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A corrected WCSPH scheme with improved interface treatments for the viscous/viscoelastic two-phase flows

Abstract

In this work, a robust corrected weakly compressible smoothed particle hydrodynamics scheme combined with several improved interface treatments (CWCSPH-IT) is proposed to investigate viscous or viscoelastic two-phase flows of high density ratios. The proposed viscoelastic two-phase CWCSPH-IT model is mainly derived from three aspects: (a) a combined elastic stress approximation in the momentum equation based on the weighted idea is proposed; (b) the transition region near the interface of two fluids is regarded as a weak polymer fluid by approximating the relaxation time with a Shepard interpolation which handles the discontinuity of elastic stress near the interface; and (c) a new mixed boundary treatment is proposed to treat the wall boundary in a viscoelastic flow. Moreover, a weighted color gradient scheme is adopted to handle the surface tension near the phase interface, and a particle shifting technique is used to regularize particle distributions and enhance numerical stability. Several two-phase benchmark problems are simulated to test the validity and reliability of the proposed CWCSPH-IT. Subsequently, the proposed particle scheme is adopted to simulate the droplet rising in viscous/viscoelastic matrix fluid with high density ratios. Further, the stable dimple shape of a polymer drop falling in a low-density matrix, and the complex overshooting, oscillation and breakup phenomena of a drop in a high-viscoelasticity shear fluid are numerically investigated. The comparison between the SPH and other reliable reference results demonstrates the ability of the present viscoelastic two-phase scheme in modeling complex viscous or viscoelastic multi-phase problems.

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Acknowledgements

The authors acknowledge the support from the National Natural Science Foundation of China (Grant Nos. 11501495, 51779215, 11672259), the Postdoctoral Science Foundation of China (Grant Nos. 2014M550310, 2015M581869, 2015T80589), the Natural Science Foundation of Jiangsu Province (Grant No. BK20150436), the Jiangsu Government Scholarship for Overseas Studies (Grant No. JS-2017-227) and the Top-notch Academic Programs Project of Jiangsu High Education Institutions (Grant No. PPZY2015B109).

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Correspondence to Tao Jiang.

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We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, and there is no professional or other personal interest of any kind in any product that could be construed as influencing the position presented in the manuscript entitled “A corrected WCSPH scheme with improved interface treatments for the viscous/viscoelastic two-phase flows.” Thank you very much. Sincerely yours, Tao Jiang, Yue Li, Pengnan Sun, Jinlian Ren, Qiang Li, Jinyun Yuan.

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Jiang, T., Li, Y., Sun, PN. et al. A corrected WCSPH scheme with improved interface treatments for the viscous/viscoelastic two-phase flows. Comp. Part. Mech. (2021). https://doi.org/10.1007/s40571-021-00435-9

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Keywords

  • Viscoelastic two-phase flow
  • SPH
  • Kernel gradient correction
  • Overshooting and breakup phenomena
  • Polymer drop rising or falling