Proceedings of the ASME 2014 4th Joint US-European Fluids Engineering Division Summer Meeting
FEDSM2014
August 3-7, 2014, Chicago, Illinois, USA
FEDSM2014-21289
CFD STUDY OF HYDRODYNAMICS AND SEPARATION PERFORMANCE OF A
NOVEL CROSSFLOW FILTRATION HYDROCYCLONE (CFFH)
Abdul Motin
Mechanical Engineering
Michigan State University
East Lansing, MI, USA
Volodymyr V. Tarabara
Civil and Environmental Engineering
Michigan State University
East Lansing, MI, USA
André Bénard*
Mechanical Engineering
Michigan State University
East Lansing, MI, USA
ABSTRACT
This research addresses various hydrodynamic aspects and
the separation performance of a novel cross-flow filtration
hydrocyclone (CFFH) using computational fluid dynamics. A
CFFH is a device that combines the desirable attributes of a
cross-flow filter and a vortex separator into one unit to separate
oil from water. The velocity and pressure fields within the
CFFH are estimated by numerically solving the filtered NavierStokes equations (by using a Large Eddy Simulation (LES)
approach). The Lagrangian approach is employed for
investigating the trajectories of dispersed droplets based on a
stochastic tracking method called the Discrete Phase Model
(DPM). The mixture theory with the Algebraic Slip Model
(ASM) is also used to compute the dispersed phase fluid
mechanics and for comparing with results obtained from the
DPM. In addition, a comparison between the statistically steady
state results obtained by the LES with the Wall Adaptive Local
Eddy-Viscosity (WALE) subgrid scale model and the Reynolds
Average Navier-Stokes (RANS) closed with the Reynolds
Stress Model (RSM) is performed for evaluating their
capabilities with regards to the flow field within the CFFH and
the impact of the filter medium. Effects of the Reynolds
number, the permeability of the porous filter, and droplet size
on the internal hydrodynamics and separation performance of
the CFFH are investigated. Results indicate that for low feed
concentration of the dispersed phase, separation efficiency
obtained based on multiphase and discrete phase simulations is
almost the same. Higher Reynolds number flow simulations
exhibit an unstable core and thereby numerous recirculation
zones in the flow field are observed. Improved separation
efficiency is observed at a lower Reynolds number and for a
lower permeability of the porous filter.
INTRODUCTION
Separation of oil from water is a critical aspect of produced
water treatment and oil spills cleanup. It is also important in
refining petroleum products. Produced water is the largest
byproduct stream associated with oil and gas production. The
US Department of Energy‟s Argonne National Laboratory
estimates a volume of produced water in the United States at 21
billion barrels a year [1]. Additional production from the rest of
the world is estimated at a volume of more than 50 billion
barrels a year [1]. As a field becomes depleted, the amount of
produced water typically increases. Several challenges exist in
the oil industry with respect to the treatment of produced water
for re-use in the underground injection or discharge to surface
water. In the United States, the U.S. Environmental Protection
Agency issued standards for underground injection [2], and
discharges to surface water [3]. Depending on the country and
location of offshore platforms the allowable concentration of oil
in the water to be discharged is in the range of 15 to 40 mg/L
[4]. Many technologies are currently used for produced water
treatment. Common techniques available for treating the oilwater mixture and the removal capacity of existing
technologies are given in Table 1.1
________________________________
* Corresponding author; benard@msu.edu
1
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Table 1 Common technologies used for produced water
treatment and their removal capacity [5]
Technology
API gravity separator
Corrugated plate separator
Induced
gas
flotation
without chemical addition
Induced gas flotation with
chemical addition
Hydrocyclones
Mesh coalescer
Media filter
Centrifuge
Membrane filter
Removal capacity by
particle size (micron)
150
40
25
3-5
10-15
5
5
2
0.01
Gravity separation and gas flotation are the primary
treatments used for separation of oil from water in highly
concentrated mixtures. Produced water is dilute and the typical
concentration of oil ranges from 100 to 5,000 mg/L [6]. The
density difference between the phases can be very small (less
than 150 kg/m3) [7]. Secondary treatments may use
hydrocyclones and centrifuges, where breakdown of oil-water
emulsion occurs and most of the free oil is removed, are widely
used in industries for produced water treatment. Filtration is
capable of separating very fine droplets but membranes can
easily be fouled by oil droplets. Hydrocyclones are simple
devices having no moving parts, compact in size, and
insensitive to orientation. However, existing hydrocyclone
technology is only effective for a droplet size larger than 10
microns [8]. Moreover, existing de-oiling hydrocyclones have a
finite turndown ratio [9] i.e. they exhibit acceptable separation
efficiency only for a certain range of feed flow rate.
A filtering hydrocyclone is a potential technology for
produced water treatment. The filtering hydrocyclone is a
swirling flow device in which the solid wall of the swirl
chamber or the tail pipe section is replaced by a filtering
medium (e.g. a membrane). The filtering hydrocyclone for
solid-liquid separation was first patented in 1991 and it
consisted of a Bradley‟s class hydrocyclone whose conical
section was replaced by a conical filtering wall [10]. For solidliquid separation, the filtration hydrocyclone increases the inlet
volumetric flow rate and decreases the energy consumption in
comparison with a conventional hydrocyclone [11-15]. The
dependency of the underflow to throughput ratio on the filtering
medium resistance was investigated by Souza et al. [15]. Based
on experimental results, they developed empirical expressions
to account for the influence of the filtering medium resistance
on the separation performance. Vieira et al. [10] and Barbosa et
al. [14] replaced the conical section of both Rietema‟s and
Bradley‟s hydrocyclones by filtering walls. They observed that
the overall efficiency for the Bradley‟s filtering hydrocyclone
decreases, but the Rietemas‟ filtering hydrocyclone shows an
increase in the overall efficiency. However, based on
experimental results, Rodrigues et al. [16] mentioned that the
overall separation efficiency of the filtering hydrocyclone is
similar to the conventional hydrocyclone, but with a reduced
energy cost due to a reduction in pressure drop. CFD
simulations performed by Vieira et al. [17] on the solid/liquid
filtering hydrocyclone demonstrated that the incorporation of
the filtering wall reduces the mixing effect and the radial drag
on solid particles. A majority of earlier research on the filtration
hydrocyclone was conducted for solid-liquid separation only.
The first study on a Crossflow Filtration Hydrocyclone (CFFH)
for liquid-liquid separation was conducted by Gaustad et al.
[18]. Simulation results of the CFFH showed poor separation
performance. Motin et al. [19] investigated the internal
hydrodynamics of the single inlet CFFH by solving the RANS
equations closed with the RSM. They observed that the swirling
flow loses its intensity quickly in the filtering zone.
This research further examines the hydrodynamics within a
dual inlet CFFH based on the LES with the WALE subgridscale model to identify favorable operating conditions. Effects
of the Reynolds number and permeability of the porous filter on
the internal flow structures are analyzed. Trajectories of oil
droplets and the volume fraction in the flow filed determined
based on the DPM and ASM, respectively are also investigated
to evaluate the separation performance of the CFFH. Effects of
dispersed droplet size, permeability of porous filter, and the
Reynolds number on the trajectories of dispersed droplets,
grade fouling, and cut size are also examined.
NOMENCLATURE
A
a
CD
D
𝒟
d
F
G
L
p
𝒫
Q
R
Re
S
U
u
VC
2
Area (m2)
Acceleration (m/s2)
Drag coefficient of droplet
Diameter (m)
Turbulent Diffusion
Droplet diameter (µm)
Grade fouling
Grade efficiency
Length (m)
Pressure (Pa)
Turbulent production
Flow rate (m3/s)
Flow ratio
Reynolds number
Rate of strain (1/s)
Velocity (m/s)
Fluctuating velocity (m/s)
Cell volume (m3)
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Greek symbols
µ
α
κ
ν
ρ
τ

χ
Π
Overflow:
“dirty”
water
Dynamic viscosity (Pa.s)
Permeability (m2)
Von Karman constant
Kinematic viscosity (m2/s)
Density (kg/m3)
Stress (Pa)
Dissipation (m2/s3)
Droplet position
Pressure strain
QF ,PF ,cF
Feed:
oil in
water
Subscripts
C
D
F
O
t
U
V
S
P
‘
sgs
T
Residual component
Sub-grid scale
Transpose
Operators
<>
Filtered component
Ensemble average
Vector
Second order tensor
CROSSFLOW FILTRATION HYDROCYCLONE
The CFFH combines the desirable attributes of a cross-flow
filter and those of a vortex separator (i.e., hydrocyclone) into
one unit to separate dispersed droplets from produced water. It
has the potential of removing smaller droplets that a
conventional hydrocyclone cannot remove; the filter‟s (or
membrane) pore size controls how small a droplet can be
removed. The swirling flow has the advantage of keeping the
dispersed droplets away from the filter medium by
hydrodynamic separation, thus possibly mitigating fouling of
the membrane. A CFFH illustration showing inflows and
outflows is presented in Fig. 1. The spiral structures inside the
CFFH represent the streamlines of the swirling flow. The
spiraling streamlines in the outer region (near the wall) form
the outer vortex and the spiraling lines at the core form the
inner vortex. The outer vortex transports the oil-water mixture
downstream while the inner vortex drives the separated oil-rich
core to the overflow orifice.
Vortex
finder
Filter
Continuous phase
Disperse phase
Feed
Overflow
Turbulent
Underflow
Vortex finder
Swirl chamber
Porous filter
Superscripts
QO ,PO ,cO
Underflow:
“clean”
water
QU ,PU ,cU
Figure 1 Illustration of feed and effluents in a crossflow
filtration hydrocyclone. Lines inside the CFFH represent the
flow streamlines. The arrow at the feed, underflow and
overflow represents the flow direction.
The main difference between the CFFH and a conventional
de-oiling hydrocyclone is that the CFFH has a radial outlet of
the underflow clean water instead of an axial outlet. Due to the
presence of the radial outlet of underflow in the CFFH, the
hydrodynamic features inside the CFFH greatly differ from
those of the conventional hydrocyclone. In the conventional deoiling hydrocyclone, the pressure drop ratio (PDR = (PFPO)/(PF-PU)) is generally greater than one [8], while the CFFH
maintains that ratio equal to or less than one. Typically, the
underflow ratio (RU = QU/QF) in the de-oiling hydrocyclone is
more than 0.90 [8, 9]. In the CFFH, because of the use of a
porous filter, the underflow rate depends on the transmembrane pressure as well as the permeability of the porous
filter. The underflow rate in the CFFH is generally less than that
of the de-oiling hydrocyclone. To achieve the rule of thumb of
the underflow ratio (more than 0.90), a staging operation can be
utilized.
A diagram with the front and top views of the CFFH is
provided in Fig. 2. Eight dimensionless geometric groups can
describe the relevant features of the CFFH (Table 2). The feed
diameter DF is the hydraulic diameter of the rectangular inlet,
which is defined as DF = 4AF ⁄P , where AF = a×b. a, b, and P
represent the thickness, height and perimeter of the rectangular
inlet, respectively. z and r are the axial and the radial coordinates of the CFFH.
3
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is achieved by solving the continuity and momentum equations
for the mixture based on the Eulerian-Eulerian approach.
(a)
In a first set of continuous phase simulations, the velocity and
pressure fields inside the CFFH are calculated by solving the
filtered Navier-Stokes equations using the LES approach. A
low-pass filter is applied to decompose the velocity into the
resolved and residual components. After the decomposition and
filtering process, the Navier-Stokes equation can be written as
[20]
̅=0
∇∙U
(1)
̅
1
∂U
2̅
sgs
̅
̅
= U ∙ ∇U = − ∇p̅ + ν∇ U − ∇ ∙ τ
(b)
ρ
∂t
̅ = U − U ′ is the resolved component and U ′ is the
where U
residual component of velocity. τsgs is the residual stress tensor,
which requires an appropriate subgrid scale turbulence model.
The τsgs is modeled using the eddy-viscosity approach as
̅ + ∇T U
̅ ) is the rate of strain
τsgs = −2νt S̅ where S̅ = 0.5(∇U
tensor for the resolved scale. Numerous issues are known to
arise with such a model [21, 22]. The turbulent kinematic
viscosity is approximated using Wall-Adapting Local EddyViscosity (WALE) subgrid scale model [23] as
νt = L2s
(S ∗S )
(S̅∗S̅)
(2)
+(S ∗S )
̅ [24]. Here 𝜅 is
where Ls = min(κ , 0.325Vc1 3 ) and S ≡ ∇U
Figure 2 Schematic of the CFFH; a) top view; b) front
sectional. The shaded region of thickness δ is the porous filter.
Table 2 Dimensionless groups for the CFFH geometry and their
magnitude. The swirl chamber diameter is D = 20 mm.
Do/D
a/D
b/D
Ls/D
Lp/D
Lo/D
Lv/D
δ/D
0.25
0.15
0.5
4
4
1
1
0.25
SIMULATION APPROACH
Two different simulation approaches are utilized in this
research: Eulerian-Lagrangian and Eulerian-Eulerian. The
continuous phase (water) and the dispersed phase (oil droplets)
are calculated separately in the Eulerian-Lagrangian approach.
The velocity and pressure fields of the continuous phase are
obtained using the Eulerian approach based on the LES and the
RANS equations. The motion of the dispersed phase is then
measured by tracking a large number of dispersed (oil) droplets
through the calculated flow field using the Lagrangian
approach. The multiphase flow simulation of oil-water mixture
the von Karman constant, is the distance to the closest wall,
and VC is the volume of the computational cell. The WALE
subgrid scale model provides correct wall asymptotic behavior
for wall bounded flows and returns a zero turbulent viscosity
for laminar shear flows [25]. WALE allows the treatment of
laminar zone (porous medium) of the CFFH.
In the second set of continuous phase simulations, the RANS
equation closed with the RSM is solved. The Reynolds average
continuity and momentum equations for a constant density and
a constant viscosity can be written as [20]
∇ ∙< U >= 0
(3)
ρ
∂<U>
+ ρ < U >∙ ∇< U >= −∇< p > +μ∇2 < U > −ρ∇ ∙< uu >
∂t
The unclosed kinematic Reynolds momentum flux, < uu > is
modeled by solving the transport equation given by [20] as
∂<u u>
ρ
+ ρ < U >∙ ∇< u u >= 𝒟 + 𝒫 + Π − ε
(4)
∂t
where the pressure/rate of strain tensor coupling, Π , is closed
using the Liner Pressure-Strain Model (LPSM) proposed by
Gibson and Launder [26], Fu et al. [27] and Launder [28]. The
details of the diffusion tensor, 𝒟, Production tensor, 𝒫, Strain
tensor, Π, and dissipation tensor, ε are not presented here for
the sake of brevity and see Pope [20] and Ansys fluent theory
guide, 2013 [24] for details.
4
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Motion of the oil droplets is estimated by tracking their
trajectories in the calculated flow field. The trajectories of the
oil droplets denoted as χD (t) are predicted from the kinematic
equation of droplet motion, shown in Eq. (5), which is written
in the Lagrangian frame of reference as
∂χ (t)
= UD (t)
(5)
where subscript „D‟ represents the dispersed phase. At any
instant, the position of an oil droplet can be estimated by
integrating Eq. (5) over a time period as
t+∆t
χD (t + ∆t) = χD (t) + ∫t
(6)
UD (t′)dt′
The dispersed phase velocity in the right hand side of Eq. (6) is
calculated by solving the following equation:
∂t
∂U (t)
∂t
=
ρ U
ρ
(t)
τ
+ ∑N
n=1 a n (t)
(7)
or
UD (t + ∆t) = UD (t) +
where τD =
4d
C ‖U
CD = f(ReD ) ,
‖
t+∆t U
(t )
*
∫t
τ
ρ
ρ
Table 4 Test cases and corresponding operating conditions.
+
∑N
n=1 a n (t′)+ dt′
, Udrift = UC − UD ,
and ReD ≡
ρ ‖U
BOUNDARY CONDITIONS AND TEST CASES
A plug flow profile is specified at the inlet. The inflow
velocities for different test cases are given in Table 4. The
average gauge pressures at the overflow and underflow outlets
are set to zero. The turbulence intensity implemented at the
inlet is 5%. For the RANS simulations, the Reynolds stresses at
the inlet boundaries are specified by the turbulent intensity, I as
< uF uF >: ei ej = (UF I)2 for i = j
and
< uF uF >: ei ej =
0 for i ≠ j [35]. The solid wall boundary conditions were set as
no-slip. The boundary between the fluid field and the porous
medium is specified as an interior region. The volume fraction
and the droplet size of the dispersed phase at the inlet for the
multiphase simulation are 0.05 and 15 microns, respectively.
The operating conditions for different test cases are presented
in Table 4.
Test
Cases
1
‖d
μ
a n above represents the acceleration of oil droplets due to the
effect pressure gradient and of virtual mass force as shown in
Table 3. The oil droplets are assumed to be spherical and the
drag coefficient, CD, is calculated by applying the spherical
drag law proposed by Mosi and Alexander [29]. The approach
has been used successfully in a variety of settings [30-32].
Table 3 Additional accelerations included in the analyses of the
droplet trajectory are shown below
Accelerations
Definition
Acceleration due to pressure
a1 = UD ∙ ∇UC
gradient force
DUdrift
Acceleration due to virtual
a2 =
mass force
Dt
Multiphase flow simulations of oil-water mixture are also
performed by solving the continuity and momentum equations
for the mixture, and the volume fraction equation for the
dispersed phase. Governing equations for the mixture are
solved using the LES approach with the WALE subgrid scale
model. Filtered equations for the mixture and the volume
fraction are not presented here for the sake of brevity (see
Ansys fluent theory guide, 2013 for detail [24]). The algebraic
slip model (ASM) is applied for the calculation of dispersed
phase velocity relative to the velocity of continuous phase [33].
The drag coefficient of the oil droplets is calculated using the
Schiller and Naumann formula [34]. There is no coalescence or
breakup considered for this simulation.
ReF
RU
α (m2)
LES
UF
(m/s)
6
27690
0.41
2×10-13
2
LES
4
18460
0.43
2×10-13
3
LES
2
9230
0.48
2×10-13
4
5
6
LES
RANS
Multiphase
4
4
4
18460
18460
18460
0.87
0.34
0.46
1×10-12
2×10-13
2×10-13
Approach
NUMERICAL METHOD
The filtered Navier-Stokes equations are solved using a
pressure-based segregated solver available with Fluent 6.0. A
converged statistically steady state solution using the standard
k-ε model is used as a precondition for the transient calculation
based on both the LES with the WALE and the RANS with
RSM. The Semi-Infinite Method for Pressure Linked Equation
(SIMPLE) algorithm [36] was used to achieve pressure-velocity
coupling between the continuity and the momentum equations.
A good stability of the numerical computations was achieved
by setting the under-relaxation factors for pressure and
momentum to 0.3 and 0.5 respectively [25]. The transient
simulations are continued until a statistically steady-state
solution is obtained. The time dependency of the mass flow
rates at the overflow and the underflow outlets are monitored
during the simulations for determining the statistically steady
state conditions of the simulation results. Simulation times
required to achieve the statistically steady-state results for all
the cases is approximately 0.5 second. At every time step the
residual levels for continuity and momentum are in the order of
10-4. The time step is set to 1x10-5 s, which provides a stable
and accurate solution for these flow conditions [25]. Pressure
interpolation is performed using the PREssure STaggering
Option (PRESTO) scheme [36]. The PRESTO scheme provides
improved results for high speed swirling flows and flows in
5
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strongly curved domain [25, 37]. The momentum equation is
discretized using Quadratic Upstream Interpolation for
Convective Kinetics (QUICK) scheme [38] since it provides
better accuracy and is suitable for hexahedral mesh [25, 37].
The transient calculations are performed using a bounded
second order implicit discretization since it provides stable
numerical solutions [25].
Bulk
flow
domain
For simulating the motion of oil droplets, Eqs. (6) and (7) are
integrated using the 5th order Runge-Kutta scheme derived by
Cash and Karp [39]. There are five integration steps used for
each grid cell. About 2700 uniformly distributed mono sized
droplets with a specific gravity 0.85 mimicking the crude oil
are injected from the inlet surfaces. For each group with a
uniform droplet size, the total number of droplets escaping
from the overflow and the underflow orifice are tracked to
estimate grade fouling. In the numerical calculations, the
droplets are allowed to reflect from the solid wall and to pass
through the porous medium. Any droplet passing through the
porous medium is considered as fouling the filter. The accuracy
of the solution is controlled by specifying a residual value of
10-6. The maximum number of time steps is set as 1x106, which
is sufficient to ensure that there are no droplets with incomplete
trajectories in the flow domain.
GRID
A structured hexahedral O-grid was generated using ANSYS
ICEM CFD and is shown in Fig. 3. A finer mesh is generated at
the core region because of the higher sensitivity of the internal
flow structure due to the core flow patterns. A finer mesh is also
generated near the wall region to capture the near-wall flow
properties without deteriorating the accuracy of the numerical
solution. A fine mesh in the porous medium near the inner wall
is created to maintain a small aspect ratio between adjacent
cells. About 650,000 cells with an orthogonal quality of 0.45
were generated. This grid size is chosen based on a grid
refinement study. The dependency of the numerical results on
the grid size is examined by comparing the results for different
meshes (400, 500, and 650 thousands). The grid convergence
index [40] is calculated for the tangential velocity component.
The tangential velocity is observed to be monotonically
increasing with grid refinement. The maximum numerical
uncertainty in the finest grid (650,000 cells) for the tangential
velocity is around 4.2%. Hence, the 650,000 cells mesh was
deemed to be sufficiently fine. The same mesh is used for both
the LES and RANS approach.
The non-dimensional wall distance (y+) of the centroid of the
first cell is less than 0.7. Therefore, the grid near the wall is
sufficiently fine for the LES and no wall function is used since
(y+ < 1) [20]. For the RANS simulation, a Scalable Wall
Function [25] is used since it provide good accuracy for y+ < 11
for high Reynolds number and wall bounded flow.
Porous
domain
Figure 3 Structured hexahedral O-grid mesh generated using
Ansys ICEM CFD. A finer grid resolution is created near the
wall and at the core. Based on the grid refinement study, this
mesh appears sufficiently fine and of good quality for the
numerical simulations.
RESULTS AND DISCUSSION
A comparison between simulation results found using the
LES with the WALE model and the RANS equation closed with
the RSM is shown in Fig. 4. The results obtained from the
LES/WALE model (Fig. 4a) show that the swirling motion
continues to the bottom of the CFFH. However, the swirling
motion dies off quickly in the filter region in the case of the
RANS/RSM (Fig. 4b). The wall reflection term in the RSM
(the LPSM) redistributes the normal stress near the wall, i.e. it
tends to damp the normal stress perpendicular to wall, while
enhancing the stress parallel to the wall [20]. The interface
between the bulk flow domain and porous medium is specified
as an interior region for the numerical simulation based on the
RSM and a viscous resistance is imposed in the filter domain to
mimic a porous medium. However, the inner surface of a very
low permeable porous medium acts as a solid wall which is
overlooked in the simulation bases on the RSM. Moreover, the
RSM requires wall function for the near wall treatment, but the
present simulation method has no capability to impose a wall
function at the interface. Therefore, the wall reflection term in
the RSM cannot redistribute the normal stress at the interface,
which may be the possible cause of the immediate drops of the
swirl intensity in the filter region. In the LES with WALE
model, no wall function is used because of high resolution of
6
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grid near the wall and at the interface between bulk flow and
porous medium. It appears that as a consequence of this, the
LES approach provides improved results near the interface
between the bulk flow and filter domain. The results presented
in the remaining part of the paper are calculated based on the
flow field obtained using the LES approach.
Inner
vortex
Outer
vortex
recirculation zones near the porous filter eventually block the
pores because of the radial outflow. On the other hand, droplets
suspended within a recirculation in the solid cylindrical region
have higher residence time. Because of the higher residence
time and of the lack of radial outflow, the suspended droplets at
z/D > 4 eventually migrate to the core and move to the
overflow orifice. Fig. 5d shows flow streamlines for a higher
magnitude of permeability (α = 1x10-12). A large number of
recirculation zones are generated in the core flow, which may
breakdown the oil rich core and provide resistance against the
movement of oil droplets to the overflow orifice.
Velocity
20.00
15.00
Porous
filter
10.00
5.00
0.00
[ms^-1]
LES with WALE
RANS with RSM
(a)
(b)
Figure 4 Three dimensional streamlines calculated using a) the
LES with the subgrid WALE model b) the RANS equations
with the RSM for ReF = 18460 and α = 2x10-13. The color map
represents the velocity magnitude. The swirl intensity drops off
rapidly in the filter region in the case of results obtained by
solving the RANS equation combined with the RSM.
The time-averaged velocity streamlines obtained using the
LES approach are shown in Fig. 5 for the test cases of 1 to 4. At
a high Reynolds number (ReF = 27690) the inner core is
“strong” but unstable. Moreover, a large number of
recirculation zones are generated in the filter region (z/D < 4).
However, the flow recirculation zones in the outer vortex at z/D
> 4 are fewer than that in the filter region. With a decrease in
the Reynolds number, the core gets “thicker and weaker” but
more stable. The number of recirculation zone decreases in the
filter region (z/D < 4) with a reduction in the Reynolds number.
The trend is opposite in the solid cylindrical region (z/D > 4).
For the low Reynolds number (ReF = 9230) the core appears
straight and stable. The recirculation in the flow field suspends
oil droplets and provides a resistance against droplets‟
movement towards the core. Droplets suspended in the
ReF=27690 ReF=18460 ReF=9230 ReF=18460
α =2x10-13 α =2x10-13 α =2x10-13 α =1x10-12
(a)
(b)
(c)
(d)
Figure 5 Plane view of time averaged velocity streamlines on
the A-B plane, as shown in Fig. 2a. A higher Reynolds number
shows more recirculation in the filter region. The opposite is
true in the solid cylindrical region. The core flow regime
appears more unstable for a higher Reynolds number.
The effect of the Reynolds number on the underflow grade
fouling is shown in Fig. 6. The grade fouling (FU) is calculated
as FU = (1 − GO )⁄R U where GO = ṁDO ⁄ṁDF [30, 31] is the
overflow grade recovery and R U = Q U ⁄Q F is the underflow
ratio. Here ṁD is the mass flow rate of dispersed droplets. The
grade fouling represents a mass fraction of oil droplets deposits
on the filter surface for a given operating condition. Figure 6
indicates that all the droplets having a size less than one micron
deposit on the filter. In other word, the vortex motion cannot
separate any droplets smaller than one micron. The grade
fouling decreases with an increase in the droplet size.
According to Stokes‟ law, a larger droplet creates a greater
7
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FU
centrifugal force which in turns increases the migration of oil
droplets towards the core. It is interesting that the grade fouling
increases with an increase in the Reynolds number. The lowest
grade fouling is observed for the ReF = 9230. The grade fouling
should increase again for a Reynolds number below a specific
value. An insufficient swirling intensity due to a small
Reynolds number lessens the migration probability of droplets
towards the core. The unstable core (see Fig. 5) for the higher
Reynolds number redirects the migrated droplets in the outer
flow field. Moreover, the larger number of recirculation zones
for a higher Reynolds number trap droplets near the filter
surface. These suspended droplets eventually are deposited on
the filter surface and foul the membrane. For ReF = 9230, there
is no fouling of porous filter found for oil droplets greater than
20 microns.
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Re= 27690
Re = 18460
Re = 9230
0
20 25 30 35 40
dD (μm)
Figure 6 Grade fouling versus droplet size plot for the different
Reynolds number. The fraction of oil droplets deposited on the
porous wall increases with the Reynolds number.
FU
correspond to permeability values of 2x10 -13 m2 and 1x10-12 m2
respectively. The grade fouling increases with an increase in the
permeability of porous filter. For a higher magnitude of the
permeability, a larger number of recirculation zones found in
both the inner core and outer vortex (see Fig. 5d) destroy the oil
rich core as well as move oil droplets in random directions. As
a consequence, grade fouling increases with an increase in the
underflow rate.
5
10
15
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Ru = 0.43
Ru = 0.87
0
10
20
30
40
50
60
dD (μm)
Figure 7 Grade fouling versus droplet size plot for different
underflow ratio. RU = 0.43 and 0.87 correspond to permeability
values of 2x10-13 m2 and 1x10-12 m2 respectively. Higher radial
outlet through the porous filter increases the grade fouling.
Effect of the underflow ratio on the grade fouling is
presented in Fig. 7. The underflow ratios of 0.43 and 0.87
Figure 8 Contours of volume fraction of the dispersed phase for
ReF = 18460 and dD = 15 μm. The feed volume fraction of
dispersed phase is 0.05. An oil-rich core is developed in the
filter region (z/D < 4). The calculated grade fouling is 0.5.
Contours of the volume fraction of the oil phase in the flow
field for ReF = 18460 are shown in Fig. 8. The inlet volume
fraction of the dispersed phase is 5% of the total mixture at the
feed. The results obtained using the multiphase flow
simulations support the single phase flow pattern as shown in
Fig. 5b. An oil-rich core is generated in the filter region. In the
lower half of the solid cylindrical section, there is no
considerable oil-rich core developed. In the filter region, the
inner vortex core is stronger and more stable than that in the
upstream region (Fig. 5b). Oil droplets can easily move and
stay in a stable core. Flow structures in the core in both the
filter and upstream regions, obtained from single phase
simulations, correlated with the patterns of volume fraction
distributions calculated using multiphase flow simulations. In
the solid cylindrical section, the recirculation and the unstable
core (Fig. 5b) create a mixing effect in the flow field. As a
consequence, oil droplets randomly distribute over the domain
and no considerable oil-rich core is observed in the solid
cylindrical section.
The normalized volume fraction of the dispersed phase at the
middle of the filter region (z/D = 2) is shown in Fig. 9. At the
oil rich core (2r/D = 0) the volume fraction of the dispersed
phase is less than the feed volume fraction. It indicates that a
fraction of the dispersed phase volume separates in the solid
cylindrical section. However the normalized volume fraction
decreases in the outer periphery of the inner vortex (2r/D ≈
0.4). It again increases near the filter surface (2r/D ≈ 0.9). It
appears that the recirculation near the filter surface (Fig. 5b)
suspends oil droplets which yield a higher volume fraction near
the filter surface.
8
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resistance against the movement of oil droplets towards the
core and enable the stable oil-rich core to move easily to the
overflow orifice.
1
ϕ/ϕF
0.9
0.8
0.7
0.6
0.5
0
0.2
0.4
0.6
0.8
1
2r/D
Figure 9 Normalized volume fraction of dispersed phase at z/D
= 2. ϕF = 0.05 is the feed volume fraction. The concentration of
dispersed droplets is higher at the core and near the filter wall.
CONCLUSIONS
Based on the results presented above the following
observations can be made
i) Flow disturbances and recirculation increase with an
increase in the feed Reynolds number.
ii) The core flow becomes unstable at high values of the
feed Reynolds number, which destroys an oil-rich core
and redirects oil droplets in the outer flow field.
iii) Recirculation and an unstable core generate a mixing
effect in the flow field which reduces the separation
performance of the CFFH
iv) Grade fouling decreases with an increase in the size of
oil droplet.
v) Grade fouling also decreases with a reduction of the
feed Reynolds number up to a certain value.
vi) A higher permeability as well as a higher underflow
ratio increases the grade fouling.
vii) The LES with the WALE subgrid scale model appears
to provide improved simulations of swirling turbulent
flow in the CFFH when compared to the RANS
equation closed off with the RSM.
viii) For the operating conditions simulated, the CFFH
appears to be very efficient device. However, high
pressure is required due to the low permeability of the
filter.
ACKNOWLEDGMENTS
Support for this research from the U.S Environmental
Protection Agency (award no. RC-83518301), the U.S. National
Science Foundation (award no. IIA-1243433), and MSU
Foundation (Strategic Partnership Grant no. 71-1624) is
gratefully acknowledged.
ReF=27690
ReF=18460
ReF=9230
(a)
(b)
(c)
Figure 10 Trajectories of oil droplets for dD=15 µm for different
Reynolds numbers. Five droplets are injected from an inlet
surface. The color code is used to identify individual droplets.
No droplets foul the filter for ReF = 9230 for dD = 15 µm which
corresponds to result shown in Fig. 6.
Trajectories of oil droplets for different operating conditions
are shown in Fig. 10. A total of five uni-sized oil droplets (dD =
15 μm) having a specific gravity of 0.85 are released from an
inlet surface. Different colors in the trajectories indicate distinct
oil droplets. Figure 10 shows oil droplets rotating in the outer
vortex for ReF = 27690. The migration probability of oil
droplets toward the core increases with a decrease in the
Reynolds number. The unstable core and a larger number of
recirculation zones for higher Reynolds number reduce the
migration of oil droplets toward the core. Fewer disturbances in
the flow field for a lower Reynolds number provide less
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