Accounting for the effects of buoyancy on the turbulent scalar fluxes

Abstract

The paper reports on the development of an explicit, algebraic model for the turbulent scalar fluxes which properly reflects the dependence of these fluxes on the gradients of mean velocity and on gravitational acceleration. Such dependencies are required by the exact equations governing the conservation of the turbulent fluxes but are absent from models which are based on the notion of eddy diffusivity and constant Prandtl or Schmidt number. In the present contribution, tensor representation theory is used to express the scalar fluxes in terms of its vector and tensor dependencies and then by applying a few assumptions to arrive at a model that includes the proper dependencies while being sufficiently compact and robust to be of use in practical applications. Model calibration was accomplished by reference solely to data from Large-Eddy Simulations of homogeneous turbulence in neutral and stable stratification while model performance was assessed by comparisons with experimental data from two-dimensional heated plane and free jets and buoyant plumes. In all cases, the model’s performance was found to be better than an alternative implicit algebraic model, and on par with that of a differential scalar-flux transport closure.