A Navier-Stokes Analysis of 3-D Transonic Cascade Flow and its Visualization

The purpose of this paper is, first, to analyze 3-D transonic cascade flow by using the TVD Navier-Stokes code developed by the authors. Since the momentum equations of contravariant velocities are used in the code, the treatments of boundary conditions, especially the solid wall and the periodic boundaries for the 3-D cascade flow, become very easy. A Chakravarthy-Osher type TVD scheme modified by the authors is adopted in order to clearly simulate 3-D complex flow having shock waves and separation bubbles. The second purpose is to visualize the computed results by using the 3-D color graphic display. As numerical examples, the 3-D viscous flows thorough a transonic axial-flow compressor rotor with or without a tip clearance are computed, and the colored oli-flow patterns, 3-D particle paths, 3-D time lines which show the shock boundary layer interactions and a leakage vortex near the casing wall are obtained. In particular, the mechanism of occurrence of the leakage vortex is investigated in detail.