A.A. Aganin∗, T.S. Guseva∗∗
Institute of Mechanics and Engineering, FRC Kazan Scientific Center, Russian Academy of Sciences, Kazan, 420111 Russia
E-mail: ∗aganin@kfti.knc.ru, ∗∗ts.guseva@mail.ru
Received March 30, 2018
DOI: 10.26907/2541-7746.2019.1.39-52
For citation: Aganin A.A., Guseva T.S. The influence of the end shape of the liquid jet on its impact onto a dry wall. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2019, vol. 161, no. 1, pp. 39–52. doi: 10.26907/2541-7746.2019.1.39-52. (In Russian)
Abstract
The influence of the end shape of a jet normally impacting onto a rigid wall on the characteristics of a shock wave in liquid and the pressure pulses on a wall has been studied. The water jet is axisymmetric, its end is hemispheroidal, with semi-axes R and бR where R is the jet radius, б varies from 0 through 2. The jet speed is 250 m/s. The dynamics of the liquid in the jet and the surrounding gas is governed by the Euler equations in the density, velocity, and pressure. Their solution has been derived numerically by the CIP-CUP method on an adaptive Soroban-grid without explicit separation of the liquid-gas interface. It has been found that for б > 0.38 the jet action on the wall before the shock wave detachment is similar to that of a hemispherically-ended jet with a radius of R/б. Qualitative differences from the hemispherically-ended jet case after the shock wave detachment are caused by the jet end non-sphericity at a distance from the jet axis. For all the considered values of б, the mean level of the wall pressure remains close to that in the hemispherically-ended jet case (б = 1). With decreasing б, the characteristic size of the maximum pressure load area and the radius of its central part with the quasi-uniform load increase.
Keywords: jet impact on wall, jet end shape, shock waves in liquid, radial convergence of rarefaction waves
Acknowledgments. The study was supported by the Russian Science Foundation, project no. 17-11-01135.
References
1. Bourne N.K. On impacting liquid jets and drops onto polymethylmethacrylate targets. Proc. R. Soc. A., 2005, vol. 46, no. 2056, pp. 1129–1145. doi: 10.1098/rspa.2004.1440.
2. Kornfeld M., Suvorov L. On the destructive action of cavitation. J. Appl. Phys., 1944, vol. 15, no. 6, pp. 495–506. doi: 10.1063/1.1707461.
3. Philipp A., Lauterborn W. Cavitation erosion by single laser-produced bubbles. J. Fluid Mech., 1998, vol. 361, pp. 75–116. doi: 10.1017/S0022112098008738.
4. Crum L.A. Surface oscillations and jet development in pulsating bubbles. J. Phys. Colloq., 1979, vol. 40, no. C8, pp. C8-285–C8-288. doi: 10.1051/jphyscol:1979849.
5. Aganin A.A., Ilgamov M.A., Kosolapova L.A., Malakhov V.G. Dynamics of a cavitation bubble near a solid wall. Thermophys. Aeromech., 2016, vol. 23, no. 2, pp. 211–220. doi: 10.1134/S0869864316020074.
6. Aganin A.A., Guseva T.S., Kosolapova L.A., Khismatullina N.A. The calculation of weakly nonspherical cavitation bubble impact on a solid. IOP Conf. Ser.: Mater. Sci. Eng., 2016, vol. 158, art. 012003, pp. 1–6. doi: 10.1088/1757-899X/158/1/012003.
7. Lesser M. The impact of a compressible liquid. In: Rein M. (Ed.) Drop-Surface Interactions. CISM International Centre for Mechanical Sciences (Courses and Lectures). Vol. 456. Vienna, Springer, 2002, pp. 39–102.
8. Hwang J.-B.G., Hammitt F.G. High-speed impact between curved lipid surface and rigid flat surface. J. Fluids Eng., 1977, vol. 99, no. 2, pp. 396–404. doi: 10.1115/1.3448774.
9. Aganin A.A., Guseva T.S. Impact of a liquid cone on a plain rigid wall. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2016, vol. 158, no. 1, pp. 117–128. (In Russian)
10. Aganin A.A., Guseva T.S. Influence of the jet end shape at the jet impact on the liquid surface. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2017, vol. 159, no. 2, pp. 135–142. (In Russian)
11. Yabe T., Wang P.Y. Unified numerical procedure for compressible and incompressible fluid. J. Phys. Soc. Japan, 1991, vol. 60, no. 7, pp. 2105–2108. doi: 10.1143/JPSJ.60.2105.
12. Takizawa K., Yabe T., Tsugawa Y., Tezduyar T.E., Mizoe H. Computation of free-surface flows and fluid-object interactions with the CIP method based on adaptive meshless Soroban grids. Comput. Mech., 2007, vol. 40, no. 1, pp. 167–183. doi: 10.1007/s00466-006-0093-2.
13. Aganin A.A., Guseva T.S. Numerical simulation of contact interaction of compressible fluids on Eulerian grids. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2012, vol. 154, no. 4, pp. 74–99. (In Russian)
14. Aganin A.A., Guseva T.S. Numerical simulation of dynamics of nonuniform compressible media based on the CIP-CUP method on dynamically adaptive soroban grids. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2014, vol. 156, no. 2, pp. 55–71. (In Russian)
15. Aganin A.A., Guseva T.S. Numerical simulation of impact of a jet on a wall. Math. Models Comput. Simul., 2017, vol. 9, no. 5, pp. 623–635. doi: 10.1134/S2070048217050027.
16. Voinov O.V., Voinov V.V. On the process of collapse of a cavitation bubble near a wall and the formation of a cumulative jet. Sov. Phys. Dokl., 1976, vol. 21, pp. 133–136.
17. Heymann F.J. High-speed impact between a liquid drop and a solid surface. J. Appl. Phys., 1969, vol. 40, no. 13, pp. 5113–5122. doi: 10.1063/1.1657361.
18. Bowden F.P., Field J.E. The brittle fracture of solids by liquid impact, by solid impact and by shock. Proc. R. Soc. Lond. A., 1964, vol. 282, no. 1390, pp. 331–352. doi: 10.1098/rspa.1964.0236.
19. Lesser M.B., Field J.E. The impact of compressible liquids. Ann. Rev. Fluid Mech., 1983, vol. 15, pp. 97–122. doi: 10.1146/annurev.fl.15.010183.000525.
20. Rein M. Phenomena of liquid drop impact on solid and liquid surfaces. Fluid Dyn. Res., 1993, vol. 12, no. 2, pp. 61–93. doi: 10.1016/0169-5983(93)90106-k.
21. Lesser M.B. Thirty years of liquid impact research: A tutorial review. Wear, 1995, vol. 186–187, pp. 28–34. doi: 10.1016/0043-1648(95)07190-3.
22. Field J.E. ELSI conference: Invited lecture: Liquid impact: Theory, experiment, applications. Wear, 1999, vols. 233-235, pp. 1–12. doi: 10.1016/S0043-1648(99)00189-1.
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