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Accueil > Actualités > Séminaires > Séminaires 2018

Lundi 4 juin 2018 à 15h00 en amphi K118

Alberto Passalacqua, associate professor, Université of Iowa.

Titre/Title : Quadrature-based moment methods for polydisperse gas-liquid flows

Contact : Martin Obligado (Equipe EDT)

Résumé/Abstract :
Disperse gas-liquid flows, often encountered in industrial, environmental, and biochemical systems, are characterized by the presence of bubbles with different sizes (polydispersity) and with different velocities (polycelerity), with both size and velocity evolving in space and time.
The aspect of polydispersity and the evolution of the bubble size distribution has been often addressed by solving a population balance equation (PBE) on top of a two-fluid model (Sanyal et al., 2005, 1999) using the mean gas velocity for all the bubbles in a computational cell, neglecting the local effect of polycelerity. A more refined approach, which accounts for polycelerity, consists in solving for one momentum equation for each bubble size, leading, however, to a higher computational cost.
In this talk, a quadrature-based moment method for the simulation of polydisperse bubbly flow is presented and its implementation into OpenFOAM® as part of the OpenQBMM project (OpenQBMM, 2017 ; Passalacqua et al., 2017) is discussed. The proposed approach aims at accounting for both polydispersity and polycelerity, while limiting the computational cost by leveraging the fact that the Stokes number of the disperse gas phase is low. This allows the bubble phase to be assumed mono-kinetic. Because of this assumption, only the first-order velocity moments are considered, while p moments in size are transported. In order to ensure the boundedness of the numerical solution, and to allow a simple integration of the proposed approach in existing Euler-Euler codes, the moment method is formulated as a function of the mean gas-phase velocity, and of the deviation of the bubble size velocity from the mean. Key element of the algorithm is the treatment of the moment advection term, which is split into two stages. First, moments of the disperse phase are advected with respect to the deviation velocity with respect to the mean using kinetic fluxes. Then, a continuity and momentum equation for the disperse phase, like those used in traditional two-fluid solvers are solved and coupled to the equations for the liquid phase. These equations are solved with an iterative procedure (Spalding, 1980), supplemented by a bounded scheme based on the Multi-dimensional Universal Limiter for Explicit Solution (MULES) (Weller, 2006) for the volume fraction. Notable difference, with respect to the traditional two-fluid model is the definition of the momentum exchange term, which is function of the bubble size distribution in the proposed approach, while it relies on a mean bubble size diameter in the traditional two-fluid model. Once the updated mean volume fraction and mean velocity are found, size and joint size-velocity moments are updated because of the mean transport. The effect of the force term on velocity moments is included by directly integrating the ordinary differential equation for the velocity abscissae, as discussed in Fox (2008).
The proposed numerical approach was tested considering two bubble columns studied in the literature. A mono-disperse case (Pfleger et al., 1999) was used to verify the approach in the limit case of monodisperse bubbles, to ensure the solution reproduces the results of the equivalent two-fluid model. Results are in agreement with the predictions of the two-fluid model implementation available in OpenFOAM. A polydisperse case (Díaz et al., 2008) was also considered, obtaining results in agreement with their experimental data for what concerns the gas mean axial velocity and hold-up.
Alberto Passalacqua is the recipient of the Jean d’Alembert junior research fellowship at Université Paris-Saclay. He is associate professor of Mechanical Engineering at Iowa State University, with a courtesy appointment in Chemical and Biological Engineering. He is team leader for device scale numerical simulation in the Center for Multiphase Flow Research and Education (CoMFRE) at Iowa State University, and the lead developer of OpenQBMM, the first open-source implementation of quadrature-based moment methods into OpenFOAM. He was recipient of the American Chemical Society – Petroleum Research Fund Doctoral New Investigator award. His research, funded by the US National Science Foundation and by the US Department of Energy, focuses on the development, implementation and validation of meso- and macro-scale computational models for reacting multiphase flows.
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Yuan, C., Kong, B., Passalacqua, A., Fox, R.O., 2014. An extended quadrature-based mass-velocity moment model for polydisperse bubbly flows. The Canadian Journal of Chemical Engineering 92, 2053–2066. doi:10.1002/cjce.22006