Consistent modeling of differential molecular diffusion to yield desired Reynolds-number power-law scaling

Abstract

Differential molecular diffusion (DMD) is a fundamental physical phenomenon that occurs in many fluid flow problems such as turbulent reactive flows. Because DMD is a small-scale event, its modeling is intrinsically challenging, and hence in practical applications, it is more feasible to develop phenomenological models for treating the effect of DMD. In order to develop these phenomenological models, a set of model constraints based on physical observations are needed in order to constrain the model development to yield consistent results with the physical observations. In this work, we adopt an existing power-law Reynolds number scaling of DMD as the model constraints and examine the turbulence modeling requirement of DMD in order to yield the desired scaling. The Reynolds-averaged Navier-Stokes simulations are employed as the modeling framework, and a turbulent mixing layer test case is used as a test case. Perturbation analysis is conducted to examine the model consistency in order to yield the power-law scaling for DMD in the mixing layer test case. It is found that a differential mixing time scale model is needed to yield the power-law scaling, and the commonly used equal mixing time scale model cannot produce the scaling correctly. Numerical simulations of the turbulent mixing problem are also performed to further demonstrate the turbulence modeling requirement for producing the desired power-law scaling of DMD.