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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Homogeneous Premixed and Nonpremixed Flames in Microgravity - A Review

Combustion studies under microgravitational conditions are discussed in which fire-safety issues, near-limit phenomena, and flammability limits are addressed. The studies use ground-based drop towers to produce up to 5 s of about 10 exp -6 g and aircraft facilities to generate up to 20 s of about 10 exp -2 g. The limits of flammability and radiative-heat loss are important research objectives, and experimentally derived values are discussed. Other phenomena are reported including stationary spherical flames and self-extinguishing flames, and the effects of the Taylor instability are documented in the experiments. The flame-surface geometry is examined concurrently by means of numerical simulations, and flame processes are concluded to be unique under microgravity except when the flow velocities are large.

Faeth, G. M.↗
NASA NTRS1993

The Structure and Stability of Laminar Flames

This review paper on the structure and stability of laminar flames considers such phenomena as heterogeneous mixtures, acoustic instabilities, flame balls and related phenomena, radiation effects, the iodate oxidation of arsenous acid and 'liquid flame fronts', approximate kinetic mechanisms and asymptotic approximations, and tribrachial or triple flames. The topics examined here indicate three themes that may play an important role in laminar flame theory in the coming years: microgravity experiments, kinetic modeling, and turbulence modeling. In the discussion of microgravity experiments it is pointed out that access to drop towers, the Space Shuttle and, in due course, the Space Station Freedom will encourage the development of experiments well designed to isolate the fundamental physics of combustion.

Buckmaster, John↗
NASA NTRS1992

Perspectives on hypersonic viscous and nonequilibrium flow research

An attempt is made to reflect on current focuses in certain areas of hypersonic flow research by examining recent works and their issues. Aspects of viscous interaction, flow instability, and nonequilibrium aerothermodynamics pertaining to theoretical interest are focused upon. The field is a diverse one, and many exciting works may have either escaped the writer's notice or been abandoned for the sake of space. Students of hypersonic viscous flow must face the transition problems towards the two opposite ends of the Reynolds or Knudsen number range, which represents two regimes where unresolved fluid/gas dynamic problems abound. Central to the hypersonic flow studies is high-temperature physical gas dynamics; here, a number of issues on modelling the intermolecular potentials and inelastic collisions remain the obstacles to quantitative predictions. Research in combustion and scramjet propulsion will certainly be benefitted by advances in turbulent mixing and new computational fluid dynamics (CFD) strategies on multi-scaled complex reactions. Even for the sake of theoretical development, the lack of pertinent experimental data in the right energy and density ranges is believed to be among the major obstacles to progress in aerothermodynamic research for hypersonic flight. To enable laboratory simulation of nonequilibrium effects anticipated for transatmospheric flight, facilities capable of generating high enthalpy flow at density levels higher than in existing laboratories are needed (Hornung 1988). A new free-piston shock tunnel capable of realizing a test-section stagnation temperature of 10(exp 5) at Reynolds number 50 x 10(exp 6)/cm is being completed and preliminary tests has begun (H. Hornung et al. 1992). Another laboratory study worthy of note as well as theoretical support is the nonequilibrium flow experiment of iodine vapor which has low activation energies for vibrational excitation and dissociation, and can be studied in a laboratory with modest resources (Pham-Van-Diep et al. 1992).

Cheng, H. K.↗
NASA NTRS1992

Multi-dimensional high order essentially non-oscillatory finite difference methods in generalized coordinates

The nonlinear stability of compact schemes for shock calculations is investigated. In recent years compact schemes were used in various numerical simulations including direct numerical simulation of turbulence. However to apply them to problems containing shocks, one has to resolve the problem of spurious numerical oscillation and nonlinear instability. A framework to apply nonlinear limiting to a local mean is introduced. The resulting scheme can be proven total variation (1D) or maximum norm (multi D) stable and produces nice numerical results in the test cases. The result is summarized in the preprint entitled 'Nonlinearly Stable Compact Schemes for Shock Calculations', which was submitted to SIAM Journal on Numerical Analysis. Research was continued on issues related to two and three dimensional essentially non-oscillatory (ENO) schemes. The main research topics include: parallel implementation of ENO schemes on Connection Machines; boundary conditions; shock interaction with hydrogen bubbles, a preparation for the full combustion simulation; and direct numerical simulation of compressible sheared turbulence.

Shu, Chi-Wang↗
NASA NTRS1994

Parametric study of shock-induced combustion in a hydrogen air system

A numerical parametric study is conducted to simulate shock-induced combustion under various free-stream conditions and varying blunt body diameter. A steady combustion front is established if the free-stream Mach number is above the Chapman-Jouguet speed of the mixture, whereas an unsteady reaction front is established if the free-stream Mach number is below or at the Chapman-Jouguet speed of the mixture. The above two cases have been simulated for Mach 5.11 and Mach 6.46 with a projectile diameter of 15 mm. Mach 5.11, which is an underdriven case, shows an unsteady reaction front, whereas Mach 6.46, which is an overdriven case, shows a steady reaction front. Next for Mach 5. 11 reducing the diameter to 2.5 mm causes the instabilities to disappear, whereas, for Mach 6.46 increasing the diameter of the projectile to 225 mm causes the instabilities to reappear, indicating that Chapman-Jouguet speed is not the only deciding factor for these instabilities to trigger. The other key parameters are the projectile diameter, induction time, activation energy and the heat release. The appearance and disappearance of the instabilities have been explained by the one-dimensional wave interaction model.

Ahuja, J. K.↗
NASA NTRS1981

Development of a simplified procedure for thrust chamber life prediction

An analytical design procedure for predicting thrust chamber life considering cyclically induced thinning and bulging of the hot gas wall is developed. The hot gas wall, composed of ligaments connecting adjacent cooling channel ribs and separating the coolant flow from the combustion gas, is subjected to pressure loading and severe thermal cycling. Thermal transients during start up and shut down cause plastic straining through the ligaments. The primary bending stress superimposed on the alternate in-plane cyclic straining causes incremental bulging of the ligaments during each firing cycle. This basic mechanism of plastic ratcheting is analyzed and a method developed for determining ligament deformation and strain. The method uses a yield surface for combined bending and membrane loading to determine the incremental permanent deflection and pregressive thinning near the center of the ligaments which cause the geometry of the ligaments to change as the incremental strains accumulate. Fatigue and tensile instability are affected by these local geometry changes. Both are analyzed and a failure criterion developed.

Porowski, J. S.↗
NASA NTRS1975

The oxygen and carbon dioxide balance in the earth's atmosphere

The oxygen-carbon dioxide cycle is described in detail, and steps which are sensitive to perturbation or instability are identified. About half of the carbon dioxide consumption each year in photosynthesis occurs in the oceans. Phytoplankton, which are the primary producers, have been shown to assimilate insecticides and herbicides. The impact of such materials on phytoplankton photosynthesis, both direct and as the indirect result of detrimental effects higher up in the food chain, cannot be assessed. Net oxygen production is very small in comparison with the total production and occurs almost exclusively in a few ocean areas with anoxic bottom conditions and in peat-forming marshes which are sensitive to anthropogenic disturbances. The carbon dioxide content of the atmosphere is increasing at a relatively rapid rate as the result of fossil fuel combustion. Increases in photosynthesis as the result of the hothouse effect may in turn reduce the carbon dioxide content of the atmosphere, leading to global cooling.

Johnson, F. S.↗
NASA NTRS1988

SRB combustion dynamics analysis computer program (CDA-1)

A two-dimensional numerical model is developed for the unsteady oscillatory combustion of the solid propellant flame zone. Variations of pressure with low and high frequency responses across the long flame, such as in the double-base propellants, are accommodated. The formulation is based on a premixed, laminar flame with a one-step overall chemical reaction and the Arrhenius law of decomposition for the gaseous phase with no condensed phase reaction. Numerical calculations are carried out using the Galerkin finite elements, with perturbations expanded to the zeroth, first, and second orders. The numerical results indicate that amplification of oscillatory motions does indeed prevail in high frequency regions. For the second order system, the trend is similar to the first order system for low frequencies, but instabilities may appear at frequencies lower than those of the first order system. The most significant effect of the second order system is that the admittance is extremely oscillatory between moderately high frequency ranges.

Chung, T. J.↗
NASA NTRS1985

Thrust chamber life prediction

The reusable life of the Space Shuttle main engine (SSME) is influenced by the cyclic life of the regeneratively liquid cooled main combustion chamber (MCC). During an operational duty cycle the MCC liner is subjected to a large transient thermal gradient that imparts a high thermal cyclic strain to the liner hot gas wall. Life predictions of such chambers have usually been based on low cycle fatigue (LCF) evaluations. Hot-fire testing, however, has shown significant mid-channel wall deformation and thinning during accrued cyclic testing. This phenomenon is termed cyclic creep and appears to be significantly accelerated at elevated temperatures. An analytical method that models the cyclic creep phenomenon and its application to thrust chamber life prediction is presented. The chamber finite element geometry is updated periodically to account for accrued wall thinning and distortion. Failure is based on the tensile instability failure criterion. Cyclic life results for several chamber life enhancing coolant channel designs are compared to the typically used LCF analysis that neglects cyclic creep. The results show that the usable cyclic creep life is approximately 30 to 50% of the commonly used LCF life.

Kasper, H. J.↗
NASA NTRS1964

Photographic Study of Liquid-Oxygen Boiling and Gas Injection in the Injector of a Chugging Rocket Engine

High-speed motion pictures were taken of conditions in the injector liquid-oxygen cavity of an RL-10 rocket engine during throttled engine operation. Photographs were taken during operation of the engine in the chugging region as the helium gas was injected to stabilize combustion, during operation at rated thrust, and during transition into chugging conditions as the gas injection was discontinued. Results of the investigation indicate that, during chugging rocket operation of the RL-10 engine, a high population of fairly large bubbles formed and collapsed within the liquid-oxygen cavity at the same frequency as the chamber pressure oscillations. When gaseous helium was injected into the liquid-oxygen cavity, a fog rapidly spread over the entire field of view, and the system immediately became stable. The injection of gaseous helium at rated conditions produced a very slight increase in engine performance but not enough to produce a net gain in a typical mission payload with the extra equipment needed. The inherent low-frequency system instability associated with the fuel system at low thrust levels was reduced by injecting either gaseous helium or hydrogen. Complete stabilization was achieved in some cases, and a reduction in the severity of the oscillations in others. This was apparently due to the ·anchoring of the phase change front to the location of the gas injection.

Conrad, E. William↗
NASA NTRS1993

Time-dependent Computational Studies of Premixed Flames in Microgravity

This report describes the research performed at the Center for Reactive Flow and Dynamical Systems in the Laboratory for Computational Physics and Fluid Dynamics, at the Naval Research Laboratory, in support of NASA Microgravity Science and Applications Program. The primary focus of this research is on investigating fundamental questions concerning the propagation and extinction of premixed flames in earth gravity and in microgravity environments. Our approach is to use detailed time-dependent, multispecies, numerical models as tools to simulate flames in different gravity environments. The models include a detailed chemical kinetics mechanism consisting of elementary reactions among the eight reactive species involved in hydrogen combustion, coupled to algorithms for convection, thermal conduction, viscosity, molecular and thermal diffusion, and external forces. The external force, gravity, can be put in any direction relative to flame propagation and can have a range of values. Recently more advanced wall boundary conditions such as isothermal and no-slip have been added to the model. This enables the simulation of flames propagating in more practical systems than before. We have used the numerical simulations to investigate the effects of heat losses and buoyancy forces on the structure and stability of flames, to help resolve fundamental questions on the existence of flammability limits when there are no external losses or buoyancy forces in the system, to understand the interaction between the various processes leading to flame instabilities and extinguishment, and to study the dynamics of cell formation and splitting. Our studies have been able to bring out the differences between upward- and downward-propagating flames and predict the zero-gravity behavior of these flames. The simulations have also highlighted the dominant role of wall heat losses in the case of downward-propagating flames. The simulations have been able to qualitatively predict the formation of multiple cells and the cessation of cell-splitting. Our studies have also shown that some flames in a microgravity environment can be extinguished due to a chemical instability and without any external losses. However, further simulations are needed to more completely understand upward-propagating and zero-gravity flames as well as to understand the potential effect of radiative heat losses.

Kailasanath, K.↗
NASA NTRS2016

Predictive Evaluations of Oxygen-Rich Hydrocarbon Combustion Gas-Centered Swirl Coaxial Injectors using a Flamelet-Based 3-D CFD Simulation Approach

NASA Marshall Space Flight Center (MSFC) has embarked upon a joint project with the Air Force to improve the state-of-the-art of space application combustion device design and operational understanding. One goal of the project is to design, build and hot-fire test a 40,000 pound-thrust Oxygen/Rocket Propellant-2 (RP-2) Oxygen-Rich staged engine at MSFC. The overall project goals afford the opportunity to test multiple different injector designs and experimentally evaluate the any effect on the engine performance and combustion dynamics. To maximize the available test resources and benefits, pre-test, combusting flow, Computational Fluid Dynamics (CFD) analysis was performed on the individual injectors to guide the design. The results of the CFD analysis were used to design the injectors for specific, targeted fluid dynamic features and the analysis results also provided some predictive input for acoustic and thermal analysis of the main Thrust Chamber Assembly (TCA). MSFC has developed and demonstrated the ability to utilize a computationally efficient, flamelet-based combustion model to guide the pre-test design of single-element Gas Centered Swirl Coaxial (GCSC) injectors. Previous, Oxygen/RP-2 simulation models utilizing the Loci-STREAM flow solver, were validated using single injector test data from the EC-1 Air Force test facility. The simulation effort herein is an extension of the validated, CFD driven, single-injector design approach applied to single injectors which will be part of a larger engine array. Time-accurate, Three-Dimensional, CFD simulations were performed for five different classes of injector geometries. Simulations were performed to guide the design of the injector to achieve a variety of intended performance goals. For example, two GCSC injectors were designed to achieve stable hydrodynamic behavior of the propellant circuits while providing the largest thermal margin possible within the design envelope. While another injector was designed to purposefully create a hydrodynamic instability in the fuel supply circuit as predicted by the CFD analysis. Future multi-injector analysis and testing will indicate what if any changes occur in the predicted behavior for the single-element injector when the same injector geometry is placed in a multi-element array.

Richardson, Brian R.↗
NASA NTRS1990

Qualification of the RSRM field joint CF case-to-insulation bondline inspection using the Thiokol Corporation ultrasonic RSRM bondline inspection system

Qualification testing of Combustion Engineering's AMDATA Intraspect/98 Data Acquisition and Imaging System that applies to the redesigned solid rocket motor field joint capture feature case-to-insulation bondline inspection was performed. Testing was performed at M-111, the Thiokol Corp. Inert Parts Preparation Building. The purpose of the inspection was to verify the integrity of the capture feature area case-to-insulation bondline. The capture feature scanner was calibrated over an intentional 1.0 to 1.0 in. case-to-insulation unbond. The capture feature scanner was then used to scan 60 deg of a capture feature field joint. Calibration of the capture feature scanner was then rechecked over the intentional unbond to ensure that the calibration settings did not change during the case scan. This procedure was successfully performed five times to qualify the unbond detection capability of the capture feature scanner. The capture feature scanner qualified in this test contains many points of mechanical instability that can affect the overall ultrasonic signal response. A new generation scanner, designated the sigma scanner, should be implemented to replace the current configuration scanner. The sigma scanner eliminates the unstable connection points of the current scanner and has additional inspection capabilities.

Cook, M.↗
NASA NTRS2002

Splashing Droplets

Current data on droplet breakup is scarce for the sizes and velocities typical of practical applications such as in spray combustion processes and coating processes. While much more representative of practical applications, the small spatial scales and rapid time-scales prevent detailed measurement of the internal fluid dynamics and liquid property gradients produced by impinging upon surfaces. Realized through the extended spatial and temporal scales afforded by a microgravity environment, an improved understanding of drop breakup dynamics is sought to understand and ultimately control the impingement dynamics of droplets upon surfaces in practical situations. The primary objective of this research will be to mark the onset of different 'splashing modes' and to determine their temperature, pressure and angle dependence for impinging droplets representative of practical fluids. In addition, we are modeling the evolution of droplets that do not initially splash but rather undergo a 'fingering' evolution observed on the spreading fluid front and the transformation of these fingers into splashed products. An example of our experimental data is presented below. These images are of Isopar V impacting a mirror-polished surface. They were acquired using a high-speed camera at 1000 frames per second. They show the spreading of a single droplet after impact and ensuing finger instabilities. Normal gravity experimental data such as this will guide low gravity measurements in the 2.2 second drop tower and KC-135 aircraft as available. Presently we are in the process of comparing the experimental data of droplet shape evolution to numerical models, which can also capture the internal fluid dynamics and liquid property gradients such as produced by impingement upon a heated surface. To-date isothermal numerical data has been modeled using direct numerical simulations of representative splashing droplets. The data obtained so far indicates that the present model describes well the droplet wall interactions to a point in time just before splash. Additional information is included in the original extended abstract.

VanderWal, Randall L.↗
NASA NTRS1995

Excitable dynamics in high-Lewis number premixed gas combustion at normal and microgravity

Freely-propagating, premixed gas flames in high-Lewis (Le) number, quiescent mixtures are studied experimentally in tubes of various diameter at normal (lg) and microgravity (mu g). A premixture of lean butane and oxygen diluted with helium, argon, neon, nitrogen or a mixture of multiple diluents is examined such that the thermal diffusivity of the mixture (and to a lesser extent, the mass diffusivity of the rate-limiting component) is systematically varied. In effect, different diluents allow variation of the Le without changing the chemistry. The flames are recorded with high speed cinematography and their stability is visually assessed. Different modes of propagation were observed depending on the diameter of the tubes (different conductive heat loss), the composition of the mixture and the g-level. At 1g, four modes of propagation were observed in small and intermediate diameter tubes (large conductive heat loss): (1) steadily propagating flames, (2) radial and longitudinal pulsating flames, (3) 'wavering' flames, and (4) rotating spiral flames. As the diameter of the tube increases, the radial modes become more pronounced while the longitudinal modes systematically disappear. Also, multiple, simultaneous, spatially-separated 'pacemaker' sites are observed in intermediate and large diameter tubes. Each site starts as a small region of high luminosity and develops into a flamelet which assumes the form of one of the fore mentioned modes. These flamelets eventually interact, annihilate each other in their regions of intersection and merge at their newly created free-ends. For very large tubes, radially-propagating wave-trains (believed to be 'trigger waves') are observed. These are analogous to the radial pulsations observed in the smaller diameter tubes. At mu g, three modes of propagation have been observed: (1) steadily propagating flames, (2) radial and longitudinal pulsating flames, and (3) multi-armed, rotating flames. Since the pulsating mode exists at mu g and 1g, buoyant flicker is not the mechanism which drives the pulsations. Moreover, all of the instabilities at 1g and mu g have characteristic frequencies on the O(100Hz). This value is lower than the fundamental, longitudinal acoustic frequencies of the tubes which suggests that the instabilities are not acoustically driven. The patterns formed by this reaction bear remarkable similarities with the patterns formed in most excitable media when the behavior of the system is driven by couplings between chemical reaction and diffusion (e.g., Belousov-Zhabotinsky reaction, Patterns in slime molds, spiral waves in the retina of a bird's eye). While it is recognized that the chemical mechanism associated with this premixed gas reaction is exponentially sensitive to temperature and undoubtedly different from those which govern previously observed excitable media (most are isothermal, or weakly exothermic, liquid phase reactions), similar spatial and temporal patterns should not come as a complete surprise considering heat and mass diffusion are self similar. It is concluded that this premixed gas system is a definitive example of a diffusive-thermal, gas-phase oscillator based on these experimental results and their favorable comparison with theory.

Pearlman, Howard↗
NASA NTRS2014

NASA One-Dimensional Combustor Simulation--User Manual for S1D_ML

The work presented in this paper is to promote research leading to a closed-loop control system to actively suppress thermo-acoustic instabilities. To serve as a model for such a closed-loop control system, a one-dimensional combustor simulation composed using MATLAB software tools has been written. This MATLAB based process is similar to a precursor one-dimensional combustor simulation that was formatted as FORTRAN 77 source code. The previous simulation process requires modification to the FORTRAN 77 source code, compiling, and linking when creating a new combustor simulation executable file. The MATLAB based simulation does not require making changes to the source code, recompiling, or linking. Furthermore, the MATLAB based simulation can be run from script files within the MATLAB environment or with a compiled copy of the executable file running in the Command Prompt window without requiring a licensed copy of MATLAB. This report presents a general simulation overview. Details regarding how to setup and initiate a simulation are also presented. Finally, the post-processing section describes the two types of files created while running the simulation and it also includes simulation results for a default simulation included with the source code.

combustion↗
NASA NTRS2001

Characterization of a Laminate Flat Plate Diffusion Flame in Microgravity using PIV, Visible and CH Emissions

Motivated by fire safety concerns and the advent of long-term micro-gravity facilities, a cooperative program has been developed to study the mechanisms and material properties that control flow assisted (co-current) flame spread. This program has used as a common fire scenario a reacting steady-state boundary layer. Preliminary studies explored the aerodynamics of a reacting boundary layer by simulating a condensed fuel by means of a gas burner. Stability curves for ethane air flames were obtained and different burning regimes were identified. An important feature of this study was the independent identification of the different mechanisms leading to the instability of the flow. It was observed that fuel injection velocity and thermal expansion independently contributed to the separation of the flow at the leading edge of the burner. The occurrence of separation resulted in complex three-dimensional flow patterns that have a dominant effect on critical fire safety parameters such as the stand-off distance and flame length. This work was extended to a solid fuel (PMMA) leading to a Sounding Rocket experiment (Mini-Texus-6). The solid phase showed similar flow patterns, mostly present at low flow velocities (<100 mm/s) but the results clearly demonstrated that the thermal balance at the pyrolyzing fuel surface is the dominant mechanism that controls both stand-off distance and flame length. This thermal balance could be described in a global manner by means of a total mass transfer or "B" number. This "B" number incorporates surface re-radiation, radiative feedback and in-depth heat conduction as first prescribed by Emmons. The mass transfer number becomes the single parameter that determines the evolution of these fire safety variables (flame length, stand-off distance) and therefore can be used as a ranking criterion to assess the flammability of materials. The particular configuration is representative of the NASA upward flame spread test (Test 1) therefore this approach can be used in the interpretation of the results obtained from this test. Nevertheless, complete validation of this approach has not been fully achieved due, mainly because all the measurements necessary to compare with the theoretical predictions have not been obtained. Following these studies two different directions have been taken. The first attempts to elucidate the details of the gas phase combustion reaction and the associated flow field by means of quantitative and qualitative measurements. The second approach, a more practical one, is to apply this methodology to the assessment of material flammability. The former is currently being conducted with a gas burner because it allows for easier control and longer experimentation time. The results obtained so far will be presented in more detail. The latter is a new program therefore only a brief summary of the objectives will be presented.

Joulain, P.↗
NASA NTRS1997

Strain-Rate-Free Diffusion Flames: Initiation, Properties, and Quenching

For about a half century, the stabilization of a steady planar deflagration on a heat-sink-type flat-flame burner has been of extraordinary service for the theoretical modeling and diagnostic probing of combusting gaseous mixtures. However, most engineering devices and most unwanted fire involve the burning of initially unmixed reactants. The most vigorous burning of initially separated gaseous fuel and oxidizer is the diffusion flame. In this useful idealization (limiting case), the reactants are converted to product at a mathematically thin interface, so no interpenetration of fuel and oxidizer occurs. This limit is of practical importance because it often characterizes the condition of optimal performance (and sometimes environmentally objectionable operation) of a combustor. A steady planar diffusion flame is most closely approached in the laboratory in the counterflow apparatus. The utility of this simple-strain-rate flow for the modeling and probing of diffusion flames was noted by Pandya and Weinberg 35 years ago, though only in the last decade or so has its use become internationally common place. However, typically, as the strain rate a is reduced below about 20 cm(exp -1), and the diffusion-flame limit (reaction rate much faster than the flow rate) is approached, the burning is observed to become unstable in earth gravity. The advantageous steady planar flow is not available in the diffusion-flame limit in earth gravity. This is unfortunate because the typical spatial scale in a counterflow is (k/a)(sup 1/2), where k denotes a characteristic diffusion coefficient; thus, the length scale becomes large, and the reacting flow is particularly amenable to diagnostic probing, as the diffusion-flame limit is approached. The disruption of planar symmetry is owing the fact that, as the strain rate a decreases, the residence time (l/a) of the throughput in the counterflow burner increases. Observationally, when the residence time exceeds about 50 msec, the inevitably present convective (Rayleigh-Benard) instabilities, associated with hot-under-cold (flame-under-fresh-reactant) stratification of fluid in a gravitational field, have time to grow to finite amplitude during transit of the burner.

Fendell, Francis↗