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

ID: CaltechAUTHORS:20101118-105039121

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

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

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

Vol.: 2
ID: CaltechAUTHORS:20101119-113430324

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

Vol.: 306
ID: CaltechAUTHORS:20110208-095101547

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

Vol.: 306
ID: CaltechAUTHORS:20110128-112158907

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Abstract: N/A

No.: 169
ID: CaltechAUTHORS:20101122-074028101

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Abstract: N/A

ID: CaltechAUTHORS:20101119-084519588

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

Vol.: 4
ID: CaltechAUTHORS:20101123-144201485

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

No.: 512
ID: CaltechAUTHORS:20110121-134650696

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Abstract: N/A

No.: 143
ID: CaltechAUTHORS:20110125-152359532

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

ID: CaltechAUTHORS:20101130-075321569

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

Vol.: 3
ID: CaltechAUTHORS:20101130-083327723

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

ID: CaltechAUTHORS:20110127-073132186

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

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

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

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

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

ID: CaltechAUTHORS:20101207-085326836

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Abstract: N/A

ID: CaltechAUTHORS:20101210-141234875

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

ID: CaltechAUTHORS:20101220-133221838

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

Vol.: 4
ID: CaltechAUTHORS:20110208-113026851

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

ID: CaltechAUTHORS:20110127-120321921

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Abstract: N/A

ID: CaltechAUTHORS:20110208-103139308

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

ID: CaltechAUTHORS:20110204-080105852

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

ID: CaltechAUTHORS:20110121-101804833

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Abstract: N/A

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

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

No.: 1
ID: CaltechAUTHORS:20110111-110838368

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Abstract: N/A

ID: CaltechAUTHORS:20110204-101842249

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

ID: CaltechAUTHORS:20110204-103536323

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

ID: CaltechAUTHORS:20110124-084010424

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

Vol.: 10
ID: CaltechAUTHORS:20110113-152309073

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Vol.: 1
ID: CaltechAUTHORS:20110118-102541769

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

ID: CaltechAUTHORS:20091221-144345839

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

ID: CaltechAUTHORS:20091221-152152667

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

ID: CaltechAUTHORS:20091221-143436496

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