Sp. Song et Bq. Li, A hybrid boundary/finite element method for simulating viscous flows and shapes of droplets in electric fields, INT J C FL, 15(4), 2001, pp. 293-308
Citations number
24
Categorie Soggetti
Mechanical Engineering
Journal title
INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS
A mixed boundary element and finite element numerical algorithm for the sim
ultaneous prediction of the electric fields, viscous flow fields, thermal f
ields and surface deformation of electrically conducting droplets in an ele
ctrostatic field is described in this paper. The boundary element method is
used for the computation of the electric potential distribution. This allo
ws the boundary conditions at infinity to be directly incorporated into the
boundary integral formulation, thereby obviating the need for discretizati
on at infinity. The surface deformation is determined by solving the normal
stress balance equation using the weighted residuals method. The fluid flo
w and thermal fields are calculated using the mixed finite element method.
The computational algorithm for the simultaneous prediction of surface defo
rmation and fluid flow involves two iterative loops, one for the electric f
ield and surface deformation and the other for the surface tension driven v
iscous flows. The two loops are coupled through the droplet surface shapes
for viscous fluid flow calculations and viscous stresses for updating the d
roplet shapes. Computing the surface deformation in a separate loop permits
the freedom of applying different types of elements without complicating p
rocedures for the internal flow and thermal calculations. Tests indicate th
at the quadratic, cubic spline and spectral boundary elements all give appr
oximately the same accuracy for free surface calculations; however, the qua
dratic elements are preferred as they are easier to implement and also requ
ire less computing time. Linear elements, however, are less accurate. Numer
ical simulations are carried out for the simultaneous solution of free surf
ace shapes and internal fluid flow and temperature distributions in droplet
s in electric fields under both microgravity and earthbound conditions. Res
ults show that laser heating may induce a non-uniform temperature distribut
ion in the droplets. This non-uniform thermal field results in a variation
of surface tension along the surface of the droplet, which in turn produces
a recirculating fluid flow in the droplet. The viscous stresses cause addi
tional surface deformation by squeezing the surface areas above and below t
he equator plane.