Numerical–analitical method for the problems of aerodynamic noise generations in helicopter and quadrotors

The subject of this paper is to demonstrate the capabilities of numerical-analytical method for solving problems of sound generation by helicopter and quadrocopter rotors. In particular, the finite difference schemes for the implementation of the numerical-analytical method for steady, non-steady 2-D potential flows describing the generation of noise of aerodynamic origin by a helicopter rotor blade are presented. Examples of the application of the numerical-analytical method to the problems of sound generation by a 3-D unsteady potential flow for the aerodynamic noise of a quadrotor are presented. It should be noted that until recently there was no unified finite difference scheme for solving helicopter rotor acoustics problems for different levels of physical approximations. The numerical-analytical method developed by the author of this paper has been shown to be capable of solving the problems of helicopter and quadrotor blade aeroacoustics for both simplified potential and significantly non-potential flows. The research methods are based on numerical schemes for the aerodynamic near and far sound fields calculations. The paper gives examples of the solution of these problems, analyses the application of the numerical-analytical method and compares it with existing finite difference methods. In particular, the calculation templates of the method for a stationary 2-D flow and a transient 3-D flow are presented and the special features of the selection of the number of points in the calculation template are explained. Depending on the specifics of a particular problem, the number of calculation templates and points in the calculation mesh can vary. This makes it possible to set up a stable calculation for each of the problems to be solved using the numerical-analytical method. In this case, the convergence of the method occurs automatically each time based on the idea of the numerical-analytical method itself. Results and conclusions. The results of a comparative analysis of existing numerical methods for calculating the sound field of helicopter and quadrocopter rotors have shown that the numerical-analytical method developed in detail is effective both for the calculation of sound formation problems in the potential approximation based on the Karman-Guderley equation and for the full system of sound generation equations based on the Navier-Stokes equation for the case of non-potential flow. The efficiency of the numerical-analytical method consists in the fact that it is implicit and allows to adjust the numerical scheme for each specific problem to be solved.