On element mass conservation in Eulerian stochastic fields modeling of turbulent combustion

Abstract

Eulerian stochastic fields (ESF) based transported PDF method has evolved as one of the general purpose methods for the numerical simulation of complex chemically reactive turbulent flows in which the effect of turbulence on the chemical reaction rates can be computed directly without the need of modeling. It is found that ESF method may suffer from violation of the element mass conservation law due to the stochastic Wiener process and the highly non-linear dependence of the chemical reaction rates on the stochastic fields. This paper presents a modified ESF method to remove the error in the element mass conservation. The method is evaluated in numerical simulation of two turbulent flames, (i) Reynolds averaged Navier-Stokes (RANS) simulation of a turbulent non-premixed methane/air counterflow flame under stationary burning and transient flame extinction conditions, (ii) large eddy simulation of swirling turbulent methane/air non-premixed flames under local extinction and re-ignition conditions. The original ESF method violates the element mass conservation in both flames, and the element mass error would not disappear even if a large number of stochastic fields were used. The new method yields a satisfactory prediction of the element mass conservation even with a small number of stochastic fields. The new and original methods predict similar stationary flame structures but the results under flame extinction and re-ignition conditions are rather different.