Conditional moment methods for polydisperse cavitating flows

TL;DR

This paper introduces a computational model using conditional quadrature-based moment methods to efficiently simulate the effects of polydisperse cavitating bubbles on flow dynamics, enabling larger scale and more accurate flow predictions.

Contribution

It adapts QBMMs to solve a population balance equation for bubble dynamics, improving efficiency and accuracy in modeling cavitating flows.

Findings

CHyQMOM reduces computational costs by ten times.

The model accurately predicts bubble statistics in flow simulations.

Implementation in MFC enables practical large-scale flow analysis.

Abstract

The dynamics of cavitation bubbles are important in many flows, but their small sizes and high number densities often preclude direct numerical simulation. We present a computational model that averages their effect on the flow over larger spatiotemporal scales. The model is based on solving a generalized population balance equation (PBE) for nonlinear bubble dynamics and explicitly represents the evolving probability density of bubble radii and radial velocities. Conditional quadrature-based moment methods (QBMMs) are adapted to solve this PBE. A one-way-coupled bubble dynamics problem demonstrates the efficacy of different QBMMs for the evolving bubble statistics. Results show that enforcing hyperbolicity during moment inversion (CHyQMOM) provides comparable model-form accuracy to the traditional conditional method of moments and decreases computational costs by about ten times for a broad range of test cases. The CHyQMOM-based computational model is implemented in MFC, an open-source multi-phase and high-order-accurate flow solver. We assess the effect of the model and its parameters on a two-way coupled bubble screen flow problem.