Jet noise prediction based on a self-adjoint operator

The adjoint method introduced by Tam and Auriault [1] enables the proper taking into account of acoustic propagation effects when jet noise is modelled from the statistics of a turbulent flow. This technique is recast in a systematic way valid for arbitrary propagation media, linear operators and sound sources. An acoustic analogy based on Pierce’s wave equation for the acoustic potential [2] is proposed and Tam and Auriault’s mixing noise model [3] is reformulated for this operator. This formulation presents three main advantages; no instability wave can occur since the acoustic energy conservation is enforced, then for being self-adjoint the adjoint solution to the propagation problem may straightforwardly be computed by flow reversal, finally Pierce’s wave equation is a simple and cheap equation that several existing solver are able to solve. Work performed with FFT’s software Actran TM is presented illustrating the ability of a commercial tool to solve this equation and to compute adjoint Green’s function required in statistical jet noise modelling.