Twenty-Third Symposium (International) on Combustion/The Combustion Institute, 1990/pp. 685-692 A MIXEDNESS-REACTEDNESS FLAMELET MODEL FOR TURBULENT DIFFUSION FLAMES D. BRADLEY, P. H. GASKELL AND A.K.C. LAU Department of Mechanical Engineering The University of Leeds Leeds LS2 9JT, UK. A novel, non-equilibrium, combustion model is proposed, to simulate turbulent diffusion flames, based on a laminar flamelet approach that was originally developed for premixed combustion. The model embodies a mixedness factor to describe the mixture strength and a reactedness parameter to describe the degree of completeness of combustion. The effect of straining is accounted for in prior laminar flame computations and the imposition of a known distribution of flame straining on the flamelets. Profiles of laminar, heat release rate against temperature and the assumed independence of fluctuations in mixedness, reactedness and flame straining enable a simple evaluation of turbulent mean heat release rate to be made, This approach is used to predict numerically the field solutions for lifted, turbulent jet, methane-air, diffusion flames, in conjunction with the k - 9 turbulence model. The com- putations predict an approximately linear relationship between lift-off height and fuel jet ve- locity, in good agreement with available experimental data. Results suggest that the mech- anism of flame stabilization is associated with the complex interactions between convection, turbulent mixing, heat release rate under strain and thermal expansion, rather than with a single phenomenological parameter such as, for example, the flame strain extinction limit. Introduction Because of the practical importance of diffusion flames, their theoretical study has been pursued with growing intensity since the 1929 seminal paper, on laminar diffusion flames by Burke and Schumann, reprinted in the First Symposium on Combustion volume. 1 The simplicity of a fast chemistry ap- proach that eschewed chemical kinetics and made the mixing process rate limiting was attractive and often revealing, notwithstanding the conclusion of these authors that more fundamental investigations on the basis of chemical kinetics might be both in- teresting and profitable. Diffusive fluxes of fuel and oxygen into the thin flame sheet were in the stoi- chiometric proportion. However, with an assumed infinite reaction rate it is impossible to derive re- alistic spatial dis~butions either of heat release rate or of concentrations of chemical species. Rather more realistically, whilst still eschewing chemical kinetic 2 detail, Bilger showed the heat release rate to be a function of the scalar dissipation rate, X, where 2 ~ is a conserved scalar fuel stream mixture fraction variable, with a value of unity in the fuel stream and of zero in the oxidant and D is the diffusion coefficient of ~. Experimental studies of laminar flames have supported and utilized this ap- proach, a-4 Most of the reaction occurs close to the stoichiometric value of ~. More recently, detailed computational studies of laminar diffusion flames have embodied comprehensive chemical kinetics and the influences of flame straining. 5 The conserved scalar has been employed also in the mathematical modelling of turbulent diffusion flames, together with an expression for its proba- bility density function (pdf). The k - e model of turbulence has described complex engineering flow fields, in association with a conservation equation for such a scalar. 6 Fast chemistry assumptions per- sisted, in that for each value of ~ the composition and temperature were those associated with the adiabatic equilibrium products of combustion. However, an examination of experimental compo- sitional and temperature profiles against ~ for lam- inar diffusion flames showed them to be signifi- cantly different from those based on the equilibrium assumption. 7 Janicka and Kollmans introduced hydrogen oxi- dation partial equilibrium chemistry in a turbulent H2-air diffusion flame model, with two dependent variables. One was a reaction variable in terms of //2 concentration and the other a mixture fraction 685