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Nonlinear Harmonic Analysis of Unsteady Transonic Inviscid and Viscous Flows

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Unsteady Aerodynamics and Aeroelasticity of Turbomachines

Abstract

The nonlinear harmonic approach has been recently developed, in order to effectively include nonlinear effects in turbomachinery blade flutter analysis. In this paper, the effectiveness in dealing with nonlinear effects associated with shock oscillations are assessed by examining unsteady flows around an oscillating transonic cascade. The computed results using a nonlinear harmonic Euler method are compared with those by a nonlinear time-marching Euler solver. The capability of the new approach is clearly demonstrated, although its limitation in a very nonlinear situation is also indicated. Using the nonlinear harmonic approach, the inviscid Euler method has been extended to a viscous solver with the Navier-Stokes equations and a calculation of unsteady turbulent flow in a transonic diffuser is presented.

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References

  1. Verdon, J.M. and Caspar, J.R., “A Linearized Unsteady Aerodynamic Analysis for Transonic Cascades”, Journal for Fluid Mechanics, Vol.149, pp.403–429.

    Google Scholar 

  2. Whitehead, D.S. (1990), “A Finite Element Solution of Unsteady Flow in Cascades”, International Journal for Fluid Mechanics, Vol.149, pp.403–429.

    Google Scholar 

  3. Hall, K.C. and Crawley, E.F. (1989), “Calculation of Unsteady Flows in Turbomachinery Using the Linearized Euler Equations”, AIAA Journal, Vol.27, No.6, pp.777–787.

    Article  ADS  Google Scholar 

  4. Linquist, D.R. and Giles, M.B. (1994), “Validaity of Linearized Unsteady Euler Equations with Shock Capturing”, AIAA Journal, Vol.32. No.1, pp.46–53.

    Article  ADS  Google Scholar 

  5. Ayer, T.C. and Verdon, J.M., (1996), “Validation of Nonlinear Unsteady Aerodynamic Simulator for Vibrating Blade Rows,”, ASME Paper 96-GT-340, to appear in the ASME Journal of Turbomachinery.

    Google Scholar 

  6. Ning, W. and He, L., (1997), “Computation of Unsteady Flows Around Oscillating Blades Using Linear and Nonlinear Harmonic Euler Methods”, ASME Paper 97-GT-229, to appear in the ASME Journal of Tu rbomachinery.

    Google Scholar 

  7. He, L. (1994), “Integration of 2-D Fluid/Structure Coupled System for Calculations of Turbomachinery Aerodynamics/Aeroelastic Instabilities”, International Journal of Computational Fluid Dynamics, Vol.3, pp217–231.

    Article  ADS  Google Scholar 

  8. He, L. (1996), “I. Modelling Issues for Computation of Unsteady Turbomachinery Flows”, VKI Lectures Series “Unsteady Hows in Turbomachines”, 1996-2005.

    Google Scholar 

  9. He, L. (1990), “An Euler Solution for Unsteady Hows Around Oscillating Blades”, ASME Journal of Turbomachinery, Vol.112, pp714–722, 1990.

    Article  Google Scholar 

  10. Sajben, M., Bogar, T.J. and Kroutil, J. C. (1984), “Forced Oscillation Experiments in Supercritical Diffuser Flows”, AIAA Journal, Vol. 22, No.4, 1984.

    Article  Google Scholar 

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© 1998 Springer Science+Business Media Dordrecht

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He, L., Ning, W. (1998). Nonlinear Harmonic Analysis of Unsteady Transonic Inviscid and Viscous Flows. In: Fransson, T.H. (eds) Unsteady Aerodynamics and Aeroelasticity of Turbomachines. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5040-8_12

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  • DOI: https://doi.org/10.1007/978-94-011-5040-8_12

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6116-2

  • Online ISBN: 978-94-011-5040-8

  • eBook Packages: Springer Book Archive

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