Computation of Flow Noise Using Source Terms in Linearized Euler's Equations

TLDR

The study investigates an acoustic analogy using linearized Euler’s equations forced with aerodynamic source terms to compute the acoustic field. The authors apply a hybrid method that solves Navier–Stokes equations for three model problems, compares the predicted acoustic field from LEE with reference solutions, studies noise from corotating vortices in quiescent and sheared flows, investigates vortex pairings in a subsonic mixing layer, and proposes a simplified LEE formulation to suppress instability wave growth. The LEE solutions agree well with reference Navier–Stokes results, confirming that the introduced source terms are suitable for free sheared flows and that acoustic–mean flow interactions are correctly captured by the wave operator. The paper provides a nomenclature of symbols used in the LEE formulation, including variables for source terms, flow parameters, and acoustic quantities.

Abstract

An acoustic analogy using linearized Euler’ s equations (LEE) forced with aerodynamic source terms is investigated to computetheacousticfare eld. Thishybridmethod isappliedto threemodelproblemssimulatedby solving Navier‐Stokes equations. In this way, its validity is estimated by comparing the predicted acoustic e eld with the reference solution given directly by the Navier ‐Stokes equations. The noise radiated by two corotating vortices is studied: e rst, in a medium at rest and, second, in a mean sheared e ow with no convection velocity. Then the sound e eld generated by vortex pairings in a subsonic mixing layer is investigated. In this case, a simplie ed formulation of LEE is proposed to prevent the exponential growth of instability waves. The acoustic e elds obtained by solving LEE are in good agreement with the reference solution. This study shows that the source terms introduced into the LEE are appropriate for free sheared e ows and that acoustic ‐mean e ow interactions are properly taken into account in the wave operator. Nomenclature b = half-width of the monopolar source c = sound velocity E;F;H = vectors in linearized Euler’ s equations (LEE) f = frequency f0 = fundamental frequency of the mixing layer k = complex wave number, kr Ciki M = Mach number p = pressure Re = Reynolds number rc = vortex core radius r0 = initial half distance between the two vortices S = sound source vector in LEE Si = source terms in the momentum equations T = period Tij = Lighthill’ s tensor t = time U = unknown vector in LEE U1 = slow stream velocity of the mixing layer U2 = rapid stream velocity of the mixing layer u = velocity vector, .u1;u2/ Vµ = initial tangential velocity of vortices