A novel one-way coupled Euler-Lagrangian approach, including bubble-bubble collisions, coalescence and variable bubble radius, was developed in the context of simulating large numbers of cavitating bubbles in complex geometries using direct numerical simulation (DNS) and large-eddy simulation (LES). This dissertation (i) describes the development of the Euler-Lagrangian approach, (ii) outlines the novel bubble coalescence model derived for this approach and (iii) describes simulations performed of bubble migration in a turbulent boundary layer, bubble coalescence in a turbulent pipe flow and cavitation inception in turbulent flow over a cavity.

The coalescence model uses a hard-sphere collision model is used and determines coalescence stochastically. The probability of coalescence is computed from a ratio of coalescence timescales, which are dynamically determined from the simulation. Coalescence in a bubbly, turbulent pipe flow (Re _τ = 1920) in microgravity was simulated with conditions similar to experiments by Colin et al. [1] and excellent agreement of bubble size distribution was obtained. With increasing downstream distance, the number density of bubbles decreases due to coalescence and the average probability of coalescence decreases due to an increase in overall bubble size.

The Euler-Lagrangian approach was used to simulate bubble migration in a turbulent boundary layer (420 < Re_τ < 1800). Simulation parameters were chosen to match Sanders et al. [2], although the Reynolds number of the simulation is lower than the experiment. The simulations show that bubbles disperse away from the wall as observed experimentally. Mean bubble diffusion and profiles of bubble concentration are found to be similar to the passive scalar results, except very near the wall. The carrier-fluid acceleration was found to be the reason for moving the bubbles away from the wall.

The one-way coupled Euler-Lagrangian approach was applied to simulate the experiment of cavitating turbulent flow over a cavity by Liu and Katz [3]. The classical Rayleigh-Plesset equation is integrated using adaptive time-stepping to accurately and efficiently solve for the change of the bubble radius over time. The one-way coupled Euler-Lagrangian model predicts cavitation inception at the trailing edge of the cavity and also in the vortices shed from the leading edge, in qualitative agreement with experiment.