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

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