Compressibility Effects on the Extended Crocco Relation and the Thermal Recovery Factor in Laminar Boundary Layer Flow

[+] Author and Article Information
B. W. van Oudheusden

Department of Aerospace Engineering, Delft University of Technology, PO Box 5058, 2600 GB Delft, The Netherlandse-mail: B.W.vanOudheusden@LR.TUDelft.nl

J. Fluids Eng 126(1), 32-41 (Feb 19, 2004) (10 pages) doi:10.1115/1.1637626 History: Received February 20, 2003; Revised August 27, 2003; Online February 19, 2004
Copyright © 2004 by ASME
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Dorrance, W. H., 1962, Viscous Hypersonic Flow, McGraw-Hill.
Anderson, J. D., 1989, Hypersonic and High Temperature Gas Dynamics, McGraw-Hill.
White, F. M., 1991, Viscous Fluid Flow, 2nd edn. McGraw-Hill.
Schetz, J. A., 1993, Boundary Layer Analysis, Prentice Hall.
Schlichting, H., and Gersten, K., 1979, Boundary-Layer Theory, 8th edn. Springer.
Smits, A. J., and Dussauge, J. P., 1996, Turbulent Shear Layers in Compressible Flow, American Institute of Physics.
Van Driest, E. R., 1952, “Investigation of the Laminar Boundary Layer in Compressible Flow Using the Crocco Method,” NACA TN 2597.
Tifford,  A. N., and Chu,  S. T., 1952, “On Heat Transfer, Recovery Factors, and Spin for Laminar Flows,” J. Aeronaut. Sci., 19, pp. 787–789.
Brun, E. A., 1956, “Quelques considérations sur la convection de la chaleur aux grandes vitesses et aux températures élevées,” Selected Combustion Problems, Vol II, AGARD, Pergamon Press, pp. 185–198.
Le Fur,  B., 1960, “Convection de la chaleur en régime laminaire dans le cas d’un gradient de pression et d’une température de paroi quelconques, le fluide étant à propriétés physiques constantes,” Int. J. Heat Mass Transfer, 1, pp. 68–80.
Kaye,  J., 1954, “Survey of Friction Coefficients, Recovery Factors and Heat-Transfer Coefficients for Supersonic Flow,” J. Aeronaut. Sci., 21, pp. 117–129.
Van Driest, E. R., 1959, “Convective Heat Transfer in Gasses,” High Speed Aerodynamics and Jet Propulsion, Volume V, Turbulent Flows and Heat Transfer, C. C. Lin, ed., Princeton University Press, pp. 339–427.
Eckert,  E. R. G., 1986, “Energy Separation in Fluid Flows,” Int. Commun. Heat Mass Transfer, 13, pp. 127–143.
Van Oudheusden,  B. W., 1997, “A Complete Crocco Integral for Two-Dimensional Laminar Boundary Layer Flow Over an Adiabatic Wall for Prandtl Numbers Near Unity,” J. Fluid Mech., 353, pp. 313–330.
Herwig,  H., 1987, “An Asymptotic Approach to Compressible Boundary-Layer Flow,” Int. J. Heat Mass Transfer, 30, pp. 59–68.
Cohen, C. B., and Reshotko, E., 1956, “Similarity Solutions for the Compressible Laminar Boundary Layer With Heat Transfer and Arbitrary Pressure Gradient,” NACA Rept 1293.
Chapman,  D. R., and Rubesin,  M. W., 1949, “Temperature and Velocity Profiles in the Compressible Laminar Boundary Layer With Arbitrary Distribution of Surface Temperature,” J. Aeronaut. Sci., 16, pp. 547–565.
Li,  T. Y., and Nagamatsu,  H. T., 1955, “Similar Solutions of Compressible Boundary-Layer Equations,” J. Aeronaut. Sci., 22, pp. 607–616.


Grahic Jump Location
Nonsimilar boundary layer development (Pr=0.7); top: Me=M0(1+ξ); bottom: Me=M0(1−ξ). Solid lines are for ω=1 (dotted line indicates M0=∞), dashed lines are for ω=0.75.
Grahic Jump Location
Self-similar solutions for the transformed profiles of the velocity f, the enthalpy θ and the total enthalpy θ+f′2. Symbols indicate calculations with Sutherland’s viscosity law, lines for the power-law, see legend in the figure (Pr=0.7,β̃=0,Me=5).
Grahic Jump Location
Effect of Mach number, viscosity law and pressure gradient on f (0) and recovery factor r; top: β̃=0, center: β̃=1, bottom: β̃=−0.15; dashed lines indicate results for Sutherlands’s law with Tt=300 K (Pr=0.7).  
Grahic Jump Location
Normalized recovery factor data and Mach number scaling; left: effect of viscosity-law exponent ω in flat-plate flow (β̃=0); right: effect of pressure-gradient parameter β̃ with linear viscosity law (ω=1), dotted line indicates Me=∞. Symbols apply to numerical data for Pr=0.7. Lines in the bottom diagrams represent the exact (solid) or approximate (dashed) results of the perturbation analysis.




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