Experimental Distribution of Phases and Pressure Drop in a Two Phase Offset Strip Fin Type Compact Heat Exchanger

International Journal of Multiphase Flow 37 (2011) 576–584

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International Journal of Multiphase Flow

journal homepage: www.elsevier .com/locate / i jmulflow

Experimental distribution of phases and pressure drop in a two-phase offset stripfin type compact heat exchanger

Selma Ben Saad a,b,⇑, Patrice Clément a, Caroline Gentric b,1, Jean-François Fourmigué a, Jean-Pierre Leclerc b

a LITEN/LETh, CEA Grenoble, 17 rue des martyrs, 38054 Grenoble Cedex 9, Franceb Laboratoire Réactions et Génie des Procédés (LRGP), UPR 3349, CNRS-ENSIC-INPL, 1 rue Grandville, BP 20451, 54001 Nancy, France

a r t i c l e i n f o

Article history:Received 20 October 2010Received in revised form 17 March 2011Accepted 20 March 2011Available online 13 April 2011

Keywords:Compact heat exchangersOffset strip finsTwo-phase flowFlow distributionFlow regimesPressure distributionCFD

0301-9322/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.ijmultiphaseflow.2011.03.009

⇑ Corresponding author at: LITEN/LETh, CEA GrenobGrenoble Cedex 9, France. Tel.: +33 4 38 78 45 12.

E-mail address: [email protected] (S.B1 Present address: Laboratoire Génie des Procédés-En

(GEPEA), UMR 6144, Université de Nantes – CNRS, CRTT406, 44602 Saint-Nazaire Cedex, France.

a b s t r a c t

Uniform distribution of fluids is crucial to obtain high performance in compact heat exchangers. Maldis-tribution has been studied by many authors, especially for parallel channels heat exchangers. But theo-retical models and experimental studies for predicting flow maldistribution in offset strip fins exchangersare scarce. Offset strip fins, besides their higher thermal hydraulic performances, favour lateral distribu-tion due to their geometry. In this work, an experimental investigation has been carried out for this typeof heat exchanger. The experimental set-up consists in a flat vertical compact heat exchanger (1 m � 1 marea and 7.13 mm thickness) equipped with offset strip fins with a hydraulic diameter of 1.397 mm. Airand water are the working fluids. The flow rates of each phase in seven zones regularly distributed at theoutlet have been measured as well as the pressures at the inlet, the outlet and two intermediate posi-tions. These measurements were completed with visualisations using a high-speed camera.

First, the single-phase flow has been investigated. A correlation for friction factor has been derived fromexperiments covering laminar, transition and turbulent regimes. CFD simulations of the single-phase flowhave been performed. The numerical results were compared with the determined correlation and withcorrelations available in the literature. In single-phase flow, a uniform distribution was experimentallyobserved.

Then, the two-phase hydrodynamics was characterised. A flow regime map was established and theinfluences of phases inlet directions (co-current and counter-current inlets of the phases) and of super-ficial velocities on the distribution were studied. The gas superficial velocity has more effect on the dis-tribution than the liquid one. Comparison between pressure drop profiles and flow rate distributionprofiles shows that information about pressure drop can provide information about phase distribution.It must be noticed that the nonuniform distribution of phases can entail the coexistence of several flowregimes in the heat exchanger.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

The use of compact heat exchangers for both single- and two-phase applications in the process industries has increased in recentyears. Offset strip fins heat exchangers are interesting because theypresent high heat transfer areas per unit volume. They offer thepossibility of integrating various processes (up to 20 fluids flowingsimultaneously through a single heat exchanger) over a wide rangeof dimensions. Brazed aluminium plate–fin heat exchangers areespecially suitable for processes requiring a high level of heat

ll rights reserved.

le, 17 rue des martyrs, 38054

. Saad).vironnement-Agroalimentaire, Boulevard de l’Université BP

transfer under low temperature difference (1–2 �C or less) betweenwarm and cold fluids. The plate–fin heat exchangers have manyindustrial applications: separation of air gases, hydrocarbon pro-cessing, natural gas liquefaction and industrial gas liquefaction(oxygen, nitrogen, argon, helium, etc.). Recent studies, both numer-ical and experimental, have determined relations between ther-mal–hydraulic performances and flow distribution in compactheat exchangers. The thermal–hydraulic performances of such heatexchangers are strongly influenced by their geometry and flowconfiguration. Offset strip fins heat exchangers have been studiedby several researchers (Bhowmik and Lee, 2009; Lihua et al.,2008; Manglik and Bergles, 1995; Kays and London, 1984).

Nevertheless, general correlations for the friction factor f arescarce. The main correlation used in industry is the Manglik andBergles correlation (Manglik and Bergles, 1995), which was deter-mined from experimental data obtained for 18 offset strip fins types.This correlation predicts the friction factor as a single continuous

S.B. Saad et al. / International Journal of Multiphase Flow 37 (2011) 576–584 577

function of fin geometrical parameters and of Reynolds number andcan be used in the laminar, transition and turbulent flow regimes.But the equation is complex and the uncertainty for the predictionof friction factor f is ±20%. Bhowmik and Lee (2009) carried out anumerical study to provide a single correlation covering all regimes.But no correlation has been developed for all fin types. Manglik andBergles indicated that more experiments should be done to extendthe correlation validity, especially for liquid as working fluid.Wieting (1975) tested 23 samples and Kays and London (1984) 21samples of offset strip fins with different geometrical parameters.Since these correlations were established for different operatingparameters, such as manufacturing aspects and testing conditions,it is difficult to explain the variations between the friction factorsthey predict. Lihua et al. (2008) tested experimentally 16 samplesof offset strip fin cores with different flow angles (angle betweenthe fluid flow orientation and the fin surface), fin heights, finlengths and fin widths. They concluded that, among the consideredgeometries, the flow angle had the strongest influence on the finperformance. Numerical analyses were done to predict flow frictionfactors and validate experimental results. Peng and Ling (2008)performed 3D CFD simulations to predict friction factors character-istics of serrated fins in a compact heat exchanger.

For two-phase flows, one of the factors that most strongly influ-ence the performance of compact heat exchangers is the degree offlow rate uniformity in the channels where heat transfer occurs.The good distribution in the bottom zone of the heat exchangeris important to obtain an homogeneous phase change across thewhole heat transfer zone and to avoid too large regions with va-pour only. The studies of Marchitto et al. (2008, 2009) about thetwo-phase distribution in parallel channels heat exchangers con-firm the complexity of this two-phase flow distribution. Theirexperiments with air and water have been carried out in a horizon-tal cylindrical two-phase flow header supplying 16 vertical chan-nels and have shown the strong influence of the operatingconditions on the two-phase flow pattern and on the flow distribu-tion in the channels. The fluid tends to go preferentially into thechannels that face the inlet tube (Marchitto et al., 2008; Kim andSin, 2006). The effects of flow maldistribution have been studiedand discussed by many authors (Marchitto et al., 2008; Kim andSin, 2006). For the optimal design of plate heat exchangers, the ef-fect of the flow arrangement on pressure drop has to be taken intoaccount (Raquel et al., 2008). The study of Marchitto et al. (2008)has shown that the gas phase was preferentially distributed intothe first channels near the inlet of mixing phases, while the liquidphase was generally distributed into the last channels, even at lowgas superficial velocities. If the gas flow rate increases, the gas isbetter distributed, but the liquid phase tends to mal distribute.Thus, the number of tubes (or channels) also affects the flow distri-bution. An experimental study of a compact heat exchanger withparallel channels as the one of Marchitto et al. but with 30 verticalflat tubes was presented by Kim and Sin (2006). They showed thatthe header diameter and shape, the mass flux and quality affectedthe flow distribution. Thonon et al. (1992) determined numericallythat maldistribution affects pressure drop more than thermal per-formance. Bassiouny and Martin (1984) predicted a maldistribu-tion parameter that depends on the area, number of plates andaverage friction.

The objective of the present study is to address the above men-tioned problem of mal distribution in offset strip fins compact heatexchangers and to determine its relation with pressure drop distri-bution. To focalize the study on hydrodynamics aspects, it has beencarried out in an experimental quasi two-dimensional compactheat exchanger test section using air or/and water in adiabatic con-ditions. The two-dimensional character of the experimental testsection allows a visual characterisation of the hydrodynamics. Be-sides, its width is large enough to put into evidence operating

parameters leading to flow maldistribution. Pressure drop at differ-ent locations along the test section and flow rates distribution ofboth phases among the channels were measured. Firstly, single-phase flow has been characterised in terms of pressure drop andflow rate distribution. The experimental friction factor has beencompared to CFD simulation results. For two-phase flows, a regimemap was first established. Pressure drop was measured as well asthe flow rate distribution of the gas and liquid phases. By usingmaldistribution parameters (STD, NSTD), it has been possible tocompare the uniformity of the gas and liquid flow rates and thusto determine the relative effectiveness of various inlet configura-tions and superficial velocities. Comparison between pressure dropprofiles and flow rate distribution profiles shows that informationabout pressure drop can be useful in real heat exchangers where itis difficult to determine phase distribution.

2. Experimental set-up and operating conditions

The experimental set-up is presented in Fig. 1. The test sectionis a quasi two-dimensional vertical compact heat exchanger(height 1 m, width 1 m, thickness 7.13 mm) and consists in offsetstrip fins placed between two transparent flat plates. The offsetstrip fin type is presented in Fig. 2. The main fin geometricalparameters are: fin height h, fin transverse spacing s, fin thicknesst and fin width l (h = 7.13 mm, s = 0.77 mm, t = 0.2 mm andl = 3.175 mm). Fluids (gas and liquid) injections are designed to ob-tain easily different inlet flow configurations: co-current or coun-ter-current flows in the distributor (Fig. 3).In the industrialpractice, the inlet configuration: co-current or counter-current in-lets of phases, depends on the fluid main positions relative to theheat exchanger header. It is thus mainly governed by availablespace for the pipe connections. In the present study, both situa-tions have been tested to determine if one configuration is prefer-able to the other. This horizontal distributor is rectangular andcontains 18 circular orifices (diameter d = 1.85 mm) to mix phasesbefore injection into the offset strip fin channels. Then, the mixtureflows upwards through the test section. At the top, the flow is di-vided into seven zones regularly distributed on the width. In eachzone, gas and liquid are separated and the flow rate of each phasein each zone is measured to appreciate the uniformity of the phasedistribution across the exchanger. Two absolute pressure transduc-ers are installed to measure the inlet pressures for gas and liquid.Differential pressure transducers are installed along four horizon-tal lines to measure pressure drop across the test section at differ-ent heights. The distances between pressure lines are: P0–P1 = 213 mm, P0–P2 = 433 mm and P2–P3 = 425 mm. A systemwith high-speed camera, light source and acquisition by PC is in-stalled to perform flow visualisation.

Experiments are carried out using air and water in adiabaticconditions at ambient temperature and atmospheric pressure.The range of gas and liquid superficial velocities are Vsg = 0.1–1.9 m/s and Vsl = 0.1–0.39 m/s respectively. The investigated rangeof superficial gas and liquid velocities is deduced from a real appli-cation of brazed plate–fin heat exchanger. Besides, it allows to cov-er a large range of flow regimes.

The pressure at the inlet of the test section varies between 1.1and 2.5 bar depending on the operating conditions.

The total uncertainty in the pressure drop and mass flow ratemeasurements, taking into account the experimental uncertaintyin real experimental conditions, reach up to +5%.

3. Numerical simulations

The measured pressure drop characteristics of the single-phaseflow in the offset strip fin test section were compared to 3D

Liquid outlet

Visualisation system

PΔ

lm.

PP

Light source

High speed camera

Liquid inletGas inlet

Gas outlet

1 2 3 4 5 6 7

Test section1m×1m×7.13mm

Gas/liquid separators

Distributor

Flow

P0

P1

P2

P3

.

gm

Fig. 1. Scheme of the experimental set up.

h

s

tl

Fig. 2. Geometry of the offset strip fins.

Water

Air

Distributor

WaterAir

1 2 3 4 5 6 7

Water

Air

WaterAir

1 2 3 4 5 6 7

(a) (b)

Fig. 3. Co-current and counter-current inlet configurations of the test section: (a) Co-current fluid inlets and (b) Counter-current fluid inlets.

578 S.B. Saad et al. / International Journal of Multiphase Flow 37 (2011) 576–584

simulations using the commercial code Fluent. CFD simulations arebased on the resolution of the Navier–Stokes equations. The stan-dard k–e (Launder and Spalding, 1974) as well as the SST k–x tur-bulence models were used to predict the turbulencecharacteristics. The SST k–x model allows for a more accurate near

wall treatment since the k–x model is used near the walls and thek–e model is employed away from the walls. It should also be moreadapted to the hydrodynamics of offset strip fin heat exchangerwhich presents flow separation. The enhanced wall function ap-proach was adopted to predict the wall-bounded turbulent flow.

S.B. Saad et al. / International Journal of Multiphase Flow 37 (2011) 576–584 579

3.1. 3D meshes

The pre-processor Gambit was used to build the geometry anddifferent grids with increasing mesh refinement. The complete testsection contains 300 fins along the flow direction; therefore, to re-duce the calculation time, the CFD simulation was limited to ageometry containing only five fins in the flow direction and twochannels in the cross section. This calculation domain is shownin Fig. 4. The simulated length allows to observe the flow establish-ment from the third fin. Thus the flow analysis, in particular thepressure drop determination, was based on the flow field in thezone of the third and fourth fins.

Nonuniform mesh was used: the mesh was refined near thewalls where velocity gradients are important. The adequacy be-tween the y+ values of the cells adjacent to the walls and the walltreatment was verified a posteriori: the y+ values of those cellswere of the order of 1. The mesh is composed of hexahedral cells.Their advantage is that they can be aligned with the main flowdirection and provide more accurate flow solution than with tetra-hedral or polyhedral meshes. Interface zones were defined at thejunction between two successive fins since the mesh is noncon-formal at this location.

3.2. Fluid properties and boundary conditions

Simulations have been performed with air or water as the fluidphase. The liquid viscosity is 10�3 Pa s and its density is 1000 kg/m3. For the air, a viscosity of 1.17 � 10�5 Pa s and a density of1.25 kg/m3 are used.

The following boundary conditions are considered:

– At the inlet, uniform velocities were imposed with flow ratescorresponding to the experimental conditions. Inlet velocitiesare in the range 0.1–1.9 m/s to describe laminar to turbulentregions.

– A pressure outlet condition has been defined at the outlet.

3.3. Influence of mesh refinement

Different grids were tested to determine the influence of gridrefinement on simulation results. In order to show that the meshresolution is sufficient for a given case, the number of cells of theexisting case was increased and it was verified that the results be-came invariable. For the two fluids, we used the same mesh reso-lution. Comparison between the results obtained with meshrefinement only near the walls and mesh refinement on the wholechannel shows only 2% difference. The nonuniform mesh is usedbecause the calculation times are shorter than with uniform mesh.

Flow direction

Fins 1 and 3

Fins 2 and 4

Symmetry

Fig. 4. Calculation domain.

4. Results and discussion

4.1. Simulated single-phase flow structure

Fig. 5 shows a typical calculated flow field in a vertical mid-plane for water at Vsl = 0.2 m/s. The vector plot shows the presenceof low velocity zones (indicated with circles). They are locateddownstream of the fins. Flow acceleration can be observed in thepassage between two fins.

4.2. Friction factor in single-phase flow

Experiments have been conducted to analyse the pressure dropalong the test section, firstly for single-phase flow. The total pres-sure drop is equal to the sum of gravitational, acceleration and fric-tion pressure losses:

�dpdz

�t¼ �dp

dz

�G� dp

dz

�A� dp

dz

�F

ð1Þ

In the present experiments, pressure losses due to gravity andacceleration are negligible compared to the pressure drop due tofriction inside the micro channels. The experimental results werecompared to literature correlations and to CFD results in terms offriction factors. The pressure drop (DP) of serrated fins is relatedto the friction factor f by the following equation:

f ¼ Dh

4LDP

1=2qu2 ð2Þ

The experimental value of the friction factor f has thus been de-duced from the experimental pressure drop measurements accord-ing to Eq. (2).

The Reynolds number is defined on the basis of the hydraulicdiameter Dh:

ReDh ¼quDh

lð3Þ

The Manglik and Bergles (1995) correlation is the most oftenused in industry to predict the friction factor:

f ¼ 6:6243Re�0:7422Dh a�0:1856d0:3053c�0:2659 � ½1þ 7:669

� 10�8Re4:429Dh a0:920d3:767c�0:236��1 ð4Þ

where Dh ¼ 4shl2ðslþhlþthÞþtsÞ

� �, a ¼ s

h, d ¼ tl and c ¼ t

s.The Manglik and Bergles correlation for friction factor was

established from literature studies of 18 different geometries andthus corresponds to a large range of geometric parameters. Ourhydraulic diameter (Dh = 1.397 mm) lies in the range of diametersexamined by Manglik and Bergles (1995). The experimental,

Low velocities zones

High velocities zones

Fig. 5. Simulated velocity contours and flow field in a vertical plane parallel to thetest section walls – Results obtained for water at Vsl = 0.1 m/s.

0.01

0.10

1.00

10 100 1000 10000

Re

f

simulation "fluent"

Experimental points

Manglik and Bergles (1995)

Bhowmik and Lee (2009)

Joshi and Webb (1987)

Mochiziki et al. (1987)

Wieting (1975)

Manson (1950)

Fig. 7. Experimental friction factor compared with correlations in the literature(see above mentioned references for further information).

580 S.B. Saad et al. / International Journal of Multiphase Flow 37 (2011) 576–584

simulated, and Manglik and Bergles friction factors are comparedfor low Prandtl (air Pr = 0.7) and for high Prandtl number (waterPr = 7) in Fig. 6.

The friction factor is decreasing for increasing Reynolds num-bers. Comparing friction factors for air and water confirms the re-sult of Bhowmik and Lee (2009) who showed that f is not affectedby the Prandtl number. The regime transitions can be deducedfrom a change in the slope of the experimental variation of frictionfactor with Reynolds number. The laminar zone is observed forReDh < 500, the transition for 500 < ReDh < 1250 and the turbulentzone corresponds to ReDh > 1250.

Numerical simulations using Fluent show good agreement withmeasurements in the laminar flow regime except at very low Rey-nolds number where a difference of 15% is observed. The same dis-crepancy was already noticed by Peng and Ling (2008) forReDh < 200 and by others authors. The regime transitions are wellpredicted by CFD. But a deviation between experimental andnumerical values of about 35% exists in the transition and turbu-lent regimes when the k–e model is used. This discrepancy maybe due to the complex flow structure around the fins which isnot accurately taken into account via two-equation turbulencemodels based on the Boussinesq hypothesis. The SST k–x modelpresents the same problem in the transition regime but allows sat-isfying f predictions for turbulent flow (8% of difference), in fact itallows a better description of flows presenting separation as in theconsidered geometry.

The Manglik and Bergles correlation has been established forReynolds numbers from 120 to 104, so its extrapolation for

0

1

2

3

4

5

0 50 100 150 200

Re

f

Simulation (Fluent)

Experimental points

Manglik and Bergles (1995)

0.010

0.100

1.000

100001000100

Re

f

Experimental pointsk- standardk-w SSTsimulation(laminar region)Manglik and Bergles (1995)

(b)

(a)

Fig. 6. Friction factors from experimental and numerical results and from theManglik and Bergles correlation: (a) low Prandtl (air Pr = 0.7) and (b) higher Prandtl(water Pr = 7).

Re < 120 does not show good accordance with experiments. ForRe > 120, the Manglik and Bergles correlation shows good accor-dance with experimental points.

Fig. 7. shows large differences between friction factor predic-tions for offset strip fins according to different literature correla-tions. This is due to the difference in the geometrical parametersused by the authors.

The following correlation for the friction factor describing all re-gimes has been obtained from our measurements:

f ¼ 20:362Re�0:7661Dh ð5Þ

The analysis of literature results and of the obtained experimentaldata shows that there is a need to increase experimental andnumerical studies to better understand the influence of geometricalparameters on the hydraulic characteristics of offset strip fins andto develop general correlations describing friction factors adaptedto different offset strip fins types.

4.3. Distribution in single-phase flow

Before characterising two-phase flows, which present muchmore complexity, flow rate and pressure drop distributions in sin-gle-phase flows must be evaluated. A good flow rate distributionalong the seven zones is observed for water and for air as shownin Fig. 8 where the flow ratio is defined as follows:

Flow ratio ¼ Q i

Qi ¼ 1;7 ð6Þ

where Qi is the flow rate of a phase in zone i and Q is the averageflow rate in a zone.

This good flowrate distribution corresponds to a uniform pres-sure drop distribution in the exchanger parts containing offset stripfins, i.e. between the horizontal levels P1–P2 and P2–P3 respec-tively as presented in Fig. 9 (the positions of the pressure dropmeasurements P0–P3 are defined in Fig. 1). For the distributionzone (P0–P1), the pressure drop is maximal near the inlet (zone7) and decreases along the distributor which can be explained bythe distributor geometry and confirms the distributor highefficiency.

4.4. Flow patterns in two-phase flow

Fig. 10 shows different flow behaviours observed using a high-speed camera. The flow patterns observed in the micro channelsare bubbly flow, slug flow and churn flow. The slug flow patternis characterised by elongated bubbles. In the region of high gas

12

34

56

7 2.43.5

6.47.2

0

0.2

0.4

0.6

0.8

1

1.2

Q (m3/h)

Zones

Flo

w r

atio

F

low

rat

io

12

34

56

7 2.1 813.4 34.6

0

0.2

0.4

0.6

0.8

1

1.2

Zones

Q (m3/h)

(a)

(b)

Fig. 8. Flow rate distributions along the seven outlet zones of the compact heatexchanger test section: (a) water and (b) air.

0

20

40

60

80

100

120

140

160

0 1 2 3 4 5 6 7 8zones

Pre

ssur

e dr

op (

mba

r)

P1-P2

P1-P3

P0-P1

Fig. 9. Single phase (water, Vsl = 0.35 m/s) pressure drop distributions.

S.B. Saad et al. / International Journal of Multiphase Flow 37 (2011) 576–584 581

superficial velocities, churn flow can appear. It is characterised bythe simultaneous presence of several flow patterns: bubbles withdifferent diameters, slug flow and annular flow.

Our flow regime experimental points are superimposed to theTaitel et al. (1980), the Triplett et al. (1999) and the Desrats(2006) flow regime maps in Fig. 11.

The Taitel et al. (1980) map was established from experimentalresults obtained with vertical pipes of 20–60 mm diameter andair–water flow. They distinguished bubbly, dispersed bubbly, slug,churn and annular flow regimes and suggested physical mecha-nisms for each flow transition. The slug/churn transition for ourcompact heat exchanger is the same as the one of Taitel et al.

The transition from bubble to slug flow comes for larger superficialgas velocities than the transition line of Taitel et al. This can be ex-plained by the narrow width of the offset strip fin channels(l = 770 lm). Desrats (2006) flow map was established in an offsetstrip fins heat exchanger with Dh = 1.4 mm for boiling propane. Thetransition from bubbly, slug and churn are shifted to the low gassuperficial velocity compared to our results due to the differencesof fluid properties and boiling mechanism. Triplett et al. (1999)investigated flow regimes in circular channels (1.097 mm diame-ter) using air–water mixtures. The slug/churn flow transition ofthe present study is obtained for the same conditions as thechurn/annular transition of Triplett et al.

In parallel adjacent channels, different distributions of gas andliquid can be observed across the test section. This can entail thesimultaneous presence of different flow patterns at given inlet flowrates of gas and liquid. For example, the three regimes are seen indifferent regions of the compact heat exchanger for the three con-ditions indicated with circles in Fig. 11. The following study ofphase distribution characterisation and pressure drop analysis cov-ers this large range of regimes.

4.5. Pressure drop and flow rate distributions in two-phase flow

The standard deviation (STD) and Normalised standard devia-tion (NSTD) parameters have been used by Marchitto et al.(2008) and by other authors. These parameters reflect the qualityof the distribution of the two phases under different operating con-ditions. They indicate how a particular zone flow rate deviatesfrom the average flow rate per zone. The smaller their value is,the more uniform the flow distribution is. They have been usedin the present work to compare the quality of the flow distributionat different flow rates and different flow configurations.

STDk ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXN

j¼1ðm�k;j � 1Þ2=N

rð7Þ

with

m�k;j ¼mk;jPN

j¼1mk;j=Nðk ¼ g; lÞ

and N the number of channels.

NSTDk ¼STDk

STDk max¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXN

j¼1ðm�k;j � 1Þ2=NðN � 1Þ

rð8Þ

The liquid and gas superficial velocities are defined by the fol-lowing equations:

Vsl ¼Ql

Sð9Þ

Vsg ¼Qg

Sð10Þ

where Ql, Qg are the volume flow rates of liquid and gas and S is thecross sectional area between fins.

Theoretically, the flow maldistribution is linked to pressurevariations. The pressure drop distribution for the air/water mixtureis presented in Fig. 12 (Vsl = 0.35 m/s, Vsg = 1.9 m/s, counter-currentconfiguration). The distribution of the flow rates in terms of gasand liquid flow ratio along the seven zones dividing the test sectionis illustrated in Fig. 13 for contre-current fluid inlets. At a constantlow value of Vsl (Vsl = 0.13 m/s) and for increasing values of Vsg, theexperimental distribution of the two phases at the outlet is pre-sented in Fig. 13a. For a higher value of Vsl (Vsl = 0.35 m/s) and forthe same increasing values of Vsg, the characteristics of the distri-bution do not change as can be seen in Fig. 13b.

Churn flowVsg=2.05 m/sVsl=0.42 m/s

Slug flowVsg=0.826 m/sVsl=0.42 m/s

Gas slug

Gas-liquid interface

Liquid

Bubbly flowVsg=0.39 m/sVsl=0.23 m/s

Gas bubble

(b) (c)(a)

Fig. 10. Flow regimes: (a) bubbly flow; (b) slug flow and (c) churn flow.

Triplett flow pattern transitions lines Dh=1.097mm (1999)

bubbly Slug-Annular Slug Churn Annular

This study (Dh =1.397mm)

Bubbly

Slug

Churn

C.Desrats (2006)

Bubbly

Slug

Churn

Taitel et al. (1980)

Gas superficial velocity Vsg (m/s)

Liq

uid

supe

rfic

ial v

eloc

ity

Vsl

(m

/s)

Slug flow

Churn flow

Bubbly flow

Fig. 11. Flow regimes versus gas and liquid superficial velocities comparisons with Taitel et al. (1980) and Triplett et al. (1999) and Desrats (2006) maps.

582 S.B. Saad et al. / International Journal of Multiphase Flow 37 (2011) 576–584

At low gas superficial velocity (Vsg = 0.12 m/s), the gas phase ispresent in the first zones near the gas inlet (zones 1 and 2). Whilethe gas flow rate increases, the distribution of the gas becomesmore and more uniform. For all the investigated flow rates, the li-quid is mainly present near its inlet and the liquid flow rate de-creases going from zone 7 to 1. Furthermore, the liquidmaldistribution increases while increasing Vsg. We observe thatthe liquid flow rate has less effect than the gas flow rate on theflow distribution at the outlet. This behaviour has already been ob-

served by different authors (Marchitto et al., 2008; Horiki andOsakabe, 1999; Kim and Sin, 2006) in parallel channels compactheat exchangers.

The pressure drop of the two-phase mixture is plotted in Fig. 12.In the distributor zone (P0–P1), a decreasing pressure drop fromthe side of the liquid inlet to the other side can be observed. Thisresult is similar to the single phase water distribution. The pres-sure drop in the zone (P1–P3) is still nonuniform. For bubble flowregime in the distributor, the pressure drop depends on both the

0

40

80

120

160

200

0 1 2 3 4 5 6 7 8zones

Pre

ssur

e dr

op (

mba

r)

P1-P2

P1-P3

P0-P1

Fig. 12. Pressure drop distribution for the two-phase flow (Vsl = 0.35 m/s andVsg = 1.9 m/s) for counter-current fluid inlets.

0

0.5

1

1.5

2

2.5

3

3.5

4

0 2 4 6 8Zones

Flo

w r

atio

Vsg=0.12 m/s STDg=1.42Vsg=0.44 m/s STDg=0.87Vsg=0.73 m/s STDg=0.56Vsg=1.9 m/s STDg=0.26Vsg=0.12 m/s STDl=0.36Vsg=0.44 m/s STDl=0.56Vsg=0.73 m/s STDl=0.64Vsg=1.9 m/s STDl=0.78

Liquid phaseGas phase

0

0.5

1

1.5

2

2.5

3

3.5

4

0 2 4 6 8Zones

Flo

w r

atio

Vsg=0.12 m/s STDg=0.98Vsg=0.44 m/s STDg=0.80Vsg=0.73 m/s STDg=0.73Vsg=1.9 m/s STDg=0.48Vsg=0.12 m/s STDl=0.33Vsg=0.44 m/s STDl=0.34Vsg=0.73 m/s STDl=0.42Vsg=1.9 m/s STDl=0.65

Liquid phaseGas phase

(a)

(b)

Fig. 13. Profiles of gas and liquid flow ratio at the outlet of the compact offset stripfin heat exchanger for counter-current fluid inlets: (a) Vsl = 0.13 m/s and (b)Vsl = 0.35 m/s.

Fig. 14. View of real distribution in counter-current configuration: (a) Vsl = 0.35 m/sand Vsg = 1.9 m/s; (b) Vsl = 0.13 m/s and Vsg = 0.73 m/s.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0.12 0.44 0.73 1.9

Gas superficial velocity (m/s)

Stan

dard

Dev

iati

on S

TD

k

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Nor

mal

ized

Sta

ndar

d D

evia

tion

NST

Dk

STDg Vsl=0.13 m/sNSTDg Vsl=0.13 m/sSTDg Vsl=0.35 m/sNSDg Vsl=0.35 m/sSTDl Vsl=0.13 m/sNSTDl Vsl=0.13 m/sSTDl Vsl=0.35 m/sNSDl Vsl=0.35 m/s

Fig. 15. Gas and liquid standard deviations as a function of gas superficial velocityfor counter-current fluid inlets.

S.B. Saad et al. / International Journal of Multiphase Flow 37 (2011) 576–584 583

liquid and the gas Reynolds numbers (Eisenklam and Ford, 1962).Since the liquid flow rate has more influence on the pressure dropthan the gas flow rate, the aspects of the pressure drop and the li-quid phase distributions are quite similar. Association of Figs. 12and 13 show that the pressure drop profile at the outlet is similarto the liquid distribution aspect.

All these behaviours are represented with real images in Fig. 14.The fins outlet, divided in seven zones along the test section, can beobserved. The agitated zones with white colour indicate the pres-ence of the gas phase. When the free surface of water is seenclearly, it indicates the presence of water only. We observe inFig. 14a that all zones are agitated. By contrast, Fig. 14b shows

the existence of phase agitation in four zones only and the remain-ing zones contain only water.

To better see the superficial velocities effects on the flow distri-bution, Fig. 15 presents the STD and NSTD parameters variationsfor both phases. When the gas flow rate increases, the STDg de-creases, thus the distribution of the gas phase is more uniform,but at the same time, the STDl increases and the liquid fills onlythe first zones from the inlet.

Typical distribution profiles were also studied in co-current inletsconfiguration. Distributions for a constant liquid superficial velocity

0

0.5

1

1.5

2

2.5

3

3.5

4

0 2 4 6 8

Zones

Flo

w r

atio

Vsg=0,12 m/s STDg=0,79Vsg=0,44 m/s STDg=0,55Vsg=0,73 m/s STDg=0,45Vsg=1,9 m/s STDg=0,14Vsg=0,12 m/s STDl=0,53Vsg=0,44 m/s STDl=0,57Vsg=0,73 m/s STDl=0,58Vsg=1,9 m/s STDl=0,61

Liquid phaseGas phase

Fig. 16. Effects of gas and liquid superficial velocities in the distribution of twophases for co-current fluid inlets (Vsl = 0. 13 m/s).

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0.12 0.44 0.73 1.9

Gas superficiel velocity (m/s)

Stan

dard

Dev

iati

on S

TD

k

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6N

orm

alis

ed S

tand

ard

Dev

iati

on N

STD

kSTDg Vsl=0,13 m/sNSTDg Vsl=0,13 m/sSTDl Vsl=0,13 m/sNSTDl Vsl=0,13 m/s

Fig. 17. Gas and liquid standard deviation as a function of gas superficial velocityfor co-current fluid inlets.

584 S.B. Saad et al. / International Journal of Multiphase Flow 37 (2011) 576–584

(Vsl = 0.13 m/s) and for increasing values of the gas superficialvelocity are shown in Fig. 16. At the lowest gas superficial velocity,the gas phase flows mainly into the first zones and forces theliquid to go to the opposite zone. With increasing Vsg, gas dis-tribution becomes more uniform: its presence in the last zones in-creases and STDg decreases. For increasing superficial gas velocity,the STDg and NSTDg decrease but STDl and NSTDl increase (Fig. 17).Comparison between Figs. 13a and 16 on the one hand and be-tween 15 and 17 on the other hand shows that the co-current in-lets configuration allows a more uniform fluids distribution bothfor the gas and liquid phases. So in practice, if both configurationsare possible, co-currents phases inlets would allow a better effi-ciency of the heat exchanger than the counter-current inlets.

Finally, for the two configurations studied (co-current andcounter-current fluids inlets), the phase distribution aspect ismainly affected by the superficial velocity of the gas phase.

5. Conclusions

In this paper, the hydrodynamics of an offset strip fins heat ex-changer has been investigated. A correlation for single phase fric-tion factor in offset strip fin microchannels has been establishedfor laminar to turbulent flow of water and air and compared with3D CFD simulations. With a high-speed camera technique, two-

phase flow regimes have been investigated and a flow map wasestablished in vertical air–water flow configuration. Distributionsof pressure drop and of the two phases were experimentally stud-ied. The pressure drop profile study inside the distributor is veryimportant to be able to describe phases distribution inside thechannels. Co-current and counter-current fluid inlets have beentested and the position of the injection of air and water has beenshown to have an important effect on the distribution. The analysisof the results for varying superficial velocities of gas and liquidproves that the quality of two-phase flow distribution is more af-fected by the gas superficial velocity than by the liquid one. Theco-current inlets configuration allows a more uniform fluids distri-bution both for the gas and liquid phases. This work constitutes afirst step in the optimisation of the design of plate–fin heatexchanger.

Acknowledgement

This work has been supported by the ADEME ‘‘French Environ-ment and Energy Management Agency’’.

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