Application of harmonic balance method in forward flight simulation for helicopter rotors

The unsteady flow around helicopter rotor in forward flight is simulated by using harmonic balance method based on Euler equations. For the periodical characteristics in forward flight, the flow variables can be represented by Fourier series in time. Thus, the unsteady governing equations in time domain can be converted to steady equations in frequency domain, so the well-developed steady computational fluid dynamics(CFD) techniques can be used to solve the steady equations in frequency domain, and the unsteady solution is obtained. The main advantage of the present method is that only one blade needs to be simulated by implementation of the periodical condition. Compared with the traditional dual-time stepping method, harmonic balance method improves unsteady calculation efficiency greatly. The calculated pressure distributions and thrust coefficients agree well with the results of experimental data or dual-time stepping method. Message passing interface(MPI) parallel computing technique is utilized to improve the computational efficiency further.