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Implementation and Validation of the Harmonic Balance Method for Temporally Periodic Non–Linear Flows

An efficient method for tackling non-linear, temporally–periodic incompressible flows is presented in this paper. Assuming temporally fully periodic flow, Harmonic Balance method deploys Fourier transformation in order to formulate transient problem as a multiple quasi-steady state problems. The method is implemented in OpenFOAM and developed for a general transport equation and incompressible Navier–Stokes equations. Validation is presented on three test cases: oscillating scalar case for scalar transport validation, a flow around a 2D NACA airfoil and a 3D Onera M6 wing for turbulent incompressible Navier–Stokes validation. For all test cases Harmonic Balance results are compared to transient simulation results. Verification of the model is performed by changing the number of harmonics for all test cases.

harmonic balance method; periodic flows; openFoam; fourier expansion; turbomachinery

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