<p>This study proposes an extention of the harmonic balance method to large-eddy simulations of cascade flutter flows which have low non-dimensionlal frequency. The cascade flutter flows are quasi-periodic in time due to periodic vibration of the blades. It takes huge computational cost to simulate these flows using conventional unsteady time-marching approach because of their low non-dimensional frequency. A harmonic balance method is an efficient numerical simulation technique dedicated to such periodic unsteady flows and has been applied to various cascade flows. However, the classical harmonic balance method is based on RANS formulation, where all the turbulent fluctuations are averaged in time. Therefore effect of turbulence have to be modelled, and the reliability of the numerical results depends on the model accuracy. In order to improve the efficiency and reliability of the numerical analysis of turbomachinery flows, cost-effective numerical method which can provide insight into such turbulence is required. To address this needs, we are developing an efficient scale-resolving simulation method dedicated to time-periodic flows by originally extending harmonic balance approach to large-eddy simulation. This method combines convergence calculations based on harmonic balance method for the periodic component, and unsteady time-marching method for the turbulent fluctuations. Using the proposed method, the deterministic periodic component and stochastic turbulent fluctuations are calcuculated simultaneously. Furthermore, it will improve the accuracy of deterministic periodic flows, since the effect of turbulent fluctuations to them is directly calculated without turbulence models. To demonstrate the efficiency and accuracy of the method, we conduct the computation of an oscillating channel flow with sinusoidal fluctuations in bulk velocity.</p>

Extension of Harmonic Balance Approach for Large-Eddy Simulation of Unsteady Flows in Cascade

Paper Proceedings: https://asmedigitalcollection.asme.org/GT/GT2021/volume/84898

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