Page 320 - Process Modelling and Simulation With Finite Element Methods

Modeling of Multi-Phase Flow Using the Level Set Method 307

8.4.3 Coalescence between two drops approaching each other

The coalescence between two drops approaching each other in opposing
directions can be achieved by defining a driving force that attracts two drops to
each other. This can be simulated by incorporating a driving force term in sub-
domain settings for Incompressible Navier-Stoke application mode.

Subdomain Mode
Select Incompressible N-S from Multiphysics Menu
Select the Coefficient tab
Set Fy = sigma*kappa*smdelta*phiy + ro*gy*tanh(-(y-yc))
Apply/OK

The new constant used ye is a midpoint of the line of centres of two drops and
set to 1.5. The force term defined in this manner applies force equal to pg when
(y-yc) < 0 and -pg when (y-yc)>O. Thus, upper and lower drop experiences
exactly equal force but in the opposite direction.
Computational results are represented in terms of a contour plot of the level
set function where @ =0, a surface plot for pressure field and arrows for velocity
field as shown in Figure 8.3. Two drops separated by a distance equal to two
times their diameter attract to each other, ultimately resulting in coalescence at
time t=2 sec. Cusp formation has been clearly brought out at that time step. The
coalesced drop regains its original shape at later time steps. The important
feature of this simulation is that symmetry is observed at the midplane between
the two drops.
The velocity field is also found to be symmetrical for both the drops which
retains after the coalescence event as well. Another important feature is that both
the drops are identical in their shape and size. This can be explained on the basis
of a surface plot of pressure that is found to be symmetrical around the midplane
between the two drops. Since the two drops experience same pressure force,
they follow the same change in radii of curvature. Also, less droplet deformation
is observed for the present simulation as compared to the earlier two cases. This
can also be attributed to lower magnitude of the pressure force.
Curvature Analysis

The curvature analysis performed for two drops approaching one another is
shown in Figure 8.7. The peak in standard deviation and mean value of Ild is
confirmed at the time of the coalescence. No other spikes were observed for the
present simulation because the deformation of the drops was found to be smaller
than that in the earlier two cases considered. Thus, it can be concluded that peaks
observed in the mean and standard deviation value of Ild are indeed due to the
rupture of the interface.