Derivation and investigation of a new explicit algebraic model for the passive scalar flux

Abstract

An algebraic relation for the scalar flux, in terms of mean flow quantities, is formed by applying an equilibrium condition in the transport equations for the normalized scalar flux. This modeling approach is analogous to explicit algebraic Reynolds stress modeling (EARSM) for the Reynolds stress anisotropies. The assumption of negligible advection and diffusion of the normalized passive scalar flux gives, in general, an implicit, nonlinear set of algebraic equations. A method to solve this implicit relation in a fully explicit form is proposed, where the nonlinearity in the scalar-production-to-dissipation ratio is considered and solved. The nonlinearity, in the algebraic equations for the normalized scalar fluxes, may be eliminated directly by using a nonlinear term in the model of the pressure scalar-gradient correlation and the destruction and thus results in a much simpler model for both two-and three-dimensional mean flows. The performance of the present model is investigated in three different flow situations. These are homogeneous shear flow with an imposed mean scalar gradient, turbulent channel flow, and the flow field downstream a heated cylinder. The direct numerical simulation (DNS) data are used to analyze the passive scalar flux in the homogeneous shear and channel flow cases and experimental data are used in the case of the heated cylinder wake. Sets of parameter values giving very good predictions in all three cases are found.