A quantitative comparison of phase-averaged models for bubbly, cavitating flows. (June 2019)

• Record Type: Journal Article
• Authors: Bryngelson, Spencer H.; Schmidmayer, Kevin; Colonius, Tim
• Is Part Of: International journal of multiphase flow. Volume 115(2019)
• Page Start: 137
• Page End: 143
• Publication Date: 2019-06
• Subjects: Multiphase flow -- Periodicals; Écoulement polyphasique -- Périodiques; Multiphase flow; Periodicals; 620.1064
• DOI: 10.1016/j.ijmultiphaseflow.2019.03.028
• Languages: English
• ISSNs: 0301-9322

Abstract

Highlights: First direct comparison of volume- and ensemble-averaging methods for dilute bubbly flows. Convergence study of phase-averaged models. Simulation costs of reference simulations. Conclusions regarding method preferences as they depend upon flow configuration. Abstract: We compare the computational performance of two modeling approaches for the flow of dilute cavitation bubbles in a liquid. The first approach is a deterministic model, for which bubbles are represented in a Lagrangian framework as advected features, each sampled from a distribution of equilibrium bubble sizes. The dynamic coupling to the liquid phase is modeled through local volume averaging. The second approach is stochastic; ensemble-phase averaging is used to derive mixture-averaged equations and field equations for the associated bubble properties are evolved in an Eulerian reference frame. For polydisperse mixtures, the probability density function of the equilibrium bubble radii is discretized and bubble properties are solved for each representative bin. In both cases, the equations are closed by solving Rayleigh–Plesset-like equations for the bubble dynamics as forced by the local or mixture-averaged pressure, respectively. An acoustically excited dilute bubble screen is used as a case study for comparisons. We show that observables of ensemble- and volume-averaged simulations match closely and that their convergence is first order under grid refinement. Guidelines are established for phase-averaged simulations by comparing the computational costs of methods. The primary costs are shown to be associated with stochastic closure; polydisperse ensemble-averaging requires many samples of the underlying PDF and volume-averaging requires repeated, randomized simulations to accurately represent a homogeneous bubble population. The relative sensitivities of these costs to spatial resolution and bubble void fraction are presented.