A Computational Study of the Inertial Collapse of Gas Bubbles Near a Rigid Surface

Abstract

Cavitation research is essential to a variety of applications ranging from naval hydrodynamics to medicine and energy sciences. Vapor cavities can grow from sub-micron-sized nuclei to millimeter-sized bubbles, and collapse violently in an inertial fashion. This implosion, which concentrates energy into a small volume, can produce high pressures and temperatures, generate strong shock waves, and even emit visible light. One of the main consequences of cavitation is structural damage to neighboring surfaces due to bubble collapse.

The propagation of shock and rarefaction waves in a multiphase medium results in a complicated multiscale and multiphysics problem. Laboratory experiments of such flows are challenging due to the wide range of spatial and temporal scales, difficult optical access, and limitations of measurement devices. To better understand these flows, we use highly resolved numerical simulations of the inertial collapse of individual vapor bubbles near a rigid surface. For this purpose, we developed a novel numerical multiphase model combined with high-performance computing techniques to perform accurate and efficient simulations of the three-dimensional compressible Navier-Stokes equations for a binary, gas-liquid system. We present the detailed dynamics of the Rayleigh collapse of a single vapor bubble near a rigid wall for different geometrical configurations and driving pressures. We explain that the presence of a rigid boundary breaks the symmetry of the collapse and hinders the energy concentration. As a result, a liquid re-entrant jet directed toward the wall forms, ultimately giving rise to lower pressure and temperatures produced upon collapse. We characterize the collapse non-sphericity, and show that this quantity, which strongly depends on the initial stand-off distance of the bubble from the wall, significantly affects the overall dynamics. We further show that bubbles initially close to the wall or attached to the surface are responsible not only for the high pressure loads along the wall, but also the elevated temperatures on the solid surface. In fact, for certain soft materials, instantaneous temperatures greater than the melting point may be achieved on the surface, thus confirming that thermal damage is a potential threat to such materials exposed to cavitating flows. Furthermore, the development of scalings for important collapse properties (jet velocity, shock pressure, wall pressures/temperatures), in terms of the initial stand-off distance and driving pressure, not only illustrates universality of non-spherical bubble dynamics but also provides means to predict these phenomena.

Since real flows involve many bubbles, we also investigate the inertial collapse of a pair of vapor bubbles near a rigid surface. We explain that the presence of a second bubble in the vicinity of the original (primary) bubble leads to far more complicated dynamics and completely changes the single-bubble scalings. Strong interactions between the bubbles and the boundary drastically increase the collapse non-sphericity and amplify/hinder the pressures and temperatures produced by the collapse. Our simulations show that the re-entrant jets in both bubbles form at distorted angles, and for certain configurations, ``double jetting'', occurs, in which two jets penetrate the primary bubble. The results indicate that bubble-bubble interactions and their effects on collapse dynamics near a wall are non-negligible. Furthermore, given the complexity of even this simple problem and the large number of parameters, the value of extending such high-resolution simulations to develop scalings for the collapse of many bubbles is debatable at the present time; it may be worth considering alternative modeling approaches.