Closure Relations for Fluxes of Flame Surface Density and Scalar Dissipation Rate in Turbulent Premixed Flames

Abstract

In this study, closure relations for total and turbulent convection fluxes of flame surface density and scalar dissipation rate were developed (i) by placing the focus of consideration on the flow velocity conditioned to the instantaneous flame within the mean flame brush and (ii) by considering the limiting behavior of this velocity at the leading and trailing edges of the flame brush. The model was tested against direct numerical simulation (DNS) data obtained from three statistically stationary, one-dimensional, planar, premixed turbulent flames associated with the flamelet regime of turbulent burning. While turbulent fluxes of flame surface density and scalar dissipation rate, obtained in the DNSs, showed the countergradient behavior, the model predicted the total fluxes reasonably well without using any tuning parameter. The model predictions were also compared with results computed using an alternative closure relation for the flame-conditioned velocity.

Application of conditioned structure functions to exploring influence of premixed combustion on two-point turbulence statistics

“…Because the DNS data analyzed here were extensively discussed by various research groups [12,13,15,16,[24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43], we will restrict ourselves to a brief summary of those compressible simulations. They dealt with statistically 1D, planar, adiabatic flames modeled by unsteady 3D continuity, Navier-Stokes, and energy equations, supplemented with a transport equation for the mass fraction 𝑌 of a deficient reactant and the ideal gas state equation.…”

Computational Fluid Dynamics Model for Analysis of the Turbulent Limits of Hydrogen Combustion

“…Later in [25], this two-parameter Markstein length model was successfully implemented for the description of premixed turbulent combustion and verified against the DNS data on turbulent flame displacement speed. In the context of flame surface density methods, problems related to the prediction of convection fluxes are of particular importance (see, e.g., [26]). Another promising technique is employing a statistical description of the flow via evolution equations for probability density functions [27,28].…”

Numerical Simulations of Turbulent Combustion

“…Lipatnikov et al [7] suggest new closure relations for turbulent scalar fluxes of flame surface density and scalar dissipation rate in the corresponding transport equations. These closure relations are validated by analyzing direct numerical simulation data obtained from three statistically stationary, one-dimensional, planar, weakly turbulent premixed flames characterized by three different density ratios.…”