Investigations On The High-order Finite Difference Schemes And Numerical Simulations On The Aeroacoustic Characteristics Of Mixing Layers

Computational aeroacousitcs has been one of the most significant and difficultproblems which are concerned by the field of computational fluid dynamics at present.The computation of acoustic problems has many difficulties since it requires not onlythe flow and acoustic structure at different magnitudes and scales being resolvedaccurately, but also the futures of frequency spectrum and wave propagation beingdescribed correctly. The high order finite difference schemes, for their high accuracyand good resolution, have become effective methods for the acoustic simulations. Toobtain high order difference schemes with good dispersion and dissipation, thebandwidth optimization may be used to optimize the free parameters in the schemecoefficients. Simultaneously, for the possibility of presence of shock discontinuity inthe compressible flows, it is necessary for the high order schemes to be able to capturethe shock wave smoothly. The introducing of the nonlinear weighting mechanism justsatisfies the requirement of shock-capturing. In this thesis, deep and comprehensiveanalyses have been carried out surrounding the new bandwidth optimization methodand nonlinear optimization method developed by our research group and the newlydevelopped fourth-order and fifth-order optimized symmetrical weighted ENN scheme(OSWENN) based on the optimization method. Furthermore, the problem-independenttechnique in the nonlinear weighting optimization process has been developped, andeffectively improves the adaptability of the algorithm to different actual problems.Through our work, the final scheme has been constructed to be adaptive to thesimulation of the flow in various speed range, and be able to resolve the propagation ofacousitc waves accurately.Aeroacoustic problems of mixing layers have been simulated using the newdevelopped numerical method, and the acoustic field characteristics under the twodifferent mechanisms of complex vortices merging and shocklets induced by vorticeshave been obtained in the mixing layer of different convective Mach numbers. Detailedqualitative and quantitative analyses have been made based on the simulation results.The thesis is divided into eight chapters, the content of each chapter can besummarized as follows.The first chapter is introduction, which introduces the research progress in Chinaand foreign countries of the work related to this thesis. About the high order scheme,the typical finite difference schemes, compact difference schemes, linear and nonlinearoptimization technique and the geometric conservation law problems in the applicationof high order schemes are discussed. As for the acoustic problems of mixing layers, two kinds of approaches in computing the computational aeroacoustics problems andthe relation between fluid dynamic problems and acoustic problems in mixing layersare elaborated. The main work of this thesis are introduced at last.In the second chapter, several issues related to high order difference schemes arediscussed and investigated. Comprehensive and deep computation and analysis havebeen carried out surrounding the work of our research group about the linear andnonlinear optimization of high order schemes. Through the computation and analysis,the coefficients in the algorithm are determined, and the algorithm to eliminate theproblem-dependency in the relinearization process is developped. The part of linearoptimization in high order schemes includes: analyses on the dispersion overshoot andinverse dissipation of the high order finite difference scheme, a new optimizationobject function and the optimized fourth-order and fifth-order symmetrical WENNschemes. The part of nonlinear optimization includes: new smoothness measurement,variable exponent relinearization method and the algorithm to eliminate theproblem-dependency. The one-dimensional and two-dimensional typical problems(including viscous, inviscid flow with speed from subsonic, supersonic to hypersonic)are computed using the newly developped numerical method, and the comparisonswith computational, experimental or theoretical solutions are carried out.The third chapter discusses several special techniques associated with thecomputation of aeroacoustics. First the comparative study between two boundaryconditions is carried out through the computation of the case that test thecharacteristics when the acoustic disturbance move across the open boundary. Theresults show that the characteristic boundary condition proposed by our research groupis able to be applied to the acoustic problems; secondly the buffer zone technique ofthe acoustic boundaries in the computation of mixing layers is discussed and a newdamping function is proposed. At last, a method which uses the feature that theextreme points on wavefront propagate along straight lines is proposed to determinethe qualitative position of the acoustic sources of mixing layers.In the fourth chapter, two-dimensional temporal-developping mixing layers withMc=0.18and Mc=0.75are simulated and analyzed. For the subsonic convective Machnumber mixing layer, first different vortices merging processes are obtained throughadding different disturbance patterns(mode), and then the research on the differentacoustic field is carried out; For the transonic convective Mach number mixing layer,shocklet structures are induced by the vortices when adding disturbance patternssimilar to Mc=0.18case, and the studies about the complex sound radiation structurecaused by shocklets are carried out.In the fifth chapter, two-dimensional spatial-developping mixing layers withMc=0.18and Mc=0.75are simulated and analyzed. By adding different spatial disturbance patterns, the flow patterns of complex vortices merging process andshocklets induced by vortices are obtained separately. The fluid dynamics analysesabout the thickness of the shear layers, the energy of the disturbances etc. and theacousitc field analyses about the sound field modes, directivity and attenuation law ofacoustic waves etc. are carried out based on the different flow patterns.The Mc=0.18and Mc=0.866three-dimensional spatial-developping mixing layersare simulated and analyzed in the sixth chapter. For the Mc=0.18mixing layer, H-typetransition process is obtained by adding the two-dimensional disturbance offundamental frequency and the subharmonic oblique waves. For the Mc=0.866mixinglayer, through adding the oblique wave disturbances on the inlet, the existence ofthree-dimensional shocklets at local spatial extent is confirmed. Based on the results ofnumerical simulation, qualitative and quantitative analyses about the mixing layers’fluid dynamics and acoustics features under the two different convective Mach numberconditions are carried out in detail.The seventh chapter mainly discusses the frequency characteristics of fluiddynamics region and acoutics region of the spatial-developping mixing layer computedin the former two chapters. Through Fourier analysis of the pressure signals at differentlocations of inner-field region/near-field region and far-field region, the frequencyevolving law proposed by our research group is verified.Concluding remarks are given in the eighth chapter, in which the main work andconclusions of this thesis are summarized, and the future work is given.