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Chen Qi;Chen Jianqiang;Yuan Xianxu;Xie Yufei;State Key Laboratory of Aerodynamics;Computational Aerodynamics Institute of China Aerodynamics Research and Development Center;  
Harmonic balance method is constructed on the base of the Fourier series expansion. In the method, the unsteady solution process of a periodically unsteady flow is transformed into coupled solution processes of several steady flows, and then the whole time history of the unsteady aerodynamic forces and moments are rebuilt from the steady results. A rapid prediction method for dynamic stability derivatives is established, utilizing the harmonic balance method. In this way, the dynamic supersonic flow around a pitching winged missile is numerically simulated, with the dynamic derivative in pitch obtained via integration method. The results agree well with those from experiments. The computational efficiency could achieve about thirteen times of that of the dual-time-stepping method, while the order of computational accuracy being the same. The harmonic balance method is then utilized to investigate the effects of reduced frequency on the computation of dynamic derivative in pitch within a broad range. The results show that, with the decrease of the reduced frequency, the variation of the dynamic derivative in pitch is great, and in some cases even sign change could happen. At last, the applicability of the present method at high angles of attack flow is also studied, aiming at the strong nonlinearity of dynamic flow fields in this case. Results show that good agreement could be achieved with the wind tunnel data.
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