Influence of the Tetradecane Temperature and Pressure on the Formation of Radially Converging Shock Waves Inside a Collapsing Cavitation Bubble

Abstract

The influence of the tetradecane temperature $T_{0}$ and pressure $p_{0}$ in the ranges from 423 to 663 K and from 15 to 70 bar, respectively, on the formation of radially converging shock waves in a collapsing cavitation bubble is studied. The bubble collapse is spherical, at the beginning of collapse the bubble is filled with tetradecane vapor in the saturation state at temperature $T_{0}$, the initial bubble radius is 500 $\mu$m. The dynamics of the vapor in the bubble and the surrounding liquid is governed by the gas dynamics equations taking into account the non-stationary thermal conductivity of both fluids, the nonequilibrium condensation and evaporation on the interface. A special modification of the known wide-range equations of state by Nigmatulin and Bolotnova, suitable for not very high temperatures of the liquid, is applied. It is shown that at any liquid temperature $T_{0}$ in the range considered, the bubble content is compressed with the formation of radially converging shock (at $p_{0}$ in the range 15–70 bar) and isentropic (at $p_{0}$ in the subrange 15–20 bar) waves. The extreme temperatures and pressures of the vapor in the bubble at the boundary of a ‘‘hot’’ core with a radius of 0.25 $\mu$m first increase with decreasing $T_{0}$ and then decrease. The highest values of those extremes in the rectangle area of the ($T_{0}$, $p_{0}$) plane under study are of the order of $7\cdot 10^{6}$ bar and $3\cdot 10^{5}$ K.