ON THE MODELING OF SCALAR DIFFUSION IN ISOTROPIC TURBULENCE

The objectives of this paper are (i) to establish analytically some important features of the scalar diffusion process in turbulence and (ii) to derive a closure model for this process in terms of the scalar probability density function (pdf). The present analysis shows that in isotropic turbulence the conditional scalar dissipation [chi(psi) = D[partial derivative phi/partial derivative x(i)partial derivative phi/partial derivative x(i)\phi = psi]], its derivative (partial derivative chi/partial derivative psi), and the conditional scalar diffusion [THETA(psi) = D [partial derivative2phi/partial derivative x(i) partial derivative x(i)\phi = psi]] are zero at the extreme values of scalar concentration. Models for conditional-dissipation ratio (chi/epsilon(s)) and conditional-diffusion ratio (THETA/epsilon(s)) are derived from the observation [Girimaji, Combust. Sci. Technol. 78, 177 (1991); NASA Contract. Rep. CR 4446 (1992)] that the scalar pdf can be characterized by the beta pdf at all stages of non-premixed mixing. The conditional-dissipation model is compared with the DNS data of Eswaran and Pope [Phys. Fluids 31, 506 (1988)] and the mapping-closure-based model [O'Brien and Jiang, Phys. Fluids A 3, 3121 (1991)]. The application of the model to multiscalar mixing is also briefly discussed.