7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Modeling of Turbulent Flow with Particle Deposition in Curved Pipes
P. Zhang Y. Gros R. M. Robertst and A. B~nard*
Department of Mechanical Engineering
Michigan State University
East Lansing, MI 48824
tChevron Energy Technology Company
1400 Smith Street
Houston, TX 77002
Keywords: turbulent bend flow, EulerianLagrangian simulations, pressure drop, particle deposition, curved pipe
Abstract
Multiphase flows through circular curved pipes exhibit important physical phenomena characterized by large pressure drop
and separation of different phases. Those phenomena are especially sensitive to the secondary flows (the Dean vortices)
induced by the centrifugal force associated flow through a bend. Much work has been done in the past on measuring and
modeling pressure drop and particle deposition in turbulent bend flows. The accuracy of the numerical simulations however
is often in question when compared with experiments. This may be due to a number of factors which include the selection of
an appropriate turbulence closure or the quality of the treatment of the near wall behavior. In this work, the performance of
the ReynoldsAveraged NavierStokes equation (RANS) combined with the linear pressurestrain Reynolds Stress Model
(RSM) is investigated. Different nearwall treatments are used in the commercial code FLUENT including the Standard Wall
Function (SWF), the Nonequilibrium Wall Function (NEWF) and the Enhanced Wall Treatment (EWT). A qualitatively
study is first performed of the complex flow patterns obtained using the RSM with EWT. Subsequently, the accuracy of using
RSM with EWT in predicting pressure drop and particle deposition is investigated by comparing the numerical results with
experimental works from literature. The particle deposition is modeled using a simple Lagrangian particle tracking scheme.
Grade efficiency curves are computed for several bend geometries. Results show that, as expected, turbulent bend flows
exhibit complex flow patterns which are influenced by the bend curvature ratio and the flow Re number. The pressure drop
along the curved pipe is well predicted for all nearwall treatments except at the inner wall and outer wall of the 1800bend
where an error of about 7% is obtained. With respect to particle deposition, however, using an EWT can improve the
accuracy up to 30% in a 900 bend and 50% in a 1800 bend compared to other nearwall treatments.
1 Introduction
Turbulent flows in curved pipe are commonplace in the oil
and gas industry. For example, natural gas transported in
pipes is often wet and water droplets, as they pass through
the bend, may impact the pipe wall where they accumulate
and form a wall film. The presence of bends is wellknown
to be associated with large pressure drops and to affect the
performance of downstream equipment. This is especially
important for multiphase flows as the centrifugal force
affects the phase distribution. Secondary flow patterns in
curved pipes are thus studied in this work in order to
evaluate their effects on the disperse phase.
Much work has been done on studying pressure drop and
particle deposition in curved bends. Thomson (1876) first
observed the curvature effects of bends on flows. Eustice
(1910) also observed the existence of secondary flows by
injecting ink into water passing through a coiled pipe.
Wilson et al. (1922) observed that the pressure drop is
dependent on the flow Reynolds number and Dean (1928)
studied the stability of a curved pipe flow and identified
the condition for the onset of secondary vortices. Ito (1959)
indicated that secondary flows can cause a rapid rise in
friction and lead to a much increased pressure drop.
Tunstall and Harvey (1968) observed the presence of a
main or primary flow recirculation at the inner wall for
tight bends (8 < 3). Berger et al. (1983) have provided a
comprehensive review of literature on flows through
curved pipes. The intensity of such secondary flows
depends on the combination of the main flow Reynolds
number (Re) and the curvature ratio (8=%Rb t and can be
characterized by the dimensionless number called the Dean
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
particle residence time and bend curvature ratio on the
grade efficiency are investigated.
2 Modeling the Continuous Phase
The ReynoldsAveraged NavierStokes (RANS) equation
governs the transport of all meanflow properties of
turbulent flows with the range of all scales being modeled.
This allows computing costs to be reduced provided that
an accurate closure model is used. The commercial
software ANSYS FLUENT 12 was used for the
simulations presented below. The software provides
several models for closing the RANS equation and these
include models based on eddvviscosity closure
approaches the "standard" kepsilon, and km models.
Various formulations of the Reynolds Stress Model (RSM)
are also available: these involve solving transport
equations for approximating the Reynolds stress and an
equation for the dissipation rate. For bounded flows, the
SpalartAllmaras model and the km model are designed to
resolve the entire domain comprising the nearwall region.
However, Matida et al. (~ll*** used a mouththroat
geometry and found that the grade efficiency curves
computed from those models are highly overpredicted
over the entire range of particle diameters. The discrepancy
reaches the order of 15%25%. The agreement to the
experiment of the standard kepsilon model is observed to
be even worse than that of the km model. To avoid using
the Boussinesq approximation, McFarland et al. (1997)
employed the RSM and calculated the turbulent fluctuation
by using a onestep correction of Abuzid et al. (1991).
However, deviation from the results of Pui et al. (1987)
was still up to 17% at Stokes number St=0.2. Although
much work has been done using different closure models,
the effect of the nearwall treatments on pressure drop
along curved pipes and particle deposition on the pipe wall
are rarely discussed. An accurate representation of the flow
in the nearwall region is needed to represent appropriately
particle deposition to the wall. ANSYS FLUENT 12
allows to use the standard wall function (SWF), the non
equilibrium wall function (NEWF) or the enhanced wall
treatment (EWT) as the nearwall treatments. Zhang et al.
(2009) used the RSM and the EWT for the nearwall
treatment. Results are compared to the work of Pui et al.
(1987) which show that the EWT based on the RSM
closure is promising in predicting particle deposition in a
900 bend. An error of only about 3% is observed at small
Stokes number. This work is an extension of Zhang et al.
(2009).
3 Modeling the Discrete Phase
A Lagrangian method is used to track particles moving in
the continuous phase through the curved pipes. Particles
are released in the continuous phase and treated as a
number which is defined here as De = Re/81". Ito (1987)
demonstrated that the size of the secondary flow patterns
matches the size of the duct radius. Based on theoretical
calculations, Cheng and Wang (1975) ignored the
existence of secondary flows in bends and derived a
formula to predict particle deposition in bends. However,
the formula is accurate only for low Reynolds number for
1000
complex flow patterns as well as turbulent fluctuations
play a major role in particle deposition patterns. They
obtained a correlation of particle deposition efficiency for
turbulent flow in a 900bend based on experiments and
stated that the deposition efficiency is only the function of
the Stokes number (St). Peters and Leith (2003) measured
the deposition efficiency in industrial curved pipes with
different bend angles, a large pipe diameter and high flow
Reynolds number, which shows a different efficiency from
that in the work of Pui et al.(1987). Brockman (1993)
provided a correlation including the Stokes number as well
as the bend angle, while McFarland et al. (1997), based on
their numerical results, developed a correlation that
includes the bend angle, the St number and the bend
curvature ratio to predict the deposition efficiency, the
correlation however differs from Pui et al. (1987) results.
Computer simulations provide an efficient approach for
studying flows through curved pipes under various
conditions. Practical simulations can be performed today
by solving the filtered NavierStokes equation using a
LargeEddy Simulation (LES) or by solving the Reynolds
Average NavierStokes (RANS) equation with an
appropriate closure model for the Reynolds stress. For
example, Breuer et al. (2006) and Berrouk et al. (2008)
used LES and predicted results for particle deposition are
in good agreement with the work of Pui et al. (1987)
except for small Stokes number St<0.2. A RANS approach
was selected even though LES appears appropriate due to
the large number of simulations expected. A Reynolds
stress model was selected to complete the formulation of
the RANS equation due to the anticipated presence of
strong streamline curvatures.
The impact of bend curvature ratio and Reynolds number
on the flow patterns of 1800 bends (Ubends) is first
studied below. The intensity distribution of secondary
flows is investigated at different cross sections of the U
bend with a fixed curvature ratio. Numerical calculations
from different nearwall treatments of the pressure drop are
compared to the experimental works of Sudo et al. (1998
and 2000). Lagrangian calculations for particle deposition
are examined. The effect of turbulent fluctuations on
particle deposition is also discussed. Grade efficiency
curves are compared to the experimental work of Pui and
Liu (1987) and Brockmann (1993). Finally, the effects of
Table 1: Summary of test cases
Cases Flow patterns Pressure drop Particle deposition
Diameter, d [nun] 8.51 104 8.51
8 1.5,5.6 4.0 3~9
9 [degree] 180 90,180 60~180
Re (x10 ) 1~ 5 6 1
NearWall Treatments EWVT SWF, NEWF, EWT SWF, NEWF,EWVT
Table 2: Boundary conditions
Calculated from the known
velocity inlet [m/s]
Re and d
Inlet
turbulent kinetic energy [nr1 i'] k=1
turbulent dissipation rate [nr/s ] E=1
Outlet pressure outlet [Pa] Ptati=0
Wall noslip boundr ms uwanl=0
Temperature [K] 300
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
velocity at the pipe entrance. Turbulent flow is fully
developed before it enters into the bend: this is ensured by
keeping a long entrance length. At the pipe wall, a noslip
boundary condition is applied. The wall is "sticky" so that
particles adhere to it on contact. The boundary condition
for the outflow is pressure outlet with the static pressure
equal to zero. The applied boundary conditions are
summarized in Table 2.
discrete phase by assuming that their concentration is
dilute i.e. the particles do not interact and they have no
effects on the continuous phase. The particle trajectories
are obtained by integrating the equation of force balance,
which is achieved by using a 5th Order RungeKutta
scheme (Cash and Karp, 1990). The effects of turbulent
fluctuations on the droplet deposition are modeled in
Fluent by using a discrete random walk model (DRWM),
or stochastic turbulent model. While the mean gas
velocities are obtained from the continuous phase
calculation, the fluctuating components are computed
using a random Gaussian distribution.
4 Description of Test Cases
A parametric study was perfonned to study the effects of
various parameters at particle deposition and the test cases
are summarized in Table 1. A tight bend with a curvature
ratio 6=1.5 and a regular bend with 8=5.6 are used to study
the curvature effect on the flow patterns. In addition, the
effect of the flow Re number on the flow patterns is
investigated by changing the flow velocities. The pressure
drops are predicted numerically from different nearwall
treatments in a 900 bend and a 1800 bend and compared to
the experimental work of Sudo et al. (1998 & 2000). The
perfonnance of the nearwall treatments in predicting
particle deposition is evaluated by comparing the grade
efficiency to the experimental work of Pui et al. (1987).
Varying the bend curvature ratio and flow residence time
is achieved by changing the bend radius and bend angles.
Inlet
 D
Entrance Length D
/"
Figure 1: Schematic of the geometric configuration of
the curved pipe used in this study.
The mesh construction for each cross section along the
curved pipe is shown in Figure 2. The density of the mesh
is a function of the type of the nearwall treatments. The
dimensionless value v' is used to describe the distance
from the wall. y = ypu, / 9L, where y is the real distance of a
location in the calculation domain from the wall [m]; u,
Figure 1 shows the geometry of a curved pipe with an
unspecified angle 9. The selection of the geometric
configuration is based on the experimental setups available
for comparison. The outer and inner bends of the pipes are
labeled as "O" and "I", respectively. The boundary
conditions in all simulations are specified to be unifonn
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
flows are observed at the 00 deflection. A pair of courter
rotating vortices occurs at the 450 deflection and becomes
distorted at 900. It then evolves into two pairs of vortex
cells at the 1350 deflection and becomes more distorted at
the 1800 deflection. The additional pair of vortices at the
inner bend is caused by the recirculation which generates a
low velocity zone at the inner bend. This leads to a high
pressure drop at the bend. Moreover, it changes the
downstream flow patterns, which can be seen from the
cross section after the recirculation. At this location,
incomplete Dean vortices are observed.
denotes the friction velocity [m/s] and 9L is the dynamic
viscosity of air [n?/s]. For SWF and NEWF, the distance
of the first cell centroid from a wall has to be laid above
the buffer layer at y' between 30 and 300 so that those
semiempirical equations work effectively. A coarse mesh
with 4000 nodes is sufficient to meet this requirement. For
EWT, the centroid of walladjacent cells is made at y+ 1
and at least 3 grid nodes are put inside the viscous sublayer
(y <5) to ensure the accuracy of the numerical solution. A
fine mesh with 8800 nodes is used. Along the streamwise
direction of the pipe, the number of cross sections is
changed according to the length of the pipes. The mesh is
dense for the bend and the section after the bend but
relatively coarse for the entrance section of the pipe to
reduce the costs of the simulations. The maximal domain is
around 4.5 million grid nodes.
I
Figure 3: Streamlines show the development of flow in
a tight bend; the secondary flow patterns are also
shown at different locations.
Figure 2: Otype structured mesh used for a cross
section. It allows refining the mesh close to the wall and
prevents a singularity at the center of the pipe.
5 Results and Discussions
No primary recirculation (along the main flow direction) is
observed in a generic bend with 8=5.6. The streamlines,
secondary flow intensity and pressure distribution at the
450, 900 and 1350 deflections are shown in Figure 4. The
streamlines at all cross sections show pronounced
secondary flows. Two cells at the 900 deflection develop
into four cells at the 1350 deflection. The vortices are
pushed to the wall side due to the centrifugal force. Figures
4.d, 4.e and 4.f show the contours of the corresponding
flow intensity to the secondary flows in Figure 4.a, 4.b and
4.c, which is calculated by using uplane/UOI X 100%,
where uplane is the absolute velocity in the plane of a
cross section and Uo is the mean axial flow velocity.
Graphs show that the mean velocity of the secondary flow
can reach up to 36% of the mean flow velocity magnitude
outside the boundary layer close to the inner bend at 450
deflection. It also can be observed that the intensity of the
vortices at the centre location becomes weaker when the
The complexity of the flow patterns observed in curved
pipes and secondary flow intensity are first discussed
below, followed by a comparison between the computation
and the measurement of pressure drops and grade
efficiency.
5.1 Flow Patterns and Secondary Flow Intensity
The numerical simulation results of flow patterns in curved
pipe are presented in Figures 35. The streamlines at the
middle plane of a tight bend with 8=1.5 are shown in
Figure 3, which describes a strong recirculation of the
primary flow that occurs at the inner bend as the flow is
passing through the tight bend. Meanwhile, the
development of the secondary flows is shown at different
cross sections (at 00, 450, 900, 1350, 1800 deflection and
right after the recirculation, respectively). No secondary
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
450 deflection
900 deflection
1350 deflection
(b) (c)
01I
(e) (f)
01I
126 300 500 700 90 1100 1269
315 500 70 900 1100 1300 1440
270 400 600 800 1000 1200 1400
(h)
Figure 4: The streamlines associated with secondary flow patterns are studied at a 450, 900 and 1350 deflection and
shown in (a),(b) and (c); the contours of the relative inplane velocity magnitude defined as uplane/Uo are shown in
(d), (e) and (f); and the corresponding pressure distribution of the cross sections are shown in (g), (h), (i).
O
O
Re5 X IV
Figure 5: Plots of the streamlines associated with the inplane flow patterns to demonstrate the effect of an increasing
flow Re number.
Re~l X 1(0 Re3 X 10 '
1 0' 30" a00 90" 1 2 3 4 .5
z'/d z/d
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
time), but for flows with a longer residence time in a bend,
the pressure drop is not predicted accurately.
(a) 02
o 
0.0 
outer Side inner
PS~? Exp. n o n
SYa
flow proceeds along the bend, which indicates that the
intensity of secondary flow reaches a maximum very
quickly and weakens gradually downstream until the flow
becomes again fully developed. This can also be observed
by studying the pressure distribution at different cross
sections in Figures 4.g, 4.h and 4.i. The pressure is high at
the outer wall bend and low at the inner bend due to the
centrifugal force; the pressure difference becomes smaller
downstream.
In Figure 5, flows with a Reynolds number equal to 10,000,
30,000 and 50,000 are used and the flow patterns at a 1350
deflection of the same bend are compared. Instead of two
cells of vortices for flow with Re= 10,000, four and six
cells are observed at the higher Reynolds number.
5.2 Pressure Drop along Curved Pipes
Calculations of the pressure coefficient (Cp) along the
900 bend and the 1800 bend are compared to the
experiments of Sudo et al. (1998 and 2000) in which the
pressure drop is computed with
0.2 
0.0 
0.2
04
06
S0.4
1
1
Cp = (P Prr)/ (pU02)
2
where P denotes the local static pressure [Pa], Pref
represents a reference pressure and p is air density (1.225
kg/m3). The flow has a mean velocity of 8.7 m/s2 and is
passing through a bend with a radius ratio of 8 = 4. The
flow is highly turbulent with Re=60,000. The pressure is
predicted by using RSM with different nearwall
treatments. Comparison between the numerical results and
the experiment data are shown in Figure 6. z' and z are
used to locate a cross section along the pipe direction and d
is the pipe diameter [m]. The cross sections at the
beginning and the end of the bend are located at z'= 0 and z
= 0, respectively. The reference pressure is the pressure
located at the outer bend at the cross section z' = 17.6d
from the beginning of the bend. Figure 6.a shows that all
three nearwall treatments are capable of modeling the
pressure drop along the outer wall and the side wall of the
900 bend. At the inner bend, however, the SWF and
NEWF overestimate the pressure drop at the inner wall of
the straight pipe after the bend. The plot shows that results
from EWT have a better agreement at those locations. For
the 1800 bend, the results from different nearwall
treatments have a good agreement except for the inner wall
and the outer wall of the Ubend portion. SWF and NEWF
seem to get better results than EWT at this portion. The
factors that influence the pressure drop along a bend
include the separation at the inner bend, excess friction at
the outer bend, and secondary flows. Results show that
both models are doing well in short bends (small residence
4. go. 444. Ia 1 3 1 5 g
Figure 6: A comparison between the computed and
predicted pressure drop values from different near
wall treatments is made at the outer bend, inner
bend, and the sides with the experimental data of
Sudo et al [1998, 2000].
5.3 Modeling Particle Deposition
Grade efficiency curves can be obtained from the results of
particle tracking simulations in order to evaluate the
performance of a device in separating particles. The grade
efficiency is defined as
M N
r(St) = a
M N
where M, is the mass of particles separated from the total
particle mass M released. Since monodisperse particles
having the same density are tracked, M, and M are
replaced respectively by No which is the number of
particles trapped in the bend plus the straight pipe after the
bend and by the total number of particles tracked N. The
grade efficiency is presented as a function of the Stokes
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
deviation is observed for the results from SWF
and NEWF (55%). The EWT captures more
Grade efficiency in a 90* bend
a %@419870gal) 3%
A EW wl Stochas~cModel
SE'WT wlo Stochasitc Modle
et
number St which describes how fast particles respond to
the flow. St is the ratio of the particle response time zP and
the system response time z,,,, it is given as
higher
(50%)
(a)
ZP CpPD U i
St = P )(3) so
z,, 18tpd/2
where C is the Cunningham correction factor to"
(Cunningham, 1910), DP iS the particle diameter [m], Ut, is E s
the mean flow velocity [m/s] and pP denotes the particle 5
density [kg/m3]. For given values of Ut,, d, pP and p., St is u so
then proportional to the particle size. The grade so 3
efficiencies are compared to the experiment of Pui et al. 2
(1987), who provided a correlation for predicting grade lo
efficiency in a 90degree bend as a
r= 1_10 0.963St (4
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Stokes Number, St
1.4 1.8
Only particles depositing on the bend were counted in their
experiments. Brockmann (1993) extended the above
formula and applied it to bends with different angles, and
provided the following correlation
Ty = 1 exp(1.4 12St68) (5)
where 9 is bend angle in radians. Both correlations are
stated with a 3% uncertainty.
In this work, particle mimicking droplets are released at
upstream 3d prior to the bend. At this place, the flow can
be treated as fully developed and the bend effect on
particles can be neglected. 25,000 monodisperse spherical
droplets are released at the mean flow velocity Ut, with the
density 895 kg/m3. Released particles are uniformly
distributed and kept away from the wall at the very
beginning.
The grade efficiency curves of the 900 bend and the 1800
bend computed from the RSM combined with different
wall functions and the stochastic turbulent model are
plotted against St and shown in Figure 7 together with the
empirical correlations. The results from SWF and NEWF
are in relatively good agreement for large St. However,
when the value of St becomes small, a large discrepancy
from the experiments can be observed. The maximal
discrepancy (of 31%) occurs for a very small value of St
(St=0.001). Small particles are very sensitive to turbulent
fluctuation because of their fast response to the system.
The failure of the SWF and NEWF to adequately capture
the turbulent fluctuations near the wall may explain this
deviation. On the other hand, using EWT agrees well with
the experimental data and the maximal deviation of the
comparison is only 3% at St=0.46. Comparison in Figure
7.b looks similar to that in Figure 7.a. At small St, however,
a
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Stokes Number, St
Figure 7: Comparisons between computed and
experimental data for the grade efficiency show
a discrepancy occurs at small value of St for SWF
and ENWF and an improvement by using an
EWT in the 900 and the 1800 bends.
accurately the actual velocity profile in the boundary layer
especially if separation and strong streamline curvature
occur. A more accurate solution is thus expected when
compared to the more approximate SWT and NEWT. This
is achieved at the cost of a finer mesh. Although an error
of about 10% is observed at very small St for the results
from EWT simulations, the results match the experiment
very well for other values of St. The larger deviation is due
to a longer particle residence time in the bend. In addition,
a very poor agreement is observed without using the
stochastic model. Small particles are especially sensitive to
the fluctuating velocity because of their low inertia, which
account for the great discrepancy of the model when not
considering particle dispersion. Figure 8 shows the
computed grade efficiency for curved pipes when changing
Grade efficiency in a 180* bend
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
centrifugal force. This trend is consistent with the
observation of the experiment done by McFarland et al.
(1997). In Figure 9, Brockmann's correlation appears to
provide accurate results except when the bend with
curvature ratio equal to 9, which probably indicates that
the correlation should include the effect of a bend
curvature ratio.
the particle residence time. The grade efficiency for the U
bend is obviously higher than that for the 900 bend for the
whole range of St, which indicates that particles
experiencing a longer time inside a bend have larger
chance to deposit on a pipe wall and thus higher grade
efficiency can be obtained. The particle cutsize for the
1800bend is 3/5 of that for the 900 bend.
6 Summary and Conclusions
Effect of particle residence time in a bend
a xx
a n
a x
 . . . . . . . . . . . . . . .
x Residence Ume ttau
an y a Resiuencesmmaus,
ox
Turbulent flows passing through circular curved pipes are
studied in this work using computational fluid dynamic
simulations. The simulations are performed using the
RANS equation closed with the Reynolds Stress Model.
Results of these computations show that turbulent bend
flows possess complicated patterns that significantly affect
the pressure drop and particle deposition. These patterns
are influenced by the flow Re number and the bend
geometric configuration. Computed results for the pressure
drop through a bend obtained from different nearwall
treatments are all close to experimental measurements
provided that the mesh meets the y+ requirement for the
wall treatment selected except at the outer and inner pipe
of the 1800bend. Using an RSM with EWT performed
best in predicting particle deposition patterns. The
inaccuracy of SWF and NEWF for particle deposition
indicates that these nearwall treatments are not
appropriate. Using EWT as the nearwall treatment based
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Stokes Number, st
1.4 1.6
Figure 8: Comparison of grade efficiency due to
different particle residence times (tau=2.1ms).
Effect of bend curvature ratio
  a a 
50 j /
40" 6: RMwlEWI 6
soARSMwlE~WF,&R~II, ..9
20 /Af~  Brackmann's corelatlr
0.0 0.5 1 .0 1.5 2.0
Stokes Number, st
Figure 9: Comparison of results for curved
different curvature ratios and fixed particl
times shows the grade efficiency is increa~
decrease of the bend curvature ratio
Bends with curvature ratios of 3, 5 and 9 corr
different bend angles of 1800, 1080 and 600 a
comparison of the computed grade effil
Brockmann's empirical correlation (Eqn. 5)
Figure 9. The plot shows that the increasing cr
reduces the grade efficiency of a curved
centrifugal force is inversely proportional
radius, thus the increasing grade efficiency is
 on an RSM appears to be adequate for simulating the
pressure drop and particle deposition in curved pipes.
Based on the above study, broad guidelines can be derived
to help predict particle deposition in curved pipes. First, a
turbulence closure appropriate for flows with streamline
culvatures should be used. In this work, the RSM is
emplOyed with the linear pressurestrain correlation. The
on (1993)
selection of an EWT as the nearwall treatment appears
crucial in correctly predicting particle deposition along
with constructing a highquality mesh. For example, an O
2.5 3.0
type mesh structure was selected for the cross sections and
the centroid of the walladjacent cells should be located at
Spies with about y+1 and have at least 3 cells within a y+ < 5.
e residence..
The grade efficiency for curved pipes is influenced by the
sed with a
bend diameter d, the curvature ratio 8 and the particle
residence time inside the bend z for a fixed flow rate. The
responding to grade efficiency of a bend is decreased with a decrease of
re studied. A the residence time z, but increases as d and 8 are smaller.
ciecy ith Acknowledgements
is shown mn
urvature ratio Support for this work from the NSFI/UCRC on
Pipe. The Multiphase Transport Phenomena and the Chevron Energy
to the bend Technology Company (Advanced Production Systems) is
due to larger gratefully acknowledged.
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
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