INTRODUCTION
The process of two-phase flow occurs in a wide variety of
technological applications such as chemical plants, nuclear
reactors, oil and geothermal pipelines and wells, evapora-
tors, and condensers, among others. However, the mecha-
nisms of mass, momentum, and energy transfer through the
two-phase interface are extremely complicated due to the
existence of interfaces and their associated discontinuities
so that solutions via numerical models largely depend on
relevant empirical correlations for a wide range of operat-
ing and design conditions.
558
Valdés-Parada and Espinosa-Paredes
NOMENCLATURE
a
k
,
a
m
,
p
pressure, Pa
d
k
,
d
m
auxiliary vectors defined in Eq. (87)
r
k
position vector that locates any point
for the
k
and
m
phases, Pa
⋅
s/m
in the
k
th phase, m
km
interface area, m
2
r
0
radius of the averaging volume, m
b
j
,
C
j
closure variables, Pa
⋅
s/m (
j
=
m
,
k
)
t
∗
characteristic time, s
B
k
,
B
m
closure variables, dimensionless
t
time, s
A
k
,
A
m
,
T
stress tensor, Pa
D
k
,
D
m
auxiliary tensors defined in Eq. (87)
averaging volume, m
3
for the
k
and
m
phases, dimensionless
V
k
volume of the
k
th phase, m
3
g
gravity vector, m/s
2
v
velocity vector, m/s
g
k
,
g
m
auxiliary vectors defined in Eq. (67)
w
speed of displacement of the surface
for the
k
and
m
phases, Pa
⋅
s/m
vector, m/s
G
k
,
G
m
auxiliary tensors defined in Eq. (67)
x
position vector that locates the centroid
for the
k
and
m
phases, dimensionless
of the averaging volume, m
h
k
,
h
m
auxiliary vectors defined in Eq. (77)
y
k
relative position vector that locates
for the
k
and
m
phases, Pa
⋅
s/m
points in the
k
th phase relative
H
k
,
H
m
auxiliary tensors defined in Eq. (77)
to the centroid of
,
m
for the
k
and
m
phases, dimensionless
Z
m
auxiliary tensor defined in Eq. (55)
I
identity tensor, dimensionless
for the
m
phase, diensionless
K
k
tensor defined in Eq. (35), m