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Progress on the Calculation of Large-Scale Separation at High Reynolds Numbers

  • Conference paper
Studies of Vortex Dominated Flows

Part of the book series: ICASE NASA LaRC Series ((ICASE/NASA))

Abstract

The computation of high Reynolds number laminar separation has been one of the central issues in fluid mechanics over the past two decades. Laminar separation has eluded a description based on Prandtl’s boundary layer theory primarily due to the presence of the Goldstein [10J singularity at separation (see also Stewartson [28J). However, this state of affairs changed abruptly with the development of the tripledeck theory by Stewartson & Williams [27] and Neiland [14] for supersonic flows. Drawing upon Lighthill’s -[12] earlier work with viscous sublayers, Stewartson & Williams [27] were able to show that a boundary layer in a supersonic flow could “spontaneously” separate by setting up a local interaction between a viscous sublayer lying within the depths of the boundary layer and the local inviscid flow just outside the boundary layer. The work of Neiland [14] and Stewartson & Williams [27] introduced a very new concept to viscous flow theory, that of a freeinteraction. Prior to this time it had generally been thought that separation occurs due to a gradual reaction of the boundary layer to an externally imposed adverse pressure gradient.

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Reference

  1. Achenbach, E., “Distribution of Local Pressure and Skin Friction Around a Circular Cylinder in Cross-Flow up to Re=5x106,” J. Fluid Mech, vol. 34, 1968.

    Google Scholar 

  2. Cheng, H.K., and Rott, N., “Generalizations of the Inversion Formula of Thin Airfoil Theory,” J. Rat. Mech. An, No.3, 1954.

    Google Scholar 

  3. Cheng, H.K., and Smith, F. T., “The Influence of Airfoil Thickness and Reynolds Number on Separation,” J. of Applied Maths. and Physics vol. 33, 1982.

    Google Scholar 

  4. Cheng, H.K., “Laminar Separation from Airfoils Beyond Trailing-Edge Stall,” AIAA 84-1612 presented at the AIAA 17th Annual Fluid Dynamics, Plasma DynamiCS and Lasers Conference, 1984.

    Google Scholar 

  5. Cheng, H.K., and Lee, C.J., “Laminar Separation Studied as an Airfoil Problem,” Numerical and Physical Aspects of Aerodynamic Flows, ed. T. Cebeci, SpringerVerlag, 1985.

    Google Scholar 

  6. Daniels, P.G., “Laminar Boundary-Layer Reattachment in Supersonic Flow. Part 2. Numerical Solution,” J. Fluid Mech., 97, part 1,1980.

    Google Scholar 

  7. Davis, R. T., “Numerical Methods for Coordinate Generation Based on SchwarzChristoffel Transformations,” AIAA79-1463 presented at the 4th Computational Fluid Dynamics Conference, 1979.

    Google Scholar 

  8. Davis, R.T., and Werle, M.J., “Progress on Interacting Boundary Layer Computations at High Reynolds Number,” Numerical and Physical Aspect of Aerodynamic Flows, Springer-Verlag, 1982.

    Google Scholar 

  9. Fornberg, B., “Steady Viscous Flow Past a Circular Cylinder up to Reynolds Number 600,” submitted to J. Compo Phys., 1985.

    Google Scholar 

  10. Goldstein, S., “On Laminar Boundary Layer Flow Near a Position of Separation,” Quart. J. Mech. Appl. Math., vol. 1, 1948.

    Google Scholar 

  11. Kirchhoff, G., “Zur Theorie freier Flussigkeitsstrahlen,” J. Reine Angew. Math., vol. 70, 1869.

    Google Scholar 

  12. Lighthill, M.J., “On Boundary Layers and Upstream Influence II. Supersonic Flows Without Separation,” Proc. Roy. Soc., Series A 217, 1953.

    Google Scholar 

  13. Messiter, A.F., and Enlow, R.L., “A Model for Laminar Boundary-Layer Flow Near a Separation POint,” SIAM J . Appl. Math., vol. 25 no. 4, 1973.

    Google Scholar 

  14. Neiland, V. Ia., “Supersonic Flow of a Viscous Fluid Around a Separation POint,” presented at the 3rd pan-Soviet meeting on Theoretical and Applied Mechanics, 1968.

    Google Scholar 

  15. Rothmayer, A.P., “The Development of a Comprehensive Two-Dimensional Linearized Airfoil Theory,” AIAA 9th Annual Mini -Symposium on Air Science and Technology, Wright Patterson AFB, Dayton OH, 1983.

    Google Scholar 

  16. Rothmayer, A.P., and Davis, R.T., “An Interacting Boundary Layer Model for Cascades,” AIAA83-1915 presented at the AIAA 6th Computational Fluid Dynamics Conference, 1983.

    Google Scholar 

  17. Rothmayer, A.P., and Davis, R.T., “Massive Separation and Dynamic Stall on a Cusped Trailing-Edge Airfoil,” to be published in Numerical and Physical Aspects of Aerodynamic Flows, Springer-Verlag, 1985.

    Google Scholar 

  18. Rothmayer, A.P., and Smith, F.T., “Large Scale Separation and Hysteresis in Cascades,” to be published in Proc. Roy. Soc., Series A, 1985.

    Google Scholar 

  19. Rothmayer, A.P., Ph.D. Dissertation, Univ. of Cincinnati, 1985.

    Google Scholar 

  20. Sadovskii, V.S., “Vortex Regions in a Potential Stream with a Jump of Bernoulli’s Constant at the Boundary,” Prikl. Math. Mech, vol. 35, transl. Appl. Math. Mech., vol. 35, 1971.

    Google Scholar 

  21. Smith, F.T., “The Laminar Separation of an Incompressible Fluid Streaming Past a Smooth SUrface,” Proc. Roy. Soc., Series A 356, 1977.

    Google Scholar 

  22. Smith, F.T., “Laminar Flow of an Incompressible Fluid Past a Bluff Body: The Separatton, Reattachment, Eddy Properties and Drag,” J. Fluid Mech., vol. 92, 1979.

    Google Scholar 

  23. Smith, F.T., “On the High Reynolds Number Theory of Laminar Flows,” IMA J. Appl. Math., vol. 28. 1982.

    Google Scholar 

  24. Smith, F.T., “Large-Scale Separation and Wake Closure/Reattachment - The Cascade Problem,” to appear in J. Maths. Phys. Sci. 1985.

    Google Scholar 

  25. Smi th, F. T., “A Structure for Laminar Flow Past a Bluff Body at High Reynolds Number,” J. Fluid Mech., 155, 1985.

    Google Scholar 

  26. Smith, F.T., and Merkin, J.H., “Triple-Deck Solutions for Subsonic Flow Past Humps, Steps, Concave or Convex Corners and Wedged Trailing Edges,” Computers and Fluids, vol. 10 no. 1, 1982

    Google Scholar 

  27. Stewartson, K., and Williams, P.G., “Self-Induced Separation,” Proc. Roy. Soc., Series A 312, 1969.

    Google Scholar 

  28. Stewartson, K., “Is the Singularity at Separation Removable?,” J. Fluid Mech., vol. 44, 1970.

    Google Scholar 

  29. Stewartson, K., “Multistructured Boundary Layers on Flat Plates and Related Bodies,” Adv. Appl. Mech., vol. 14, Academic Press, 1974.

    Google Scholar 

  30. Sychev, V.V., “On Laminar Separation,” Meck. Zhid. i Gaza, vol. 3, 1972

    Google Scholar 

  31. Van-Dyke, M.D., Perturbation Methods in Fluid Mechanics, The Parabolic Press, 1975.

    MATH  Google Scholar 

  32. Veldman, A.E.P., “New Quasi-Simultaneous Method to Calculate Interacting Boundary Layers,” AIAA Journal, vol. 19, 1981.

    Google Scholar 

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© 1987 Springer-Verlag New York Inc.

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Rothmayer, A.P., Davis, R.T. (1987). Progress on the Calculation of Large-Scale Separation at High Reynolds Numbers. In: Hussaini, M.Y., Salas, M.D. (eds) Studies of Vortex Dominated Flows. ICASE NASA LaRC Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4678-7_8

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  • DOI: https://doi.org/10.1007/978-1-4612-4678-7_8

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-96430-0

  • Online ISBN: 978-1-4612-4678-7

  • eBook Packages: Springer Book Archive

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