旋转声源延迟时间方程求解的数值研究

Numerical Research on Retarded-Time Equation for Uniformly Rotating Aeroacoustic Sources

为提高气动噪声时域数值算法的计算速度,针对亚音速匀速圆周运动的点声源,将延迟时间方程的求解问题转化为求抛物线与余弦曲线的交点,转化后的方程形式简洁并且数值计算效率更高。使用分段二次函数对延迟时间方程中的余弦函数进行替换,得到一种新的高精度迭代初值计算方法,并分别采用Newton迭代和Halley迭代算法求解延迟时间方程。研究表明:相对于通常的固定初值给定法,所提出的分段二次近似迭代初值计算方法可以减少约20%的计算时间,且Halley迭代算法具有较好的计算效率和收敛特性。

To speed up the noise prediction of aeroacoustic sources,the retarded-time equation for a subsonic uniformly rotating point source was transformed into a simple and efficient one.A more accurate initial value estimation method based on the piecewise parabolic approximation of the trigonometric function was presented.Moreover,the Newton＇s method and the Halley＇s method were applied to solve the reformed retarded-time equation iteratively.The results show that the present initial value estimation method will reduce the computational time by 20%,and the Halley＇s method behaves better than the Newton＇s method in computation efficiency and convergence characteristics.