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Kinetic modeling of multiphase flow based on simplified Enskog equation

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Abstract

A new kinetic model for multiphase flow was presented under the framework of the discrete Boltzmann method (DBM). Significantly different from the previous DBM, a bottom-up approach was adopted in this model. The effects of molecular size and repulsion potential were described by the Enskog collision model; the attraction potential was obtained through the mean-field approximation method. The molecular interactions, which result in the non-ideal equation of state and surface tension, were directly introduced as an external force term. Several typical benchmark problems, including Couette flow, two-phase coexistence curve, the Laplace law, phase separation, and the collision of two droplets, were simulated to verify the model. Especially, for two types of droplet collisions, the strengths of two non-equilibrium effects, \(\bar{D}^{\ast}_{2}\) and \(\bar{D}^{\ast}_{3}\), defined through the second and third order non-conserved kinetic moments of (f − feq), are comparatively investigated, where f (feq) is the (equilibrium) distribution function. It is interesting to find that during the collision process, \(\bar{D}^{\ast}_{2}\) is always significantly larger than \(\bar{D}^{\ast}_{3},\bar{D}^{\ast}_{2}\) can be used to identify the different stages of the collision process and to distinguish different types of collisions. The modeling method can be directly extended to a higher-order model for the case where the non-equilibrium effect is strong, and the linear constitutive law of viscous stress is no longer valid.

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Acknowledgements

Many thanks to the anonymous referees for their helpful comments and suggestions. This work was supported by the China Postdoctoral Science Foundation Grant No. 2019M662521, the National Natural Science Foundation of China under Grant No. 11772064, CAEP Foundation (Grant No. CX2019033), and the Opening Project of State Key Laboratory of Explosion Science and Technology (Beijing Institute of Technology) under Grant No. KFJJ19-01 M.

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Authors and Affiliations

  1. School of Mechanics and Safety Engineering, Zhengzhou University, Zhengzhou, 450001, China

    Yu-Dong Zhang, Jing-Jiang Qiu, Hong-Tao Wei & Zung-Hang Wei

  2. Institute of Applied Physics and Computational Mathematics, Laboratory of Computational Physics, P. O. Box 8009-26, Beijing, 100088, China

    Ai-Guo Xu

  3. Center for Applied Physics and Technology, MOE Key Center for High Energy Density Physics Simulations, College of Engineering, Peking University, Beijing, 100871, China

    Ai-Guo Xu

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  1. Yu-Dong Zhang
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Correspondence to Ai-Guo Xu or Zung-Hang Wei.

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Zhang, YD., Xu, AG., Qiu, JJ. et al. Kinetic modeling of multiphase flow based on simplified Enskog equation. Front. Phys. 15, 62503 (2020). https://doi.org/10.1007/s11467-020-1014-0

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