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NASA NTRS1987

An asymptotic analysis of supersonic reacting mixing layers

The purpose of this paper is to present an asymptotic analysis of the laminar mixing of the simultaneous chemical reaction between parallel supersonic streams of two reacting species. The study is based on a one-step irreversible Arrhenius reaction and on large activation energy asymptotics. Essentially it extends the work of Linan and Crespo to include the effect of free shear and Mach number on the ignition regime, the deflagration regime and the diffusion flame regime. It is found that the effective parameter is the product of the characteristic Mach number and a shear parameter.

Jackson, T. L.↗

NASA NTRSDate not supplied

Asymptotic Analysis of Premixed N-alkane Cool Flame Propagation

A simplified chemical-kinetic cool-flame mechanism for n-alkanes developed recently is applied to premixed laminar cool-flame deflagrations. The present contribution derives the structure of the associated freely propagating cool premixed flame controlled by the low-temperature chemistry and develops formulas for calculating the corresponding laminar burning velocity. Application of activation-energy asymptotics reveals finite-rate chemistry without heat release occurring throughout the preheat zone and leakage of both fuel and oxygen through the thin heat-release zone, there being zones of consumption of an intermediate species on each side of the heat-release zone, thicker than that zone but still thin compared with the preheat-zone thickness. Predicted laminar burning velocities are compared with recently reported measurements for n-dodecane, performed in a newly deigned high-pressure ignition apparatus, resulting in reasonable agreement.

Cool flames↗

NASA NTRSDate not supplied

Asymptotic Analysis of Premixed N-alkane Cool Flame Propagation

cool flames↗

NASA NTRS1982

The premixed flame in uniform straining flow

Characteristics of the premixed flame in uniform straining flow are investigated by the technique of activation-energy asymptotics. An inverse method is used, which avoids some of the restrictions of previous analyses. It is shown that this method recovers known results for adiabatic flames. New results for flames with heat loss are obtained, and it is shown that, in the presence of finite heat loss, straining can extinguish flames. A stability analysis shows that straining can suppress the cellular instability of flames with Lewis number less than unity. Strain can produce instability of flames with Lewis number greater than unity. A comparison shows quite good agreement between theoretical deductions and experimental observations of Ishizuka, Miyasaka & Law (1981).

Durbin, P. A.↗

NASA NTRS1986

Theory of interactive combustion of counterflow premixed flames

The framework of large activation energy asymptotics is used in an investigation of the extinction characteristics of two interacting premixed flames in counterflow configuration, analyzing the interactive combustion modes of two lean premixed flames, two rich premixed flames, and one of each type of flame separated by a diffusion flame. Regions corresponding to symbiotic combustion of two lean or two rich premixed flames exist in which either flame will be extinguished in the absence of the other. Conditions for the existence of superadiabatic flames within mixtures outside of the conventional flammability limit compositions are established, and practical implications of flame interaction for combustion in inhomogeneous mixtures are discussed.

Sohrab, S. H.↗

NASA NTRS1989

A Theoretical Study of Propagation and Extinction of Nonsteady Spherical Flame Fronts

Freely propagating expanding spherical flame fronts are studied analytically using the method of activation energy asymptotics. Effects of Lewis number (Le), curvature, heat loss, and thermal expansion on propagation rates and extinction conditions are examined. The behavior of spherical flame fronts is found to be determined primarily by the values of Le and a heat-loss parameter. Results are compared to recent experimental observations of spherical flame fronts in mixtures near the flammability limits; for Le less than 1, it is found that many of the features of these experimental results are described by the analysis presented here. For Le greater than 1, however, unrealistic dynamic behavior is predicted due to the nature of diffusive-thermal instabilities under these conditions.

Ronney, P. D.↗

NASA NTRS1994

Stabilization Mechanisms and Burning Rates of Cylindrical Burner Flames

A study is conducted of the structure and response of curved (but unstretched), cylindrically-symmetric 1D premixed flames from a cylindrical porous burner. The study has employed (1) activation-energy asymptotics with one-step reaction constant and constant properties; (2) a numerical computation which encompassed detailed chemistry and transport behavior, and (3) drop-tower microgravity tests. Attention was given to the relative importance of heat loss vs. flow divergence as the dominant mechanism for flame stabilization; the results show that, with increasing flow discharge rate, the dominant flame stabilization mechanism changes from heat loss to flow divergence.

Eng, J. A.↗

NASA NTRS1996

Ignition, Burning, and Extinction of a Strained Fuel Strip

Flame structure and ignition and extinction processes associated with a strained fuel strip are explored numerically using detailed transport and complex kinetics for a propane-air reaction. Ignition modes are identified that are similar to those predicted by one-step activation energy asymptotics, i.e., modes in which diffusion flames can ignite as independent or dependent interfaces, and modes in which single premixed or partially premixed flames ignite. These ignition modes are found to be dependent on critical combinations of strain rate, fuel strip thickness, and initial reactant temperatures. Extinction in this configuration is seen to occur due to fuel consumption by adjacent flames, although viscosity is seen to have the effect of delaying extinction by reducing the effective strain rate and velocity field experienced by the flames.

Selerland, T.↗

NASA NTRS1998

Ignition, Burning and Extinction of a Strained Fuel Strip with Complex Kinetics

Flame structure and ignition and extinction processes associated with a strained fuel strip are explored numerically using detailed transport and complex kinetics for a propane-air reaction. Ignition modes are identified that are similar to those predicted by one-step activation energy asymptotics, i.e., modes in which diffusion flames can ignite as independent or dependent interfaces and modes in which single premixed or partially premixed flames ignite and burn. These ignition modes have been found to be dependent on critical combinations of strain rate, fuel strip thickness and initial reactant temperatures. The formation of NO/NO2 is found to be strongly dependent on strain rate and the local molecular mixing of reactants which occurs as a consequence of strain. Extinction in this configuration is seen to occur due to fuel consumption by adjacent flames, although viscosity is seen to have the effect of delaying extinction by reducing the effective strain rate experienced by the flames. Response of the flames to oscillatory strain rates is seen to be strongly dependent on the amplitude and frequency of the oscillation.

Selerland, T.↗

NASA NTRS1996

Ignition Delay Associated with a Strained Strip

Ignition processes associated with two adjacent fuel-oxidizer interferences bounding a strained fuel strip are explored here using single-step activation energy asymptotics. Calculations are made for constant as well as temporally decaying strain fields. There possible models of ignition are determined: one in which the two interfaces ignite independently as diffusion flames; one in which the two interfaces ignite dependently and in which ignition occurs to form a single , premixed flame at very high strain rates before ignition is completely prevented. In contrast to a single, isolated interface in which ignition can be prevented by overmatching heat production with heat convection due to strain, ignition of a strained fuel strip can also be prevented if the finite extend of fuel is diluted by oxidizer more quickly than heat production can cause a positive feedback thermal runaway. These behaviors are dependent on the relative sizes of timescales associated with species and heat diffusion, with convection due to strain, and with the chemical reaction. The result here indicate that adjacent, strained species interfaces may ignite quite differently in nature from ignition of a single, strained intrface and that their interdependence should be considered as the interfaces are brought closer together in complex strain fields. Critical strain rates leading to complete ignition delay are found to be considerably smaller for the fuel strip than those for single interfaces as the fuel strip is made thin in comparison to diffusion and chemical length scales.

Gerk, T. J.↗

NASA NTRS2000

Scale-Invariant Forms of Conservation Equations in Reactive Fields and a Modified Hydro-Thermo-Diffusive Theory of Laminar Flames

A scale-invariant model of statistical mechanics is applied to present invariant forms of mass, energy, linear, and angular momentum conservation equations in reactive fields. The resulting conservation equations at molecular-dynamic scale are solved by the method of large activation energy asymptotics to describe the hydro-thermo-diffusive structure of laminar premixed flames. The predicted temperature and velocity profiles are in agreement with the observations. Also, with realistic physico-chemical properties and chemical-kinetic parameters for a single-step overall combustion of stoichiometric methane-air premixed flame, the laminar flame propagation velocity of 42.1 cm/s is calculated in agreement with the experimental value.

Sohrab, Siavash H.↗

NASA NTRS1998

On Soot Inception in Nonpremixed Flames and the Effects of Flame Structure

A simplified three-step model of soot inception has been employed with high activation energy asymptotics to study soot inception in nonpremixed counterflow systems with emphasis on understanding the effects of hydrodynamics and transport. The resulting scheme yields three zones: (1) a fuel oxidation zone wherein the fuel and oxidizer react to form product as well as a radical R, (e.g., H), (2) a soot/precursor formation zone where the radical R reacts with fuel to form "soot/precursor" S, and (3) a soot/precursor consumption zone where S reacts with the oxidizer to form product. The kinetic scheme, although greatly simplified, allows the coupling between soot inception and flame structure to be assessed. The results yield flame temperature, flame location, and a soot/precursor index S(sub I) as functions of Damkohler number for S formation. The soot/precursor index indicates the amount of S at the boundary of the formation region. The flame temperature indirectly indicates the total amount of S integrated over the formation region because as S is formed less heat release is available. The results show that unlike oxidation reactions, an extinction turning-point behavior does not exist for soot. Instead, the total amount of S slowly decreases with decreasing Damkohler number (increasing strain rate), which is consistent with counterflow flame experiments. When the Lewis number of the radical is decreased from unity, the total S reduces due to reduced residence time for the radical in the soot formation region. Similarly, when the Lewis number of the soot/precursor is increased from unity the amount of S increases for all Damkohler numbers. In addition to studying fuel-air (low stoichiometric mixture fraction) flames, the air-side nitrogen was substituted into the fuel, yielding diluted fuel-oxygen (high stoichiometric mixture fraction) flames with the same flame temperature as the fuel - air flames. The relative flame locations were different however, and, consistent with counterflow flame experiments, this difference was found to dramatically reduce the total amount of S generated because the change in stoichiometric mixture fraction affects residence times, temperatures and concentrations in the soot/precursor formation and consumption zones. Furthermore, while the soot/precursor consumption reaction had a negligible effect on the soot process for fuel-air flames it was very important to diluted fuel - oxygen flames.

Chao, B. H.↗

NASA NTRS2005

Control of Combustion-Instabilities Through Various Passive Devices

It is well known that under some operating conditions, rocket engines (using solid or liquid fuels) exhibit unstable modes of operation that can lead to engine malfunction and shutdown. The sources of these instabilities are diverse and are dependent on fuel, chamber geometry and various upstream sources such as pumps, valves and injection mechanism. It is believed that combustion-acoustic instabilities occur when the acoustic energy increase due to the unsteady heat release of the flame is greater than the losses of acoustic energy from the system [1, 2]. Giammar and Putnam [3] performed a comprehensive study of noise generated by gasfired industrial burners and made several key observations; flow noise was sometimes more intense than combustion roar, which tended to have a characteristic frequency spectrum. Turbulence was amplified by the flame. The noise power varied directly with combustion intensity and also with the product of pressure drop and heat release rate. Karchmer [4] correlated the noise emitted from a turbofan jet engine with that in the combustion chamber. This is important, since it quantified how much of the noise from an engine originates in the combustor. A physical interpretation of the interchange of energy between sound waves and unsteady heat release rates was given by Rayleigh [5] for inviscid, linear perturbations. Bloxidge et al [6] extended Rayleigh s criterion to describe the interaction of unsteady combustion with one-dimensional acoustic waves in a duct. Solutions to the mass, momentum and energy conservation equations in the pre- and post-flame zones were matched by making several assumptions about the combustion process. They concluded that changes in boundary conditions affect the energy balance of acoustic waves in the combustor. Abouseif et al [7] also solved the one-dimensional flow equations, but they used a onestep reaction to evaluate the unsteady heat release rate by relating it to temperature and velocity perturbations. Their analysis showed that oscillations arise from coupling between entropy waves produced at the flame and pressure waves originating from the nozzle. Yang and Culick [8] assumed a thin flame sheet, which is distorted by velocity and pressure oscillations. Conservation equations were expressed in integral form and solutions for the acoustic wave equations and complex frequencies were obtained. The imaginary part of the frequency indicated stability regions of the flame. Activation energy asymptotics together with a one-step reaction were used by McIntosh [9] to study the effects of acoustic forcing and feedback on unsteady, one-dimensional flames. He found that the flame stability was altered by the upstream acoustic feedback. Shyy et al [10] used a high-accuracy TVD scheme to simulate unsteady, one-dimensional longitudinal, combustion instabilities. However, numerical diffusion was not completely eliminated. Recently, Prasad [11] investigated numerically the interactions of pressure perturbations with premixed flames. He used complex chemistry to study responses of pressure perturbations in one-dimensional combustors. His results indicated that reflected and transmitted waves differed significantly from incident waves.

Frendi, Kader↗

NASA NTRS2013

Methanol Droplet Combustion in Oxygen-Inert Environments in Microgravity

The Flame Extinguishment (FLEX) experiment that is currently underway in the Combustion Integrated Rack facility onboard the International Space Station is aimed at understanding the effects of inert diluents on the flammability of condensed phase fuels. To this end, droplets of various fuels, including alkanes and alcohols, are burned in a quiescent microgravity environment with varying amounts of oxygen and inert diluents to determine the limiting oxygen index (LOI) for these fuels. In this study we report experimental observations of methanol droplets burning in oxygen-nitrogen-carbon dioxide and oxygen-nitrogen-helium gas mixtures at 0.7 and 1 atmospheric pressures. The initial droplet size varied between approximately 1.5 mm and 4 mm to capture both diffusive extinction brought about by insufficient residence time at the flame and radiative extinction caused by excessive heat loss from the flame zone. The ambient oxygen concentration varied from a high value of 30% by volume to as low as 12%, approaching the limiting oxygen index for the fuel. The inert dilution by carbon dioxide and helium varied over a range of 0% to 70% by volume. In these experiments, both freely floated and tethered droplets were ignited using symmetrically opposed hot-wire igniters and the burning histories were recorded onboard using digital cameras, downlinked later to the ground for analysis. The digital images yielded droplet and flame diameters as functions of time and subsequently droplet burning rate, flame standoff ratio, and initial and extinction droplet diameters. Simplified theoretical models correlate the measured burning rate constant and the flame standoff ratio reasonably well. An activation energy asymptotic theory accounting for time-dependent water dissolution or evaporation from the droplet is shown to predict the measured diffusive extinction conditions well. The experiments also show that the limiting oxygen index for methanol in these diluent gases is around 12% to 13% oxygen by volume.

Nayagam, Vedha↗

NASA NTRS2024

Simplified Structure Models for Premixed n-Alkane Cool Flames

The chemical kinetics of cool flames in mixtures of normal alkanes, oxygen, and nitrogen recently have been reduced to obtain simplified asymptotic flame-structure models that can be used to compare theoretical predictions with experimental measurements. A key step that affects flame structures strongly, namely the abstraction of a hydrogen atom from the alkyl radical by an oxygen molecule, had not been taken into account in those models. This deficiency has now been remedied for diffusion flames. The present contribution reports the corresponding remedy for premixed-flame analyses. In the new model, non-zero chemical reaction rates are restricted to narrow regions in the vicinity of the maximum temperature, whereas previously they extended throughout the preheat zone. Comparisons of the new predictions with experimental burning-velocity measurements seem favorable.

premixed cool flames↗

NASA NTRS1984

Heat and mass transfer in combustion - Fundamental concepts and analytical techniques

Fundamental combustion phenomena and the associated flame structures in laminar gaseous flows are discussed on physical bases within the framework of the three nondimensional parameters of interest to heat and mass transfer in chemically-reacting flows, namely the Damkoehler number, the Lewis number, and the Arrhenius number which is the ratio of the reaction activation energy to the characteristic thermal energy. The model problems selected for illustration are droplet combustion, boundary layer combustion, and the propagation, flammability, and stability of premixed flames. Fundamental concepts discussed include the flame structures for large activation energy reactions, S-curve interpretation of the ignition and extinctin states, reaction-induced local-similarity and non-similarity in boundary layer flows, the origin and removal of the cold boundary difficulty in modeling flame propagation, and effects of flame stretch and preferential diffusion on flame extinction and stability. Analytical techniques introduced include the Shvab-Zeldovich formulation, the local Shvab-Zeldovich formulation, flame-sheet approximation and the associated jump formulation, and large activation energy matched asymptotic analysis. Potentially promising research areas are suggested.

Law, C. K.↗

NASA NTRS1994

Numerical Analysis of an Impinging Jet Reactor for the CVD and Gas-Phase Nucleation of Titania

We model a cold-wall atmospheric pressure impinging jet reactor to study the CVD and gas-phase nucleation of TiO2 from a titanium tetra-iso-propoxide (TTIP)/oxygen dilute source gas mixture in nitrogen. The mathematical model uses the computational code FIDAP and complements our recent asymptotic theory for high activation energy gas-phase reactions in thin chemically reacting sublayers. The numerical predictions highlight deviations from ideality in various regions inside the experimental reactor. Model predictions of deposition rates and the onset of gas-phase nucleation compare favorably with experiments. Although variable property effects on deposition rates are not significant (approximately 11 percent at 1000 K), the reduction rates due to Soret transport is substantial (approximately 75 percent at 1000 K).

Gokoglu, Suleyman A.↗

NASA NTRS1984

Extinction of premixed flames by stretch and radiative loss

The extinction of laminar premixed flames by stretch and radiative loss is studied for the model problem of counterflow opposed-jet combustion by using the matched asymptotic expansion technique for the highly temperature sensitive processes of radiative heat loss and large-activation-energy reaction kinetics. Explicit expressions for the critical Damkoehler number at extinction are derived and the influence of upstream vs downstream heat losses assessed. Results show that stretch exerts a much stronger influence than radiative loss on flame extinction.

Sohrab, S. H.↗