Acoustic Source Terms for the Linearized Euler Equations in Conservative Form

Abstract

A rather novel approach to predict jet noise is the Stochastic Noise Generation and Radiation (SNGR) method. The SNGR method uses the linear Euler equations as an acoustic analogy together with source terms which are modeled. In other studies the Euler equations on primitive form are used. In the present work the linear Euler equations on conservative form are used. Due to this, new source terms have to be derived for the conservative set of equations. A formal derivation of the correct source terms for the linear Euler equations on conservative form is presented. Simplified versions of the derived source terms are also developed. To validate the derived source terms a direct simulation of a forced 2D mixing layer is carried out. The solutions to the linearized Euler equations with source terms are compared to the solution of the direct simulation and show a good agreement. All simulations are performed using Tam and Webb's fourth order DRP scheme and a four step fourth order Runge-Kutta time marching technique. Artificial selective damping introduced through the numerical scheme is used to avoid spurious waves. Absorbing boundary conditions based on characteristic variables, Engquist and Majda, are used at the free boundaries and a buffer layer is added at the outflow.