Modeling the Effects of System Rotation on the Turbulent Scalar Fluxes

Abstract

A proposal for modeling the effects of system rotation on the turbulent scalar fluxes is presented. It is based on extension to rotating frames of an explicit algebraic model derived using tensor-representation theory. The model is formulated to allow for the turbulent scalar fluxes to depend on the details of the turbulence field and on the gradients of both the mean-velocity and the scalar. Such dependence, which is absent from conventional models, is required by the exact equations governing the transport of the scalar fluxes. The model’s performance is assessed, both a priori and by actual computations, by comparisons with results from recent direct numerical simulations (DNS) of flows in heated channels rotated about their streamwise, spanwise, and wall-normal axes. To place the new model’s performance in context, additional comparisons are made with predictions obtained from three alternative models, namely, the conventional gradient-transport model, a model that is implicit in the scalar fluxes derived by simplification of the modeled transport equations for the scalar fluxes, and a differential scalar-flux transport model. The results show that the present model yields predictions that are substantially in better agreement with the DNS results than the algebraic models, and which are indistinguishable from those obtained with the more complex differential model. However, important differences remain and reasons for these are discussed.