8/9/2019 Modeling Pulsating Heat Pipes

1/9

'UDIW$XJ

7KHRUHWLFDO0RGHOLQJRI3XOVDWLQJ+HDW3LSHV

*6ZDQHSRHO $%7D\ORU57'REVRQ

'HSDUWPHQWRI0HFKDQLFDO(QJLQHHULQJ

8QLYHUVLW\RI6WHOOHQERVFK3ULYDWH%DJ;0DWLHODQG6RXWK$IULFD7HO)D[(PDLOFKRJDOO#PZHEFR]D

$EVWUDFW

$SXOVDWLQJKHDWSLSH3+3FRQVLVWVRIDFRQWLQXRXVWXEHILOOHGZLWKERWKWKHOLTXLGDQGYDSRXU

SKDVHVRIWKHZRUNLQJIOXLG7KHLQWHUQDOGLDPHWHULVRQWKHFDSLOODU\VFDOHRIWKHZRUNLQJIOXLG

ZKLFKFDXVHVWKHIRUPDWLRQRIERWKOLTXLGSOXJVDQGYDSRXUEXEEOHV:KHQFHUWDLQDUHDVRIWKH3+3DUHKHDWHGVRPHRIWKHOLTXLGHYDSRUDWHVFDXVLQJDSUHVVXUHGLIIHUHQWLDODFURVVVRPHRIWKH

SOXJV7KHVHSOXJVPRYHWRFRXQWHUDFWWKHSUHVVXUHGLIIHUHQWLDOFDXVLQJDOOWKHSOXJVWRPRYHLQD

FRPSOH[SDWWHUQ:KLOHWKHSOXJVPRYHWKHYDSRXUEXEEOHVJHWH[SRVHGWRFRROHUDUHDVFDXVLQJ

WKH YDSRXU WR FRQGHQVH +HDW LV WKHUHIRUH WUDQVIHUUHG LQ WKH IRUP RI HYDSRUDWLRQ DQGFRQGHQVDWLRQIURPWKHKHDWHGWRWKH FRROHG]RQHV,QDQDWWHPSWWRH[SODLQWKHPRYHPHQWRIWKH

SOXJVDWKHRUHWLFDOPRGHORID3+3FRQVLVWLQJRIDWXEHDQGVLQJOHSOXJZLWKYDSRXUEXEEOHVRQERWKVLGHVKDVEHHQGHYHORSHG7KHUHVXOWVRIWKHWKHRUHWLFDOPRGHOFRPSDUHGWRH[SHULPHQWDO

UHVXOWVDUHSUHVHQWHGKHUH)URPWKLVFRPSDULVRQLWFDQEHFRQFOXGHGWKDWWKHWKHRUHWLFDOPRGHO

SUHGLFWVWKHPRYHPHQWRIWKHSOXJVDWLVIDFWRU\

.H\ZRUGV

$NDFKLKHDWSLSHVSXOVDWLQJKHDWSLSHVRVFLOODWRU\KHDWSLSHVOLTXLGYDSRXULQWHUIDFHPDVVIOX[

,1752'8&7,21

$SXOVDWLQJKHDWSLSH3+3FRQVLVWVRIDFRQWLQXRXVWXEHILOOHGZLWKERWKWKHOLTXLGDQGYDSRXU

SKDVHVRIWKHZRUNLQJIOXLG7KHLQWHUQDOGLDPHWHULVRQWKHFDSLOODU\VFDOHRIWKHZRUNLQJIOXLG

ZKLFKFDXVHVWKHIRUPDWLRQRIERWKOLTXLGSOXJVDQGYDSRXU:KHQFHUWDLQDUHDVRIWKH3+3DUHKHDWHGVRPHRIWKHOLTXLGHYDSRUDWHVFDXVLQJDSUHVVXUHGLIIHUHQWLDODFURVVVRPHRIWKHSOXJV

7KHSOXJVPRYHWRFRXQWHUDFWWKHSUHVVXUHGLIIHUHQWLDO7KHPRYHPHQWRIWKHVHSOXJVFDXVHV

QHLJKERXULQJSOXJVWRPRYHDVZHOO$OOWKHSOXJVVWDUWWRPRYHLQDFRPSOH[SDWWHUQ:KLOHWKHSOXJVPRYHWKHYDSRXUEXEEOHVJHWH[SRVHGWRFRROHUDUHDVFDXVLQJWKHYDSRXUWRFRQGHQVH

+HDWLVWKHUHIRUHWUDQVIHUUHGLQWKHIRUPRIHYDSRUDWLRQDQGFRQGHQVDWLRQIURPWKHKHDWHGWRWKH

FRROHG]RQHV,QDQDWWHPSWWRH[SODLQWKHPRYHPHQWRIWKHSOXJVDWKHRUHWLFDOPRGHORID3+3FRQVLVWLQJRIDWXEHDQGVLQJOHSOXJZLWKYDSRXUEXEEOHVRQERWKVLGHVKDVEHHQGHYHORSHG

)LJXUHVKRZVWKHWXEHFRQWDLQLQJWKHOLTXLGSOXJZLWKYDSRXUEXEEOHVRQERWKVLGHVDQGWKH

KHDWHGDGLDEDWLFDQGFRROHGUHJLRQV

'(5,9$7,212)*29(51,1*(48$7,216

mailto:chogall@mweb.co.zamailto:chogall@mweb.co.za

8/9/2019 Modeling Pulsating Heat Pipes

2/9

'UDIW$XJ

7KHJRYHUQLQJHTXDWLRQVDUHGHULYHGE\FRQVLGHULQJWKHFRQVHUYDWLRQRIHQHUJ\DQGPDVVRIWKH

EXEEOHVOLTXLGILOPDQGHQHUJ\RIWKHJODVVWXEHDQGWKHQFRQVHUYDWLRQRIWKHPRPHQWXPRIWKH

OLTXLGSOXJ&RQVLGHUDOHQJWK'[RQWKHOHIWKDQGVLGHRIWKHWLEHLQILJXUHVKRZQHQODUJHGLQILJXUH$WKHUPDOUHVLVWDQFHPRGHOLVVKRZQLQILJXUH+HDWLVWUDQVIHUUHGIURPWKH EXEEOH

DWWHPSHUDWXUH7Y WRWKHOLTXLGILOPDWWHPSHUDWXUH75ILQWKHIRUPRIVHQVLEOHDQGODWHQWKHDWWUDQVIHU+HDWLVWKHQWUDQVIHUUHGIURPWKHOLTXLGILOPWRWKHJODVVWXEHDWWHPSHUDWXUH7JDQGXOWLPDWHO\WRWKHH[WHUQDOVXUURXQGLQJVDWWHPSHUDWXUH7H&RQVLGHUWKHYDSRXUEXEEOHDVVKRZQ

LQILJXUH7KHKHDWWUDQVIHUUHGIURPWKHEXEEOHWRWKHOLTXLGILOPFDXVHVWKHLQWHUQDOHQHUJ\RI

WKHEXEEOHWRFKDQJH7KHFKDQJHLQLQWHUQDOHQHUJ\FDXVHVWKHWHPSHUDWXUHRIWKHEXEEOHWRFKDQJH7KHFKDQJH LQWKHWHPSHUDWXUHRIWKHEXEEOHUHVXOWVLQWKHFKDQJHRISUHVVXUH7KH

FKDQJHLQSUHVVXUHZLOOFDXVHWKHOLTXLGSOXJWRPRYH:RUNLVWKHUHIRUHGRQHE\WKHEXEEOH

RQWRWKHOLTXLGSOXJ&DUU\LQJRXWDHQHUJ\EDODQFHRQWKHEXEEOHFRQWUROYROXPHVKRZQLQILJXUHWKHUDWHRIFKDQJHRILQWHUQDOHQHUJ\RIWKHEXEEOHLVJLYHQE\

GW

G9

S'[KP'[77KGW

G8 YYILYLILIYIY

Y 'cc'

& /5/5

ZKHUH

GW

G7FP

GW

G8 YYYY

Y

DQGWKHPDVVIOX[DFURVVWKHEXEEOHDQGOLTXLGLQWHUIDFHLVJLYHQE\&DUH\93[[

ccI

I

Y

YL

7

S

7

S

5

P

&

58

8

7KHLQWHUIDFLDOPDVVIOX[DVGHWHUPLQHGE\LVSRVLWLYHIRUFRQGHQVDWLRQDQGQHJDWLYHIRU

HYDSRUDWLRQ&RQVLGHUDOHQJWK'[RIWKHOLTXLGILOPDVVKRZQLQILJXUH7KHGLIIHUHQFHLQWKHHQHUJ\HQWHULQJDQGOHDYLQJWKHOLTXLGILOPZLOOFDXVHDFKDQJHLQLQWHUQDOHQHUJ\RIWKHOLTXLG

ILOP$QHQHUJ\EDODQFHRQWKHOLTXLGILOPJLYHVWKHUDWHRIFKDQJHRIWKHLQWHUQDOHQHUJ\RIWKH

OLTXLGILOPDV

ILYLILIYIYLJIIJI

'[KP'[77K'[77KGW

G8

& /5/55 '''

ZKHUH

GW

G7FP

GW

G8 IIYI

I

8/9/2019 Modeling Pulsating Heat Pipes

3/9

'UDIW$XJ

7KHPDVVIOX[UHVXOWVLQWKHFKDQJHRIPDVVRIERWKWKHYDSRXUEXEEOHDQGWKHOLTXLGILOP)RU

WKHYDSRXUEXEEOHWKHUDWHRIFKDQJHLQPDVVLVJLYHQE\

LILY P/'

GW

GP&

cc

DQGIRUWKHOLTXLGILOP

LIL

IP'

GW

GP&

cc /5

&RQVLGHUDOHQJWK'[RIWKHJODVVWXEH7KHGLIIHUHQFHLQWKHHQHUJ\HQWHULQJDQGOHDYLQJWKHJODVVWXEHZLOOFDXVHDFKDQJHLQLQWHUQDOHQHUJ\RIWKHJODVVWXEH$QHQHUJ\EDODQFHRQWKH

JODVVWXEHJLYHVWKHUDWHRIFKDQJHRIWKHLQWHUQDOHQHUJ\RIWKHJODVVWXEHDV

HJJHJIIJJ

77K77KGW

G8

ZKHUH

GW

G7FP

GW

G8 JYJJ

J

7KHYDSRXUEXEEOHVDUHDSSUR[LPDWHGDVDQLGHDOJDV7KHEXEEOHSUHVVXUHFDQWKHUHIRUHEH

UHODWHGWRWKHEXEEOHWHPSHUDWXUHE\WKHLGHDOJDVODZ)RUDEXEEOHWKHSUHVVXUHLVWKHUHIRUH

JLYHQE\

Y

YYY

9

57PS

'XHWRWKHSUHVVXUHGLIIHUHQWLDOEHWZHHQWZREXEEOHVRQERWKVLGHVRIDOLTXLGSOXJMDQGNDQHW

SUHVVXUHIRUFHZLOOEHH[HUWHGRQWKHSOXJ,QDGGLWLRQWRWKLVSUHVVXUHIRUFHWKHOLTXLGSOXJZLOOH[SHULHQFHZDOOVKHDUVWUHVVLQDGLUHFWLRQRSSRVLWHWRLWVPRYHPHQWDVZHOODVDJUDYLWDWLRQDO

IRUFH7KHVHWKUHHIRUFHVDUHUHODWHGWRWKHDFFHOHUDWLRQRIWKHOLTXLGSOXJE\WKHFRQVHUYDWLRQRIPRPHQWXPDVIROORZV

JP/'SS'GW

[GP SZSLYNYMIL

S

S 95/5

62/87,212)*29(51,1*(48$7,216

8/9/2019 Modeling Pulsating Heat Pipes

4/9

'UDIW$XJ

7KHGLIIHUHQWLDOHTXDWLRQVDERYHZHUHVROYHGXVLQJDQH[SOLFLWILQLWHGLIIHUHQFHVFKHPH

(TXDWLRQUHVXOWVLQWKHIROORZLQJH[SOLFLWUHODWLRQIRUWKHWHPSHUDWXUHRIWKHYDSRXUEXEEOH

L

Y

L

Y

L

YL

Y

L

IL

L

Y

L

L

L

IL

L

I

L

YIY

YYY

L

Y 7W

99S'[KP'[77K

FP

W7

'

'cc''

& /5/5

7KHHQWKDOS\RIWKHYDSRXU LYK KYLLVFDOFXODWHGIURPWKHUHODWLRQ 77FKK LY

L

YSY

L

Y

L

Y

,WLV

DVVXPHGWKDWWKHSUHVVXUHRIWKHOLTXLGILOP L IS LVWKHVDWXUDWLRQSUHVVXUHRIWKHIOXLG

FRUUHVSRQGLQJWRWKHOLTXLGILOPWHPSHUDWXUH LI

7

&DUH\93[[

7KHPDVVIOX[LQLVJLYHQE\

cc

L

I

L

IL

Y

L

YLL

7

S

7S

5P

&58

8

9DULRXVYDOXHVIRUWKHDFFRPPRGDWLRQFRHIILFLHQWIRUWKHVDPHIOXLGDUHTXRWHGLQWKH

OLWHUDWXUH0LOOV$))RUWKLVPRGHODYDOXHRI[[LVXVHG)URPHTXDWLRQWKH

H[SOLFLWUHODWLRQIRUWKHOLTXLGILOPWHPSHUDWXUHDWWKHQHZWLPHVWHSLV

L

IL

IL

L

Y

L

L

L

IL

L

I

L

YIYL

L

J

L

IIJ

IYI

L

I 7'[KP

'[77K'[77K

FP

W7

&

'cc

'''

/5

/55

)URPWKHYDSRXUPDVVLV

L

YLIL

L

Y PWP/'P 'cc

&

DQGIURPWKHOLTXLGILOPPDVVLV

L

ILIL

L

I PWP'P & 'cc

/5

$VVXPLQJDXQLIRUPOLTXLGILOPWKLFNQHVVWKHOLTXLGILOPWKLFNQHVVFDQEHGHWHUPLQHGIURP)URPWKHWHPSHUDWXUHRIWKHWXEHLVJLYHQ E\

LJRHLJJHLLJLIIJYJJ

L

J 7'[77K'[77KFP

W7 ''

' 55

)URPWKHYDSRXUSUHVVXUHLVJLYHQE\

8/9/2019 Modeling Pulsating Heat Pipes

5/9

'UDIW$XJ

L

Y

L

Y

L

YL

Y9

57PS

7KHDFFHOHUDWLRQRIWKHSOXJLVWKHQFDOFXODWHGIURP

JP/'SS'PGW

[GS

L

ZSL

L

YN

L

YM

L

IL

S

L

S95/

5

7KHVKHDUVWUHVVLQLVHVWLPDWHGIURPZ&IS!5YSL :KHUHWKHFRHIILFLHQWRIIULFWLRQLVJLYHQ

E\&IS5H

LI5H!5YSL'L5 RWKHUZLVH&IS5H'REVRQ57DQG+DUPV

7KHYHORFLW\RIWKHOLTXLGSOXJLVWKHQFDOFXODWHGIURP

GW

G[W

GW

[G

GW

G[ LSL

S

L

S '

$QGIURPWKHSRVLWLRQRIWKHSOXJLVJLYHQE\

L

S

L

SL

S [WGW

G[[ '

$IWHUFDOFXODWLQJWKHSRVLWLRQRIWKHSOXJIURPWKHYROXPHRIWKHYDSRXUEXEEOHV9YL

FDQ

EHFDOFXODWHGDQGWKHSURFHGXUHLVUHSHDWHGIRUWKHQH[WWLPHVWHS

(;3(5,0(17$/ 6(783

$QH[SHULPHQWDOPRGHODVVKRZQLQILJXUHZDVFRQVWUXFWHG$8VKDSHGJODVVWXEHRI' L

PPDQG'R PPLVLQVHUWHGWKURXJKDUXEEHUSOXJDVVKRZQ7ZRYDOYHVDUHDWWDFKHGWRWKH

WXEHIRUFKDUJLQJSXUSRVHVRIWKHZRUNLQJIOXLG7KHUXEEHUSOXJLVZHGJHGLQWRDKROORZJODVVWXEHWRIRUPDFRQWDLQHULQZKLFKZDWHULVDGGHGWRVHUYHDVDKHDWVRXUFHRUVLQN7KHGHVFULEHG

DVVHPEO\LVSRVLWLRQHGVRWKDWWKHGHVLUHGOHQJWKRIWKHWXEHLVH[SRVHGWRZDWHULQWKHERWWRP

JODVVFRQWDLQHUZKLFKVHUYHVDVDKHDWVRXUFHRUVLQN

',6&866,21$1'5(68/76

$W\SLFDOUHVXOWRIWKHSOXJPRYHPHQWREVHUYHGXVLQJWKHH[SHULPHQWDODSSDUDWXVLVVKRZQLQILJXUH

&21&/86,216

120(1&/$785(

8/9/2019 Modeling Pulsating Heat Pipes

6/9

'UDIW$XJ

$OSKDEHWLFDO

&I )DQQLQJIULFWLRQIDFWRU

F VSHFLILFKHDW-NJ.' GLDPHWHUP

G RUGLQDU\GLIIHUHQWLDO

J JUDYLWDWLRQDOFRQVWDQWPV

K KHDWWUDQVIHUFRHIILFLHQW:P.

HQWKDOS\-NJ.

/ OHQJWKP

P PDVVNJ

P&cc PDVVIOX[NJPV S SUHVVXUHNJPV

5 VSHFLILFJDVFRQVWDQW-NJ.

7 WHPSHUDWXUHq&W WLPH V8 LQWHUQDOHQHUJ\-

9 YROXPHP

Y YHORFLW\PV

[ GLVWDQFHP

*UHHNOHWWHUV

' GLIIHUHQFHG WKLFNQHVVP

P G\QDPLFYLVFRVLW\NJPVV DFFRPPRGDWLRQFRHIILFLHQWU GHQVLW\NJP

W VKHDUVWUHVVNJPV

6XSHUVFULSWV

L LQGLFDWHWLPHVWHS

6XEVFULSWV

H H[WHUQDOJ JODVV

L LQVLGHLQWHUIDFH

M LQGH[XVHGWRGLVWLQJXLVKEHWZHHQWKHVDPHSURSHUW\RIGLIIHUHQWHQWLWLHVN LQGH[XVHGWRGLVWLQJXLVKEHWZHHQWKHVDPHSURSHUW\RIGLIIHUHQWHQWLWLHV

5I OLTXLGILOPR RXWVLGH

8/9/2019 Modeling Pulsating Heat Pipes

7/9

'UDIW$XJ

S SOXJFRQVWDQWSUHVVXUH

Y YDSRXUFRQVWDQWYROXPH

Z ZDOO

5HIHUHQFHV

&DUH\93/LTXLG9DSRXU3KDVH&KDQJH3KHQRPHQD

0LOOV$)+HDW7UDQVIHU,5:,1

'REVRQ57DQG+DUPV70/XPSHG3DUDPHWHU$QDO\VLVRI&ORVHGDQG2SHQ2VFLOODWRU\

+HDW3LSHV[WK,QWHUQDWLRQDO+HDW3LSH&RQIHUHQFH'DWH

$GLDEDWLF/HQJWK

+HDWHG/HQJWK

/LTXLG3OXJ

$GLDEDWLF/HQJWK

&RROHG

/HQWK

3OXJ

/HQJWK/LTXLG)LOP

9DSRXU

+HDWHG/HQJWK

7XEH

GL

3OXJ3RVLWLRQ

)LJXUH 3XOVDWLQJKHDWSLSHPRGHO

['

9 D S R X U

/ LT X LG ) LOP

: D OO

+ H D W 6 R X UF H 6 LQ N

I/

Z/

['

)LJXUH(QODUJHGYLHZRID

OHQJWK '[RIWKHWXEH

8/9/2019 Modeling Pulsating Heat Pipes

8/9

'UDIW$XJ

Y7

Y7

LP5

&

IY5

I7

IJ5

J7

JH5

H7

)LJXUH 7KHUPDOUHVLVWDQFHPRGHOIRUDOHQJWK'[RIWXEH

'[KP ILL & /5 'cc Y '[77K ILIIY /5 ' Y

I7

YYY S7P GW

G9'S YILY

/5

)LJXUH(QHUJ\EDODQFHRIYDSRXUEXEEOH

)LJXUH(QHUJ\EDODQFHRIDOHQJWK

'[RIWKHOLTXLGILOP

I/

['

Y7

J7

LJIIJ '[77K 5'

'[77KILIYIY /5 ' '[KP ILYL & /5 'cc

I7

8/9/2019 Modeling Pulsating Heat Pipes

9/9

'UDIW$XJ

*ODVV&RQWDLQHU

*ODVV&RQWDLQHU

5XEEHU3OXJ

*ODVV7XEH

:DWHU/HYHO)RU+HDWLQJ&RROLQJ

:DWHU/HYHO)RU&RROLQJ+HDWLQJ

9DSRXU

/LTXLG3OXJ

9DOYHV

)LJXUH([SHULPHQWDOVHWXS

RI3+3PRGHO

7LPHWV

3RVLWLRQ[SPP

([SHULPHQW

)LJXUH3OXJSRVLWLRQDVDIXQFWLRQRIWLPH