Application of the complex differentiation method to the sensitivity analysis of aerodynamic noise

Abstract

The complex differentiation method (CDM) is applied to the sensitivity analysis of the noise generated by two-dimensional mixing layers, simulated by Direct Numerical Simulation (DNS), in order to investigate its capabilities to highlight the effects of a key parameter on the aerodynamic noise. For this purpose, simulations are carried out using the CDM for different flow Mach numbers, Reynolds numbers and mesh spacings. In each case, the derivatives of the noise levels with respect to one of the three parameters are obtained using the CDM, implemented by adding a small imaginary perturbation to the parameter under study. In most cases, vortex pairings occur in the mixing layers and produce acoustic waves at a single frequency. The derivatives of the acoustic intensity obtained using the CDM show that the sound radiation is stronger and less directed downstream as the Mach number increases, in agreement with dimensional analyses. They also indicate that the radiation is more intense and directive as the Reynolds number increases. The magnitude of the derivatives of the acoustic intensity with respect to the mesh size decreases for finer meshes, showing that the grid sensitivity of the radiated noise is reduced for the latter meshes, as expected. In all cases, the derivatives obtained using the CDM are in good agreement with results from parametric studies. This suggests that the CDM can be used to describe the effects of physical parameters and of the grid resolution on the sound produced by a high-speed flow.