Aeroacoustic simulations and stochastic approach using linearized Euler’s equations

Abstract

Sound generation and propagation in a turbulent flow is a very difficult numerical problem. Indeed, acoustic fluctuations are very small by comparison to the mean and turbulent fields. Linearized Euler’s equations provide accurate numerical solutions only in working on perturbations. In the stochastic noise generation and radiation model, the mean flow is calculated by solving the Reynolds-averaged Navier–Stokes equations. Then, Euler’s equations are linearized around this mean flow field. A turbulent source term is introduced in the equations, and the turbulent velocity field is modeled by a sum of random Fourier modes. The numerical solution is obtained by using a dispersion-relation-preserving scheme in space, combined with a fourth-order Runge–Kutta algorithm in time. In order to validate the numerical method, radiation of multipolar sources in a uniform and sheared mean flow has been investigated in a two-dimensional case. The calculated solutions favorably compare with analytical solutions or with ray tracing. Then, the SNGR model is applied to a subsonic jet noise in a 3-D geometry. Numerical results and future developments will be discussed.