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
Tabl
e1
Sum
mar
yof
mod
elin
gan
dex
peri
men
tson
puls
atin
ghe
atpi
pes
(PH
P)
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
Aka
chie
tal.
[2]
(199
6)N
one
N/A
Cop
per
Ope
nC
ircu
lar
254,
1000
0.7,
1.2
R14
2b50
70–1
00,
450
The
rmal
resi
stan
ceis
inde
pend
ento
fhe
atin
puta
ndin
clin
atio
nan
gle
ifth
enu
mbe
rof
turn
sis
grea
ter
than
80.
Mae
zaw
aet
al.
[27]
(199
6)N
one
N/A
Cop
per
Ope
nC
ircu
lar
8090
,0,−
902
Wat
er,
R14
2b50
50–1
000
R14
2bpe
rfor
ms
bette
rth
anw
ater
.Bot
tom
heat
mod
epe
rfor
ms
bette
rth
anto
phe
atm
ode.
Osc
illat
ion
has
nosp
ecifi
cpe
riod
ical
feat
ure.
Miy
azak
iand
Aka
chi[
28]
(199
6)
Dif
fere
ntia
lre
latio
nshi
pbe
twee
npr
opag
atio
nw
ave
of�
pan
d�
α
Pres
sure
osci
llatio
nan
dos
cilla
tory
flow
reci
proc
ally
exci
teea
chot
her.
Cop
per
Clo
sed
Cir
cula
r60
90,0
,−90
1R
142b
25–7
020
–180
Opt
imiz
edch
arge
ratio
for
botto
man
dto
phe
atm
odes
are
70%
and
35%
,res
pect
ivel
y.A
sym
met
rica
lwav
eis
obta
ined
atpr
oper
char
gera
tio.
Miy
azak
iand
Aka
chi[
48]
(199
8)
Wav
eeq
uatio
nof
pres
sure
was
deri
ved.
Aco
ntin
uous
dist
ribu
tion
ofvo
idfr
actio
nw
asas
sum
ed.
N/A
Cir
cula
rT
hepr
ogre
ssiv
ew
ave
for
acl
osed
-loo
pch
anne
lan
dth
est
andi
ngw
ave
for
acl
osed
-end
chan
nelc
anbe
obta
ined
from
the
wav
eeq
uatio
n.M
iyaz
akia
ndA
rika
wa
[49]
(199
9)
Non
eN
/AC
oppe
r/po
lyca
rbon
ate
Rec
tang
ular
50−9
0R
-142
b42
Mea
sure
dw
ave
velo
citie
sfa
irly
agre
edw
ithE
q.(1
4).
Nis
hio
[29]
(199
9)N
one
N/A
Gla
ssC
lose
dC
ircu
lar
490
1.8,
2.4,
5.0
Wat
er,
soap
-su
ds,
etha
nol,
R14
1b
20–1
0070
PHP
perf
orm
edbe
stw
ithch
arge
ratio
of35
%.
PHP
ther
mal
cond
uctiv
ityis
500
times
high
erth
anco
pper
.Hea
ttra
nsfe
rra
tehi
gher
than
the
conv
entio
nalh
eatp
ipe
with
the
sam
edi
amet
er.
Gie
tal.
[4]
(199
9)N
one
N/A
Teflo
nO
pen/
clos
edC
ircu
lar
1030
–50
2R
142b
20–5
0,
30–7
0
60–1
00Fl
owvi
sual
izat
ions
(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
Hos
oda
etal
.[1
9](1
999)
Num
eric
also
lutio
nof
1-D
liqui
dan
dva
por
flow
.
Thi
nliq
uid
film
,pr
essu
relo
ssat
bend
s,an
dvi
scou
sdi
ssip
atio
nar
ene
glec
ted.
Gla
ssC
lose
dC
ircu
lar
2090
1.2
Wat
er30
–90
80–2
20PH
Ppe
rfor
med
best
atch
arge
ratio
of60
%.
Num
eric
alre
sults
for
pres
sure
are
high
erth
anex
peri
men
tal
resu
ltsbu
tosc
illat
ion
issi
mul
ated
.L
eeet
al.[
15]
(199
9)N
one
N/A
Bra
ss,a
cryl
icC
lose
dR
ecta
ngul
ar8
30–9
01.
5×
1.5
Eth
anol
20–8
0—
Osc
illat
ion
caus
edby
form
atio
nor
extin
ctio
nof
bubb
les.
No
fluid
circ
ulat
ion.
Mos
tact
ive
osci
llatio
nis
obse
rved
inbo
ttom
heat
ing
with
char
gera
tioof
40–6
0%.
Zuo
etal
.[6]
(199
9)O
scill
ator
yflo
wm
odel
edsi
mila
rto
mec
hani
cal
vibr
atio
nw
ithvi
scou
sda
mpi
ng.
Vap
oris
anid
eal
gas.
Lam
inar
liqui
dflo
w.
Hea
ttra
nsfe
ris
negl
ecte
d.
Sint
ered
and
plat
eco
pper
Clo
sed
Tri
angu
lar
—0,
90—
Wat
er40
–80
5–25
0T
hew
ick
stru
ctur
edi
stri
bute
sliq
uid
even
ly,a
ndre
duce
slo
calt
empe
ratu
reflu
ctua
tion.
The
rmal
resi
stan
ceis
aslo
was
0.16
◦ C/W
atan
optim
umch
arge
ratio
of70
%.
Zuo
etal
.[7]
(200
1)M
ass,
mom
entu
m,
and
ener
gyeq
uatio
nsof
1-D
tran
sien
ttw
o-ph
ase
flow
are
solv
edus
ing
SIM
PLE
Csc
hem
e.
Liq
uid
and
vapo
rph
ases
are
atlo
cal
equi
libri
um.
Con
vect
ion
dom
inat
ein
axia
ldir
ectio
n.
Cop
per
Clo
sed
Rec
tang
ular
——
—W
ater
40–8
010
–250
Exp
erim
ents
how
sth
atpe
rfor
man
ceof
PHP
isse
nsiti
veto
char
gera
tio.N
umer
ical
resu
ltsw
ere
notr
epor
ted
inth
epa
per.
Dob
son
and
Ham
s[9
](1
999)
Exp
licit
finite
diff
eren
cesc
hem
eis
used
toso
lve
equa
tions
for
mot
ion
and
heat
tran
sfer
.
Vap
oris
anid
eal
gas.
Inco
mpr
essi
ble
liqui
d.N
ohe
attr
ansf
erin
liqui
d.
Cop
per
Unl
oope
dw
ithop
enen
d
Cir
cula
r2
03.
34W
ater
——
Thr
ustp
rodu
ced
byPH
Pis
0.00
27N
.O
pen-
ende
dPH
Pm
ount
edon
aflo
atin
wat
er.
Dob
son
[18]
(200
4)M
ass,
mom
entu
m,
and
ener
gyeq
uatio
nsar
eso
lved
usin
gex
plic
itsc
hem
e.
Vap
oris
idea
lgas
.M
omen
tum
ofva
por
bubb
lean
dliq
uid
film
are
negl
ecte
d.
Cop
per
Ope
nC
ircu
lar
290
–90
3.34
Wat
erT
hedo
min
ate
forc
esfo
rliq
uid
plug
mot
ion
are
vapo
rpr
essu
redi
ffer
ence
,fri
ctio
nan
dgr
avity
.
Dob
son
[11]
(200
5)—
——
—0
3.34
Wat
er—
—U
seof
anop
enPH
Pto
pum
pw
ater
.Mas
sflo
wra
teof
the
pum
pis
0.2
mg/
sfo
r10
0m
mhe
ight
.K
isee
van
dZ
olki
n[4
3](1
999)
Non
eN
/ASt
ainl
ess
stee
lO
pen
Cir
cula
r46
01.
1A
ceto
ne60
15–3
00E
vapo
rato
rte
mpe
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
isbe
tter
whe
nop
erat
ing
ina
hori
zont
alor
ient
atio
n.B
ette
rpe
rfor
man
ces
wer
eob
tain
edw
hen
acet
one
was
used
inve
rtic
alor
ient
atio
nan
dm
etha
nolw
asus
edon
hori
zont
alor
ient
atio
n.Z
hang
etal
.[5
](2
004)
Non
eN
/AC
oppe
rO
pen
and
clos
edC
ircu
lar
690
1.18
FC-7
2,et
hano
l,w
ater
60–9
05–
60O
pen
loop
PHP
did
not
wor
k.A
min
imum
heat
inpu
tis
nece
ssar
yto
initi
ate
puls
atin
gflo
w.
Clo
sed
loop
PHP.
Opt
imum
char
gera
tiois
70%
for
allt
hree
fluid
s.Sa
kulc
han-
gsat
jata
iet
al.[
51]
(200
4)
Mas
s,m
omen
tum
,an
den
ergy
equa
tions
for
each
liqui
dsl
ugan
dva
por
plug
are
solv
ed.
Vap
oris
anid
eal
gas.
Inco
mpr
essi
ble
liqui
d.N
opr
essu
relo
ssin
bend
s.
—O
pen
and
clos
ed—
—−9
0—
——
—M
odel
issa
me
asSh
afii
etal
.(20
01).
The
pred
icte
dhe
attr
ansf
erra
teis
com
pare
dto
expe
rim
enta
lres
ults
inlit
erat
ure.
Kat
prad
itet
al.
[37]
(200
5)N
one
N/A
Cop
per
Ope
nC
ircu
lar
10,2
0,30
0,90
0.66
,1.
06,
2.03
R-1
23,
etha
nol,
wat
er
50—
Hea
tflux
incr
ease
sw
ithde
crea
sing
evap
orat
orle
ngth
,and
incr
easi
ngla
tent
heat
and
num
ber
oftu
rns.
Cor
rela
tion
topr
edic
thea
ttra
nsfe
rch
arac
teri
stic
sw
aspr
opos
ed.
(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
Xu
etal
.[25
](2
005)
Non
eN
/AG
lass
/cop
per
Clo
sed
Cir
cula
r8
902
Wat
er,
met
hano
l7010
,30
Flow
circ
ulat
ion
was
obse
rved
.Flo
ws
inso
me
chan
nels
are
inth
eop
posi
tedi
rect
ion
ofbu
lkci
rcul
atio
nX
uan
dZ
hang
[41]
(200
5)N
one
N/A
Cop
per
Clo
sed
Cir
cula
r8
902
FC-7
270
10–2
5.6
Bot
hst
artu
pan
dst
eady
ther
mal
osci
llatio
nsw
ere
stud
ied.
Osc
illat
ion
flow
atlo
whe
atin
gpo
wer
disp
lays
rand
ombe
havi
oran
dbe
com
esqu
asi-
peri
odic
athi
ghhe
atpo
wer
.H
olle
yan
dFa
ghri
[8]
(200
5)
Mas
s,m
omen
tum
and
ener
gyeq
uatio
nsar
eso
lved
for
PHP
with
sint
ered
copp
erw
ick
and
vary
ing
chan
nel
diam
eter
.
Liq
uid
isin
com
pres
sibl
e.N
egle
ctin
glo
sses
atbe
nds.
Satu
rate
dva
por
with
negl
igib
leflo
wfr
ictio
n.
−90,
−45,
90W
ater
20–6
0V
aryi
ngdi
amet
erbe
twee
npa
ralle
lcha
nnel
sin
duce
sflo
wci
rcul
atio
nan
dm
ayin
crea
sehe
attr
ansf
erca
paci
ty.B
otto
mhe
atm
ode
perf
orm
edbe
tter
than
top
heat
mod
e.Se
nsiti
vity
togr
avity
decr
ease
sw
hen
incr
easi
ngth
enu
mbe
rof
chan
nels
.C
aiet
al.[
40]
(200
6)N
one
N/A
Stai
nles
sst
eel,
copp
er—
Cir
cula
r24
01.
397,
1.56
8W
ater
40,5
5,70
100–
400
Min
imal
tem
pera
ture
diff
eren
cean
dflu
ctua
tion
appe
arat
oper
atin
gte
mpe
ratu
rebe
twee
n12
0◦C
and
160◦
C.
Ma
etal
.[45
](2
006)
Non
eN
/AC
oppe
rC
lose
dC
ircu
lar
2490
1.65
Nan
oflui
d(w
ater
with
diam
ond
nano
-pa
rtic
les)
505–
336
At1
00W
,the
tem
pera
ture
diff
eren
ceca
nbe
redu
ced
from
42◦ C
to25
◦ Cfo
rth
ena
noflu
idO
HP
asop
pose
dto
the
pure
wat
erO
HP.
Ma
etal
.[55
](2
006)
Lap
lace
tran
sfor
mat
ion
was
used
toso
lve
the
OD
Eth
atac
coun
tsfo
rth
eba
lanc
eof
ther
mal
lydr
iven
,fr
ictio
nal,
and
elas
ticre
stor
ing
forc
es.
Pres
sure
diff
eren
cebe
twee
nev
apor
ator
and
cond
ense
ris
rela
ted
tote
mpe
ratu
redi
ffer
ence
byC
lape
yron
-C
laus
iseq
uatio
n.
N/A
—C
ircu
lar
—0
1.65
Wat
er,
acet
one
50—
Osc
illat
ing
mot
ion
depe
nds
onch
arge
ratio
,tot
alch
arac
teri
stic
leng
th,
diam
eter
,tem
pera
ture
diff
eren
cebe
twee
nth
eev
apor
atio
nan
dco
nden
ser
sect
ions
,w
orki
ngflu
id,a
ndop
erat
ing
tem
pera
ture
.
Cha
roen
saw
anan
dTe
rdto
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the
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nel
perf
orm
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tter
than
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[47]
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onof
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ight
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uctiv
ityof
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plat
eis
low
.
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�i
dt= [
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 ′′ = q
2π 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)/ρ2
v
]1/4
= 0.0052
[(D4.3L0.1
t
L4.4e
)N 0.5
(ρv
ρ�
)−0.2
Pr−25v
]0.116
(7)
where Lt is the total length of the PHP tube and D4.3L0.1t /L4.4
e isa 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
[(D3.1L0.1
t
L3.2e
)N 0.9
(ρv
ρ�
)−0.1 (ωμ3
v
σ2ρv
)]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
)1.127
Ja1.417Bo−0.66 (9)
and
Ku90 = 0.0002
(D
Le
)0.92
Ja−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 ′′ RgT0
4π 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+ 2A2 RgTsat
(L Aρ�ϕ)[(L/2)Aρ�(1 − ϕ)/ρv]2
×[
L Aρ�(1 − ϕ)
2+ qe
h�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 = 5) [53].
Figure 8 Displacement of liquid slugs (n = 10) [53].
These ends are submerged in water, while the evaporator sectionis coiled and attached to a float so that it is out of the water. Theevaporator is heated and the oscillatory fluid motion produces anet thrust. A numerical solution of the energy equation and theequation of motion for a vapor plug is presented to predict theplug’s temperature, position, and velocity. Oscillatory motion inthe PHP generated a net average thrust of 0.0027N. Heat transferdue to sensible heat was not taken into account. Recently, Dob-son [11, 18] proposed to use the open-ended PHP in conjunctionwith two check valves to pump water, but the maximum attain-able mass flow rates are on the order of mg/s—hardly enoughto irrigate fields. An improved model for liquid slug oscillationthat considered pressure difference, friction, gravity, and surfacetension was also presented.
Zhang and Faghri [10] proposed models for heat transferin the evaporator and condenser sections of a PHP with oneopen end by analyzing thin film evaporation and condensation(see Figure 9). The liquid film thicknesses in the evaporator andcondenser sections respectively satisfy
d
dx(σK−pd ) = 3μ�
2π Rρ�δ3
[m�,in − 2π Rk�(Th − Tv)
h′�v
∫ x
0
1
δdx
](16)
σh�vρ�
3μ�
[δ3
(d3δ
dx3+ 1
(R − δ)2
dδ
dx
)]= k� (Tv − Tc)
∫ s
0
1
δds
(17)
heat transfer engineering vol. 29 no. 1 2008
Y. ZHANG and A. FAGHRI 39
Figure 9 Film evaporation and condensation in a PHP: (a) heating section,(b) cooling section [10].
where K is the curvature, pd is the disjoining pressure, R is theradius of the PHP, m�,in is the mass flow rate of the liquid filmat x = 0 (see Figure 9a), and Th , Tc, and Tv are the tempera-tures of the heating section, cooling section and vapor phase,respectively. Phase changes over this film drive oscillatory flowin the PHP. Heat transfer in the evaporator is the sum of evapora-tive heat transfer in the thin liquid film and at the meniscus. Heattransfer in the condenser is similarly calculated and sensible heattransfer to the liquid slug is also considered. It is found that theoverall heat transfer is dominated by the exchange of sensibleheat, not by the exchange of latent heat. Shafii et al. [14] furtherdeveloped their earlier numerical model [13] by including ananalysis of the evaporative and condensation heat transfer in thethin liquid film separating the liquid and vapor plugs. Both open-and closed-loop PHPs are considered, and they display similarresults. As can be seen from Figure 10, the total heat transfer isdue mainly to the exchange of sensible heat (∼95%). Total heattransfer slightly increases as surface tension of the working fluidincreases. The total heat transfer significantly decreased with de-creasing heating section wall temperature. Increasing the diam-eter of the tube resulted in higher total heat transfer. Liang andMa [54] presented a mathematical model describing the oscilla-tion characteristics of slug flow in a capillary tube. In additionto the modeling of oscillating motion, numerical results indicatethat the isentropic bulk modulus generates stronger oscillationsthan the isothermal bulk modulus. While it demonstrates that thecapillary tube diameter, bubble size, and unit cell numbers deter-
Figure 10 Heat transfer rate: (a) sensible heat; (b) evaporative heat [14].
mine the oscillation, the capillary force, gravitational force, andinitial pressure, distribution of the working fluid significantlyaffects the frequency and amplitude of oscillating motion in thecapillary tube. By performing a force balance of the thermallydriven, capillary, frictional, and elastic restoring forces on a liq-uid slug, the oscillating motion is analytically described by Ma etal. [32, 55]. Pressure differences between the evaporator and thecondenser are related to the temperature difference between theevaporator and the condenser by the Clapeyron-Clausius equa-tion. The temperature difference between the evaporator and thecondenser of a PHP is utilized as a driving force of the oscillat-ing motion. With frictional and restoring forces considered butthe gravitational force neglected, the equation that governs themotion of the working fluid in an oscillating heat pipe can befound as
(L�ρ� + Lvρv)Ad2x
dτ2+
[(f� · Re�
)(μ�L�
2D2h
)
+ ( fv · Rev)
(μv Lv
2D2h
)]· A
dx
dτ+ Aρv RT
Lv
x
=(
Ah�vρv,c
Te
)(�Tmax − �Tmin
2
)[1 + cos(ωτ)] (18)
where L� and Lv are the length of liquid and vapor, �Tmax and�Tmin are the maximum and the minimum temperature differ-ences between the condenser and the evaporator sections, andf� and fv are friction coefficients for liquid and vapor phases,respectively. Ma et al. [55] obtained the exact solution of Eq.(18) using Laplace transformation. Oscillating motion dependson charge ratio, total characteristic length, diameter, tempera-ture difference between the evaporation and condenser sections,working fluid, and operating temperature. The mathematicalmodel underpredicted the temperature difference between theevaporator and condenser when compared to experimental re-sults [32].
Holley and Faghri [8] presented a numerical model for aPHP with a sintered copper capillary wick with flow channelsthat have different diameters. The effects of the varying chan-nel diameter, inclination angle, and number of parallel channelsare presented. When one channel was of a smaller diameter, itinduced the circulation of the fluid which in turn increased theheat load capability of the PHP. The modeled PHP performedbetter in the bottom heat mode (smaller temperature differential)than the top heat mode. Varying the mean Nusselt number hadlittle effect on the PHP performance. As the number of parallelchannels increases, the PHP sensitivity to gravity decreases andits heat load capability increases.
Khandekar et al. [56] used an Artificial Neural Network(ANN) to predict PHP performance. The ANN is of the fullyconnected feed forward configuration and is trained using 52sets of experimental data from a closed-loop PHP. The ANN isfed the heat input and fill ratio of each data set and calculates theeffective thermal resistance of the PHP. The ANN model learned
heat transfer engineering vol. 29 no. 1 2008
40 Y. ZHANG and A. FAGHRI
to predict thermal performance for this type of PHP but neglectsmany parameters that affect PHP performance, including tubediameter, number of parallel channels, length of the PHP, incli-nation angle, and properties of the working fluid. If the ANNhad more input nodes with which to consider these parameters,it would be a more effective model, though even then it wouldrequire considerably well organized experimental data for theANN to learn from.
Khandekar and Gupta [42] modeled heat transfer in a ra-diator plate with PHP embedded using a commercial packageFLUENT. However, oscillatory flow and heat transfer of thePHPs were not modeled. The contribution of PHPs on the heattransfer in the radiator plate was considered using an effectivethermal conductivity obtained from experiment.
UNRESOLVED ISSUES AFFECTING PHPPERFORMANCE
In spite of significant efforts in the last decade, no compre-hensive tools exist to aid engineers in designing a PHP. Thisis because either the issue remains uninvestigated properly orthey have been studied and conflicting results were found. Also,the diversity of experiments and analyses make them difficultto compare directly. Nonetheless, the following issues requirefurther investigation:
Sensible Heat vs. Latent Heat
Analyses by Zhang and Faghri [10] and Shafii et al. [13, 14]conclude that the majority of the overall heat transfer (greaterthan 90%) in a PHP is due to the exchange of sensible heat. Also,Groll and Khandekar [12] showed that for ethanol the ratio ofsensible enthalpy to total enthalpy is greater than 98% for therange of charge ratios in which PHPs operate. On the otherhand, the role of latent heat becomes important when the flowpattern becomes annular directional flow. Further experimentalevidence is needed to reveal the roles of sensible and latent heatsunder different conditions.
Optimum Charge Ratio
It has been shown that PHPs operate correctly with charge ra-tios ranging from 20–80%. Also, most researchers agree that foreach PHP, some optimal charge ratio exists. Unfortunately, dueto the differences in PHP geometry and the properties of variousworking fluids, the optimum charge ratio can reside anywherewithin that range. There are no robust correlations or models thatcan accurately predict the best charge ratio for a given PHP. Themodel by Zuo et al. [7] was capable of predicting the optimalcharge ratio for their experimental setups within 10%, but themodel was extremely simplified, and there is no proof that sucha model could be applied to other PHPs.
Gravity/Inclination Angle
Most of the above theoretical investigations include gravity intheir calculations, and they have found that its effects are domi-nated by surface tension forces. However, experiments show thatgravity may yet play a significant role. As the inclination angleis varied from vertical to horizontal, the thermal performanceof many PHPs degraded, and some did not operate at all. OtherPHPs, often with many turns, were able to perform satisfactorilyindependent of orientation. If the inner diameter of the PHP isdecreased, it may also aid in the PHP’s ability to perform at lowinclination angles.
Number of Turns
The number of turns in a PHP and the associated flow pertur-bations in each turn may account for a PHP’s ability to function inthe horizontal orientation. Experimental results from Rittidechet al. [3], who reported heat flux rather than heat transferred be-cause PHP with evaporators of different sizes were compared,have shown that the heat flux decreases as the number of turnsincreases. It was proposed that some optimum number of turnsmight exist that would achieve maximum heat flux.
Losses at Bends
A typical simplifying assumption in many of the mathemat-ical models is to neglect the pressure lost at each bend in thepipe. Because it has been shown experimentally that the num-ber of turns affects a PHP thermal performance and its abilityto operate at low inclination angles, it may not be totally validto treat the PHP as a straight pipe. Perturbations at each bendmay not be negligible, but including them in a numerical modelgreatly increases its complexity.
Onset Heat Flux/Temperature
PHPs are thermally driven non-equilibrium devices, and al-though they may be very effective heat spreaders, a temperaturedifference must exist between the evaporator and condenser tomaintain their operation. In many cases, there was observed tobe some minimum heat flux or differential temperature neces-sary to initiate oscillating flow. Like the optimum charge ratio,the onset heat flux was different for each experiment. Therefore,parametric investigation is required to fully understand this phe-nomenon.
Evaporator Dryout
Some investigators claim that PHPs have an advantageover conventional heat pipes because they are not limited by
heat transfer engineering vol. 29 no. 1 2008
Y. ZHANG and A. FAGHRI 41
evaporator dryout, but others have observed local dryout, espe-cially at low charge ratios. The oscillating flow should quicklyreturn liquid to the evaporator, but dryout and the associated risein local wall temperature should still be avoided.
Surface Tension
One of the most important properties of the working fluidused in a PHP is surface tension. Surface tension determinesthe critical diameter of the PHP, pressure drop along the PHP,and affects the flow within the PHP, but conflicting conclusionshave been drawn as to whether higher or lower values of surfacetension improve PHP performance. Analysis by Shafii et al. [14]concluded that heat transfer increases as the surface tension ofthe fluid increases. However, Groll and Khandekar [12] indicatethat a low surface tension is desirable because it reduces thepressure drop necessary to drive the flow.
Capillary Wick
Typical PHPs have no internal capillary wick structure, butZuo et al. [6, 7] were able to achieve very high heat fluxes froma PHP with a sintered copper wick. The wick aids in the dis-tribution of the liquid throughout the PHP and provides morenucleation sites for bubbles to form. However, except for thework by Zuo’s group and Holley and Faghri [8], little investiga-tion has been performed in this area.
Non-Dimensional Parameters
Nearly all current PHP studies rely on the dimensional pa-rameters that were already discussed, which makes the develop-ment of general design tools challenging. If PHP performancecan be correlated with certain non-dimensional parameters, itwould provide a better understanding of the complex phenom-ena governing PHP operation. Rittidech et al. [3] attempted todo so with Kutateladze and Prandtl numbers, but this correlationis limited to open-loop PHPs in the horizontal heat mode over acertain temperature range. Khandekar et al. [23] also developeda semi-empirical model based on the Reynolds, Karman, liq-uid Prandtl, and Jakob numbers. The resulting function is onlyvalid for charge ratios of 50%. Zhang and Faghri’s model [53]does well to describe the motion of the two-phase flow whiletaking various parameters such as number of turns and chargeratio into account, but it does not predict heat transfer perfor-mance. Obviously, further investigation is required to expandsuch semi-empirical models.
Numerical Simulations
The existing theoretical models of PHPs are mainly lumped,one-dimensional, or quasi-one-dimensional, and many unreal-
istic assumptions are often introduced. In order to significantlyadvance the understanding of oscillatory flow and heat transferin PHPs, transient evaporation and condensation of thin film,effect of surface tension, and heat transfer in directional annularflow at high heat flux must be considered. In addition, the model-ing of flow pattern transition, transient evaporation/boiling, andcondensation in PHPs with more advanced techniques, such asthe volume of fluid (VOF) model [57, 58] to simulate 2-D/3-Dtwo-phase flow and heat transfer, will be very helpful to obtaina more realistic description of transient flow and heat transfer inthe PHPs.
Nanofluid PHPs
While most research on electronics cooling focuses on the en-hancement of heat transfer using various techniques, very fewpeople paid attention to the inherently low thermal conductivityof the working fluid. It was demonstrated that dispersion of atiny amount of nanoparticles in traditional fluids, which results innanofluids, dramatically increases their thermal conductivities.For example, a small amount (less than 1% volume fraction) ofcopper nanoparticles or carbon nanotubes dispersed in ethyleneglycol or oil can increase their inherently poor thermal conduc-tivity by 40% and 150%, respectively [59, 60]. Ma et al. [45,46] demonstrated that the performance of a PHP can be signif-icantly improved by charging nanofluids into the PHP. On thecontrary, Chiang et al. [47] showed that the performance of thePHP by the addition of nanoparticle is only improved slightly.The mechanism of performance enhancement, oscillatory flow,and phase change of the nanofluids in the PHP needs to beinvestigated.
COMMERCIAL AVAILABILITY AND APPLICATIONS
Although PHPs are being studied mostly in the academiccommunity, as indicated in this review, the commercial avail-ability of pulsating heat pipes is limited. Thermacore, Inc. andthe Rockwell Scientific Co. have done research regarding pul-sating heat pipes, but do not currently manufacture PHPs asstandard items. Two companies that do offer PHPs for sale areTSHeatronics Co., Ltd. of Japan and Advanced Cooling Tech-nologies, Inc. (ACT) in the United States. TSHeatronics callstheir technology Heatlane. Heatlane AL-EX is an aluminum flatplate PHP that can be formed in different configurations. Theworking fluids used are butane and HFC-134a. The HeatlaneAL-EX can be combined with aluminum fins and used as a heatsink to cool power semiconductors, laser generators, and CPUs.A similarly finned PHP can be used as a heat absorber. Ap-plications for aluminum Heatlanes without fins include coolingplasma screens and LCD monitors. TSHeatronics also makes astainless steel version of their product with water as the workingfluid. This style PHP has found uses in the food service indus-try. Applications include a rice cooker and a Sushi display case.
heat transfer engineering vol. 29 no. 1 2008
42 Y. ZHANG and A. FAGHRI
Stainless steel Heatlanes have also been used in fluid to fluidheat exchangers.
CONCLUSIONS
Since their invention, there have been a considerable numberof studies relating to pulsating heat pipes, and their ability totransfer heat at very low effective thermal resistances has beenproven. The work compiled here significantly increases the un-derstanding of the phenomena and parameters that govern thethermal performance of pulsating heat pipes. Many unresolvedissues still exist, but continued exploration should be able toovercome these challenges. The development of comprehensivedesign tools for the prediction of pulsating heat pipe performanceis still lacking.
ACKNOWLEDGMENTS
The authors would like to acknowledge supports by NationalScience Foundation (NSF), National Aeronautics and Space Ad-ministration (NASA), and Office of Naval Research (ONR).
NOMENCLATURE
A tube cross sectional area, m2
Bo Bond numberc wave velocity, m/scp specific heat at constant pressure, J/kg KD diameter, mf friction factorg gravitational acceleration, m2/sh�v latent heat, J/kgJa Jakob numberk thermal conductivity, W/m-KKa Karman numberKu Kutateladze numberL length, mm�i mass of the i th liquid slug, kgm� liquid mass flow rate, kg/sN number of turnsp pressure, PaP flow channel perimeter, mPr Prandtl numberq heat transfer rate, Wq ′′ heat flux, W/m2
R radius, mRg gas constant, J/kg-KRe Reynolds numbers coordinate, mt time, sT temperature, K
v�i velocity of the i th liquid plug, m/sx Coordinate, m
Greek Symbols
α void fractionβ inclination angleδ liquid film thickness, m�p pressure change, Pa�α change of void fractionμ dynamic viscosity, kg/m-sρ density, kg/m3
σ surface tension, N/mτ shear stress, N/m2
ϕ charge ratioω frequency of oscillation motion
Subscripts
a adiabaticc condensere evaporatoreff effective� liquidle left endre right endsat saturationt totalv vapor
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Yuwen Zhang is an associate professor in theDepartment of Mechanical and Aerospace Engi-neering at the University of Missouri-Columbia.His research interests include phase change heattransfer; heat pipes; ultrafast, ultra-intense lasermaterials processing; and transport phenomena inmaterials processing and manufacturing. He hasauthored more than 130 archival technical pub-lications, including 80 journal papers, and co-authored a textbook, Transport Phenomena in
Multiphase Systems. He has been a reviewer for 20 archival journals and numer-ous conferences, and served as a panelist in proposal review panels for NationalScience Foundation and National Aeronautics and Space Administration. Heis a member of American Society of Mechanical Engineers (ASME), Amer-ican Society for Engineering Education (ASEE), and an Associate Fellow ofAmerican Institute of Aeronautics and Astronautics (AIAA). He is a recipient ofthe 2002 Office of Naval Research (ONR) Young Investigator Award. Dr. Zhangreceived his Ph.D. in mechanical engineering from the University of Connecticut(1998).
Amir Faghri is the United Technologies En-dowed Chair Professor in Thermal-Fluids Engi-neering, and formerly the Dean of the School ofEngineering (1998–2006) and Head of Depart-ment of Mechanical Engineering (1994–1998) atthe University of Connecticut. While holding suchacademic and industrial positions as distinguishedas chair professor, department head, and dean, heauthored six books and edited volumes; more than250 archival technical publications, including 150
journal papers; and six U.S. patents for which he was the sole inventor. He hasserved as a consultant to several major research centers and corporations, in-cluding Los Alamos and Oak Ridge national laboratories, Intel Corporation,and Exxon Mobile. As a principal investigator conducting research in heat andmass transfer, he has received numerous external research contracts from theNational Science Foundation, National Aeronautics and Space Administration,Department of Defense, Department of Energy, and various industrial compa-nies. He currently serves on the editorial boards of eight scientific journals. Hehas received many honors and awards, including the prestigious 1998 Amer-ican Institute of Aeronautics & Astronautics (AIAA) Thermophysics Award,the 1998 American Society of Mechanical Engineering (ASME) Heat Trans-fer Memorial Award, and 2005 ASME James Harry Potter Gold Medal. Hereceived his M.S. and Ph.D. from the University of California at Berkeley(1974, 1976) and a B.S. with highest honors from Oregon State University(1973).
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