Theoretical studies of recirculating duct flows for the UTSI MHD combustor and diffuser designs

The present research work is concerned with the theoretical investigation for duct flows in the Energy Conversion Research and Development Programs at the University of Tennessee Space Institute. A computational procedure is employed to determine the planar, axisymmetric flow fields within a confined duct. It is based on solving a stream function and vorticity formulation of the Navier-Stokes equations for fully elliptic flows. The tangential momentum effect of swirl for axisymmetric flow has been introduced. The working fluid is assumed to be a perfect gas. The wall is assumed to be smooth, rigid and impermeable. The gravity forces and thermal radiation exchanges are neglected in this study. The partial differential equations for steady-state, two-dimensional, compressible, viscous flow are solved by a finite difference method. The coordinate transformation and decay function are used in the current study to solve complex geometry and to provide numerical solution stability. A constant viscosity is used for some simple flows, and a two-equation turbulence model is used for more complicated flows. Some of the numerical solutions are favourably compared with analytical solutions and existing experimental data. For the remaining numerical solutions, more information not being available in the literature, the predicted results require verification.