Assessing wall-modeled les for low-speed flows with heat transfer

This paper reports wall-modeled large-eddy simulation (WMLES) results of low-speed turbulent flows in plane channel, in ribbed ducts, and around a film cooling jet. We compare our WMLESs to Pirozzoli’s direct numerical simulations (DNSs) of low-speed plane channel flow [Pirozzoli, Bernardini, and Orlandi, J. Fluid Mech., 2016, 788, 614-639], our own DNSs of ribbed ducts with various pitch to height ratios, and Milani’s wall-resolved LES (WRLES) and water-tunnel experiment of film cooling [Milani, Gunady, Ching, Banko, Elkins, and Eaton, Int. J. Heat Fluid Flow, 2019, 80, 108472]. We consider Mach number effects below the often quoted low Mach number limit Ma=0.2. The results show that Mach number has significant effects on the normalized mean temperature profile even below the often quoted low Mach number limit Ma= 0.2 due to the associated viscous heating. In addition, we compare the first-point implementation (FGI) and the third-point implementation (TGI) of the equilibrium wall model. We show that, by placing the LES/wall-model matching location away from the wall, TGI practically reduces the near-wall resolution seen by the wall model, which in turn leads to under-performance of the wall model. By considering three types of flows with increasing levels of complexities, the objective of this study is to systematically assess WMLES in terms of its ability to predict heat transfer for low-speed flows. For the flows considered here, i.e., plane channel, ribbed duct, and film cooling, we show that WMLES with FGI is able to accurately model heat transfer at a much reduced cost than WRLES and DNS.