Unsteady three-dimensional thin layer Navier-Stokes solutions for turbomachinery in transonic flow

This dissertation concerns the development of a numerical scheme to simulate the flow field generated by rotating machinery. The implicit Euler solver "TURBO" developed at MSU and in use at NASA Lewis Research Center for analyzing compressible flows in general rotating machinery was augmented by including viscous effects. This was accomplished by making the thin-layer approximation with a Baldwin-Lomax turbulence model to simplify the Reynolds-averaged Navier-Stokes equations. This code is an implicit finite volume scheme with flux Jacobians evaluated by flux-vector-splitting and residual fluxes by Roe's flux-difference-splitting. Diffusive flux terms were treated explicitly in order to preserve the existing code structure. A modified two-pass matrix solver based on the Gauss-Seidel iterative method was used in place of the standard LU approximate factorization to enhance the code's stability. Newton subiterations were used for unsteady flow computations. A localized grid distortion technique was applied for data communication between blocks in relative motion. An inlet boundary condition for preserving total reservoir conditions and a new approach for computing wall shear stress for nonorthogonal grids are also presented.; Three engineering problems have been examined by this computational technique with fair results. Hamilton-Standard's advanced propfan design SR7 served as a test case for external flows. NASA's Rotor 67 with a rotating blade row and NASA's Stage 67 with both rotating and static blade rows with a different number of blades in each row test the code's ability for internal flows. Although some improvements are still needed for this code to become a real engineering design tool, the decent results obtained from applying this code to the above three real-world engineering problems suggest that it is moving in the right direction.