- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Role of gravity and capillary waves in the origin of circular hydraulic jumps

Hossein Askarizadeh1,2, Hossein Ahmadikia2,*, Claas Ehrenpreis1, Reinhold Kneer1, Ahmadreza Pishevar3, and Wilko Rohlfs1,†

  • 1Institute of Heat and Mass Transfer, RWTH Aachen University, Augustinerbach 6, 52056 Aachen, Germany
  • 2Department of Mechanical Engineering, University of Isfahan, 81746-73441 Isfahan, Iran
  • 3Department of Mechanical Engineering, Isfahan University of Technology, 84156-83111 Isfahan, Iran

  • *Corresponding author: ahmadikia@eng.ui.ac.ir
  • †Corresponding author: rohlfs@wsa.rwth-aachen.de
PDF

Phys. Rev. Fluids 4, 114002 – Published 14 November, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.114002

Abstract

In almost all of the studies on the circular hydraulic jump (CHJ), gravity had been considered as a significant variable that affects the formation of the jump. Most recently, gravity was deprived of being important in the origin of the CHJ, which challenged researchers in this field of fluid mechanics. This study addresses in detail the physical concepts behind this intriguing phenomenon occurring in the radial outspreading of a vertically downward free-surface liquid impinging jet upon a horizontal plate. The aim is to find out whether gravity plays any role in the origin of the CHJ. Accordingly, the jump evolution is investigated in two cases: first, the initial formation of the CHJ in which the subcritical flow downstream from the jump is approaching the outlet boundary (developing jump). Second, the final evolution of the CHJ in which a steady-state flow is circumventing an obstacle at the edge of the impinged plate and falling uniformly down from the outlet boundary (developed jump). The results indicate the existence of two different flow regimes in the jump formation: gravity- and capillary-dominant flow regimes. In general, the role of gravity in the formation of developing or developed jumps cannot be eliminated; however, its importance lies in the fact of which regime dominates the flow. Intensification of gravitational effects is observed when capillary waves are dampened by increasing viscosity, density, or volume flow rate as well as by decreasing surface tension. Finally, a generalized scaling relation for the jump radius is obtained considering both capillary and gravitational effects in the critical flow condition. In contrast to the previous results, this generalized scaling relation predicts more accurately the radius of both a developing and a developed jump.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (42)

  1. W. H. Hager, Energy Dissipators and Hydraulic Jump (Springer Netherlands, Dordrecht, 2010).
  2. R. K. Bhagat, N. K. Jha, P. F. Linden, and D. I. Wilson, On the origin of the circular hydraulic jump in a thin liquid film, J. Fluid Mech. 851, 11 (2018).
  3. E. J. Watson, The radial spread of a liquid jet over a horizontal plane, J. Fluid Mech. 20, 481 (1964).
  4. T. Bohr, P. Dimon, and V. Putkaradze, Shallow-water approach to the circular hydraulic jump, J. Fluid Mech. 254, 635 (1993).
  5. K. Yokoi and F. Xiao, Relationships between a roller and a dynamic pressure distribution in circular hydraulic jumps, Phys. Rev. E 61, R1016 (2000).
  6. N. Rojas, M. Argentina, and E. Tirapegui, A progressive correction to the circular hydraulic jump scaling, Phys. Fluids 25, 042105 (2013).
  7. X. Liu and J. H. Lienhard, The hydraulic jump in circular jet impingement and in other thin liquid films, Exp. Fluids 15, 108 (1993).
  8. J. W. M. Bush and J. M. Aristoff, The influence of surface tension on the circular hydraulic jump, J. Fluid Mech. 489, 229 (2003).
  9. B. Mohajer and R. Li, Circular hydraulic jump on finite surfaces with capillary limit, Phys. Fluids 27, 117102 (2015).
  10. R. Fernandez-Feria, E. Sanmiguel-Rojas, and E. Benilov, On the origin and structure of a stationary circular hydraulic jump, Phys. Fluids 31, 072104 (2019).
  11. I. Tani, Water jump in the boundary layer, J. Phys. Soc. Jpn. 4, 212 (1949).
  12. M. Kurihara, On hydraulic jumps, Proceedings of the Report of the Research Institute for Fluid Engineering, Kyusyu Imperial University 3, 11 (1946).
  13. T. Bohr, V. Putkaradze, and S. Watanabe, Averaging Theory for the Structure of Hydraulic Jumps and Separation in Laminar Free-Surface Flows, Phys. Rev. Lett. 79, 1038 (1997).
  14. S. Watanabe, V. Putkaradze, and T. Bohr, Integral methods for shallow free-surface flows with separation, J. Fluid Mech. 480, 233 (2003).
  15. K. Yokoi and F. Xiao, Mechanism of structure formation in circular hydraulic jumps: Numerical studies of strongly deformed free-surface shallow flows, Physica D 161, 202 (2002).
  16. T. Bohr, C. Ellegaard, A. E. Hansen, and A. Haaning, Hydraulic jumps, flow separation and wave breaking: An experimental study, Physica B 228, 1 (1996).
  17. C. Ellegaard, A. E. Hansen, A. Haaning, and T. Bohr, Experimental results on flow separation and transitions in the circular hydraulic jump, Phys. Scr. T67, 105 (1996).
  18. S. T. Hansen, S. Hørlück, D. Zauner, P. Dimon, C. Ellegaard, and S. C. Creagh, Geometric orbits of surface waves from a circular hydraulic jump, Phys. Rev. E 55, 7048 (1997).
  19. Y. Wang and R. E. Khayat, The role of gravity in the prediction of the circular hydraulic jump radius for high-viscosity liquids, J. Fluid Mech. 862, 128 (2019).
  20. A. Duchesne, A. Andersen, and T. Bohr, Surface tension and the origin of the circular hydraulic jump in a thin liquid film, Phys. Rev. Fluids 4, 084001 (2019).
  21. C. W. Hirt and B. D. Nichols, Volume of fluid (VOF) method for the dynamics of free boundaries, J. Comput. Phys. 39, 201 (1981).
  22. J. Brackbill, D. Kothe, and C. Zemach, A continuum method for modeling surface tension, J. Comput. Phys. 100, 335 (1992).
  23. D. Kothe and R. C. Mjolsness, Ripple—A new model for incompressible flows with free surfaces, AIAA J. 30, 2694 (1992).
  24. G. P. Sasmal and J. I. Hochstein, Marangoni convection with a curved and deforming free surface in a cavity, J. Fluids Eng. 116, 577 (1994).
  25. J. R. Richards, A. M. Lenhoff, and A. N. Beris, Dynamic breakup of liquid–liquid jets, Phys. Fluids 6, 2640 (1994).
  26. G. Wang, Finite element simulations of free surface flows with surface tension in complex geometries, J. Fluids Eng. 124, 584 (2002).
  27. H. Jasak, Error analysis and estimation for finite volume method with applications to fluid flow, Ph.D. thesis, Imperial College, University of London, London, 1996.
  28. O. Ubbink, Numerical prediction of two fluid systems with sharp interfaces, Ph.D. thesis, Imperial College, University of London, London, 1997.
  29. H. Rusche, Computational UID dynamics of dispersed two-phase flows at high phase fractions, Ph.D. thesis, Imperial College, University of London, London, 2002.
  30. S. S. Deshpande, L. Anumolu, and M. F. Trujillo, Evaluating the performance of the two-phase flow solver interfoam, Comput. Sci. Disc. 5, 014016 (2012).
  31. B. Lafaurie, C. Nardone, R. Scardovelli, S. Zaleski, and G. Zanetti, Modelling merging and fragmentation in multiphase flows with surfer, J. Comput. Phys. 113, 134 (1994).
  32. W. Rohlfs and P. Pischke, Introduction and application of a smooth interface compression method in VOF (unpublished).
  33. W. Rohlfs, P. Pischke, and B. Scheid, Hydrodynamic waves in films flowing under an inclined plane, Phys. Rev. Fluids 2, 170 (2017).
  34. W. Rohlfs, C. Ehrenpreis, H. D. Haustein, and R. Kneer, Influence of viscous flow relaxation time on self-similarity in free-surface jet impingement, Intl. J. Heat Mass Transf. 78, 435 (2014).
  35. W. Rohlfs, M. Binz, and R. Kneer, On the stabilizing effect of a liquid film on a cylindrical core by oscillatory motions, Phys. Fluids 26, 022101 (2014).
  36. M. Bieber, R. Kneer, and W. Rohlfs, Self-similarity of heat transfer characteristics in laminar submerged and free-surface slot jet impingement, Intl. J. Heat Mass Transf. 104, 1341 (2017).
  37. A. Duchesne, Constant froude number in a circular hydraulic jump and its implication on the jump radius selection, Europhys. Lett. 107, 54002 (2014).
  38. E. C. Button, J. F. Davidson, G. J. Jameson, and J. E. Sader, Water bells formed on the underside of a horizontal plate. Part 2. Theory, J. Fluid Mech. 649, 45 (2010).
  39. J. F. Prince, D. Maynes, and J. Crockett, On jet impingement and thin film breakup on a horizontal superhydrophobic surface, Phys. Fluids 27, 112108 (2015).
  40. C. Avedisian and Z. Zhao, The circular hydraulic jump in low gravity, Proc. R. Soc. London A 456, 2127 (2000).
  41. M. Mathur, R. DasGupta, N. R. Selvi, N. S. John, G. U. Kulkarni, and R. Govindarajan, Gravity-Free Hydraulic Jumps and Metal Femtoliter Cups, Phys. Rev. Lett. 98, 164502 (2007).
  42. R. Dasgupta, G. Tomar, and R. Govindarajan, Numerical study of laminar, standing hydraulic jumps in a planar geometry, Eur. Phys. J. E 38, 45 (2015).

Outline

Information

Phys. Rev. Fluids 4, 114002– Published 14 November, 2019
  • Received 24 June 2019
Crossmark - Check for updates button

©2019 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation