Towards Numerical Simulation of Cavitating Flows in Complex Geometries

This paper discusses our efforts to simulate large systems of bubbles in complex geometries, with specific application to modeling cavitation instabilities. An important unstable regime is the transition from sheet-to-cloud cavitation (SCC). Experiments performed by Callenaere et al. (2001) highlight the unsteady flow structures of SCC, which is characterized by unstable regions of vapor bubbles that suddenly appear near the leading edge of a hydrofoil. These bubble “clouds” violently collapse as the free-stream pressure increases downstream of inception. This collapse leads to unsteady loading and emanates intense acoustic waves. Also, experiments by Ceccio (personal communication) will investigate drag reduction in marine applications by injecting an air jet from the face of a backward-facing step. The air jet is more stable and therefore considered more effective at drag reduction than a layer of micro-bubbles. This paper investigates two methods to simulate and predict such flows: I. a one-way coupled Lagrangian bubble model and II. the force coupling method (Lomholt et al., 2002), which is extended to account for bubble volume variation. In both methods, the bubble dynamics are governed by the Rayleigh-Plesset (RP) equation, which is integrated in time using a fourthorder accurate Runge-Kutta solver (RK4) with adaptive time stepping. The bubble models are coupled with a robust, unstructured, DNS carrier phase solver. This paper describes our numerical approaches and compares results between one-way and two-way coupling in channel flows.