A subgrid model for nonlinear functions of a scalar

Abstract

In applications of large eddy simulation of turbulent flows, subgrid models are often required for closure of strongly nonlinear functions of a scalar. The Arrhenius dependence of the reaction rate on temperature, T, the T4 dependence of radiation heat transfer, as well as the species mass fractions and temperature dependence on the mixture fraction in solutions of the strained laminar flamelet model are among some of the problems of interest. A moment-based reconstruction methodology is proposed here in which the scalar field is estimated by an approximate deconvolution operation but, unlike the usual deconvolution operation with given coefficients, the coefficients in the expansion are obtained by requiring that the statistical filtered moments of the scalar field up to a certain order are matched. The estimated scalar field is then used as a surrogate for the exact scalar field to directly calculate the subgrid contribution. Tests of the proposed approach are performed by using our direct numerical simulation database of scalar transport in a turbulent shear layer using two filter sizes: 12 points and 6 points per vorticity thickness. It is found that a simple moment-based model with one coefficient performs well for polynomial nonlinearities. The performance of the model in the case of an exponential Arrhenius-type nonlinearity is generally good and can be very good depending on the stoichiometric mixture fraction and the filter size. © 2001 American Institute of Physics.