Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 11.4.2 - Separation of oil droplets in swirling water flow
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 Material Information
Title: 11.4.2 - Separation of oil droplets in swirling water flow Computational Techniques for Multiphase Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Slot, J.J.
van Campen, L.J.A.M.
Hoeijmakers, H.W.M.
Mudde, R.F.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: oil-water separation
CFD
experimental
Euler-Lagrangian method
 Notes
Abstract: An oil-water separator utilizing swirling flow is investigated both numerically and experimentally. The results from simulations and experimental data are compared. Qualitative agreement is observed near the swirl element of the separator, but the agreement deteriorates further downstream. Furthermore, droplet tracking simulations are carried out to evaluate the behavior of the oil droplets in the flow. Turbulent dispersion is shown to have a negative impact on the separation performance, frustrating the separation of smaller droplets.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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Volume ID: VID00285
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Resource Identifier: 1142-Slot-ICMF2010.pdf

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7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


Separation of Oil Droplets in Swirling Water Flow


J.J. Slot*, L.J.A.M. van Campent, H.W.M. Hoeijmakers* and R.F. Muddet

Faculty of Engineering Technology, University of Twente, Enschede, The Netherlands
t Department of Applied Sciences, Delft University of Technology, The Netherlands
J.J.Slot@ ctw.utwente.nl and L.J.A.M.vanCampen@tudelft.nl
Keywords: Oil-water separation, CFD, Experimental, Euler-Lagrangian method




Abstract

An oil-water separator utilizing swirling flow is investigated both numerically and experimentally. The results from
simulations and experimental data are compared. Qualitative agreement is observed near the swirl element of the
separator, but the agreement deteriorates further downstream. Furthermore, droplet tracking simulations are carried
out to evaluate the behavior of the oil droplets in the flow. Turbulent dispersion is shown to have a negative impact on
the separation performance, frustrating the separation of smaller droplets.


Nomenclature


Roman symbols
d oil droplet diameter (m)
g gravitational constant (ms 1)
n Swirl number curve fitting parameter (-)
p pressure (Nm 2)
U instantaneous velocity vector (ms 1)
u mean velocity vector (ms 1)
u' turbulent velocity fluctuations vector (ms 1)
u velocity increments in dispersion model (nms1)
U instantaneous velocity in dispersion model (ms
k turbulent kinectic energy (m2s 2)
1, eddy length scale (m)
R Pipe radius (m)
S Swirl number (-)
So Swirl number curve fitting parameter (-)
Greek symbols
a Swirl number curve fitting parameter (-)
6 turbulent dissipation rate (m2s-3)
p dynamic viscosity (Pas)
p density (kgmn3)
Td droplet response time (s)
T, eddy lifetime (s)
Tint droplet-eddy interaction time (s)
Ttr transit time (s)
Subscripts
d droplet
c continuous phase
b bulk


z axial direction
r radial direction
0 azimuthal direction




Introduction

The current oil market is governed by a continuing
worldwide demand for oil and decreasing numbers of
easily accessible fields. Therefore, new technologies are
1) required for fields with hydrocarbons that are difficult
to produce. These difficulties can arise due to location,
such as offshore or sub sea, or due to the properties of
the oil, such as high viscosity and high density.
In addition, as many oil fields mature, crude oil is pro-
duced with increasing quantities of water. The large wa-
tercut makes the separation of the oil from the water an
important processing step. The separation of the phases
is required in order to efficiently use transport facilities,
or for the purpose of re-injecting the separated water in
order to maintain well pressure.
Currently, separation is mostly achieved in very large
vessels employing the action of gravity. This method has
not changed significantly for the last decades. The large
weight and space requirements of these vessels lead to
high costs for the on-site processing facilities.
The present research investigates a much smaller and
cheaper alternative for the oil-water separation, i.e. uti-
lizing in-line equipment that employs swirling flow to
separate the phases. Moreover, the smaller equipment


















Figure 1: Cut away of 100 mm diameter pipe show-
ing internal swirl element (ISE). non-swirling
fluid with an axial velocity of 2 m/s enters
from the left.


size leads to a reduced hydrocarbon inventory. This is
beneficiary in terms of for example emergency proce-
dures. Also, lower costs for maintenance and inspection
can be realized.
Swirling flow has been used successfully for other appli-
cations, such as the separation of solids from either gas
(Hoekstra (2000)) or liquid (Bradley (1965)). Liquid-
liquid separation is more challenging due to the smaller
density difference, high volume fractions, poor coales-
cence and the danger of emulsion formation. Dirkzwa-
ger (1996) designed an in-line liquid-liquid separator.
Subsequently, single-phase experiments were carried
out for this separator. Murphy et al. (2007) compared
these measurements with numerical results from two dif-
ferent CFD packages. It was found that the main fea-
tures of the flow were qualitatively well represented nu-
merical. However, large quantitative differences were
observed between the numerical results mutually and
between numerical results and experimental data. The
in-line separator was further developed and investigated
numerically by Delfos et al. (2004). This involved the
design of an oil extraction outlet and development of a
computational inexpensive numerical tool for separator
prototyping.
The current project aims at the design and investigation,
both numerically and experimentally, of an oil-water
separator utilizing swirling flow to be applied to oil-in-
water mixtures with a relatively high oil volume fraction.
For this purpose an in-line separator has been designed
and an experimental facility has been build. This paper
will discuss the first stage of the project in which results
of single-phase numerical simulations and experimental
measurements are compared. Subsequently, small quan-
tities of oil droplets are introduced into the flow to nu-
merically assess the behavior of the droplets in the sep-
arator.


Geometry internal swirl element

The swirling flow is generated by an internal swirl ele-
ment (ISE) placed in a 100 mm diameter pipe, as shown
in figure 1. The design condition corresponds to an axial


7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


bulk velocity ub in the pipe of 2 m/s, leading to a flow
rate of 56.5 m3/hr. The ISE consists of a central body
divided into a nose section, a vane section and an aft
section. From the vanes section 9 vanes protrude which
are attached to the wall of the pipe. In the vane section
the central body has a diameter of 80 mm. The vanes
have a chord length of 100 mm and at the trailing edge
have a 72 angle with respect to the pipe axis. Down-
stream of the vane section, the aft section of the central
body si, ,dil\l reduces in diameter and is closed off by
a spherical cap.
In the ISE the flow accelerates in the nose section lead-
ing to the annular vane section. The higher axial velocity
in the vane section and the larger radius at which the flow
is deflected both contribute to a further increase in angu-
lar momentum of the flow. In the aft section the flow can
gradually adjust to the increase in cross-sectional area.


Experimental setup

Experiments have been performed for a pipe with the
ISE. A scheme of the experimental setup is shown in
figure 2. The experimental setup used for the investiga-
tions presented in this research has been built to conduct
fluid/fluid separation using a centrifugal flow field, and
therefore contains more equipment than is needed for the
current single-phase research. Figure 2 only shows the
relevant parts.


r Flowstraightener
oil
reject


3.87 m


Swirl
element
1.16 m

Flow
straightener


Static mixer


Figure 2: Scheme of the experimental setup.







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


Nignilk .,iiI impact on the velocity measurements.


line of measurement
locations


Single-phase governing equations


Numerical simulations have been carried out in which
the flow field is computed using the Reynolds aver-
aged Navier-Stokes equations for transient incompress-
ible flow:


Figure 3: Schematical cross section of the measurement
tube.



The flow is driven by a centrifugal pump, which is fed
from a storage vessel. The flow passes a connection sec-
tion and a static mixer. Downstream of the static mixer,
an aluminum, honeycomb flow straightener is placed (65
mm high, 5 mm hole size). The center of the body of the
ISE is located 1.16 m downstream of the exit of the flow
straightener. In streamwise direction, the ISE is directly
followed by a Poly Methyl MethAcrylate (PMMA) mea-
surement tube, which is surrounded by a square tube, the
latter to reduce refraction of laser light used for investi-
gations of the flow in the tube. The most upstream mea-
surement position that can be reached is 31 cm down-
stream of the center of the ISE. At 3.87 m downstream
of the ISE, a second flowstraightener is placed, consist-
ing of a 40 mm thick disc of Poly Vinyl Chloride, with
89 holes in it with 5 mm diameter. The disc is equipped
with an oil reject in its center. The oil reject is a stain-
less steel tube of 50 mm diameter with its inlet 215 mm
upstream of the flowstraightener in the tube. The wa-
ter returns through a settling tank, containing coalescing
plate packs, into the storage tank.
The fluid flow is examined using Laser Doppler
Anemometry (LDA), with the laser beams entering the
experimental setup via a planar wall of the square tube of
PMMA. Since the optical transition between the PMMA
tube wall and the water causes refraction, measurements
are only done along lines passing through the center of
the tube, see figure 3.
An Argon laser is used, from which the 488.0 nm beams
are used for the axial velocity component and the 514.5
nm beams for the azimuthal velocity component. The
burst correlation is conducted in a Dantec F60 BSA sig-
nal processor. The average velocity is calculated using a
software package developed by Belt (2007), correcting
the LDA time averaged results for white noise, multiple
validation and a bias towards high velocities.
Experiments are carried out for a flow rate of 55.4 m3/h.
The temperature was monitored and rose due to pump
heat. The changing temperature did not show to have a


V.u 0
(u.V)u
+ (u.V)u
att


+ VV2u + g


V.(u'u') (2)


Here p is the density of the continuous phase, p is the
static pressure, u is the mean velocity and u' are the
turbulent velocity fluctuations. They are related to the
instantaneous velocity U as

U u + u' (3)

It is assumed that the timescales of the turbulent veloc-
ity fluctuations u' are much smaller than the timescale
of the mean velocity u.
The Reynolds stresses are modeled using a second mo-
ment closure model or Reynolds stress model (RSM). In
a Reynolds stress model the Reynolds stresses ( '.,'.)
are provided by transport equations. One of the advan-
tages of the model is that the production terms of the
Reynolds stresses can be represented exactly. Therefore,
the strain rates associated with streamline curvature and
flow skewness are incorporated into the production of
turbulence, see Hanjalic (1999). Both streamline cur-
vature and flow skewness are encountered in swirling
flow. Moreover, the separate transport equations for the
Reynolds stresses allow for anisotropic behavior of the
turbulent flow.
The use of eddy-viscosity models is not well suited for
swirling flow, see Pope (2000). The skewness of the flow
is not in accordance with the eddy-viscosity assump-
tion that the shear stresses and the velocity gradients


Figure 4: Mesh around the afterbody of the internal
swirl element.


LDAprobei






























Figure 5: Mesh on cross-section through pipe down-
stream of internal swirl element.


have the same direction, as pointed out by Kitoh (1991).
Various sources of turbulence, i.e. strain rates, are not
represented when using eddy viscosity models. More-
over the assumed isotropic turbulence leads to overpre-
dictions of the shear stresses and a strong radial diffu-
sion of momentum, see Murphy et al. (2007). In the
present research the Reynolds stress model of Speziale
et al. (1991), named SSG, is used. This model features a
quadratic pressure-strain relation. This RSM is recom-
mended for swirling flows, e.g. by Cullivan (2003) and
Chen et al. (1999). To close the SSG model, a seventh
transport equation for the dissipation rate is included.


Computational method

The governing equations were solved using Ansys CFX
12.0. This commercial CFD software package uses a
cell-centered finite volume method. The CFX solver
uses a co-located grid in which pressure and velocity
components are computed at the same location. The spa-
tial and temporal discretizations are second-order accu-
rate. A computational mesh has been generated for the
pipe with ISE. This mesh consists of 4.2 million hexa-
hedral elements. The mesh around the afterbody of the
ISE can be seen in figure 4. A cross-section of the mesh
further downstream in the pipe is shown in figure 5. The
pipe extends 0.075 m upstream and 2 m downstream of
the swirl element. The oil reject is not yet implemented
in the computational grid.
Near the walls the mesh is refined in order to capture the
near wall behavior of the flow. Wall functions are em-
ployed to represent the flow structure in the region adja-
cent to the wall. This reduces the computational require-
ments. Wall functions use empirical relations to impose


7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


the wall shear stress at the nodes next to the wall, which
all are located outside the viscous sublayer.
At the inlet of the pipe a swirl-free parabolic axial ve-
locity profile is imposed. The profile is attained from
numerical calculations of the flow in a long pipe with
the same diameter and the same mass flow. The bulk
axial velocity ub is 2 m/s, yielding the flow rate of 56.5
m3/hr. The inlet flow Reynolds number equals 2.2x105.
At the outlet a so-called opening condition is applied.
This imposes a relative pressure of 0 Pa and allows in
and out flow through the outlet.
The transient simulations are run until an operational
state is established. In this operational state the mean ve-
locity u oscillates around some final mean value. After
the operational state has established, the time-averaged
values of the mean velocity and other quantities are cal-
culated using sufficient time steps to capture several pe-
riods of the oscillation.


Results for flow of single-phase water

Inspection of the results showed that, in the flow over
the vanes, flow separation did not occur, which gives
the flow an averaged deflection of 67.5 measured with
respect to the axial direction. The generation of the
swirling flow is accompanied by a drop in pressure of
1.47.105 Pa, averaged over the cross-flow plane, just up-
and downstream of the ISE. Just aft of the trailing edge,
the bulk axial velocity ub is 5.6 m/s. The averaged az-
imuthal velocity us reaches values up to 13.5 m/s at that
point.
The strongly swirling flow leads to reversed axial flow
in the pipe downstream of the ISE. This has been re-
ported in the literature earlier by, among others, Kitoh
(1991) and Dirkzwager (1996). However, near the cen-
terline the fluid flows again in the positive axial direc-
tion. This results in a flow structure with an annular

6-
S
5- ~

4- ~

3-

2
0 0.5 1 1.5 z(m) 2

Figure 6: Decay of swirl number S as function of ax-
ial distance from the ISE, attained from sim-
ulations. Exponential decay curve is fitted
through the data points: S = So e-("/2R)"
So = 5.6, a = 3.9 and n = 0.88.





























































(c) pressure distri-
bution


Figure 7: Snapshot of axial and azimuthal velocity and
pressure distribution on plane through center
of pipe.


region of reversed flow. The outer surface of zero ax-
ial velocity is quite steady in time, showing only small


7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


variations with time of its radius. On the other hand,
the inner surface of zero axial velocity is very unsteady
and non-axisymmetric. The surface has ridges and val-
leys which, while rotating with the flow, travel upstream
towards the ISE. It often encapsulates regions of fluid
with negative axial velocity. One meter downstream of
the swirl element, the inner surface of zero axial veloc-
ity behaves similar to the outer surface, i.e. it is about
stationary.
A measure for the swirl intensity is given by the swirl
number S, the non-dimensional angular momentum flux:


S ., (4)

Here u us and ub are the axial, azimuthal and bulk axial
velocities, respectively. R is the radius of the pipe. Fig-
ure 6 shows the calculated evolution of the swirl number
S as function of axial distance from the ISE. A rapid re-
duction of the swirl intensity is seen; 1.5 m downstream
of the ISE the swirl number is approximately reduced
by half. An non-linear exponential decay curve is fitted
through the data points: S = Soe" (/2R)" with So = 5.6,
a = 3.9 and n = 0.88. The non-linear decay rate provides
a better fit compared to the linear case of n = 1, used by
Kitoh (1991) and Dirkzwager (1996).
Figure 7 shows the axial and azimuthal velocity as well
as the pressure distribution on a plane through the center
of the pipe at a certain time. The relatively thin annu-
lar region of reversed flow can clearly be seen. Near
the ISE a region with negative axial velocity is entrained
by the core with unsteady positive axial flow. The az-
imuthal velocity reaches a maximum velocity of 16 m/s


40 20 0 20 40
r(mm)


Figure 8: Comparison of numerical (solid) and experi-
mental results (dotted) for radial distribution
of time-averaged axial velocity at z = 0.13 m
downstream of ISE


p
(xlO0Pa)

1.8


U
(m1s)
E8.0


(a) Axial veloc-
ity


(m s)
16.0


(b) Azimuthal
velocity







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


U (m/s)


r (mm)


r(mm)


Figure 9: Comparison of numerical (solid) and experi-
mental results (dotted) for radial distribution
of time-averaged axial velocity at z = 0.53 m
downstream of ISE



near the surface of the afterbody of the ISE. In the outer
region of the pipe the azimuthal velocity is about 12 m/s
and gradually decreases to about 8 m/s one meter down-
stream of the ISE. Some precession of the vortex core
is observed in which the center of the vortex meanders
slightly around the geometric center of the pipe. The
pressure drop over the ISE can clearly be seen. Fur-
ther downstream the low pressure region in the center
becomes more narrow and the pressure decreases.
The numerical and experimental results for the radial
distribution of the time-averaged axial velocity along a
line through the center in the cross-sectional plane at z =
0.13, 0.53 and 1.288 m downstream of the ISE are com-
pared in the figures 8, 9 and 10, respectively. At z =
0.13 m both experimental and numerical results reveal
the annular region of reversed flow, although the mea-
surement indicates that the region is located at a smaller
radius. The numerical time-averaged results even show
a small negative velocity at the center due to entrainment
of fluid with negative axial velocity. The flow in the near
wall region is predicted well by the simulations. At the
station at z = 0.53 m, a core with positive axial velocity
is seen in the numerical results, while the experimental
measurements show reversed flow in the center of the
pipe. This situation is exacerbated further downstream
at z = 1.288 m, where the difference in axial velocity
along the pipe axis has increased. The differences at z
= 0.53 m and 1.288 m may be caused by the presence
of the closed oil reject in the experimental setup, which
is not present in the numerical setup. The closed oil re-
ject introduces a blockage into the flow at the centerline.
This blockage may prevent the formation of a region of


Figure 10: Comparison of numerical (solid) and experi-
mental results (dotted) for radial distribution
of time-averaged axial velocity at z = 1.288
m downstream of ISE


positive axial velocity at the centerline. Due to technical
difficulties measurements with an open oil reject could
not be carried out a this time.
The comparison for the the radial distribution of the
time-averaged azimuthal velocity at the same locations
is shown in figures 11, 12 and 13, respectively. The
numerical solutions and experimental data agree more
closely for this velocity component than for the axial
component. The azimuthal velocity distribution can be
divided into three regions. Near the wall a thin boundary


U (m/s)
15


40 2 0 20 40
r(mm)


Figure 11: Comparison of numerical (solid) and experi-
mental results (dotted) for radial distribution
of time-averaged azimuthal velocity at z =
0.13 m downstream of ISE







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


layer is observed. Further away from the wall a region
exists with high azimuthal velocities and a distribution
similar to that of a potential flow vortex. Near the center
the distribution resembles that of a solid body rotation.
To be more precise, at the z = 0.13 m station the solid
body rotation consists of two parts. Near the center the
gradient in the azimuthal velocity is relatively low. Fur-
ther away from the center a distinct rise in the gradient
occurs. The simulation shows a brief decrease in gradi-
ent between the flatter inner region and the steeper outer
part. This pattern is still seen at 0.53 m in the numerical
results but no longer in the experiments. Further down-
stream both show a solid body-like velocity distribution.
As can be seen from figures 7(a) and 7(b), the flow de-
taches from the afterbody. Fluid with high azimuthal ve-
locity is thus diverted to the outer region of the pipe. The
flow detachment therefore shields off the central region
downstream of the ISE. This central region is fed by fluid
with lower angular momentum flowing upstream in the
annular reversed flow region. This mechanism presum-
ably yields the azimuthal velocity distribution seen at z =
0.13 m. Further downstream the angular momentum dif-
fuses over the cross-section and a single gradient of the
azimuthal velocity is observed in the center of the pipe.
The numerical predictions show a higher maximum az-
imuthal velocity than observed in the experiment.

Lagrangian Droplet tracking method

To investigate the behavior of the dispersed oil phase,
droplet tracking calculations were carried out. A small
number of oil droplets was released at the inlet and fol-


U (m/s)
15 -


40 20 0 20 40
r (mm)

Figure 12: Comparison of numerical (solid) and experi-
mental results (dotted) for radial distribution
of time-averaged azimuthal velocity at z =
0.53 m downstream of ISE


40
r (mm)


Figure 13: Comparison of numerical (solid) and experi-
mental results for radial distribution of time-
averaged azimuthal velocity at z = 1.288 m
downstream of ISE


lowed through the separator. One-way coupling was
used, so there is no influence of the dispersed droplets
on the continuous flow field. The one-way coupling is
justified as indicated by Crowe et al. (1998), since the
droplets are small (d < lmm), the number of droplets is
low (n ~ 103) and due to the low density difference be-
tween the phases and relatively high viscosity of water.
The equation of motion of a droplet is given by:


aud 1
mdd = CDAd I u ud I(uc
at 2


+ (md mc)g

1 M e (
+ mc t


Ud) (5)


aud\
at )


+ me Vp
PC
Here md is the mass of the oil droplet, me is the mass of
the displaced water and Ad is the effective droplet cross
sectional area. The correlation of Schiller and Naumann
(1933) is used to determine the drag coefficient CD:
24 687
CD (1 + 0.15Re067) (6)
Rer
Here Rer is the Reynolds number based on the relative
velocity:
Pc uc-udld
Re, =- (7)
ftc
The terms on the right hand side of equation 5 repre-
sent the drag force, the buoyancy due to gravity, added
mass force and the pressure gradient force, respectively.
When a droplet accelerates, it also accelerates some of







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


the surrounding fluid. The added mass force accounts
for the force experienced by the droplet due to this ac-
celeration of the fluid. Note that the Basset history force
is not included.
The small droplets are affected by the turbulent fluctua-
tions of the continuous flow. Turbulent eddies can dis-
place a droplet and therefore frustrate the segregation
process. This turbulent dispersion is accounted for by
using the model of Gosman et al. (1983). This model
assumes that the droplet is present in and interacts with
a single turbulent eddy. The interaction with the eddy is
modeled by adding velocity increments it to the mean
velocity uc of the fluid surrounding the droplet. it is an
approximation to u'. These increments have different
values in different directions. The new estimate of the
instantaneous fluid velocity Uc is used in the calcula-
tion of the drag force and the relative Reynolds number,
replacing uc. The velocity increment is defined as:

Uc F 2k/3 (8)

Here F is a normal-distributed random number and k is
the local turbulent kinetic energy. Note that /2k73 is
the magnitude of the velocity fluctuations in isotropic
turbulent flow.
The velocity increment Ui is constant during the
droplet-eddy interaction time Tit. This is the minimum
of two timescales: the eddy lifetime T, and transit time
t,r. The transit time is defined as the time required for
the droplet to transverse the eddy. The characteristic
lengthscale of the eddy is

1 C12k3/2/ (9)

Here C, is a turbulence constant of 0.09 and c is the tur-
bulent dissipation rate. The eddy lifetime is then given
by
T 1,/V2k/3 (10)
The transit time is estimated from the solution of the
simplified equation of motion of the droplet


Tt, -Tdln (1


Td(Uc Ud))


Here Ud is the velocity of the droplet and Td is the droplet
response time, given by:
pdd2
Td =(12)
18P,

The product Td(Uc Ud) is an estimate of the distance
which the droplet travels before it adjusts to the charac-
teristic velocity of the eddy. This needs to be larger than
Ie, if the droplet is to cross the eddy at all. When the
droplet-eddy interaction time is reached, new Ui, 1 and
Tit are calculated based on local values of the velocity,
k and c at the position of the droplet.


(a) 50 pm (b) 75 pm (c) 100 pm (d) 200 pm

Figure 14: Trajectories of 50 (a), 75 (b), 100 (c) and
200 pm (d) diameter droplets at 2.8 s after
release at inlet. 40 trajectories are shown for
each diameter size.


Droplet trajectories

Transient flow simulations are performed in which at a
given time 200 droplets are simultaneously released at


)I







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


the inlet. The droplets are randomly distributed over the
cross-section area of the inlet. The droplets have a den-
sity Pd of 800 kg/m3, the water has a density of 997
kg/m3. In the mono-dispersed calculations the droplet
diameter was 50, 75, 100 or 200 pm. Due to computa-
tional constraints a somewhat coarser mesh was used for
the droplet trajectory simulation. The mesh consists of
1.25x106 hexahedral elements. Figure 14 shows trajec-
tories of 50, 75, 100 and 200 pm diameter droplets, re-
spectively, at 2.8 s after release at the inlet. For each di-
ameter size 40 randomly selected trajectories are shown.
After 2.8 s not all droplets have reached the outlet. Some
droplets have segregated towards the center of the pipe
and are slowly transported downstream. Away from the
center the axial velocity is much higher and here the
droplets quickly move to the outlet. The figure clearly
demonstrates the influence of the droplet size on the sep-
aration. Almost half of the 50 pm diameter droplets stay
in the region near the wall. For the 75 diameter pm
droplets this number is greatly reduced. Only a single
trajectory of a 100 pm diameter droplet out of the 40
shown here reaches the outlet at large radius. The 200
pm droplets move rapidly inwards and most of them re-
circulate in the region just downstream of the ISE.
Many trajectories of the smaller droplet remain near the
wall and no apparent inward motion is observed. This is
caused by the turbulent dispersion which often counter-
acts the segregation. The effect of the turbulent disper-
sion is further illustrated in figure 15. This figure shows
the radial distance from the pipe axis of a 50 pm and
a 100 pm diameter droplet as function of the axial dis-
tance z. The 50 and the 100 pm diameter droplet tra-
jectories are drawn with solid and dotted lines, respec-
tively. The droplets follow erratic trajectories through
the separator. Apparently the forces due to the turbulent
eddies on the droplets are of the same order of magni-
tude as the centrifugal force. Therefore, the turbulent
dispersion can very well frustrate the segregation pro-
cess. As the trajectories indicate, droplets can also be
transported away from the center after being segregated.
The effect of the turbulent dispersion decreases with in-
creasing droplet diameter due to their higher droplet re-
sponse times. However, the 100 pm diameter droplets
can still be considered small since both 50 and 100 pm
diameter droplets experience radial in- and outward dis-
placement of roughly the same order of magnitude and
frequency. The larger centrifugal force on the 100 pm
diameter droplets is responsible for the better segrega-
tion of these droplets. Close inspection of the 100 pm
droplet trajectory reveals the annular reversed flow re-
gion, since around z = 1.1 m the droplet briefly moves
upstream.
The separation of 50 pm diameter droplets will be dif-
ficult. Out of 200 droplets 94 have left the domain after


r (m) 'i '
0.04- vn
.i i '

0.03 -


0.02
-50 m
--- 100 u rn
0.01 I



0 0.5 1 1.5 2

Figure 15: Radial distance from pipe axis of two 50 pm
diameter droplets (solid) and one 100 pm di-
ameter droplet (dotted) as function of axial
distance z.


2.8 s. These droplets remained in the outer regions of the
pipe where a high axial velocity is seen. 80 droplets had
a radial position larger than 25 mm, the radius of the oil
reject in the experimental setup, at the outlet. However,
of the droplets still inside the separator all were found
inside the 25 mm radius.
Of the 75 pm diameter droplets 58 left the domain, 39 of
which at a radius larger than 25 mm. Of the remaining
droplets 138 had reached a radius smaller than 25 mm.
The separation of 100 pm diameter droplets was more
successful: 30 droplets reached the outlet, of which 8
were outside the 25 mm radius and all droplets still in-
side the separator were also within the 25 mm radius.
The 200 pm diameter were all collected in the center
just downstream of the ISE.


Conclusions

An in-line separator for oil-water flows has been inves-
tigated both numerically and experimentally. For this
purpose an experimental setup has been realized. The in-
vestigation shows regions of reversed flow downstream
of the swirl element due to the highly swirling flow.
The time-averaged results from the numerical simula-
tions and experimental LDA measurements are com-
pared for the ISE at various stations downstream of the
ISE. Near the ISE the axial velocity distribution com-
pares well qualitatively. In the center differences are
seen; the experimental data shows the annular reversed
flow region to be located at a smaller radius compared to











the region observed in the numerical results and the sim-
ulations predict a small velocity decrease in the center
which is not seen in the experiments. However, the ve-
locity in the near wall region agrees well quantitatively.
Further downstream the numerical and experimental re-
sults for the axial velocity distribution deviate more. The
simulations predict the region of annular reversed flow to
persist downstream, but experiments show the region of
reversed flow to cover the center of the pipe completely.
The calculated and measured azimuthal velocity distri-
butions agree more closely compared to the axial veloc-
ity distribution. The difference in axial velocity distribu-
tion may be caused by differences in outlet conditions in
the numerical model and the situation in the experimen-
tal setup. The closed oil reject in the experimental setup
introduces an obstruction into the flow at the centerline.
This may prevent the formation of a region of positive
axial velocity at the centerline. Measurements with an
open oil reject could not be carried out yet due to tech-
nical difficulties.
To assess the behavior of a dispersed oil phase in the sep-
arator droplet tracking simulations have been performed.
These simulations involve a mono-dispersed release of
200 droplets of 50, 75, 100 and 200 pm diameter. A
one-way coupling between fluid and droplets was used.
The simulations show the effect of the turbulent disper-
sion to be large. The turbulent dispersion is seen to
cause an erratic motion of the droplets. The forces on
the droplets due to the turbulent dispersion are of the
same order of magnitude as the centrifugal forces act-
ing on the droplets. Especially for smaller droplets, on
which smaller centrifugal forces are acting, turbulence
can frustrate the separation process. Only partial segre-
gation of 50 pm diameter droplets is to be expected. The
segregation improves for larger droplet diameter and the
separator is expected to function well for droplets of a
diameter equal to or higher than 100 pm.
Finally it is noted that for bulk oil-water separation, nu-
merical simulations based on an Euler-Euler formulation
are required. This together with considering models for
coalescence is subject of future work.


Acknowledgements

This research was made possible by the Dutch Separa-
tion Technology Institute (DSTI). This research is part
of project Oil & Gas 00-004.


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