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Research Papers: Fundamental Issues and Canonical Flows

Parametric Analysis of Turbulent Wall Jet in Still Air Over a Transitional Rough, With Asymptotes of Fully Rough and Fully Smooth Wall Jets

[+] Author and Article Information
Noor Afzal

Aero-Space Consultancy Division,
Golden Apartment,
Sahab Bagh,
Aligarh 202002, India

Abu Seena

Plant Eng. Unit,
Samsung C&T Headquarters,
Seocho-2-dong,
SeoCho-Gu, Seoul 137-956, Korea

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received September 28, 2012; final manuscript received July 1, 2013; published online September 4, 2013. Assoc. Editor: Mark F. Tachie.

J. Fluids Eng 135(11), 111203 (Sep 04, 2013) (9 pages) Paper No: FE-12-1481; doi: 10.1115/1.4025005 History: Received September 28, 2012; Revised July 01, 2013

The novel scalings for streamwise variations of the flow in a turbulent wall jet over a fully smooth, transitional, and fully rough surfaces have been analyzed. The universal scaling for arbitrary wall roughness is considered in terms of the roughness friction Reynolds number (that arises from the stream wise variations of roughness in the flow direction) and roughness Reynolds number at the nozzle jet exit. The transitional rough wall jet functional forms have been proposed, whose numerical constants power law index and prefactor are estimated from best fit to the data for several variables, like, maximum wall jet velocity, boundary layer thickness at maxima of wall jet velocity, the jet half width, the friction factor and momentum integral, which are supported by the experimental data. The data shows that the two asymptotes of fully rough and fully smooth surfaces are co-linear with transitional rough surface, predicting same constants for any variable of flow for full smooth, fully rough and transitional rough surfaces. There is no universality of scalings in terms of traditional variables as different expressions are needed for each stage of the transitional roughness. The experimental data provides very good support to our universal relations.

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References

Rajaratnam, N., 1967, “Plane Turbulent Wall Jets on Rough Boundaries,” Water Power, 19, pp. 196–242.
Hogg, A. J., Ruppert, R. E., and Dade, W. B., 1997, “Erosion by Planar Turbulent Wall Jets,” J. Fluid Mech., 338, pp. 317–340. [CrossRef]
Narasimha, R., Narayan, K. Y., and Parthasarathy, S. P., 1973, “Parametric Analysis of Turbulent Wall Jet in Still Air,” Aeronaut. J., 77, pp. 355–359.
Afzal.N., and Seena, A., 2011, “Analysis of a Power Law and Log Law for a Turbulent Wall Jet Over a Transitional Rough Surface: Universal Relations,” ASME J. Fluid Eng., 133, p. 091201. [CrossRef]
Afzal, N., 2005, “Analysis of Power Law and Log Law Velocity Profiles in Overlap Region of a Turbulent Wall Jet,” Proc. R, Soc, Ser. A, 461, pp. 1889–1910. [CrossRef]
Smith, B. S., 2008, “Wall Jet Boundary Layer Flows Over Smooth and Rough Surfaces.” Ph.D. thesis, Virginia Tech, Blacksburg, VA.
Afzal, N., 2007, “Friction Factor Directly From Transitional Rough Pipes,” ASME J. Fluid Eng., 129(10), pp. 1255–1261; Erratum 2011, ASME J. Fluid Eng., 133(10), p. 107001. [CrossRef]
Clauser, F. H., 1956, “The Turbulent Boundary Layers,” Advances in Applied Mechanics, Academic, New York, Vol. 4, pp. 1–51.
Afzal, N., Seena, A., and Bushra, A., 2013, “Effects of Machined Surface Roughness on High Reynolds Number Turbulent Pipe Flow: Universal Scaling,” J. Hydro-Environment Res., 7, pp. 81–90. [CrossRef]
Afzal, N., 2013, “Roughness Effects of Commercial Steel Pipe in Turbulent Flow: Universal Scaling,” Can. J. Civ. Eng., 40(2), pp. 188–193. [CrossRef]
Colebrook, C. F., 1939, “Turbulent Flow in Pipes With Particular Reference to the Transition Region Between the Smooth and Rough Pipe Laws,” J. Inst. Civ. Eng., 11, pp. 133–156. [CrossRef]
Albayraki, I., Hopfinger, E. T., and Lemming, U., 2008, “Near-Field Flow Structure of a Confined Wall Jet on Flat and Concave Rough Walls,” J. Fluid Mech., 606, pp. 27–49. [CrossRef]
Wygnanski, I., Katz, Y., and Horev, E., 1992, “On the Applicability of Various Scaling Laws to the Turbulent Wall Jet,” J. Fluid Mech., 234, pp. 669–690. [CrossRef]
Tachie, M. F., Balachander, R., and Bergstrom, D. J., 2004, “Roughness Effects on Turbulent Plane Wall Jets in an Open Channel,” Exp. Fluids, 37, pp. 281–292. [CrossRef]
Rostamy, N., Bergstrom, D. J. and Sumner, D., 2010, “Experimental Study of a Turbulent Wall Jet on a Rough Surface,” IUTAM Symposium on the Physics of Wall-Bounded Flows on Rough Walls, T. B.Nickles, ed., Cambridge, UK, July 7–9, Springer, New York.
Rostamy, N., Bergstrom, D. J., Sumner, D., and Bugg, J. D., 2011, “An Experimental Study of a Turbulent Wall Jet on Smooth and Transitionally Rough Surfaces,” ASME J. Fluids Eng., 133, p. 111207. [CrossRef]
Tachie, M. F., Balachandar, R., and Bergstrom, D. J., 2002, “The Inner Region of a Turbulent Wall Jet,” Exp. Fluids, 33, pp. 351–354. [CrossRef]
Banyassady, R., and Piomelli, U., 2012, “Turbulent Wall Jets Over Rough Surfaces,” 65th Annual Meeting of the APS Division of Fluid Dynamics, Vol. 57, American Physics Society, San Diego, CA, Nov. 18-20. Available at: http://meetings.aps.org/link/BAPS.2012.DFD.G21.10
George, W., Abrahamsson, H., Eriksson, J., Karlsson, R. L., Lofdahl, L., and Wosnik, M., 2000, “A Similarity Theory for the Turbulent Plane Wall Jet Without External Stream,” J. Fluid Mech., 425, pp. 367–411. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Transverse length scales associated with a wall jet on a transitional rough surface, without a free stream

Grahic Jump Location
Fig. 2

The stream wise variation of the roughness scales from the data of Smith [6] for the turbulent wall jet on a fully rough surface

Grahic Jump Location
Fig. 3

The roughness scale ϕ versus ke+ from data of Smith [6], Tachie et al. [14], Rostamy et al. [15] and Banyassady and Piomelli [18] for the turbulent wall jet on a rough flat surface, and proposed monotonic lines for Smith data and Colebrook type roughness

Grahic Jump Location
Fig. 4

The stream wise variation of the maximum wall jet velocity from the data of Smith [6] for the turbulent wall jet over a fully smooth and fully rough data of Smith [6] and fully rough wall correlation of Hogg et al. [2]. Proposed universal relation for transitional rough surface: (a) y = (Um/U0)(φ/Re) = 4.21x-0.507, where x = ζ, line marked UR-NS is due to Narasimha et al. [3] smooth wall constants, line marked UR-WS is due to Wygnanski et al. [13] smooth wall constants and line marked UR-RR is due to Rostamy et al. rough wall based on smooth wall relationship constants. (b) y = (Um/U0)(φ/Re) = 1.14x-0.499, where x = (δ/b)(Re/φ)2.

Grahic Jump Location
Fig. 5

The stream wise variation of the length scales from the data of Smith [6] for the turbulent wall jet on a fully rough and fully smooth surface. Proposed universal relations for transitional rough surface: (a) Boundary layer thickness δm at velocity maxima as y = (δm/b)(Re/φ)2 = 0.018x0.979, where x = ζ. (b) Boundary layer thickness δ based on location of velocity Um/2 (the half of the maximum wall jet velocity) as y = (δ/b)(Re/φ)2 = 0.089x0.997, where x = ζ.

Grahic Jump Location
Fig. 6

The stream wise variation of the length scales from the data of Smith [6] for the turbulent wall jet over fully smooth and fully rough wall. (a) Displacement thickness universal relation δ* as y = (δ*/b)(Re/φ)2 = 0.032x0.944, where x = ζ. (b) Momentum thickness universal relation y = (θ/b)(Re/φ)2 = 0.00188x0.944, where x = ζ.

Grahic Jump Location
Fig. 7

The stream wise variation of friction factor from the data of Smith [6] for the turbulent wall jet over fully smooth, fully rough and transitional rough surfaces. Proposed Universal relation y = (τw/ρU02)(φ/Re)2 = 0.063x-1.017, where x = ζ. The alternate universal relation y = (τw/ρU02)(φ/Re)2 = 0.146x-1.07, where x = ζ based on Wygnanski et al. [13] constants for wall jet over a fully smooth flat surface.

Grahic Jump Location
Fig. 8

The stream wise variation of velocity ratio Um/U0 of the maximum wall jet velocity Um to slot exit velocity U0 multiplied with square root of the ratio of δ/b the wall jet half-defect thicness δ to slot at exit jet b for turbulent wall jet over a fully smooth and fully rough from data of Smith [6]. Proposed universal relation for transitional rough surface: y=(Um/U0)(δ/b)1/2=1.3 x-0.01, where x = ζ.

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