应用于跨声速旋翼气动声学计算的两种时域方法的比较

Comparison of Time-Domain Prediction Methods for Transonic Aeroacoustic Noise Generated by Helicopter Rotors

高速脉冲噪声(HSI)与流动非线性效应密切相关,是跨声速旋翼的主要声源之一。采用理论分析和数值实验相结合的方法,对预测HSI噪声的Ffowcs Williams-Hawkings方法(简称FW-H方法)和Kirchhoff方法进行了比较和分析。理论分析从两种方法的控制方程出发,采用广义函数方法对方程源项进行整理和比较,证实在线性区域Kirchhoff方程可视为FW-H方程的有效近似。数值实验以UH-1H悬停旋翼跨声速气动噪声计算为例,由三维Euler方程数值模拟提供近场气动数据,并在同一控制面上分别采用FW-H方法和Kirchhoff方法对远场噪声进行定量预测。计算结果表明,如果适当构造控制面,2种方法均能有效地预测跨声速旋翼非线性HSI噪声。进一步研究了控制面位置及控制面上物理参数时间导数计算精度对计算结果的影响,发现控制面位置对Kirchhoff方法计算结果具有决定性的影响,而控制面上物理参数时间导数的计算精度对FW-H方法计算结果具有重要影响。

High Speed Impulsive （HSI） Noise is closely associated with the nonlinear flow around the rotor blades and is immensely intensive for transonic helicopter rotors. In this study, two methods of predicting HSI noise, Ffowcs Williams/Hawkings （FW-H） method and Kirchhoff method, are compared through the theoretical analysis in conjunction with numerical experiment. Using general function theory, the source terms of FW- H equation and Kirchhoff equation are rearranged and compared. It is shown that the Kirchhoff equation can be taken as a reasonable approximation of FW-H equation provided that the control surface is located in the linear flow region. The numerical experiment is preformed for an UH-1H rotor in hover with transonic tip Mach number that ranges from 0. 85 to 0.95. The near-field aerodynamic data is obtained by numerically solving three-dimensional Euler equations with a finite-volume scheme and multi-stages Runge-Kutta method. The integration of FW-H method and Kirchhoff formula are carried out over the same permeable surface which allowed the flow past through. Both rotating and none-rotating integration surfaces are employed and the retarded-time equation is solved with an iteration scheme. It is demonstrated that both FW-H method and Kirchhoff method can be used to effectively predict the nonlinear noise generated by transonic helicopter rotors if the integration surface is carefully constructed. Further study shows that the result of Kirchhoff method is sensible to the location of rotating integration surface, and that the result of FW-H method is strongly affected by the discretization accuracy of time derivatives for flow parameters on the integration surface.