Unsteady Navier-Stokes Simulation of transonic cascade flow using an unfactored implicit upwind relaxation scheme with inner iterations

Masato Furukawa, T. Nakano, M. Inoue

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

An implicit upwind scheme has been developed for Navier-Stokes simulations of unsteady flows in transonic cascades. The two-dimensional, Reynoldsaveraged 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 the 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 inner 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
Title of host publicationTurbomachinery
PublisherAmerican Society of Mechanical Engineers (ASME)
ISBN (Electronic)9780791878989
DOIs
Publication statusPublished - Jan 1 1991
EventASME 1991 International Gas Turbine and Aeroengine Congress and Exposition, GT 1991 - Orlando, United States
Duration: Jun 3 1991Jun 6 1991

Publication series

NameProceedings of the ASME Turbo Expo
Volume1

Other

OtherASME 1991 International Gas Turbine and Aeroengine Congress and Exposition, GT 1991
CountryUnited States
CityOrlando
Period6/3/916/6/91

Fingerprint

Unsteady flow
Fluxes
Cascades (fluid mechanics)
Vortex shedding
Turbulence models
Factorization
Linearization
Navier Stokes equations
Turbines
Composite materials

All Science Journal Classification (ASJC) codes

  • Engineering(all)

Cite this

Furukawa, M., Nakano, T., & Inoue, M. (1991). Unsteady Navier-Stokes Simulation of transonic cascade flow using an unfactored implicit upwind relaxation scheme with inner iterations. In Turbomachinery (Proceedings of the ASME Turbo Expo; Vol. 1). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/91-GT-223

Unsteady Navier-Stokes Simulation of transonic cascade flow using an unfactored implicit upwind relaxation scheme with inner iterations. / Furukawa, Masato; Nakano, T.; Inoue, M.

Turbomachinery. American Society of Mechanical Engineers (ASME), 1991. (Proceedings of the ASME Turbo Expo; Vol. 1).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Furukawa, M, Nakano, T & Inoue, M 1991, Unsteady Navier-Stokes Simulation of transonic cascade flow using an unfactored implicit upwind relaxation scheme with inner iterations. in Turbomachinery. Proceedings of the ASME Turbo Expo, vol. 1, American Society of Mechanical Engineers (ASME), ASME 1991 International Gas Turbine and Aeroengine Congress and Exposition, GT 1991, Orlando, United States, 6/3/91. https://doi.org/10.1115/91-GT-223
Furukawa M, Nakano T, Inoue M. Unsteady Navier-Stokes Simulation of transonic cascade flow using an unfactored implicit upwind relaxation scheme with inner iterations. In Turbomachinery. American Society of Mechanical Engineers (ASME). 1991. (Proceedings of the ASME Turbo Expo). https://doi.org/10.1115/91-GT-223
Furukawa, Masato ; Nakano, T. ; Inoue, M. / Unsteady Navier-Stokes Simulation of transonic cascade flow using an unfactored implicit upwind relaxation scheme with inner iterations. Turbomachinery. American Society of Mechanical Engineers (ASME), 1991. (Proceedings of the ASME Turbo Expo).
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