Труды Института механики им. Р.Р. Мавлютова

Liquid temperature dependence of the shock formation in a cavitation bubble. Proceedings of the Mavlyutov Institute of Mechanics. 2017. 12(1). 89–95.

2017. Vol. 12. Issue 1, Pp. 89–95
URL: http://proc.uimech.org/uim2017.1.013,en
DOI: 10.21662/uim2017.1.013

Liquid temperature dependence of the shock formation in a cavitation bubble

Aganin A.A., Khalitova T.F.

Institute of Mechanics and Engineering, Kazan

Abstract

The dependence of the radially convergent shock wave formation in a cavitation bubble on the surrounding liquid temperature T_L in the range from 273.15 to 400 K is investigated at the liquid pressure equal to 50 bar. Realistic mathematical model is applied, in which the effects of the liquid compressibility, the heat conductivity of the vapor and liquid, the evaporation and condensation on the bubble surface are taken into account, wide-range equations of state are utilized. The governing equations of the vapor and liquid dynamics are solved numerically using a modification of the Godunov method of the second order of accuracy. It has been found that a radially convergent shock wave arises in the bubble in 273.15≤T_L≤375 К. In this interval, the distance between the shock wave formation position and the bubble surface decreases with decreasing the liquid temperature. The possibility of using a known simplified criterion of the formation of a shock wave inside a bubble to estimate its formation position under the studied conditions is considered. It is shown that with applying that criterion the shock wave formation position turns out to be correctly predicted at T_L≈325 К, while at T_L>325 К and T_L<325 К it is predicted closer to and more distant from the bubble surface, respectively.

Keywords

shock wave,
cavitation bubble,
TVD-scheme,
Rayleigh-Plesset equation

Article outline

Purpose.

Numerical investigation of influence of the liquid temperature on the shock wave formation inside a cavitation bubble in acetone. Estimate of applicability of one simplified criterion of shock wave formation.

Methodology.

A mathematical model is used, in which the liquid and vapor flow is described by gas dynamics equations. Evaporation and condensation, heat conductivity of the liquid and vapor are taken into account, wide-range equations of state are applied. A relatively simple criterion is also used, in which the values of the thermodynamics parameters on the interphase boundary are calculated by solving Rayleigh-Plesset equation. The vapor is assumed uniform, its state is described be the Van der Waals equation.

Findings.

It has been shown that the optimum grid for the stated investigation is that with external area radius by more than 9 times greater than the bubble radius, with 1200 cells in vapor and 700 cells in liquid, with refinement in vapor and liquid to the bubble surface.

It has been found that in the liquid temperature range 273.15≤T_L≤375 К a radially convergent shock wave arises in the bubble if 273.15≤T_L≤375 К. In this interval, the distance between the shock wave formation position and the bubble surface decreases with decreasing the liquid temperature.

It is shown that a simplified criterion of shock wave formation position predicts it correctly in comparison with the numerical simulation data at T_L≈325 К, while at TL>325 К and T_L<325 К it gives its position closer to and more distant from the bubble surface, respectively, with a gradual increase in error to 25% in the first case and to 85% in the second one.

Originality/value.

Shock wave compression of the medium in a cavitaion bubble in acetone at 50 bar pressure can only be realized at the liquid temperature less than 375 К. The simplified criterion of the shock wave formation inside the bubble can be used for approximate prediction of the corresponding temperature dependence of the shock wave formation position.