SESSION 2
FLOW CHARACTERISTICS: MODELLING AND EXPERIMENTS
Chairmen: G.F. Hewitt, D. Stevens
MOTION OF SWARMS OF DROPLETS
I. Wagner, J. Stichlmair Technische Universität München Lehrstuhl A für Verfahrenstechnik Arcisstr. 21, D80333 München Germany Tel.: 00498928916506; Fax: 00498928916510
The motion of a swarm of drops in liquidliquid systems is a fundamental phenomenon in twophase
flow. The prediction of the settling velocity in mixersettler devices, spray columns or
sieve plate towers for heat and mass transfer is of practical importance. Due to this wide scope
the fluiddynamic behavior of twophase droplet flow has been target of countless
investigations. The dispersed phase holdup as well as the flooding point is strongly dependent
on the relative velocity of droplet swarm and continuous phase. It had been demonstrated by
many investigations that the droplet motion in dispersions decreases significantly with holdup
due to interactions between particles, wake effects and enhanced effective velocities.
Fluiddynamic behavior of fixed and fluidized beds of solid particles had been studied
extensively by many researchers and there are numberless models available to predict pressure
drop and bed extension. However due to the more complex behavior of liquidliquid systems
there is still a lack of predictive models to determine the settling velocity by taking into
account the swarm effects. Existing models (Ishii and Zuber 1979, Pilhofer and Mewes 1979,
Kumar and Hartland 1989) are not satisfying with respect to theoretical background, accuracy
and range of validity. In this work we will develop a new, theoretically based model for the
motion of dropletswarms in liquidliquid systems as well as a new way for predicting flooding
rates in countercurrent columns.
Because of the similar behavior of solid and fluid particles, the proceeding is based on the well
known model for rigid particles of Stichlmair et al. 1989 which goes back to the work of
Richardson and Zaki 1954. According to these authors, the ratio of the relative velocity in a
swarm and the terminal velocity of a single particle is a function of the void fraction to the
power of 4.65 for laminar and 2.325 for turbulent flow. Applying this relationship for the solid
particles to any correlation for the terminal velocity of droplets a novel swarm model for fluid
particles is achieved. Using a modified relationship for terminal velocities of single drops based
on the equations of Ishii and Zuber 1979 and Hu and Kintner l955 results in a generalized
correlation for the swann velocity valid for the whole range of Reynolds numbers. This
procedure leads, in comparison to the turbulent flow around solid spheres, to a smaller
dependency of the relative velocity on the holdup for oscillating drops. This finding is in
agreement with other investigations. The equation was developed theoretically without any
adjusted parameter and does reduce to a single drop correlation for very low holdup.
To prove the quality of the new developed model a data base comprising 534 experimental
data points collected from different sources had been assembled. It could be shown that the
model represents the data with an average relative deviation of 15.5 % for Reynolds numbers
in the range of 2.4 · 10^{2} to 2.6 · 10^{3} , including oscillating droplets. The new equation can be
applied to a dispersed phase holdup up to 52.3% which is equal to cubic arranged, dense
packed spheres. At higher holdup deformation of the drops will influence the particle
movement strongly.
The presentation will include all informations on the model development as well as a
comparison with existing models. Additionally, a novel flooding point diagram for countercurrent
operation will be presented.
REFERENCES
 Hu, S. und Kintner, R. C.: AIChE J.1 (1955), 42/48
 Ishii, M., Zuber, N.: AIChE J. 25 (1979), 843/855
 Kumar, A., Hartland, C.: Can. J. Chem. Engng. 67 ( 1989),17/25
 Pilhofer, Th., Mewes, D.: Reprotext, Verlag Chemie, Weinheim, New York,1979
 Richardson, J. F., Zaki, W. N.: Trans. Inst. Chem. Eng. 32 (1954), 32/35
 Stichlmair, J., Bravo, J. L., Fair, J. R.: Gas Sep. Purif. 3 (1989),19/28
THE EFFECT OF EMULSIFICATION ON THE FLOW BEHAVIOUR OF TWO IMMISCIBLE LIQUIDS IN HORIZONTAL PIPES
Dieter Mewes, Martin Nädler and Alexander Tokarz Institut für Verfahrenstechnik, Universität Hannover Callinstr. 36, 30167 Hannover, Germany dms@c36.unihannover.de
Mixtures of water and oil are frequently being transported in pipelines over long distances. For
the design of theses pipelines and the adhering pumping equipment, it is necessary to know in
advance the flow pattern and pressure drop for given volumetric flow rates of the two phases.
In particular, it is known that there is a strong dependence of the pressure drop on the flow
regime present. Due to the turbulent energy dissipation, the formation of dispersions and
emulsions of the immiscible phases is observed over a wide range of volume fractions. The
flow behaviour of these emulsions may significantly defer from the flow behaviour of the single
phases oil and water.
In the present study, the effect of the emulsification on the flow behaviour of oil and water in a
horizontal tube is investigated. The flow rig consists of a horizontal pipe with an inner diameter
of 59 mm the total length of which is 48 m. The liquid phases are fed into the test section in
layers according to their density by a nozzle specifically designed to prevent entrance effects.
By this methods, the observed dispersion downstream are solely due to the momentum transfer
as a result of the flow. The investigated oil is a mineral white oil, the viscosity of which is
varied between 22 and 35 mPas by controlling the temperature of the oil. The pressure drop of
the twophase mixture is measured at two different positions being at an entrance length of
l_{e}/d = 225 and l_{e}/d = 680, respectively.
The results indicate that there is a maximum in the pressure drop for the flow of waterinoil
emulsions at an input water fraction of approximately 10 %. This maximum is above the
pressure drop for the single phase flow of the water as well as of the oil phase. It can partly be
attributed to the rheological behaviour of the emulsions which determine the flow. Within this
region of the water fraction, the emulsions flow in a significantly nonNewtonian manner. The
apparent viscosity of the emulsion is larger than the viscosity of the pure oil even at high shear
rates.
At the point of local phase inversion from the flow of an waterinoil emulsion to the flow of a
layer of a waterinoil dispersion above a layer of pure water, a sharp decrease of the pressure
drop is observed. At an input water fraction of around 40%, a pressure drop minimum is
measured which is in the order of the value for the single phase flow of water. Transition
regions at different input water fractions are observed where phase inversion occurs either
locally within the dispersion layer or in the entire cross sectional area. No significant effect of
the temperature on the flow characteristics is noticed.
A NOTE ON THE LAMINAR COREANNULAR FLOW OF TWO IMMISCIBLE FLUIDS IN A HORIZONTAL TUBE
Sayavur I. Bakhtiyarov*, Dennis A. Siginer** *Space Power Institute, Auburn University Auburn, AL 868495820, USA **Department of Mechanical Engineering, Auburn University Auburn, AL 868495841, USA
ABSTRACT
Most crude oils are high in paraffin and asphaltene content. Deposits of these constituents on
equipment and downhole cause severe problems which hamper and slow down production and
transportation of crude oil. A simple, efficient and economically preferable method to prevent
transportation problems caused by wax and asphaltene deposits on the inner surface of pipelines
is to wet the inside wall with water based surfactants. The water film with surfactant additives
acts as a barrier to prevent oil contact with the inner surface of the wall. If the film is replaced
with a thicker layer, that is, if the water oil ratio is increased, the use of surfactants may not be
required, and the flow of oil may be lubricated by the water layer. Experiments on water
lubricated pipelining show that water in a stratified oilwater flow tends to encapsulate the oil. If
the effects of gravity are negligible, the highviscosity phase is centrally located; that is, the low
viscosity fluid has a strong tendency to migrate to the region of high shear.
An experimental setup based on an optomechanical principle to measure flow velocities is
described in this note. The lubrication of a nonNewtonian liquid by a Newtonian fluid in the
concentrically stratified laminar flow of two immiscible fluids in a horizontal tube is investigated
experimentally and data for the interfacial velocity and the total volume flow rate for two zero
shear rate viscosity ratios are reported. The results thus obtained can be used to validate the
predictions of a theoretical solution to the coreannular flow problem .
