Assessing Wall-Modeled Large-Eddy Simulation for Low-Speed Flows with Heat Transfer

Abstract

This paper reports wall-modeled large-eddy simulation (WMLES) results of low-speed turbulent flows in a plane channel, in ribbed ducts, and around a film cooling jet. We compare our WMLESs to Pirozzoli et al.’s direct numerical simulations (DNSs) of low-speed plane channel flow (Pirozzoli, S., Bernardini, M., and Orlandi, P., “Passive Scalars in Turbulent Channel Flow at High Reynolds Number,” Journal of Fluid Mechanics, Vol. 788, Feb. 2016, pp. 614–639), our own DNSs of ribbed ducts with various pitch-to-height ratios, and Milani et al.’s WRLES and water-tunnel experiment of film cooling (Milani, P. M., Gunady, I. E., Ching, D. S., Banko, A. J., Elkins, C. J., and Eaton, J. K., “Enriching MRI Mean Flow Data of Inclined Jets in Crossflow with Large Eddy Simulations,” International Journal of Heat and Fluid Flow, Vol. 80, Dec. 2019, Paper 108472). We consider Mach number effects below the often-quoted low-Mach-number limit of . The results show that the Mach number has significant effects on the normalized mean temperature profile, even below the often-quoted low-Mach-number limit of , due to the associated viscous heating. In addition, we compare the first-grid point implementation (FGI) and the third-grid point implementation (TGI) of the equilibrium wall model. We show that, by placing the large-eddy-simulation/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 underperformance 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 (that is, plane channel, ribbed duct, and film cooling), we show that WMLES with FGI is able to accurately model heat transfer at a much more reduced cost than WRLES and DNS.