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

作　　者：董帆[1] 陈启明[1] 于跃平[1] 

机构地区：[1]合肥通用机械研究院压缩机技术国家重点实验室,合肥230031

出　　处：《西安交通大学学报》2013年第7期120-123,共4页Journal of Xi'an Jiaotong University

基　　金：国家重点基础研究发展计划资助项目(2012CB026001)

摘　　要：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.

关 键 词：气动噪声 延迟时间方程 运动声源 迭代算法 

分 类 号：O355[理学—流体力学]