Development of a Steady Potential Solver for Use with Linearized Unsteady Aerodynamic Analyses

  • Daniel Hoyniak
  • Joseph M. Verdon
Conference paper

Abstract

The need for accurate and numerically efficient response predictions for vibrating turbomachinery blading has resulted in the development of linearized unsteady aerodynamic analyses for cascade flows. One such model is the linearized inviscid flow (LINFLO) analysis developed by Verdon and Caspar, (1982,1984). This model assumes that the unsteady flow can be represented as a perturbation of the underlying nonuniform mean flow. Thus, in order to predict the unsteady aerodynamic response of a cascade using this technique, the steady flow field must first be calculated. A full potential solver developed explicitly for use with the LINFLO analysis is described herein. The solver uses the nonconservative form of the nonlinear potential flow equations together with an implicit, least-squares, finite-difference approximation to solve for the steady flow field. The difference equations are developed on a composite mesh which consists of a C-grid embedded in a rectilinear (H-grid) cascade mesh. The composite mesh is capable of resolving blade-to-blade and farfield phenomena on the H-grid, while accurately resolving local phenomena on the C-grid. The resulting system of algebraic equations are arranged in matrix form using a sparse matrix package and solved by Newton’s method.

Steady and unsteady results are presented for two cascade configurations, a high speed compressor, and a turbine with high exit Mach number. The compressor configuration is composed of airfoils having a NACA 6% thickness distribution superimposed on a circular arc camber line. The turbine cascade is the fourth standard configuration reported on by Bölcs and Fransson (1986).

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References

  1. Atassi, H., and Akai, Ti., 1980, “Aerodynamic and aeroelastic Characteristics of Oscillating Loaded Cascades at Low Mach Number. I Pressure Distribution, Forces and Moments,” Transactions of American Society of Mechanical Engineering Journal of Engineering for Power, Vol 102,No. 2, pp. 344–351.Google Scholar
  2. Bailey, H.E. and Beam, R.M., 1991, “Newton’s Method Applied to Finite-Difference Approximations for the Steady-State Compressible Navier-Stokes Equations”, Journal of Computational Physics, Vol 93., pp 108–127.Google Scholar
  3. Bender, E.E., and Khosla, P.K., 1988, “Application of Sparse Matrix Solvers and Newton’s Method to Fluid Flow Problems”, AIAA paper number 88–3700CP.Google Scholar
  4. Bôlcs, A., and Fransson, T.H., 1986, “Aeroelasticity in Turbomachines - Comparison of Theoretical and Experimential Cascade Results”, Communication du Laboratorie de Thermique Appliquèe et de Turbomachines, No. 13, Lausanne, EPFL.Google Scholar
  5. Caruthers, J.E., and Dalton, W.N., 1991, “Unsteady Aerodynamic Response of a Cascade to Nonuniform Inflow,” ASME Paper 91-GT-174, Presented at the International Gas Turbine and Aeroengine Congress and Exposition, Orlando, Florida, June 3–6, 1991.Google Scholar
  6. Caspar, J.R., Hobbs, D.E., and Davis, R.L., 1980, “Calculation of Two-Dimensional Potential Cascade Flow Using Finite Area Methods,” AIAA Journal, Vol. 18, pp. 103–109.ADSCrossRefGoogle Scholar
  7. Caspar, J.R., and Verdon, J.M., 1981, “Numerical Treatment of Unsteady Subsonic Flow Past an Oscillating Cascade,” AIAA Journal, Vol. 19, pp 1531–1539.ADSMATHCrossRefGoogle Scholar
  8. Eisenstat, S.C., Grusky, M.C., Schultz, M.H., and Sherman, A.H., 1977, “The Yale Sparse Matrix Package. II. The Non-symmetric Codes,” Research Report No. 114, Yale University, Department of Computer Science, New Haven, CT.Google Scholar
  9. Giles, M., 1985, “Newton Solution of Steady Two-Dimensional Transonic flows”, PhD thesis, Massachusetts Institute of Technology, Cambridge, Massachusetts.Google Scholar
  10. Hall, K.C., and Clark W.S., 1991, “Prediction of Unsteady Aerodynamic Loads in Cascades Using Time Linearized Euler Equations on Deforming Grids,” AIAA Paper 91–3378, Presented at the 27’ AIAA Joint Propulsion Conference, 1991, Sacramento Calf.Google Scholar
  11. Hall, K.C., and Crawley, E.F., 1989, “Calculations of Unsteady Flows in Turbomachinery Using The Linearized Euler Equations,” AL4A Journal, Vol. 27, No. 6, pp 777–787.Google Scholar
  12. Verdon, J.M., and Caspar, J.R., 1982, “Development of a Linear Unsteady Aerodynamic Analysis for Finite-Deflection Subsonic Cascades,” AIAA Journal, Vol. 20, pp 1259–1267.ADSMATHCrossRefGoogle Scholar
  13. Verdon, J.M., and Caspar, J.R., 1984, “A Linearized Unsteady Aerodynamic Analysis for Transonic Cascades,” Journal of Fluid Mechanics, Vol. 149, pp 403–429.ADSMATHCrossRefGoogle Scholar
  14. Whitehead, D.S., 1982, ‘The Calculation of Steady and Unsteady Transonic Flows in Cascades,“ Cambridge University Engineering Dept. Rept. CUED/ATurbo/TR 118, Cambridge, UK.Google Scholar
  15. Usab, W.J., and, Verdon, J.M., 1989, “Advances in the Numerical Analysis of Linearized Unsteady Cascades Flows,” ASME Paper 90GT-11, Presented at the International Gas Turbine and Aeroengine Congress and Exposition, Brussels, Belgium.Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 1993

Authors and Affiliations

  • Daniel Hoyniak
    • 1
  • Joseph M. Verdon
    • 2
  1. 1.NASA Lewis Research CenterClevelandUSA
  2. 2.United Technologies Research CenterEast HartfordUSA

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