Unsteady Navier–Stokes Simulation of Transonic Cascade Flow Using an Unfactored Implicit Upwind Relaxation Scheme With Inner Iterations

[+] Author and Article Information
M. Furukawa, T. Nakano, M. Inoue

Department of Mechanical Engineering for Power, Kyushu University, Fukuoka, Japan

J. Turbomach 114(3), 599-606 (Jul 01, 1992) (8 pages) doi:10.1115/1.2929184 History: Received March 04, 1991; Online June 09, 2008


An implicit upwind scheme has been developed for Navier–Stokes simulations of unsteady flows in transonic cascades. The two-dimensional, Reynolds-averaged Navier–Stokes equations are discretized in space using a cell-centered finite volume formulation and in time using the Euler implicit method. The inviscid fluxes are evaluated using a highly accurate upwind scheme based on a TVD formulation with the Roe’s approximate Riemann solver, and the viscous fluxes are determined in a central differencing manner. The algebraic turbulence model of Baldwin and Lomax is employed. To simplify grid generations, a zonal approach with a composite zonal grid system is implemented, in which periodic boundaries are treated as zonal boundaries. A new time linearization of the inviscid fluxes evaluated by Roe’s approximate Riemann solver is presented in detail. No approximate factorization is introduced, and unfactored equations are solved by a pointwise relaxation method. To obtain time-accurate solutions, 30 linear iterations are performed at each time step. Numerical examples are presented for unsteady flows in a transonic turbine cascade where periodic unsteadiness is caused by the trailing edge vortex shedding.

Copyright © 1992 by The American Society of Mechanical Engineers
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