M.S. Thesis Presentation by Roman Blancher
Wednesday, April 10, 2002

(Dr. Damir Juric, advisor)

"Numerical Simulation of High Speed Droplet Collision"

Abstract
    The main objective of this project is to numerically simulate high
speed head-on droplet collision with several different codes. This type
of multi-fluid system is influenced by numerous parameters and phenomena
such as interface rupture and fusion, which can be difficult to
simulate, especially at high speed.
    The governing equations of this incompressible multiphase flow are
solved for the both phases on the whole domain with a front
tracking/finite difference technique. The drops are accelerated towards
each other by a body force. To compute the movement of the interface,
the Marker-and-Cell method is used with a level contour reconstruction
method which takes in to  account the surface tension. The interface is
represented by elements advected in a Lagrangian fashion and physically
linked.
    The original code used a centered second-order in space and explicit
first-order in time scheme. Although collision simulations are
consistent with experimental observations at average and low speed, an
important number of parameters limit the numerical simulations of high
speed collisions using this code.
    Thus, different numerical schemes : second-order in time, upwind,
Roe and MacCormack have been developed here to compute the advection and
diffusion term. Both staggered and colocated grids have been used and
compared to find which code has the best behavior with high Reynolds
number. The influence of other important parameters such as Laplace
number, Weber number and grid size has been studied for all the codes.
    A significant improvement has been found by using the Roe or the
second-order in time for high speed collisions.