Page 322 - Process Modelling and Simulation With Finite Element Methods

Modeling of Multi-Phase Flow Using the Level Set Method 309

8.4.4 Multi-body coalescence

The coalescence between three drops is simulated assuming the symmetry of the
domain. Hence, only half of the domain is simulated in the present case defining
one boundary as an axis of symmetry.
The above system brings out the effect of horizontal offset amongst
interacting drops. In the present case, centers of drops are more than one radius
apart from each other. Two drops are initiated using following initial condition,
@(t = 0) = min(4- - 0.5, min((4 - y),J(x -0.75)* + (y -l)* - 0.5)) (8.17)

Above initial condition generates two uniform sized drops of radius 0.5 whose
centers are separated by a distance equal to 0.75. The present simulation is
similar to earlier one where two drops are traveling towards each other except
the horizontal offset. Hence, there is no other change in the formulation of the
problem than the initial condition. The contour plot of level set function at @ =
0, surface plot and arrows of velocity field are represented in Figure 8.8.

d
35
3
25
2
15
1
05
0
-2 -1 0 1 2 3 4

Mar 033
4 03
02
35
01
3
0
25
01
2
02
15
03
1
04
05
05
0 06
2 1 0 1 2 3 4 MnaM7
Figure 8.8 Contour plot of 4 with velocity field at different time steps for three-body coalescence.
The interaction between drops with horizontal offset is found to be very different
from that without offset. The velocity field of the lower drop is found to be
diverted due to the influence of the velocity field of upper drop that is traveling