13
Effect of flow maldistribution and axial conduction on compact microchannel heat exchanger Seungwhan Baek , Cheonkyu Lee 1 , Sangkwon Jeong 2 Cryogenic Engineering Laboratory, #5119, Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, Republic of Korea article info Article history: Received 10 September 2013 Received in revised form 24 November 2013 Accepted 9 January 2014 Available online 20 January 2014 Keywords: Heat exchanger Axial conduction Flow maldistribution Microchannel Cryogenic abstract When a compact microchannel heat exchanger is operated at cryogenic environments, it has potential problems of axial conduction and flow maldistribution. To analyze these detrimental effects, the heat exchanger model that includes both axial conduction and flow maldistribution effect is developed in con- sideration of the microchannel heat exchanger geometry. A dimensionless axial conduction parameter (k) is used to describe the axial conduction effect, and the coefficient of variation (CoV) is introduced to quantify the flow maldistribution condition. The effectiveness of heat exchanger is calculated according to the various values of the axial conduction parameter and the CoV. The analysis results show that the heat exchanger effectiveness is insensitive when k is less than 0.005, and effectiveness is degraded with the large value of CoV. Three microchannel heat exchangers are fabricated with printed circuit heat exchanger (PCHE) technology for validation purpose of the heat exchanger model. The first heat exchan- ger is a conventional heat exchanger, the second heat exchanger has the modified cross section to elim- inate axial conduction effect, and the third heat exchanger has the modified cross section and the cross link in parallel channel to mitigate flow maldistribution effect. These heat exchangers are tested in cryo- genic single-phase, and two-phase environments. The third heat exchanger shows the ideal thermal char- acteristic, while the other two heat exchangers experience some performance degradation due to axial conduction or flow maldistribution. The impact of axial conduction and flow maldistribution effects are verified by the simulation results and compared with the experimental results. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction Demand of high performance compact heat exchangers is increasing for volume-limited cryogenic processes. The most rep- resentative example of the volume limited cryogenic process is the natural gas liquefaction process for Liquefied Natural Gas- Floating Production Storage and Offloading (LNG-FPSO). The compact cryogenic liquefaction process inevitably requires small components due to space limitation of a ship, as well as high performance heat exchanger (e > 0.90 NTU > 10) for efficient oper- ation. Microchannel heat exchangers satisfy these requirements. First, the heat transfer area is increased due to small hydraulic diameter of the channel, therefore, the area density is large within same volume. Since the heat transfer coefficient is larger than that of macrochannel in laminar flow, the higher effectiveness can be achieved within small volume of heat exchanger. A design method of compact microchannel heat exchanger for cryogenic environment is not different from that of conventional heat exchanger. When designing a high effectiveness heat exchan- ger, however, one must consider some particular problems such as flow maldistribution and axial conduction effects that are not commonly treated in conventional heat exchangers [1]. The flow maldistribution occurs when a heat exchanger is composed of bun- dles of parallel channels. Since a microchannel heat exchanger does have parallel channels, therefore, the flow maldistribution problem should be considered. Moreover, the axial conduction problem appears when large temperature difference exists in a sin- gle heat exchanger. Compact (short) heat exchangers are usually accompanied with larger temperature gradient than conventional (long) heat exchangers due to small geometry. Axial conduction effect, therefore, is not negligible, but sometimes critical for its thermal performance. The flow maldistribution problems have been treated in various counter-flow heat exchanger geometries. Because actual flow dis- tribution is hard to measure, some simplified flow maldistribution http://dx.doi.org/10.1016/j.cryogenics.2014.01.003 0011-2275/Ó 2014 Elsevier Ltd. All rights reserved. Corresponding author. Tel.: +82 42 350 3079; fax: +82 42 350 8207. E-mail addresses: [email protected] (S. Baek), [email protected] (C. Lee), [email protected] (S. Jeong). 1 Tel.: +82 42 350 3079; fax: +82 42 350 8207. 2 Tel.: +82 42 350 3039; fax: +82 42 350 8207. Cryogenics 60 (2014) 49–61 Contents lists available at ScienceDirect Cryogenics journal homepage: www.elsevier.com/locate/cryogenics

Mal Distribution in PCHE

Embed Size (px)

DESCRIPTION

This is a research paper in cryogenics

Citation preview

  • on

    2

    a Ad

    Received 10 September 2013Received in revised form 24 November 2013Accepted 9 January 2014Available online 20 January 2014

    Keywords:Heat exchangerAxial conductionFlow maldistribution

    When a compact microchannel heat exchanger is operated at cryogenic environments, it has potentialproblems of axial conduction and ow maldistribution. To analyze these detrimental effects, the heat

    First, the heat transfer area is increased due to small hydraulicdiameter of the channel, therefore, the area density is large withinsame volume. Since the heat transfer coefcient is larger than that

    ers [1]. The owcomposed of bun-l heat excmaldistr

    problem should be considered. Moreover, the axial condproblem appears when large temperature difference exists igle heat exchanger. Compact (short) heat exchangers areaccompanied with larger temperature gradient than conventional(long) heat exchangers due to small geometry. Axial conductioneffect, therefore, is not negligible, but sometimes critical for itsthermal performance.

    The owmaldistribution problems have been treated in variouscounter-ow heat exchanger geometries. Because actual ow dis-tribution is hard to measure, some simplied ow maldistribution

    Corresponding author. Tel.: +82 42 350 3079; fax: +82 42 350 8207.E-mail addresses: [email protected] (S. Baek), [email protected] (C. Lee),

    [email protected] (S. Jeong).1 Tel.: +82 42 350 3079; fax: +82 42 350 8207.2 Tel.: +82 42 350 3039; fax: +82 42 350 8207.

    Cryogenics 60 (2014) 4961

    Contents lists availab

    Cryoge

    journal homepage: www.elseThe compact cryogenic liquefaction process inevitably requiressmall components due to space limitation of a ship, as well as highperformance heat exchanger (e > 0.90 NTU > 10) for efcient oper-ation. Microchannel heat exchangers satisfy these requirements.

    commonly treated in conventional heat exchangmaldistribution occurs when a heat exchanger isdles of parallel channels. Since a microchannedoes have parallel channels, therefore, the owhttp://dx.doi.org/10.1016/j.cryogenics.2014.01.0030011-2275/ 2014 Elsevier Ltd. All rights reserved.hangeributionuctionn a sin-usuallyDemand of high performance compact heat exchangers isincreasing for volume-limited cryogenic processes. The most rep-resentative example of the volume limited cryogenic process isthe natural gas liquefaction process for Liqueed Natural Gas-Floating Production Storage and Ofoading (LNG-FPSO).

    achieved within small volume of heat exchanger.A design method of compact microchannel heat exchanger for

    cryogenic environment is not different from that of conventionalheat exchanger. When designing a high effectiveness heat exchan-ger, however, one must consider some particular problems such asow maldistribution and axial conduction effects that are notMicrochannelCryogenic

    1. Introductionexchanger model that includes both axial conduction and owmaldistribution effect is developed in con-sideration of the microchannel heat exchanger geometry. A dimensionless axial conduction parameter (k)is used to describe the axial conduction effect, and the coefcient of variation (CoV) is introduced toquantify the ow maldistribution condition. The effectiveness of heat exchanger is calculated accordingto the various values of the axial conduction parameter and the CoV. The analysis results show that theheat exchanger effectiveness is insensitive when k is less than 0.005, and effectiveness is degraded withthe large value of CoV. Three microchannel heat exchangers are fabricated with printed circuit heatexchanger (PCHE) technology for validation purpose of the heat exchanger model. The rst heat exchan-ger is a conventional heat exchanger, the second heat exchanger has the modied cross section to elim-inate axial conduction effect, and the third heat exchanger has the modied cross section and the crosslink in parallel channel to mitigate ow maldistribution effect. These heat exchangers are tested in cryo-genic single-phase, and two-phase environments. The third heat exchanger shows the ideal thermal char-acteristic, while the other two heat exchangers experience some performance degradation due to axialconduction or ow maldistribution. The impact of axial conduction and ow maldistribution effectsare veried by the simulation results and compared with the experimental results.

    2014 Elsevier Ltd. All rights reserved.

    of macrochannel in laminar ow, the higher effectiveness can beArticle history:Effect of ow maldistribution and axial cmicrochannel heat exchanger

    Seungwhan Baek , Cheonkyu Lee 1, Sangkwon JeongCryogenic Engineering Laboratory, #5119, Department of Mechanical Engineering, KoreDaejeon 305-701, Republic of Korea

    a r t i c l e i n f o a b s t r a c tduction on compact

    vanced Institute of Science and Technology (KAIST), 291 Daehak-ro, Yuseong-gu,

    le at ScienceDirect

    nics

    vier .com/locate /cryogenics

  • pDh hydraulic diameter, m

    enicconditions have been assumed with the heat exchanger geometry.Fleming [2] and Jung [3,4] have investigated ow maldistributioneffect in plate type heat exchanger geometry. Their studies haveassumed that the ow distribution on one side is uniformly distrib-uted, and the other side is not. The fraction of FL is introduced todene the degree of ow maldistribution, where FL indicates thepercentage of layer with lower-than-average ow. Rao [5] investi-gated the effectiveness loss due to ow maldistribution in conven-tional plate heat exchangers. The ow distribution prole in U andZ type plate type heat exchanger header is used, and the effective-ness is calculated analytically. Pacio and Dorao [6] considered theimpact of ow maldistribution in a shell and tube heat exchangergeometry, and assumed that the ow maldistribution occurs in

    G mass ux, kg/m2 sh heat transfer coefcient, W/m2 Kk thermal conductivity, W/m KL length of heat exchanger, m_m mass ow rate, kg/sN number of channels, number of dataNTU number of transfer unitsNu Nusselt numberP precision errorq heat transfer rate, WRe Reynolds numberS standard deviation of datat T-distribution for a condence levelT temperature, Kth thickness of separator, mU heat transfer conductance, W/m2 KNomenclature

    A area, m2

    B bias errorC heat capacity rate, W/Kc heat capacity, J/kg K

    50 S. Baek et al. / Cryogcylindrical layers. However, the ow maldistribution in micro-channel heat exchanger geometry has not been carefully treatedyet.

    Axial conduction problem in heat exchangers have been studiedby many researchers. Among those researchers, Kroeger [7] solvede-NTU relation analytically, and Nellis [8] investigated axial con-duction in counterow heat exchanger numerically. Since theseheat exchanger models were composed with only one hot and coldchannels, the ow maldistribution problem was not considered.

    None of the preceding researchers studied the coupled problemof ow maldistribution and axial conduction effects at the sametime in the heat exchanger. The objective of this study is to quan-tify the ow maldistribution and axial conduction effect simulta-neously in the microchannel heat exchanger. The method tomitigate ow maldistribution and axial conduction are proposed,and the performance improvement is measured experimentallyin microchannel heat exchangers.

    2. Heat exchanger modeling

    2.1. Heat exchanger model with axial conduction effect

    The one dimensional counterow heat exchanger model includ-ing axial conduction effect is rst developed by using MATLAB[8,9]. The model is composed with the hot uid channel, the colduid channel, and the metal separator as displayed in Fig. 1. Thegoverning equations are developed from the energy balance ofthe uid streams and the metal separator, as equations from (1)(3).

    _mhcp;hdThdx

    hhAh;HTL

    Th Tw 1

    _mccp;c dTcdx hcAc;HT

    L

    Tw Tc 2

    ddx

    kwAwdTwdx

    _mhcp;h dThdx _mccp;c

    dTcdx

    3

    Since the numerical scheme of heat exchanger model is fully ex-plained in the literature [9], the important assumptions are only

    x axial position, m

    Greeka aspect ratio of square channele effectivenessk dimensionless axial conduction parameterl average value or viscosityr standard deviationH nondimensional temperature

    Subscriptc cold uidh hot uidideal ideal conditionin inletmax maximummin minimumMR mixed refrigerantout outletw wall or wall cross sectional area

    s 60 (2014) 4961highlighted in this paper. The model inputs are as followings:

    constant heat transfer coefcients (hh, hc) on both sides thickness (thw) and constant thermal conductivity (kw) of thewall (or separator)

    mass ow rate (mh,mc) on both sides inlet temperature (Th,in, Tc,in) on both sides constant heat capacity (cp,h, cp,c) on both sides

    The pressure drop in the microchannel is neglected in thisstudy. The output results from the heat exchanger model are thetemperature prole in the heat exchanger. The heat transfer coef-cients and heat capacity values on both streams are assumed tohave constant values. The number of transfer unit (NTU) is denedas the following equation.

    NTU UAHT _mcpmin4

    The thermal resistance of metal separator between hot and colduids is neglected. Therefore, the overall heat conductance is de-ned with only the local heat transfer coefcients and the heattransfer area, excluding the thermal resistance of the metal separa-tor, as the following equation.

    1UAHT

    1hhAh;HT

    1hcAc;HT

    5

    The effectiveness of heat exchanger is calculated with the fol-lowing equation

  • e q 6

    exchanger. The metal separator receives heat from the hot uid,however, not all of the heat is transferred to the cold uid. Heatis partially transferred through the metal plate in axial direction.Therefore, the outlet temperature shows the degraded values,resulting in the effectiveness loss. When a compact heat exchangeris designed for cryogenic purpose, it is very important to have lowk by controlling the length of heat exchanger, and the cross sec-tional area of heat exchanger body.

    2.2. Heat exchanger model with axial conduction and owmaldistribution effect

    Before the ow maldistribution effect on the heat exchanger

    Fig. 1. Heat exchanger geometry used in numerical sim

    0.0 0.2 0.4 0.6 0.8 1.00.0

    x*

    Fig. 3. Temperature proles of uids and metal separator (k = 0.1, NTU = 8).

    S. Baek et al. / Cryogenicqmax

    The developed heat exchanger model is validated in advancewith Kroegers analytic solution [7] according to the dimensionlessaxial conduction parameter k. The k is dened with heat exchangerlength (L), cross sectional area of wall (Aw), thermal conductivity ofwall (kw) and heat capacity rate (C) as the following equation.

    k kwAwLCmin

    7

    Fig. 2 displays the comparison between e-NTU relation of Kroe-gers analytic solution and numerical solution with various valuesof k in balanced ow condition (Ch = Cc) and constant properties.The numerical solution accurately predicts the analytical solutionover the entire range of NTU and k. The effectiveness degradationat the same NTU value is also observed in Fig. 2; the effectivenessis dramatically decreased when k has higher values than 0.005.Fig. 3 shows the temperature prole of hot/cold uids and themetal separator in the heat exchanger when k = 0.2. The non-dimensional temperature and heat exchanger is used to describethe temperature prole in the heat exchanger as the followingequations,

    H T Tc;inTh;in Tc;in 8

    x xL

    9

    The reason of effectiveness decrease due to high k is the largetemperature gap phenomena at the inlet and the outlet of heat5 10 15 20 25 300.80

    0.85

    0.90

    0.95

    1.00

    Numerical solution

    =0.0002=0.0022=0.0043=0.0217=0.1085

    Effe

    ctiv

    enes

    s (

    )

    NTU

    =0.0002=0.0022=0.0043=0.0217=0.1085

    Analytic solution

    Fig. 2. Effectiveness predicted by the numerical model as a function of NTU fordifferent values of k compared with Kroegers analytical solution.0.2

    0.4

    0.6

    ulation of a simple counterow heat exchanger.

    0.8

    1.0

    Hot Wall Cold

    s 60 (2014) 4961 51performance is considered, it is important to dene the specicow maldistribution condition in microchannel heat exchanger.Fig. 4 displays the typical structure of counterow heat exchangerwith microchannels. The horizontally parallel channels are in-stalled on one layer, and another set of horizontally parallelchannels are installed on the different layer. Four major ow mal-distribution conditions can be assumed with the header congura-tion of heat exchanger, as displayed in Fig. 5. When the inlet pipe isinstalled in perpendicular direction, the channel near the inlet pipewill have higher mass ow rate (Fig. 5a and c, linear weighted con-dition). When the inlet pipe is installed in axial direction, the massow rate at the center channels has higher values than the sidechannels (Fig. 5b and d, center weighted condition).

    To simulate these ow maldistribution condition, two kinds ofcounterow heat exchanger models are developed; the verticaland the horizontal heat exchanger model. These heat exchangermodels are developed based on the simple counterow heatexchanger model (Fig. 6a). The vertical heat exchanger model

  • ing equation.

    enicFig. 4. Typical microchannel counterow heat exchanger conguration.

    52 S. Baek et al. / Cryogconsists of hot and cold channels located alternatively. The sepa-rating walls are situated between the hot and cold uid channels.Fig. 6b displays the schematic of vertical heat exchanger model.The governing equation for the each stream is modied from Eqs.(1) and (2). From the cold uid 1, the uid encounters two separat-ing walls upward and downward. The heat transfer rate from theadditional wall should be considered in the uid energy balanceas the following equation.

    _mc1cp;cdTc1dx

    hc1Ac;HTL

    Tc1 Tw1 hc1Ac;HTL

    Tc1 Tw2 10

    The energy balance equations of additional walls are alsoconsidered. For example, the energy balance of the Wall 2, whichis located between cold uid 1 and hot uid 2 in Fig. 6b can bewritten as the following equation.

    ddx

    kwAwdTw2dx

    _mc1cp;c1 dTc1dx _mh2cp;h2

    dTh2dx

    11

    The number of walls are also determined when the number ofuid pair is given. Eqs. (10) and (11) are added and modied forthe additional uid pairs and separating walls.

    Fig. 5. Various ow maldistribution cases regarding header conguration: (a)horizontally linear weighted condition, (b) horizontally center weighted condition,(c) vertically linear weighted condition and (d) vertically center weighted condition._mh2cp;h2dTh2dx

    hh2Ah;HTL

    Th2 Tw3

    hh2Ah;HTL

    Th2 Tw4 hh2Ah;HTL

    Th2 Tw5 12

    The energy balance equation for the separating walls are iden-tical with Eq. (11) except the description of adjacent walls. Asthe vertical heat exchanger model, when the number of uid pairis given, the number of energy balance equations for uids andwalls are added and modied.

    The effect of owmaldistribution can be simulated by assumingdifferent mass ow rate at each channel. Table 1 summarizes thelinear weight ow-mal distribution condition, and Table 2 showsthe center weighted ow maldistribution condition for the threeuid pair heat exchanger models. The mass ow rate of hot sideis distorted, and the cold side mass ow rate is kept uniform asthe preceding studies [2,3]. To dene the degree of ow maldistri-bution, the coefcient of variation (CoV) is introduced. The CoV isdened as the following equation.

    CoV standard deviation raverage l

    PNi1 _mi m

    2

    N

    rm

    13

    The CoV can vary from 0 to very large positive values, and zerovalue of CoV indicates the ideally distributed ow condition. Theinlet temperatures are assumed to be identical, and the mean out-let temperatures are dened as the following equation.

    Tout PN

    i1 _miTi;outPNi1 _mi

    14

    The heat transfer coefcients at each channel is assumed tobe identical regardless of the mass ow rate. This assumptionis particularly valid for microchannel heat exchanger, wherethe ow regime is laminar and the Nusselt number is constant[3]. The total number of transfer unit (NTU) is dened as Eq.(4). The effect of ow maldistribution to effectiveness is calcu-lated in two heat exchanger models with different degree of owmaldistribution.

    3. Simulation results

    3.1. Impact of ow maldistribution

    The impact of ow maldistribution can be identied with thetemperature proles in the heat exchanger. The dotted lines inFig. 7a are the average temperature proles in the horizontal heatexchanger model with balanced ow condition (C = 1). When theow is distributed ideally, the temperature proles of hot and colduids are linear (the dash lines in Fig. 7a); however, the tempera-Fig. 6c displays the schematic of horizontal heat exchangermodel. The difference with the vertical heat exchanger model isthat the uid set is expanded in the horizontal direction. The sec-ond pair of uid set is situated on the right side of the rst pairof the uid set. Between each uid, the separating wall is located.The walls are located between every hot and hot uids and hot andcold uids to simulate multichannel effects. The energy balanceequations are added for the each uid and the separating wall asthe vertical heat exchanger model. For example, the energy balanceequation for the hot uid 2 in Fig. 6c can be written as the follow-

    s 60 (2014) 4961ture proles are curved (the solid lines in Fig. 7a) when there isow maldistribution. Moreover, the outlet temperatures aredegraded as a result of poor heat exchange. Fig. 7b shows the

  • enicS. Baek et al. / Cryogtemperature prole at each channel of the parallel heat exchanger.The hot channel 1 has excessive mass ow rate, which has a largecapacity ow rate, accordingly the temperature does not decreaseas much as expected. The hot channel 3 has insufcient mass owrate, having low capacity ow rate, its temperature drastically de-creases at the inlet of the heat exchanger. However, the outletaverage temperature is mainly dominated by the excessive massow rate channel, resulting in the degradation of heat exchangerperformance.

    The simulation is continued to observe the effectiveness loss atdifferent NTU values. Fig. 8a shows the e-NTU relation in horizontalheat exchanger model, when the mass ow rate is concentrated atone side of heat exchanger (linear weighted condition). Fig. 8bshows e-NTU relation when the mass ow rate is concentrated atthe center channels (center weighted). Comparison of the tworesults indicate that the effectiveness loss is greater when the massow rate is concentrated at one side of heat exchanger.

    Fig. 9a and b display the e-NTU relation in the vertical heatexchanger model with two ow maldistribution conditions. The

    Fig. 6. (a) the simple counter ow heat exchanger model, (b) vertical heat exchanger modexchanger model: the ow channels are located in the right or left side simultaneously

    Table 1Linear weighted ow mal-distribution conditions.

    Cases CoV mh1 (%) m2 (%) mh3 (%)

    Ideal 0 100.0 100.0 100.0Case 1 0.2 124.5 100.0 75.5Case 2 0.4 149.0 100.0 51.0Case 3 0.6 173.5 100.0 26.5Case 4 0.8 198.0 100.0 2.0

    Table 2Center weighted ow maldistribution conditions.

    Cases CoV mh1 (%) mh2 (%) m3 (%)

    Ideal 0 100 100 100Case 5 0.2 85.8 128.3 85.85Case 6 0.4 71.5 157.0 71.5Case 7 0.6 57.5 185.0 57.5Case 8 0.8 43.0 214.0 43.0s 60 (2014) 4961 53effectiveness loss due to ow maldistribution in the vertical heatexchanger model is greater when the ow rate is concentrated atone side of heat exchanger as the horizontal heat exchanger model.

    el: the ow channels are located up and down alternatively, and (c) horizontal heat.

    0.0

    0.2

    0.4

    0.6

    0.8

    1.0

    x*

    Hot-Ideal Cold-Ideal Hot-Flow mal Cold-Flow mal

    (a)

    0.0 0.2 0.4 0.6 0.8 1.0

    0.0 0.2 0.4 0.6 0.8 1.00.0

    0.2

    0.4

    0.6

    0.8

    1.0(b)

    x*

    Hot 1=190% Hot 2=100% Hot 3=10% Cold 1=100% Cold 2=100% Cold 3=100%

    Fig. 7. (a) Average temperature prole of hot and cold uid in the horizontal heatexchanger (Perfect case and ow maldistribution case). (b) Temperature prole ofthree hot and three cold uids (ow maldistribution case).

  • 0.80

    0.85

    0.90

    Effe

    ctiv

    enes

    NTU

    Ideal Case 1: CoV=0.2 Case 2: CoV=0.4 Case 3: CoV=0.6 Case 4: CoV=0.8

    5 10 15 20 25 30

    0.90

    0.95

    1.00(b)Vertical heat exchangerCenter weighted

    fect

    iven

    ess

    ()

    enic0.80

    0.85

    0.90

    0.95

    1.00Horizontal heat exchangerLinear weighted

    (a)Ef

    fect

    iven

    ess

    ()

    NTU

    Ideal Case 2: CoV=0.2 Case 3: CoV=0.4 Case 4: CoV=0.6 Case 5: CoV=0.8

    5 10 15 20 25 30

    0.90

    0.95

    1.00Horizontal heat exchangerCenter weighted

    (b)

    ctiv

    enes

    s (

    )54 S. Baek et al. / CryogThe amount of absolute degradation with identical CoV value,however, is larger than that of horizontal heat exchanger model.In overall, the effectiveness degradation is insensitive when CoVis lower than 0.2 in both heat exchanger models.

    The above results assert that it is better to install a header at thecenter of the parallel channels, and it is important to avoid owmaldistribution over the vertical (laminating) direction of micro-channel heat exchanger.

    The e-NTU relation at different heat capacity ratio is also calcu-lated by changing the heat capacity value of one stream. Fig. 10shows the result of effectiveness ratio with various heat exchangeroperating conditions. The effectiveness ratio is dened with theeffectiveness with the ideal ow distribution condition, as the fol-lowing equation.

    eratio eeideal 15

    The effectiveness degradation due to ow maldistribution isclearly observed when the heat capacity rate ratio has a value near1. The heat capacity rate ratio of cryogenic processes is near 1. Forexample, a helium recuperation process has C = 1, and a mixedrefrigerant Joule Thomson process has C 0.9. Then, the thermalperformance of a heat exchanger or a system is supposed to bestrongly dependent on the ow maldistribution condition. If theow maldistribution condition, such as CoV value at the inlet, isfound at the header, the more accurate heat exchanger perfor-mance estimation is possible.

    5 10 15 20 25 300.80

    0.85

    Effe

    NTU

    Ideal Case 6: CoV=0.2 Case 7: CoV=0.4 Case 8: CoV=0.6 Case 9: CoV=0.8

    Fig. 8. (a) e-NTU relation at linear weighted ow-mal distribution condition inhorizontal heat exchanger model (C 1; k 0;3 pairs), (b) e-NTU relation at centerweighted ow-mal distribution condition in horizontal heat exchanger model(C 1; k 0;3 pairs).0.95

    1.00

    s (

    )

    Vertical heat exchangerLinear weighted

    (a)

    s 60 (2014) 49613.2. Impact of ow maldistribution and number of channels

    The heat exchanger model is capable to simulate the arbitrarynumber of channels. The effectiveness degradation is observedwith the different number of channels. Fig. 11 indicates the linearweighted ow distribution proles in the 3, 5, 11, and 21 channels.The slopes of ow distribution prole are little different each other,however, the CoV values are identical. The four horizontal heat

    5 10 15 20 25 300.80

    0.85Ef

    NTU

    Ideal Case 7: CoV=0.4 Case 8: CoV=0.6 Case 9: CoV=0.8

    Fig. 9. (a) e-NTU relation at linear weighted ow-mal distribution condition invertical heat exchanger model (C 1; k 0;3 pairs) (b) e-NTU relation at centerweighted ow-mal distribution condition in vertical heat exchanger model(C 1; k 0;3 pairs).

    5 10 15 20 25 300.95

    0.96

    0.97

    0.98

    0.99

    1.00

    1.01

    1.02

    / 0

    NTU

    C*=1

    C*=0.8

    C*=0.6

    C*=0.4

    C*=0.2

    Fig. 10. e-NTU relation with various operating conditions at ow maldistributioncondition, calculated with the horizontal heat exchanger model (CoV = 0.48, k 0).

  • exchanger models are examined, which have 3, 5, 11 and 21 pairsof hot and cold uid channels, with the ow distribution proleindicated in Fig. 11.

    Fig. 12 displays the e-NTU relation of four different heatexchangers at identical CoV value. As seen from the gure, theeffectiveness degradation is intensied when the heat exchangerhas more channels. When the number of channels are increased,the uid outlet temperatures are determined with relatively largermass ow rate channels (Eq. (14)). It brings the degradation of out-let temperatures, resulting amplied effectiveness degradation ofthe multichannel heat exchanger.

    3.3. Impact of ow maldistribution and axial conduction

    In the previous section, the dimensionless axial conductionparameter (k) is assumed to be zero. It is certain that the heat ex-changer model developed in this study is capable of simulatingboth ow maldistribution and the axial conduction effect. The nextcalculation is meaningful in that these two effects are simulta-neously considered. Fig. 13a shows the temperature proles atevery channels in the vertical heat exchanger model. The large ax-ial conduction parameter of k = 0.37 is simulated, and also ow

    maldistribution condition is applied in this result. The temperaturejump phenomena at the heat exchanger inlet and outlet is ob-served, moreover, the different temperature prole of each channelis observed in Fig. 13a. When these two effects are coupled, thethermal performance is degraded even more. Fig. 13b displaysthe e-NTU relation regarding to the CoV and the axial conductionparameter. The effectiveness loss is amplied when two effects oc-cur together.

    3.4. Mitigation of ow maldistribution problem

    The effect of ow maldistribution was quantied in the analysisof the previous section to reveal the thermal performance degrada-tion of heat exchanger. It is a very important engineering task tomitigate the ow maldistribution effect in order to operate a de-signed heat exchanger properly. In this paper, a ow redistributiondevice inside the heat exchanger is proposed. The effect of owredistribution device is simulated with the heat exchanger modelby the spatially modied mass ow rate in the heat exchanger.For example, if the ow redistribution device is installed at the rstthird length of the heat exchanger, the mass ow rate is recalcu-lated at that position as the following equation

    at x 0! _mh1 1:4 g=s; _mh2 1:0 g=s; _mh3 0:6 g=sat x 1=4! _mh1 1:0 g=s; _mh2 1:0 g=s; _mh3 1:0 g=s

    16

    The mass ow rate at each channels after the ow redistribu-tion device is decided with the pressure drop of the ow redistri-bution device in actual condition. However, the mass ow rate ateach channels after the ow redistribution device is assumed tobe identical, because the pressure drop is neglected in this study.

    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2120

    40

    60

    80

    100

    120

    140

    160

    180 21 channels: CoV=0.4 11 channels: CoV=0.4 5 channels: CoV=0.4 3 channels: CoV=0.4

    1 2 3 4 51 2 3 4 5 6 7 8 9 10 11

    % m

    ass

    flow

    rate

    21 channels: 11 channels: 5 channels:

    Linear weighted condition

    0.95

    )

    1.0NTU~8, ~50

    S. Baek et al. / Cryogenics 60 (2014) 4961 555 10 15 20 25 300.80

    0.85

    0.90

    Effe

    ctiv

    enes

    s (

    NTU

    Ideal flow distribution, ~0 5 pairs, CoV=0.4, ~0 11 pairs, CoV=0.4, ~0 21 pairs, CoV=0.4, ~0Channel Number 3 channels: 1 2 3

    Fig. 11. The ow distribution proles at different heat exchangers with identicalCoV.

    1.00Horizontal heat exchanger Linear weightedFig. 12. e-NTU relation with different heat exchangers (5 pairs, 11 pairs, and 21pairs). The performance degradation is intensied with the increase of the numberof channels.0.0

    0.2

    0.4

    0.6

    0.8

    x*

    Hot 1=160% Hot 2=100% Hot 3=40%

    Cold 1=100% Cold 2=100% Cold 3=100%

    (a)

    0.0 0.2 0.4 0.6 0.8 1.0

    5 10 15 20 25 300.80

    0.85

    0.90

    0.95

    1.00

    Effe

    ctiv

    enes

    s (

    )

    NTU

    ~0, CoV=0~0, CoV=0.6

    =0.37, CoV=0=0.37, CoV=0.6

    (b)Fig. 13. (a) Temperature prole in the horizontal heat exchanger when owmaldistribution and axial conduction occur simultaneously. (b) Example of e-NTUrelation with axial conduction and ow maldistribution effect, (C = 1).

  • Fig. 14 shows the temperature proles of the uids in the heatexchanger with the ow redistribution device located at the hotside. The temperature proles are very different from the resultof Fig. 7b after the x* = 1/4. The owmaldistribution occurs in threehot channel inlets, which results in different temperature prolesat the inlet until the rst third part of the heat exchanger. Whenthe hot uids go through the ow redistribution device, the massow rate at each channel becomes identical. Then, the temperatureproles overlap each other, which indicate that the ow redistribu-tion device is effective to protect the thermal performance fromthe ow maldistribution problem. The ow rates at two cold inletsare ideally distributed, and show the overlapped temperature pro-le after the location of ow redistribution device. Due to the owmaldistribution of the hot side, the temperature proles of the colduid diverge at their outlets.

    To validate the heat exchanger model discussed above, three

    channel layers alternatively, diffusion bonding is carefully per-formed to make complete heat exchanger in a vacuum furnace.These PCHEs are identically composed of 10 hot streams and 10cold streams in a counter ow arrangement. The PCHE has coredimensions of 220 77 8 mm3. Four 1/4 in. stainless steel tubesare welded at each entrance of the ows as headers of the PCHE.

    The heat exchanger model is capable of simulating both axialconduction and ow maldistribution effects; accordingly, threeheat exchangers are fabricated to conrm these two effects.

    0.90

    0.92

    0.94

    0.96

    0.98

    1.00

    Effe

    ctiv

    enes

    s ra

    tio (

    /0)

    ~0, CoV=0.4, ~0, CoV=0.4 Redistribution @ 1/10th~0, CoV=0.8~0, CoV=0.8 Redistribution @ 1/10th

    (a)

    Horizontal heat exchanger model

    5 10 15 20 25 30

    5 10 15 20 25 300.80

    0.85

    Effe

    ctiv

    NTU

    ~0, CoV=0.4~0, CoV=0.4, Redistribution @ 1/10th~0, CoV=0.8~0, CoV=0.8, Redistribution @ 1/10th

    Vertical heat exchanger model

    Fig. 15. (a) Effectiveness ratio between ow maldistribution heat exchanger andow redistribution structured heat exchanger in horizontal heat exchanger model(C 1; k 0;3 pairs), and (b) effectiveness ratio between ow maldistributionheat exchanger and ow redistribution structured heat exchanger in vertical heatexchanger model (C 1; k 0;3 pairs).

    56 S. Baek et al. / Cryogenics 60 (2014) 4961counterow microchannel heat exchangers are fabricated. Themicrochannel heat exchangers are manufactured with printedcircuit heat exchanger (PCHE) fabrication process. The detailedfabrication procedure of PCHE is explained in the preceding re-searches [10,11].

    The PCHEs are composed of thin stainless steel plates (stainless304) stacked together. Fig. 16 displays the fabrication componentsof the PCHEs. There are two types of plates, the walls (or owdividers) and the channel layers. The ow dividers are 100 lmthick plane plate to serve as a ow separator. The channel layersare congured to have 22 rectangular shapes which are mostlymade by full etching of the plates. The size of channel is 300 lmheight and 400 lm wide. After stacking the dividers and the

    0.0 0.2 0.4 0.6 0.8 1.00.0

    0.2

    0.4

    0.6

    0.8

    1.0

    Cold-1 Cold-2 Cold-3

    Hot - Ideal Cold - Ideal

    x*

    Hot-1 Hot-2 Hot-3

    Flow re-distribution deviceFlow mal-distributionIt is evident that the ow redistribution device should be lo-cated near the uid inlet to mitigate the owmaldistribution effectin the heat exchanger. Fig. 15 shows the performance improve-ment expressed by effectiveness ratio when the ow redistributiondevice is installed at the rst tenth point of the heat exchanger.Fig. 15a displays the effectiveness ratio over different NTU valuesin the horizontal heat exchanger model, and Fig. 15b shows thesimulation results at the vertical heat exchanger model. Eventhough the ow maldistribution does initially exist, performanceis almost recovered when CoV is low. When the ow maldistribu-tion is severe (CoV = 0.8), the performance is recovered from 90% to97% in terms of the effectiveness ratio at NTU of 20 in the verticalheat exchanger model (Fig. 15b).

    4. Cryogenic heat exchanger experiments

    4.1. Microchannel heat exchangerFig. 14. Temperature prole with ow redistribution device in vertical heatexchanger model with ow maldistribution condition.NTU

    0.90

    0.95

    1.00

    enes

    s ra

    tio (

    /0)

    (b)Fig. 16. The schematic of fabricated PCHE components.

  • Fig. 17 displays the fabricated three heat exchangers; PCHE-1,PCHE-2 and PCHE-3. Although these heat exchangers have identi-cal heat transfer area (identical channel geometry and number oflayers), small modications are expected to improve their thermalperformances. The PCHE-1 is a microchannel heat exchanger withconventional fabrication technology. The PCHE-2 has the modiedheat exchanger cross section from the PCHE-1 by EDM wire cut toincrease the axial conduction length. The PCHE-3 has the modiedcross section and the ow redistribution device in channels. Thecross link between the parallel channels is selected as a ow redis-tribution device. There are several reports that cross link may im-prove ow distribution over the parallel channels [12,13]. It isexpected that the PCHE-3 will show the better performance thanPCHE-1 and PCHE-2.

    All three heat exchangers have ow maldistribution at theheader, which conrmed by CFD analysis [14]. Fig. 18 shows theheader geometry for CFD analysis. The test geometry consists ofparallel microchannels, the space of the header, and the 5 mm IDpipe attached to the header. The objective of CFD work is to ndthe horizontal and vertical ow distribution at the entrance ofthe channels. The heat transfer is neglected in this analysis. Theinlet velocity at the 5 mm pipe is given as the inlet boundary con-dition, and the constant pressure at the parallel channel ends are asgiven as the outlet boundary condition.

    Fig. 19a and b shows the velocity streamlines at the fabricatedheat exchanger header and the velocity distribution at each chan-nel when the 1 g/s of helium gas (300 K, 1500 kPa) is passingthrough the test geometry. Fig. 19c displays velocity distributionat each channel. The vertical ow distribution shows fairly ideal

    PCHE-2 and 3, which means that it has higher axial conductionparameter. The degree of ow maldistribution on all heat exchan-ger have the same value, however, the PCHE-3 is expected to havea lower CoV value due to ow redistribution device in it.

    4.2. Single phase experiments

    Thermal performances of the PCHEs are experimentally mea-sured in a cryogenic test facility as shown in Fig. 20. The experi-ments are performed between 300 K and 77 K. Compressedhelium gas (Genesis Vacuum Technology, Helium 2.1 compressor)ows in the hot side of the heat exchanger. The gas is cooled byliquid nitrogen (LN2) bath and then ows back to the cold side be-fore returning to the compressor inlet. Four silicon diode ther-mometers (Lakeshore, DT-670SD) are attached to the surface ofinlet and outlet tubes of the heat exchanger to measure the owtemperatures with respect to various mass ow rates. Four pres-sure transducers (SENSYS, PSH 30 bar) are also installed at each in-let and outlet for hot and cold ow streams. The mass ow rate iscontrolled by a mass ow controller (Bronkhorst: In-Flow, Helium,4000 slpm). Pressure and mass ow data are monitored utilizingNational Instruments Devices (SCXI-1000, SCXI-1125, and SCXI-1328). Silicon diode thermometers are monitored by LakeshoreTemperature Monitor model 218. All instrument data are then ac-quired by a computer utilizing LABVIEW software. In order to pre-vent heat loss and improve measurement accuracy during theexperiment, tests are conducted in a vacuum chamber.

    The effectiveness is calculated by Eq. (6), using the enthalpy

    S. Baek et al. / Cryogenics 60 (2014) 4961 57distribution, however, the horizontal distribution shows centerweighted distribution, and its CoV value is 0.15. The consistent re-sults are obtained when the inlet conditions are changed.

    The specications of these three heat exchangers are shown inTable 3. The PCHE-1 has shorter axial conduction length than theFig. 17. Fabricated three microchannel heat exchangers by Pvalues of the four inlet and outlets of the heat exchanger. Theenthalpy values are deduced from the measured temperature andpressure using REFPROP 9 [15]. The NTU values of heat exchangersare calculated with Eq. (4), and the single phase local heat transfercoefcients are referred from the preceding literature [16].CHE technology (a) PCHE-1 (b) PCHE-2, and (c) PCHE-3.

  • met

    enicThe uncertainty of measured data is determined with the fol-

    Fig. 18. The header geo58 S. Baek et al. / Cryoglowing equation [17]. Table 4 shows the instrumentation errorsfor the experimental setup. The experimental results show theuncertainty around 1.5%.

    U B2 t95%;v S

    N 1p

    2s17

    Fig. 21 displays the effectiveness comparison results betweenthe simulation and the experiment. The physical properties ofthe fabricated heat exchangers, such as the axial conductionparameter (k), the degree of ow maldistribution (CoV) and num-ber of channels are considered in the simulation results. The exper-imental results show the effectiveness improvement on the sameNTU value as predicted by the simulation results. As explainedabove, the PCHE-1 has both axial conduction and owmaldistribu-tion problems; therefore, the effectiveness shows the lowest valueamong three heat exchangers. The PCHE-2 has eliminated the axialconduction effect by increasing axial conduction length; the effec-tiveness shows higher value than the PCHE-1. Since the PCHE-3 haseliminated both axial conduction and ow maldistribution effect,the effectiveness is the greatest. Moreover, the calculated effective-ness values coincide with the experimental results.

    The experiments are continued to observe the performanceimprovement at cryogenic two phase condition.

    4.3. Two-phase experiments

    A mixed refrigerant Joule Thomson (MR-JT) process is used forthe representative example of cryogenic two phase ow condition.Condensation takes place in the hot side of the heat exchanger, andevaporation takes place in the cold side of the heat exchanger. Theimportant characteristic of MR-JT process is that the attainableno-load temperature strongly depends on the heat exchangerseffectiveness [18]. The microchannel heat exchangers are tested

    ry for the CFD analysis.

    s 60 (2014) 4961as the recuperator of the cryogenic MR-JT process.Experimental setup is modied to test the MR-JT process with

    the heat exchangers. Fig. 22 shows the schematic of experimentalsetup for the MR-JT test. A helium compressor (Helix, CTI-8200) isused to circulate the mixed refrigerants. The MR (Ar, R14, R23,R218, R134a) is charged from each separate component bottles tothe compressor. The MR passes through the heat exchanger, andwhen the MR goes through a JT expansion part, it creates low tem-perature. After passing through a heater, the MR enters the heat ex-changer again. The MR from the heat exchanger goes back to thecompressor to be pressurized to constant high pressure. The massow rate of themixed refrigerant is measured by amass owmeter(Micromotion, CMF025 with 1700 transmitter) which is located be-tween the compressor and the cold out ow of heat exchanger.Temperature and pressure are measured at inlet/outlet tubes ofthe heat exchanger as the previous experiment. The mixed refriger-ant composition is measured with Gas Chromatography (Younglin,GC6000) during the operation. The mixture in terms of mole frac-tion consists of 12% argon, 19% R14, 20% R23, 25% R218, and 24%R134a. The MR-JT process is operated with 1500:400 kPa pressureratio. The mass ow rate of mixed refrigerant is kept as 1.2 g/s.

    To ensure the experiments at identical conditions, the temper-atures before and after expansion are compared. Fig. 23 shows theresult of the measured temperatures before and after expansion.Two experimental results are found almost identical. From thiscomparison, we can conrm that the mixed refrigerant composi-tion and the pressure ratio are kept identical in two experiments.The only difference is the achieved minimum temperature. It issure that the ow maldistribution is mitigated in PCHE-3; there-fore the lower no-load temperature is obtained.

    Fig. 24 shows the e-NTU relation of experimental andsimulation results. For the estimation of NTU of heat exchanger,the fully-developed laminar ow is assumed based on the linearfriction factor characteristic at low Reynolds number [10]. The

  • enicS. Baek et al. / Cryogcalculated Reynolds number based on averaged physical property(Eq. (18)) shows around 80.

    Re GDhl

    18

    1 2 3 4 5 6 7 8 9 10 110

    1

    2

    3

    4

    5

    6

    Horizontal Vertical

    Velo

    city

    (m/s

    )

    Channel

    Horizontal direc Vertical direction

    1 2 3 4 5 6

    (c)

    Fig. 19. Velocity streamlines at the fabricated heat exchanger header (a) upp

    Table 3Specications of fabricated heat exchanger.

    Specication PCHE-1

    Hydraulic diameter (Dh) 340 lmTotal heat transfer area (AHT) 0.2024 m2

    Total ow area (Aow) 2.64 105 m2Total axial conduction area (Acond) 6.21 104 m2Axial conduction length (L) 0.2 mAxial conduction parameter (k) 0.020Horizontal CoV of velocity 0.15s 60 (2014) 4961 59For the better estimation of NTU, the local heat transfercoefcients must be veried to calculate the overall heat transfercoefcient. In this case, the two-phase condensation heat transfercoefcient is required for the high pressure stream, and thetwo-phase evaporation heat transfer coefcient is required for

    12 13 14 15 16 17 18 19 20 21 22

    Number

    tion (Line A) CoV=0.15 (Line B) CoV=0.04

    7 8 9 10

    er view, (b) side view, and (c) velocity distribution at specic locations.

    PCHE-2 PCHE-3

    340 lm 340 lm0.2024 m2 0.2024 m2

    2.64 105 m2 2.64 105 m21.55 104 m2 1.55 104 m20.55 m 0.55 m0.001 0.0010.15 0

  • Compressor

    Supply Return

    P4, T5P1, T1 Mass flow meter

    enicHelium Compressor

    Supply Return

    MFC

    Liquid nitrogen Supply

    60 S. Baek et al. / Cryogthe low pressure stream. Although those two-phase heat transfercorrelations for the mixed refrigerant in the microchannel arenot well known, the two-phase Nusselt can be presumed basedon the experimental results from literatures at very small Reynoldsnumber. The Reynolds number in our experimental condition isless than 100. The evaporation heat transfer coefcient measure-ment of cryogenic mixed refrigerant results from Nellis [19]indicate that the Nusselt number converges to small number atvery small Reynolds number. The several evaporative heat transfercorrelations also indicate that the low Nusselt number is calculated

    LN2 Bath

    T,PCold Out

    T,PCold In

    T,PHot out

    T,PHot in

    Vacuum Chamber

    Test PCHE

    Fig. 20. Experimental setup to measure heat exchanger effectiveness in cryogenicsingle phase environment.

    Table 4The instrument errors for the experimental setup.

    Measurement Number Error Note

    Temperature 4 0.1 K (Surface mount)Pressure 4 0.5%Mass ow rate 1 0.5%Gas chromatography 1 1%

    Total uncertainty 1.5%

    5 10 15 20 25 300.80

    0.85

    0.90

    0.95

    1.00

    Effe

    ctiv

    enes

    s (

    )

    NTU

    Numerical~0.001, CoV=0~0.001, CoV=0.15, Horizontal, 22 pairs, center weighted~0.020, CoV=0.15, Horizontal, 22 pairs, center weighted

    Experimental PCHE-3 PCHE-2 PCHE-1

    Fig. 21. Comparison of experimental effectiveness with simulation e-NTU results invarious NTU values (C = 1).s 60 (2014) 4961at very small Reynolds number [20]. Moreover, the condensationheat transfer coefcient in the microchannel at extremely lowmass ux shows also small values [21]. Therefore, the two phaselocal heat transfer coefcients are estimated using Eq. (19), which

    Cold Out

    P3, T4 Cold In

    P2, T2Hot out

    Hot in

    Vacuum Chamber

    HEX

    Expansiondevice

    T3 : Cold end

    Fig. 22. Experimental setup to measure heat exchanger effectiveness in cryogenictwo phase ow environment (mixed refrigerant Joule Thomson process).

    160 180 200 220 240 260 280 300160

    180

    200

    220

    240

    260

    280

    300

    Tem

    pera

    ture

    afte

    r exp

    ansi

    on (K

    )

    Temperature before expansion (K)

    PCHE-2 (experimental) PCHE-3 (experimental) Temperature before/after (calculation)

    Fig. 23. Comparison of temperature before/after expansion for two experimentresults.

    40200.90

    0.92

    0.94

    0.96

    0.98

    1.00

    Numerical~0.001, CoV=0~0.001, CoV=0.15

    (Horizontal, 22 pairs, Center weighted) ~0.020, CoV=0.15

    (Horizontal, 22 pairs, Center weighted)

    Experimental PCHE-3 PCHE-2 PCHE-1 (Expected)

    Effe

    ctiv

    enes

    s (

    )

    NTU

    C*=0.98

    Fig. 24. Comparison of experimental effectiveness with simulation e-NTU results invarious NTU values (C = 0.98).

  • is the Nusselt number for the fully developed laminar ow in thesquare duct [22].

    Nu hDhkMR 7:5411 2:61a 4:97a2 5:119a3 2:702a4 0:548a5

    19where the a is the aspect ratio of the square duct.

    The average thermal conductivity of the mixed refrigerant iscalculated with REFPROP 9, and then NTU values are estimated.The calculated NTU shows the value around 30. The heat capacityrate ratio (C) is 0.98 in the given operating condition. The effec-tiveness value from the experiments is calculated by the measuredtemperature and pressure conditions. Note that the experimentalresults include uncertainties in both NTU and effectiveness.

    and Planning (KETEP) Grant funded by the Korea government Min-istry of Knowledge Economy (No. 2011101050002B).

    References

    [1] Pacio JC, Dorao CA. A review on heat exchanger thermal hydraulic models forcryogenic applications. Cryogenics 2011;51(7):36679.

    [2] Fleming R. The effect of ow maldistribution in parallel channels ofcounterow heat exchangers. Adv Cryogenic Eng 1967:1235262.

    [3] Jung J, Jeong S. Effect of ow mal-distribution on effective NTU in multi-channel counter-ow heat exchanger of single body. Cryogenics2007;47(4):23242.

    [4] Jung J, Hwang G, Baek S, Jeong S, Rowe AM. Partial ow compensation bytransverse bypass conguration in multi-channel cryogenic compact heatexchanger. Cryogenics 2012;52(1):1926.

    [5] Prabhakara Rao B, Krishna Kumar P, Das SK. Effect of ow distribution to thechannels on the thermal performance of a plate heat exchanger. Chem EngProcess: Process Intensicat 2002;41(1):4958.

    [6] Pacio JC, Dorao CA. A study of the effect of ow maldistribution on heattransfer performance in evaporators. Nucl Eng Des 2010;240(11):386877.

    [7] Kroeger P. Performance deterioration in high effectiveness heat exchangers

    S. Baek et al. / Cryogenics 60 (2014) 4961 61It is certain in Fig. 24 that the PCHE-3 shows the higher effec-tiveness than that of PCHE-2 on similar NTU values. BecausePCHE-3 has ow redistribution device in the heat exchanger, owmaldistribution effect must be mitigated. The effectiveness valuesdeduced from the experimental results indicate that the two-phaseow maldistribution exists in PCHE-2, but resolved in PCHE-3,which is also veried by numerical simulations.

    5. Conclusion

    The heat exchanger model that includes axial conduction andow maldistribution effect is developed in this paper. The dimen-sionless axial conduction parameter (k) and ow maldistributioncoefcient (CoV) are used to describe axial conduction effect andthe ow maldistribution condition. The heat exchanger effective-ness is specically calculated based on k and CoV. The effectivenessis degraded with high values of k and CoV. The heat exchangergeometry modication is one solution to have low axial conductioneffect. The thermal performance degradation due to owmaldistri-bution effect can be mitigated by ow redistribution device insidethe heat exchanger.

    The microchannel heat exchangers are fabricated to examinethe geometry effect on axial conduction and ow maldistribution.The modied geometry in the heat exchanger successfully dimin-ishes axial conduction and ow maldistribution problems, whichresultantly increase effectiveness values.

    Acknowledgements

    This work was supported by the Power Generation & ElectricityDelivery of the Korea Institute of Energy Technology Evaluationdue to axial heat conduction effects. Adv Cryogenic Eng 1967:1236372.[8] Nellis GF. A heat exchanger model that includes axial conduction, parasitic

    heat loads, and property variations. Cryogenics 2003;43(9):52338.[9] Nellis G, Klein S. Heat transfer. Cambridge University Press; 2009.[10] Baek S, Kim J-H, Jeong S, Jung J. Development of highly effective cryogenic

    printed circuit heat exchanger (PCHE) with low axial conduction. Cryogenics2012;52(79):36674.

    [11] Baek S, Kim J, Hwang G, Jeong S. Elongating axial conduction path design toenhance performance of cryogeinc compact PCHE (Printed Circuit HeatExchanger). AIP Conf Proc 2012;1434(1):6318.

    [12] Dang MN. A study on two-phase ow characteristics in cross-linkedmicrochannel heat sinks. Concordia University; 2007.

    [13] Megahed A. Experimental investigation of ow boiling characteristics in across-linked microchannel heat sink. Int J Multiph Flow 2011;37(4):38093.

    [14] ANSYS. ANSYS Fluent Theory Guide; 2012.[15] Lemmon EW, Huber ML, McLinden MO. NIST Standard Reference Database 23:

    reference uid thermodynamic and transport properties-REFPROP. Version 9.0ed: National Institute of Standards and Technology, Standard Reference DataProgram, Gaithersburg; 2010.

    [16] Peng XF, Peterson GP. Convective heat transfer and ow friction for water owin microchannel structures. Int J Heat Mass Transf 1996;39(12):2599608.

    [17] Moffat RJ. Describing the uncertainties in experimental results. Exp ThermalFluid Sci 1988;1(1):317.

    [18] Barron RF. Cryogenic systems. Oxford University Press; 1985.[19] Nellis G, Hughes C, Pfotenhauer J. Heat transfer coefcient measurements for

    mixed gas working uids at cryogenic temperatures. Cryogenics2005;45(8):54656.

    [20] Riehl RR, Seleghim Jr P, Ochterbeck JM. Comparison of heat transfercorrelations for single- and two-phase microchannel ows formicroelectronics cooling. In: Thermal and thermomechanical phenomena inelectronic systems, 1998 ITHERM 98 The Sixth Intersociety Conference on1998; p. 40916.

    [21] Su Q, Yu GX, Wang HS, Rose JW. Microchannel condensation: correlations andtheory. Int J Refrig 2009;32(6):114952.

    [22] Hesselgreaves JE. Compact heat exchangers: selection, design, and operation:Pergamon Pr; 2001.

    Effect of flow maldistribution and axial conduction on compact microchannel heat exchanger1 Introduction2 Heat exchanger modeling2.1 Heat exchanger model with axial conduction effect2.2 Heat exchanger model with axial conduction and flow maldistribution effect

    3 Simulation results3.1 Impact of flow maldistribution3.2 Impact of flow maldistribution and number of channels3.3 Impact of flow maldistribution and axial conduction3.4 Mitigation of flow maldistribution problem

    4 Cryogenic heat exchanger experiments4.1 Microchannel heat exchanger4.2 Single phase experiments4.3 Two-phase experiments

    5 ConclusionAcknowledgementsReferences