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: 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: 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: 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: 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: 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: 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 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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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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: 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: 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: 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: 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: 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 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: 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 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: 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: 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: 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: 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: 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: 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 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: 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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Abstract: N/A

ID: CaltechAUTHORS:20110204-094751496

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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: 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: 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: 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: 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: 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: 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: 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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