Influence of the Jet End Shape at the Jet Impact on the Liquid Surface
A.A. Aganin* , T.S. Guseva**
Institute of Mechanics and Engineering,
Kazan Science Center, Russian Academy of Sciences, Kazan, 420111 Russia
E-mail: *aganin@kfti.knc.ru, **ts.guseva@mail.ru
Received April 12, 2017
Abstract
The paper presents the results of a numerical simulation of water jet (250 m/s) impact onto the surface of motionless liquid (water). The main attention has been paid to the influence of the jet end shape on the liquid dynamics in the vicinity of the impact site. This is of interest for the applications characterized by the destructive action of a liquid mass on the wetted surfaces of solids. The Constrained Interpolation Profile-Combined Unified Procedure (CIP-CUP) method and the dynamically adaptive Soroban grids have been applied. It has been shown that the impact features do not qualitatively change with sharpening the jet end in comparison with the hemispherical one. Two dome-like shock waves occur, propagating up the jet and down the target liquid. The maximum pressure is localized at the boundary of the expanding jet-target contact region where a thin radially directed liquid splash develops with time. In the jet near its lateral boundary at a distance from the target surface on the order of the jet radius, a region of metastable liquid (with negative pressures) is formed, which increases with time to cover the entire cross section of the jet. In reality, cavitation can arise in that region, but this has not been taken into account in the model of the present work. With increasing the jet end bluntness, the maximum pressures are realized in a large region bounded by the shock waves from below and above and by the rarefaction waves converging to the symmetry axis, from the lateral side. In the vicinity of the jet-target contact zone, a large region of metastable liquid is formed. Finally, it divides into two parts: one in the jet, the other in the target. Even greater blunting of the jet end to the plane one manifests itself in the initial stage of the impact: the shock waves in the jet and the target become initially flat, and the metastable liquid region arises at a point of the symmetry axis to which the rarefaction waves converge. Thus, it has been found that the jet end sharpening relative to the hemispherical one does not affect the qualitative characteristics of the impact, whereas its blunting leads to their significant changes. The higher the degree of bluntness becomes, the earlier the changes in the features of impact manifest themselves with the increasing end bluntness.
Keywords: jet impact on liquid surface, shape of jet end, shock waves in liquid, liquid splash, radial convergence of rarefaction waves
Acknowledgments. This study was supported by the Russian Science Foundation (project no. 17-11-01135).
Figure Captions
Fig. 1. The shape of water jets at the moment of their impact onto a part of the bubble surface having a shape of a slightly elongated spheroid (a) and a shape close to spherical (b).
Fig. 2. A scheme of the liquid jet impact onto liquid.
Fig. 3. The liquid jet impact onto a liquid jet with a semispherical end (α = 1). The pressure fields are shown for six points of time (t1 –t6) : V t/R = 0.07, 0.14, 0.21, 0.28, 0.36, 0.44. The regions of negative pressure are shown with white color.
Fig. 4. The impact of a jet with a more blunt end compared to the semispherical one α = 0.25 (a) and α = 0 (b)) onto the liquid. Pressure fields are shown for six points of time (t1 –t6) : a) V t/R = 0.09, 0.14, 0.23, 0.28, 0.39, 0.57, b) V t/R = 0.08, 0.12, 0.21, 0.25, 0.39, 0.5.
Fig. 5. The impact of the jet with a sharper end compared to the semispherical one (α = 2) onto the liquid. Pressure fields are shown for six points of time (t1 –t6) : V t/R = 0.07, 0.14, 0.22, 0.3, 0.39, 0.56.
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For citation: 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)
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