谐波平衡法在低速非定常流模拟中的应用

Application of harmonic balance method in simulations of low speed unsteady flows

谐波平衡法是一种有效的周期性非定常流的计算方法.采用基于可压缩流的谐波平衡方程在计算低速不可压流动时,会由于对流通量计算格式中的数值粘性污染,降低解的精度和收敛性.采用预处理技术,使得基于可压缩流的谐波平衡方程可以直接用于低速周期性非定常流的计算中.选取典型的不可压方腔驱动流和低雷诺数圆柱绕流为例进行了时间推进法和谐波平衡法的计算对比.计算结果表明预处理后的谐波平衡方程适合于低速流的计算,在谐波平衡法中采用较少阶数的谐波计算就可以还原出几乎准确的非定常流场.

The harmonic balance method is an effective computational method in simulating time periodic unsteady flows. When using the harmonic balance method based on compressible flow equations to solve low Mach number flows, both the accuracy and convergence of the solution would be deteriorated due to the large dissipation of the convective scheme which is specially designed for compressible flows. To solve this problem, the low speed preconditioning was adopted; therefore, the harmonic balance method based on compressible flow equations could he used to compute low speed periodic unsteady flow directly. Both the time marching calculation and the harmonic balance calculation were performed in simulating the incompressible lid-driven flow and the low Reynolds number vortex shedding cylinder flow. The results show the capability of using the preconditioned harmonic balance equation in simulating low speed periodic unsteady flows, and the unsteady flowfield could be well reconstructed by using only a few harmonics retained in the harmonic balance method.