Trailing-Edge Noise Prediction by Solving Helmholtz Equation with Stochastic Source Term

A numerical approach to predict broadband trailing-edge noise for low Mach number flows is presented. It is based on the combination of a Helmholtz solver to propagate sound waves with a sound source term computed stochastically. The sound propagation is performed in the frequency domain using a high-order finite element solver. The stochastic approach is based on a random particle-mesh method. The performance of this numerical approach is first examined for a Gaussian source. The numerical approach is then applied to a NACA0012 airfoil for flow Mach numbers of 0.11 and 0.16 and to a controlled-diffusion airfoil for a Mach number of 0.047. The predicted sound levels are compared with experimental data and acoustic results obtained from the acoustic perturbations equations. The mean flow does not significantly modify the acoustic propagation. Using a no-flow propagation model like the Helmholtz equation is therefore a valid approach for low Mach numbers. The reduced computational cost of a Helmholtz calculation, together with the speed of the random-particle mesh turbulence synthesis, allows for fast predictions. While this approach provides relative assessments between different configurations (in particular the spectrum shape), it often requires the inclusion of calibration factors determined from reference measurement or numerical data.