Reynolds number effect on statistics of turbulent flows over periodic hills

Abstract

The wall-resolved large-eddy simulations of turbulent flows over periodic hills are carried out to study the Reynolds number effect on flow statistics. Five different Reynolds numbers ranging from 2800 to 37 000 are considered. The present simulations are validated by comparing the time-averaged flow statistics with those from the literature. The Reynolds number effect is first examined on the skin friction and pressure coefficients, the isosurfaces of p′ and Q criteria, and the vertical profiles of flow statistics. The results show that (1) at most locations the magnitude of friction coefficient decreases with the increase in Reynolds number, while the pressure coefficient varies in the opposite direction; (2) smaller turbulence structures arise at higher Reynolds numbers; and (3) the mean velocities and Reynolds stresses in general exhibit asymptotic behaviors with the increase in Reynolds number. The statistical properties of turbulence structures are further examined via the probability density function and time correlation of velocity fluctuations. At last, the dynamics in the separation bubble is investigated by examining the flow statistics and the budget equation of mean kinetic energy (MKE) on the coordinate with its origin fixed at the recirculation center, and the power spectral density of the velocity fluctuations. Similarities are in general observed for the mean velocities, Reynolds stresses, and the MKE budget in the rear part of the separation bubble. The mean convection term and turbulence convection term are observed playing a key role on the decrease in bubble size with the increase in Reynolds number.