Temperatures produced by inertially collapsing bubbles near rigid surfaces

Abstract

The dynamics of bubbles inertially collapsing in water near solid objects have been the subject of numerous studies in the context of cavitation erosion. While non-spherical bubble collapse, re-entrant jet dynamics and emitted shock waves have received significant interest, less is known about the temperatures thereby produced and their possible connection to damage. In this article, we use highly resolved numerical simulations of a single bubble inertially collapsing near a rigid surface to measure the temperatures produced in the fluid and estimate those in the solid, as well as to identify the responsible mechanisms. In particular, we find that elevated temperatures along the wall can be produced by one of two mechanisms, depending on the initial stand-off distance of the bubble from the wall and the driving pressure: for bubbles initially far from the wall, the shock generated by the bubble collapse is the source of the high temperature, while bubbles starting initially closer migrate towards the wall and eventually come into contact with it. A scaling is introduced to describe the maximum fluid temperature along the wall as a function of the initial stand-off distance and driving pressure. To predict the temperature of the solid, we develop a semianalytical heat transfer model, which supports recent experimental observations that elevated temperatures achieved during collapse could play a role in cavitation damage to soft heat-sensitive materials.

An assessment of multicomponent flow models and interface capturing schemes for spherical bubble dynamics

“…This problem can be averted via the thermodynamically consistent model of Kapila et al [2] [20,21], which includes a term (K∇ · u) in the volume-fraction evolution equation to represent compressibility in mixture regions. Unfortunately, this additional term leads to numerical instabilities during strong compression and expansion near the interface [3,22]. Instead, we propose using a pressure-disequilibrium model [3], which relaxes the phase-specific pressures algorithmically at each time step, and averts the stability issues of the K∇ · u term.…”

“…equation model of Allaire et al [1] is unable to accurately represent a spherical bubble collapse and demonstrated how the additional K∇ · u term introduced by Kapila et al[2] is required to ensure good agreement with the Keller-Miksis solution[54]. Since the 5-equation model with K∇ · u is known to produce instabilities in some numerical experiments[3,22], we investigated the 6-equation pressure-disequilibrium model as a potential surrogate. We observed good agreement between these models for challenging test problems, including a 1D water-air shock tube, a 1D vacuum developing in a water-air mixture, and the collapse of a 3D spherical bubble.…”

A smoothed particle hydrodynamics study of the collapse for a cylindrical cavity

“…with C = 10 −4 , γ = 9 and σ equal to the initial particle spacing. The initial radius of the cavity is R 0 = 100μm (typical radius of a collapsing cavity [26,59]). The ratio R C /R 0 = 30 is used as a compromise between computational cost and accuracy.…”

“…However, this work focuses only on the bubble collapse (as usual in computer simulations of cavitation e.g. [7,26,59]) and the rebound phase is not considered.…”

Thermodynamic effect of single bubble near a rigid wall

“…Although Boundary Element Method (BEM) [15] , Smooth Particle Hydrodynamics (SPH) [16] , and Lattice Boltzmann Method (LBM) [17] have been applied in simulating bubble dynamics, the numerical simulation of investigating single bubble thermodynamics is a typical compressible problem, mainstreamedly realized by coupled solving the compressible Naiver-Stokes equations (N-S equation), phase equation, and interface capture model (like VOF and LS) [18] . Beig et al [19] applied the compressible N-S equation to simulate a single bubble inertially collapsing near a rigid surface to measure the temperatures produced in the fluid. And they found that elevated temperatures along the wall can be produced by one of two factors, depending on the initial standoff distance of the bubble from the wall and the driving pressure.…”