Unsteady jet flow computation towards noise prediction

An attempt has been made to combine a wave solutionmethod and an unsteady flow computation to produce an integratedaeroacousticcode to predictfar-field jet noise. An axisymmetric subsonic jet is considered for thispurpose. A fourth order space accurate Pade compact scheme isused for the unsteady Navier-Stokes solution.A Kirchhoffsurfaceintegralforthe wave equation isemployed through the use of an imaginary surface which isa circularcylinderenclosingthe jet at a distance.Information such as pressureand itstime and normal derivativesisprovided on the surface.The sound predictionisperformed side by side with the jet flow computation. Retarded time isalsotaken into considerationsincethe cylinderbody isnot acousticallycompact. The far-field sound pressure has the directivity and spectra show that low frequency peaks shifttoward higher frequency region as the observationangle increasesfrom the jetflow axis. I.utroduction Jet noisesuppressionhas appeared as a critical issue forthe viability offuturesupersonicflight.The FAR 36 StageIllimposes the same noiselimitationon future supersoniccommercial flightas itdoes on subsonic aircraft.This bringsfortha challengingtask toreduce the jet noisein the High Speed CivilTransport Program. In orderto accomplish thistask,assessment of far-field noisegenerated by a jet plume is a prerequisiteto the designofthe engine.Jet noiseisgenerated as a byproduct ofthe plume flow behind the exhaust nozzle.Flow turbulencehas been believedtobe a sourceofthe sound. Lighthill I showed that the flow turbulence,which isreferredtoas the fluctuatingReynolds stressorLighthill's tensor,isthe sound source.Since then, turbulent flow, which had been generallyaccepted as a totallychaotic entity,has been a centraltheme in the aeroacousticresearch. For an estimation of the sound pressure using the acousticanalogy approach, the two-pointfourth order correlationof the fluctuatingReynolds stressmust be computed. To make thistractable,Proudman 2 pursued a noise generation theory that assumes the isentropicturbulence.A varietyof manipulation and modellingof the flow turbulence has been made based on a fully turbulent assumption since then. Freymuth 3 observed organized large eddy structures in a separated flow of a jet. Brown and Roshko 4 also found large vortical structures in a free shear layer. These findings of the vortical pattern in the free shear layer filled the gap between an initial wave region, in which a linear theory is applied, and the fully turbulent downstream region. The flow regime dominated by the large vortical structure is not fully random and is predictable in a deterministic way. This organized structure maintains its identity up to the point where the potential core begins to collapse but is still discernable even in the fully turbulent region far downstream. Winant and Browand s reported that a mechanism of the mixing layer growth is an interaction of adjacent large vortices. These investigators have shown that the flow in free shear layers such as jet and plane mixing flow is well behaved and more organized than previously thought. Shear flow is dominated by laxge vortical structures, which are very predictable and controllable. This shear flow, which had been thought to be fully turbulent and therefore random and chaotic, has become research subject with a quite different perspective since the observation of these organized structures. A decomposition of the fluctuating flow quantity into the organized flow entity and the fully random entity makes it possible to study turbulent shear flows in a certain deterministic way. Experiments s have shown that the sound power emitted from the jet column is greatest within 4 or 5 diameters downstream, and then decays rapidly through a transition region. This indicates that the initial development of the jet, before it becomes fully turbulent, should be clearly resolved so that an accurate noise prediction can be made. This region is characterized by large vortical structures and is not fully turbulent, which gives the motivation that we solve the unsteady flow equation directly to provide the sound source for an acoustic computation of the far-field noise. Numerical solution of turbulent flow is difficult because the turbulent flow field is made up of a range of length scales from the Kolmogorov scale to the integral scale. If numerical mesh size can be made fine enough to resolve the smallest scales which dissipate the kinetic energy, then direct numerical simulation (DNS) is the tool to obtain the entire turbulent flow structure. However, the dissipative scale becomes finer as the Reynolds number is increased and practical hardware limitations are rapidly reached. Therefore, the DNS method is limited to simulating only low Reynolds number turbulence. For practical computation of higher Reynolds number flows, small scale fluctuations can be modeledsothat desiredlargescaleeddiescanbecomputeddirectly,whileproperdissipationis providedby thesmallscaleeddymodel. Thisapproach, whichis referredto aslargeeddysimulation(LES),hasbeen successfully employed in manyflowswithpractical applications. In orderto obtainthe flowfield asthesourceof soundusingDNSor LES,thesimulations mustbeperformedusingnumerical techniques withminimaldistortionanddiffusivecharacteristics. Thesourceof numerical diffusionandphaseerroris knownto bemainly fromthenumerical formulationoftheconvective t rms. Thesenumerical artifactsgetworsefor highReynolds number flow simulations. Typically, free shear flows of interest have very high .Reynolds numbers. Therefore, a higher order accurate numerical scheme which meets the previously mentioned requirements is needed. Fourth order Pade compact differencing scheme with a dispersion relation preserving property is used here. It is the purpose of this paper to present a method to predict the far-field pressure directly from the numerically generated unsteady flow solution without recourse to empirical factors. Therefore, only an axisymmetric laminar jet is considered in the process of incorporating a wave solution into the higher order accurate flow solver. Furthermore, the flow solution is limited to the subsonic case since supersonic jets often generate shock related noise in addition to the shear noise due to flow turbulence, which makes the problem more complicated. The Kirchhoff surface integral method is chosen for the solution of the wave equation. The acoustic result obtained is the far-field sound caused by the wavy motion and large vortical structure of the free shear layer. Fine scale random turbulence is not addressed in this study. Governing Equation of Fluid Flow f pu