### 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 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 language | English |
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Journal | American Society of Mechanical Engineers (Paper) |

Publication status | Published - Jan 1 1991 |

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### All Science Journal Classification (ASJC) codes

- Mechanical Engineering

### Cite this

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

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Unsteady Navier-Stokes simulation of transonic cascade flow using an unfactored implicit upwind relaxation scheme with inner iterations

AU - Furukawa, Masato

AU - Nakano, T.

AU - Inoue, M.

PY - 1991/1/1

Y1 - 1991/1/1

N2 - 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 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.

AB - 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 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.

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M3 - Article

JO - American Society of Mechanical Engineers (Paper)

JF - American Society of Mechanical Engineers (Paper)

SN - 0402-1215

ER -