A nonperiodic boundary approach for computation of compressible viscous flows in advanced turbine cascades

Abstract

A two-dimensional flow solver is presented for advanced turbine cascades, with high turning, with or without embedded shocks. Options allow for solution of the steady or unsteady Euler, thin layer or the full Reynolds averaged Navier-Stokes equations. A cellcentered finite volume formulation with variable artificial viscosity is used for viscous flows. The time stepping is achieved by a hybrid multi-stage RungeKutta scheme, and the solution is accelerated using local time stepping, enthalpy damping and implicit residual averaging. For turbine cascades with high stagger, conventional periodic C-type grids are highly skewed, leading to u considerable solution degradation. A nonperiodic boundary grid has been used to overcome this problem; In this work, grid generation and the treatment of the nonperiodic boundary is discussed. Results are presented for two-dimensional flow in two transonic turbine cascades. Good agreement with the experimental data is found. Nomenclature P Density u,v Velocity Components e Total Energy h Enthalpy P Pressure k Thermal Conductivity Y Ratio of Specific Heats X ? Y Cartesian Coordinates t Time O,T Stress U, Molecular Viscositv * Assistant Professor, Director, Computational Fluid * Graduate Research Assistant Graduate Student Dynamics Laboratory 1 ut Turbulent Viscosity A Bulk Viscosity T Temperature F Inviscid Flux Vector G Viscous Flux Vector D Artificial Dissipation Flux INTRODUCTION The application of CFD to turbomachinery design has evolved rapidly in recent years. The need for increased efficiency coupled with weight reduction has driven the investigation of specific details of complex flow fields. As core engine pressure and temperature increases to insure high propulsive efficiency and as engine overall length is decreased to reduce weight, stage loading in the compressor and turbine sections must increase. The work output of the high and low pressure turbine sections must'also increase. This calls for turbine rotor blades with high degrees of turning. This high turning leads to a large pan of the blade being uncovered. Additionally the exit flow could be supersonic with shock waves forming near the pressure surface trailing edge and intersecting with the suction surface leading to complex reflections and possible flow separation. Numerical schemes attempting to model flowfields in turbomachinery should be capable of predicting these flow phenomena accurately. In the past few years considerable work has been done on the development of numerical schemes for simulation of cascade flows with success, Inviscid flow solvers' have advanced considerably and are now used routinely for preliminary design work. However an inviscid analysis has limited value due to its inability to predict the total pressure loss as well as ambiguity when dealing with round trailing edges. One approach to alleviating some of these limitations is the use 'of an viscous-inviscid interaction technique. This approach has been used successfully by Micklow' for analyzing high subsonic and transonic compressor