Direct numerical simulation of hypersonic wall-bounded turbulent flows: An improved inflow boundary condition and applications

Abstract

In this paper, the method of generating inflow turbulence based on turbulence fluctuation library (TFL) in direct numerical simulation (DNS) of the hypersonic turbulent boundary layer (TBL) is investigated. The application of the TFL method to the DNS of a supersonic TBL shows that, although there are significant differences in freestream between the TFL and the target TBL, the flow could successfully develop to the target TBL downstream as the fluctuations of TFL are suitably scaled and added to the DNS inflow. However, there is a “transition”-like recovery process from the inflow to the target turbulence. To deal with the defects of the thermodynamic fluctuations scaling laws in the current TFL method under the hypersonic TBL, new thermodynamic fluctuations scaling laws are theoretically derived by introducing the generalized Reynolds analogy. The application in the DNS of Mach 7.25 TBL shows that the new scaling laws for thermodynamic fluctuations are more rational and accurate than the previous ones. Furthermore, the study on the recovery process shows that the matching degree between the TFL and the target TBL on the friction Reynolds number (Reτ) is the dominant factor in determining the length of recovery distance. Guaranteeing the similar Reτ of the TFL and the target TBL can make the two possess similar coherence structures, which can avoid the distortion of the coherence structures at the inflow after spanwise and normal interpolation, prevent the process of Reynolds stress decay and readjustment downstream the inflow, and finally effectively shorten the recovery distance.