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Published: June 01, 2011
r 2011 American Chemical Society 13230
dx.doi.org/10.1021/ie2002473 | Ind. Eng. Chem. Res. 2011, 50,
1323013235
ARTICLE
pubs.acs.org/IECR
LiquidLiquid Mixing in Coiled Flow InverterMonisha Mridha
Mandal, Palka Aggarwal, and K. D. P. Nigam*
Department of Chemical Engineering, Indian Institute of
Technology, Delhi, Hauz Khas, New Delhi 110 016, India
ABSTRACT:Themixing of liquids is a common operation in process
industries such as reneries and chemical and
pharmaceuticalindustries, etc. However, the problem of mixing of
dierent liquids has not been rigorously characterized. Therefore,
the objective ofthis paper is to investigate liquidliquid mixing in
a novel coiled ow inverter (CFI). The device works on the principle
of owinversion which is achieved by bending a coiled tube to 90 at
equidistant length. In the present study, velocity eld and
scalarconcentration distribution of liquids were characterized. The
mixing performances and pressure drop in CFI was investigated
andcompared with that of a straight, coiled tube and helical
element mixer (HEM) for a liquid ow range of 98 e Re e 1020.
CFIexhibits signicant mixing of two liquids with negligible change
in pressure drop as compared to a coiled tube as well as a HEM.
Thepresent study reveals that CFI is an ecient device for the
mixing of two liquids in process industries.
1. INTRODUCTION
Mixing in the laminar ow regime is mainly driven bymolecular
diusion. Liquid-phase mixing generally inuencesthe heat and mass
transfer rates and reactant conversion in anyreactor. However, a
careful analysis of the data reported inliterature shows that very
high uid ow rate is required in orderto induce signicant mixing in
coiled tubes.1,2 It is not possible tonarrow the residence time
distribution (RTD) beyond a certainlimit in coils with xed
curvature ratio. Hence, in order to reduceaxial dispersion, many
devices such as motionless mixers,39 owinverters,10 and chaotic
congurations1114 have been reportedin the past. Static mixers have
limitations for very viscous uids asit can induce prohibitive
pressure drop resulting in higherpumping cost. To overcome this
limitation a novel conceptwas introduced to develop an economical
and eective alter-native named as the coiled ow inverter
(CFI).1
The conguration of a CFI is a novel design, which works onthe
principle of complete ow inversion. The geometrical con-guration of
a CFI consists of 90 bends at equal intervals oflength in coiled
tube geometry. This device helps in intensifyingthe convective
transfer processes and provides enhanced transferarea per unit
volume of space. Its performance is substantiallycloser to plug ow.
A modied axial dispersion model has beenpresented to describe the
liquid-phase RTD in gasliquid owunder the conditions of both
negligible and signicant moleculardiusion in a CFI.2 It was
observed that the axial dispersion wasreduced with an increase in
liquid ow rate and number of bends.The reduction in dispersion
number was 2.6 times in the CFIhaving 15 bends as compared to a
coiled tube for two phasegasliquid ow under identical process
conditions. Furtherexperiments have been carried out to investigate
the eect ofdesign parameters such as gas and liquid ow rates,
curvatureratio, pitch, and the number of bends on pressure drop
forgasliquid ow in the CFI.15 The transition of ow regimes
ingasliquid ow was observed at critical Reynolds numbers
of800010000. Pitch had negligible eect on the pressure drop
ofgasliquid ow in the CFI. The empirical correlations for
thefriction factor have been reported for the dierent
gasliquidregimes in the CFI. These correlations take into account
the
eect of number of bends, curvature ratio, and gas and liquid
owrates.
The void fraction of gasliquid ow in a CFI was in-vestigated.16
The gas void fraction decreased with the increasein number of
bends. The eect of pitch on gas void fractionwas found to be
negligible. At a given gas ow rate, the gas hold-up decreased with
the increase liquid ow rate. An empiricalcorrelation to predict the
void fraction for dierent ow regimeshas been developed.
Liquidliquid ow exists in chemical process
industries.Information about liquid ow development, pressure drop,
andmixing eciency is required to design as well as
optimizeoperating conditions in the industries. Literature survey
showsthat information on liquidliquid ow is available for a
straighttube conguration.1720 However, very limited eorts have
beenmade in the past to explore the hydrodynamics of liquidliquidow
in coiled tubes.21 Therefore, the objective of the presentwork is
to investigate the ow development and distribution ofscalar
concentration in a CFI with = 10 and a pitch of 0.02 m.An attempt
is made to study the mixing of two liquids in straight,coiled, and
CFI tubes for the ow range of 98e Ree 1020. Theeect of Reynolds
number and number of 90 bends in the CFIon themixing eciency has
been investigated. The pressure dropas well as mixing performance
in the CFI was also compared withthe existing experimental data of
the helical element mixer(HEM).6,7 All the computations were
carried out on a SUNFIRE V440 workstation in the Chemical Reaction
Engineeringlaboratory at Indian Institute of Technology, Delhi,
India.
2. NUMERICAL MODEL
The coiled ow inverter device with circular
cross-sectionalhaving diameter, d; coil diameter,D, and pitch,Hwas
considered
Special Issue: Ananth Issue
Received: February 2, 2011Accepted: June 1, 2011Revised: May 24,
2011
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13231 dx.doi.org/10.1021/ie2002473 |Ind. Eng. Chem. Res. 2011,
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Industrial & Engineering Chemistry Research ARTICLE
for the present study. The details of the geometry considered
forcomputation has been shown in Figure 1.22
2.1. Governing Equations. The governing equations formass,
momentum, and scalar transport in the CFI were solvedwith the
control volume finite difference method (CVFDM)using commercial CFD
code Fluent 6.3.23 In the present study,the mixture model was used
to model the liquidliquid flow inthe tube. This model is used to
study flows where the phasesmove at different velocities. It works
for the case where phases areinterpenetrating. This model has been
previously used to simu-late mixing of liquids in different
configurations.8,9 The mixturemodel approach is used which assumes
homogeneous flow withvariable volume fraction of each phase. The
summed up mo-mentum equation of the phases with phase averaged
physicalproperties is solved. Unlike the Eulerian model, where
theconservation equations are coupled via interphase
interactionsterms, in the mixture model, the mixture continuity,
momentumequation, and energy equation are solved along with
additionaltransport equations for the volume fraction of secondary
phases.In the present study, the governing continuity equationmay
be
written as
tFm rFm uBm _m 1
where Fm is the mixture density where Fm = k = 1n RkFk, Rk is
thevolume fraction of phase k, uBm is the mass-averaged
velocitywhere uBm = (k = 1
n RkFkuk)/(Fm), _m represents mass transfer, trepresents time.
In the case of secondary phase, the volumefraction equation for
secondary phase p can be expressed as
tRpFp r 3 RpFp uBm r 3 RpFp uBdr, p 2
The momentum equation for the mixture can be obtained bysumming
the individual momentum equations for all phases. Itcan be
expressed as
tFm uBm r 3 Fm uBm uBm
rPr 3 mr uBm r uBTm Fm gB FBr 3
n
k 1RkFk uBdr, k uBdr, k 3
where r(FmuBmuBm) represents convection term, 3P,
representspressure, r 3 [m(ruBm ruBmT)] represents viscous
forces,
FmgB represents gravity, n is the number of phases, FB is a
bodyforce, m is the viscosity of the mixture. (m = k = 1
n Rkk). uBdr,k isthe drift velocity for secondary phase k. The
last term denotes thenet rate of momentum transfer per unit volume
by the action ofdrift velocity. The drift velocity for secondary
phase can beexpressed as uBdr,p = uBp uBm where uBp is velocity of
secondaryphase. The energy equation for the mixture can be
expressed as
t n
k 1RkFkEk r 3
n
k 1Rk vBkFkEk p r 3 kef frT 4
where Ek is the sensible enthalpy for phase k, ke is the
eectiveconductivity; ke was calculated as Rkkk where Rk is the
volumefraction of any phase k and kk is the conductivity of phase
k.The term on the right-hand side of equation represents
energytransfer due to conduction. The ow of incompressible uids
wasassumed in the given two-phase system.The transport equation for
an arbitrary scalar k is
FmCk
tr 3 Fm uBmCk kmrCk Skm k 1, ::::,N 5
where mk = Rllk and Smk = lSlk are the mixture diusivity and
source term for transport variable Ck.The mesh of the geometry
was built in GAMBIT software. It
was then computed in FLUENT 6.3 software. Segregated solverwas
used to model the ow of liquids. Liquids with constantvelocity were
employed at the inlet. No-slip boundary conditionand the zero
derivative conditions for the scalars were treated onthe tube wall.
Flow was considered as fully developed at theoutlet. The scalar
transport technique was used to compute themixing characteristics
of liquids. Dierent scalar concentrationswere employed in the two
halves of the tube inlet. The interfacefor initializing the scalar
concentration was perpendicular tothe direction of the secondary
ow. Second-order upwindscheme was used to model the convection term
in the governingequations. The coupling between velocity and
pressure wasresolved using SIMPLE algorithm. The computation was
con-sidered converged when the residual summed over all
thecomputational nodes at nth iteration, R
n , satised the followingcriterion: R
n/ Rm e 108, where R
m denotes the maximumresidual value of variable after m
iterations, applied for p, ui,and for scalars.The mixing
performance of the geometry was measured in
terms of coecient of variation (COV). It is represents
thestandard deviation of concentration to themean concentration
ofliquids.
COV
ZCavg Ci2 dA
!0:5
Cavg6
where
Cavg 1AZ A0
Ci dA 7
Cavg is the ow weighted average value of the scalar
concentra-tion over the cross-sectional area.A systematic grid
sensitivity investigation was performed.
Grid-sensitivity tests were carried out with three grids
consistingof 625 2050, 625 3100, 690 3100 (cross-section x
axial).The pressure drop values calculated for the three grids is
shown
Figure 1. Coiled ow inverter.
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13232 dx.doi.org/10.1021/ie2002473 |Ind. Eng. Chem. Res. 2011,
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Industrial & Engineering Chemistry Research ARTICLE
in Table 1. It was observed that the 625 3100 grid wasnecessary
to obtain grid independent results. Hence, geometrywith 625 3100
grids was used in the present study because itproduced data with
good accuracy and also saved computationtime.
3. RESULT AND DISCUSSION
3.1. Comparison of Numerical Predictions with Experi-mental
Results. There is lack of quantitative analysis
forliquidliquidmixing in coiled tube. Hence, to check the
accuracyand reliability of the computation technique, computations
werefirst validated with the experimental data set reported in
theliterature19 for liquidliquid flow in straight tube. CFD
simula-tions were carried out to calculate the pressure drop of
two-phaseflow of oil and water in a 0.055 m diameter, 8 m long
straighttube. The oil had a density of 790 kg/m3 and dynamic
viscosity of0.0016 kg/(m s) at 25 C. Figure 2 shows the
comparisonbetween the existing experimental values and predicted
values ofpresent CFD study for different water volume fraction
rangingfrom 0.2 to 0.75. The maximum deviation between the
CFDpredictions and the experimental data was within (2.5%.3.2.
Development of Velocity Contours. The computations
were further carried out for an industrially important system
oftwo crude oils, named Arab Mix and Mangla crude, flowing
instraight, coiled, and CFI tubes of equal length (L = 5.34 m)
andtube diameter (d = 0.01 m). The pitch (H) and curvature ratio()
of the tubes considered for the coiled tube and the CFI were0.02 m
and 10, respectively. Table 2 presents the properties ofliquids
used in the present study. The study was carried out foraverage
Reynolds numbers varying from 98 to 1020 and thenumber of 90 bends
in CFI being from 1 to 3.Figure 3 shows the development of velocity
prole at dierent
axial length for straight, coiled and CFI tube of equal length
andtube diameter. It can be seen from the gure that the
velocitycontours were fully developed for the straight tube within
lengthequivalent to rst bend (i.e., L = 1.33 m). There was no
change incontours with the increase in axial length. However, the
velocitycontours in coiled tube as well as CFI became asymmetrical
as
the axial length was increased. The unbalanced centrifugal
forceon the uid ow due to the curvature of the coil shifted the
liquidwith maximum velocity toward the outer wall of the coil.
Theow was fully developed in coiled tube at axial length of 1.33
mwhich is also length of CFI equivalent to one bend. No further
Table 1. Grid Test
cell density,
cells/mm3pressure drop
(100 Pa/m)625 2050 1.75625 3100 1.69690 3100 1.69
Figure 2. Comparison between CFD prediction and experiment
valuesof pressure drop at dierent water volume fraction of oilwater
owingin straight tube with D = 0.055 m, L = 8 m.
Table 2. Properties of Liquids
parameter inlet 1 inlet 2
density (kg/m3) 780 872
viscosity (kg/(m s)) 0.007 0.069
diusion coecient (m2/s) 10 108 10 108
Figure 3. Velocity contours of liquids owing at v = 2 m/s at
dierentaxial distance in straight tube, coiled tube, and CFI with
one, two, andthree bends having d = 0.01 m.
Figure 4. Distribution of scalar concentrations of liquids owing
at v = 2m/s at dierent axial distances in straight, coiled, and CFI
tubes havingd = 0.01 m.
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Industrial & Engineering Chemistry Research ARTICLE
modication of contours was observed with further increase
inaxial length. It was further found that the velocity contours in
CFIwas inverted to 90 at second bend (L = 2.67 m). This was due
tochange in the direction of uid owing with an introduction of a90
bend. The contours were again rotated to 90 due to therotation of
the plane of vortex at third bend (L = 4.01
m).3.3.MixingPerformance.The scalar concentrations of 0 and 1
were set in the two halves of the inlet of the tube. The
initialconcentration was prescribed perpendicular to the direction
ofthe secondary flow. Figure 4 represents the distribution of
scalarconcentration of liquids at different axial lengths in
straight tube,coiled tube, and CFI with one, two, and three 90
bends havingd = 0.01 m. The red and blue color denotes the
different scalarconcentrations of two liquids. It was observed that
the stream-lines of scalar concentrations were straight in the
straight tube.The two liquids came out from the straight tube
exactly as theyentered except at the interface where the mixing
takes place dueto molecular diffusion. There was no convective
mixing in eitherthe tangential or radial directions. This shows
that mixing ofliquids was not significant in case of straight tube.
However, inthe case of the coiled tube, the mixing in the coiled
tube wasenhanced due to the presence of Dean vortices. These
vorticesmix two liquids through advection. It was also observed
that theCFI displays a significant increase in uniformity of
concentrationcontours as compared to the straight tube and the
coiled tubehaving equivalent length. The figure clearly shows that
the con-centrations were almost uniform within 3 bends (L = 4.01
m).This was due to increase in radial mixing of the liquids
afterintroduction of each bend.
3.3.1. Effect of Reynolds Number. COV values computedusing eq 6
at the outlet of different geometries were normalizedwith a COV0
value at the inlet. Normalized COV represents theratio of standard
deviation of concentration to the mean con-centration of the
unmixed fluid at the injection stage. Figure 5shows the value of
normalized COV with varying Reynoldsnumber for straight, helical
coil tube, and CFI of equal lengths. Itcan be observed from the
figure that there was no significantchange in normalized COV of
liquids flowing in the straight tubewith an increase in Reynolds
number. However, the COV valueof liquids decreased with increase in
Reynolds number in coiledas well as CFI. The mixing efficiency
increased because of anincrease in intensity of secondary flows.
However, the normal-ized COV value of liquids flowing in the CFI
was found to benearly 1626 times lower than that of the coil tube
having equallength. This was due to the increase in radial mixing
of liquidsowing to the fluid flow inversion after the 90o bend in
the CFI.
The mixing performance of the CFI was also compared with
theexisting experimental data available for the HEM.7 It was
alsoobserved that the COV value for the CFI was found to be 5 to8
times lower than that for an equivalent length of motionlessmixer
such as HEM having 18 elements over the range of 98 eRe e 1020.
This shows that the CFI performance is superioras compared to a
motionless mixer under identical processconditions
3.3.2. Effect of Number of Bends. Figure 6 represents the
effectof number of bends on COV of liquids flowing at Re = 490
instraight, coiled, and CFI tube having d= 0.01m. The figure
showsthat there was no substantial variation in mixing
performancewith an increase in length of straight tube. It was
observed for theCFI having one bend and the coiled tube having
equivalentlength that the COV value of liquids was nearly the
same.Nevertheless, the mixing efficiency increased with the
introduc-tion of bends in the CFI as compared to that of the
straight tubeand coiled tube of equal lengths. This shows that the
mixing ofthe two liquids increased with an increase in the number
ofbends. The figure shows that significant mixing was taking
placein the CFI within three bends. The length of CFI is not
effectivelyutilized for mixing after the third bend. This
observation agreeswith the uniformity of scalar concentration shown
in Figure 3.COV values for an SMX static mixer46 were calculated
for anequivalent length of CFI from the following equation:
COV a exp bLd
8
Here a and b are adjustable constants and are predicted
fromlaminar flow experimental results of the SMX static mixer
withliquid viscosity ratio greater than 1. The values of the
exponentsin eq 8 were a 15 and b0.505 for the SMX static mixer
inlaminar flow.5,6 Figure 6 shows that COV values for the
staticmixer are significantly higher with respect to coiled and CFI
tubehaving length an equivalent one bend. The COV values
decreasewith an increase in mixer length. Nevertheless, the COV
value isstill nearly 4 times higher for the static mixer as
compared to thatfor the CFI at the outlet (n = 4).3.4. Friction
Factor in CFI. The multiphase flow studies in
coiled tubes mostly use the correlations based on the
LockhartMartinelli parameter.24 Studies show that the pressure drop
fortwo-phase gasliquid flow through coiled tubes satisfies
theLockhartMartinelli correlation.2527 In the present study,
thefriction factor was computed from the pressure drop in
differentgeometries. The details for calculation have been reported
in ourpreviouspapers.28The friction factor values fordifferent
configurations
Figure 5. Eect of Reynolds number on relative coecient of
variationfor straight, coiled, CFI tube, and HEM.
Figure 6. Eect of number of bends on coecient of variation of
twophase liquids owing in straight, coiled, CFI tube, and SMX
static mixer.
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Industrial & Engineering Chemistry Research ARTICLE
were plotted against Reynolds number as shown in Figure 7.
Thefigure shows that the friction factor is least in the case of
thestraight tube. It is interesting to observe that there was
nosignificant difference between the friction factor in the
coiledtube and the CFI with three bends over the Reynolds
numberrange studied in the present study. Similar observations
werereported in the literature for single phase flow.29 The
experi-mental data for the friction factor in HEM6 has been
comparedwith that of the CFI. The friction factors in HEM were
found to3.36 times higher than that of CFI.To assess the
suitability of a given mixer for the homogeniza-
tion of two liquids, it is essential to assess the combined eect
ofmixing performance as well as power consumed by the mixers.Hence,
eorts were made to investigate the variation of productof COV and
friction factor with Reynolds number for straight
tube, coiled tube, and CFI of equivalent length. Figure 8
showsthe variation of product of COV and friction factor
againstReynolds number. It was observed that the product of COVand
friction factor in the coiled tube was nearly 14 to 26 timeshigher
than the CFI. The values were found to be 26 to 35 timeshigher in
HEM than in CFI for Reynolds numbers varying from981020.The
performance of coiled tube, HEM, and CFI with respect
to straight tube was analyzed in terms of gure of merit. Figure
ofmerit represents the ratio of the unmixedness of liquid in
asystem to the increase in pumping power by the system. Figure
9shows the ratio of the gure of merit in coiled tube, HEM, andCFI
to that of the straight tube. The gure shows that unmixed-ness in
the CFI is nearly 1825 times lower than that in thecoiled tube and
nearly 24 times lower than that in the HEM.
4. CONCLUSION
In the present study, the physics of ow of twomiscible
liquidswas examined in a complex ow generated in CFI geometry.
Itwas observed that the mixing performance in the CFI increasedwith
increase in Reynolds number as well as number of bends.This was
further substantiated by velocity and scalar concentra-tion
contours of two liquids. The product of COV and frictionfactor, a
new parameter, has been dened to quantify the mixingof two liquids
in ow systems. It was found that the enhancementof mixing eciency
in the CFI as compared to that of coiled tubeand HEM is higher than
the increase in pressure drop of theliquids. It was observed that
the CFI oers higher mixingeciency as compared to a coiled tube and
motionless mixers(HEM) of equivalent length. Hence, it may be
concluded that theCFI is a more ecient motionless mixer with
reasonably lowerpumping cost as compared to conventional static
mixer.
AUTHOR INFORMATION
Corresponding Author*Tel: 91-11-26591020. E-mail:
[email protected].
NOTATIONSA = cross-sectional area (m2)d = internal diameter of
tube (m)D = coil diameter (m)g = gravity (m2/s)H = dimensionless
pitch, H = p/dL = length (m)Re = Reynolds numberp = pitch (m)P =
pressure (N/m2)Rc = coil radius (m)u = velocity, m/sx = spatial
position in x-direction, my = spatial position in y-direction,
m
Greek symbolsr = volume fractionk = curvature of free surface =
curvature ratio (D/d) = surface tension (N/m) = viscosity (kg/(m 3
s))F = density of uid (kg/m3)
Figure 7. Eect of friction factor on Reynolds number for
dierentcongurations.
Figure 8. Eect of product of COV and friction factor for
dierentcongurations.
Figure 9. Figure of merit in dierent congurations as compared to
thatof straight tube.
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