Propagation of Pressure Waves, Caused by a Thermal Shock, in Liquid Metals Containing Gas Bubbles

Abstract

The propagation of pressure waves caused by a thermal shock in liquid mercury containing micro gas bubbles has been simulated numerically. In the present study, we clarify the influences of the introduced bubble size and void fraction on the absorption of thermal expansion of liquid mercury and attenuation of pressure waves. The mass, momentum and energy conservation equations for both bubbly mixture and gas inside each bubble are solved, in which the bubble dynamics is represented by the Keller equation. The results show that when the initial void fraction is larger than the rate of the thermal expansion of liquid mercury, the pressure rise caused by the thermal expansion decreases with decreasing the bubble radius, because of the increase of the natural frequency of bubbly mixture. On the other hand, as the bubble radius increases, the peak of pressure waves which propagate at the sound speed of mixture decreases gradually due to the dispersion effect of mixture. When the natural frequency of the mixture with large bubbles is lower than that of the thremal shock, the peak pressure at the wall increases because the pressure waves propagate through the mixture at the sound speed of liquid mercury. The comparison of the results with and without heat transfer through the gas liquid interface shows that the pressure waves are attenuated greatly by the thermal damping effect with the decrease of the void fraction which enhances the nonlinearity of bubble oscillation.

Keywords

• cavitation
• bubble dynamics
• thermal shock
• liquid mercury
• numerical analysis