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Spatial stability of the incompressible corner flow

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Abstract

The linear spatial stability of the incompressible corner flow under pressure gradient has been studied. A self-similar form has been used for the mean flow, which reduces the related problem to the solution of a two-dimensional problem. The stability problem was formulated using the parabolised stability equations (PSE) and results were obtained for the viscous modes at medium and high frequencies. The related N-factors indicate that the flow is stable at these frequencies, but probably unstable for small frequencies. Furthermore the inviscid mode for each mean flow was obtained and the results indicate that its importance increases considerably with an increase in the adverse pressure gradient. Finally the dependence of the stability characteristics on the extent of the domain is also considered.

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References

  1. Andersson, P., Henningson, D.S., Hanifi, A.: On a stabilization procedure for the parabolic stability equations. J. Eng. Math. 33(3), 311–332 (1998)

    Google Scholar 

  2. Balachandar, S., Malik, M.R.: Inviscid instability of streamwise corner flow. J. Fluid Mech. 282, 187–201 (1995)

    Google Scholar 

  3. Barclay, W.H.: Experimental investigation of the laminar flow along a straight 135° corner. Aero. Q. 24(2), 147–154 (1973)

    Google Scholar 

  4. Barclay, W.H., El-Gamal, H.A.: Streamwise corner flow with wall suction. AIIA J. 21, 31–37 (1983)

    Google Scholar 

  5. Barclay, W.H., Ridha, A.H.: Flow in streamwise corners of arbitrary angle. AIAA J. 18(12), 1413–1420 (1980)

    Google Scholar 

  6. Bertolotti, F.B., Herbert, Th.: Analysis of the linear stability of compressible boundary layers using the PSE. Theoret. Comput. Fluid Dyn. 3, 117–124 (1991)

    Google Scholar 

  7. Bertolotti, F.B., Herbert, Th., Spalart, P.R.: Linear and nonlinear stability of the Blasius boundary layer. J. Fluid Mech. 242, 441–474 (1992)

    Google Scholar 

  8. Boyd, J.P.: Chebyshev and Fourier Spectral Methods, 2nd edn. Dover, New York (2000)

  9. Dhanak, M.R.: On the instability of flow in a streamwise corner. Proc. R. Soc. Lond. A 441, 201–210 (1993)

    Google Scholar 

  10. Dhanak, M.R., Duck, P.W.: The effects of freestream pressure gradient on a corner boundary layer. Proc. R. Soc. London A 453, 1793–1815 (1997)

    Google Scholar 

  11. Duck, P.W., Stow, S.R., Dhanak, M.R.: Non-similarity solutions to the corner boundary-layer equations (and the effects of wall transpiration). J. Fluid Mech. 400, 125–162 (1999)

    Google Scholar 

  12. El-Hady, N.M.: Nonparallel Stability Theory of Three-Dimensional Compressible Boundary Layers Part I – Stability Analysis. NASA Contractor Report CR-3245 (1980)

  13. Gallionis, I.: Instability of three-dimensional flows. Dissertation, London University (2003)

  14. Herbert, Th.: Parabolised stability equations. Annu. Rev. Fluid Mech. 29, 245–283 (1997)

    Google Scholar 

  15. Janke, E., Balakumar, P.: On the Stability of Three-dimensional Boundary Layers. Part 1: Linear and Nonlinear Stability. NASA/CR-1999-209330, ICASE Report No. 99-16 (1999)

  16. Joslin, R.D., Streett, C.L., Chang, C.L.: Spatial direct numerical simulation of boundary-layer transition mechanisms: validation of PSE theory. Theoret. Comput. Fluid Dyn. 4(6), 271–288 (1993)

  17. Lakin, W.D., Hussaini, M.Y.: Stability of the laminar boundary layer in a streamwise corner. Proc. R. Soc. Lond. A 393, 101–116 (1984)

    Google Scholar 

  18. Li, F., Malik, M.R.: On the nature of PSE approximation. Theoret. Comput. Fluid Dyn. 8, 253–273 (1996)

    Google Scholar 

  19. Lin, C.C.: On the stability of two-dimensional parallel flows. Q. Appl. Math. 3, 117–142 (1945); 3, 213–234 (1945); 3, 277–301 (1946)

    Google Scholar 

  20. Lin, R.S., Wang, W.P., Malik, K.R.: Linear stability of incompressible flow along a corner. ASME Fluids Engineering Division Summer Meeting (1996)

  21. Malik, M.R., Li, F.: Three-Dimensional Boundary Layer Stability and Transition. SAE Technical Paper Series 921991 (1992)

  22. Mughal, M.S.: Transition Prediction in Fully 3D Compressible Flows. I.C. Contract Report prepared for QinetiQ/BAe(MAD) (2001)

  23. Pal, A., Rubin, S.G.: Asymptotic features of the viscous flow along a corner. Q. Appl. Math. 29, 91–108 (1971)

    Google Scholar 

  24. Parker, S.J., Balachandar, S.: Viscous and inviscid instabilities of flow along a streamwise corner. Theoret. Comput. Fluid Dyn. 13, 231–270 (1999)

    Google Scholar 

  25. Ridha, A.: Sur la couche limite incompressible laminaire le long d’un dièdre. C. R. Acad. Sci. Paris Sér. II 311, 1123–1128 (1990)

    Google Scholar 

  26. Ridha, A.: On the dual solutions associated with boundary-layer equations in a corner. J. Eng. Math. 26, 525–537 (1992)

    Google Scholar 

  27. Ridha, A.: On laminar natural convection in a vertical corner. C. R. Acad. Sci. Paris t. 328, Sér. II b, 485–490 (2000)

  28. Ridha, A.: Combined free and forced convection in a corner. Int. J. Heat Mass Transf. 45, 2191–2205 (2000)

    Google Scholar 

  29. Rubin, S.G.: Incompressible flow along a corner. J. Fluid Mech. 26, 97–110 (1966)

    Google Scholar 

  30. Rubin, S.G., Grossman, B.: Viscous flow along a corner: numerical solution of the corner layer equations. Q. Appl. Math. 29, 169–186 (1971)

    Google Scholar 

  31. Schubauer, G.B., Skarmstad, H.K.: Laminar boundary-layer oscillations and stability of laminar flow. J. Aero. Sci. 14(2), 69–78 (1947)

    Google Scholar 

  32. Sorenson, D.C.: Implicit application of polynomial filters in a k-step Arnoldi method. SIAM J. Matrix Anal. Appl. 13, 357–185 (1992)

    Google Scholar 

  33. van der Vorst, H.: BICGSTAB: A fast and smoothly converging variant of BiCG for the solution of non-symmetric linear systems. SIAM J. Sci. Statist. Comput. 13, 631–644 (1992)

    Google Scholar 

  34. Weinberg, B.C., Rubin, S.G.: Compressible corner flow. J. Fluid Mech. 56, 753–774 (1972)

    Google Scholar 

  35. Zamir, M.: Further solution of the corner boundary-layer equations. Aero. Q. 24(3), 219–226 (1973)

    Google Scholar 

  36. Zamir, M., Young, A.D.: Pressure gradient and leading edge effects on the corner boundary layer. Aero. Q. 30(3), 471–484 (1979)

    Google Scholar 

  37. Barrett, R., Berry, M., Chan, T.F., Demmel, J., Donato, J., Dongarra, J., Eijhkout, V., Pozo, R., Romine, C., Vorst, H.: Templates for the solution of linear systems. Building blocks for iterative methods. SIAM (1994)

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  1. Department of Mathematics, Imperial College, London, SW7 2AZ, UK

    Ioannis Galionis & Philip Hall

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  1. Ioannis Galionis
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  2. Philip Hall
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Correspondence to Philip Hall.

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M.Y. Hussaini

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Galionis, I., Hall, P. Spatial stability of the incompressible corner flow. Theor. Comput. Fluid Dyn. 19, 77–113 (2005). https://doi.org/10.1007/s00162-004-0153-1

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