Unsteady navier-stokes simulation of transonic cascade flow using an unfactored implicit upwind relaxation scheme with inner iterations

M. Furukawa, T. Nakano, M. Inoue

Research output: Contribution to journalArticle

29 Citations (Scopus)

Abstract

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 andLomax 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.

Original languageEnglish
Pages (from-to)599-606
Number of pages8
JournalJournal of Turbomachinery
Volume114
Issue number3
DOIs
Publication statusPublished - Jul 1992

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering

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