Harmonic Balance Developments in OpenFoam

The Harmonic Balance method for unsteady non-linear periodic flows is presented in this work. Its recent, yet rapid development was motivated by the achieved reduction of CPU time compared to conventional transient methods, while providing sufficient accuracy. Harmonic Balance was initially developed as a periodic boundary condition by He, while He and Ning extended its application to solving the two–dimensional Navier–Stokes equations and presented the efficiency improvement compared to nonlinear time–marching methods. Based on the assumption of a periodic flow, primary variables are considered in form of Fourier series with a finite number of harmonics, n, and inserted in Navier-Stokes equations. The time derivative term becomes an additional source term, while single transient equation becomes a set of 2n + 1 steady state equations which are then converged to final solution. Each of the equations represents a point in time, and due to coupling yields a flow field of a complete period. In this work current developments of the Harmonic Balance method within the foam-extend are presented. The method is applicable to a number of periodic problems, of which the most noticable ones are turbomachinery and naval hydrodynamics. Other applications include oscillating wings, pulsating flows, problems with periodic boundary conditions such as opening and closing valves, etc. Turbomachinery cases to be presented include ERCOFTAC centrifugal pump and a 3D propeller case. Turbulent flow with moving mesh is simulated in both cases and compared with conventional steady state and transient results. In order to tackle naval hydrodynamic problems, a two phase variant of the Harmonic Balance method was developed and tested. Naval hydrodynamic cases consist of regular wave propagation solved using a variable number of harmonics, and a test case of wave diffraction on a DTMB ship hull. The results are compared with conventional transient solver.