Lagrangian Point Force regularization for dispersed two-phase flows

International audienceThe present paper presents a regularization procedure of the Lagrangian point-particle approach for the simulation of dispersed two-phase flows in a statistical framework. The aim is to regularize the probability presence of a particle, written as a Dirac delta function centered on the particle position in the standard formulation, by a Gaussian like distribution. The associated regularization length scale is obtained by solving additional transport equations in the Lagrangian framework. The regularization itself is then achieved by solving two non-linear diffusion equations. The first diffusion equations allows to spread the field of spatially varying diffusion coefficients required for regularization over the computational mesh. Once this field is defined, regularization of the Lagrangian fields to be projected on the Eulerian grid such as particle density, particle velocity, etc... is performed. These ideas are then tested on simplified one-dimensional test cases. While preliminary results seem encouraging as the dispersed phase fields projected on the Eulerian grid appear much less sensitive to the initial sampling of the spray, further tests on more realistic test cases are necessary to conclude on precision gains with repect to the additional computational expense resulting from the regularization procedure

Conditional moment methods for polydisperse cavitating flows

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.Comment: 19 pages, 9 figures, submitted to J. Comp. Phy

A Gaussian moment method and its augmentation via LSTM recurrent neural networks for the statistics of cavitating bubble populations

Phase-averaged dilute bubbly flow models require high-order statistical moments of the bubble population. The method of classes, which directly evolve bins of bubbles in the probability space, are accurate but computationally expensive. Moment-based methods based upon a Gaussian closure present an opportunity to accelerate this approach, particularly when the bubble size distributions are broad (polydisperse). For linear bubble dynamics a Gaussian closure is exact, but for bubbles undergoing large and nonlinear oscillations, it results in a large error from misrepresented higher-order moments. Long short-term memory recurrent neural networks, trained on Monte Carlo truth data, are proposed to improve these model predictions. The networks are used to correct the low-order moment evolution equations and improve prediction of higher-order moments based upon the low-order ones. Results show that the networks can reduce model errors to less than 1% of their unaugmented values