Predicting buoyant shear flows using anisotropic dissipation rate models

This paper examines the modeling of two-dimensional homogeneous stratified turbulent shear flows using the Reynolds-stress and Reynolds-heat-flux equa tions. Several closure models have been investigated; the emphasis is place d on assessing the effect of modeling the dissipation rate tensor in the Re ynolds-stress equation. Three different approaches are considered; one is a n isotropic approach while the other two are anisotropic approaches. The is otropic approach is based on Kolmogorov's hypothesis and a dissipation rate equation modified to account for vortex stretching. One of the anisotropic approaches is based on an algebraic representation of the dissipation rate tensor, while another relies on solving a modeled transport equation for t his tensor. In addition, within the former anisotropic approach, two differ ent algebraic respresentations are examined; one is a function of the Reyno lds-stress anisotropy tensor, and the other is a function of the mean veloc ity gradients. The performance of these closure models is evaluated against experimental and direct numerical simulation data of pure shear flows, pur e buoyant flows and buoyant shear flows. Calculations have been carried out over a range of Richardson numbers (Ri) and two different Prandtl numbers (Pr); thus the effect of Pr on the development of counter-gradient heat flu x in a stratified shear flow can be assessed. At low Ri, the isotropic mode l performs well in the predictions of stratified shear flows; however, its performance deteriorates as Ri increases. At high Ri, the transport equatio n model for the dissipation rate tensor gives the best result. Furthermore, the results also lend credence to the algebraic dissipation rate model bas ed on the Reynolds stress anisotropy tensor. Finally, it is found that Pr h as an effect on the development of counter-gradient heat flux. The calculat ions show that, under the action of shear, counter-gradient heat flux does not occur even at Ri = 1 in an air flow.