Hostname: page-component-7c8c6479df-5xszh Total loading time: 0 Render date: 2024-03-29T00:50:26.139Z Has data issue: false hasContentIssue false

Hydraulic jumps due to oblique impingement of circular liquid jets on a flat horizontal surface

Published online by Cambridge University Press:  05 February 2007

R. P. KATE
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur 721302, India
P. K. DAS
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur 721302, India
SUMAN CHAKRABORTY*
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur 721302, India
*
Author to whom correspondence should be addressed: suman@mech.iitkgp.ernet.in

Abstract

An obliquely inclined circular water jet, impinging on a flat horizontal surface, confers a series of hydraulic jump profiles, pertaining to different jet inclinations and jet velocities. These jump profiles are non-circular, and can be broadly grouped into two categories, based on the angle of jet inclination, φ, made with horizontal. Jumps corrosponding to the range (25° < φ≤ 90°) are observed to be bounded by smooth curves, whereas those corresponding to φ≤ 25° are characterized by distinct corners. The present work attempts to find a geometric and hydrodynamic characterization of the spatial patterns formed as a consequence of such non-circular hydraulic jump profiles. Flow-visualization experiments are conducted to depict the shape of demarcating boundaries between supercritical and subcritical flows, and the corresponding radial jump locations are obtained. Theoretical calculations are also executed to obtain the radial locations of the jumps with geometrically smooth profiles. Comparisons are subsequently made between the theoretical predictions and the experimental observations, and a good agreement between these two can be observed. Jumps with corners, however, turn out to be comprised of strikingly contrasting profiles, which can be attributed to the ‘jump–jet’ interaction and the ‘jump-jump’ interaction mechanisms. A phenomenological explanation is also provided, by drawing an analogy from the theory of shock-wave interactions.

Type
Papers
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Abramovich, G. N. 1963 The Theory of Turbulent Jets (ed. Schindel, L. H.). MIT Press.Google Scholar
Arakeri, J. H. & Rao, A. 1996 On radial flow on a horizontal surface and the circular hydraulic jump. J. Indian Inst. Sci. 76, 7391.Google Scholar
Beltos, S. 1975 Oblique impingement of circular turbulent jets. J Hydraul. Res. 14, 1736.CrossRefGoogle Scholar
Blackford, B. L. 1996 The hydraulic jump in radially spreading flow: a new model and new experimental data. Am. J. Phys. 64, 164169.CrossRefGoogle Scholar
Bohr, T., Dimon, P. & Putkaradze, V. 1993 Shallow-water approach to the circular hydraulic jump. J. Fluid Mech. 254, 635648.CrossRefGoogle Scholar
Bouainouche, M., Bourabaa, N. & Desmet, B. 1997 Numerical study of the wall shear produced by the impingement of a plane turbulent jet on a plate. Intl J. Numer. Meth. Heat Fluid Flow. 7, 548564.CrossRefGoogle Scholar
Bradshaw, P. & Love, E. M. 1959 The normal impinging jet of a circular air jet over a flat surface. ARC R &M 3205. Aero. Res. Council, UK.Google Scholar
Brechet, Y. & Néda, Z. 1999 On the circular hydraulic jump. Am. J. Phys. 67, 723731.CrossRefGoogle Scholar
Bush, J. W. M. & Aristoff, J. M. 2003 The influence of surface tension on the circular hydraulic jump. J. Fluid. Mech. 489, 229238.CrossRefGoogle Scholar
Craik, A., Lathman, R., Fawkes, M. & Gibbon, P. 1981 The circular hydraulic jump. J. Fluid. Mech. 112, 347362.CrossRefGoogle Scholar
Gilmore, F. R., Plesset, M. S. & Crossley Jr, H. E. 1950 The analogy between hydraulic jumps in liquids and shock wave in gases. J. Appl. Phys. 21, 243249.CrossRefGoogle Scholar
Glauart, M. B. 1956 The wall jet. J. Fluid. Mech. 1, 625643.CrossRefGoogle Scholar
Godwin, R. 1993 The hydraulic jump (‘shocks’ and viscous flow in the kitchen sink). Am. J. Phys. 61, 829832.CrossRefGoogle Scholar
Hansen, S. H., Horlúck, S., Zauner, D., Dimon, P., Ellegaard, P. & Watanabe, S. 1997 Geometrical orbits of surface waves from a circular hydraulic jump. Phy. Rev. E 55, 70487061.CrossRefGoogle Scholar
Higuera, F. J. 1994 Hydraulic jump in a viscous laminar flow. J. Fluid Mech. 274, 6992.CrossRefGoogle Scholar
Higuera, F. J. 1997 The circular hydraulic jump. Phys. Fluids 9, 14761478.CrossRefGoogle Scholar
Ishigai, S., Nakanishi, S., Mizunao, M. & Imamura, T. 1977 Heat transfer of the impinging round water jet in the interference zone of film flowing along the wall. Bull. JSME 20, 8592.CrossRefGoogle Scholar
Liu, X. & Lienhard, J. 1993 The hydraulic jump in circular jet impingement and in other thin liquid films. Exps. Fluids 15, 108116.CrossRefGoogle Scholar
Looney, M. K. & Walsh, J. J. 1984 Mean-flow and turbulent characteristics of free and impinging jet flow. J. Fluid Mech. 147, 397429.CrossRefGoogle Scholar
Nakoryakov, V., Pokusaev, B. & Troyan, E. 1978 Impingement of an axisymmetric liquid jet on a barrier. Intl J. Heat Mass Transfer 21, 11751184.CrossRefGoogle Scholar
Olsson, R. G. & Turkdogan, E. T. 1966 Radial spread of a liquid stream on a horizontal plate. Nature 211, 813816.CrossRefGoogle Scholar
Phares, D. J., Smedley, G. T. & Flagan, R. C. 2000 The wall shear stress produced by the normal impingement of a jet on a flat surface. J. Fluid Mech. 418, 351375.CrossRefGoogle Scholar
Preiswerk, E. 1940 Applications of the methods of gas dynamics to water flows with free surfaces. NACA TM 934 and 935.Google Scholar
Rajaratnam, N. 1976 Turbulent Jets. Elsevier.Google Scholar
Rao, A. & Arakeri, J. H. 1998 Integral analysis applied to radial film flows. Intl J. Heat Mass Transfer 41, 27572767.CrossRefGoogle Scholar
Rubel, A. 1981 Computations of the oblique impingement of round jets upon a plane wall. AIAA J. 19, 863871.CrossRefGoogle Scholar
Rubel, A. 1982 Oblique impingement of a round jet on plane surface. AIAA J. 20, 17561758.CrossRefGoogle Scholar
Schlichting, H. 1960 Boundary Layer Theory. McGraw-Hill.Google Scholar
Scholtz, M. T. & Trass, O. 1970 Mass transfer in nonuniform impinging jet. AIChE J. 16, 8290.CrossRefGoogle Scholar
Sparrow, E. M. & Lovell, B. J. 1980 Heat transfer characteristics of an obliquely impinging circular jet. Trans. ASME C: J. Heat Transfer 102, 202209.CrossRefGoogle Scholar
Stevens, J. & Webb, B. W. 1991 The effect of inclination on local heat transfer under an axisymmetric free liquid jet. Intl J. Heat Mass Transfer 34, 12271236.CrossRefGoogle Scholar
Tong, A. Y. 2003 On the oblique impingement heat transfer of an oblique free surface plane jet. J. Heat Mass Transfer 46, 20772085.CrossRefGoogle Scholar
Taylor, G. 1960 Formation of thin flat sheets of water. Proc. R. Soc. Lond. A 259, 117.Google Scholar
Watson, E. J. 1964 The spread of a liquid jet over a horizontal plane. J. Fluid Mech. 20, 481499.CrossRefGoogle Scholar
Yokoi, K. & Xiao, F. 2002 Mechanism of structure formation in circular hydraulic jumps: numerical studies of strongly deformed free-surface shallow flows. Physica D 161, 202219.CrossRefGoogle Scholar