Paul A. Libby

Turbulent Reacting Flows

1. Fundamental Aspects, Paul A Libby and F A Williams 2. Laminar Flamelets in Turbulent Flames, K N C Bray and Norbert Peters 3. Recent Developments in MBL-Model of Premixed Turbulent Combustion, K N C Bray and Paul A Libby 4. Reduced Chemical Systems and Their Application in Turbulent Combustion, K Seshadri and Forman A Williams 5. Comparison of Prediction and Measurement in Nonpremixed Turbulent Flames, J Y Chen and W Kollmann 6. Turbulence Modeling and Numerical Solution Methods for Variable Density and Combusting Flows, W P Jones 7. Recent Development in PDF Methods, Cesar Dopazo 8. Spectral and Random Vortex Methods in Turbulent Reacting Flows, Peyman Givi 9. Flames in Stagnating Turbulence, K N C Bray, M Champion and Paul A Libby 10. High Speed Turbulent Combustion, K N C Bray, Paul A Libby and Forman A Williams.

Unified modeling approach for premixed turbulent combustion—Part I: General formulation☆

Abstract The aerothermochemistry of premixed turbulent combustion as given by the Bray-Moss-Libby model is used to develop a Reynolds stress/flux description of a flow field consisting of constant density regions of either reactants or products and of reaction zones in which density fluctuations arise as a consequence of heat release. The third-moment terms in such a description are treated on the basis of simple physical notions, while the additional modeling required for the description of the reaction zones is based on the laminar flamelet model of reacting surfaces. Finally, conventional modeling for the constant density regions is adopted. The result is a general formulation for premixed turbulent combustion based on a particular aerothermochemical model.

Countergradient Diffusion in Premixed Turbulent Flames

Recent theoretical and experimental results demonstrating the interaction between force fields and density inhomogeneities as they arise in premixed turbulent flames are discussed. In such flames, the density fluctuates between two levels, the high density in reactants rho sub r and the low density in products rho sub p, with the ratio rho sub r/rho sub p on the order of five to ten in flows of applied interest. The force fields in such flames arise from the mean pressure drop across the flame or from the Reynolds shear stresses in tangential flames with constrained streamlines. The consequence of the interaction is nongradient turbulent transport, countergradient in the direction normal to the flame and nongradient in the tangential direction. The theoretical basis for these results, the presently available experimental support therefore and the implications for other variable density turbulent flows are discussed.

Turbulence Production in Premixed Turbulent Flames

Abstract —A second order closure theory developed earlier is used to study the processes influencing the turbulent velocity field in a premixed turbulent flame with degrees of heat release of practical interest. The flow field is chosen so that the time-averaged flame structure is one-dimensional and statistically stationary. Earlier work suggests that in the absence of turbulence production due to Reynolds stresses as is the case in a flame orthogonal to the oncoming reactants, the case we consider, dilatation resulting from heat release reduces the level of turbulence. In contrast it is shown here that with sufficient heat release turbulence increases on passage through the flame because of a buoyancy production mechanism arising from the self-induced, mean pressure gradient. This mechanism overwhelms the effects of dilatation at temperature ratios characteristic of combustion. The same buoyancy mechanism also causes counter-gradient diffusion as predicted in an earlier paper and as observed in recent e...

Flamelet Crossing Frequencies and Mean Reaction Rates in Premixed Turbulent Combustion

Abstract Abstraet–The one-point, one-time description contained in the Bray-Moss-Libby model of premixed turbulent combustion is first generalized to a two-point, two-time formulation which includes information on the time and length scales of the scalar field within turbulent flames. This formulation is then specialized to a one-point, two-time description which is treated in detail so as to yield expressions for the autocorrelation of the progress variable, for the time scale of the scalar field, for the mean crossing frequency of the flamelets and, finally, for the mean rate of chemical reaction. Although the latter expression closely resembles results developed earlier on an intuitive basis, its derivation in the present study permits an assessment of various assumptions and intermediate results by comparison with experimental measurements. Such comparisons as are currently possible are shown to lend support to the analysis and to enhance the prospects of future exploitation of the general formulation.

Structure of laminar flamelets in premixed turbulent flames

Abstract The method of activation energy asymptotics is used to describe the behavior and characteristics of adiabatic laminar flamelets involving counterflowing reactants and products as they arise in premixed turbulent flames. For moderate and low rates of strain the results are analogous to those obtained in earlier applications of the method, namely, there are reaction surfaces that maintain a diffusive-reactive balance in the first approximation. For high rates of strain we identify an extinction regime in which there is a reaction zone having a diffusive-convective-reactive balance and which thus requires a modification of the usual treatment. The asymptotic analyses are used to give the variation of the rate of product creation over the entire range of Damkohler numbers.

Strained Premixed Laminar Flames with Nonunity Lewis Numbers

Abstract The method of activation energy asymptotics is used to study the effects of Lewis numbers different from unity on nonadiabatic flamelets in counterflowing streams of reactants and products. A sequence of analyses parallels those reported earlier for such flamelets having Lewis number unity. Thus initial results relate to nearly adiabatic flows with Lewis numbers close to unity. It is found that the effect of nonunity Lewis numbers is accentuated in flamelets subjected to low rates of strain and that Lewis numbers greater than unity tend to promote extinction. Thus abrupt extinction and ignition events can occur even under adiabatic conditions. Next fully nonadiabatic flamelets with Lewis numbers near unity are treated in order to consider cases involving relatively large degrees of product heating and cooling. These results relate to reaction zones as they arise under conditions of low-to-moderate rates of strain with the customary diffusive-reactive balance. We also treat flamelets subjected to ...

Interaction effects in turbulent premixed flames

The Bray–Moss model for turbulent, premixed combustion is applied to plane, oblique combustion waves. The analysis takes into account the influence of turbulence and inhomogeneity on the effective rate of heat release, and also the competing effects of dilatation and turbulent production due to shear in the turbulent kinetic energy balance. Predictions are made of the flame speed and the structure of the reaction zone in cases where turbulent mixing is rate limiting. Qualitiative agreement is found with relevant experimental data.

Implications of the laminar flamelet model in premixed turbulent combustion

Abstract The consequences of the description of a premixed turbulent flame in terms of an ensemble of laminar flamelets are pursued and are shown to lead to new physical insight into the processes occurring in such flames and to new models for use in their analysis. In prticular, extension of the Bray-Moss model for premixed combustion leads to new models for turbulent transport providing physically appealing closure schemes. In addition, the physicochemical connection between the chemical source term and the dissipation of product fluctuations is developed and used to construct a new model for that dissipation. Similar considerations lead to new models for other dissipations. Similar considerations lead to new models for other dissipation effects. The general conclusion is reached that consistent application of the laminar flamelet model raises doubts as to the applicability to turbulent flames of some of the notions developed for constant density, nonreactive turbulence.

Theoretical study of burning carbon particles

Abstract The dynamic behavior of single carbon particles in a hot oxidizing ambient is studied. The theoretical model is based on a uniform-temperature, constant-density, spherical particle of carbon surrounded by a quiescent gas phase. With simplifying assumptions regarding the transport and thermochemical properties of the gases, the influences of the gas phase are examined (for the limiting cases of frozen and equilibrium gas chemistry). These include the contributions of radial convection and radial diffusion in mass and energy transport from the particle. Both the direct oxidation of carbon via the reaction C + 1 2 O 2 and the indirect oxidation via the reaction C + CO2 are taken into account, and both are found to play significant roles in the dynamic behavior of carbon particles. Several comparisons with available experimental data establish the validity of the theory for practical purposes. Comparison is also made when possible with previous theoretical studies. The theoretical results indicate that the history of a particle during consumption involves complex interactions of convective, diffusion, and thermochemical effects. Analytical expressions are derived and numerical results are presented for the rate of carbon mass loss showing the relative influences of the gas-phase chemistry, the gas-phase convective and diffusive transport, and the heterogeneous reaction kinetics on the overall reaction rate.