SCI和EI收录∣中国化工学会会刊

中国化学工程学报 ›› 2022, Vol. 50 ›› Issue (10): 75-84.DOI: 10.1016/j.cjche.2022.05.004

• Fluid Dynamics and Transport Phenomena • 上一篇    下一篇

Exploration on the stability conditions in bubble columns by noncooperative game theory

Jiachen Liu1,2, Xiaoping Guan1, Ning Yang1,2   

  1. 1 State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China;
    2 School of Chemical Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
  • 收稿日期:2022-02-13 修回日期:2022-05-14 出版日期:2022-10-28 发布日期:2023-01-04
  • 通讯作者: Ning Yang,E-mail:nyang@ipe.ac.cn
  • 基金资助:
    The authors acknowledge the long-term support from National Natural Science Foundation of China (21925805, 22178354, 91834303) and the "Transformational Technologies for Clean Energy and Demonstration" Strategic Priority Research Program of the Chinese Academy of Sciences Grant No. XDA21000000. We thank Yifen Mu and Zhixin Liu of Academy of Mathematics and Systems Science, Chinese Academy of Sciences for helpful discussion on game theory.

Exploration on the stability conditions in bubble columns by noncooperative game theory

Jiachen Liu1,2, Xiaoping Guan1, Ning Yang1,2   

  1. 1 State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China;
    2 School of Chemical Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
  • Received:2022-02-13 Revised:2022-05-14 Online:2022-10-28 Published:2023-01-04
  • Contact: Ning Yang,E-mail:nyang@ipe.ac.cn
  • Supported by:
    The authors acknowledge the long-term support from National Natural Science Foundation of China (21925805, 22178354, 91834303) and the "Transformational Technologies for Clean Energy and Demonstration" Strategic Priority Research Program of the Chinese Academy of Sciences Grant No. XDA21000000. We thank Yifen Mu and Zhixin Liu of Academy of Mathematics and Systems Science, Chinese Academy of Sciences for helpful discussion on game theory.

摘要: The energy-minimization multiscale (EMMS) model, originally proposed for gas-solid fluidization, features a stability condition to close the simplified conservation equations. It was put forward to physically reflect the compromise of two dominant mechanisms, i.e., the particle-dominated with minimal potential energy of particles, and the gas-dominated with the least resistance for gas to penetrate through the particle bed. The stability condition was then formulated as the minimization of the ratio of these two physical quantities. Analogously, the EMMS approach was later extended to the gas-liquid flow in bubble columns, termed dual-bubble-size model. It considers the compromise of two dominant mechanisms, i.e., the liquid-dominated regime with small bubbles, and the gas-dominated regime with large bubbles. The stability condition was then formulated as the minimization of the sum of these two physical quantities. Obviously, the two stability conditions were expressed in different manner, though gas-solid and gas-liquid systems bear some analogy. In addition, both the conditions transform the original multi-objective variational problem into a single-objective problem. The mathematical formulation of stability condition remains therefore an open question. This study utilizes noncooperative game theory and noninferior solutions to directly solve the multi-objective variational problem, aiming to explore the different pathways of compromise of dominant mechanisms. The results show that only keeping the single dominant mechanism cannot capture the jump change of gas holdup, which is associated with flow regime transition. Hybrid of dominant mechanisms, noninferior solutions and noncooperative game theory can predict the flow regime transition. However, the game between the two mechanisms makes the two-bubble structure degenerate and reduce to the single-bubble structure. The game of the three mechanisms restores the two-bubble structure. The exploration on the formulation of stability conditions may help to understand the roles and interactions of different dominant mechanisms in the origin of complexity in multiphase flow systems.

关键词: Bubble column, Flow regimes, Mesoscale, Noncooperative game theory

Abstract: The energy-minimization multiscale (EMMS) model, originally proposed for gas-solid fluidization, features a stability condition to close the simplified conservation equations. It was put forward to physically reflect the compromise of two dominant mechanisms, i.e., the particle-dominated with minimal potential energy of particles, and the gas-dominated with the least resistance for gas to penetrate through the particle bed. The stability condition was then formulated as the minimization of the ratio of these two physical quantities. Analogously, the EMMS approach was later extended to the gas-liquid flow in bubble columns, termed dual-bubble-size model. It considers the compromise of two dominant mechanisms, i.e., the liquid-dominated regime with small bubbles, and the gas-dominated regime with large bubbles. The stability condition was then formulated as the minimization of the sum of these two physical quantities. Obviously, the two stability conditions were expressed in different manner, though gas-solid and gas-liquid systems bear some analogy. In addition, both the conditions transform the original multi-objective variational problem into a single-objective problem. The mathematical formulation of stability condition remains therefore an open question. This study utilizes noncooperative game theory and noninferior solutions to directly solve the multi-objective variational problem, aiming to explore the different pathways of compromise of dominant mechanisms. The results show that only keeping the single dominant mechanism cannot capture the jump change of gas holdup, which is associated with flow regime transition. Hybrid of dominant mechanisms, noninferior solutions and noncooperative game theory can predict the flow regime transition. However, the game between the two mechanisms makes the two-bubble structure degenerate and reduce to the single-bubble structure. The game of the three mechanisms restores the two-bubble structure. The exploration on the formulation of stability conditions may help to understand the roles and interactions of different dominant mechanisms in the origin of complexity in multiphase flow systems.

Key words: Bubble column, Flow regimes, Mesoscale, Noncooperative game theory