Impact-induced cavitation in a cylindrical container with liquid

A.A. Aganin^∗ , M.A. Ilgamov^∗∗ , I.N. Mustafin^∗∗∗

Institute of Mechanics and Engineering, FRC Kazan Scientific Center, Russian Academy of Sciences, Kazan, 420111 Russia

E-mail: ^∗aganin@kfti.knc.ru, ^∗∗ilgamov@anrb.ru, ^∗∗∗Ildarmn@mail.ru

Received July 3, 2019

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DOI: 10.26907/2541-7746.2020.1.27-37

For citation: Aganin A.A., Ilgamov M.A., Mustafin I.N. Impact-induced cavitation in a cylindrical container with liquid. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2020, vol. 162, no. 1, pp. 27–37. doi: 10.26907/2541-7746.2020.1.27-37. (In Russian)

Abstract

The dynamics of liquid in a cylindrical container and the pulse action on its bottom under impact on its upper end was considered. The case with cavitation in the liquid column near the bottom was investigated. The study was performed in the conditions of the known experiments on the bottle breaking resulting from impacting on its upper end. One-dimensional models of hydrodynamics, linear acoustics, and incompressible liquid were applied. The hydrodynamic equations were solved by the Godunov method. Variation of the bottom acceleration was described by a piecewise-constant function, the cavitation was simulated by a single cavity in the form of a cylindrical layer near the bottom. It was shown that in the experiments the bottle breaks because of the water hammer pressure resulting from the cavity collapse. The influence of the waves in the liquid column on the bottom load is insignificant. With decreasing the pressure on the external liquid surface from the atmospheric value, the action on the bottom decreases. There is an optimal height to attain large pressures on the bottom.

Keywords: cylindrical container, impact on bottom, cavitation, cavity, cavity collapse, gas dynamics equations, Godunov method

Figure Captions

Fig. 1. Dynamics of a liquid in a container at an impact on its upper end (a, b) and the schematic used in the simulation (c).

Fig. 2. The change in the axial acceleration of the bottle bottom (before the beginning of intensive action on the bottom) at an impact on its neck in experiments [12–14] (solid line) and its piecewise-constant approximation (dotted line).

Fig. 3. Pressure (a, b) and velocity (c) distributions in the liquid column along its axis at three moments (curves 1–3): t₁ = 0.0055 ms, t₂ = 0.047 ms and t₃ = 0.029 ms. The arrows indicate the direction of wave propagation, horizontal dashed lines show the upper boundary of the liquid column x_t.

Fig. 4. Change of velocity (a) and positions (b) of the bottom and the lower boundary of the liquid column from the beginning of the impact to the moment of collapse (indicated by a dot) of the cavity between the bottom and the liquid column, h = 13.3 cm. Dash-dotted lines 1 correspond to the bottom, solid lines 2, dotted lines 3, and dashed lines 4 correspond to the models of hydrodynamics, linear acoustics, and incompressible liquid, respectively.

Fig. 5. Influence of the liquid column height on the water hammer pressure on the bottom p_wh resulted from the cavity collapse (curve 1) and on the moment of attaining the water hammer pressure t_wh (curve 2); these are the results by the linear acoustics model.

Fig. 6. The influence of the liquid pressure p0 on the water hammer pressure on the bottom p_wh (curve 1) and on the moment of attaining the water hammer pressure twh (curve 2); these are the results by the linear acoustics model.

Fig. 7. The influence of the bottom acceleration, characterized by the parameter k, on the water hammer pressure on the bottom p_wh (curve 1) and on the moment of attaining the water hammer pressure t_wh (curve 2); these are the results by the linear acoustics model.

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