Basics of Fluid Mechanics, 2014a

13.6. MULTI–PHASE FLOW VARIABLES DEFINITIONS 543
13.5.1.3 Vertical Flow Under Micro Gravity
The above discussion mostly explained the
flow in a vertical configuration when the
surface tension can be neglected. In cases
where the surface tension is very important.
For example, out in space between gas and
liquid (large density difference) the situa-
Liquid Flow Rate
Dispersed
Bubble
Trickling
Flow
Pulsing
Gas Flow Rage
Pulsing &
Bubbling
Spray or
Mist Flow
Dispersed
Bubble
Fig. -13.7. A dimensional vertical flow map
under very low gravity against the gravity.
tion is different. The flow starts as dispersed
bubble (some call it as “gas continuous”)
because the gas phase occupies
most of column. The liquid flows through
a trickle or channeled flow that only partially
wets part of the tube. The interaction
between the phases is minimal and can be
considered as the “open channel flow” of
the vertical configuration. As the gas flow
increases, the liquid becomes more turbulent
and some parts enter into the gas phase as drops. When the flow rate of the gas
increases further, all the gas phase change into tiny drops of liquid and this kind of
regime referred to as mist flow. At a higher rate of liquid flow and a low flow rate of
gas, the regime liquid fills the entire void and the gas is in small bubble and this flow
referred to as bubbly flow. In the medium range of the flow rate of gas and liquid,
there is pulse flow in which liquid is moving in frequent pulses. The common map is
based on dimensionless parameters. Here, it is presented in a dimension form to explain
the trends (see Figure 13.7). In the literature, Figure 13.7 presented in dimensionless
coordinates. The abscissa is a function of combination of Froude ,Reynolds, and Weber
numbers. The ordinate is a combination of flow rate ratio and density ratio.
Flow With The Gravity
As opposed to the flow against gravity, this flow can starts with stratified flow. A
good example for this flow regime is a water fall. The initial part for this flow is more
significant. Since the heavy liquid can be supplied from the “wrong” point/side, the
initial part has a larger section compared to the flow against the gravity flow. After the
flow has settled, the flow continues in a stratified configuration. The transitions between
the flow regimes is similar to stratified flow. However, the points where these transitions
occur are different from the horizontal flow. While this author is not aware of an actual
model, it must be possible to construct a model that connects this configuration with
the stratified flow where the transitions will be dependent on the angle of inclinations.
13.6 Multi–Phase Flow Variables Definitions
Since the gas–liquid system is a specific case of the liquid–liquid system, both will be
united in this discussion. However, for the convenience of the terms “gas and liquid”
will be used to signify the lighter and heavier liquid, respectively. The liquid–liquid (also