A Phenomenological Study of Polygonal Hydraulic Jumps

Document Type : Original Article

Authors

• Ali asadi
• Ali Reza teymourtash

-

10.22067/fum-mech.v31i1.83280

Abstract

Polygonal hydraulic jump is among the subjects widely studied by scientists in recent years. Although this phenomenon was discovered nearly two decades ago, many of the probable reasons behind it remain unknown. Accordingly, the main goal of the present study is to conduct a laboratory-scale phenomenological investigation on polygonal hydraulic jumps. The results indicated that the main cause of polygonal hydraulic jumps is the presence of disturbances and instabilities in flows, systems, or environments. Given the Plateau–Rayleigh instability, in the presence of surface tension and viscosity effects, the disturbances and instabilities create stable circular jumps unstable and then turn them into polygonal jumps. A stable circular jump was created with the elimination of instabilities, and the jump, unlike what observed in previous studies, was stable at a low to high range of Reynolds number. In addition, the behavior of polygonal hydraulic jumps formed in previous studies in the presence of instabilities was investigated. In a constant flow rate, the area inside the jump was equal for all the possible jumps at an error level of less than 10%. Among the polygons with an equal number of sides, which are possibly observed in a particular flow rate, the jump changes into a regular polygon, as the surface tension naturally tends to create the minimum possible surface area for the jump.

Keywords

• Phenomenology
• Plateau–Rayleigh Instability
• Polygonal Jump
• Regular Polygon
• Stable Circular Jump

---

References

1. Avedisian, C. and Zhao, Z., "The circular hydraulic jump in low gravity", Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, The Royal Society, pp. 2127-2151, (2000).

2. Kate, R., Das, P. and Chakraborty, S., "An Investigation on non-circular hydraulic jumps formed due to obliquely impinging circular liquid jets", Experimental Thermal and Fluid Science, Vol. 32, pp. 1429-1439, (2008).

3. Rayleigh, L., "On the theory of long waves and bores", Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, pp. 324-328, (1914).

4. Birkhoff, G. and Zarantonello, E., "Jets, Wakes, and Cavities", Academic Press, New York, (1957).

5. Watson, E., "The radial spread of a liquid jet over a horizontal plane", Journal of Fluid Mechanics, Vol. 20, pp. 481-499, (1964).

6. Craik, A., Latham, R., Fawkes, M. and Gribbon, P., "The circular hydraulic jump", Journal of Fluid Mechanics, Vol. 112, pp. 347-362, (1981).

7. Errico, M., "A study of the interaction of liquid jets with solid surfaces", University of California, San Diego, (1986).

8. Liu, X. and Lienhard, J. H., "The hydraulic jump in circular jet impingement and in other thin liquid films", Experiments in Fluids, Vol. 15, pp. 108-116, (1993).

9. Higuera, F., "The hydraulic jump in a viscous laminar flow", Journal of Fluid Mechanics, Vol. 274, pp. 69-92, (1994).

10. Bush, J.W. and Aristoff, J.M., "The influence of surface tension on the circular hydraulic jump", Journal of Fluid Mechanics, Vol. 489, pp. 229-238, (2003).

11. Bush, J.W., Aristoff, J.M. and Hosoi, A., "An experimental investigation of the stability of the circular hydraulic jump", Journal of Fluid Mechanics, Vol. 558, pp. 33-52, (2006).

12. Yokoi, K. and Xiao, F., "A numerical study of the transition in the circular hydraulic jump", Physics Letters A, Vol. 257, pp. 153-157, (1999).

13. Yokoi, K. and Xiao, F., "Mechanism of structure formation in circular hydraulic jumps: Numerical studies of strongly deformed free-surface shallow flows", Physica D: Nonlinear Phenomena, Vol. 161, pp. 202-219, (2002).

14. Mikielewicz, J. and Mikielewicz, D., "A simple dissipation model of circular hydraulic jump", International Journal of Heat and Mass Transfer, Vol. 52, pp. 17-21, (2009).

15. Passandideh-Fard, M., Teymourtash A. R. and Khavari, M., "Numerical study of circular hydraulic jump using Volume-of-fluid method", Journal of Fluids Engineering, Vol. 133, p. 011401, (2011).

16. Hirt, C. W. and Nichols, B. D. "Volume of fluid (VOF) method for the dynamics of free boundaries", Journal of Computational Physics, Vol. 39, pp. 201-225, (1981).

17. Ellegaard, C., Hansen, A. E., Haaning, A., Hansen, K., Marcussen, A., Bohr, T., Hansen, J. L. and Watanabe, S., "Cover illustration: Polygonal hydraulic jumps", Nonlinearity, Vol. 12, p. 1, (1999).

18. Teymourtash, A.R. and Mokhlesi, M., "Experimental investigation of stationary and rotational structures in non-circular hydraulic jumps", Journal of Fluid Mechanics, Vol. 762, pp. 344-360, (2015).

19. Martens, E.A., Watanabe, S. and Bohr, T., "Model for polygonal hydraulic jumps", Physical Review E, Vol. 85, p. 036316, (2012).

20. Rojas, N. and Tirapegui, E., "Harmonic solutions for polygonal hydraulic jumps in thin fluid films", Journal of Fluid Mechanics, Vol. 780, pp. 99-119, (2015).

21. Rojas, N.O., Argentina, M., Cerda, E. and Tirapegui, E., "Inertial Lubrication Theory", Physical Review Letters, Vol. 104, p. 187801, (2010).

22. Ellegaard, C., Hansen, A.E., Haaning, A. and Bohr, T., "Experimental results on flow separation and transitions in the circular hydraulic jump", Physica Scripta, Vol. 105, (1996).

23. Kasimov, A.R., "A stationary circular hydraulic jump, the limits of its existence and its gasdynamic analogue", Journal of Fluid Mechanics, Vol. 601, pp. 189-198, (2008).

24. Plateau, J., "Statique Expe´rimentale et The´orique des Liquides", Gauthier-Villars, Paris, (1873).

25. Rayleigh, L., "On the Instability of Jets", Proceeding London Mathematical Society, Vol. 10, pp. 4-13, (1878).

26. Javadi, A., Eggers, J., Bonn, D., Habibi, M. and Ribe, N.M., "Delayed Capillary Breakup of Falling Viscous Jets", Physical Review Letters, Vol. 110, pp. 144501-144504, (2013).

27. Shames, I.H., "Mechanics of Fluid", 4th Edition, McGraw-Hill, (2003).