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Experimental and Computational Multiphase Flow 2021, 3(1): 21-37 https://doi.org/10.1007/s42757-019-0050-x
Research Article | Issue | Published: 06 March 2020

A coupled immersed interface and level set method for simulation of interfacial flows steered by surface tension

Show Author's Information H. V. R. Mittal1( ),  Rajendra K. Ray1,  Hermes Gadêlha2,  Dhiraj V. Patil3
School of Basic Sciences, Indian Institute of Technology Mandi, P.O. Box 175005, Kamand, Mandi, India
Faculty of Engineering, University of Bristol, Clifton BS8 1UB, United Kingdom
Department of Mechanical Engineering, Indian Institute of Technology Dharwad, Dharwad, Karnataka, 580011, India
Keywords:
immersed interface, level set (LS), surface tension, multiphase, Navier-Stokes equations, shear flows, HOC
Cite this article:
Mittal HVR, Ray RK, Gadêlha H, et al. A coupled immersed interface and level set method for simulation of interfacial flows steered by surface tension. Experimental and Computational Multiphase Flow, 2021, 3(1): 21-37. https://doi.org/10.1007/s42757-019-0050-x
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Abstract Full text About this article

This work presents a methodology to address the problems of bubbles and drops evolving in incompressible, viscous flows due to the effect of surface tension. It is based on the combination of a recently developed immersed interface method to resolve discontinuities, with the level set (LS) method to reproduce the evolving interfaces. The paramount feature of this immersed interface method is the use of Lagrange interpolation enclosing grid points positioned in the vicinity of the interface and few exceptional grid points positioned on the interface. Different problems are considered to assert the accurateness of the proposed methodology, involving both simple and complex interface geometries. Precisely, the following problems are addressed: circular flow with a fixed interface, the dispersion of capillary waves, initially circular, ellipse, star shaped bubbles oscillating to an equilibrium state, and circular drops deforming in shear flows. The transient evolution of bubbles/drops in terms of their shapes, pressure profiles, velocity vectors, deformation ratios of major and minor axis is analyzed to observe the effect of surface tension. The proposed methodology is seen to recover the exact numerical equilibrium between the surface tension and pressure gradient in the vicinity of complex interface geometries as well, while recreating the flow physics with an adequate level of accuracy with well representation of overall trends. Moreover, the numerical results yield a good level of agreement with the reference data.


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About this article

A coupled immersed interface and level set method for simulation of interfacial flows steered by surface tension

Show Author's information H. V. R. Mittal1( ), Rajendra K. Ray1, Hermes Gadêlha2, Dhiraj V. Patil3
School of Basic Sciences, Indian Institute of Technology Mandi, P.O. Box 175005, Kamand, Mandi, India
Faculty of Engineering, University of Bristol, Clifton BS8 1UB, United Kingdom
Department of Mechanical Engineering, Indian Institute of Technology Dharwad, Dharwad, Karnataka, 580011, India

Abstract

This work presents a methodology to address the problems of bubbles and drops evolving in incompressible, viscous flows due to the effect of surface tension. It is based on the combination of a recently developed immersed interface method to resolve discontinuities, with the level set (LS) method to reproduce the evolving interfaces. The paramount feature of this immersed interface method is the use of Lagrange interpolation enclosing grid points positioned in the vicinity of the interface and few exceptional grid points positioned on the interface. Different problems are considered to assert the accurateness of the proposed methodology, involving both simple and complex interface geometries. Precisely, the following problems are addressed: circular flow with a fixed interface, the dispersion of capillary waves, initially circular, ellipse, star shaped bubbles oscillating to an equilibrium state, and circular drops deforming in shear flows. The transient evolution of bubbles/drops in terms of their shapes, pressure profiles, velocity vectors, deformation ratios of major and minor axis is analyzed to observe the effect of surface tension. The proposed methodology is seen to recover the exact numerical equilibrium between the surface tension and pressure gradient in the vicinity of complex interface geometries as well, while recreating the flow physics with an adequate level of accuracy with well representation of overall trends. Moreover, the numerical results yield a good level of agreement with the reference data.

Keywords: immersed interface, level set (LS), surface tension, multiphase, Navier-Stokes equations, shear flows, HOC

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Publication history
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Publication history

Received: 13 July 2019
Revised: 18 September 2019
Accepted: 10 October 2019
Published: 06 March 2020
Issue date: March 2021

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© Tsinghua University Press 2019
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