Analysis of the energy-minimization multiscale model with multiobjective optimization--颗粒学报PARTICUOLOGY

Mo, Y., Du, M., Ge, W., & Zhang, P. (2020). Analysis of the energy-minimization multiscale model with multiobjective optimization. Particuology, 48, 109-115. https://doi.org/10.1016/j.partic.2018.09.004

Analysis of the energy-minimization multiscale model with multiobjective optimization

Yi Mo^a, Mengjie Du ^{b c}, Wei Ge ^{b c *}, Pingwen Zhang ^a *

a School of Mathematical Sciences, Peking University, Beijing 100871, China
b State Key Laboratory of Multi-phase Complex Systems (MPCS), Institute of Processing Engineering (IPE), Chinese Academy of Sciences (CAS), Beijing 100190, China
c School of Chemical Engineering, University of the Chinese Academy of Sciences (UCAS), Beijing 100049, China

10.1016/j.partic.2018.09.004

Volume 48, February 2020, Pages 109-115

Received 11 July 2018, Revised 5 September 2018, Accepted 28 September 2018, Available online 26 February 2019, Version of Record 27 January 2020.

E-mail: wge@ipe.ac.cn; pzhang@pku.edu.cn

Highlights

• Solutions to the multi-objective optimization problem (MOP) in the EMMS model.

• Mathematical and physical meanings of the stability condition in the EMMS model.

• Regime transitions corresponding to the solutions of the MOP.

Abstract

Gas–solid two-phase flow is ubiquitous in nature and many engineering fields, such as chemical engineering, energy, and mining. The closure of its hydrodynamic model is difficult owing to the complex multiscale structure of such flow. To address this problem, the energy-minimization multi-scale (EMMS) model introduces a stability condition that presents a compromise of the different dominant mechanisms involved in the systems, each expressed as an extremum tendency. However, in the physical system, each dominant mechanism should be expressed to a certain extent, and this has been formulated as a multiobjective optimization problem according to the EMMS principle generalized from the EMMS model. The mathematical properties and physical meanings of this multiobjective optimization problem have not yet been explored. This paper presents a numerical solution of this multiobjective optimization problem and discusses the correspondence between the solution characteristics and flow regimes in gas‒solid fluidization. This suggests that, while the most probable flow structures may correspond to the stable states predicted by the EMMS model, the noninferior solutions are in qualitative agreement with the observable flow structures under corresponding conditions. This demonstrates that both the dominant mechanisms and stability condition proposed for the EMMS model are physically reasonable and consistent, suggesting a general approach of describing complex systems with multiple dominant mechanisms.

Graphical abstract

Keywords

Energy-minimization multi-scale model; Multiobjective optimization; Flow regime transition

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