derived for a set of independent, coexistent continua obeying the laws of dynamics and thermodynamics. The idea of a control volume and a control surface for each continuum is used in the analysis. The derived results are practically identical with relations obtained previously by Th. von Kármán. A direct comparison is conducted between the continuum theory results and those obtained from kinetic theory by assuming that, for each of the species, the kinetic theory definitions apply. It is found that the new terms appearing in the conservation equations derived from continuum theory are precisely those which are required to make these equations identical with the results obtained from the kinetic theory of multicomponent, reacting gas mixtures. However, the continuum theory forms of the equations are not useful because they require knowledge of the transport properties for individual species in the mixture.

Publication: Quarterly of Applied Mathematics Vol.: 17 No.: 1 ISSN: 0033-569X

ID: CaltechAUTHORS:20110125-094239088

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Abstract: N/A

Publication: Journal of Applied Physics Vol.: 30 No.: 1 ISSN: 0021-8979

ID: CaltechAUTHORS:20110113-073257572

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Abstract: Diffusion in vortex flows is considered as a simple case of the more general problem of diffusion in flows with large pressure gradients normal to the principal flow direction. Two examples are considered. In the first the two gases are assumed electrically neutral, and pressure and concentration diffusion are equally important. In the second, diffusion of the electrons of an ionized gas is studied. Diffusion due to electromagnetic body forces is of equal importance with pres sure diffusion in this case, while concentration diffusion is negligible. It is found in the first example that the ratio of the radial mass flow of one species to the total radial mass flow is a characteristic value of the diffusion equation. The rates of diffusion are such that significant separation of the isotopes of uranium should be possible in vortices with supersonic tangential velocities. The radial pressure gradient leads to a radial electric field in the second example. A solution is obtained for the case of zero currents. By means of a perturbation technique, the solution is then extended to the case of small currents and induced fields.

ID: CaltechAUTHORS:20110204-103536323

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Abstract: Experimentally determined pressure profiles in a diverging reactor have been used to estimate effective mean drop diameters and size distributions at the injector end. The available results may be correlated in terms of two simplified models using (a) a uniform mean drop size for the spray and (b) a generalized size distribution of the Rosin-Rammler type. Mean drop sizes of the order of 5 to 10 microns, and effective overall reaction orders between ⅓ and 2 are obtained if the phenomenological burning rate law familiar from single droplet studies is used for heterogeneous burning in bipropellant LOX-RP1 mixtures.

Publication: Combustion and Flame Vol.: 3 No.: 3 ISSN: 0010-2180

ID: CaltechAUTHORS:20110121-094732263

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Abstract: Theoretical expressions have been derived for the relations between gas absorptivities and emissivities for the limit of zero optical depth and for the following models of vibration-rotation bands: bands with constant average absorption coefficients and well-defined widths; just-overlapping spectral lines; non-overlapping dispersion lines with constant collision half-width and either regular line spacing or with lines of equal intensity; randomly distributed spectral lines with dispersion contom; non-overlapping Doppler lines with either regular line spacing or with lines of equal intensity; randomly distributed Doppler lines for a special {unrealistic} assumption relating to the temperature dependence of the effective mean line spacing; non-overlapping spectral lines with combined Doppler and collision broadening, constant collision half-width and either regular line spacing or with lines of equal intensity. The theoretical formulae have been shown to provide a good correlation for the available experimental data on CO_2, H_2O and CO.

ID: CaltechAUTHORS:20110124-084010424

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Abstract: It is demonstrated that the multicomponent diffusion equation can be derived from elementary kinetic-theory considerations without employing the results of the mathematical theory of nonuniform gases. By using the approach described by Furry, elementary expressions for the binary diffusion coefficients are also obtained. The advantage of the concept of the equivalence of partial pressure gradients and momentum gradients is thereby emphasized.

Publication: American Journal of Physics Vol.: 26 No.: 7 ISSN: 0002-9505

ID: CaltechAUTHORS:20110113-131911310

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Abstract: An experimental and analytical investigation was undertaken to determine the influence of asymmetric inlet flows on the performance of axial turbomachinery. Overall performance measurements and circumferential surveys of total pressures, velocities and flow angles were obtained in an axial compressor with inlet disturbances covering approximately 25% of the inlet annulus area. Three configurations were tested to find the principal effects in a single rotor, a complete stage and a multi-stage machine. A two-dimensional linearized theory was developed which includes the effect of losses and leaving angle deviations in the blade rows. The analysis may also be applied to propagating stall so that this theory allows a unified treatment of the two phenomena. Introducing the inlet disturbances did not alter the two-dimensional character of the flow in the compressor. Considerable attenuation of the disturbances occurred through a single rotor and the disturbances were almost completely attenuated downstream of a three stage configuration. The mutual interference of the blade rows with small axial spacing was responsible for significant stator losses. The overall performance deteriorated primarily due to losses occurring in the blade rows. In the three configurations tested the inception of propagating stall, as based on the mean flow rate, was essentially unchanged. The theory qualitatively described the flow behavior and a simple application of the theory would give an estimate of the blade forces.

ID: CaltechAUTHORS:20151105-165306203

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Abstract: N/A

Publication: Journal of Chemical Physics Vol.: 28 No.: 5 ISSN: 0021-9606

ID: CaltechAUTHORS:20110113-133050026

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Abstract: The conservation equations for multicomponent reacting gas mixtures are generally given only in Cartesian or orthogonal curvilinear coordinate systems. Actually, the conservation equations are easily expressed in an arbitrary coordinate system. We present the general equations in tensor notation and then indicate the simplifications which arise for orthogonal curvilinear coordinates.

Publication: Journal of the Aeronautical Sciences Vol.: 25 No.: 5 ISSN: 1936-9956

ID: CaltechAUTHORS:20110113-111427872

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Abstract: There has recently been some discussion on the use of the model of a wrinkled laminar flame for an approximate description of turbulent flame structure. In particular, Summerfield has claimed that some of his observations contradict theoretical predictions based on the use of this model. 4 It is the purpose of the following discussion to clarify 150me of the consequences of the wrinkled laminar flame model.

Publication: Jet Propulsion Vol.: 27 No.: 10 ISSN: 0095-8751

ID: CaltechAUTHORS:20110114-103237722

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Abstract: The scaling procedures of Penner and Tsien, of Crocco and of Barrère have been generalized by using the assumption that the mean drop size is proportional to the product of powers of the Weber number and the Reynolds number, together with the hypothesis that the total conversion time varies as a power (usually the second) of the drop diameter. The results obtained for the steady aero thermochemistry and for unstable motor operation (low-frequency and high-frequency oscillations) are shown to reduce to previously published rules when suitable simplifying assumptions are made.

Publication: Combustion and Flame Vol.: 1 No.: 2 ISSN: 0010-2180

ID: CaltechAUTHORS:20110118-105514911

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Abstract: FLAME stabilization is of importance in the practical design of ramjets and afterburners. It has been studied extensively in recent years, particularly with reference to bluff-body flame-holders. In the present survey we describe the investigations relating to flame holding by bluff bodies as well as new techniques (e.g.,. flame holding by the use of reverse jets) which may prove to be of practical importance in new engine configurations. In Section II we consider the flow field downstream of a bluff-body flame-holder which includes the recirculation zone behind the body and a region of flame spreading farther downstream. Explicit reference is made to crucial experiments which illustrate the nature and magnitude of the velocity field, the physical extent, the temperature, and the gas composition of the recirculation zone. Experimental studies and theoretical predictions of the angle of flame spreading, as well as some observations on unstable flow and the onset of blowoff, will be reviewed. The variation of blowoff velocity with flame-holder design, pressure, and mixture composition is considered briefly in Section III both for single and for adjacent bluff bodies. Also included is a summary of results for blowoff velocities obtained with a reverse-jet flame-holder and with wall recesses. Theoretical studies on the mechanism of flame stabilization form the subject of Section IV. We shall indicate the points on which various proposed models agree and disagree with experiment and attempt to formulate a composite description which is consistent with most of the currently available experimental data both for bluff-body and for reverse-jet flameholders.

Publication: Applied Mechanics Reviews Vol.: 10 No.: 6 ISSN: 0003-6900

ID: CaltechAUTHORS:20110203-143842451

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Abstract: Approximate analytic expressions are obtained for the "effective band widths" and emissivities of diatomic molecules at elevated pressures. The absorptivities of molecular vibration‐rotation bands are evaluated for radiation emitted by similar molecular vibration‐rotation bands and for radiation emitted by blackbodies. The results obtained for the absorptivity calculations compare favorably with available empirical correlations for H_2O. The postulated model does not apply to CO_2 and, therefore, no satisfactory theoretical formula has been derived for the absorptivities of this molecule. The appendix (by A. Thomson) is devoted to a critical examination of the limits of validity of the effective band‐width concept for different molecules.

Publication: Journal of Applied Physics Vol.: 28 No.: 5 ISSN: 0021-8979

ID: CaltechAUTHORS:20110113-141408696

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Abstract: N/A

Publication: Jet Propulsion Vol.: 27 No.: 5 ISSN: 0095-8751

ID: CaltechAUTHORS:20110113-144556140

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Abstract: Absolute intensities have been measured for three of the ultraviolet γ bands of NO. The corresponding electronic absorption oscillator strength is estimated to be 0.0024±0.0004.

Publication: Journal of Chemical Physics Vol.: 26 No.: 4 ISSN: 0021-9606

ID: CaltechAUTHORS:20110113-140209278

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Abstract: A critical summary is presented of recent theoretical studies concerning similarity analysis and the scaling of liquid-fuel rocket engines. On the basis of this work, some suggestions are offered for an experimental program which has as its objective the development of rational scaling procedures.

Publication: Jet Propulsion Vol.: 27 No.: 2 ISSN: 0095-8751

ID: CaltechAUTHORS:20110113-134244485

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Abstract: The present analysis considers ignition and combustion in the laminar boundary layer of a constant temperature, semi-infinite flat plate. A one step unopposed "global" reaction following any order reaction kinetics with temperature dependence according to the Arrhenius rate law is assumed. For the case where the Prandtl and Schmidt numbers are equal, the determination of a similarity function relating the species concentrations to the local temperature greatly simplifies the analysis. The similarity function is shown to be equal to the dimensionless streamwise velocity when the Prandtl and Schmidt numbers are both equal to unity. A general analytic solution for the N'th approximation to the temperature and concentration profiles in the reacting laminar boundary layer is obtained. For all values of plate temperature and free stream velocity, it is found that for some finite distance downstream of the leading edge the plate acts as a heat source; at all points downstream of this characteristic length, however, the plate acts as a heat sink. This characteristic length is closely related to the "flame attachment distance" and is indicative of the minimum plate length required to stabilize a laminar deflagration flame. Although the characteristic length is always finite, it is found that for plate temperatures below a critical threshold band, this length increases so enormously that name attachment cannot occur on physical apparatus of reasonable finite dimension. Inasmuch as the classical boundary layer assumptions are invalidated in the immediate region of flame attachment, the complete development of the laminar flame front cannot be obtained within the framework of the present boundary layer type analysis.

Vol.: 10
ID: CaltechAUTHORS:20110113-152309073

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Abstract: Of the various unsteady flows that occur in axial turbomachines certain asymmetric disturbances, of wave length large in comparison with blade spacing, have become understood to a certain extent. These disturbances divide themselves into two categories: self-induced oscillations and forced disturbances. A special type of propagating stall appears as a self-induced disturbance; an asymmetric velocity profile introduced at the compressor inlet constitutes a forced disturbance. Both phenomena have been treated from a unified theoretical point of view in which the asymmetric disturbances are linearized and the blade characteristics are assumed quasi-steady. Experimental results are in essential agreement with this theory wherever the limitations of the theory are satisfied. For the self-induced disturbances and the more interesting examples of the forced disturbances, the dominant blade characteristic is the dependence of total pressure loss, rather than the turning angle, upon the local blade inlet angle.

ID: CaltechAUTHORS:20110204-111252490

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Abstract: N/A

Publication: Journal of Chemical Physics Vol.: 25 No.: 5 ISSN: 0021-9606

ID: CaltechAUTHORS:20110118-101201095

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Abstract: N/A

Publication: Jet Propulsion Vol.: 26 No.: 9 ISSN: 0095-8751

ID: CaltechAUTHORS:20110118-095615981

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Abstract: Some of the unique features of thermonuclear power plants and the essential problems in the technical design of such plants are discussed in this paper. The thermonuclear reaction rate for the fusion of deuterium is calculated on the basis of a similar analysis published by Gamow and Teller. The pressure, temperature, and minimum dimensions of the necessary reaction chamber are determined largely by consideration of reaction quenching and energy loss near the walls. Results are presented for the power output and the efficiency of a power station utilizing the deuterium fusion reaction. The comment by Greenstein that follows this paper deals particularly with the difficult problem of calculating the reaction quenching and energy loss rates at the walls.

Publication: Jet Propulsion Vol.: 26 No.: 7 ISSN: 0095-8751

ID: CaltechAUTHORS:20110118-092852136

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Abstract: N/A

Publication: Journal of Chemical Physics Vol.: 24 No.: 6 ISSN: 0021-9606

ID: CaltechAUTHORS:20110118-083257648

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Abstract: An experimental investigation was made of the behavior of a small two-dimensional combustion chamber, burning a uniform mixture of air and fuel vapor under conditions of high-frequency oscillation or screech. Measurements were made of the limits of stable screech, the amplitude and frequency of pressure oscillations over a wide range of mixture ratio, inlet air temperature, and combustor flow rate. Spark schlieren photographs and high-speed motion pictures taken of the combustion process showed, in agreement with other investigations, that the high-frequency oscillation is accompanied by vortices shed periodically from the flameholder lip with the same frequency as the oscillation. The following mechanism of exciting the oscillations is suggested. A mode of transverse oscillation is excited as the result of periodic transport of combustible material, associated with the vortices, into the hot wake of the flameholder. The vortices, in turn, are generated at the flameholder lips by the fluctuating transverse velocity. When the ignition time delay lies in the proper range, the phase relationship between oscillations in transverse velocity and combustion intensity is such that the oscillation is amplified.

Publication: Jet Propulsion Vol.: 26 No.: 6 ISSN: 0095-8751

ID: CaltechAUTHORS:20110114-111632665

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Abstract: The performance of a modified peak-holding optimalizing control system depends in part on the ability of the controller to detect the input signal frequency component in the output of the controlled system. This paper describes several techniques that may be used for detecting this component and analyzes one of them in great detail. The subject of the detailed analysis is the method of filtering through cross-correlation. A statistical analysis is also carried out in order to demonstrate the efficiency of this method.

Publication: Jet Propulsion Vol.: 26 No.: 6 ISSN: 0095-8751

ID: CaltechAUTHORS:20110118-084749497

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Abstract: The study of combustion processes is in a sufficiently early stage so that there is no strong connection between combustion theory and the technology of combustion chamber development. To clarify such a connection is the principal task of workers engaged in establishing combustion as an engineering science. The equations of aerothermochemistry are reviewed for the case in which temperature and composition gradients are small. Solutions have been obtained in very few cases and under very restrictive circumstances; most detailed considerations are restricted to the plane laminar flame front. The current situation in the theory of plane laminar flames is discussed. The few extensions that have been made to two-dimensional problems are then described. Several directions of work which would assist in establishing theoretical results approaching technological requirements appear possible.

Publication: Journal of the Aeronautical Sciences Vol.: 23 No.: 5 ISSN: 1936-9956

ID: CaltechAUTHORS:20110118-074645504

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Abstract: The problems of heat transfer in turbulent shear flow along a smooth wall are discussed from the point of view of von Karman's well-known 1939 paper on the analogy between fluid friction and heat transfer. Methods for extending the analysis to higher Prandtl Numbers are suggested.

Publication: Journal of the Aeronautical Sciences Vol.: 23 No.: 5 ISSN: 1936-9956

ID: CaltechAUTHORS:20110118-081648471

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Abstract: Experiments have been performed in order to measure the mass rate of consumption of single drops of liquid fuel suspended on a quartz filament and burning under various ambient conditions. The influence of increased oxidizer concentration, increased pressure, and elevated temperature in the surrounding atmosphere on mass burning rate has been studied. Comparison is made with theoretical calculations based on the concept of a heterogeneous diffusion flame, with burning rate controlled by heat and mass transfer. The influence of forced convection on burning rate and extinction of burning has also been investigated.

Publication: Jet Propulsion Vol.: 26 No.: 3 ISSN: 0095-8751

ID: CaltechAUTHORS:20110114-135926585

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Abstract: Experiments have been conducted for the determination of the evaporation constant and flame shapes of two and of five closely spaced droplets burning in air. Droplets of approximately the same and of different diameters were used at various distances between the droplet centers. The apparent flame shape, which was observed only for n-heptane droplets, changes very little during burning. The square of the droplet diameter decreases linearly with time for fixed spacing between droplet centers, at least within the experimental limits of accuracy. In general, the average evaporation constant for two droplets, K', must be assumed either to vary continuously during burning or else to be a function of average initial drop diameter, D^0. The change of K' with time corresponds to the second derivative in plots of the square of the diameter vs. time. These second derivatives are not defined in our work because of unavoidable scatter of the experimental data. Attempts at understanding the observed results by considering published theories for single droplets, as well as groupings obtained from dimensional analysis, have been unsuccessful. It appears that the diffusion model for the heterogeneous burning of single fuel droplets will require serious revision and extension before the burning of droplets arrays and sprays can be understood quantitatively. Furthermore, the effective value of K' for a spray probably depends not only on the fuel-oxidizer system but also on the injection pattern. For this reason additional studies had best be carried out under conditions corresponding to those existing in service models.

Publication: Jet Propulsion Vol.: 26 No.: 3 ISSN: 0095-8751

ID: CaltechAUTHORS:20110114-142438756

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Abstract: A method is described for making estimates of the total emissivity of hydrogen in the temperature and pressure ranges where hydrogen atoms predominate under equilibrium conditions. For a typical geometrical depth of 50 cm, and temperatures of the order of 12 500ºK and higher, with pressures of the order of 100 atmos and higher, the emissivity approaches unity (є ≳ 0.95), while for temperatures of the order of 9500ºK and lower, with pressures of the order of 10 atmos and lower, the emissivity approaches zero (є ≾ 0.05). The variations of the emissivity between these approximate limits are shown graphically as functions of temperature and pressure with the geometrical depth set at 50 cm. The variation of the emissivity with geometrical depth is also shown graphically at 12 600ºK and 20 atmos.

Publication: Journal of Applied Physics Vol.: 27 No.: 2 ISSN: 0021-8979

ID: CaltechAUTHORS:20110114-132802630

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Abstract: A method is described for making estimates of the total emissivity of hydrogen in the temperature and pressure ranges where hydrogen atoms predominate under equilibrium conditions. For a typical geometrical depth of 50 cm, and temperatures of the order of 12 500ºK and higher, with pressures of the order of 100 atmos and higher, the emissivity approaches unity (є≳0.95), while for temperatures of the order of 9500ºK and lower, with pressures of the order of 10 atmos and lower, the emissivity approaches zero (є≾0.05). The variations of the emissivity between these approximate limits are shown graphically as functions of temperature and pressure with the geometrical depth set at 50 cm. The variation of the emissivity with geometrical depth is also shown graphically at 12 600ºK and 20 atmos.

Publication: Journal of Applied Physics Vol.: 27 No.: 2 ISSN: 0021-8979

ID: CaltechAUTHORS:20110126-072952200

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Abstract: The method of W. R. Hawthorne for the calculation of the secondary vorticity is generalized for compressible flow. It is shown that in the linearized theory (small vorticity) the influence of compressibility upon the secondary vorticity is due to (1) the entropy gradient in the approaching flow and (2) the compression of the fluid during the turning of the flow. The analysis is applied to the secondary vorticity which generates in a cascade or bend if the approaching flow has a boundary layer with a Prandtl Number equal to unity and has been developed along an insulated wall.

Publication: Journal of the Aeronautical Sciences Vol.: 23 No.: 1 ISSN: 1936-9956

ID: CaltechAUTHORS:20110118-073556293

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Vol.: 1
ID: CaltechAUTHORS:20110118-102541769

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Abstract: The physical principles involved in conventional absolute intensity measurements are reviewed. Experimental difficulties rule out the use of extrapolation techniques for some spectral transitions. For this reason it is of interest to re-examine the possibility of using total absorption measurements, in conjunction with the curves of growth, for making intensity estimates. Extrapolation methods yield results which are independent of spectral line shape. Use of the curves of growth, on the other hand, implies the assumption that the line contour can be described by combined Doppler and Lorentz broadening. The curves of growth permit a unique correlation between total absorption and f-value either for spectral lines with pure Doppler broadening or for pure collision broadening. Furthermore, a simple experimental procedure can be devised for estimating both the absolute intensity and the spectral line profile on the basis of single-path and multiple-path absorption measurements. The suggested procedure involves absorption' measurements for optical densities (path lengths) under conditions in which the integrated fractional absorption is a relatively sensitive function of spectral line shape. Representative calculations referring to utilization of the proposed method have been carried out for spectral lines belonging to the ^2∑→^2II transitions, (0,0)-band, of OH, and also for lines belonging to the fundamental vibration-rotation spectrum of CO.

Publication: Journal of Chemical Physics Vol.: 23 No.: 12 ISSN: 0021-9606

ID: CaltechAUTHORS:20110119-112148460

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Abstract: N/A

Publication: Jet Propulsion Vol.: 25 No.: 9 ISSN: 0095-8751

ID: CaltechAUTHORS:20110119-111358754

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Abstract: The peak-holding optimalizing control is analyzed under the assumption of first-order input linear group and output linear group. Design charts are constructed for determining the required input drive speed and the consequent hunting loss with specified time constants of the input and output linear groups, the hunting period, and the critical indicated difference for input drive reversal.

Publication: Journal of the Aeronautical Sciences Vol.: 22 No.: 8 ISSN: 1936-9956

ID: CaltechAUTHORS:20110119-105101344

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Abstract: Recent experimental observations on compressors, in particular those of Rannie and Iura, have clarified some features of the phenomenon of stall propagation. Using these observations as a guide, the process of stall in an airfoil cascade has been characterized by a static pressure loss across the cascade which increases discontinuously at the stall angle, the turning angle being affected in only a minor way. Deductions from this simple model yield the essential features of stall propagation such as dependence of the extent of stalled region upon operating conditions, the pressure loss associated with stall, and the angular velocity of stall propagation. Using two-dimensional approximation for a stationary or rotating blade row, free from interference of adjacent blade rows, extent of the stalled region, the total pressure loss and stall propagation speed are discussed in detail for a general cascade characteristic. Employing these results, the effect of stall propagation upon the performance of a single-stage axial compressor is illustrated and the mechanism of entering the regime of stall propagation is discussed. The essential points of the results seem to agree with experimental evidence.

Publication: Journal of the Aeronautical Sciences Vol.: 22 No.: 8 ISSN: 1936-9956

ID: CaltechAUTHORS:20110119-110427631

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Abstract: Computations are presented for the variation of vibrational excitation probabilities with temperature for mixtures of O_2 and N_2, and of HF and H_2. The values of six different excitation probabilities in each mixture are reported for temperatures up to 3000ºK. For each of the probabilities there is a lower temperature limit given, below which the theory of Schwartz, Slawsky, and Herzfeld, which is used here, is not applicable. Using the results for H_2-HF mixtures, we present some considerations which suggest that the expansion through the de Laval nozzle for representative H_2-F_2 rocket motors may be taken as vibrational near-equilibrium flow.

Publication: Journal of Chemical Physics Vol.: 23 No.: 7 ISSN: 0021-9606

ID: CaltechAUTHORS:20110119-103028935

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Abstract: A thermal theory of laminar flame propagation for hydrocarbon-oxygen flames is described. The method of analysis follows the earlier work of von Karman and his collaborators. In Section III the problem is formulated and approximate solutions are given for hydrocarbon-oxygen flames, assuming a second order rate-controlling step. Approximate analytic solutions have been obtained for all mixture ratios. Hydrocarbon-oxygen-inert gas mixtures are considered in Section IV. A second order rate-controlling step is again assumed and solutions are given for various initial gas compositions. An attempt is made to correlate experimentally determined burning velocity data in Section V. Reference to Section V shows that a good correlation was obtained only for lean mixtures. Absolute values for the laminar burning velocity cannot be estimated because of the lack of data concerning reaction mechanism and specific reaction rate constants.

ID: CaltechAUTHORS:20110121-073203540

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Abstract: N/A

Publication: Journal of Chemical Physics Vol.: 23 No.: 4 ISSN: 0021-9606

ID: CaltechAUTHORS:20110119-101940015

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Abstract: In order to illustrate the use of two‐path experiments for correcting for self‐absorption, experimental studies to determine the rotational "temperatures" and concentrations of OH in flames burning at atmospheric pressure have been carried out. For mixtures of H_2, C_2H_2, and O_2, as well as for C_2H_2-O_2 flames diluted with A, "anomalous" rotational "temperatures" were observed under conditions in which strong self‐absorption was clearly indicated by the intensity ratios for the double‐path to the single‐path experiments. Unequivocal quantitative estimates of rotational temperatures and of OH concentrations cannot be carried out, even on the assumption that the emitting system is isothermal and in equilibrium. However, by using the results of theoretical studies on two‐path experiments carried out by one of us, it is possible to obtain reasonable upper limits for the temperatures and lower limits for the OH‐concentrations, based on an assumed Doppler contour for the line‐shape and utilizing Oldenberg's estimates for the f values of representative spectral lines. Our experimental studies lead to reasonable rotational temperatures at the tip of luminous cones for mixtures of H_2, C_2H_2, and O_2 and for C_2H_2-O_2 flames diluted with up to 60 percent argon. These observations do not disprove the reality of rotational temperature anomalies in the inner cones of flames. Significant improvement of experimental procedure, and quantitative interpretation of results along the lines used by us, requires additional basic studies with emphasis on the measurement of spectral line‐shape and absolute intensities

Publication: Journal of Chemical Physics Vol.: 23 No.: 1 ISSN: 0021-9606

ID: CaltechAUTHORS:20110118-134330601

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Abstract: The incompressible laminar boundary layer over a flat plate is studied for the simple case where the stream lines in the free flow have a parabolic shape. An exact solution of the boundary layer equations is derived. No separation occurs, even when there is a strong adverse pressure gradient along the stream lines, so that in this instance the secondary flow has a favorable influence. Because of the variation of total pressure from one stream line to another in the free stream, the total pressure within the boundary layer at a given point can exceed that of the corresponding free stream.

Publication: Journal of the Aeronautical Sciences Vol.: 22 No.: 1 ISSN: 1936-9956

ID: CaltechAUTHORS:20110118-132624864

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Abstract: Two points of view may be taken with regard to the undesirable pressure oscillations in rocket motors which arise from instability of combustion, acoustic resonance, coupled oscillations of chamber pressure and propellant flow rate, as well as from more obscure sources. One is to eliminate the underlying cause of instability through change in mechanical design or modification of propellant properties; this is possible when the mechanism of instability is understood and its removal is not detrimental to rocket performance. The alternative is, as was demonstrated by H. S. Tsien [1], to modify the system dynamics by utilizing a feedback servo control which, for example, senses pressure fluctuations in the combustion chamber and modifies the propellant feeding rate at the proper frequency and phase to damp the fluctuation. Servo-stabilization provides the distinct advantage that stability need not be a major concern during rocket design, relying upon the feedback system to insure stable operation. Furthermore these concepts suggest the possibility of eliminating empirically an undesirable oscillation even when its basic cause is not known.

Publication: Zeitschrift für Angewandte Mathematick und Physik Vol.: 6 No.: 1 ISSN: 0044-2275

ID: CaltechAUTHORS:20110118-140949997

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Abstract: N/A

Publication: Jet Propulsion Vol.: 25 No.: 1 ISSN: 0095-8751

ID: CaltechAUTHORS:20110118-131142281

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Abstract: No abstract

Publication: Symposium (International) on Combustion Vol.: 5 No.: 1 ISSN: 0082-0784

ID: CaltechAUTHORS:20110131-082519111

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Abstract: Important problems involving three-dimensional boundary layer occur in almost all internal and external aerodynamic configurations. For many of these, the flow outside the boundary layer may be resolved into a large principal component and a small crosswise velocity. In this paper, three-dimensional laminar boundary-layer flows over flat and curved surfaces are treated under such a simplification. For flat surfaces, the solutions demonstrate the effect of the free stream turning on the velocity profiles in the crosswise and primary flow directions. When the surface curvature is large and varies so as to resemble a corner, the computed examples show the manner in which the asymmetric behavior of the boundary layer results from the cross-flow. The detailed examples are chosen to illustrate flows occurring on the casing and in the blade fillets of turbomachinery.

Publication: Journal of the Aeronautical Sciences Vol.: 21 No.: 12 ISSN: 1936-9956

ID: CaltechAUTHORS:20110120-101407892

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Abstract: Thin liquid wall films flowing under the influence of high-velocity turbulent gas streams were studied for the purpose of obtaining an understanding of the mechanics of film cooling. Conditions which insure liquid-film attachment to solid surfaces without loss of unevaporated liquid to the gas stream when simple radial-hole injectors are used were found; the maximum allowable coolant flow rate for a stable coolant film was determined (a stable coolant film is obtained when no unevaporated coolant is entrained by the gas stream as the result of interfacial disturbances); and a method for calculating the evaporation rate and the surface temperature for a stable inert coolant film was found.

Publication: Jet Propulsion Vol.: 24 No.: 6 ISSN: 0095-8751

ID: CaltechAUTHORS:20110118-114609834

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Abstract: N/A

Publication: Journal of Chemical Physics Vol.: 22 No.: 7 ISSN: 0021-9606

ID: CaltechAUTHORS:20110120-091949408

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Abstract: A simplified model for the process of steady burning of a stationary droplet of fuel in an oxidizing atmosphere has been examined. Explicit expressions have been obtained for the burning rate of the fuel droplet, for the temperature at the flame front, and for the radius of the combustion surface. The principal assumptions on which our analysis is based are: the flame front is established at a spherical surface surrounding the drop; the rates of delivery of fuel and oxygen to this surface are in stoichiometric proportions; the rates of reaction at the flame front are fast compared to the rates of delivery of combustible gases. Our analysis is an extension and generalization of the work of G. A. E. Godsave. We are able to delete several of Godsave's restrictive assumptions by use of an efficient method for formulating the problem in which only integrated forms appear for the expressions of conservation of mass and energy. Our theoretical formulas provide a satisfactory correlation of Godsave's experimental results.

Publication: Jet Propulsion Vol.: 24 No.: 4 ISSN: 0095-8751

ID: CaltechAUTHORS:20110120-093347600

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Abstract: Approximate emissivity calculations for CO_2 have been carried out, as a function of optical density, at 300 and at 600°K. The calculations involve the assumption that the rotational lines overlap extensively. This condition appears to be satisfied at total pressures above about 1 atmos. Comparison of the values calculated from spectroscopic data with the emissivities tabulated by Hottel and his collaborators shows satisfactory agreement. The analysis presented in this manuscript emphasizes the fact that it is possible to obtain reasonable estimates for the engineering emissivity without performing extensive analytical work, provided the physical principles are understood and the needed spectroscopic data are available.

Publication: Journal of Applied Physics Vol.: 25 No.: 5 ISSN: 0021-8979

ID: CaltechAUTHORS:20100622-165045361

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Abstract: The analytic investigation of laminar combustion processes which are essentially two- or three-dimensional present some mathematical difficulties. There are, however, several examples of two-dimensional flame propagation which involve transverse velocities that are small in comparison with that in the principal direction of flow. Such examples occur in thc problem of flame quenching by a cool surface, flame stabilization on a heated flat plate, combustion in laminar mixing zones, etc. In these cases the problem may be simplified by employing what is known in fluid mechanics as the boundary-layer approximation, since it was applied first by Prandtl in his treatment of the viscous flow over a flat plate. Physically it consists in recognizing that if the transverse velocity is small, the variations of flow properties along the direction of main flow are small in comparison with those in a direction normal to the main flow. The analytic description of the problem simplifies accordingly. The present analysis considers the ignition and combustion in the laminar mixing zone between two parallel moving gas streams. One stream consists of a cool combustible mixture, the second is hot combustion products. The two streams come into contact at a given point and a laminar mixing process follows in which the velocity distribution is modified by viscosity, and the temperature and composition distributions by conduction, diffusion, and chemical reaction. The decomposition of the combustible stream is assumed to follow first-order reaction kinetics with temperature dependence according to the Arrhenius law. For a given initial velocity, composition, and temperature distribution, the questions to be answered are: (1) Does the combustible material ignite; and (2) how far downstream of the initial contact point does the flame appear and what is the detailed process of development. Since the hot stream is of infinite extent, it is found that ignition always takes place at some point of the stream. However, when the temperature of the hot stream drops below a certain value, the distance required for ignition increases so enormously that it essentially does not occur in a physical apparatus of finite dimension. The complete development of the laminar flame front is computed using an approximation similar to the integral technique introduced by von Kármán into boundary layer theory.

Publication: Jet Propulsion Vol.: 24 No.: 2 ISSN: 0095-8751

ID: CaltechAUTHORS:20100120-092445763

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Abstract: It is the purpose of this letter to call attention to a study entitled "Some Considerations in the Application of a Gas Turbine Cycle to the Manufacture of Nitric Oxide," which was carried out by the author in 1951 and 1952 at the California Institute of Technology, in partial fulfillment of requirements for the degree of mechanical engineer.

Publication: Jet Propulsion Vol.: 24 No.: 2 ISSN: 0095-8751

ID: CaltechAUTHORS:20100622-163253405

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Abstract: The effect on apparent rotational temperatures (of OH) of adjacent radiating and absorbing regions at different temperatures and of spectral line shape, coupled with varying degrees of self-absorption, has been studied. The calculations emphasize the fact that definitive conclusions regarding interpretation of flame spectra are difficult to obtain by use of conventional low-resolution spectroscopic studies of flames. Multiple path experiments, or absorption studies with a discrete line source, appear promising provided they are restricted to conditions under which the spectral line shape is known.

Publication: Journal of Chemical Physics Vol.: 22 No.: 1 ISSN: 0021-9606

ID: CaltechAUTHORS:20091222-143729042

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Abstract: The complete system of equations for a theory of laminar flame equations is presented, taking into account both heat conduction and diffusion, for the case of an arbitrary number of simultaneous reactions. The eigenvalue problem determining the flame velocity is formulated. Two examples are given in order to show that explicit analytical expressions for the flame velocity can be obtained, which are in good agreement with the results obtained by numerical integration of the equations. In the first example (hydrazine decomposition) one reaction is considered as global, i.e., rate-controlling, reaction. In the second example (ozone decomposition) a hypothesis is introduced for the concentration of the free radical O, which corresponds to the steady-state approximation generally used in classical chemical kinetics. In both cases approximate explicit formulae are obtained for the flame velocity using legitimate approximation methods, without making drastic assumptions. The steady-state assumption used for the ozone flame has a bearing on a better understanding of the mechanism of chain reactions in general. The method indicated in the paper gives hope that the more complicated chain reactions, such as the combustion of hydrocarbons, will also be made accessible to theoretical computation.

ID: CaltechAUTHORS:20091221-144345839

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Abstract: A critical review is presented of the results obtained by spectroscopic observations on flames. The objective of the survey is to examine the status, promise, and deficiencies of combustion spectroscopy in its relation to (a) elucidation of the mechanism of combustion and (b) the solution of technical combustion problems. Since important spectroscopic studies have been carried out on low-pressure flames, a discussion of the probable effects of pressure on laminar flame propagation is also included.

ID: CaltechAUTHORS:20091221-152152667

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Abstract: The one-dimensional thermal theory of constant-pressure deflagration has been discussed in a recent publication by the senior author and G. Millán. In this paper an explicit relation was given for the linear burning velocity in flames supported by first-order global reactions. It is the purpose of the present analysis to extend this work by dropping the assumptions (a) that the average molecular weight of the gas mixture remains constant, and (b) that the thermal conductivity is constant. As the result, the one-dimensional theory of constant-pressure deflagration described in this paper is complete except in so far as the following reasonable approximations are concerned: (a) a constant average specific heat equal to the ratio of heat release per gram of reactant to total temperature rise may be used; (b) the ideal gas law constitutes a satisfactory equation of state for reacting gas mixtures.

ID: CaltechAUTHORS:20091221-143436496

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Abstract: Calculations have been carried out in order to determine the rate of evaporation of a liquid droplet surrounded by hot gases. The present study represents an extension of earlier work by Penner on evaporation rates for isothermal droplets. In particular, allowance was made for temperature gradients within the droplet by considering a droplet composed of an isothermal core and an isothermal shell. The results obtained in the present investigation were found to be in satisfactory agreement with the known data for evaporation of isothermal droplets, thus justifying calculations for isothermal droplets as a reasonable first approximation.

Publication: Journal of the American Rocket Society Vol.: 23 No.: 4 ISSN: 0095-9073

ID: CaltechAUTHORS:20091218-141505043

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Abstract: The mass ratio or the characteristic velocity for the take-off of a space ship from the satellite orbit is computed for two cases: the radial thrust, and the circumferential thrust. The circumferential thrust is much more efficient in that the required mass ratio is much less than for the radial thrust. Both cases show, however, an increase of the required mass ratio and the characteristic velocity with a reduction in acceleration. With circumferential thrust, the characteristic velocity increases by a factor of two, when the acceleration is reduced from 1/2 g to 1/3000 g.

Publication: Journal of the American Rocket Society Vol.: 23 No.: 4 ISSN: 0095-9073

ID: CaltechAUTHORS:20091215-133451765

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Abstract: Thermodynamic calculations to determine the theoretical performance of ethylene oxide as a monopropellant have been carried out for various possible decomposition reactions.

No.: 53
ID: CaltechAUTHORS:20100622-162318414

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Abstract: Altman and Adelman have studied the equilibrium between hydrazine and water in the vapor phase by following the pressure change in a constant-volume apparatus. They found the heat of dissociation of hydrazine hydrate to be 13.97 Kcal/mole. Their data on hydrazine hydrate have been checked within the limits of our experimental error. Furthermore, the heat of dissociation of N_2H_4•CH_3OH has been found to be 8.6 ± 0.3 Kcal/mole, using essentially the same experimental technique as Altman and Adelman.

No.: 52
ID: CaltechAUTHORS:20100621-124738906

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Abstract: A nomogram has been constructed for the determination of blackbody radiancy and of peak and total intensities for spectral lines with Doppler contour. The basic equations used for the construction of the nomogram and the use of the nomogram are described briefly. A method is outlined for determining absolute values of total intensities for spectral lines with combined Doppler and resonance contour by using the nomogram in conjunction with the “curves of growth.”

Publication: Journal of the Optical Society of America Vol.: 43 No.: 5 ISSN: 0030-3941

ID: CaltechAUTHORS:20091215-110238137

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Abstract: A nomogram has been constructed for the determination of blackbody radiancy and of peak and total intensities for spectral lines with Lorentz contour. The basic equations used for the construction of the nomogram and the use of the nomogram are described briefly.

Publication: Journal of the Optical Society of America Vol.: 43 No.: 5 ISSN: 0030-3941

ID: CaltechAUTHORS:20091215-104935690

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Abstract: A brief survey is presented of optical methods for the determination of temperatures which can be used in rocket engines. The data are presented in outlines and include an outline of basic principles involved in application of a given technique, a sketch of the experimental arrangement, and key references which should he consulted for further details.

Publication: Journal of the American Rocket Society Vol.: 23 No.: 3 ISSN: 0095-9073

ID: CaltechAUTHORS:20091215-125945046

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Abstract: Methods for the calculation of spectral absorption coefficients for combined Doppler and Lorentz broadening are summarized. The “curves of growth” have been extended to cover the ranges of parameters which arise in spectroscopic studies on flames.

Publication: Journal of the Optical Society of America Vol.: 43 No.: 5 ISSN: 0030-3941

ID: CaltechAUTHORS:20091215-113204848

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Abstract: The effect of spectral line shape on apparent rotational temperatures of OH has been investigated for the P_1 branch, ^2Σ-->^2π transitions, (0, 0) band, by treating the ratio of collision half-width to Doppler half-width as a variable parameter. The results of calculations for emission experiments, using conventional plots, show a large effect of line shape on apparent temperature. In general, the greater the ratio of collision half-width to Doppler half-width, the smaller the distortion of experimental data. The analysis predicts higher apparent rotational temperatures for isothermal systems at reduced pressures than at atmospheric pressures. Although this result is in agreement with experimental observations on flames, it cannot be used as an explanation for the observed data without auxiliary studies proving that distortion of data is of importance in any given case. The two-path method for determining temperatures and emissivities (concentrations) in flames has been extended to spectral lines with combined Doppler- and collision-broadening.

Publication: Journal of Chemical Physics Vol.: 21 No.: 4 ISSN: 0021-9606

ID: CaltechAUTHORS:20091215-130819123

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Abstract: The experimental determination of absolute intensities for isolated spectral lines or for entire vibration-rotation bands involves formidable experimental difficulties. For this reason it is highly desirable to consider the use of techniques which permit the determination of absolute f values from relative intensity measurements performed by the use of a low resolution spectrograph. It is the purpose of this note to call attention to a useful experimental procedure for spectral lines with Doppler contour and for optical densities which are sufficiently large to assure a nonlinear dependence of intensity on optical density. The method is a generalization of a two-path experiment proposed for emission studies on flames.

Publication: Journal of the Optical Society of America Vol.: 43 No.: 3 ISSN: 0030-3941

ID: CaltechAUTHORS:20091215-085513442

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Abstract: Upper limits have been estimated for the rate of evaporation of small liquid droplets in representative rocket combustion chambers. The droplets are assumed to be isothermal at all times. The droplet temperature as a function of time is determined by an appropriate heat balance. The calculations are useful in determining the significance of inelastic collisions between liquid droplets for complete combustion. Radiant heat transfer to moving liquid droplets is considered briefly.

Publication: Journal of the American Rocket Society Vol.: 23 No.: 2 ISSN: 0095-9073

ID: CaltechAUTHORS:20091215-123319557

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Abstract: The recent work of H. S. Tsien concerning the servostabilization of rocket motors is extended to the liquid bipropellant rocket motor. It is shown that by use of a feedback system containing a device to sense the combustion chamber pressure, a suitably designed amplifier, and a servomechanism which governs the propellant How, the low-frequency oscillations which occur in the rocket configuration may be stabilized for any value of combustion time lag. A method is given for determining a transfer function of the feedback loop which will assure stable operation. The technique of the Satche diagram is employed in stability analysis.

Publication: Journal of the American Rocket Society Vol.: 23 No.: 2 ISSN: 0095-9073

ID: CaltechAUTHORS:20091215-101526652

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Abstract: Accurate calculations to evaluate the performance of the stoichiometric carbon-oxygen propellant system have been carried out for nozzle flow with and without chemical reactions and with and without vibrational adjustment. The calculations show that, for frozen chemical flow, a lag of vibrational energy states at chamber conditions nearly doubles the reduction in I_(sp), as compared with flow in which complete vibrational equilibrium is maintained. On the other hand, lags in vibrational adjustment have practically no effect on the theoretical performance of hot propellant systems if chemical equilibrium is maintained during nozzle flow. The preceding conclusions are in agreement with the results on other propellant systems obtained previously by use of an approximate evaluation procedure.

Publication: Journal of the American Rocket Society Vol.: 23 No.: 1 ISSN: 0095-9073

ID: CaltechAUTHORS:20091214-134536542

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Abstract: The purpose of physical mechanics is to predict the engineering behavior of matter in bulk form from the microscopic properties of its molecular and atomic constituents. The constants and basic concepts of this new engineering science, of particular importance to rocket and jet propulsion, are discussed in this paper.

Publication: Journal of the American Rocket Society Vol.: 23 No.: 1 ISSN: 0095-9073

ID: CaltechAUTHORS:20091214-144949544

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Abstract: Even if a Boltzmann distribution exists for the population of molecules in various energy levels, it is not possible to obtain a satisfactory interpretation of experimental data by the use of conventional procedures unless the product of maximum spectral absorption coefficient P_(max) and optical density χ is sufficiently small. Detailed calculations are presented which show that the experimental results, which suggest an anomalous rotational temperature for the ^2Σ state of OH in low pressure combustion flames, can be accounted for by using sufficiently large values for P_(max)χ (Sec. II). Whether or not experimental data should be interpreted in this manner must be determined by auxiliary studies. Representative absorption studies for the determination of rotational temperatures in isothermal systems have been analyzed for the P_1 branch, (0,0) band, ^2π-->^2Σ transitions of OH at 3000°K. The calculations show that erroneous interpretation of experimental results occurs if the product P_(max)χ is not small compared to unity. Sample calculations for a blackbody light source show that the customary procedure for treating experimental results will permit adequate correlation of the data by straight lines up to relatively large values for P_(max)χ. It is remarkable that the preceding statement remains true even under conditions in which emission data clearly indicate that P_(max)χ is no longer small compared to unity (Sec. III). Representative calculations to determine observable peak and total intensity ratios in emission for spectral lines with Doppler contour have been carried out for ^2Σ-->^2π transitions, (0,0) band, P_1 branch of OH at 3000°K. The calculations show that the ratios of peak and total intensities are functions of the products of maximum absorption coefficients (P_(max)) and optical density (χ) for the lines under study (Sec. IV). Quantitative calculations have been carried out of apparent rotational temperatures in systems containing nonequilibrium distributions of OH at 3000°K and at 6000°K. The calculations on the P_1 branch, ^2Σ-->^2π transitions, indicate that, in the absence of self-absorption, conventional plots showing discontinuities necessarily overestimate one and underestimate the other of the known temperatures of 3000°K and 6000°K (Sec. V). Quantitative calculations on the nature of distortions produced when an isothermal region at 3000°K is viewed through an isothermal region at 1500°K show that the presence of a non-isothermal field of view magnifies the distortion produced by self-absorption alone (Sec. VI). On the basis of the noncontroversial quantitative calculations described in Secs. II to VI for idealized systems, some speculations regarding the significance of reported flame temperature anomalies for OH are presented in Sec. VII.

Publication: Journal of Chemical Physics Vol.: 21 No.: 1 ISSN: 0021-9606

ID: CaltechAUTHORS:20091214-164334316

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Abstract: It will be shown that the differential equations for a heated plate with large temperature gradient and for a similar plate at constant temperature can be made the same by a proper modification of the thickness and the loading for the isothermal plate. This fact leads to the result that the stresses in the heated plate can be calculated from measured strains on the unheated plate by a series of relations, called the "similarity laws." The application of this analog theory to solid wings under aerodynamic heating is discussed in detail. The loading on the unheated analog wing is, however, complicated and involves the novel concept of feedback and "body force" loading. The problem of stressing a heated box-wing structure can be solved by the same analog method and is briefly discussed.

Publication: Journal of the Aeronautical Sciences Vol.: 20 No.: 1
ID: CaltechAUTHORS:20091214-142900787

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Abstract: By a semiempirical approach, a method is found to calculate the specific heat of a normal pure liquid at constant pressure form the specific heat of the gaseous state at the same temperature. It is also found that the coefficient of thermal expansion, the compressibility, and the velocity of sound of the liquid can be calculated accurately if the density, the molecular weight, and the normal boiling temperature of the liquid at atmospheric pressure are known. Finally, a method of computing the thermal conductivity of all liquids, except liquid metals, from compressibility and density is developed. For normal liquids, the thermal conductivity can again be determined if only the normal boiling temperature, the density, and the molecular weight are known.

Publication: Journal of the American Rocket Society Vol.: 23 No.: 1 ISSN: 0095-9073

ID: CaltechAUTHORS:20091214-143421207

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Abstract: Total absorptivity measurements have been carried out at room temperature as a function of partial pressure of CO_2 and of total pressure using nitrogen as pressurizing gas.

Publication: Journal of Applied Physics Vol.: 23 No.: 11 ISSN: 0021-8979

ID: CaltechAUTHORS:20091214-131602254

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Abstract: As a result of recent theoretical studies on transport properties of gases by Hirschfelder, et al., and others, the dynamic viscosity (µ), the thermal conductivity (λ), and the mechanical diffusivity (D), as well as the dimensionless ratios Prandtl Number (Pr = C_p µ/λ, where C_p = specific heat at constant pressure), Schmidt Number (Sc =µ/ρD, where ρ = density), anq λ/ρC_pD may now be calculated rapidly and with a reasonable degree of accuracy both for pure gases and for mixtures of gases, provided that the temperature of the gases is not too low. This happy state of affairs does not seem to be realized by aeronautical engineers, and it is the purpose of the present note to call attention to it.

Publication: Journal of the Aeronautical Sciences Vol.: 19 No.: 9
ID: CaltechAUTHORS:20091214-094124089

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Abstract: This paper shows that the combustion in the rocket motor can be stabilized against any value of time lag in combustion by a feedback servo link from a chamber pressure pickup, through an appropriately designed amplifier, to a control capacitance on the propellant feed line. The technique of stability analysis is based upon a combination of the Satche diagram and the Nyquist diagram. For simplicity of calculation, only low-frequency oscillations in monopropellant rocket motors are considered. However, the concept of servo-stabilization and method of analysis are believed to be generally applicable to other cases.

Publication: Journal of the American Rocket Society Vol.: 22 No.: 5 ISSN: 0095-9073

ID: CaltechAUTHORS:20091214-130734801

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Abstract: It is the purpose of the current note to outline a two-path method for the determination of flame temperatures. The method is valid for isothermal systems and spectral lines with Doppler contour. All errors arising from self-absorption are eliminated. Practical applications are made by determining the ratio of the total intensity observed when the flame is viewed with a cool blackbody as background to the total intensity obtained with a cool mirror as background.

Publication: Journal of Chemical Physics Vol.: 20 No.: 8 ISSN: 0021-9606

ID: CaltechAUTHORS:20091211-092800465

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Abstract: It is the purpose of this note to present an evaluation of the experimental evidence for and against "anomalous" temperatures of OH in flames. Experimental studies have been carried out on low pressure flames, and on flames burning at atmospheric pressure. The results have usually been interpreted by using relations which are applicable only to isothermal systems. Attempts to correct for self-absorption have been made by using isointensity methods. For spectral lines with Doppler contour it has been demonstrated by quantitative calculations that the isointensity methods do not correct for self-absorption unless self-absorption is weak. In particular, Shuler's method, without allowance for the effect of frequency on intensity, has been shown to yield nonlinear plots for strong self-absorption and to be inferior to conventional procedures in the absence of self-absorption. Extensive studies on the effect of self-absorption in falsifying experimental data have been carried out by Cowan and Dieke. We have recently attempted to estimate absolute emission intensities for OH in low pressure flames by using data obtained by Oldenberg and Rieke.

Publication: Journal of Chemical Physics Vol.: 20 No.: 8 ISSN: 0021-9606

ID: CaltechAUTHORS:20091211-093848025

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Abstract: Simplified expressions have been developed for the engineering emissivity of uniformly distributed diatomic gases for nonoverlapping rotational lines with a resonance contour. Unfortunately the rotational half-widths for spectral lines arising from transitions between excited vibrational energy levels are generally not known. For this reason it was necessary to make the assumption that the rotational half-widths for transitions of the form n-->n+v, v=1 or 2, are identical. The theoretical analysis is, however, sufficiently general to be useful without modification when accurate data concerning the dependence of line-width on vibrational excitation become available. Explicit expressions have been obtained for the contributions to the total emissivity associated with individual vibration-rotation bands. Representative emissivity calculations have been carried out for CO and HCl. Comparison of the calculated emissivities of CO with experimental data shows only fair agreement, suggesting either that the assumed description of rotational half-widths is inadequate or else that the empirical emissivity data are not reliable at elevated temperatures.

Publication: Journal of Applied Physics Vol.: 23 No.: 8 ISSN: 0021-8979

ID: CaltechAUTHORS:20091211-094656109

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Abstract: A new method of power plant selection for vertical flight is proposed. It can be used to determine whether the performance of a rocket design can be improved by substituting for the rocket motor a different power plant such as a ramjet. Calculations indicate that there are advantages in using the ramjet provided the power plant can be made to operate under rapid acceleration and at high altitudes.

Publication: Journal of the American Rocket Society Vol.: 22 No.: 4 ISSN: 0095-9073

ID: CaltechAUTHORS:20091211-152054111

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Abstract: The flight of a rocket vehicle in the equatorial plane of a rotating earth is considered with possible disturbances in the atmosphere due to changes in density, in temperature, and in wind speed. These atmospheric disturbances together with possible deviations in weight and in moment of inertia of the vehicle tend to change the flight path away from the normal flight path. The paper gives the condition for the proper cut-off time for the rocket power, and the proper corrections in the elevator angle so that the vehicle will land at the chosen destination in spite of such disturbances. A scheme of tracking and automatic navigation involving a high-speed computer and elevator servo is suggested for this purpose.

Publication: Journal of the American Rocket Society Vol.: 22 No.: 4 ISSN: 0095-9073

ID: CaltechAUTHORS:20091210-142418746

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Abstract: It should be obvious to anyone reading our recent papers objectively that our "principle thesis" was (a) to examine the origin of the basic relations involved in the customary procedure for the determination of population temperatures in flames, with emphasis on the effect of spectral line shape on the final equations, and (b) to present experimental data on low pressure combustion flames which support the earlier experimental findings of Gaydon and Wolfhard.

Publication: Journal of Chemical Physics Vol.: 20 No.: 7 ISSN: 0021-9606

ID: CaltechAUTHORS:20091210-140920447

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Abstract: When a thin cylindrical shell of uniform thickness is very rapidly heated by hot high-pressure gas flowing inside the shell, the temperature of material decreases steeply from a high temperature at the inside surface to ambient temperatures at the outside surface. Young's modulus of material thus varies. The purpose of the present paper is to reduce the problem of stress analysis of such a cylinder to an equivalent problem in conventional cylindrical shell without temperature gradient in the wall. The equivalence concept is expressed as a series of relations between the quantities for the hot cylinder and the quantities for the cold cylinder. These relations give the similarity law whereby strains for the hot cylinder can be simply deduced from measured strains on the cold cylinder and thus greatly simplify the problem of experimental stress analysis.

Publication: Journal of the American Rocket Society Vol.: 22 No.: 3 ISSN: 0095-9073

ID: CaltechAUTHORS:20091209-140147995

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Abstract: A simple closed-form expression is obtained for the fractional intensity of radiation absorbed by vibration-rotation bands with collision-broadened spectral lines. The resulting expressions greatly reduced the labor involved in obtaining apparent rotational half-widths from experimental measurements.

Publication: Journal of Chemical Physics Vol.: 20 No.: 5 ISSN: 0021-9606

ID: CaltechAUTHORS:20091209-141443391

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Abstract: The transfer function is defined as the fractional oscillating mass flow rate divided by the fractional sinusoidal pressure oscillation in the rocket combustion chamber. This is calculated as a function of the frequency of oscillation. For very small frequencies, the transfer function is approximately 1 with a small "lead component." For very large frequencies, the transfer function is considerably larger than 1, and is approximately 1 + (γM_1)^(-1) where γ is the ratio of specific heats of the gas, and M_l is the Mach nUlllber at entrance to the nozzle.

Publication: Journal of the American Rocket Society Vol.: 22 No.: 3 ISSN: 0095-9073

ID: CaltechAUTHORS:20091209-134942869

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Abstract: The kinetics of evaporation of liquids has been reconsidered from the point of view of classical kinetic reactions and also by application of the theory of absolute reaction rates. It is shown that evaporation treated as a unimolecular rate process, with a rate proportional to the surface concentration of energetic molecules, leads to the Knudsen equation for spherical molecules provided 6 square terms contribute to the energy of activation. As was pointed out in an earlier publication, the theory of absolute reaction rates, after correction for lack of equilibrium between normal molecules and the activated complex, leads to the Knudsen equation for spherically symmetric molecules if reasonable assumptions are made concerning the nature of the activated complex. Evidence is presented in support of the idea that the equilibrium theory of absolute reaction rates is not consistent with the model of the liquid used to determine evaporation rates. The theoretical treatment is next extended to polar liquids with restricted rotation and it is shown that the evaporation coefficient should be identified with the free-angle ratio, a conclusion which has been verified quantitatively by Wyllie.

Publication: Journal of Physical Chemistry Vol.: 56 No.: 4 ISSN: 0022-3654

ID: CaltechAUTHORS:20091209-112654154

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Abstract: One problem encountered in the theory of turbomachines is that of calculating the fluid velocity components when the inner and outer boundaries of the machine as well as the shape of or forces imparted by the blade row are given. The present paper discusses this problem under the restrictions that the fluid is inviscid and incompressible and that the blade rows consist of an infinite number of infinitely thin blades so that axially symmetric flow is assumed. It is shown, in general, that the velocity components in a plane through the turbomachine axis may be expressed in terms of the angular momentum and the leading-edge blade force normal to the stream surfaces. The relation is a nonlinear differential equation to which analytic solutions may be obtained conveniently only after the introduction of linearizing assumptions. A quite accurate linearization is effected through assuming an approximate shape of the stream surfaces in certain nonlinear terms. The complete linearized solution for the axial turbomachine is given in such form that blade loading, blade shape, distribution of angular momentum, or distribution of total head may be prescribed. Calculations for single blade rows of aspect ratio 2 and 2/3 are given for a radius ratio of 0.6. They indicate that the process of formation of the axial velocity profile may extend both upstream and downstream of a high-aspect-ratio blade row, while for low aspect ratios the major portion of the three-dimensional flow occurs within the blade row itself. When the through-flow velocity varies greatly from its mean value, the simple linearized solution does not describe the flow process adequately and a more accurate solution applicable to such conditions is suggested. The structure of the first-order linearized solution for the axial turbomachine suggested a further approximation employing a minimizing operation. The simplicity of this solution permits the discussion of three interesting problems: Mutual interference of neighboring blade rows in a multistage axial turbomachine, solution for a single blade row of given blade shape, and the solution for this blade row operating at a condition different from the design condition. It is found that the interference of adjacent blade rows in the multistage turbomachine may be neglected when the ratio of blade length to the distance between centers of successive blade rows is 1.0 or less. For values of this ratio in excess of 3.0, the interference may be an important influence. The solution for the single blade row indicated that, for the blade shape considered, the distortion of the axial velocity profile caused by off-design operation is appreciably less for low- than for high-aspect-ratio blades. To obtain some results for a mixed-flow turbomachine comparable with those for the axial turbomachine as well as to indicate the essential versatility of the method of linearizing the general equations, completely analogous theoretical treatment is given for a turbomachine whose inner and outer walls are concentric cones with common apex and whose flow is that of a three-dimensional source or sink. A particular example for a single rotating blade row is discussed where the angular momentum is prescribed similarly to that used in the examples for the axial turbomachine.

ID: CaltechAUTHORS:MARnacatn2614

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Abstract: Equations are developed for observable intensities in emission and absorption for spectral lines with Doppler contour. It is shown that the theoretical relations which are usually employed in estimating effective temperatures of internal energy states (a) require slight modifications when proper allowance is made for the shape of spectral lines, and (b) are not valid unless the product of spectral absorption coefficient and optical density is sufficiently small. Illustrative calculations on several spectral lines belonging to the (0,0) band of the 2Sigma-->2Pi band system of OH suggest that the conditions under which the basic relations hold are probably not satisfied for representative combustion flames.

Publication: Journal of Chemical Physics Vol.: 20 No.: 3 ISSN: 0021-9606

ID: CaltechAUTHORS:20090805-134446096

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Abstract: A general criterion for near-frozen adiabatic expansion in one-dimensional nonviscous flow through a Laval nozzle has been described in a recent publication [1]. Unfortunately it appears that the discussion was so condensed that it is hardly possible to apply the results, Eq. (28a), without a few explanatory remarks.

Publication: Journal of Chemical Physics Vol.: 20 No.: 2 ISSN: 0021-9606

ID: CaltechAUTHORS:20090805-145128570

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Abstract: Numerical emissivity calculations at 300°K and atmospheric pressure for nonoverlapping rotational lines have been carried out for CO using a dispersion formula for the line-shape representation. Use of the best available experimental data on integrated absorption and rotational line-width leads to calculated emissivities which are in excellent agreement with extrapolated empirical data published by Hottel and Ullrich. In particular, the theoretical dependence of emissivity on optical density, for small optical densities at 300°K, has been shown to follow experimental observations with satisfactory precision.For small optical densities the calculated emissivity is found to be proportional to the square root of the assumed rotational line-width, thus emphasizing the need for accurate line-width determinations at elevated temperatures. The limits of validity of the treatment utilizing nonoverlapping rotational lines are defined by examining overlapping between adjacent weak and strong rotational lines.The calculation of emissivities can be simplified by the use of approximate treatments. Thus absolute values of the emissivity can be predicted within 10 percent by utilizing a treatment for nonoverlapping, equally spaced, and equally intense lines, together with empirically determined values for the equivalent mean integrated absorption of the rotational lines of CO. A better analytic solution, which does not involve the assumptions of equal spacing and equal intensity of the rotational lines, has been obtained by utilizing asymptotic relations for large values of modified Bessel functions.

Publication: Journal of Applied Physics Vol.: 23 No.: 2 ISSN: 0021-8979

ID: CaltechAUTHORS:20090805-142635076

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Abstract: The chemical propellants form a special class of compounds. Some of the members of this class are usually not considered as being important enough to warrant special discussion in chemistry courses. For this reason it appears to be of interest to present a catalogue of representative chemicals with emphasis on the particular characteristics which make them useful or usable rocket propellants.

Publication: Journal of Chemical Education Vol.: 29 No.: 1 ISSN: 0021-9584

ID: CaltechAUTHORS:20090805-152312511

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Abstract: N/A

Publication: Journal of the American Rocket Society Vol.: 22 No.: 1 ISSN: 0095-9073

ID: CaltechAUTHORS:20110127-085951497

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Abstract: A method for the quantitative evaluation of chemicals as rocket propellants is described. The procedure utilizes the fact that adiabatic expansion through a nozzle may be considered to be isentropic. Treatments are presented for two limiting conditions of expansion, corresponding to flow without chemical change and to flow which is characterized, at all times, by the existence of thermodynamic equilibrium.

Publication: American Journal of Physics Vol.: 20 No.: 1 ISSN: 0002-9505

ID: CaltechAUTHORS:20090805-150338262

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Abstract: [no abstract]

ID: CaltechAUTHORS:20151111-143742969

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Abstract: The purpose of this investigation is to demonstrate that the resistance of ceramic and ceramal materials to thermal shock can he determined by analyzing the nonsteady thermal stresses in the material. First the nonuniform temperature distribution is computed by using the heat conduction equation. This temperature distribution is then used to compute the thermal stress. The material parameters which enter into the calculations are the coefficients of thermal conduction and of thermal expansion, the ultimate strength, Young's modulus, and Poisson's ratio of the material. These quantities together with the heating conditions then specify the resistance to thermal shock. The theory is verified by comparing the results with NACA test data.

Publication: Journal of the American Rocket Society Vol.: 21 No.: 6
ID: CaltechAUTHORS:JPC011

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Abstract: This paper presents a method for the approximate calculation of the ideal specific heats of polyatomic molecules occurring in rocket combustion processes. The method is based on the assignment of characteristic frequencies to individual interatomic bonds, the simplification consisting in the use of the same characteristic frequency for a particular bond irrespective of the over-all structure of the molecule in which it occurs. The method can be applied to molecules for which precise spectroscopic data are not available.

Publication: Journal of the American Rocket Society Vol.: 21
ID: CaltechAUTHORS:JPC007

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Abstract: The problem of optimal thrust programming for a sounding rocket of minimum starting weight to reach specified height with given final weight and propellant characteristics is first formulated as a problem in variational calculus. The general solution for arbitrary drag function is given. The solution is then applied to two special cases, one with quadratic drag dependence on velocity and the other with linear drag dependence on velocity. Complete numerical data are given. The results are then compared with the results of constant thrust to show the advantages of thrust programming. Thrust programming is shown to be able to increase appreciably the pay load of a high altitude sounding rocket.

Publication: Journal of the American Rocket Society Vol.: 21
ID: CaltechAUTHORS:JPC006

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Abstract: Explicit relations have been obtained for the enthalpy changes in one-dimensional nonviscous flow through a Laval nozzle, where arbitrary deviations from thermodynamic equilibrium of chemical composition and of internal electronic, vibrational, or rotational energy states may occur. These relations are of interest in connection with calculations on the effect of deviations from equilibrium on performance of jet engines.Starting with the equation of continuity for a multicomponent mixture of reacting gases, criteria for near-equilibrium and for near-frozen flow with respect to chemical reactions are derived. The near-equilibrium criteria agree with results obtained previously. The near-frozen flow criteria are new and have not yet been applied to the study of chemical reactions during nozzle flow.

Publication: Journal of Chemical Physics Vol.: 19 No.: 7 ISSN: 0021-9606

ID: CaltechAUTHORS:JPC005

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Abstract: Flame front is a region in the flow field where rapid change in the chemical composition of the fluid occurs with consequent release of chemical energy in the form of heat. In the majority of cases the phenomenon is a very complicated one involving the heat transfer by conduction and radiation, the changes in concentration of the different components by diffusion and chemical reaction. Owing to this and the difficult problem of chemical kinetics, only recently the complete theory of flame front has been formulated, particularly by the group under J. O. Hirschfelder.[2] Fortunately, as a result of the rapid rate of chemical reaction, the thickness of the flame front under ordinary conditions is generally very small, being less than 1 mm. Therefore, if one is interested in the influence of flame front on the flow field but not on the detailed structure of the flame, the flame can be assumed as infinitesimally thin, and only the final changes of the state of fluid due to combustion need be considered. This procedure is entirely analogous to that of treating the shock wave as having zero thickness in studying dynamics of compressible fluids. This simplification will be adopted for the present investigation.

Publication: Journal of Applied Mechanics Vol.: 18 No.: 2 ISSN: 0021-8936

ID: CaltechAUTHORS:JPC004

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Abstract: In "America Fledges Wings" R. M. Cleveland [1] stated: "Despite the importance of the role played by the Daniel Guggenheim Fund for the promotion of aeronautics as a herald, as an awakener, as a quickening spark in the manifold fields of practical aviation, its most important and probably most lasting contribution lay in its implementation and its creation of centers of research." These centers of research are the well-known great schools of aeronautical engineering at the New York University, the Stanford University, the University of Michigan, the Massachusetts Institute of Technology, the California Institute of Technology, the University of Washington, and the Georgia School of Technology. It is a fact that a great majority of practicing aeronautical engineers today are either wholly educated in one of these centers or have had contact with one of these centers. Moreover, the strong influence of the Guggenheim Fund is not limited to this phase of aeronautical engineering. These centers of research contributed to a large extent to the fundamental knowledge of aeronautical science which forms the scientific basis of aeronautical engineering. Today we see an even more broadened effect exerted by the Guggenheim schools as men originally educated in these Guggenheim research centers establish new research laboratories and new schools of aeronautics in universities all over the world.

Publication: Journal of the American Rocket Society No.: 81
ID: CaltechAUTHORS:JPC003

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Abstract: For the non-homogeneous stresses in isotropic incompressible visco-elastic media characterized by linear relations between the components of stress, strain and their derivatives with respect to time, T. Alfrey has shown (Ref. 1) that in the case of the first boundary value problem, the stress distribution is identical with that in an incompressible elastic material under the same instantaneous surface forces. A similar result was obtained for the second boundary value problem where the displacements at the boundary are specified. It is the purpose of the present note to generalize this theorem to isotropic compressible media for problems involving body forces. Only the first boundary value problem will be discussed, as the corresponding theorem on the second boundary value problem is self-evident.

Publication: Quarterly of Applied Mathematics Vol.: 8 No.: 1 ISSN: 0033-569X

ID: CaltechAUTHORS:JPC002

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Abstract: When considering the problems of basic research in rocket and jet propulsion, it is profitable to keep in mind the salient features of rocket- and jet-propulsion engineering. These are: short duration of operation of the power-plant and extreme intensity of reaction in the motor.

Publication: Aero DigestISSN: 0096-4344

ID: CaltechAUTHORS:JPC001

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Abstract: This paper is a summary of work carried out during the past five years as part of an ONR/NAVAIR Research Initiative. The effort has been devoted to developments and applications of an approximate analysis intended to provide understanding of observed behavior and guidelines for design and development. Although most of the work has been carried out for longitudinal modes, quite extensive results have been obtained for transverse modes in a circular chamber, for both second and third order nonlinear gasdynamics. Especially important are the useful conclusions based on the simplified two-mode approximation. Preliminary results obtained for the influences of stochastic sources suggest that some of the observed behavior of the amplitudes of oscillations may be attributed to random inputs, such as flow separation and turbulence. Some important aspects of the problem of existence and stability of limit cycles in linearly stable systems ("triggering") remain unclear.

ID: CaltechAUTHORS:20110207-095215895

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Abstract: This paper summarizes work accomplished chiefly during the past five years on analysis of stability related to recent experimental results on combustion instabilities in dump combustors. The primary purpose is to provide the information in a form useful to those concerned with design and development of operational systems. Thus most substantial details are omitted and the material is presented in a qualitative fashion.

ID: CaltechAUTHORS:20110207-112022288

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Abstract: Flame stabilization and flame spreading are two processes of paramount importance in the design of combustion chambers. Sufficient experimental work has been carried out to make clear the mechanism of stabilization; however understanding of the process of flame spreading in a duct is still imperfect. This is perhaps not surprising because, in technically interesting cases, the spreading is turbulent and the behavior of even the simplest turbulent flame is still controversial. Furthermore, studies that have been made of flame spreading have been primarily directed at solving the practical problem of the determination of combustion efficiency rather than providing insight into the physical phenomena involved in the spreading process. The present investigation was undertaken to define the influence of certain chemical and fluid dynamic parameters on the spreading of a simple flame in a duct, with the view that the results would yield some understanding of the mechanism of flame spreading.

ID: CaltechAUTHORS:20110208-141332872

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Abstract: This paper describes and discusses some recent experiments conducted with low-temperature seeded plasmas. The plasma was obtained by mixing potassium vapor with arc-heated argon. The experiments indicated two modes of steady, stable current conduction between the electrodes. In the first mode, the effect of gas phase phenomena predominated in fixing the current. Under certain conditions, a transition to a second mode of operation occurred. In this mode, the current was found to be thermionically limited, and was determined solely by electrode surface effects. A comparison between the observed voltage current characteristics and two current conduction theories is presented. Analysis of electrode temperature data indicated that the chief heat transfer mechanism was the penetration of the surface work function barrier as electrons entered or left the surface.

ID: CaltechAUTHORS:20110208-110426658

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