ISSN 2542–0380 
Труды Института механики им. Р.Р. Мавлютова
Электронный научный журнал  Electronic Scientific Journal
Proceedings of the Mavlyutov Institute of Mechanics

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, widerange 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
shock wave,
cavitation bubble,
TVDscheme,
RayleighPlesset equation
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, widerange 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 RayleighPlesset 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
It is shown that a simplified criterion of shock wave formation position predicts it
correctly in comparison with the numerical simulation data at
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.