Page 310 - Process Modelling and Simulation With Finite Element Methods

Modeling of Multi-Phase Flow Using the Level Set Method 291

8.3 Curvature Analysis: Methodology

In the present simulations of multi-phase modeling, the coalescence phenomenon
is demonstrated for the various scenarios where the motion of the interface is
significant, particularly at the time of coalescence. The curvature analysis is an
attempt to capture the rupture of the interface during the coalescence event.
In the level set method, the curvature of the interface is represented as
shown in the equation (8.3). The mean value of the curvature can be estimated
by integrating I id over the interface as,

(8.12)

R
Similarly, standard deviation of lid can also be evaluated by first calculating
variance as,

JK%Q*(@=O)
var = ' -(Kmea, )2 (8.13)
jdQ*($=O)
n
The standard deviation, 0 is,

o=G (8.14)

Thus, the first and the second moments of Id can be evaluated at different time
steps to study the behaviour of lid at the time of coalescence. The numerical
results are shown for coalescence, followed by the curvature analysis with the
associated MATLAB m-file script in the next section.

5.4 Results and Discussion

The numerical simulation presented here demonstrates the power of FEMLAB
in the modeling of multi-phase flow. We use multiphysics, the basic versatility of
FEMLAB that enables us to incorporate as many modes (physics) as we wish to
include. The level set method, which requires two application modes:
Incompressible Navier-Stokes and ChEM: Convection and Diffusion modes,
respectively, has been applied extensively here to capture the coalescence of two
drops in a two-phase system. Since the interface can be tracked by setting the
zero level set at the interface, this permits the study of the evolution of the