### 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 language | English |
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Title of host publication | Turbomachinery |

Publisher | American Society of Mechanical Engineers (ASME) |

ISBN (Electronic) | 9780791878989 |

DOIs | |

Publication status | Published - Jan 1 1991 |

Event | ASME 1991 International Gas Turbine and Aeroengine Congress and Exposition, GT 1991 - Orlando, United States Duration: Jun 3 1991 → Jun 6 1991 |

### Publication series

Name | Proceedings of the ASME Turbo Expo |
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Volume | 1 |

### Other

Other | ASME 1991 International Gas Turbine and Aeroengine Congress and Exposition, GT 1991 |
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Country | United States |

City | Orlando |

Period | 6/3/91 → 6/6/91 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Engineering(all)

### Cite this

*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, M.; Nakano, T.; Inoue, M.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

TY - GEN

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

AU - Furukawa, M.

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, 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.

AB - 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.

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U2 - 10.1115/91-GT-223

DO - 10.1115/91-GT-223

M3 - Conference contribution

AN - SCOPUS:84924794733

T3 - Proceedings of the ASME Turbo Expo

BT - Turbomachinery

PB - American Society of Mechanical Engineers (ASME)

ER -