Page 306 - Process Modelling and Simulation With Finite Element Methods

Chapter 8

MODELING OF MULTI-PHASE FLOW USING THE
LEVEL SET METHOD

K. B. DESHPANDE and W.B.J. ZIMMERMAN
Department of Chemical and Process Engineering, University of Sheffield,
Newcastle Street, Sheffield Sl 3JD United Kingdom
E-mail: w.zimmemzan@sheJ:ac.uk

Multiphysics, the feature of FEMLAB that allows coupling of different types of physics,
is demonstrated in this chapter for the level set method for modeling multiphase flow,
illustrating various scenarios for the coalescence of drops. In the level set method for
biphasic fluid systems, one fluid has strictly positive phase function @, the other strictly
negative @, so the interface is tracked by the zero level set of @. The transport of @ is
computed by solving an advection-diffusion equation for @ and the incompressible
Navier-Stokes equations simultaneously. The level set method is extensively applied here
to study the coalescence of drops in biphasic flows for different configurations such as
drops under influence of gravity, an acoustically suspended drop, drops approaching one
another and the interaction among three drops. The curvature analysis here shows the
power of FEMLAB’s post integration tools for statistical analysis of evolving fields,
capturing the occurrence of coalescence by a distinguished feature - cusp formation.

8.1 Introduction

Multiphase flows are often difficult to model computationally, especially
because of the difficulty in tracking the fluid-fluid interface. Furthermore, there
is a steep change in physical properties such as density, viscosity etc., which
makes the computation yet more stiff. There are various computational methods
available to solve incompressible two-phase problems such as the front tracking
method [l], the boundary integral method [2], the volume of fluid method [3],
the Lattice Boltzmann method [4], diffuse interface modeling [5], and the level
set method [6][11]. We use the level set method in this chapter, illustrating its
use to compute the coalescence of two drops.
All the above mentioned methods have their advantages and disadvantages.
In the front tracking method, marker particles are explicitly introduced to keep
track of the front that reduces the resolution needed to maintain the accuracy.
However, re-gridding algorithms should be employed with front tracking method
to prevent marker particles from coming together, especially at the points of
larger curvature.
The volume of fluid method (VOF) is based on discretization of the volume
fraction of one of the fluids. The motion of the interface is captured by solving a

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