Regularized lattice Boltzmann model for immiscible two-phase flows with power-law rheology

Yan Ba, Ningning Wang, Haihu Liu, Qiang Li, and Guoqiang He
Phys. Rev. E 97, 033307 – Published 13 March 2018

Abstract

In this work, a regularized lattice Boltzmann color-gradient model is developed for the simulation of immiscible two-phase flows with power-law rheology. This model is as simple as the Bhatnagar-Gross-Krook (BGK) color-gradient model except that an additional regularization step is introduced prior to the collision step. In the regularization step, the pseudo-inverse method is adopted as an alternative solution for the nonequilibrium part of the total distribution function, and it can be easily extended to other discrete velocity models no matter whether a forcing term is considered or not. The obtained expressions for the nonequilibrium part are merely related to macroscopic variables and velocity gradients that can be evaluated locally. Several numerical examples, including the single-phase and two-phase layered power-law fluid flows between two parallel plates, and the droplet deformation and breakup in a simple shear flow, are conducted to test the capability and accuracy of the proposed color-gradient model. Results show that the present model is more stable and accurate than the BGK color-gradient model for power-law fluids with a wide range of power-law indices. Compared to its multiple-relaxation-time counterpart, the present model can increase the computing efficiency by around 15%, while keeping the same accuracy and stability. Also, the present model is found to be capable of reasonably predicting the critical capillary number of droplet breakup.

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  • Received 20 November 2017

DOI:https://doi.org/10.1103/PhysRevE.97.033307

©2018 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Yan Ba1, Ningning Wang2, Haihu Liu2,*, Qiang Li1, and Guoqiang He1

  • 1School of Astronautics, Northwestern Polytechnical University, 127 West Youyi Road, Xi'an 710072, China
  • 2School of Energy and Power Engineering, Xi'an Jiaotong University, 28 West Xianning Road, Xi'an 710049, China

  • *haihu.liu@xjtu.edu.cn

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Vol. 97, Iss. 3 — March 2018

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