liquid-liquid mixing.pdf

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

13231 dx.doi.org/10.1021/ie2002473 |Ind. Eng. Chem. Res. 2011, 50, 1323013235

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.



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.



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.



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.



REFERENCES

(1) Saxena, A. K.; Nigam, K. D. P. Coiled conguration for owinversion and its eect on residence time distribution. AlChE J 1984,30, 363368.

(2) Vashisth, S.; Nigam, K. D. P. Liquid-phase residence timedistribution for two-phase ow in coiled ow inverter. Ind. Eng. Chem.Res. 2008, 47, 36303638.

(3) Nauman, E. B.; Kothari, D.; Nigam, K. D. P. Static mixers topromote axial mixing. Chem. Eng. Res. Des. 2002, 80, 15.

(4) Pahl, M. H.; Muschelknautz, E. Static mixers and their applica-tions. Int. Chem. Eng. 1982, 22, 197205.

(5) Grosz-Roll, F. Assessing homogeneity in motionless mixers. Int.Chem. Eng. 1980, 20, 542549.

(6) Cybulski, A.; Werner, K. Static mixers-criteria for applicationsand selection. Int. Chem. Eng. 1986, 26, 171180.

(7) Myers, K. J.; Bakker, A.; Ryan, D. Avoid agitation by selectingstatic mixers. Chem. Eng. Progress 1997, 93, 2838.

(8) Jaworski, Z.; Murasiewicz, H. LES and URANS modelling ofturbulent liquidliquid ow in a static mixer: Turbulent kinetic energyand turbulence dissipation rate. Chem. Pap. 2010, 64, 182192.

(9) Jaworski, Z.; Pianko-Oprych, P. Two-phase laminar ow simula-tions in a Kenics static mixer Standard Eulerian and LagrangianApproaches. Trans. IChemE 2002, 80, 910916.

(10) Zitny, R.; Strasak, P.; Sestak, J. Laminar Flow Invertors for RTDImprovement and Heat Transfer Enhancement. 12th International ChISA,1996; Czech Society of Chemical Engineering, Prague, pp 2530.

(11) Kaufman, A. D.; Kissinger, P. T. Extra-column band spreadingconcerns in post-column photolysis reactors for microbore liquidchromatography. Curr. Sep. 1998, 17, 9.

(12) Castelain, C.; Mokrani, A.; Legentilhomme, P.; Peerhossaini,H. Residence time distribution in twisted pipe ow: Helically coiledsystem and chaotic. Exp. Fluids 1997, 22, 359.

(13) Castelain, C.; Berger, D.; Legentilhomme, P.; Mokrani, A.;Peerhossaini, H. Experimental and numerical characterization of mixingin a steady spatially chaotic ow by means of residence time distributionmeasurements. Int. J. Heat Mass Transfer 2000, 43, 3687.

(14) Castelain, C.; Legentilhomme, P. Residence time distributionof a purely viscous non-Newtonian uid in helically coiled or spatiallychaotic ows. Chem. Eng. J. 2006, 120, 181191.

(15) Vashisth, S.; Nigam, K. D. P. Experimental investigation ofpressure drop during two-phase ow in a coiled ow inverter. Ind. Eng.Chem. Res. 2007, 46, 50435050.

(16) Vashisth, S.; Nigam, K. D. P. Experimental investigation of voidfraction and ow patterns in coiled ow inverter. Chem. Eng. Proc. 2008,47, 12811291.

(17) Hasson, D.; Mann, U.; Nir, A. Annular ow of two immiscibleliquids. Part I: Mechanisms. Can. J. Chem. Eng. 1970, 48, 514520.

(18) Wyslouzi, L B. E.; Kessick, M. A. Pipeline ow behaviour ofheavy crude oil emulsions. Can. J. Chem. Eng. 1987, 65, 353360.

(19) Elseth, G.; Kvandal, H. K.; Melaaen, M. C. Measurement ofvelocity and phase fraction in stratied oil/water ow. InternationalSymposium on the Multiphase Flow Transport Phenomenon, Antalya,Turkey, 2000.

(20) Lovick, J.; Angeli, P. Experimental studies on the dual contin-uous ow pattern in oilwater ows. Int. J. Multiphase Flow 2004,30, 139157.

(21) Chen, X.; Guo, L. Flow patterns and pressure drop in oil-air-water three- phase ow through helically coiled tubes. Int. J. MultiphaseFlow 1999, 25, 10531072.

(22) Mridha, M.; Nigam, K. D. P. Coiled ow inverter as an inlinemixer. Chem. Eng. Sci. 2008, 63, 17241732.

(23) Fluent Users Guide, version 6.2; Fluent Inc.: Lebanon, NH, 1996.(24) Lockhart, V; Martinelli, R. C. Proposed correlation of data for

isothermal two-phase, two-component ow in pipes. Chem. Eng. Prog.1949, 45, 3948.

(25) Ripple, G. R.; Eidt, C. M.; Jordan, H. B. Two-phase ow in acoiled tubes. Ind. Eng. Chem. Proc. Des. Dev. 1966, 5, 3239.

(26) Owhadi, A.; Bell, K. J.; Crain., B. Forced convection boilinginside helically-coiled tubes. Int. J. Heat Mass Transfer 1968,11, 17791793.

(27) Hart, J.; Ellenberger, J.; Hamersma, P. J. Single and two phaseow through helically coiled tubes. Chem. Eng. Sci. 1987, 43, 775783.

(28) Vashisth, S.; Nigam, K. D. P. Prediction of ow proles andinterfacial phenomena for two-phase ow in coiled tubes. Chem. Eng.Process 2009, 48, 452463.

(29) Kumar, V.; Nigam, K. D. P. Numerical simulation of steady owelds in coiled ow inverter. Int. J. Heat Mass Transfer 2005, 48,48114828.

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