Application of Harmonic Balance Method to Numerical Model Unsteady Viscous Flow around Oscillating Cascade
A harmonic balance approach has been developed to compute nonlinear viscous unsteady flows around oscillating blades. The computed results using two orders harmonic balance method are compared with those by conventional dual-time stepping method. Results obtained with the present method agree well with those from dual-time stepping method, which demonstrate the ability of the present analysis method to model accurately the unsteady flow. Furthermore，the present method is highly efficient. It is about 36 times fast than conventional dual-time stepping method in the present computation. Then the effects of oscillation amplitude and reduced frequency on unsteadiness of flows are studied. The analysis exploits the fact that, (1) the hysteresis effect of unsteady flow is hardly affected by oscillation amplitude, but the first harmonic unsteady pressure across the blade is proportional to oscillation amplitude; (2) the higher the reduced frequency, the wider the range of unsteady aerodynamic forces, the more intense the hysteresis effect.
Shaobo Zhong, Yimin Cheng and Xilong Qu
Y. Q. Shi et al., "Application of Harmonic Balance Method to Numerical Model Unsteady Viscous Flow around Oscillating Cascade", Applied Mechanics and Materials, Vols. 50-51, pp. 583-588, 2011