The inner law for transpired turbulent boundary layers is used as the velocity profile in the integral form of the x momentum equation. The resulting ordinary differential equation is solved numerically for the skin friction coefficient, as well as boundary layer thicknesses, as a function of position along the surface. Predicted skin friction coefficients are compared to experimental data and exhibit reasonably good agreement with the data for a variety of different cases. These include blowing and suction, with constant blowing fractions F for both mild and severe acceleration. Results are also presented for more complicated cases where F varies with x along the surface.
Issue Section:
Technical Briefs
1.
Andersen
P. S.
Kays
W. M.
Moffat
R. J.
1975
, “Experimental Results for the Transpired Turbulent Boundary Layer in an Adverse Pressure Gradient
,” Journal of Fluid Mechanics
, Vol. 69
, pp. 353
–375
.2.
Bradshaw
P.
1967
, “Mixing Length Velocity Profile in Boundary Layers with Transpiration
,” AIAA Journal
, Vol. 5
, No. 9
, pp. 1674
–75
.3.
Coles, D., 1971, “A Survey of Data for Turbulent Boundary Layers with Mass Transfer,” Rand Corporation Report, No. P-4697, pp. 25-1 to 25-15.
4.
Das
D. K.
White
F. M.
1986
, “Integral Skin Friction Prediction for Turbulent Separated Flows
,” ASME JOURNAL OF FLUIDS ENGINEERING
, Vol. 108
, pp. 476
–482
.5.
Das
D. K.
1988
, “A Simple Theory for Calculating Turbulent Boundary Layers Under Arbitrary Pressure Gradients
,” International Journal of Engineering Fluid Mechanics
, Vol. 1
, pp. 83
–99
.6.
Julien
H. L.
Kays
W. M.
Moffat
R. J.
1971
, “Experimental Hydrodynamics of the Accelerated Turbulent Boundary Layer With and Without Mass Injection
,” ASME JOURNAL OF HEAT TRANSFER
, Vol. 93
, pp. 373
–379
.7.
Kearney
D. W.
Kays
W. M.
Moffat
R. J.
1973
, “Heat Transfer to a Strongly Accelerated Turbulent Boundary Layer: Some Experimental Results, Including Transpiration
,” International Journal of Heat Mass Transfer
, Vol. 16
, pp. 1289
–1305
.8.
Kline, S. J., Cantwell, B. J., and Lilley, G. M., eds., 1981, “The 1980–81 AFOSR-HTMM Stanford Conference on Complex Turbulent Flows,” Stanford University, Stanford, CA, Vol. II, pp. 650–67; Vol. I, pp. 112–116; Vol. III, p. 1158.
9.
Mellor
G. L.
Gibson
D. M.
1966
, “Equilibrium Turbulent Boundary Layers
,” Journal of Fluid Mechanics
, Vol. 24
, Part 2, pp. 225
–253
.10.
Ralston, A., and Rabinowitz, P., 1978, A First Course in Numerical Analysis, Second Edition, McGraw-Hill, New York, pp. 217–222.
11.
Silva-Freire
A. P.
1988
, “An Asymptotic Solution for Transpired Incompressible Turbulent Boundary Layers
,” International Journal of Heat Mass Transfer
, Vol. 31
, pp. 1011
–1021
.12.
Simpson
R. L.
Moffat
R. J.
Kays
W. M.
1969
, “The Turbulent Boundary Layer on a Porous Plate: Experimental Skin Friction with Variable Injection and Suction
,” International Journal of Heat Mass Transfer
, Vol. 12
, pp. 771
–89
.13.
Stevenson, T. N., 1963, “A Law of the Wall for Turbulent Boundary Layers with Suction or Injection,” Report Aero No. 166, College of Aeronautics, Cranfield, 18 pages, also available from NTIS as N64-19323.
14.
Sucec
J.
Lu
Y.
1990
, “Heat Transfer Across Turbulent Boundary Layers with Pressure Gradient
,” ASME JOURNAL OF HEAT TRANSFER
, Vol. 112
, pp. 906
–912
.15.
Thielbahr
W. H.
Kays
W. M.
Moffat
R. J.
1972
, “The Turbulent Boundary Layer on a Porous Plate: Experimental Heat Transfer with Uniform Blowing and Suction, with Moderately Strong Acceleration
,” ASME JOURNAL OF HEAT TRANSFER
, Vol. 94
, pp. 111
–118
.16.
Thomas
L. C.
Kadry
H. M.
1990
, “A One Parameter Integral Method for Turbulent Transpired Boundary Layer Flow
,” ASME JOURNAL OF FLUIDS ENGINEERING
, Vol. 112
, pp. 423
–436
.17.
Torii, K., Nishiwaki, N., and Hirata, M., 1966, “Heat Transfer and Skin Friction in Turbulent Boundary Layer with Mass Injection,” Proceedings of the Third International Heat Transfer Conference, Chicago, Vol. 3, pp. 34–48.
18.
White, F. M., 1991, Viscous Fluid Flow, Second Edition, McGraw-Hill, New York, pp. 451–452, 459–464.
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