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TECHNICAL PAPERS

Streamwise Curvature Effect on the Incompressible Turbulent Mean Velocity Over Curved Surfaces

[+] Author and Article Information
N. Kim, D. L. Rhode

Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123

J. Fluids Eng 122(3), 547-551 (Feb 14, 2000) (5 pages) doi:10.1115/1.1287268 History: Received March 23, 1999; Revised February 14, 2000
Copyright © 2000 by ASME
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References

Bradshaw,  P., 1969, “The Analogy Between Streamline Curvature and Buoyancy in Turbulent Shear Flow,” J. Fluid Mech., 36, pp. 177–191.
Bradshaw, P., 1973, “Effects of Streamline Curvature on Turbulent Flows,” AGARDograph No. 169.
So, R. M. C., and Mellor, G. L., 1972, “An Experimental Investigation of Turbulent Boundary Layers Along Curved Surfaces,” NASA CR-1940.
So,  R. M. C., and Mellor,  G. L., 1973, “Experiment on Convex Curvature Effects in Turbulent Boundary Layers,” J. Fluid Mech., 60, pp. 43–62.
So,  R. M. C., and Mellor,  G. L., 1975, “Experiment on Turbulent Boundary Layers on a Concave Wall,” Aeronaut. Q., XXVI, pp. 25–40.
So, R. M. C., 1975, “Effects of Streamline Curvature on the Law of the Wall,” Proc. 12th Annual Meeting, Society of Engineering Science, The University of Texas at Austin, Texas, pp. 787–796.
So,  R. M. C., 1975, “A Turbulence Velocity Scale For Curved Shear Flows,” J. Fluid Mech., 70, pp. 37–57.
Meroney,  R. N., and Bradshaw,  P., 1975, “Turbulent Boundary-Layer Growth over a Longitudinally Curved Surface,” AIAA J., 13, pp. 1448–1453.
Hunt,  I. A., and Joubert,  P. N., 1979, “Effects of Small Streamline Curvature on Turbulent Duct Flow,” J. Fluid Mech., 91, pp. 633–659.
Barlow,  R. S., and Johnston,  J. P., 1988, “Structure of a Turbulent Boundary Layer on a Concave Surface,” J. Fluid Mech., 191, pp. 137–176.
Wilcox,  D. C., and Chambers,  T. L., 1977, “Streamline Curvature Effects on Turbulent Boundary Layers,” AIAA J., 15, pp. 574–580.
Galperin,  B., and Mellor,  G. L., 1991, “The Effects of Streamline Curvature and Spanwise Rotation on Near-Surface, Turbulent Boundary Layers,” ZAMP, 42, pp. 565–583.
So, R. M. C., 1977, “Turbulence Velocity Scales for Swirling Flows,” Turbulence in Internal Flows, Murthy, S. N. B., ed., Hemisphere.
Gibson, M. M., 1988, “Effects of Surface Curvature on the Law of the Wall,” Near-Wall Turbulence, Kline, S. J., and Afgan, N. H., eds., Hemisphere.
Kim,  N., and Rhode,  D. L., 1999, “Swirling Streamline-Curvature Law of The Wall From a Novel Perturbation Analysis,” Numer. Heat Transfer, Part B, 36, pp. 331–350.
Aziz, A., 1984, Perturbation Methods in Heat Transfer, Hemisphere.
Adams,  E. W., and Johnston,  J. P., 1984, “A Mixing-Length Model for the Prediction of Convex Curvature Effects on Turbulent Boundary Layers,” ASME J. Fluids Eng., 106, pp. 142–148.

Figures

Grahic Jump Location
Definition of coordinates for the concave and convex surfaces
Grahic Jump Location
Comparison of the present curvature law of the wall (— ) with measurements (So and Mellor 5) along a concave wall (R+=35,000); [(—A—): the classical log-law, (—B—): Meroney and Bradshaw 8, (—C—): Wilcox and Chambers 11, and (—D—): So 6]; [(○○○):x=159.49 cm,(×××):x=166.95 cm;(+++):x=174.47 cm;(□□□):x=182.37 cm].
Grahic Jump Location
Comparison of the present curvature law of the wall (— ) with measurements (Barlow and Johnston 10) along a concave wall (R+=10,100); [(—A—): the classical log-law, (—B—): Meroney and Bradshaw 8, (—C—): Wilcox and Chambers 11, and (—D—): So 6]; [(○○○ ): flat; (×××):θ=15 deg;(+++):θ=30 deg;(□□□):θ=60 deg;(▪▪▪):θ=75 deg].
Grahic Jump Location
Comparison of the present curvature law of the wall (— ) with measurements along a convex wall (R+=13,500);[(—A—): the classical log-law, (—B—): Meroney and Bradshaw 8, (—C—): Wilcox and Chambers 11, and (—D—): So 6]; [measurements were adapted from Gibson 14 and Galperin and Mellor 12]; [(○○○):x/δ0=9.0;(×××):x/δ0=14.3;(+++):x/δ0=21.7].
Grahic Jump Location
Comparison of the present curvature law of the wall (— ) with measurements (So and Mellor 4) along a convex wall (R+=17,400); [(—A—): the classical log-law, (—B—): Meroney and Bradshaw 8, (—C—): Wilcox and Chambers 11, and (—D—): So 6]; [(○○○):x=61.0 cm;(×××):x=138.4 cm;(+++):x=149.9 cm;(□□□):x=170.2 cm;(▪▪▪):x=180.3 cm].

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