DOI QR코드

DOI QR Code

Compressible Parabolized Stability Equation in Curvilinear Coordinate System and integration

  • Published : 2006.12.31

Abstract

Parabolized stability equations for compressible flows in general curvilinear coordinate system are derived to deal with a broad range of transition prediction problems on complex geometry. A highly accurate finite difference PSE code has been developed using an implicit marching procedure. Compressible and incompressible flat plate flow stability under two-dimensional and three¬dimensional disturbances has been investigated to test the present code. Results of the present computation are found to be in good agreement with the multiple scale analysis and DNS data. Stability calculation results by the present PSE code for compressible boundary layer at Mach numbers ranging from 0.02 to 1.5 are also presented and are again seen to be as accurate as the spectral method.

Keywords

References

  1. D. Arnal, Description and prediction of transition two dimensional incompressible flows. In special Course on Stability and Transition of Laminar Flows, AGARD Report 709, 1984
  2. D. Arnal, Boundary layer transition: Predictions based on linear theory. In special Course on Progress in Transition Modeling. AGARD reports, 793, 1994
  3. V. Esfahanian and K. Hejranfar, Linear and Nonlinear PSE for Stability Analysis of the Blasius Boundary Layer Using Compact Scheme. Journal of Fluids Engineering. ASME. September 2001, Vol. 123
  4. Th. Herbert and F. P. Bertolotti, Stability analysis of nonparallel boundary layers. J. Bull. AM. Phys. Soc., 32, pp. 2079, 1987
  5. S. Hu and X. Zhong, Nonparallel stability Analysis of Compressible Boundary Layer using 3-D PSE. AIAA-1999-0813
  6. C. L. Chang and M. R. Malik, Compressible Stability of Growing Boundary Layers Using Parabolized Stability Equations. AIAA-1991-1636
  7. Th. Herbert and M. V. Morkovin, Dialogue on bridging some gaps in stability and transition research. Laminar-Turbulent Transition. (Ed) R.Eppler and H. Fasel, SpringerVerlag, 1980
  8. L. M. Mack, 1977. Transition prediction and linear stability theory. In Laminar-Turbulent Transition. AGARD CP 224
  9. F. P. Bertolotti, Compressible Boundary Layer Stability analyzed with the PSE equations. AIAA-1991-1637
  10. Th. Herbert, Parabolized stability equations. Annual Review of Fluid Mechanics. Vol. 29, January, 1997
  11. M. R. Malik, Hypersonic Flight Transition Data Analysis Using Parabolized Stability Equations with Chemistry Effects. Journal of Spacecraft and Rockets. Vol. 40, NO.3, MayJune 2003
  12. F. Tisseur and K. Meerbergen, The Quadratic Eigenvalue Problem. SIAM REVIEW. Vol. 43, No.2, 2001
  13. M. R. Malik, Numerical methods for hypersonic boundary layer stability. Journal of computational physics 86, 1990
  14. F. P. Bertolotti, Linear and nonlinear stability of boundary layers with streamwise varying properties. Ph D dissertation. The Ohio State University, 1991
  15. T. Cebeci and P. Bradshaw, Physical and Computational Aspects of Convective Heat Transfer. Springer-Verlag. New York
  16. El-Hady N. M. and Nayfeh A. H., Nonparallel stability of compressible boundary layer flows. AIAA-1980-0277