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DEVELOPMENT OF AN EFFICIENT AND ROBUST LINEARISED NAVIER-STOKES FLOW SOLVER

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UNSTEADY AERODYNAMICS, AEROACOUSTICS AND AEROELASTICITY OF TURBOMACHINES

Abstract

A time-linearised Navier-Stokes flow solver is presented. The turbulence model of Spalart & Allmaras has been included in the flow model. The main feature of the current method is that GMRES with preconditioning is used to solve the linearised equations in a robust and efficient manner. The method is verified by the presentation of solutions of test cases from Standard Configuration 10 and 11. The use of various upwind schemes is also examined.

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References

  1. S. Weber, M.F. Platzer: “A Navier-Stokes Analysis of the Stall Flutter Characteristics of the Buffum Cascade”. Journal of Turbomachinery. 122, 2000, pp. 769–776.

    Article  Google Scholar 

  2. W.S. Clark, K.C. Hall: “A Time-Linearized Navier-Stokes Analysis of Stall Flutter”. Journal of Turbomachinery. 122, 2000, pp. 467–476.

    Article  Google Scholar 

  3. L. Sbardella, M. Imregun: “Linearised Unsteady Viscous Turbomachinery Flows Using Hybrid Grids”. Journal of Turbomachinery. 123, 2001, pp. 568–582.

    Article  Google Scholar 

  4. P.R. Spalart, S.R. Allmaras: “A One-Equation Turbulence Model for Aerodynamic Flows”. In Proceedings of 30th Aerospace Sciences Meeting & Exhibit. 1992, AIAA-92-0439.

    Google Scholar 

  5. J. E. Bardina, P. G. Huang, T. J. Coakley: “Turbulence Modeling Validation, Testing, and Development”. NASA Technical Memorandum 110446, April 1997.

    Google Scholar 

  6. M. Giles: “Non-Reflecting Boundary Conditions for the Euler Calculations”. AIAA Journal. 28, 1990, pp. 2050–2058.

    Article  Google Scholar 

  7. I.A. Johnston: “Simulation of Flow Around Hypersonic Blunt-Nosed Vehicles for the Calibration of Air Data Systems”. Ph. D. Thesis. Department of Mechanical Engineering. University of Queensland. Australia. 1999.

    Google Scholar 

  8. P.L. Roe: “Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes”. Journal of Computational Physics. 43, 1981, pp. 357–372.

    Article  MATH  MathSciNet  Google Scholar 

  9. Y. Wada, M.-S. Liou: “A Flux Splitting Scheme with High-Resolution and Robustness for Discontinuities”. AIAA Paper 94–0083, Jan. 1994.

    Google Scholar 

  10. P. J. Petrie-Repar: “Numerical Simulation of Diaphragm Rupture”. Ph. D. Thesis, University of Queensland, Australia, 1998.

    Google Scholar 

  11. D. I. Pullin: “Direct simulation methods for compressible inviscid ideal-gas flow”. Journal of Computational Physics 34 pp. 231–244, 1979.

    Article  Google Scholar 

  12. P. A. Jacobs: “Single-block Navier-Stokes Integrator” NASA CR-187613, ICASE Interim Report 18, 1991.

    Google Scholar 

  13. Y. Saad: “Iterative Methods for Sparse Linear Systems”. SIAM, 2003.

    Google Scholar 

  14. T.H. Fransson, J.M. Verdon: “Updated Report on Standard Configurations for Unsteady Flow Through Vibrating Axial-Flow Turbomachine Cascades”. Report. Royal Institute of Technology, Stockholm, Sweden. URL: http://www.egi.kth.se/ekv/stck.

  15. T.H. Fransson, M. Jöcker, A. Bölcs, P. Ott. “Viscous and Inviscid Linear/Nonlinear Calculations Versus Quasi 3D Experimental Cascade Data for a New Aeroelastic Turbine Standard Configuration”. Journal of Turbomachinery. 121, 1999, pp. 717–725.

    Article  Google Scholar 

  16. D. R. Lindquist, M. B. Giles: “Validity of Linearized Unsteady Euler Equations with Shock Capturing”. AIAA Journal 32 (1), pp. 46–53, January 1994.

    MATH  Google Scholar 

  17. K.C. Hall, W.S. Clark: “Calculation of Unsteady Linearized Euler Flows in Cascades Using Harmonically Deforming Grids”. In Proceedings of Unsteady Aerodynamics, Aeroacoustics and Aeroelasticity of Turbomachines and Propellers. Editor: H.M. Atassi. University of Notre Dame. 1991.

    Google Scholar 

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© 2006 Springer

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Petrie-Repar, P. (2006). DEVELOPMENT OF AN EFFICIENT AND ROBUST LINEARISED NAVIER-STOKES FLOW SOLVER. In: Hall, K.C., Kielb, R.E., Thomas, J.P. (eds) UNSTEADY AERODYNAMICS, AEROACOUSTICS AND AEROELASTICITY OF TURBOMACHINES. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4605-7_32

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  • DOI: https://doi.org/10.1007/1-4020-4605-7_32

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-4267-6

  • Online ISBN: 978-1-4020-4605-6

  • eBook Packages: EngineeringEngineering (R0)

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