0
Research Papers: Flows in Complex Systems

An Integral Solution for Skin Friction in Turbulent Flow Over Aerodynamically Rough Surfaces With an Arbitrary Pressure Gradient

[+] Author and Article Information
James Sucec

Department of Mechanical Engineering,
University of Maine,
Orono, ME 04469-5711

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received June 4, 2013; final manuscript received March 5, 2014; published online June 2, 2014. Assoc. Editor: Feng Liu.

J. Fluids Eng 136(8), 081103 (Jun 02, 2014) (8 pages) Paper No: FE-13-1357; doi: 10.1115/1.4027140 History: Received June 04, 2013; Revised March 05, 2014

The combined law of the wall and wake, with the inclusion of the “roughness depression function” for the inner law in the “Log” region, is used as the inner coordinates' velocity profile in the integral form of the x momentum equation to solve for the local skin friction coefficient. The “equivalent sand grain roughness” concept is employed in the roughness depression function in the solution. Calculations are started at the beginning of roughness on a surface, as opposed to starting them using the measured experimental values at the first data point, when making comparisons of predictions with data sets. The dependence of the velocity wake strength on both pressure gradient and momentum thickness Reynolds number are taken into account. Comparisons of the prediction with experimental skin friction data, from the literature, have been made for some adverse, zero, and favorable (accelerating flows) pressure gradients. Predictions of the shape factor, roughness Reynolds number, and momentum thickness Reynolds number and comparisons with data are also made for some cases. In addition, some comparisons with the predictions of earlier investigators have also been made.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Schlichting, H., 1960, Boundary Layer Theory, 4th ed., McGraw-Hill, New York.
Dvorak, F. A., 1969, “Calculation of Turburlent Boundary Layers on Rough Surfaces in Pressure Gradient” AIAA J., 7, pp. 1752–1759. [CrossRef]
Taylor, R. P., Coleman, H. W., and Hodge, B. K., 1985, “Prediction of Turbulent Rough Wall Skin Friction Using a Discrete Element Approach” ASME J. Fluids Eng., 107, pp. 251–257. [CrossRef]
Coleman, H. W., Hodge, B. K., and Taylor, R. P., 1984, “A Re-Evaluation of Schlichting's Surface Roughness Experiment,” ASME J. Fluids Eng., 106, pp. 60–65. [CrossRef]
Cebeci, T., and Chang, K. C., 1978, “Calculation of Incompressible Rough Wall Boundary Layer Flows,” AIAA J., 16, pp. 730–735. [CrossRef]
Sigal, A., and Danberg, J. E., 1990, “New Correlation of Roughness Density Effect on the Turbulent Boundary Layer,” AIAA J., 28, pp. 554–556. [CrossRef]
Bons, J., 2005, “A Critical Assessment of Reynolds Analogy for Turbine Flows,” ASME J. Heat Transfer, 127, pp. 472–485. [CrossRef]
Flack, K. A., and Schultz, M. P., 2010, “Review of Hydraulic Roughness Scales in the Fully Rough Regime,” ASME J. Fluids Eng., 132(4), p. 041203. [CrossRef]
Bergstrom, D. J., Akinade, O. G., and Tachie, M. F., 2005, “Skin Friction Correlation for Smooth and Rough Wall Turbulent Boundary Layers,” ASME J. Fluids Eng., 127, pp. 1146–1153. [CrossRef]
Scraggs, W. F., Taylor, R. P., and Coleman, A. W., 1988, “Measurement and Prediction of Rough Wall Effects on Friction Factor–Uniform Roughness Results,” ASME J. Fluids Eng., 110, pp. 385–391. [CrossRef]
Taylor, R. P., Scraggs, W. F., and Coleman, H. W., 1988, “Measurement and Prediction of the Effects of Nonuniform Surface Roughness on Turbulent Flow Friction Coefficients,” ASME J. Fluids Eng., 110, pp. 380–384. [CrossRef]
Avci, A., and Karagoz, I., 2009, “A Novel Explicit Equation for Friction Factor in Smooth and Rough Pipes,” ASME J. Fluids Eng., 131(6), p. 061203. [CrossRef]
Tani, I., 1987, “Turbulent Boundary Layer Development Over Rough Surfaces,” Perspectives in Turbulence Studies, H. W.Meier and P.Bradshaw, eds., Springer-Verlag, Berlin, pp. 223–249.
Stel, H., Franco, A. T., Junqueira, S. L. M., Mendes, R., Goncalves, M. A. L., and Morales, R. E. M., 2012, “Turbulent Flow in D-Type Corrugated Pipes: Flow Pattern and Friction Factor,” ASME J. Fluids Eng., 134(12), p. 121202. [CrossRef]
Mills, A. F., and Hang, Xu, 1983, “On the Skin Friction Coefficient for a Fully Rough Flat Plate,” ASME J. Fluids Eng., 105, pp. 364–365. [CrossRef]
Coleman, H. W., 1976, “Momentum and Energy Transport in the Accelerated Fully Rough Turbulent Boundary Layer,” Ph.D. thesis, Department of Mechanical Engineering, Stanford University, Stanford, CA.
Christoph, G. H., and Pletcher, R. H., 1983, “Prediction of Rough Wall Skin Friction and Heat Transfer,” AIAA J., 21(4), pp. 509–515. [CrossRef]
Hosni, M. H., Coleman, H. W., and Taylor, R. P., 1993, “Measurement and Calculation of Fluid Dynamic Characteristics of Rough-Wall Turbulent Boundary Layer Flows,” ASME J. Fluids Eng., 115, pp. 383–388. [CrossRef]
Sucec, J., 1995, “A Simple, Accurate Integral Solution for Accelerating Turbulent Boundary Layers With Transpiration,” ASME J. Fluids Eng., 117, pp. 535–538. [CrossRef]
Raupach, M. R., Antonia, R. A., and Rajagopalan, S., 1991, “Rough Wall Turbulent Boundary Layers,” Appl. Mech. Rev., 44(1), pp. 1–25. [CrossRef]
McClain, S. T., Collins, S. P., Hodge, B. K., and Bons, J. P., 2006, “The Importance of the Mean Elevation in Predicting Skin Friction for Flow Over Closely Packed Surface Roughness,” ASME J. Fluids Eng., 128, pp. 579–586. [CrossRef]
Sucec, J., 2009, “An Integral Solution for Heat Transfer in Accelerating Turbulent Boundary Layers,” ASME J. Heat Transfer, 131(11), p. 111702. [CrossRef]
Oljaca, M., and Sucec, J., 1997, “Prediction of Transpired Turbulent Boundary Layers with Arbitrary Pressure Gradients,” ASME J. Fluids Eng., 119, pp. 526–532. [CrossRef]
Kays, W. M., Crawford, M. E., and Weigand, B., 2005, Convection Heat and Mass Transfer, 4th ed., McGraw-Hill, New York.
Young, A. D., 1989, Boundary Layers, AIAA Education Series, Washington, DC.
Cebeci, T., and Bradshaw, P., 1984, Physical and Computational Aspects of Convective Heat Transfer, Springer-Verlag, New York, p. 188.
White, F. M., 1991, Viscous Fluid Flow, 2nd ed., McGraw-Hill, New York.
Schetz, J. A., 1984, Foundations of Boundary Layer Theory for Momentum, Heat, and Mass Transfer, Prentice-Hall Inc., Englewood Cliffs, NJ, p. 150.
Ralston, A., and Rabinowitz, P., 1978, A First Course in Numerical Analysis, 2nd ed., McGraw-Hill, New York, pp. 217–222.
Perry, A. E., and Joubert, P. N., 1963, “Rough Wall Boundary Layers in Adverse Pressure Gradients,” J. Fluid Mech., 17, pp. 193–211. [CrossRef]
Moffat, R. J., Healzer, J. M., and Kays, W. M., 1978, “Experimental Heat Transfer Behavior of a Turbulent Boundary Layer on a Rough Surface With Blowing,” ASME J. Heat Transfer, 100, pp. 134–142. [CrossRef]
Liu, C. K., Cline, S. J., and Johnston, J. P., 1966, “An Experimental Study of Turbulent Boundary Layers on Rough Wall,” Department of Mechanical Engineering, Stanford University, Report No. Md 15.
Cebeci, T., and Smith, A. M. O., 1974, Analysis of Turbulent Boundary Layers, Academic Press, New York.

Figures

Grahic Jump Location
Fig. 1

Comparison of present predictions and those of Taylor et al. [3], with data for the strong equilibrium acceleration of Coleman [16], L = 2.286 m (7.5 ft)

Grahic Jump Location
Fig. 2

Comparison of present predictions and those of Taylor et al. [3], with data for the mild equilibrium acceleration of Coleman [16], L = 2.286 m

Grahic Jump Location
Fig. 3

Comparison of present predictions with data from the nonequilibrium acceleration case of Coleman [16], L = 2.286 m

Grahic Jump Location
Fig. 4

Comparison of present predictions with data for the zero pressure gradient case of Coleman [16], L = 2.286 m

Grahic Jump Location
Fig. 5

Comparison of present predictions with data for H, Rem, and Rek for Coleman's [16] strong equilibrium acceleration, L = 2.286 m, data points, (▪) Rek/10, • Rem/1000, and H

Grahic Jump Location
Fig. 6

Comparison of present predictions and data for H, Rem, and Rek for the mild acceleration case of Coleman [16], L = 2.286 m, data points, (▪) Rem /1000; • Rek /10, and H

Grahic Jump Location
Fig. 7

Comparison of present predictions with data for H, Rem and Rek for the nonequilibrium acceleration of Coleman [16], K¯ = 0.28 × 10−6, L = 2.286 m. Data points, • Rek/10, top set; Rem/1000, middle set; and H, lowest set.

Grahic Jump Location
Fig. 8

Comparison of present predictions with data for H, Rem and Rek for the zero pressure gradient case of Coleman [16]. L = 2.286 m, data points: • Rem/1000, top set; Rek/10, middle set; and H, lowest set.

Grahic Jump Location
Fig. 9

Comparison of present predictions with data for Healzer's constant Us = 58 m/s, from Moffat et al. [31], L = 2.286 m

Grahic Jump Location
Fig. 10

Comparison of present predictions with data for Pimenta's constant Us = 27 m/s, from Moffat et al. [31], L = 2.286 m

Grahic Jump Location
Fig. 11

Comparison of present predictions with data for constant Us = 58 m/s, 41.7 m/s, 9.8 m/s, and smooth surface 9.8 m/s from Moffat et al. [31]. L = 2.286 m, data points: (▪) 72.6 m/s; (▲) 58 m/s; (♦) 41.7 m/s; and (•) 9.8 m/s.

Grahic Jump Location
Fig. 12

Comparison of present predictions with data for the zero pressure gradient, λ = 12, in the case of Liu et al. [32], L = 3.66 m (12 ft)

Grahic Jump Location
Fig. 13

Comparison of present predictions and those of Dvorak [2], with experimental data of profile II of Perry and Joubert [30], L = 6.1 m (20 ft)

Grahic Jump Location
Fig. 14

Comparison of present predictions and predictions of Dvorak [2], also Cebeci and Chang [5], with data of profile III of Perry and Joubert [30]. L = 6.1 m (20 ft).

Grahic Jump Location
Fig. 15

Comparison of present predictions of the velocity wake strength parameter to data, for profile II, of Perry and Joubert [30], L = 6.1 m

Grahic Jump Location
Fig. 16

Comparison of present predictions of the velocity wake strength parameter to data, for profile III of Perry and Joubert [30], L = 6.1 m

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In