Large-Eddy Simulation for Slowly Oscillating Turbulent Flow Using Harmonic Balance Approach

Abstract

Herein, harmonic balanced large-eddy simulation (HB-LES) is proposed for the efficient high-fidelity simulation of slowly oscillating turbulent flows such as cascade flutter in turbomachinery or transonic airfoil buffet. The harmonic balance method for unsteady Reynolds-averaged Navier–Stokes simulation is introduced to large-eddy simulation (LES), utilizing the difference in timescales between the periodic flow and the turbulent fluctuations. Considering their nonlinear mutual interaction, periodic flow and turbulent fluctuations are computed by iterating short-time LES and the harmonic balance method. The HB-LES is applied to the analysis of a Stokes boundary-layer problem at the Reynolds number based on the Stokes boundary-layer thickness of 1790. The characteristics and evolution of the turbulent structures near the wall are consistent with those observed in the results of conventional LES. Both the phase-averaged periodic component and the turbulence statistics show good quantitative agreement with the experimental results and conventional LES. Furthermore, nonlinearity of the periodic component caused by the mutual interaction between turbulent fluctuations and the periodic component is reproduced as a rapid increase in wall-shear stress. The proposed HB-LES demonstrated approximately a 10-fold improvement in computational efficiency.