SESSION 3
FLOW PHENOMENA IN TWO-FLUID SYSTEMS
Chairmen: J. Kubie, A. Valle
ANALYSIS OF DROP SIZE SPECIFIC COALESCENCERATES BASED ON BIVARIATE DROP SIZE / DROP CONCENTRATION MEASUREMENTS
Volkhard Köhler, Martin Vorbach, Christian Weiß, and Rolf Marr
Institute of Chemical Engineering and Environmental Technology
Graz University of Technology, A-8010 Graz, Austria
INTRODUCTION
The behaviour of droplet swarms in liquid-liquid dispersions, especially found in extraction
columns of the RDC-type, was analysed by means of a new fluorescence measurement
technique, which represents an extension to the capillary suction method (Pilhofer and
Miller, 1972). The measuring principle developed gains profit of the detectable emission
light intensity of a fluorescent dye even in trace concentration. An addition of this
nontransferring dye to the dispersed phase enables the in-situ determination of bivariate
drop size / drop concentration distributions, which provides important information on
droplet history for the evaluation of coalescence and break-up rates. Furthermore, the
measuring method represents a new approach for the measurement of droplet size
dependent residence times in extraction columns.
MEASUREMENT PRINCIPLE
A small volume of the droplet dispersion is continuously sampled through a glass capillary
tube on which an optical device is mounted. With the help of two light beams crossing the
capillary perpendicularly to the probe axis tracer concentration in the drops, droplet volume
and suction velocity is measured simultaneously. The determination of drop-concentration
is based on the fluorescence intensity measurement of a nontransferring fluorescent dye
within the drop. A light beam of a specific wavelength is exciting the tracer to emit a
concentration-proportional light signal. The measurement and storage of the signal height is
realised by transforming the fluorescence light intensity signal to an electrical signal by
means of a photomultiplier.
The transmission light intensity of the excitation light beam shows series of rectangular
pulses caused by the difference of the refractive index between the continuous and the
dispersed phase slugs. Time-of-passage of a drop is detected from the width of the
corresponding rectangular pulse. A transmission light beam located 2 mm appart from the
first one produces a second pulse signal. The time shift between both signals allows the
calculation of the suction velocity and in combination with the time-of-passage of the drop
the droplet volume.
ANALYSIS OF DROP SIZE SPECIFIC COALESCENCERATES
Pilot-sized column experiments were conducted in an extraction column of the RDC-type.
The organic inlet stream (kerosine) was split into two streams of equal flow rates, one
supplied with the fluorescent dye. The intensity of the drop concentration equalization
process within the droplet swarm along the column height is a function of the drop
interaction rates. Measurements of the bivariate drop size / drop concentration distributions
along the column height at steady-state operation enables an extension of the experimental
data for the testing of different rate-formulations for drop coalescence by means of a
hydrodynamic model. The model developed here is a discrete, stochastic model based on
the Drop Population Balance and allows the simulation of drop size and drop tracer
distributions along the column height. With the help of a Dynamic Process Simulation tool
the estimation of drop size specific coalescence rates is possible.
MEASUREMENTSOF DROP SIZE SPECIFIC RECIDENCE TIMES
The ability to measure two independent characteristics for each droplet in combination with
a nontransferring tracer enables the determination of drop size specific recidence times.
These times were determined for the case of an extraction process without mass transfer,
i.e. coalescence and break-up can be neglected, as proved by measurements described
above. Feeding the column with dispersed phase droplets of different size classes and
producing a step input function concerning the concentration of the droplets, the response
concentration function of each droplet class, measured at the top of the column, leads to a
mean residence time for droplets of this size. Drop size specific dispersion intensity was
analysed too.
AN EXPERIMENTAL STUDY ON THE INTERACTION BETWEEN AN IMMISCIBLE DROPLET AND A LIQUID TAYLOR-VORTEX FLOW
Y. Hagiwara, T. None, M. Nakamura, M. Tanaka and H. Hana
Dept. of Mechanical and System Eng., Kyoto Institute of Technology
Matsugasaki, Kyoto 606, Japan
This study aims at understanding the interaction between a vortex in a liquid flow and an immiscible
droplet inside the vortex. Experiment has been conducted around a silicon-oil droplet of 6 mm in
diameter carried by water Taylor-vortex flow in an annulus between a stationary cylinder of 80 mm in
inner diameter and a rotating cylinder of 60 mm in outer diameter. The time-varying velocity field has
been visualised by tracer particles smaller than 0.3 mm in diameter. The velocity vectors of the
particles have been obtained from visualised images by using a particle-tracking-velocimetry method.
Experimental results show that the deformation of the contour lines of two-dimensional kinetic energy
is clearly noticeable near the upper part of the interface where the outward radial flow disappears.
This means that the attenuation of kinetic energy occurs in the form of diminishing the outward flow.
The vorticity is found to be attenuated in almost all area around the droplet except for the small zone
where the outward radial flow directly impinged the interface.
NUMERICAL STUDY OF THE ONSET OF PENETRATIVE CONVECTION IN HORIZONTAL LAYER OF COLD WATER
Konstantin A. Nadolin
Mechanical and Mathematical Department
Rostov State University, Rostov-on-Don, Russia
ABSTRACT. The goal of this communication is to present some numerical results obtained for
penetrative convection model proposed by G.Veronis1. The problem has a significant interest in
theory of hydrodynamic stability 1-6 and describes the onset of the convection in water near 40C.
REFERENCES
- Veronis, G., Penetrative convection; Astrophys.J., Vol. 137, No.2, pp 641–663, 1963.
- Debler, W.R., On the analogy between thermal and rotational hydrodynamic stability, J. Fluid Mech., Vol. 24, No.1, pp 165–176, 1966.
- Rintel, L., Penetrative convective instabilities, Phys. Fluids, Vol. 10, No.4, pp 848–854, 1967.
- Moore, D.R. and Weiss, N.O., Nonlinear penetrative convection, J. Fluid Mech.,Vol. 61, No.3, pp 553–581, 1973.
- Musman, S., Penetrative convection, J. Fluid Mech., Vol. 31, No.2, pp 343–360, 1968.
- Lin, C.C., The Theory of Hydrodynamic Stability, Cambridge University Press, 1955.
OUTFLOW OF LIQUIDS FROM SINGLE OUTLET VESSELS: COMPARISON OF LIQUID-LIQUID AND AIR-LIQUID SYSTEMS
A Prasinos and J Kubie*
School of Mechanical and Manufacturing Engineering
Middlesex University, London N11 2NQ, England/P>
EXTENDED ABSTRACT
Outflow of liquids from single outlet vessels has been recently investigated by several authors. In
such vessels the liquid leaving the vessel through the outlet is replaced by another fluid, either
gas or a lighter liquid, entering the vessel through the same opening. The simplest example of
such an arrangement is an ordinary bottle, which is being emptied of its contents. The majority of
the reported work concentrated on cases when water is being replaced by air, but work on two
liquid systems has been recently reported, in which water was discharging into, and being
replaced by, parafin.
All the investigations on the gas-liquid flow noted the oscillatory character of the flow and
identified flooding of the outlet as the controlling mechanism governing the flow. The oscillations
of the flow in the case of gas-liquid flows are due to the compressibility of the gas. The
compressibility of the gas is used to develop full equations of motion, which are similar to second
order non-linear differential equations which govern self-excited oscillations in many mechanical
systems. More recent experimental work has been concentrated on the investigation of well
defined systems. These systems consisted of an axisymmetric arrangement of a vertical perspex
cylindrical vessel with a sealed top and a central outlet in its base. The vessel was initially
completely filled with water and the outlet sealed with a stopper. The outlet was then opened by
removing the stopper, which allowed the discharge of water from the vessel and the ingress of
air. The variation of the void fraction of air in the vessel as a function of elapsed time was then
measured. The most significant experimental result was that for a wide range of conditions the
void fraction was a linear function of time. The experimental results were described by the
flooding parameter C.
A theoretical model for the gas-liquid outflow from single outlet vessels has recently been
developed. The model provides an explanation for many of the flow phenomena observed in
gas-liquid systems, in particular the linear relationship between the void fraction and the elapsed
time and the pressure variation in the gas space above the interface in the sealed vessel.
An experimental investigation of a liquid-liquid system recently reported has shown that even in
these systems the void fraction of the lighter phase in the vessel is a linear function of the
elapsed time, and that the experimental results can also be described by using the flooding
parameter C. It has been also shown that the flooding parameter for the liquid-liquid flow is in a
close agreement with the flooding parameter for the gas-liquid flow, provided the usual correction
for the fluids densities are taken into account. It is not clear why there is such an agreement
between gas-liquid and liquid-liquid flows, since some of the phenomena observed are quite
different. Whereas the compressibility of the lighter phase in the case of the gas-liquid systems is
very high and determines the behaviour of the system, the compressibility of the lighter phase in
the case of the liquid-liquid systems is practically negligible. Hence other mechanisms must be
considered in the development of the model.
Further and more detailed experimental work for the outflow of water from a vertical cylindrical
vessel into parafin is performed and the variation of the void fraction of parafin in the vessel with
the elapsed time obtained. A theoretical model of the outflow, based on a simple physical
description of the system, is then developed. The model contains several parameters, which are
not measured directly and which must be estimated.
The theoretical model developed in this work for the liquid-liquid flow from single outlet vessels is
in reasonable agreement with the experimental data. In particular, the model shows that, as
observed experimentally, the void fraction of the lighter phase in the working vessel is a linear
function of the elapsed time. Similarly, and as discussed above, the recently developed model of
gas-liquid flow from single outlet vessels also shows that the void fraction of the lighter phase in
the vessel is a linear function of the elapsed time, as also observed experimentally.
This is rather surprising since the basic mechanisms of the two models are fundamentally
different. Whereas the theoretical model for the case of liquid-liquid flow neglects the
compressibility of the lighter phase, the theoretical model for the case of gas-liquid flow is based
on the compressibility of the lighter phase. This leads to steady-state counter current flow of the
two phases through the outlet for the case of liquid-liquid flows, and to a dynamic oscillatory
behaviour with just one phase in the outlet at any one time for the case of gas-liquid flows.
Furthermore, the flow of the lighter phase is always upward for the case of liquid-liquid flows, but
can be both upward and downward, depending on the stage in the oscillatory cycle, for the case
of gas-liquid flows.
It is interesting to note that these two different mechanisms provide the explanation for the linear
relationship between the void fraction of the lighter phase and the elapsed time for both extremes
of the lighter fluid behaviour: incompressible liquid in one case and compressible gas in the other.
Furthermore, even though the flooding parameter C provides the means for correlating the
experimental data for both extremes of the lighter fluid behaviour, neither model uses the flooding
parameter to describe the flow processes involved.
Nevertheless, further work is required to develop the model. In particular, it would be useful to
examine those two fluids systems in which the compressibility of the lighter phase is between the
two extremes examined in this work.
* Present address: Department of Mechanical, Manufacturing & Systems Engineering, Napier University,
10 Collinton Road, Edinburgh EH10 5DT, Scotland
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