Subgrid-scale modeling of turbulent heat transport in forced convection at high molecular prandtl numbers

Abstract

Assuming strong similarity between the transport of momentum and heat is a common feature of most standard subgridscale models used in Large-Eddy Simulations (LES) of turbulent flow with heat transfer. In view of the limitation of this analogy to molecular Prandtl numbers near unity the present study investigates the capability of different established model concepts in predicting the subgrid-scale heat flux, when applied in a priori LES of turbulent heated flow going well beyond this parameter range, considering Prandtl numbers Pr = 1=10=20 at Reynolds number Ret = 360. The test unveils the major deficits of the constant-coefficent Smagorinsky approach due to the nonuniversiality of the used model coefficients like the turbulent subgrid-scale Prandtl number. Apart from the removal of this basic shortcoming the dynamic Smagorinsky model is shown to yield no substantially better predictions. The same holds true for the computationally more elaborate non-linear extensions introducing a tensorial diffusivity. The scale-similarity based mixed dynamic model proposed by [1] was proven to give in general the most accurate description. Some discrepancy appeared in regions with considerable net transfer of heat from the unresolved into the smallest resolved scales observed for higher Prandtl number. This suggests to include a sub-model for the presently neglected cross-scale interaction into the formulation as path for further improvement of this best evaluated approach.