Direct Numerical Simulation Of The Interaction Of Shock Wave And Shear Layer

The interaction of shock wave and shear layer contains a lot of physical processes,it can not only induce the deformation of shock wave, change the spatial evolution ofshear layer, but also can generate sound wave——shock-associated noise. In a numberof applications of aerospace engineering, the shock-associated noise is very important.Intense shock-associated noise is a primary obstacle to develop the supersonicaerotransport. Shock-associated noise is the most dominant noise component ofbattleplan. The highly intense noise in the aircraft weapons bay can damage thestructures of the bay. Exact computing of shock-associated noise is an importantdirection of research of aeroacoustics.There are four challenges in direct numerical simulation(DNS) of the interaction ofshock wave and shear layer:(1) The noise-generating flow is inherently unsteady.(2)There are vast disparity in the magnitudes of the fluid dynamic and acousticdisturbances.(3) The scale separation between sound and flow is another salient featureof aeroacoustics,which can lead to both computational challenges and simplifications,depending on the method of choice.(4)Numerical method should simulate the motionof shock wave exactly. For these demands, the numerical scheme for DNS of theinteraction of shock wave and shear layer should have the character of high order, highresolution, low numerical dissipative, and can capture shock wave.To design a better numerical scheme to DNS of shock-associated noise, we developa family of linear high order strongly central compact schemes (SCCS) with goodspectral resolution.The SCCS schemes have the character of high order, high resolution,low numerical dissipative, that is nice numerical scheme to compute aeroacoustics.High order WENO scheme can capture strong shock wave very well. DNS of theinteraction of shock wave and shear layer was performed by solving the compressibleunsteady two-dimensional Navier-Stokes equations with fifth-order WENO schemecombined with third-order TVD Runge-Kutta scheme.This dissertaion is divided into five chapters as follows:The first chapter is the introduction, in which the progress in aeroacoustics isreviewed briefly, then we introduce the model problems of the interaction of shockwave and shear layer, and review the research of high-order methods.In the second chapter, governing equations and computational methodology used inthis dissertation are presented. Numerical methods include spatial discretization andtemporal discretization. Spatial discretization used in this dissertation includes WENOand SCCS schemes, temporal discretization presents third-order TVD Runge-Kutta and fourth-order LDDRK schemes.In the third chapter, we use sixth-order SCCS scheme and third-order TVDRunge-Kutta scheme to compute a series of problems. By numerical simulation of twoand three-dimensional Euler or Navier-Stokes equations, we find SCCS schemes havelow numerical dissipative, very good power of long time simulation, are suited tocompute aeroacoustics and turbulent flow.In the forth chapter, DNS of the interaction of shock wave and shear layer wasperformed. The mechanism of sound generation in the interaction of shock wave andshear layer was analysed. The interaction of incident shock wave and shear layergenerates shocklet, and then acoustic wave is generated and radiated at the locus ofcontact of shocklet and shear layer. Several arc-shocks are formed after reflected shockwave passing through shear layer; when reflected shock wave passing through shearlayer, shock wave is leaking in the braid region and shock-associated noise is generatedat the saddle points between vortices, this is a form of shock leakage mechanism.The last chapter contains our concluding remarks.