Finite Difference Method Based Large Eddy Simulation Of Compressible Flow

The characteristic of high thrust-weight ratio of modern aero engine makes theturbine have higher operating load, larger Mach number and larger meridionaldivergence angle. Meanwhile, the pressure ratio of the single stage of the compressor ishigher than ever. It implies that the flow inside the impeller part of the aero enginebecomes extremely complex, with the occurrence of large-scale separation, transitionand shock/boundary-layer interaction. Therefore, with CFD technology having becomethe main means of aerodynamic design and analysis of turbo machinery, it is significantto develop a numerical calculation program that has strong ability of capturingdiscontinuity and viscous flow structure. The rapid development of computerperformance makes it possible to realize the engineering application of large eddysimulation to the field of turbo machinery. Against this background, the research in thisdissertation is organized from the following aspects.In this dissertation, the variables of N-S equations are transformed to generalcurvilinear coordinate system and solved based on finite difference method, and a LESnumerical calculation program for compressible flow is developed. The time marchingmethod is used for numerical calculation and the spatial discretization schemes are thirdand fifth order accuracy WENO scheme. AUSM+-up method or Steger-Warmingmethod are applied to calculate the inviscid numerical flux. The timediscretization scheme is prediction-correction LU-SGS method. When unsteady flow isconsidered, the dual-time-step method with second order accuracy is adopted. Thesubgrid stress model embedded in the program is dynamic Smagorinskyeddy viscosity model. In this dissertation, the underlying architecture of the program isdesigned and the code is packaged by modules. The boundary condition is treated by use of subroutines.In this dissertation, the shock reflection flow in a channel with a forward step issimulated with the CFD program, and the ability of capturing discontinuity of differentschemes and flux splitting method is compared. This test case is used to check thecalculation performance of predicting supersonic flow field with complex discontinuitystructures. Both subsonic and supersonic inviscid flow in a channel with a bump as wellas the supersonic laminar flow in a Laval nozzle is simulated. The data obtained are ingood agreement with the results of calculation or experiment in the literature. Theinteraction of shock and boundary-layer of the plate is also simulated. In this case, thecalculated pressure distribution along the plate is in nice agreement with theexperimental data in the literature, and the complex structures of shock reflection, flowseparation and reattachment is clearly captured. The convergence characteristics ofdifferent schemes is assessed. Availability of the CFD program is verified with thecalculation of the test cases mentioned above.In this dissertation, the flow in NACA65compressor cascade underincompressible and subsonic operating conditions is investigated with LES method. Thepressure coefficient distribution on the airfoil surface is in good agreement with theexperimental results in the literature, as implied that the CFD program is reliable forsimulation of flow in the turbo machinery with LES method. The transient flow filedobtained shows that LES successfully captures the details of viscous flow inside thelinear cascade. The generation mechanism of self-excited turbulence in the flow field issimply discussed.The work in this dissertation implies that high resolution schemes based large eddysimulation can provide the details of viscous flow field in cascades, and lays thefoundation of further more in-depth high accuracy LES research on the complexcompressible flow in the turbo machinery, which shows that LES method has high application value and broad application prospects in investigating the complex flowmechanism in the turbo machinery and guiding the design of highly-loaded axialcompressors.