Numerical simulation of spray coalescence in an eulerian framework : direct quadrature method of moments and multi-fluid method

Autor: Marc Massot, Frédérique Laurent, Rodney O. Fox
Přispěvatelé: Department of Chemical and Biological Engineering, Iowa State University (ISU), Laboratoire d'Énergétique Moléculaire et Macroscopique, Combustion (EM2C), CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université Paris Saclay (COmUE), The present research was done thanks to a Young Investigator Award from the French Ministry of Research (New Interfaces of Mathematics - M. Massot, 2003-2006), the support of the French Ministry of Research (Direction of the Technology) in the program: 'Recherche A´eronautique sur le Supersonique' (Project coordinator: M. Massot 2003-2006) and an ANR (National Research Agency - France) Young Investigator Award (M. Massot, 2006-2009). One of the author (R. O. Fox) was partially supported by the U. S. National Science Foundation (CTS-0403864). The present research was conducted during two visits of R.O. Fox in France, supported by Ecole Centrale Paris (Feb.–July 2005 and June 2006), ANR-05-JCJC-0013,jéDYS,jeune équipe 'Dynamique des Sprays en évaporation et en combustion' : modélisation mathématique, simulation numérique et caractérisation expérimentale(2005)
Jazyk: angličtina
Rok vydání: 2008
Předmět:
Physics and Astronomy (miscellaneous)
Population
FOS: Physical sciences
Dirac delta function
[PHYS.MECA.GEME]Physics [physics]/Mechanics [physics]/Mechanical engineering [physics.class-ph]
02 engineering and technology
Physics - Classical Physics
Coalescence
01 natural sciences
010305 fluids & plasmas
Physics::Fluid Dynamics
symbols.namesake
[CHIM.GENI]Chemical Sciences/Chemical engineering
020401 chemical engineering
Quadrature based moment methods
76T10
65M12
0103 physical sciences
FOS: Mathematics
Applied mathematics
Statistical physics
Mathematics - Numerical Analysis
0204 chemical engineering
education
Mathematics
Coalescence (physics)
Numerical Analysis
education.field_of_study
Computer simulation
Applied Mathematics
[SPI.FLUID]Engineering Sciences [physics]/Reactive fluid environment
Direct Quadrature Method of Moments
Multi-fluid Model
Classical Physics (physics.class-ph)
Eulerian path
Numerical Analysis (math.NA)
Solver
MSC 76T10
MSC 65M12
Computer Science Applications
[SPI.MECA.GEME]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanical engineering [physics.class-ph]
Computational Mathematics
Spray Equation
Liquid Sprays
Modeling and Simulation
symbols
Nyström method
Number Density Function
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Zdroj: Journal of Computational Physics
Journal of Computational Physics, Elsevier, 2008, 227 (6), pp.3058-3088. ⟨10.1016/j.jcp.2007.10.028⟩
ISSN: 0021-9991
1090-2716
DOI: 10.1016/j.jcp.2007.10.028⟩
Popis: The scope of the present study is Eulerian modeling and simulation of polydisperse liquid sprays undergoing droplet coalescence and evaporation. The fundamental mathematical description is the Williams spray equation governing the joint number density function f(v,u;x,t) of droplet volume and velocity. Eulerian multi-fluid models have already been rigorously derived from this equation in Laurent et al. [F. Laurent, M. Massot, P. Villedieu, Eulerian multi-fluid modeling for the numerical simulation of coalescence in polydisperse dense liquid sprays, J. Comput. Phys. 194 (2004) 505-543]. The first key feature of the paper is the application of direct quadrature method of moments (DQMOM) introduced by Marchisio and Fox [D.L. Marchisio, R.O. Fox, Solution of population balance equations using the direct quadrature method of moments, J. Aerosol Sci. 36 (2005) 43-73] to the Williams spray equation. Both the multi-fluid method and DQMOM yield systems of Eulerian conservation equations with complicated interaction terms representing coalescence. In order to focus on the difficulties associated with treating size-dependent coalescence and to avoid numerical uncertainty issues associated with two-way coupling, only one-way coupling between the droplets and a given gas velocity field is considered. In order to validate and compare these approaches, the chosen configuration is a self-similar 2D axisymmetrical decelerating nozzle with sprays having various size distributions, ranging from smooth ones up to Dirac delta functions. The second key feature of the paper is a thorough comparison of the two approaches for various test-cases to a reference solution obtained through a classical stochastic Lagrangian solver. Both Eulerian models prove to describe adequately spray coalescence and yield a very interesting alternative to the Lagrangian solver. The third key point of the study is a detailed description of the limitations associated with each method, thus giving criteria for their use as well as for their respective efficiency.
Databáze: OpenAIRE
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