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  • Advances and Unsolved Issues in Pulsating Heat Pipesweb.missouri.edu/~zhangyu/Pubs/71_Zhang_and_Faghri_HTE...a closed loop, or pinched off and welded shut in an open loop (see Figure
25
Heat Transfer Engineering, 29(1):20–44, 2008 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457630701677114 Advances and Unsolved Issues in Pulsating Heat Pipes YUWEN ZHANG Department of Mechanical and Aerospace Engineering, University of Missouri-Columbia, Columbia, Missouri, USA AMIR FAGHRI Department of Mechanical Engineering, University of Connecticut, Storrs, Connecticut, USA Pulsating (or oscillating) heat pipes (PHP or OHP) are new two-phase heat transfer devices that rely on the oscillatory flow of liquid slug and vapor plug in a long miniature tube bent into many turns. The unique feature of PHPs, compared with conventional heat pipes, is that there is no wick structure to return the condensate to the heating section; thus, there is no countercurrent flow between the liquid and vapor. Significant experimental and theoretical efforts have been made related to PHPs in the last decade. While experimental studies have focused on either visualizing the flow pattern in PHPs or characterizing the heat transfer capability of PHPs, theoretical examinations attempt to analytically and numerically model the fluid dynamics and/or heat transfer associated with the oscillating two-phase flow. The existing experimental and theoretical research, including important features and parameters, is summarized in tabular form. Progresses in flow visualization, heat transfer characteristics, and theoretical modeling are thoroughly reviewed. Finally, unresolved issues on the mechanism of PHP operation, modeling, and application are discussed. INTRODUCTION Evolution in the design of the heat pipe—a type of passive two-phase thermal control device—has accelerated in the past decade due to continuous demands for faster and smaller mi- croelectronic systems. As modern computer chips and power electronics become smaller and more densely packed, the need for more efficient cooling systems increases. The new design of a computer chip at Intel, for instance, will produce localized heat flux over 100 W/cm 2 , with the total power exceeding 300 W. In addition to the limitations on maximum chip temperature, further constraints may be imposed on the level of temperature unifor- mity in electronic components. Heat pipes are a very promising technology for achieving high local heat-removal rates and uni- form temperatures on computer chips. True development of conventional heat pipes (CHP) began in the 1960s; since then, various geometries, working fluids, and wick structures have been proposed [1]. In the last 20 years, new types of heat pipes—such as capillary pumped loops and loop heat pipes—were introduced, seeking to separate the liquid and Address correspondence to Professor Amir Faghri, Department of Mechan- ical Engineering, University of Connecticut, Storrs, CT 06269, USA. E-mail: [email protected] vapor flows to overcome certain limitations inherent in conven- tional heat pipes. In the 1990s, Akachi et al. [2] invented a new type of heat pipe known as the pulsating or oscillating heat pipe (PHP or OHP). The most popular applications of PHP are found in electronics cooling because it may be capable of dissipat- ing the high heat fluxes required by next generation electronics. Other proposed applications include using PHPs to preheat air or pump water. This review article will describe the operation of pulsating heat pipes, summarize the research and development over the past decade, and discuss the issues surrounding them that have yet to be resolved. Pulsating heat pipes, like conventional heat pipes, are closed, two-phase systems capable of transporting heat without any ad- ditional power input, but they differ from conventional heat pipes in several major ways. A typical PHP is a small mean- dering tube that is partially filled with a working fluid, as seen in Figure 1 [3]. The tube is bent back and forth parallel to itself, and the ends of the tube may be connected to one another in a closed loop, or pinched off and welded shut in an open loop (see Figure 1a and 1b). It is generally agreed by researchers that the closed-loop PHP has better heat transfer performance [4, 5]. For this reason, most experimental work is done with closed- loop PHPs. In addition to the oscillatory flow, the working fluid can also be circulated in the closed-loop PHP, resulting in heat 20

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  • Heat Transfer Engineering, 29(1):20–44, 2008Copyright C©© Taylor and Francis Group, LLCISSN: 0145-7632 print / 1521-0537 onlineDOI: 10.1080/01457630701677114

    Advances and Unsolved Issuesin Pulsating Heat Pipes

    YUWEN ZHANGDepartment of Mechanical and Aerospace Engineering, University of Missouri-Columbia, Columbia, Missouri, USA

    AMIR FAGHRIDepartment of Mechanical Engineering, University of Connecticut, Storrs, Connecticut, USA

    Pulsating (or oscillating) heat pipes (PHP or OHP) are new two-phase heat transfer devices that rely on the oscillatoryflow of liquid slug and vapor plug in a long miniature tube bent into many turns. The unique feature of PHPs, comparedwith conventional heat pipes, is that there is no wick structure to return the condensate to the heating section; thus, thereis no countercurrent flow between the liquid and vapor. Significant experimental and theoretical efforts have been maderelated to PHPs in the last decade. While experimental studies have focused on either visualizing the flow pattern in PHPsor characterizing the heat transfer capability of PHPs, theoretical examinations attempt to analytically and numericallymodel the fluid dynamics and/or heat transfer associated with the oscillating two-phase flow. The existing experimentaland theoretical research, including important features and parameters, is summarized in tabular form. Progresses in flowvisualization, heat transfer characteristics, and theoretical modeling are thoroughly reviewed. Finally, unresolved issues onthe mechanism of PHP operation, modeling, and application are discussed.

    INTRODUCTION

    Evolution in the design of the heat pipe—a type of passivetwo-phase thermal control device—has accelerated in the pastdecade due to continuous demands for faster and smaller mi-croelectronic systems. As modern computer chips and powerelectronics become smaller and more densely packed, the needfor more efficient cooling systems increases. The new design ofa computer chip at Intel, for instance, will produce localized heatflux over 100 W/cm2, with the total power exceeding 300 W. Inaddition to the limitations on maximum chip temperature, furtherconstraints may be imposed on the level of temperature unifor-mity in electronic components. Heat pipes are a very promisingtechnology for achieving high local heat-removal rates and uni-form temperatures on computer chips.

    True development of conventional heat pipes (CHP) began inthe 1960s; since then, various geometries, working fluids, andwick structures have been proposed [1]. In the last 20 years, newtypes of heat pipes—such as capillary pumped loops and loopheat pipes—were introduced, seeking to separate the liquid and

    Address correspondence to Professor Amir Faghri, Department of Mechan-ical Engineering, University of Connecticut, Storrs, CT 06269, USA. E-mail:[email protected]

    vapor flows to overcome certain limitations inherent in conven-tional heat pipes. In the 1990s, Akachi et al. [2] invented a newtype of heat pipe known as the pulsating or oscillating heat pipe(PHP or OHP). The most popular applications of PHP are foundin electronics cooling because it may be capable of dissipat-ing the high heat fluxes required by next generation electronics.Other proposed applications include using PHPs to preheat airor pump water. This review article will describe the operation ofpulsating heat pipes, summarize the research and developmentover the past decade, and discuss the issues surrounding themthat have yet to be resolved.

    Pulsating heat pipes, like conventional heat pipes, are closed,two-phase systems capable of transporting heat without any ad-ditional power input, but they differ from conventional heatpipes in several major ways. A typical PHP is a small mean-dering tube that is partially filled with a working fluid, as seenin Figure 1 [3]. The tube is bent back and forth parallel to itself,and the ends of the tube may be connected to one another ina closed loop, or pinched off and welded shut in an open loop(see Figure 1a and 1b). It is generally agreed by researchers thatthe closed-loop PHP has better heat transfer performance [4, 5].For this reason, most experimental work is done with closed-loop PHPs. In addition to the oscillatory flow, the working fluidcan also be circulated in the closed-loop PHP, resulting in heat

    20

  • Y. ZHANG and A. FAGHRI 21

    Figure 1 Different PHPs: (a) closed-end, (b) closed-loop, (c) closed-loopwith check valve, and (d) PHP with open ends.

    transfer enhancement. Although an addition of a check valve (seeFigure 1c) could improve the heat transfer performance of thePHPs by making the working fluid move in a specific direction,it is difficult and expensive to install these valves. Consequently,the closed-loop PHP without a check valve becomes the mostfavorable choice for the PHP structures. Recently, PHPs with asintered metal wick have been prototyped by Zuo et al. [6, 7]and analyzed by Holley and Faghri [8]. The wick should aid inheat transfer and liquid distribution. There has also been someexploration into pulsating heat pipes in which one or both endsare left open without being sealed (see Figure 1d) [9–11].

    Like a CHP, a PHP must be heated in at least one sectionand cooled in another. Often the evaporators and condensers arelocated at the bends of the capillary tube. The tube is evacuatedand then partially filled with a working fluid. The liquid andits vapor will become distributed throughout the pipe as liquidslugs and vapor bubbles. As the evaporator section of the PHP isheated, the vapor pressure of the bubbles located in that sectionwill increase. This forces the liquid slug toward the condensersection of the heat pipe. When the vapor bubbles reach the con-denser, it will begin to condense. As the vapor changes phase,the vapor pressure decreases, and the liquid flows back towardthe condenser end. In this way, a steady oscillating flow is setup in the PHP. Boiling the working fluid will also cause newvapor bubbles to form. The unique feature of PHPs, comparedwith conventional heat pipes, is that there is no wick structure toreturn the condensate to the heating section, and therefore thereis no countercurrent flow between the liquid and the vapor. Dueto the simplicity of the structure of a PHP, its weight is lowerthan that of conventional heat pipe, which makes PHP an idealcandidate for space application.

    Research on PHPs can be categorized as either experimentalor theoretical. While experimental studies have focused on ei-ther visualizing the flow pattern in PHPs or characterizing theheat transfer capability of PHPs, theoretical examinations at-tempt to analytically and numerically model the fluid dynamicsand/or heat transfer associated with oscillating two-phase flow.The existing experimental and theoretical research and their pa-rameters are summarized in Table 1. The table lists the primaryinvestigators, reference number, and the year the study was pub-

    lished, followed by the details of the modeling and/or experi-ment: theoretical approaches, major assumptions, the materialused to manufacture the PHP, the geometry and configurationof the flow channel, number of parallel channels, inclination an-gles, channel diameters, the working fluids tested, the chargeratios that they were tested at, range of heat transferred by thePHP, a summary of the conclusions drawn by the investiga-tor, and other significant comments. This article also presentsthe principles of operation, flow visualization, heat transfer, andmodeling, as well as a discussion of the unresolved issues in PHPresearch.

    PRINCIPLES OF OPERATION

    Although simple in their construction, PHPs become compli-cated devices when one tries to fully understand their operation:the thermodynamics driving PHP operation, the fluid dynam-ics governing the two-phase oscillating flow, heat transfer (bothsensible and latent), and the physical design parameters of thePHP must all be considered.

    Thermodynamic Principles

    Heat addition and rejection and the growth and extinction ofvapor bubbles drive the flow in a PHP. Even though the exactfeatures of the thermodynamic cycle are still unknown, Grolland Khandekar [12] described it in general terms using a pres-sure/enthalpy diagram as seen in Figure 2. The temperature andvapor quality in the evaporator and condenser are known, or canbe assumed, so the state at the outlets of the evaporator and con-denser are known. Starting at the evaporator inlet, point A onthe P-h diagram, the processes required to get to point B on thediagram can be simplified to heat input at a constant pressurecombined with isentropic pressure increase due to bubble ex-pansion. As one travels through the adiabatic section from theevaporator to the condenser, the pressure decreases isenthalpi-cally. The thermodynamic process between the condenser’s inletand outlet are complicated, but can be simplified to constant pres-sure condensation with negative isentropic work. An isenthalpicpressure drop in the adiabatic section completes the cycle. Be-cause of the numerous assumptions made in this description,thermodynamic analysis is insufficient to study PHPs.

    Fluid Dynamic Principles

    Fluid flow in a capillary tube consists of liquid slugs andvapor plugs moving in unison. The slugs and plugs initially dis-tribute themselves in the partially filled tube. The liquid slugsare able to completely bridge the tube because surface tensionforces overcome gravitational forces. There is a meniscus re-gion on either end of each slug caused by surface tension atthe solid/liquid/vapor interface. The slugs are separated by plugs

    heat transfer engineering vol. 29 no. 1 2008

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    ratu

    reis

    incr

    ease

    dby

    30%

    byin

    crea

    sing

    acce

    lera

    tion

    from

    −6g

    to12

    g.W

    ong

    etal

    .[5

    0](1

    999)

    Mas

    san

    dm

    omen

    tum

    bala

    nces

    ina

    Lag

    rang

    ian

    fram

    e.

    Adi

    abat

    ic,h

    eat

    inpu

    twas

    mod

    eled

    asa

    sudd

    enpr

    essu

    reri

    se.N

    oliq

    uid

    film

    .

    N/A

    Ope

    nC

    ircu

    lar

    40

    ——

    50—

    The

    pres

    sure

    puls

    ein

    duce

    sos

    cilla

    tion

    but

    isda

    mpe

    dou

    tby

    fric

    tion

    betw

    een

    the

    liqui

    dan

    dpi

    pew

    all.

    Lin

    etal

    .[30

    ](2

    000)

    Non

    eN

    /AC

    oppe

    rO

    pen

    Cir

    cula

    r40

    0,90

    1.75

    Ace

    tone

    25–5

    014

    0–20

    40O

    ptim

    umch

    arge

    ratio

    is38

    %.O

    pera

    tion

    isbe

    tter

    inho

    rizo

    ntal

    .No

    oper

    atio

    nat

    25%

    char

    ge.

    Lin

    etal

    .[31

    ](2

    001)

    Non

    eN

    /AC

    oppe

    rO

    pen

    Cir

    cula

    r40

    0,90

    1.75

    FC-7

    2,FC

    -75

    30–5

    014

    0–20

    40O

    ptim

    umch

    arge

    ratio

    is50

    %.F

    C-7

    2pe

    rfor

    med

    bette

    rth

    anFC

    -75.

    Ope

    ratio

    nis

    bette

    rin

    hori

    zont

    al.N

    oop

    erat

    ion

    at25

    %ch

    arge

    .Per

    form

    ance

    isin

    depe

    nden

    tof

    orie

    ntat

    ion.

    Tong

    etal

    .[2

    0](2

    001)

    Non

    eN

    /APy

    rex

    glas

    sC

    lose

    dC

    ircu

    lar

    140,

    901.

    8M

    etha

    nol

    6050

    Cir

    cula

    tion

    was

    obse

    rved

    ,an

    dci

    rcul

    atio

    nve

    loci

    tyin

    crea

    ses

    with

    incr

    easi

    nghe

    atin

    put.

    Cir

    cula

    tion

    can

    beei

    ther

    cloc

    kwis

    eor

    coun

    ter-

    cloc

    kwis

    e.Sh

    afiie

    tal.

    [13]

    (200

    1)M

    ass,

    mom

    entu

    m,

    and

    ener

    gyeq

    uatio

    nsfo

    rea

    chliq

    uid

    slug

    and

    vapo

    rpl

    ugar

    eso

    lved

    .

    Vap

    oris

    anid

    eal

    gas.

    Inco

    mpr

    essi

    ble

    liqui

    d.N

    opr

    essu

    relo

    ssin

    bend

    s.

    N/A

    Ope

    n/cl

    osed

    Cir

    cula

    r4

    −90

    1.5,

    3.0

    Wat

    er61

    .4,

    89.4

    70–

    80M

    ajor

    ity(9

    5%)

    ofhe

    atis

    tran

    sfer

    red

    byse

    nsib

    lehe

    at.L

    aten

    thea

    tser

    ves

    only

    todr

    ive

    osci

    llatin

    gflo

    w.E

    ffec

    tof

    grav

    ityis

    negl

    igib

    le.

    (Con

    tinu

    edon

    next

    page

    )

  • Tabl

    e1

    (Con

    tinu

    ed)

    Ope

    n/In

    vest

    igat

    orT

    heor

    etic

    alcl

    osed

    Flow

    path

    Para

    llel

    Incl

    inat

    ion

    DW

    orki

    ngC

    harg

    eC

    oncl

    usio

    nsan

    d(y

    ear)

    appr

    oach

    esA

    ssum

    ptio

    nsM

    ater

    ials

    loop

    geom

    etry

    chan

    nels

    angl

    e(◦

    )(m

    m)

    fluid

    ratio

    q(W

    )co

    mm

    ents

    Shafi

    ieta

    l.[1

    4](2

    002)

    Thi

    nfil

    mev

    apor

    atio

    nan

    dco

    nden

    satio

    nw

    ere

    solv

    edto

    getl

    aten

    thea

    ttr

    ansf

    erco

    effic

    ient

    .

    Rad

    ialc

    ondu

    ctio

    non

    lyin

    thin

    film

    .Neg

    lect

    ing

    shea

    rst

    ress

    atliq

    uid-

    vapo

    rin

    terf

    ace.

    N/A

    Ope

    n/cl

    osed

    Cir

    cula

    r4

    —1.

    5,3.

    0W

    ater

    64.2

    1–89

    .50–

    119

    Hea

    ttra

    nsfe

    ris

    due

    mai

    nly

    toth

    eex

    chan

    geof

    sens

    ible

    heat

    .Hig

    her

    surf

    ace

    tens

    ion

    resu

    ltsin

    asl

    ight

    incr

    ease

    into

    talh

    eatt

    rans

    fer.

    No

    oper

    atio

    nfo

    rhi

    ghch

    arge

    ratio

    .C

    aiet

    al.[

    17]

    (200

    2)N

    one

    N/A

    Qua

    rtz,

    copp

    erC

    lose

    d,op

    enC

    ircu

    lar

    12,5

    045

    ,02.

    4,2.

    2E

    than

    ol,

    wat

    er,

    acet

    one,

    etha

    nol,

    amm

    o-ni

    a

    50,4

    0–60

    100–

    600

    Prop

    agat

    ion

    and

    extin

    ctio

    nof

    bubb

    les

    are

    obse

    rved

    .Flu

    ids

    with

    low

    late

    nthe

    ats

    are

    reco

    mm

    ende

    dto

    prom

    ote

    osci

    llato

    rym

    otio

    n.K

    hand

    ekar

    etal

    .[16

    ](2

    002)

    Non

    eN

    /AA

    lum

    inum

    /gla

    ss,

    copp

    er/g

    lass

    Clo

    sed

    Rec

    tang

    ular

    ,re

    ctan

    gula

    r,ci

    rcul

    ar

    12,1

    2,10

    0–90

    2.2×

    2,1.

    5×1,

    2.0

    Wat

    er,

    etha

    nol

    10–7

    025

    –70

    The

    met

    alPH

    Pdi

    dno

    top

    erat

    ein

    hori

    zont

    alor

    ient

    atio

    nbu

    tope

    rate

    dve

    rtic

    ally

    asth

    erm

    osyp

    hon.

    Perf

    orm

    ance

    depe

    nds

    onor

    ient

    atio

    n,ch

    arge

    ratio

    ,and

    cros

    s-se

    ctio

    nge

    omet

    ry.

    Kha

    ndek

    aret

    al.[

    56]

    (200

    2)

    Art

    ifici

    alN

    eura

    lN

    etw

    ork

    (AN

    N)

    isus

    edto

    pred

    ictP

    HP

    perf

    orm

    ance

    .

    Hea

    tinp

    utan

    dch

    arge

    ratio

    from

    52da

    tase

    tsar

    ein

    putte

    dto

    AN

    N.

    Cop

    per

    Clo

    sed

    Cir

    cula

    r10

    902

    Eth

    anol

    0–10

    0—

    AN

    NI

    istr

    aine

    dby

    expe

    rim

    ents

    .Eff

    ects

    ofdi

    amet

    er,n

    umbe

    rof

    turn

    s,le

    ngth

    ,in

    clin

    atio

    nan

    gle,

    and

    fluid

    prop

    ertie

    sar

    eno

    tin

    the

    mod

    el.

    Kha

    ndek

    aret

    al.[

    24]

    (200

    2)

    N/A

    —G

    lass

    /co

    pper

    Clo

    sed

    Cir

    cula

    r10

    0,45

    ,90

    2W

    ater

    ,et

    hano

    l0–

    100

    5–15

    Eff

    ecto

    fgr

    avity

    isne

    glig

    ible

    .Bub

    ble

    form

    atio

    nan

    dco

    llaps

    ear

    edi

    scus

    sed.

  • Ma

    etal

    .[32

    ](2

    002)

    Liq

    uid

    slug

    osci

    llatio

    nis

    desc

    ribe

    dby

    the

    bala

    nce

    ofth

    erm

    ally

    driv

    en,

    capi

    llary

    ,fr

    ictio

    nal,

    and

    elas

    ticre

    stor

    ing

    forc

    es.

    Hea

    ttra

    nsfe

    rin

    evap

    orat

    oris

    mod

    eled

    asco

    nvec

    tive

    boili

    ngin

    atu

    be.

    Cop

    per

    Ope

    nC

    ircu

    lar

    40

    1.67

    Ace

    tone

    —5–

    20M

    inim

    umon

    set

    tem

    pera

    ture

    diff

    eren

    ceis

    15◦ C

    .Ran

    geof

    oper

    atio

    nalt

    empe

    ratu

    redi

    ffer

    ence

    isst

    udie

    d.M

    odel

    unde

    rpre

    dict

    ste

    mpe

    ratu

    redr

    ops.

    Zha

    ngan

    dFa

    ghri

    [10]

    (200

    2)

    Eva

    pora

    tion

    and

    cond

    ensa

    tion

    onth

    infil

    mle

    ftbe

    hind

    byliq

    uid

    slug

    isso

    lved

    .

    Vap

    oris

    satu

    rate

    dan

    dis

    othe

    rmal

    .N

    egle

    ctin

    gin

    ertia

    ,she

    arst

    ress

    ,and

    inte

    rfac

    ial

    ther

    mal

    resi

    stan

    ceef

    fect

    s.

    N/A

    Ope

    nC

    ircu

    lar

    10

    ——

    ——

    Ove

    rall

    heat

    tran

    sfer

    isdo

    min

    ated

    byse

    nsib

    lehe

    attr

    ansf

    er.

    Freq

    uenc

    yan

    dam

    plitu

    dear

    eno

    taf

    fect

    edby

    surf

    ace

    tens

    ion.

    Zha

    nget

    al.

    [52]

    (200

    2)L

    iqui

    d–va

    por

    puls

    atin

    gflo

    win

    aU

    -sha

    ped

    min

    iatu

    retu

    beis

    inve

    stig

    ated

    .

    Vap

    oris

    anid

    eal

    gas.

    N/A

    Ope

    nC

    ircu

    lar

    2−9

    0—

    ——

    —T

    heam

    plitu

    dean

    dfr

    eque

    ncy

    ofos

    cilla

    tion

    wer

    eco

    rrel

    ated

    toth

    ehe

    attr

    ansf

    erco

    effic

    ient

    san

    dte

    mpe

    ratu

    redi

    ffer

    ence

    .Z

    hang

    and

    Fagh

    ri[5

    3](2

    003)

    Liq

    uid–

    vapo

    rpu

    lsat

    ing

    flow

    inPH

    Pw

    ithar

    bitr

    ary

    num

    ber

    oftu

    rns

    isin

    vest

    igat

    ed.

    Vap

    oris

    anid

    eal

    gas.

    N/A

    Ope

    nC

    ircu

    lar

    Any

    −90

    ——

    ——

    Am

    plitu

    dean

    dci

    rcul

    arfr

    eque

    ncy

    decr

    ease

    byde

    crea

    sing

    the

    leng

    ths

    ofth

    ehe

    atin

    gan

    dco

    olin

    gse

    ctio

    ns.

    Incr

    easi

    ngth

    ech

    arge

    ratio

    resu

    lted

    ina

    decr

    ease

    ofam

    plitu

    des

    and

    anin

    crea

    seof

    circ

    ular

    freq

    uenc

    y.C

    haro

    ensa

    wan

    etal

    .[34

    ](2

    003)

    Non

    eN

    /AC

    oppe

    rC

    lose

    dC

    ircu

    lar

    10–4

    60,

    901.

    0,2.

    0W

    ater

    ,et

    hano

    l,R

    -123

    5020

    0–11

    00G

    ravi

    tyha

    sa

    sign

    ifica

    ntef

    fect

    onPH

    Ppe

    rfor

    man

    ce.

    Min

    imum

    num

    ber

    oftu

    rns

    isne

    eded

    for

    aho

    rizo

    ntal

    PHP

    toop

    erat

    e.Pe

    rfor

    man

    ceim

    prov

    esby

    incr

    easi

    ngth

    edi

    amet

    eran

    dth

    enu

    mbe

    rof

    turn

    s.

    (Con

    tinu

    edon

    next

    page

    )

  • Tabl

    e1

    (Con

    tinu

    ed)

    Ope

    n/In

    vest

    igat

    orT

    heor

    etic

    alcl

    osed

    Flow

    path

    Para

    llel

    Incl

    inat

    ion

    DW

    orki

    ngC

    harg

    eC

    oncl

    usio

    nsan

    d(y

    ear)

    appr

    oach

    esA

    ssum

    ptio

    nsM

    ater

    ials

    loop

    geom

    etry

    chan

    nels

    angl

    e(◦

    )(m

    m)

    fluid

    ratio

    q(W

    )co

    mm

    ents

    Kha

    ndek

    aret

    al.[

    23]

    (200

    3)

    Non

    eN

    /APy

    rex,

    glas

    sC

    lose

    dC

    ircu

    lar

    20–5

    80,

    902

    R-1

    2350

    5,00

    0–70

    ,000

    W/m

    2

    Flow

    osci

    llate

    sw

    ithlo

    wam

    plitu

    de/h

    igh

    freq

    uenc

    yat

    hori

    zont

    alm

    ode.

    Cap

    illar

    ysl

    ugan

    dse

    mi-

    annu

    lar/

    annu

    lar

    flow

    depe

    ndon

    heat

    inpu

    tand

    incl

    inat

    ion

    angl

    e.E

    xper

    imen

    talr

    esul

    tsar

    eco

    rrel

    ated

    usin

    gem

    piri

    calm

    odel

    .K

    hand

    ekar

    etal

    .[33

    ](2

    003)

    Non

    eN

    /AC

    oppe

    rC

    lose

    dC

    ircu

    lar

    100,

    902

    Wat

    er,

    etha

    nol,

    R-1

    23

    0–10

    05–

    65,

    5–60

    ,5–

    25

    Opt

    imum

    char

    gera

    tios

    for

    thre

    eflu

    ids

    are

    30,

    20,a

    nd35

    %,

    resp

    ectiv

    ely.

    Ori

    enta

    tion

    affe

    cts

    perf

    orm

    ance

    .H

    oriz

    onta

    lmod

    edi

    dno

    twor

    k.K

    hand

    ekar

    and

    Gro

    ll[2

    1](2

    004)

    Non

    eN

    /AG

    lass

    /cop

    per

    Clo

    sed

    Cir

    cula

    r2

    0,90

    2E

    than

    ol0–

    100

    14.8

    –74.

    4PH

    Pdi

    dno

    tope

    rate

    inho

    rizo

    ntal

    mod

    e.C

    apill

    ary

    slug

    flow

    and

    annu

    lar

    flow

    depe

    nds

    onhe

    atin

    put.

    Ritt

    idec

    het

    al.

    [3]

    (200

    3)N

    one

    N/A

    Cop

    per

    Ope

    nC

    ircu

    lar

    38–8

    40

    0.55

    ,1.

    05,

    2.03

    Eth

    anol

    ,W

    ater

    ,R

    123

    502,

    000–

    12,0

    00W

    /m2

    For

    R-1

    23,h

    eatfl

    uxin

    crea

    ses

    with

    incr

    easi

    ngdi

    amet

    er,

    butt

    hetr

    end

    isth

    eop

    posi

    tefo

    ret

    hano

    l.C

    orre

    latio

    nfo

    rhe

    attr

    ansf

    erw

    aspr

    opos

    edba

    sed

    onex

    peri

    men

    ts.

    Ritt

    idec

    het

    al.

    [35]

    (200

    5)N

    one

    N/A

    Cop

    per

    Ope

    nC

    ircu

    lar

    16pe

    rPH

    P,32

    PHPs

    —2

    Wat

    er,

    R-1

    2350

    1460

    –350

    4(T

    otal

    )PH

    Psw

    ere

    used

    asan

    air

    preh

    eate

    rfo

    ren

    ergy

    thri

    ftin

    adr

    yer.

    Perf

    orm

    ance

    impr

    oves

    with

    incr

    easi

    ngev

    apor

    ator

    tem

    pera

    ture

    .PH

    Pw

    ithR

    -123

    perf

    orm

    sbe

    tter

    than

    PHP

    with

    wat

    er.

  • Lia

    ngan

    dM

    a[5

    4](2

    004)

    Vap

    orbu

    bble

    isco

    nsid

    ered

    asga

    ssp

    ring

    .

    Vap

    orbu

    bble

    sar

    eun

    ifor

    mly

    dist

    ribu

    ted.

    N/A

    —C

    ircu

    lar

    —0

    1,2,

    5W

    ater

    ——

    Isen

    trop

    icbu

    lkm

    odul

    usge

    nera

    tes

    stro

    nger

    osci

    llatio

    nsth

    anth

    eis

    othe

    rmal

    bulk

    mod

    ulus

    .G

    uet

    al.[

    44]

    (200

    4)N

    one

    N/A

    Alu

    min

    umC

    lose

    dR

    ecta

    ngul

    ar96

    —1

    ×1

    R11

    450

    –60

    1.4–

    5.9

    PHP

    perf

    orm

    edbe

    tter

    inm

    icro

    grav

    ityth

    anno

    rmal

    orhy

    per

    grav

    ity.N

    eweq

    uatio

    nof

    criti

    cald

    iam

    eter

    inm

    icro

    grav

    ityis

    deve

    lope

    d.R

    iehl

    [36]

    (200

    4)N

    one

    N/A

    Cop

    per

    Ope

    nC

    ircu

    lar

    130,

    901.

    5A

    ceto

    ne,

    etha

    nol,

    iso-

    prop

    yl,

    alco

    hol,

    met

    hano

    l,w

    ater

    5010

    –50

    Perf

    orm

    ance

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  • Y. ZHANG and A. FAGHRI 31

    Figure 2 Thermodynamics of a PHP [12].

    of the working fluid in the vapor phase. The vapor plug is sur-rounded by a thin liquid film trailing from the slug.

    Figure 3 shows the control volume for one liquid slug in aPHP and the forces acting on it [13]. Motion of the ith liquid slugwithin the PHP with an inner diameter of D and cross-sectionalarea of A can be described by the simplified momentum equationgiven by [13,14]:

    dm�iv�idt

    = [pvi − pv(i+1)]A − π DL�iτ (1)where m�i , v�i , and L�i are the mass, velocity and length ofthe ith liquid slug, respectively. The difference between vaporpressures of the i th and the (i + 1)th vapor plug, pvi − pv(i+1),are the driving force for the oscillatory flow. The shear stress, τ,depends on whether the liquid flow is laminar or turbulent.

    Heat Transfer Principles

    In order to properly evaluate total heat transfer in a pulsatingheat pipe, the radial heat transfer between the pipe wall and theworking fluid, the evaporative heat transfer, and the condensationheat transfer must all be considered. As the liquid slugs oscillate,they enter the evaporator section of the PHP. Sensible heat istransferred to the slug as its temperature increases, and whenthe slug moves back to the condenser end of the PHP, it gives upits heat. Latent heat transfer generates the pressure differentialthat drives the oscillating flow. The phase change heat transfer

    Figure 3 Liquid slug in a PHP [13].

    takes place in the thin liquid film between the tube wall and avapor plug and in the meniscus region between the plug andslug, which requires complex analysis.

    Physical Parameters Affecting PHP Design

    The parameters that affect PHP performance are numerousand include the following.

    Geometric Parameters of the Flow Channel

    The inner diameter must be small enough that surface tensionforces dominate gravitational forces and distinct liquid slug andvapor plugs can form. The theoretical maximum inner diameterfor a capillary tube occurs when the square of the Bond num-ber equals 4. The ratio between gravitational force and surfacetension force is known as the Bond number, which is defined as:

    Bo = g(ρ� − ρv)D2

    σ, (2)

    which can be rearranged to show that the maximum inner diam-eter of a PHP is:

    Dcrit = 2√

    σ

    g(ρ� − ρv)(3)

    Cross-sectional geometry can affect flow patterns. Sharp edgescan create capillary channels that disrupt the normal slug flowand cause stratified or annular flow. Stratified flow causes thePHP to act as a series of interconnected gravity-driven ther-mosyphons, and the fluid flow will not pulsate. This greatlydecreases the heat transfer capability of the PHP [15,16]. Cir-cular cross- sections do not pose any such challenges to flow inthe PHP.

    Working Fluid Properties

    • Surface tension. Higher surface tensions will increase themaximum allowable diameter and also the pressure drop inthe tube. Larger diameter will allow improved performance,but an increased pressure drop will require greater bubblepumping and thus a higher heat input to maintain pulsatingflow.

    • Latent heat. A low latent heat will cause the liquid to evaporatemore quickly at a given temperature and a higher vapor pres-sure; the liquid slug oscillating velocities will be increased andthe heat transfer performance of the PHP will be improved.

    • Specific heat. A high specific heat will increase the amountof sensible heat transferred. Because the majority of the totalheat transfer in a PHP is due to sensible heat, a fluid with ahigh specific heat is desirable.

    • Viscosity. A low dynamic viscosity will reduce shear stressalong the wall and will consequently reduce pressure drop inthe tube. This will reduce the heat input required to maintaina pulsating flow.

    heat transfer engineering vol. 29 no. 1 2008

  • 32 Y. ZHANG and A. FAGHRI

    The rate of change in pressure with respect to temperatureat saturated conditions (dp/dT)sat. This property affects the rateat which bubbles grow and collapse with respect to changes intemperature. At a high value of (dp/dT)sat, the difference be-tween vapor pressures in the evaporator and condenser will beincreased and the performance of a PHP will be improved byenhanced oscillatory motion of liquid slugs.

    Charge Ratio

    The charge ratio is the volume of the working fluid divided bythe total internal volume of the PHP. If the charge ratio is too low,there is not enough liquid to perpetuate oscillating slug flow andthe evaporator may dry out. If the charge ratio is too high, therewill not be enough bubbles to pump the liquid, and the device willact as a single phase thermosyphon. Charge ratios ranging from20% to 80% will allow the device to operate as a true pulsatingheat pipe. An optimal charge ratio exists for each particular PHPsetup; for many typical experiments (circular cross-section in aplanar array with less than 20 parallel channels), the optimumcharge ratio is around 40%.

    Number of Turns

    The number of turns in the PHP may affect thermal perfor-mance and may negate the effect of gravity. By increasing thenumber of turns, there are more distinct locations for heat to beapplied. The fluid within each turn may be either liquid or vapor,the heating of which creates differences in pressure at each turn.It is these pressure differences that drive the pulsating flow. If aPHP only has a few turns, it may not operate in the horizontal ortop heat modes, but a PHP with many turns can operate at anyorientation because of the perturbations in each turn.

    PHP Configuration

    A PHP may have open loop, closed loop, or open-ended con-figurations. An open loop PHP has both ends sealed off. Theends of a closed loop PHP are connected to one another, suchthat the working fluid can circulate. An open-ended PHP hasone or both ends unsealed (see Figure 1). In general, closed loopPHP offer the best performance because circulation of the work-ing fluid increases the fluid velocity and likewise the sensibleheat transferred.

    Inclination Angle

    PHP performance may or may not change with inclinationangle. The dependence on orientation may be coupled to thenumber of turns. Experimental results have shown that perfor-mance is generally better in a vertical orientation, and somePHPs with only a few turns do not operate at horizontal orienta-tions. Other experiments, usually using PHPs with many turns(greater than 40 turns), have shown that performance is inde-

    pendent of inclination angle. Also, analysis by Shafii et al. [13],has shown the effect of gravity to be negligible. For this review,the following convention will be followed regarding inclinationangle: vertical bottom heat mode = 90◦, horizontal heat mode= 0◦, vertical top heat mode = −90◦.

    Size and Capacity of Evaporator and Condenser

    These parameters can affect the overall heat transfer of thePHP and could change the flow patterns within the heat pipe.Below a particular onset heat flux from the evaporator, the fluid inthe PHP will not pulsate. Also, if the condenser can not dissipateenough heat, it will limit the maximum heat transfer from thePHP.

    FLOW PATTERNS

    The pressure difference created by evaporation/boiling in theheating section and condensation in the cooling section pushthe liquid slugs to move from the heating section to the coolingsection. The motion of the liquid slugs will lower the vaporpressure in the heating section and increase the pressure in thecooling section. This reversed pressure difference will push theliquid slug back to the heating section, and oscillatory flow isinitiated and sustained. When the liquid slug moves away fromthe heating section, there will be a liquid film left behind, andit is widely believed that evaporation and condensation on thefilm are the mechanisms that result in the pressure change inthe vapor phase [9, 10, 11, 14, 17, 18]. The pressure differencebetween the heating and cooling sections is the driving forceof oscillatory motion. In addition, vapor bubbles collapsing dueto condensation [13] or generation and growth of vapor bubble[17, 19] may also occur. Because the total volume of a PHP isfixed, the collapse of a vapor bubble must be simultaneouslycompensated by the generation of vapor bubbles or growth of avapor plug/bubble elsewhere [12].

    For the case that the PHP has closed-loop and the heat flux atthe heating section is high, the liquid slugs move from heatingsection to the cooling section at a relatively high velocity. Theinertia of the liquid slugs may be large enough so that the liquidslug can pass the cooling section and enter the next heatingsection; consequently, the flow pattern in the PHP may changefrom oscillatory flow to circulating flow.

    Gi et al. [4] performed the flow visualization experiment on aPHP made from a Teflon tube strung between hot and cold waterjackets. The PHP has 20 parallel channels, is filled with R142b,and was videotaped with an 8 mm camera to record the flow.The description of the flow patterns does not adequately explainwhat was observed, and little information can be derived fromthe flow visualization portion of the experiment. Hosoda et al.[19] performed flow visualization of a glass PHP using wateras the working fluid. The observed flow indicated that the vaporbubbles propagate in the evaporator and migrate in an oscillatory

    heat transfer engineering vol. 29 no. 1 2008

  • Y. ZHANG and A. FAGHRI 33

    fashion to the condenser, where the vapor plugs are either re-duced in size or are condensed completely to extinction. Flowvisualization of a PHP made of brass and acrylic was performedby Lee et al. [15]. The PHP had rectangular flow channels asopposed to the usual circular cross-section. The flow observedwas very different from results of other flow visualization exper-iments: the fluid did not circulate in the traditional vapor plug/ liquid slug arrangement, but rather bubbles flowed along theflow channel and liquid returned to the condenser as stratified,rivulet flow. Perhaps the rectangular cross-section did not allowfor proper capillary flow. The most active oscillation was ob-served at 90◦ inclination angle, and with charge ratios rangingfrom 40–60%.

    Tong et al. [20] visualized the flow patterns of a closed loopglass PHP filled 60% with methanol. The PHP was tested atinclination angles of 0 and 90◦. In the vertical orientation (90◦),the flow stalled due to stratified flow returning liquid to the evap-orator and trapping it there. The vapor plugs oscillated duringstartup, but circulation in the PHP was achieved with the va-por plugs traveling from one parallel channel to the next. Thecirculation velocity increased as the heat input increased, andthe fluids circulated both clockwise and counterclockwise. Thedirection of circulation was due to uneven vapor distribution atstartup. Cai et al. [17] built a PHP made of quartz and filled withethanol, and used high-speed video to record the flow pattern.The video showed the propagation of bubbles in the liquid, someof which moved to the cooled section of the PHP and condensedto extinction. Other bubbles grew large enough to become fullydeveloped vapor plugs with a thin liquid film along the wall.Local dryout was observed in the evaporator, but liquid soonreturned to the evaporator from the condenser.

    Most studies reveal that circulation occurs in a closed-loopPHP and contributes to better performance of the PHP [4, 12,20–23]. In order for the liquid slugs to be pushed by the vaporplugs to generate the oscillation or circulation in the PHP, theideal flow pattern is capillary slug flow, in which liquid slugsand vapor plugs alternatively exist in the PHP. Khandekar et al.[24] reported experiments using a closed-loop glass PHP withwater and ethanol as the working fluid. The effects of gravitywere noticeable, as this PHP had only 10 parallel channels. Theyalso observed that when liquid slugs pass the U-bends in theheating section, a small amount of liquid would always be leftbehind, and the boiling of this liquid significantly contributesto the overall heat transfer of the PHP. As heat flux increases,Groll and Khandekar [12] reported that the oscillating slug flowmay change to directional slug flow, and ultimately to direc-tional annular flow (see Figure 4). The direction that the flowtakes is arbitrary for a given experiment, but once it is estab-lished, it remains fixed and does not turn around. Khandekarand Groll [21] studied a two-phase glass loop with only twoparallel channels filled with ethanol. As heat is increased, theflow proceeded from slug flow with small amplitude oscillationto larger amplitude oscillation, to slug flow with occasionallyreversing circulation, until one leg transitions to annular flow athigh power inputs. The two-phase loop did not operate at hor-

    Figure 4 Flow patterns evolution in a PHP [12].

    izontal orientation. The photographs of the representative flowpatterns in a PHP obtained by Khandekar et al. [23] are shownin Figure 5. The slug-annular transition depends not only on theheat input, but also the geometrical constructional features andinclination angles of the PHP.

    Xu et al. [25] visualized flow in a closed-loop glass PHPcharged with methanol or water by videotaping at 125 framesper second. The fluid circulated during testing but also exhib-ited a phenomenon called “local flow direction switch,” whichinvolves the flow in some of the channels to go the opposite di-rection of bulk fluid circulation. For methanol, it was observedthat the bubble displacement followed a quasi-sine wave. Whenwater was used, the bubble displacement exhibited a quasi-rectangular oscillating motion. This difference was attributedto the difference in latent heats of vaporization.

    The flow patterns in PHPs can be summarized below:

    • The oscillatory slug flow driven by the pressure differencebetween the heating and cooling sections is the dominant flowpattern in PHPs.

    • For closed-loop PHP, the oscillatory slug flow may be com-bined with circulation of working fluid.

    • As heat flux in a closed-loop PHP increases, the circulationof working fluid may suppress oscillatory flow, and the flowpattern can change to circulating slug flow. At even higherheat flux, the directional slug flow will change to directionalannular flow.

    HEAT TRANSFER PERFORMANCES

    Although evaporation/boiling in the heating section and con-densation in the cooling section play roles on the overall heattransfer in a PHP, heat transfer from the heating section to thecooling section by the liquid slugs via sensible heat is domi-nant when the flow pattern in the PHP is slug flow [13, 14, 26].

    heat transfer engineering vol. 29 no. 1 2008

  • 34 Y. ZHANG and A. FAGHRI

    Figure 5 Flow patterns in a PHP [23].

    Therefore, the heat transfer performance of a PHP with slugflow will never be as good as an equivalent heat pipe or ther-mosyphon, which is based on pure phase change heat transfer.Groll and Khandekar [12] pointed out that the term pulsating“heat pipe” seemed apparently a misnomer because most of heatis transferred by the latent heat in the heat pipe. With increasingheat flux, evaporation of the thin liquid film, formed (left) bythe liquid slug sweeping in the U-bends in the heating section,may play an important role, and the contribution of latent heatto the total heat transfer may be increased. At a higher heat flux,the flow pattern becomes directional annular flow. In this case,the heat is transferred mostly by evaporation and condensationof the liquid film, and the heat transfer capacity becomes com-parable to a conventional heat pipe. Under this circumstance,Groll and Khandekar [12] questioned the name “pulsating” heatpipe because it really does not represent the dominant flow pat-tern. Therefore, the role of sensible heat and the flow pattern ina PHP largely depend on the heat flux: at a lower heat flux, thecontribution of sensible heat on the overall heat transfer is dom-inant and the flow pattern is pulsating flow; at higher heat fluxthe latent heat becomes dominant on the overall heat transferand the flow pattern becomes directional annular flow.

    Because the closed-loop PHP is thermally more favorable, themajority of the experimental works have focused on the closed-loop PHPs (see Table 1). Akachi et al. [2] tested a particulartype of PHP known as the Kenzan Fin, which had as manyas 500 turns packed closely together in a cylindrical array andwas charged with R142b. It was concluded that a minimumnumber of turns (as many as 80 turns in this setup) are necessaryto make the Kenzan Fin’s operation independent of inclinationangle. Maezawa et al. [27] performed experiments with an openlooped copper PHP with 40 turns and charged with R142b orwater. The PHP operated with very low thermal resistance forall inclination angles when it was charged 50% with R142b.When water was used as the working fluid, it did not performsuccessfully in top heat mode (inclination angle = −90◦) when

    the heat input rate was greater than 800 W. Chaotic analysisof temperature oscillation in the experimental PHP showed thatthe oscillation is non-periodic. Miyazaki and Akachi [28] testeda closed loop copper PHP filled with R142b, with 60 parallelchannels, at three different inclination angles and with varyingcharge ratios. Charge ratio was seen to have a significant effecton PHP operation. While the charge ratio for bottom heat modecan vary widely, the optimized charge ratio for top heat modeis 35%. They also found that the heat transfer limitations thatusually exist in traditional heat pipes were not encountered in thePHP. Gi et al. [4] concluded that the heat transfer performance fora closed-loop PHP is better than the closed-end PHP because thecirculation of the working fluid in the closed-loop PHP enhancesheat transfer. Nishio [29] reported experiments with glass PHPswith several different working fluids, inner diameters, and chargeratio. It was found that the heat transfer coefficient between thetube wall and the working fluid is independent of the temperaturedifference between the evaporator and the condenser, �T , forcharge ratios from 30–80%. For the four fluids tested (i.e., water,soapsuds, ethanol, and R141b), water performed the best at acharge ratio of 30%.

    While most PHPs consist of a smooth walled tube and donot contain an internal wick structure, as in a conventional heatpipe, it is noteworthy that Zuo et al. [6] has developed a prototypePHP with a sintered copper wick covering the inner wall of eachchannel. The wick provides more nucleation sites for boilingthe working fluid, and it also distributes liquid evenly, reducingthe local temperature fluctuation. Thermal imaging showed thePHP to be nearly isothermal during testing and was capable oftransferring heat at thermal resistances as low as 0.16◦C/W atan optimum charge ratio of 70%. Their results showed that thepulsating flow of the working fluid significantly enhanced theheat transport capability over the conventional heat pipes.

    Lin et al. [30] built an open loop planar PHP with an evap-orator in the middle of the parallel channels and a condenseron either end, which was different from the structures studied

    heat transfer engineering vol. 29 no. 1 2008

  • Y. ZHANG and A. FAGHRI 35

    by most researchers. Acetone was the working fluid, and PHPperformance was measured by thermal conductance. When thePHP was operating at the vertical position at low heat rates (lessthan 600 W), the condenser above the evaporator transferredmore heat than the condenser below the evaporator. This PHPsetup operated better at horizontal than vertical, and the optimumcharge ratio was 38%. Lin et al. [31] used the same experimentalsetup from their previous study to test two fluorocarbon fluids,FC-72 and FC-75. The prototype PHP was originally designedfor use with acetone, and thus the inner diameter (1.75 mm)was greater than the critical diameter given by the bond numberrelation for the working fluids. This led to evaporator dryout atcharge ratios less than 40%. At a charge ratio of 50%, the PHPwas capable of dissipating 2040 W of heat. Unlike the previousexperiment with acetone, PHP performance with the fluorocar-bon fluids was independent of orientation.

    Cai et al. [17] built a second PHP made out of copper andhad an evaporator in the middle with a condenser on either end.Water, acetone, ethanol, and ammonia were used as workingfluids, with charge ratios ranging from 40–80%. Working fluidswith lower latent heats had larger gradients for the temperaturedifference between the evaporator and condenser as a functionof heat input, but the amplitude of temperature fluctuations issmaller, and the frequency of the fluctuations are higher. There-fore, fluids with low latent heats are recommended for PHP topromote oscillatory motion. Ma et al. [32] constructed an open-looped copper PHP that used acetone as the working fluid. Theexperiment recorded the temperature along the PHP as the heatinput was increased from 5 to 20 W. Oscillation of the workingfluid only occurred in a certain range of power input. A minimumonset temperature difference is required to initiate oscillation,and a range of �T exists where steady state motion is possible.

    Khandekar et al. [16] fabricated a closed-loop PHP with rect-angular flow channels machined into an aluminum plate and aglass tube PHP. The metal PHP did not operate at an inclina-tion angle of 0◦, but operated as a thermosyphon rather than aPHP at 90◦ orientation. Thermographs of the glass PHP showedthat a temperature difference exists from one parallel channelto the next (inter-tube). It is hypothesized that some minimuminter-tube temperature difference is required for PHP operation.

    Khandekar et al. [33] experimentally studied the performanceof a closed-loop copper PHP with a 2 mm diameter and 10 paral-lel channels. To maximize heat transfer, each working fluid hada slightly different optimum charge ratio (water = 30%, ethanol= 20%, and R-123 = 35%) due to differences in surface tension,latent and specific heats, and the value of (dp/dT)sat. The smallnumber of turns in the PHP setup did not allow for operationat horizontal orientation. Charoensawan et al. [34] performedparametric experimental investigations on closed-loop PHPswith varying numbers of parallel channels, evaporator andcondenser lengths, and inner diameters. Three working fluids(water, ethanol, and R-123) were tested at a charge ratio of 50%,at both 0◦ and 90◦ orientations. Results show that gravity has asignificant effect on PHP performance unless the PHP has a cer-tain critical number of turns. There is a critical number of turns

    below which the PHP does not operate at horizontal orientation.If the critical diameter is exceeded, the PHP will cease to func-tion properly. Making the correct choice of working fluid canenhance PHP performance, but fluid choice is affected by severalparameters, especially inner diameter due to differences in thesurface tension and the latent heat of each fluid. Khandekar et al.[23] performed visualizations and proposed a semi-empiricalmodel based on 248 experimental data from [34]. The maximumachievable heat flux for a given closed-loop PHP with a chargeratio of 50% can be obtained from the following correlation:

    q ′′ = q2π DN Le

    = 0.54[exp(β)]0.48Ka0.47Pr0.27� Ja−1.43 N−0.27(4)

    where q is heat transfer rate (W), D is inner diameter of the PHP(m), N is number of turns, Le is the length of the evaporatorsection (m), β is the inclination angle measured from horizontalaxis, and Pr� is the liquid Prandtl number. The Karman and Jakobnumbers are defined as

    Ka = ρ�(psat,e − psat,c)D2

    μ2� Lef f(5)

    Ja = cp,�(Tsat,e − Tsat,c)h�v

    (6)

    where psat,e and psat,c are the saturation temperatures in theevaporator and condenser, respectively. The effective lengthcan be found by Leff = (Le + Lc)/2 + La . Equation (4) canbe used to predict maximum heat transfer in a PHP with anaccuracy of ±30%.

    Rittidech et al. [3] studied heat transfer characteristics ofclosed-end cooper PHPs with different inner diameters (0.66,1.06, and 2.03 mm). The lengths of evaporator, adiabatic, andcondenser sections were equal and changed to 15, 10, and 5cm. The number of turns varied from 19 to 42. The PHPs werecharged with water, ethanol, or R123 at a charging ratio of 50%.They proposed the following correlation for Kutateladze num-bers to predict the heat flux for a closed-end PHP at horizontalorientation.

    Ku0 = q′′

    ρvh�v[σg(ρ� − ρv)/ρ2v

    ]1/4

    = 0.0052[(

    D4.3L0.1tL4.4e

    )N 0.5

    (ρv

    ρ�

    )−0.2Pr−25v

    ]0.116(7)

    where Lt is the total length of the PHP tube and D4.3L0.1t /L4.4e is

    a dimensionless variable that indicates the size of the PHP. Thestandard deviation for Eq. (7) was ±30%. Rittidech et al. [35]proposed to use a closed-end PHP as an air preheater for energythrift in a dryer. The experiment applies the waste heat from thedryer exhaust to the evaporator section of 32 copper PHPs (eachPHP has 8 turns), and the PHPs reject the heat from the condensersection to the incoming air. The PHPs are made of copper tubewith an inner diameter of 2 mm and charged with water andR123 at a charging ratio of 50%. The following correlation for

    heat transfer engineering vol. 29 no. 1 2008

  • 36 Y. ZHANG and A. FAGHRI

    a vertical closed-end PHP was proposed following Rittidechet al.’s [3] approach:

    Ku90 = 0.0067[(

    D3.1L0.1tL3.2e

    )N 0.9

    (ρv

    ρ�

    )−0.1 (ωμ3vσ2ρv

    )]0.175

    (8)

    where ω is the frequency of oscillation motion of vapor plugthat is defined as the frequency of simple harmonica motion,ω = √ρ�g/ρv Lv . Equation (8) has a standard deviation of±30%. It was concluded that the PHP could be applied to re-duce energy consumption in the drying process. Riehl [36] testedan open loop PHP with 13 parallel channels made from coppertubing with an inner diameter of 1.5 mm, in vertical and horizon-tal orientation, and at a charge ratio of 50% for acetone, ethanol,isopropyl alcohol, methanol, and water. The results showed thatan onset heat input exists to drive oscillation, and each work-ing fluid gave a different onset heat input. The best performingfluid at the vertical orientation was acetone, and at the horizontalorientation, methanol was best. Zhang et al. [5] experimentallystudied both open and closed copper PHPs using FC-72, ethanol,and water as working fluids. The open-loop PHP did not per-form successfully due to having too few turns. For a closed-loopPHP, this study verified that a minimum heat input is necessaryto initiate pulsating flow, and that the thermo-physical proper-ties of the working fluid affect that onset heating power. Kat-pradit et al. [37] proposed a correlation to predict the criticalheat flux (at which dryout occurs) of a closed-end PHP basedon experiments for variety of working fluids, inner diameters,evaporator/condenser lengths, and number of parallel channels.The correlations to predict critical heat flux, q ′′cr , for horizontaland vertical heat modes are, respectively:

    Ku0 = 53680(

    D

    Le

    )1.127Ja1.417Bo−0.66 (9)

    and

    Ku90 = 0.0002(

    D

    Le

    )0.92Ja−0.212Bo0.295

    [1 +

    (ρv

    ρ�

    )0.25]13.06

    (10)

    where Ku0 and Ku90 are Kutateladze numbers for horizontaland vertical orientations defined using critical heat fluxes, q ′′cr .The Jakob number, Ja, and the Bond number, Bo, are same asthose defined in Eqs. (6) and (2). Equations (9) and (10) providedempirical correlations that can be used to predict the heat transferlimit of the PHP at different orientations.

    Charoensawan and Terdtoon [38] developed the followingempirical correlation to predict the thermal performance of ahorizontal closed-loop PHP:

    Ku = 2.13 × 10−9Pr0.75� (Ja∗)−0.38Bo−0.84Ka0.58(kc/ka) (11)where the Kutateladze number, Ku, Bond number, Bo, and Kar-man number, Ka, are the same as those defined in Eqs. (7), (2),

    and (5), respectively. The modified Jakob number is defined as

    Ja∗ = ϕcp,��T(1 − ϕ)h�v (12)

    where φ is the filling ratio. kc/ka in Eq. (11) is the ratio ofthermal conductivities of the coolant at the required temperatureand the ambient air at 25◦C. Equation (11) was obtained bycorrelating 98 sets of experimental data for water and ethanol,and the standard deviation (STD) was ±30%.

    Qu et al. [39] studied mini PHP with square and regular tri-angle cross-sections. The sides of the squares and triangles varybetween 1 and 1.5 mm. The PHPs had eight turns and weremade of copper. The filling ratio varied from 20 to 40%. Withthe same length of the side, the thermal resistance of the PHPwith the regular triangle channel is smaller than those with thesquare channel. For the same capillary structure, the thermal re-sistance of the PHP with the 1.5-mm channel is smaller than thatwith the 1-mm channel.

    Cai et al. [40] presented an experimental investigation of heattransfer characteristics of PHPs versus operating temperature.The PHP with 12 turns is made of stainless steel or copper andcharged with water at three filling ratios: 40%, 55%, and 70%.They found that minimal temperature difference and fluctuationappear at operating temperatures between 120 and 160◦C. Xuand Zhang [41] studied startup and steady thermal oscillation ofa closed-loop copper with four turns and charged with FC-72.Two types of startup processes were observed: the sensible heatreceiving startup process with fluid stationary inside, accompa-nying an apparent temperature overshoot at lower heat power,and the sensible heat receiving process without fluid motion in-side, incorporating a smooth oscillation transition period withoscillation flow at high heating power. In addition, oscillationflow at low heating power displays random behavior and be-come quasi-periodic at high heat power. Khandekar and Gupta[42] investigated embedded PHP in an alumina plate subjectto natural convection and radiation. Semicircular grooves weremilled on the radiator base plate and the closed-loop PHP witha 2 mm inner diameter and 11 turns is embedded in the grooves.They concluded that embedded PHP can be beneficial only ifthe conductivity of the plate is low.

    Because the successful operation of PHPs depends on surfacetension, not gravity, the performance of an ideal PHP should beindependent from the operation mode. Kiseev and Zolkin [43]experimentally investigated the effects of acceleration and vi-bration on the heat transfer performance of the closed-end PHPwith acetone as the working fluid and a charge ratio of 60%.There was an increase in the evaporator temperature by about30% as the acceleration varied from −6 g to +12 g. Gu et al.[44] experimentally investigated the heat transfer performanceof a PHP made of a thin aluminum plate with small internalchannels charged with R-114 under normal to high gravity (1–2.5 g) and reduced gravity (∼±0.02 g). The experiments forreduced gravity were performed aboard a parabolic aircraft, Fal-con 20, which can provide low gravity conditions (∼±0.02 g)for 15–20 seconds. The results showed that the performance of

    heat transfer engineering vol. 29 no. 1 2008

  • Y. ZHANG and A. FAGHRI 37

    a PHP under reduced gravity is better than that at normal tohypergravity.

    Ma et al. [45, 46] charged nanofluids (HPLC grade watercontaining 1.0 vol.% 5–50 nm of diamond nanoparticles) into aclosed-loop copper PHP with 12 turns and found that nanoflu-ids significantly enhance the heat transport capability. Whenthe nanofluid is charged to the PHP, the temperature differencebetween the evaporator and the condenser can be significantlyreduced. For example, when the power input added on the evap-orator is 100 W, the temperature difference can be reduced from42◦C for the pure water PHP to 25◦C for the nanofluid PHP.The heat transport capability in a nanofluid PHP depends on theoperating temperature. They also found that when the operat-ing temperature increases, the thermal resistance is significantlydecreased.

    Chiang et al. [47] studied the performance of PHPs con-structed of multiport extruded aluminum tubing with square ortriangular cross-sections. The effects of types of working fluid(ethanol and acetone), fluid fill ratio, orientation, PHP dimen-sion, and inner structures on the performance of the PHP areinvestigated. They also charged nanofluid (formed by dispersing0.5% vol. of diamond into ethanol) into the PHPs with 26 ports,and slight but consistent improvements on the performance wereobtained.

    MODELING

    Because slug flow is the primary flow pattern in PHPs, mostexisting efforts on modeling have focused on slug flow. Miyazakiand Akachi [28] proposed a simple analytical model of self-exciting oscillation based on an oscillating feature observed inthe experiments. The reciprocal excitation of pressure oscillationdue to changes in the heat transfer rate caused by the oscillationof the void fraction was investigated. Oscillation of the voidfraction is out of phase behind the pressure oscillation by π /2.This model indicates that an optimal charge ratio exists for aparticular PHP. If the charge ratio is too high, the PHP willexperience a gradual pressure increase followed by a suddendrop. Scarce charging will cause chaotic pressure fluctuation;however, proper charging will generate a symmetrical pressurewave.

    Miyazaki and Akachi [48] derived the wave equation of pres-sure oscillation in the PHP based on the self-excited oscillation,in which the reciprocal excitation between pressure oscillationand void fraction was assumed:

    ∂2 p

    ∂t2= c2 ∂

    2 p

    ∂x2(13)

    where the wave velocity is

    c =√

    q ′′ RgT04π Lα0ρ�ν

    (h�v − RgT0

    ) (14)where the subscript 0 denotes the equilibrium point, and L isthe length of a turn. The progressive wave for a closed-loop

    channel and the standing wave for a closed-end channel can beobtained from Eq. (14). Miyazaki and Arikawa [49] investigatedthe oscillatory flow in the PHP and measured the wave velocity,which was fairly agreed with the prediction of [48].

    Hosoda et al. [19] reported a simplified numerical model of aPHP, in which temperature and pressures are calculated by solv-ing the momentum and energy equations for two-dimensional,two-phase flow. However, the thin liquid film that surrounds avapor plug on the tube wall and the friction between the tubeand the working fluid were neglected. Experimental results wereused as initial conditions for the model. The numerical resultsfor pressure in the PHP are higher than the experimental results,but the model does show that propagation of vapor plugs inducedfluid flow in the capillary tubes.

    Zuo et al. [6, 7] attempted to model the PHP by comparingit to an equivalent single spring-mass-damper system, and theparameters of the system are affected by heat transfer. The fluiddisplacement was described by

    d2x

    dt2+

    (8μ� Pϕ

    ρ� D A

    )dx

    dt+ 2A

    2 RgTsat(L Aρ�ϕ)[(L/2)Aρ�(1 − ϕ)/ρv]2

    ×[

    L Aρ�(1 − ϕ)2

    + qeh�v

    t

    ]x = 0 (15)

    where P is the flow channel perimeter, A is the cross-sectionalarea, D is diameter, ϕ is the charge ratio, L is the flow channellength, and qe is heat transfer rate (W). The second and thirdterms in Eq. (15) represent the viscous damping term and thespring stiffness term. It can be seen that the spring stiffnessincreases with increasing time, and therefore the amplitude ofoscillation must decrease with increasing time; this is in con-tradiction with steady oscillations observed in PHP operation.Wong et al. [50] modeled an open-loop PHP by considering it asa multiple spring-mass-damper system, but the flow was mod-eled under adiabatic conditions for the entire PHP. A suddenpressure pulse was applied to simulate local heat input into avapor plug.

    Shafii et al. [13] developed a theoretical model to simulatethe behavior of liquid slugs and vapor plugs in both closed- andopen-loop PHPs with two turns (see Figure 6). The model solvesfor the pressure, temperature, plug position, and heat transferrates. The most significant conclusion is that the majority ofthe heat transfer (95%) is due to sensible heat, not due to thelatent heat of vaporization. Latent heat serves only to drive theoscillating flow.

    Sakulchangsatjatai et al. [51] applied Shafii et al.’s model tomodel closed-end and closed-loop PHPs as oscillating two phaseheat and mass transfer in a straight pipe and neglects the thinliquid film between the vapor plug and the pipe wall.

    Zhang et al. [52] analytically investigated oscillatory flowin a U-shaped miniature channel—a building block of PHPs.A significant difference between this model and other math-ematical models is the nondimensionalizing of the governingequations. Flow in the tube is described by two dimensionless

    heat transfer engineering vol. 29 no. 1 2008

  • 38 Y. ZHANG and A. FAGHRI

    Figure 6 Pulsating heat pipes: (a) open-loop, (b) closed-loop [13].

    parameters, the non-dimensional temperature difference and theevaporative and condensation heat transfer coefficients. It wasfound that the initial displacement of the liquid slug and gravityhave no effect on the amplitude and angular frequency of oscil-lation. Also, the amplitude and frequency of oscillation are in-creased by increasing the dimensionless temperature difference.The amplitude and frequency of oscillation were correlated tothe heat transfer coefficients and temperature difference. Zhangand Faghri [53] investigated oscillatory flow in a closed-end pul-sating heat pipe with an arbitrary number of turns (see Figure7). The results showed that for a PHP with few turns (i.e., fewerthan six) the amplitude and frequency of oscillation are inde-pendent of the number of turns. The motion of the vapor plugsis identical for odd-numbered plugs once a steady state has beenreached. Even-numbered plugs also exhibit identical motion.Odd- and even-numbered plugs have the same amplitude, butthey are out of phase by π . As the number of turns is increasedabove six, the odd- and even-numbered plugs no longer showidentical oscillation. Each plug lags slightly behind the next;however, each plug is still separated by π from the next one (seeFigure 8).

    Dobson and Harms [9] investigated a PHP with two openends. The open ends are parallel and point in the same direction.

    Figure 7 Open-loop PHP with arbitrary turns (n


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