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Two-Size Moment Multi-Fluid Model: A Robust and High-Fidelity Description of Polydisperse Moderately Dense Evaporating Sprays

Part of: Hyperbolic equations and systems Two-phase and multiphase flows Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  05 October 2016

Frédérique Laurent ,
Alaric Sibra  and
François Doisneau
Frédérique Laurent*
Affiliation:
Laboratoire EM2C, CNRS, CentraleSupélec, Université Paris-Saclay, Grande Voie des Vignes, 92295 Châtenay-Malabry cedex, France Fédération de Mathématiques de l'Ecole Centrale Paris, FR CNRS 3487, France
Alaric Sibra*
Affiliation:
Laboratoire EM2C, CNRS, CentraleSupélec, Université Paris-Saclay, Grande Voie des Vignes, 92295 Châtenay-Malabry cedex, France Fédération de Mathématiques de l'Ecole Centrale Paris, FR CNRS 3487, France Département d'Energétique Fondamentale et Appliquée, ONERA, 91120 Palaiseau, France
François Doisneau*
Affiliation:
Laboratoire EM2C, CNRS, CentraleSupélec, Université Paris-Saclay, Grande Voie des Vignes, 92295 Châtenay-Malabry cedex, France Fédération de Mathématiques de l'Ecole Centrale Paris, FR CNRS 3487, France Département d'Energétique Fondamentale et Appliquée, ONERA, 91120 Palaiseau, France
*
*Corresponding author. Email addresses:[email protected] (F. Laurent), [email protected] (A. Sibra, presently at Airbus Defense & Space), [email protected] (F. Doisneau, presently at Sandia National Laboratories)
*Corresponding author. Email addresses:[email protected] (F. Laurent), [email protected] (A. Sibra, presently at Airbus Defense & Space), [email protected] (F. Doisneau, presently at Sandia National Laboratories)
*Corresponding author. Email addresses:[email protected] (F. Laurent), [email protected] (A. Sibra, presently at Airbus Defense & Space), [email protected] (F. Doisneau, presently at Sandia National Laboratories)
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Abstract

High fidelity modeling and simulation of moderately dense sprays at relatively low cost is still a major challenge for many applications. For that purpose, we introduce a new multi-fluid model based on a two-size moment formalism in sections, which are size intervals of discretization. It is derived from a Boltzmann type equation taking into account drag, evaporation and coalescence, which are representative of the complex terms that arise in multi-physics environments. The closure of the model comes from a reconstruction of the distribution. A piecewise affine reconstruction in size is thoroughly analyzed in terms of stability and accuracy, a key point for a high-fidelity and reliable description of the spray. Robust and accurate numerical methods are then developed, ensuring the realizability of the moments. The model and method are proven to describe the spray with a high accuracy in size and size-conditioned variables, resorting to a lower number of sections compared to one size moment methods. Moreover, robustness is ensured with efficient and tractable algorithms despite the numerous couplings and various algebra thanks to a tailored overall strategy. This strategy is successfully tested on a difficult 2D unsteady case, which proves the efficiency of the modeling and numerical choices.

Keywords

Polydisperse spraysmoment methodsmulti-fluidevaporationcoalescence

MSC classification

Secondary: 35L03: Initial value problems for first-order hyperbolic equations 65M08: Finite volume methods 65M12: Stability and convergence of numerical methods 76T10: Liquid-gas two-phase flows, bubbly flows
Type
Research Article
Information
Communications in Computational Physics , Volume 20 , Issue 4 , October 2016 , pp. 902 - 943
Copyright
Copyright © Global-Science Press 2016 

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