High Order Moment Model for Polydisperse Evaporating Sprays towards Interfacial Geometry Description
| Autor: | Frédérique Laurent, Stéphane de Chaisemartin, Mohamed Essadki, Marc Massot |
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| Rok vydání: | 2018 |
| Předmět: |
Applied Mathematics
Principle of maximum entropy Numerical analysis Eulerian path 02 engineering and technology 01 natural sciences 010305 fluids & plasmas Moment (mathematics) symbols.namesake 020303 mechanical engineering & transports Distribution (mathematics) 0203 mechanical engineering 0103 physical sciences symbols Entropy maximization Statistical physics Convection–diffusion equation Mathematics Variable (mathematics) |
| Zdroj: | SIAM Journal on Applied Mathematics. 78:2003-2027 |
| ISSN: | 1095-712X 0036-1399 |
| DOI: | 10.1137/16m1108364 |
| Popis: | In this paper we propose a new Eulerian modeling and related accurate and robust numerical methods, describing polydisperse evaporating sprays, based on high order moment methods in size. The main novelty of this model is its capacity to describe some geometrical variables of the droplet-gas interface, by analogy with the liquid-gas interface in interfacial flows. For this purpose, we use fractional size-moments, where the size variable is taken as the droplet surface. In order to evaluate the evaporation of the polydisperse spray, we use a smooth reconstruction which maximizes the Shannon entropy. However, the use of fractional moments introduces some theoretical and numerical difficulties, which need to be tackled. First, relying on a study of the moment space, we extend the Maximum Entropy (ME) reconstruction of the size distribution to the case of fractional moments. Then, we propose a new accurate and realizable algorithm to solve the moment evolution due to evaporation, which preserves the structure of the moment space. This algorithm is based on a mathematical analysis of the kinetic evolution due to evaporation, where it shown that the evolution of some negative order fractional moments have to be properly predicted, a peculiarity related to the use of fractional moments. The present model and numerical schemes yield an accurate and stable evaluation of the moment dynamics with minimal number of variables, as well as a minimal computational cost as with the EMSM model, but with the very interesting additional capacity of coupling with diffuse interface model and transport equation of averaged geometrical interface variables, which are essential in oder to describe atomization. |
| Databáze: | OpenAIRE |
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