Comparison of time-domain prediction methods for transonic aeroacoustic noise generated by helicopter rotors

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.