Numerical study of explosion bubbles with phase changes in a four-phase system including non-condensable gases

Abstract

This study numerically investigates the complex dynamics of compressible four-phase flows induced by underwater bubble explosions near a free surface. To address this challenge, a numerical scheme for compressible four-phase flows, comprising liquid, vapor, and two non-condensable gas phases, has been developed. The governing equations consist of seven conservation equations for mass, momentum, and energy, coupled with three additional transport equations for the vapor and non-condensable gases. These equations are solved using a modified high-order, monotonicity-preserving, implicit, interface-capturing scheme. The solution is validated against experimental data for a single vapor-carbon dioxide bubble explosion, demonstrating the ability to accurately capture sharp interfaces, liquid jet formation, rebound, and chaotic breakup. Following validation, two four-phase flow problems are examined to study the influence of non-condensable gases on bubble collapse dynamics and free surface response. The first investigates how gas phases inside the bubble and in the surrounding medium affect condensation behavior. Increasing the gas fraction inside the bubble from 10 % to 80 % reduces the condensation rate by up to 60 %, while increasing the dissolved gas fraction from 1 % to 30 % decreases it by nearly 50 %. The second problem analyzes the explosion dynamics of three vertically aligned gas-mixture bubbles beneath the free surface. Bubbles with higher carbon dioxide content transfer less energy to the water, resulting in lower jet heights, while air-rich bubbles generate higher jets. Across mixtures with carbon dioxide and air fractions ranging from 0 % to 50 %, air-rich bubbles produce water jets at least 1.3 times higher than carbon dioxide-dominated bubbles.