谐波平衡法在动导数快速预测中的应用研究

谐波平衡法以傅里叶级数展开为基础，将周期性非定常流场的非定常求解过程转化为几个定常流场的耦合求解过程，并通过重建得到整个流场的非定常过程. 建立了基于谐波平衡法的动导数快速预测方法，数值模拟了超声速带翼导弹俯仰的动态流场，并通过积分法获取了俯仰动导数，与实验结果吻合很好；且在同等计算精度下，谐波平衡法的计算效率是双时间步方法的13 倍. 应用谐波平衡法研究了较大范围内减缩频率对俯仰动导数的影响规律. 研究发现，对于本外形，当减缩频率降低到一定值后，俯仰动导数的值迅速变化，甚至发生变号；对此现象产生的原因进行了深入分析，并通过对导弹自激俯仰运动的数值模拟验证了该结果. 此外，针对大攻角条件下动态流场非线性强的特点，开展了谐波平衡法在大攻角下的适用性研究. 结果表明，谐波平衡法在大攻角下也能取得很好的计算结果. 

APPLICATION OF A HARMONIC BALANCE METHOD IN RAPID PREDICTIONS OF DYNAMIC STABILITY DERIVATIVES

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.