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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Reference
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.
Cheng, H.K., and Rott, N., “Generalizations of the Inversion Formula of Thin Airfoil Theory,” J. Rat. Mech. An, No.3, 1954.
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.
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.
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.
Daniels, P.G., “Laminar Boundary-Layer Reattachment in Supersonic Flow. Part 2. Numerical Solution,” J. Fluid Mech., 97, part 1,1980.
Davis, R. T., “Numerical Methods for Coordinate Generation Based on SchwarzChristoffel Transformations,” AIAA79-1463 presented at the 4th Computational Fluid Dynamics Conference, 1979.
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.
Fornberg, B., “Steady Viscous Flow Past a Circular Cylinder up to Reynolds Number 600,” submitted to J. Compo Phys., 1985.
Goldstein, S., “On Laminar Boundary Layer Flow Near a Position of Separation,” Quart. J. Mech. Appl. Math., vol. 1, 1948.
Kirchhoff, G., “Zur Theorie freier Flussigkeitsstrahlen,” J. Reine Angew. Math., vol. 70, 1869.
Lighthill, M.J., “On Boundary Layers and Upstream Influence II. Supersonic Flows Without Separation,” Proc. Roy. Soc., Series A 217, 1953.
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.
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.
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.
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.
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.
Rothmayer, A.P., and Smith, F.T., “Large Scale Separation and Hysteresis in Cascades,” to be published in Proc. Roy. Soc., Series A, 1985.
Rothmayer, A.P., Ph.D. Dissertation, Univ. of Cincinnati, 1985.
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.
Smith, F.T., “The Laminar Separation of an Incompressible Fluid Streaming Past a Smooth SUrface,” Proc. Roy. Soc., Series A 356, 1977.
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.
Smith, F.T., “On the High Reynolds Number Theory of Laminar Flows,” IMA J. Appl. Math., vol. 28. 1982.
Smith, F.T., “Large-Scale Separation and Wake Closure/Reattachment - The Cascade Problem,” to appear in J. Maths. Phys. Sci. 1985.
Smi th, F. T., “A Structure for Laminar Flow Past a Bluff Body at High Reynolds Number,” J. Fluid Mech., 155, 1985.
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
Stewartson, K., and Williams, P.G., “Self-Induced Separation,” Proc. Roy. Soc., Series A 312, 1969.
Stewartson, K., “Is the Singularity at Separation Removable?,” J. Fluid Mech., vol. 44, 1970.
Stewartson, K., “Multistructured Boundary Layers on Flat Plates and Related Bodies,” Adv. Appl. Mech., vol. 14, Academic Press, 1974.
Sychev, V.V., “On Laminar Separation,” Meck. Zhid. i Gaza, vol. 3, 1972
Van-Dyke, M.D., Perturbation Methods in Fluid Mechanics, The Parabolic Press, 1975.
Veldman, A.E.P., “New Quasi-Simultaneous Method to Calculate Interacting Boundary Layers,” AIAA Journal, vol. 19, 1981.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Springer-Verlag New York Inc.
About this paper
Cite this paper
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
Download citation
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