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Scaling mean velocity in two-dimensional turbulent wall jets

  • Abhishek Gupta (a1) (a2), Harish Choudhary (a1), A. K. Singh (a2), Thara Prabhakaran (a1) and Shivsai Ajit Dixit (a1)...

Abstract

Studies in the literature on two-dimensional, fully developed, turbulent wall jets on flat surfaces, have invariably reckoned on either the nozzle initial conditions or the asymptotic conditions far downstream, as scaling parameters for the streamwise variations of length and velocity scales. These choices, however, do not square with the notion of self-similarity, which is essentially a ‘local’ concept. We first demonstrate that the streamwise variations of velocity and length scales in wall jets show remarkable scaling with local parameters, i.e. there appear to be no imposed length and velocity scales. Next, it is shown that the mean velocity profile data suggest the existence of two distinct layers – the wall (inner) layer and the full-free jet (outer) layer. Each of these layers scales on the appropriate length and velocity scales and this scaling is observed to be universal, i.e. independent of the local friction Reynolds number. Analysis shows that the overlap of these universal scalings leads to a Reynolds-number-dependent power-law velocity variation in the overlap layer. It is observed that the mean-velocity overlap layer corresponds well to the momentum-balance mesolayer and there appears to be no evidence for an inertial overlap; only the meso-overlap is observed. Introduction of an intermediate variable absorbs the Reynolds-number dependence of the length scale in the overlap layer and this leads to a universal power-law overlap profile for mean velocity in terms of the intermediate variable.

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Corresponding author

Email address for correspondence: sadixit@tropmet.res.in

References

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Afzal, N. 1982 Fully developed turbulent flow in a pipe: an intermediate layer. Ing.-Arch. 52 (6), 355377.
Afzal, N. 2005 Analysis of power law and log law velocity profiles in the overlap region of a turbulent wall jet. Proc. Math. Phys. Engng Sci. 461 (2058), 18891910.
Ahlman, D., Brethouwer, G. & Johansson, A. V. 2007 Direct numerical simulation of a plane turbulent wall-jet including scalar mixing. Phys. Fluids 19 (6), 065102.
Bailey, S. C. C., Hultmark, M., Monty, J. P., Alfredsson, P. H., Chong, M. S., Duncan, R. D., Fransson, J. H. M., Hutchins, N., Marusic, I., McKeon, B. J. et al. 2013 Obtaining accurate mean velocity measurements in high Reynolds number turbulent boundary layers using Pitot tubes. J. Fluid Mech. 715, 642670.
Banyassady, R. & Piomelli, U. 2014 Turbulent plane wall jets over smooth and rough surfaces. J. Turbul. 15 (3), 186207.
Banyassady, R. & Piomelli, U. 2015 Interaction of inner and outer layers in plane and radial wall jets. J. Turbul. 16 (5), 460483.
Barenblatt, G. I., Chorin, A. J. & Prostokishin, V. M. 2005 The turbulent wall jet: a triple-layered structure and incomplete similarity. Proc. Natl Acad. Sci. USA 102 (25), 88508853.
Bradshaw, P. 1963 Discussion on Plane turbulent wall jet flow development and friction factor by Myers et al. 1963. Trans. ASME J. Basic Engng 85 (1), 5354.
Bradshaw, P. & Gee, M. T.1962 Turbulent wall jets with and without an external stream. Aeronautical Research Council Reports and Memoranda, 3252, Her Majesty’s Stationary Office.
Bradshaw, P. & Gregory, N.1961 The determination of local turbulent skin friction from observations in the viscous sub-layer. Aeronautical Research Council Reports and Memoranda, Her Majesty’s Stationary Office.
Chauhan, K., Henry, C. H. & Marusic, I. 2010 Empirical mode decomposition and Hilbert transforms for analysis of oil-film interferograms. Meas. Sci. Technol. 21 (10), 105405.
Dejoan, A. & Leschziner, M. A. 2005 Large eddy simulation of a plane turbulent wall jet. Phys. Fluids 17, 025102.
Deo, R. C., Mi, J. & Nathan, G. J. 2008 The influence of Reynolds number on a plane jet. Phys. Fluids 20 (7), 075108.
Durst, F., Zanoun, E.-S. & Pashtrapanska, M. 2001 In situ calibration of hot wires close to highly heat-conducting walls. Exp. Fluids 31 (1), 103110.
Eriksson, J. G., Karlsson, R. I. & Persson, J. 1998 An experimental study of a two-dimensional plane turbulent wall jet. Exp. Fluids 25 (1), 5060.
George, W. K., Abrahamsson, H., Eriksson, J., Karlsson, R. I., Löfdahl, L. & Wosnik, M. 2000 A similarity theory for the turbulent plane wall jet without external stream. J. Fluid Mech. 425, 367411.
George, W. K. & Castillo, L. 1997 Zero-pressure-gradient turbulent boundary layer. Appl. Mech. Rev. 50 (12), 689729.
Gersten, K. 2015 The asymptotic downstream flow of plane turbulent wall jets without external stream. J. Fluid Mech. 779, 351370.
Glauert, M. B. 1956 The wall jet. J. Fluid Mech. 1 (6), 625643.
Gnanamanickam, E. P., Bhatt, S., Artham, S. & Zhang, Z. 2019 Large-scale motions in a plane wall jet. J. Fluid Mech. 877, 239281.
Hong, S. 2010 A new stable boundary-layer mixing scheme and its impact on the simulated East Asian summer monsoon. Q. J. R. Meteorol. Soc. 136 (651), 14811496.
Hu, X., Klein, P. M. & Xue, M. 2013 Evaluation of the updated YSU planetary boundary layer scheme within WRF for wind resource and air quality assessments. J. Geophys. Res. 118 (18), 10490.
Irwin, H. P. A. H. 1973 Measurements in a self-preserving plane wall jet in a positive pressure gradient. J. Fluid Mech. 61 (1), 3363.
Kevorkian, J. & Cole, J. D. 2013 Perturbation Methods in Applied Mathematics, vol. 34. Springer Science & Business Media.
Launder, B. E. & Rodi, W. 1979 The turbulent wall jet. Prog. Aerosp. Sci. 19, 81128.
Launder, B. E. & Rodi, W. 1983 The turbulent wall jet measurements and modeling. Annu. Rev. Fluid Mech. 15 (1), 429459.
McIntyre, R., Savory, E., Wu, H. & Ting, D. S.-K. 2019 The effect of the nozzle top lip thickness on a two-dimensional wall jet. Trans. ASME J. Fluids Engng 141 (5), 051106.
Myers, G. E., Schauer, J. J. & Eustis, R. H. 1963 Plane turbulent wall jet flow development and friction factor. Trans. ASME J. Basic Engng 85 (1), 4753.
Naqavi, I. Z., Tyacke, J. C. & Tucker, P. G. 2018 Direct numerical simulation of a wall jet: flow physics. J. Fluid Mech. 852, 507542.
Narasimha, R. 1990 The utility and drawbacks of traditional approaches. In Whither Turbulence? Turbulence at the Crossroads, pp. 1348. Springer.
Narasimha, R., Narayan, K. Y. & Parthasarathy, S. P. 1973 Parametric analysis of turbulent wall jets in still air. Aeronaut. J. 77 (751), 355359.
Rostamy, N., Bergstrom, D. J., Sumner, D. & Bugg, J. D. 2011 The effect of surface roughness on the turbulence structure of a plane wall jet. Phys. Fluids 23 (8), 085103.
Schneider, M. E. & Goldstein, R. J. 1994 Laser doppler measurement of turbulence parameters in a two-dimensional plane wall jet. Phys. Fluids 6 (9), 31163129.
Schneider, W. 1985 Decay of momentum flux in submerged jets. J. Fluid Mech. 154, 91110.
Schwarz, W. H. & Cosart, W. P. 1961 The two-dimensional turbulent wall-jet. J. Fluid Mech. 10 (4), 481495.
Smedman, A., Bergström, H. & Högström, U. 1995 Spectra, variances and length scales in a marine stable boundary layer dominated by a low level jet. Boundary-Layer Meteorol. 76 (3), 211232.
Smits, A. J., McKeon, B. J. & Marusic, I. 2011 High-Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353375.
Sreenivasan, K. R. & Sahay, A. 1997 The persistence of viscous effects in the overlap region, and the mean velocity in turbulent pipe and channel flows. In Self-Sustaining Mechanism of Wall Turbulence (ed. Panton, R. L.), pp. 253271. Computational Mechanics Publications.
Tachie, M. F.2001 Open channel turbulent boundary layers and wall jets on smooth and rough surfaces. PhD thesis, Department of Mechanical Engineering, University of Saskatchewan.
Tachie, M., Balachandar, R. & Bergström, D. 2002 Scaling the inner region of turbulent plane wall jets. Exp. Fluids 33 (2), 351354.
Tailland, A. & Mathieu, J. 1967 Jet pariétal. J. Méc. 6, 103130.
Tang, Z., Rostamy, N., Bergstrom, D. J., Bugg, J. D. & Sumner, D. 2015 Incomplete similarity of a plane turbulent wall jet on smooth and transitionally rough surfaces. J. Turbul. 16 (11), 10761090.
Wei, T., Fife, P., Klewicki, J. & McMurtry, P. 2005 Properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows. J. Fluid Mech. 522, 303327.
Wosnik, M., Castillo, L. & George, W. K. 2000 A theory for turbulent pipe and channel flows. J. Fluid Mech. 421, 115145.
Wygnanski, I., Katz, Y. & Horev, E. 1992 On the applicability of various scaling laws to the turbulent wall jet. J. Fluid Mech. 234, 669690.
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Scaling mean velocity in two-dimensional turbulent wall jets

  • Abhishek Gupta (a1) (a2), Harish Choudhary (a1), A. K. Singh (a2), Thara Prabhakaran (a1) and Shivsai Ajit Dixit (a1)...

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