- Momentum transfer in an annular duct with upward gas-Iiquid
flow was studied under the condition that the liquid flowed as a film
only on the inner core of the annulus, the outer wall remaining dry.
Previous workers have studied climbing and falling liquid
films in tubes or on vertical planes. With this type of apparatus
it is very difficult to study pressure losses, gas velocity profiles,
and the structure of the climbing film. The difficulty has been overcome
by forming a liquid film on the inner core and maintaining a
dry outer wall of an annular duct.
The column consists of a three-inch I.D. outer tube with a
concentric one-inch O.D. inner core. The inner tube was supported
laterally by sets of streamlined centering screws. The total length
of the column was about 35 feet and the test section was 20 feet long.
All measurements were made at two stations, the first was 76 inches from the liquid injector, the second 154 inches from the
liquid injector. The liquid injector is a porous stainless steel cylinder
with one inch O.D. and two inch length.
The air flow rates varied from 170 cfm to 410 cfm at 1 atmosphere
pressure and 68° F temperature. The water flow rates
used were 0.47 lbm/min and 0.79 lbm/min.
The study has two major divisions.
First division is the study of the mechanics of the air flow in
the annulus as it is affected by the presence of the climbing film of
liquid. This portion of the study involves an investigation of velocity
profiles, the point of maximum velocity, friction losses, and the
role of capillary waves in the annular flow.
It was found that:
1) the pressure loss for climbing film flow in an annulus can be
predicted by the Lockhart and Martinelli correlation for two-phase
flow in tubes,
2) the capillary waves of the climbing film affect only the location
of the point of maximum air velocity and the air velocity profile at
the inner portion of the annulue,
3) the location of the point of maximum air velocity shuts to the
outer wall as water film is introduced,
4) the air velocity profiles in the inner portion of the annulus with
the film present, plotted as u⁺ versus y⁺, are shifted downward, relative to those for annular flow without the film, although they
have same slope.
The second part is the study of the mechanics of flow of a
climbing water film which has a solid wall as one boundary and
highly turbulent air stream as the other.
The mean film thickness, wave length, and amplitude of the
climbing film were measured by a photographic method. This method
gave good results in the measurement of mean film thickness
at the lower and moderate air velocities. However, the wave length
and amplitude determined by this method have only a qualitative significance,
because of the irregularity of wave shapes. With increasing
air flow rates, the film thickness, wave length, and amplitude
decreased. Generally the ratio of wave length to amplitude varied
between 20 to 30.
As a first approximation, Kapitza's theory of wave formation
in the vertical plane with downward flow, based on laminar conditions,
was extended to the climbing film in an annular duct in order
to obtain an expression for the mean film thickness, the velocity
profile of liquid film, and the wave length. Comparison between the
prediction and the experiment was found to be reasonably good,
The mean film thickness data for climbing film flow in an
annulus was correlated with the Lockhart and Martinelli parameters,
R[subscript L] and X, and was compared with the correlation for climbing film flow in a tube. If a unique correlation for climbing film flow in
both tubes and annuli exists (this is the original proposal of Lockhart
and Martinelli), it would appear that the region in the vicinity
of x = 0.01 is a transition region. More data at high water flow
rates are necessary to reach a general conclusion concerning the