Computationally Efficient Large-Eddy Simulation of Periodic Unsteady Flow using Harmonic Balance Method

To improve the efficiency and fidelity of the numerical analysis for cascade flutter, we propose an efficient scale-resolving simulation method dedicated to time-periodic flows by incorporating the harmonic balance approach into the large-eddy simulation. This method combined convergence calculations of the steady-state problem based on the harmonic balance method for periodic components, and the nonlinear time-marching method for turbulent fluctuations. Using the proposed method, deterministic periodic components and stochastic turbulent fluctuations were calculated simultaneously, and the effect of turbulent fluctuations on deterministic periodic components was directly calculated without using turbulence models. In this paper, we explain the algorithm and feature of this simulation technique and present the results of the computation for channel flow excited in the streamwise direction as an analysis example using the proposed method. In order to validate the proposed method, an analysis of sinusoidally pulsating channel flow at the central friction-velocity Reynolds numbers Re-tau = 180 was conducted, confirming that the amplitude and phase of the mean velocity oscillation computed by the proposed method were in good agreement with those of the conventional LES. The present calculation achieved an order of magnitude improvement in computational efficiency compared to conventional LES.