Abstract
An efficient and accurate solver is developed to simulate the non-linear fluid-structural interactions in turbomachinery flutter flows. A new low diffusion E-CUSP scheme, Zha CUSP scheme, is developed to improve the efficiency and accuracy of the inviscid flux computation. The 3D unsteady Navier-Stokes equations with the Baldwin-Lomax turbulence model are solved using the finite volume method with the dual-time stepping scheme. The linearized equations are solved with Gauss-Seidel line iterations. The parallel computation is implemented using MPI protocol.The solver is validated with 2D cases for its turbulence modeling, parallel computation and unsteady calculation. The Zha CUSP scheme is validated with 2D cases, including a supersonic flat plate boundary layer, a transonic converging-diverging nozzle and a transonic inlet diffuser. The Zha CUSP2 scheme is tested with 3D cases, including a circular-to-rectangular nozzle, a subsonic compressor cascade and a transonic channel. The Zha CUSP schemes are proved to be accurate, robust and efficient in these tests.The steady and unsteady separation flows in a 3D stationary cascade under high incidence and three inlet Mach numbers are calculated to study the steady state separation flow patterns and their unsteady oscillation characteristics. The leading edge vortex shedding is the mechanism behind the unsteady characteristics of the high incidence separated flows. The separation flow characteristics is affected by the inlet Mach number.The blade aeroelasticity of a linear cascade with forced oscillating blades is studied using parallel computation. A simplified two-passage cascade with periodic boundary condition is first calculated under a medium frequency and a low incidence. The full scale cascade with 9 blades and two end walls is then studied more extensively under three oscillation frequencies and two incidence angles. The end wall influence and the blade stability are studied and compared under different frequencies and incidence angles.The Zha CUSP schemes are the first time to be applied in moving grid systems and 2D and 3D calculations. The implicit Gauss-Seidel iteration with dual time stepping is the first time to be used for moving grid systems. The NASA flutter cascade is the first time to be calculated in full scale.