A mixed-timescale SGS model for thermal field at various Prandtl numbers

Abstract

A new subgrid-scale (SGS) model for the thermal field is proposed. The model is an extended version of the mixed-timescale (MTS) SGS model for velocity field by Inagaki et al. (2005), which has been confirmed to be a refined SGS model for velocity field suited to engineering-relevant practical large eddy simulation (LES). In the proposed model for the thermal field, a hybrid timescale between the timescales of the velocity and thermal fields is introduced in a manner similar to velocity-field modeling. Thus, the present model dispenses with an ambiguous SGS turbulent Prandtl number, like the dynamic SGS model. In addition, the wall-limiting behavior of turbulence is satisfied, which is not in the original MTS model, by incorporating the wall-damping function for LES based on the Kolmogorov velocity scale proposed by Inagaki et al. (2010). The model performance is tested in plane channel flows at various Prandtl numbers, and the results show that this model gives the ratio of the timescales between the velocity and thermal fields similar to that obtained using the dynamic Smagorinsky model with locally calculated model parameters. It is also shown that the proposed model predicts better mean and fluctuating temperature profiles in cooperation with the revised MTS model for the velocity field, than the Smagorinsky model and the dynamic Smagorinsky model. The present model is constructed with fixed model parameters, so that it does not suffer from computational instability with the dynamic model. Thus, it is expected to be a refined and versatile SGS model suited for practical LES of the thermal field.