M. Miura, T. Nagasaki, Y. Ito, “Experimental study on …...M. Miura, T. Nagasaki, Y. Ito, “Experimental study on heat transport induced by phase changes associated with liquid

M. Miura, T. Nagasaki, Y. Ito, “Experimental study on heat transport induced by phase

changes associated with liquid column oscillation in pulsating heat pipes”, International

Journal of Heat and Mass Transfer, 133, pp.652-661 (Apr 2019)(Elsevier)

Experimental study on heat transport induced by phase changesassociated with liquid column oscillation in pulsating heat pipes

⇑ Corresponding author.E-mail address: [email protected] (M. Miura).

Masayoshi Miura a,⇑, Takao Nagasaki b, Yu Ito b

aKanagawa University, Department of Mechanical Engineering, 3-27-1 Rokkakubashi, Kanagawa-ku, Yokohama 221-8686, Japanb Tokyo Institute of Technology, Department of Mechanical Engineering, 4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8502, Japan

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

Keywords:Latent heat transportPhase changeLiquid filmLiquid columnOscillating flow

In this study, phase changes associated with liquid column oscillation (latent heat transport) were exper-imentally investigated in order to understand the heat transport mechanism in pulsating heat pipes (PHPs). In the experiments, a channel was partially charged with working fluid to form a liquid column after the channel was evacuated. To investigate the thermal–hydraulic phenomena in actual PHPs, a forced oscillator caused the liquid column to oscillate sinusoidally in the channel under various oscillat-ing conditions. Wall temperatures, vapor temperature, and vapor pressure were measured under several liquid column oscillation conditions. It was shown that liquid film plays an important role in latent heat transport; moreover, the liquid column plays the role of a switch in phase changes on the liquid film, according to the relationship between wall temperature fluctuations and the displacement of the tip of the liquid column. In addition, it was found that evaporation and condensation on the liquid film occur simultaneously. These experimental results helped to clarify the details of latent heat transport in PHPs.

1. Introduction

Recently, the power dissipation of semiconductor chips hasincreased dramatically [1]; as a result, small and highly efficientheat transport devices are required. Pulsating heat pipes (PHPs)are now drawing significant attention as a novel type of heat trans-port device. PHPs were originally proposed by Akachi et al. [2] andhave a different heat transport mechanism than conventional heatpipes, such as wick heat pipes and thermosyphons. PHPs consist ofa single meandering capillary tube between heating and coolingsections. The tubes are evacuated and partially filled with workingfluid. In the tube, liquid columns are formed by surface tension.When one end of a liquid column is located at the heating sectionand the other end is located at the cooling section, the liquid col-umn is pushed toward the cooling section by the vapor pressuredifference between each end. This is because vapor pressure is afunction of the local temperature. After the liquid column movesonce, it then moves inertially, and the end of the liquid columnlocated at the heating section moves to the cooling section, whilethe other end of the liquid column located at the cooling sectionmoves to the heating section. Thus, the liquid column is pushedback to the initial state. Namely, the temperature difference

between the heating and cooling sections oscillates the liquid col-umns, which carry heat from the heating section to the coolingsection.

Numerous studies on PHPs have been conducted [3–5]. How-ever, the operating mechanism and heat transport mechanismof PHPs have not been sufficiently clarified, which prevents wideapplication of PHPs. This is because the thermal-hydraulic phe-nomena associated with the oscillating flow in PHPs are verycomplicated, and there are a large number of parameters requiredfor characterizing PHPs. Therefore, several studies have been con-ducted with simplified PHPs. These studies analyzed self-sustained thermally-induced oscillations of liquid columns intwo-phase systems. Nagasaki et al. investigated the oscillationof a liquid column in a straight channel as the most simplifiedPHP (i.e., one-turn closed-end PHP) [6]. They reported the effectsof oscillation amplitude and frequency of the liquid column onthe heat transport rate. Das et al. conducted experiments with asimple PHP consisting of a liquid column and a vapor bubble ina horizontally-located straight capillary tube with a liquid reser-voir [7]. Their experimental setup corresponded to the theoreticalconfiguration studied by Dobson [8,9]. It was able to obtainself-sustained thermally driven oscillation, and the vapor pressurefluctuation and the position of the tip of the liquid column weremeasured. However, the liquid column oscillation could not bethoroughly observed, and the pressure measurement and

Nomenclature

f oscillation frequency (Hz)m mass (kg)P pressure (Pa)Q heat transport rate (W)R gas constant (J/kg∙K)S oscillation amplitude (m)T temperature (�C)t time (s)V volume (m3)x position (m)

GreekH dimensionless wall temperature (–)

Subscriptav time averagedc oscillation centercond heat conductionE electronic input power of heatersat saturatedt the tip of the liquid columnw channel wall

videography were not synchronized. Rao et al. [10–12] conductedexperiments with an improved experimental setup that overcamethe limitations of the experimental setup of Das et al. The rela-tionship between the vapor pressure and the tip of the liquid col-umn was reported in detail. In addition, they developed amathematical model of PHPs that considered liquid film. More-over, Kato et al. carried out experiments on a PHP consisting ofa horizontally-located straight tube with a diaphragm to releaseinternal pressure fluctuations [13]. The stable periodic oscillationof the liquid column was obtained, and a mechanism for enhanc-ing heat transport using liquid column oscillation was reported indetail. Ishida et al. proposed a PHP composed of a straight capil-lary tube with an external moving section (i.e., a bellows) forimproving the reliability of heat transport devices [14]. Theyinvestigated the characteristics of the thermally driven oscillationof the liquid column, and examined the effects of the cross-section geometry, the roughness of the inner surface, and themoving section. Although these previous studies employed sim-plified PHPs, it was difficult to isolate the effect of one parameterfrom the effects of other parameters. For example, when the hea-ter power input into the heating section was altered, both theoscillation frequency and oscillation amplitude of the liquid col-umn changed. In order to overcome these difficulties, the currentauthors [15] simulated thermal-hydraulic phenomena in actualPHPs by forcedly oscillating the liquid column in the channelunder several oscillation conditions, which allowed the effectsof parameters to be distinguished. In addition, the sensible andlatent heat transport in the oscillated liquid column were sepa-rated, and the contributions of the sensible and latent heat trans-port were evaluated. Here, the sensible heat transport is based onconvective heat transfer between the wall and the working fluid.The latent heat transport is based on phase changes of workingfluid, such as evaporation in the heating section and condensationin the cooling section. It was shown that the contribution of thelatent heat transport has the same order of magnitude as thatof the sensible heat transport. In addition, it was reported thatthe latent heat transport increased as the oscillation frequencyof the liquid column decreased.

This study focuses on the mechanism of latent heat transport inorder to understand the phase change phenomena associated withliquid column oscillation in PHPs. Accordingly, the liquid columnwas oscillated forcedly under the low oscillation frequency of theliquid column, such that the contribution of latent heat transportwas larger relatively and the wall temperature fluctuations couldbe measured. Wall temperatures, vapor temperature, and vaporpressure were measured under several oscillating conditions.These measurements provided useful knowledge for understand-ing the latent heat transport in actual PHPs.

2. Experimental setup and procedures

Fig. 1 shows a schematic of the experimental setup. A squarechannel (cross section 2 mm � 2 mm, length 160 mm) was formedon a copper plate (width 4 mm, thickness 3 mm). The copper platewas covered by a transparent polycarbonate plate to allow visual-ization of the working fluid motion in the channel. The channelwall in the heating section (length 50 mm) was heated with a car-tridge heater. The channel wall in the cooling section (length60 mm) was cooled by water, and the temperature was maintainedat approximately 30 �C. The channel wall in the adiabatic section(length 50 mm) was pressed against a Bakelite block. The wall tem-peratures were measured by T-type thermocouples with a wirediameter of 0.1 mm at a depth of 0.5 mm from the outer surface.Position x was defined as the distance measured from the end ofthe heating section toward the cooling section. A vapor chamber(volume 5.6 cm3) was connected to the channel at the end of theheating section to simulate the small compression ratio of actualPHPs. The vapor chamber was heated using a tape heater woundon the outer surface of the vapor chamber, and the temperatureof the vapor chamber wall was kept approximately the same asthat of the heating section in order to prevent working fluid vaporfrom condensing in the vapor chamber. The vapor pressure wasmeasured at the end of the vapor chamber. The vapor temperaturewas measured at the center of the vapor chamber by T-typesheathed thermocouples with a sheath diameter of 1 mm. An oscil-lator composed of a piston-crank mechanism was connected to thechannel at the end of the cooling section via bellows. This oscil-lated the liquid column in the channel sinusoidally, which simu-lates the thermal-hydraulic phenomena in actual PHPs. Theworking fluid degassed by boiling was charged to form a liquid col-umn in the channel after the channel was evacuated. Conse-quently, the liquid column and a vapor plug were formed in thechannel. Ethanol was used as the working fluid.

Wall temperatures, vapor temperature, and vapor pressurewere measured under several conditions of liquid column oscilla-tion. These measurements and the capture of images by thehigh-speed video camera were synchronized. The position of thetip of the liquid column (i.e., the vapor-liquid interface), which isrepresented as xt, was measured from the images captured bythe high-speed video camera. Oscillation amplitude 2Swas definedas the difference between the maximum and minimum positionsof the tip of the liquid column. Oscillation center xc was definedas the average between the maximum and minimum positions ofthe tip of the liquid column.

This paper focuses on the heat transport resulting from phasechanges associated with liquid column oscillation (i.e., the latentheat transport). As mentioned in the previous section, a previous

Working fluid vapor Liquid column

Transparent polycarbonate plate

x

Pressure transducer

Heater

Vapor chamber

Copper plate with a square channel

50 50 60Heatingsection

Adiabaticsection

Coolingsection

Working fluid

Vacuumpump

Piston-crank mechanism

[Unit: mm]

[ : Thermocouple]

4

3

Square channel[2 2]

Bellows

The tip of the liquid column xt

H1 H2 H3 H4 HA A1 A2 A3 AC C1 C2 C3 C4

Copper plate

Fig. 1. Experimental setup.

study by the current authors [15] confirmed that the ratio of thelatent heat transport to the total heat transport increases as theoscillation frequency of the liquid column decreases. Therefore,the heat transport associated with liquid column oscillation wasinvestigated experimentally in cases in which the contribution oflatent heat transport is larger relatively; that is, the oscillation fre-quency was lower than that in actual PHPs.

3. Experimental results and discussion

3.1. Wall temperature distribution

Fig. 2 shows wall temperature distributions with liquid columnoscillation and without a working fluid. In the distribution without

20

30

40

50

60

70

0 50 100 150

Wal

ltem

pera

tureT w

, C

Position x , mm

Heatingsection

Coolingsection

Adiabaticsection

Fig. 2. Wall temperature distributions.

the working fluid, the heat transport was only due to the heat con-duction along the copper plate around the square channel. The dis-tribution with the liquid column oscillation was obtained underoscillation amplitude 2S ¼ 69:5 mm, oscillation centerxc ¼ 70:5 mm, and oscillation frequency f ¼ 0:83 Hz: Both distribu-tions were obtained using the same heater input power. As shownin Fig. 2, the temperature of the heating section in the distributionwith liquid column oscillation was lower than that without theworking fluid because the oscillated liquid column conducted sen-sible and latent heat transport. First, the wall temperature distribu-tions in the adiabatic section will be discussed. The walltemperature of the adiabatic section in the distribution withoutthe working fluid decreased approximately linearly, but slightlyconvex downward, because the heat transport was only due tothe heat conduction along the copper plate around the channeland a small portion of the heat was lost to the surroundings. Onthe other hand, the wall temperature distribution with the liquidcolumn oscillation was convex upward compared to that withoutthe working fluid. This would be because, against the heat loss,the heat flowed from the channel wall into the copper plate ofthe adiabatic section, owing to the condensation of working fluidvapor onto the channel wall. In Fig. 2, the time-averaged vaporpressure Pav and the saturated temperature for the pressure Tsat(Pav) are shown. The saturated temperature is indicated by the hor-izontal dashed line. The working-fluid vapor condenses in theregion of the channel wall where Tw < Tsat.

Second, the effect of oscillation centers on the wall temperaturedistribution in the adiabatic section will be discussed. To clarify thedifference in the wall temperature distribution among variouscases of oscillation centers, the dimensionless wall temperaturewas defined by using the temperatures at both ends of the adia-batic section, as follows:

H xð Þ ¼ T xð Þ � TAC

THA � TAC; ð1Þ

where THA is the temperature at the boundary between the heatingand adiabatic sections and TAC is that between the adiabatic andcooling sections. Fig. 3(a) shows the wall temperature distributionsin the adiabatic section for three oscillation center cases. Thedashed straight line in Fig. 3(a) shows the wall temperature distri-bution for the heat conduction along the copper plate around thechannel. As shown in Fig. 3(a), the dimensionless wall temperaturedistributions changed as the oscillation center varied. In addition, inorder to make clear the difference in the wall temperature distribu-tion among the three oscillation center cases, the dimensionlesswall temperature difference was defined as follows:

DH xð Þ ¼ H xð Þ �Hcond xð Þ; ð2Þwhere Hcond is the wall temperature distribution for the heat con-duction along the copper plate, which is represented by the dashedstraight line in Fig. 3(a). Fig. 3(b) shows the dimensionless wall tem-perature differences DH xð Þ in the adiabatic section, and it is seenthat the distribution of DH changed as the oscillation center varied.In the case of xc ¼ 70:5 mm (i.e., closer to heating section), the dis-tribution of DH was overall convex upward compared to the hori-zontal dashed line for the heat conduction along the copper plate.This is because the channel wall was heated by the condensationof the working fluid vapor, as discussed in the previous paragraph.On the other hand, in the cases of xc ¼ 81:8 mm and xc ¼ 89:9 mm(i.e., xc closer to cooling section), the distributions of DH were con-vex downward in the smaller x region closer to the heating sectionand convex upward in the larger x region closer to the cooling sec-tion. This suggests that the channel wall closer to the heating sec-tion was cooled by the evaporation of a liquid film, and that thechannel wall closer to the cooling section was heated by the con-densation of the working fluid vapor. The liquid film was observedby using the high-speed video camera, and it was found that the liq-uid film was formed when the liquid column moved from the heat-ing section to the cooling section. The liquid film was observed inmany previous studies [7,10–15].

In the next section, wall temperature fluctuation is discussed inorder to understand the detailed mechanism of heat transportinduced by the evaporation and condensation of working fluid on

Fig. 3. Dimensionless wall temperature d

liquid film formed with liquid column oscillation. In addition, theboundary between the evaporation and the condensation is dis-cussed in detail, according to the measurement of the workingfluid vapor pressure fluctuation.

3.2. Wall temperature fluctuation

Fig. 4 shows the relationship between the position of the tip ofthe liquid column xt and the wall temperature fluctuations. Here,the wall temperature fluctuation is determined by subtractingthe time average of wall temperatures from the instantaneous walltemperatures:

T 0i t

�ð Þ ¼ Ti t�ð Þ � �Ti; ð3Þwhere i is the ID of the thermocouple that measured wall temper-atures in the adiabatic section (H4, HA, A1, A2, A3, AC, and C1, asshown in Fig. 1) and t⁄ is the dimensionless time obtained by mul-tiplying time t by oscillation frequency f. In Fig. 4, T 0

i tð Þ ¼ 0 for each iis shown by the horizontal dashed line at the position of each ther-mocouple. The saturated position, denoted as xsat in Fig. 4, repre-sents the position where the local channel wall temperature Tw isequal to the saturated temperature for the working fluid vapor pres-sure Tsat Pð Þ: The saturated temperature was calculated according tothe vapor pressure measured at the end of the vapor chamber (seeSection 3.4). Thus, the saturated position xsat is a function of timebecause the vapor pressure P is a function of time. It can be roughlydetermined that the working fluid evaporates in the region ofx < xsat (Tw > Tsat) and condenses in the region of x > xsat(Tw < Tsat). The relationships between the position x, the positionof the tip of the liquid column xt; and the saturated position xsatare as follows:

xt <x :The channel is filledwith the liquid column:x<xt :The channel is filledwith the vapor and coveredwith the liquid film:

xsat <x :Condensationx<xsat :Evaporation

�8>>><>>>:

ð4Þ

The tip of the liquid column is located in the heating section forxt 6 50 mm; in the adiabatic section for 50 mm 6 xt 6 100 mm;

and in the cooling section for xt P 100 mm: At t� ¼ 0; the tip of

istributions in the adiabatic section.

Fig. 4. Relationship between the wall temperature fluctuations and the position of the tip of the liquid column (QE ¼ 4:73 W; 2S ¼ 69:5 mm; f ¼ 0:83 Hz).

the liquid column most deeply enters the cooling section, att� ¼ 0:25 it is located at the oscillation center as the liquid columnmoves from the cooling to the heating section, at t� ¼ 0:5 it mostdeeply enters the heating section, at t� ¼ 0:75 it is located at theoscillation center as the liquid column moves from the heating tothe cooling section, and at t� ¼ 1 it most deeply enters the coolingsection again.

Fig. 4(a) shows the relationship between the position of the tipof the liquid column and the wall temperature fluctuation underoscillation amplitude 2S ¼ 69:5 mm; oscillation centerxc ¼ 70:5 mm; and oscillation frequency f ¼ 0:83 Hz: The thirteenthermocouples are installed at a depth of 0.5 mm from the channelwall surface. The wall temperature fluctuation occurs correspond-ing to the change of thermal condition on the wall surface due tothe liquid column oscillation; however, the damping and time lagof temperature fluctuation may occur between the wall surfaceand the temperature measurement point because of the unsteadyheat conduction through the wall. In Appendix A, the dampingratio and the time lag of the wall temperature fluctuation observedwhen the surface temperature varies sinusoidally are discussed.Under the oscillation frequency f ¼ 0:83 Hz (i.e., the oscillation fre-quency in this study), the damping ratio and the time lag are sig-nificantly smaller at a depth 0.5 mm from the surface (i.e., thetemperature measuring point). Thus, these can be ignored whendiscussing the relationship between the position of the tip of theliquid column and the channel wall temperatures.

First, THA in the case of xc ¼ 70:5 mm will be discussed. The liq-uid column moved from the heating section to the cooling section(t� � 0:5? 1) and left the liquid film on the channel wall. Asshown in Fig. 4(a), after the liquid column left the liquid film atHA at t� � 0:65; THA did not decrease immediately. The reason isas follows: the degree of superheating at HA is small immediatelyafter the liquid film is left on the channel wall. Subsequently, thesaturated position separated from the HA position (t� � 0:7? 1)when the liquid column moved to the cooling section; that is,the degree of superheating at HA increased. These events explainwhy the wall temperature did not decrease immediately after theliquid film remained on the channel wall. After that, the wall tem-perature decreased (t� � 0:9? 1.1). This is because the evapora-tion of the liquid film on the channel wall of x < xsat made thechannel wall colder. Similarly, the wall temperatures at the H4positions, where x < xsat; decreased due to the evaporation of theliquid film (t� � 0:9? 1.1).

Second, TA1, where x > xsat; will be discussed. When the liquidcolumn moved from the cooling to the heating section and thetip of the liquid column passed position A1, the wall temperaturebegan to decrease (t� � 0:2? 0.7). This is because the channel wallwas cooled by the liquid column owing to the convective heattransfer that occurred once the channel was filled with the liquid.Subsequently, when the liquid column moved from the heating tothe cooling section and the tip of the liquid column passed positionA1, the wall temperature began to increase (t� � 0:7? 1.1). Thisindicated that the condensation of the working fluid vapor madethe channel wall hotter because of the exposure of the liquid filmto the vapor. Similarly, the wall temperatures at the A2 and A3positions, where x > xsat; decreased when the channel was filledwith working liquid at each position where the wall temperaturewas measured, and increased when the liquid film was exposedto the working fluid vapor. On the other hand, the wall tempera-ture at position AC, where x > xsat; did not change. This is becausethe exposure time of the liquid film was too short for the workingfluid vapor to condense onto the liquid film at position AC.

In this manner, when the liquid columnmoves from the heatingto the cooling section and leaves the liquid film on the channelwall, the evaporation begins at x < xsat and the condensationbegins at x > xsat: When the liquid column moves from the coolingto the heating section and fills the channel, the phase changes(evaporation and condensation) on the liquid film are stopped.The liquid column plays the role of a switch for the phase changes.

Fig. 4(b) shows the result under oscillation center xc ¼ 81:8 mmfor the same amplitude and frequency as those in Fig. 4(a). Underthis oscillation condition, the tip of the liquid column in Fig. 4(b)goes back to the cooling section more deeply than that in Fig. 4(a). The wall temperature fluctuations in Fig. 4(b) were roughlythe same as those in Fig. 4(a). However, the wall temperature fluc-tuation at A1 exhibited a characteristic behavior when the liquidcolumn moved from the heating to the cooling section(t� � 0:85). The increase in the wall temperature became approxi-mately zero. The reason for this is as follows. The saturated posi-tion xsat became closer to position A1 and then the degree ofsubcooling decreased. Consequently, the oscillation amplitude ofthe wall temperature fluctuation at A1 of Fig. 4(b) was smaller thanthat of Fig. 4(a).

The results shown in Fig. 4 are consistent with the discussion ofthe wall temperature distribution in Fig. 3. The wall temperaturedistribution in the adiabatic section changed as the oscillation cen-

Transparent polycarbonate plate

wq

The cross-sectional area of copper plate

Wetted perimeter PWall heat

flux

wA

Copper platethickness

Fig. 6. Cross-section view of the channel wall.

ter xc varied. This is because the saturated position xsat; i.e., theboundary between the evaporation and condensation of the work-ing fluid, was changed and the distribution of the phase changealong the channel changed as the oscillation center varied. As theoscillation center moved from the cooling section to the heatingsection, the saturated position moved to the heating section, andfinally condensation occurred in the entire adiabatic section, asshown by the plot for xc ¼ 70:5 mm in Fig. 3. In addition, it wasfound that the evaporation in the heating and adiabatic sectionsof x < xsat; and the condensation in the cooling and adiabatic sec-tions of x > xsat occurred simultaneously on the liquid film, asshown in Fig. 5. As the result, the wall temperatures of x < xsatdecreased and those of x > xsat increased simultaneously, as shownin Fig. 4 (for example, t� � 0:9? 1.1 in Fig. 4(a)). Such heat trans-port caused by the simultaneous evaporation and condensation issimilar to that in wick heat pipes, and the liquid column oscillationplays a role to supply liquid film on the wall.

As discussed in this section, the wall temperature fluctuationsresulted from the heat input and output at the channel wall dueto phase changes and convective heat transfer. In the next section,the heat flux at the inner channel wall is estimated based on thewall temperature fluctuations.

3.3. Wall heat flux fluctuation

In this section, wall heat flux qw, as shown in Fig. 6, is calculatedbased on measured wall temperature fluctuations. In this analysis,it is assumed that the wall temperature is uniform in the cross sec-tion, as was shown in Appendix A, and the one-dimensionalunsteady heat conduction equation along the copper plate is con-sidered as follows:

Awqwcw@Tw

@t¼ Awkw

@2Tw

@x2þ Pqw: ð5Þ

Here, Aw is the area of the copper plate cross-section (8 mm2), P isthe wetted perimeter (6 mm), and qw is the wall heat flux, as shownin Fig. 6. The value of qw is positive when the heat flows into thecopper plate on the inner surface of the channel wall. Accordingto Eq. (5), qw is written as

qw ¼ dþ 2d2

P

!qwcw

@Tw

@t� kw

@2Tw

@x2

!: ð6Þ

Here, d is the thickness of copper plate. Wall temperatures Tw weregiven by the measured temperatures of Fig. 4, assuming that thewall temperature was uniform in the channel wall cross-section.Time derivative was calculated by

@Tw

@t¼ Tnþ1

i � Tn�1i

2Dt: ð7Þ

Here, n is the time step, i is the node number (the position at whichthe temperature was measured), and Dt is the time interval (1=16cycle). The spatial derivative was calculated by

Liquid column

Heating section Cooling section

Vapor flow

Working-fluidevaporation

Working-fluidcondensation

Liquid film

Fig. 5. Phase change on the liquid film.

@2Tw

@x2¼ Tn

iþ1 � 2Tni þ Tn

i�1

Dxð Þ2: ð8Þ

Here, Dx is the interval of the positions of the thermocouples(12.5 mm). The right-hand side of Eq. (6) was evaluated by usingEqs. (7) and (8). The estimation of the wall heat flux qw is ratherrough. In addition, it should be noted that the wall heat flux repre-sents the spatial average of the interval among the adjacent ther-mocouples (Dx ¼ 12:5 mm). However, this estimation helped toclarify the heat input and output on the inner surface of the channelwall.

Fig. 7 shows the temporal change of wall heat flux at the posi-tions of A1, A2, and A3 in the adiabatic section. For each position,time-averaged wall heat flux is shown by the horizontal dot-dashline. The period when the channel is filled with the liquid columnis indicated by filling with light-blue color. Fig. 7(a) shows a case inwhich xc ¼ 70:5 mm and Fig. 7(b) shows a case in whichxc ¼ 81:8 mm: First, the wall heat flux at position A1 in the caseof xc ¼ 70:5 mm (Fig. 7(a)) will be discussed. When the channelwas filled with the liquid column (t� � 0:3? 0.7), the wall heatflux was negative. As mentioned in the previous section, this isbecause the channel wall was cooled by the liquid column due tothe convective heat transfer. Subsequently, when the channelwas not filled with the liquid column, the wall heat flux was gen-erally positive owing to the condensation of the working fluidvapor. However, when the liquid column moved from the coolingsection to the heating section, the wall heat flux became negative(t� � 0:15? 0.3), although the channel was not filled with the liq-uid column. The reason for this is as follows. The working liquidchilled at the cooling section was pushed out to the meniscus ofthe tip of the liquid column when the liquid column moved fromthe cooling section to the heating section. The position of the tipof the liquid column xt represented the bottom of the concavemeniscus of the liquid column. The tip of the meniscus precededthe tip of the liquid column. Thus, the chilled working liquidarrived at A1 before the channel was not filled with the liquid col-umn, and the temperature of the working liquid on the channelwall became lower than that of the channel wall and the heat flo-wed from the channel wall to the liquid film.

Second, the wall heat flux at position A2 will be discussed.When the channel is filled with the liquid column (t� � 0:25?0.75), the wall heat flux was approximately zero. This would indi-cate that the temperature of the liquid column was approximatelyequal to that of the channel wall. As with A1, when the channel isnot filled with the liquid column, the wall heat flux at position A2is generally positive. The maximum of the wall heat flux at positionA2 was larger than that at position A1 because the degree of sub-cooling at A2 was larger than that at A1. On the other hand, the

-25

0

25

0 0.25 0.5 0.75 1 1.25

q w, k

W/m

2

Time t*Time tttt*

-25

0

25

0 0.25 0.5 0.75 1 1.25

q w, k

W/m

2

Time t*Timeeeee t*

-25

0

25

0 0.25 0.5 0.75 1 1.25

q w, k

W/m

2

Time t*

A3

A2

A1

-25

0

25

0 0.25 0.5 0.75 1 1.25

q w, k

W/m

2

Time t*Time t*

-25

0

25

0 0.25 0.5 0.75 1 1.25

q w, k

W/m

2

Time t*Time tttt*

-25

0

25

0 0.25 0.5 0.75 1 1.25

q w, k

W/m

2

Time t*

A3

A2

A1

The channel is filled with liquid column.

(a) Oscillation center xc = 70.5 mm. (b) Oscillation center xc = 81.8 mm.

Fig. 7. The wall heat flux fluctuations in the adiabatic sections (QE ¼ 4:73 W; 2S ¼ 69:5 mm; f ¼ 0:83 Hz).

wall heat flux at position A3 was always positive. This reason is asfollows: when the channel was filled with the liquid column, theoscillating liquid column released heat to the channel wall becausethe temperature of the channel wall was lower than that of the liq-uid column. In addition, when the channel was not filled with theliquid column, the channel wall was heated with the condensationof the working fluid vapor.

Next, the wall heat flux fluctuations in the case of xc ¼ 81:8 mm(Fig. 7(b)) will be discussed. When the channel was not filled withthe liquid column, the wall heat flux at position A1 was positiveonly for a short time (t� � 0:7? 0.8). This reason is as follows:the position A1 was close to the saturated position, as shown inFig. 4(b) and discussed in the previous section. Thus, both the heat-ing due to the condensation and the cooling due to the evaporationof the liquid film affected the channel wall. In addition, as men-tioned above, the wall heat flux represented the spatial averageof the interval among the adjacent thermocouples. These suggestthat the condensation was slightly predominant over the evapora-tion at the neighborhood of position A1. Subsequently, when theliquid column moved from the heating section to the cooling sec-tion and the channel was not filled with the liquid column, the wallheat flux at position A1 became negative (t� � 0:85). This isbecause the evaporation became predominant over the condensa-tion as spatial average at the neighborhood of position A1. The wallheat flux fluctuations at positions A2 and A3 in the case ofxc ¼ 81:8 mm were approximately the same as those in the caseof xc ¼ 70:5 mm; respectively.

In this manner, the estimated wall heat flux confirmed that thewall in the adiabatic section receives or releases heat due to phase-change or convective heat transfer with the liquid columnoscillation.

3.4. Vapor mass fluctuations

In Section 3.2, wall temperature fluctuations were discussedand it was shown that the saturated position plays an importantrole in understanding the phase change associated with the liquidcolumn oscillation. In this section, vapor mass fluctuation due tothe evaporation and condensation will be discussed. Fig. 8 showsthe relationship between the displacement of the tip of the liquidcolumn, the vapor pressure fluctuations, and the vapor mass fluc-

tuations. The vapor pressure was measured at the top of the vaporchamber. The vapor mass was calculated by assuming that theworking fluid vapor was an ideal gas according to

m ¼ PVRT

; ð9Þ

where P is the working fluid vapor pressure, V is the vapor volume,R is the gas constant of the vapor, and T is the vapor temperaturemeasured at the center of the vapor chamber. It should be notedthat the vapor mass fluctuation estimated by Eq. (9) is the net vapormass fluctuation that occurs when evaporation and condensationoccur simultaneously. Fig. 8(a) shows the results forxc ¼ 70:5 mm; and Fig. 8(b) for xc ¼ 81:8 mm: The oscillation ampli-tude and frequency of the liquid column are the same in both Fig. 8(a) and (b).

According to the relationship between the vapor pressure andthe position of the tip of the liquid column in Fig. 8(a) and (b),the working fluid vapor pressure increased as the liquid columnmoved to the heating section because the vapor was com-pressed. Subsequently, the pressure decreased as the liquid col-umn moved to the cooling section because the vapor wasexpanded. The vapor pressure fluctuations resulted from boththe effect of liquid column oscillation (vapor compression andexpansion) and the effect of phase change (evaporation and con-densation). In order to understand the phase change of theworking fluid, the vapor mass fluctuation in Fig. 8(a) is describedin the following paragraph.

The vapor mass decreased when the liquid column moved fromthe heating to the cooling section because the exposure of the liq-uid film in the adiabatic and cooling sections to the working fluidvapor caused the condensation of the vapor onto the liquid film.Conversely, the vapor mass increased when the liquid columnmoved from the cooling to the heating section. The reason for thisis as follows. The liquid film in the heating section continued toevaporate. Meanwhile, the cooling section that contributed to thecondensation of the working fluid vapor was covered with the liq-uid column, which suppressed the condensation of the workingfluid vapor. The vapor mass began to decrease approximately whenxt < xsat at t� � 0:35: This is because the liquid film in the heatingsection that contributed to the evaporation was covered with theliquid column, and the working fluid vapor condensed onto the

Fig. 8. Relationship between the position of the tip of the liquid column, the working fluid vapor pressure, and the vapor mass (QE ¼ 4:73 W; 2S ¼ 69:5 mm; f ¼ 0:83 Hz).

tip of the liquid column (i.e., direct contact condensation [11,15]).When the liquid column moved from the cooling section to theheating section, the liquid chilled by the cooling section waspushed out from the core to the tip of the liquid column, as shownin Fig. 9(a). This promoted the direct contact condensation at thetip of the liquid column. Subsequently, the vapor mass increasedagain when the tip of the liquid column moved from the heatingto the cooling section (t� � 0:5? 0.7) because the evaporating liq-uid film was formed again in the heating section and the directcontact condensation was suppressed. When the liquid columnmoved from the heating to the cooling section, the working liquidheated at the heating section rolled up from the circumference tothe tip of the liquid column, which suppressed the direct contactcondensation at the tip of the liquid column, as shown in Fig. 9(b). The vapor mass fluctuation in Fig. 8(b) was roughly the sameas that in Fig. 8(a), even though the oscillation center was fartherfrom the heating section in Fig. 8(b). However, the mass decrease

Liquid column movesfrom cooling to heating sections.

Heating section Cooling sectionCore of liquid column

(a) Promotion of direct contact condensation.

Fig. 9. Condensation on the t

due to the direct contact condensation DmDCC in Fig. 8(b) wassmaller than that in Fig. 8(a). This would occur because the liquidcolumn covered the heating section for a shorter time, and theevaporation of the liquid film was suppressed shorter as the oscil-lation center increased, that is, more distance from the heating sec-tion. In order to discuss vapor mass fluctuations in detail, the rateof evaporation or condensation must be estimated or measuredbecause, as mentioned above, the estimated vapor mass fluctua-tion is the net vapor mass fluctuation. This is a subject for futurework.

As discussed above, the direct contact condensation affects thevapor pressure, i.e., the saturated position, and the saturated posi-tion affects the liquid film evaporation and condensation. Such anindirect contribution of the direct contact condensation on thelatent heat transport would be important, and the direct contactcondensation would have to be considered for the detailed estima-tion of the latent heat transport.

Liquid column movesfrom heating to cooling sections.

Heating section Cooling section

(b) Suppression of direct contact condensation.

ip of the liquid column.

4. Conclusions

To investigate the thermal-hydraulic phenomena in actual pul-sating heat pipes, the phase changes associated with liquid columnoscillation were investigated experimentally by using an apparatusin which a liquid column was oscillated sinusoidally between heat-ing and cooling sections by forced oscillator under several oscillat-ing conditions. The following conclusions were obtained.

1. When the liquid column moved from the heating to the coolingsection, the wall temperatures in the region of Tw > Tsat (i.e.x < xsat) decreased, and those in the region of Tw < Tsat (i.e.x > xsat) increased simultaneously. From this result, the evapo-ration and condensation of the working fluid occur simultane-ously on the liquid film formed on the channel wall. This heattransport mechanism is similar to that in wick heat pipes.

2. The liquid film plays an important role in latent heat transportbecause the latent heat transport occurs due to the evaporationof the liquid film formed with the liquid column oscillation. Inaddition, the liquid column plays the role of a switch in thephase changes (evaporation and condensation) on liquid filmbecause the phase changes are stopped when the liquid columnfills the channel and start when the liquid column moves fromthe heating to the cooling section and leaves the liquid film onthe channel wall.

3. The vapor mass began to decrease approximately when the liq-uid column began to cover the evaporating liquid film (that is,xt < xsat). This indicates that the working fluid vapor condensesto the tip of the liquid column. This condensation is promotedbecause the cold liquid is pushed out from the core to the tipof the liquid column when the liquid column moves from thecooling to the heating section.

z0

exp iT t

Tz

Temperature measuringpoint in this study

/2

0

ω )(

Fig. A1. Periodic heat conduction in the infinite plate of thickness d.

Fig. A2. Frequency response of

Conflict of interest

None declared.

Appendix A

Consider the periodic heat conduction in the infinite plate of thethickness d, as shown in Fig. A1. The heat conduction equation withno heat generation is

@T@t

¼ a@2T@z2

: ðA1Þ

Here, the temperature of the surface at z ¼ 0 varies sinusoidally,and the surface of z ¼ d is insulated, that is, the boundary conditionsare

Tjz¼0 ¼ exp ixtð Þ ðA2Þ

@T@z

����z¼d

¼ 0: ðA3Þ

Here, i is imaginary unit, x is angular frequency, and t is time.Assuming that the solution of the differential equation is written as

T z; tð Þ ¼ / zð Þ exp ixtð Þ; ðA4Þ

the function / is

/ zð Þ ¼ exp �b � z=dð Þ þ exp �2bð Þ � exp b � z=dð Þ1þ exp �2bð Þ ; ðA5Þ

where b is

b ¼ 1þ iffiffiffi2

pffiffiffiffiffiffiffiffiffixd2

a

s: ðA6Þ

Eq. (A4) is rewritten as

T z; tð Þ ¼ / zð Þj j exp i xt � hð Þ½ � ðA7Þ

where / zð Þj j is the damping ratio and h is the time lag. Note that h isa function of z. Based on the above analysis, the frequency responsefor a copper plate with a thickness d ¼ 1 mm can be obtained.Fig. A2 shows the frequency response at the position of the temper-ature measurement (z ¼ 0:5 mm) and the end of the plate(z ¼ 1 mm).

cyclic thermal conduction.

References

[1] A. Danowitz, K. Kelley, J. Mao, J.P. Stevenson, M. Horowitz, CPU DB: Recordingmicroprocessor history, Commun. ACM 55 (4) (2012) 55–63.

[2] H. Akachi, F. Polášek, P. Štulc, Pulsating heat pipes, in: J. Andrews, A.Akbarzadeh, I. Sauciuc (Eds.), Proceedings of the 5th International Heat PipeSymposium, 1997, pp. 208–217.

[3] Y. Zhang, A. Faghri, Advances and unsolved issues in pulsating heat pipes, HeatTransf. Eng. 29 (1) (2008) 20–44.

[4] X. Tang, L. Sha, H. Zhang, Y. Ju, A review of recent experimental investigationsand theoretical analyses for pulsating heat pipes, Frontiers in Energy 7 (2)(2013) 161–173.

[5] X. Han, X. Wang, H. Zheng, X. Xu, G. Chen, Review of the development ofpulsating heat pipe for heat dissipation, Renew. Sustain. Energy Rev. 59 (2016)692–709.

[6] T. Nagasaki, Y. Shimazaki, Y. Ito, S. Hojo, Fundamental study on heat transportin pulsating heat pipe using a straight rectangular channel, in: Proceedings ofthe 7th JSME-KSME Thermal and Fluids Engineering Conference, 2008, p. B141.

[7] S.P. Das, V.S. Nikolayev, F. Lefèvre, B. Pottier, S. Khandekar, J. Bonjour,Thermally induced two-phase oscillating flow inside a capillary tube, Int. J.Heat Mass Transf. 53 (19–20) (2010) 3905–3913.

[8] R.T. Dobson, Theoretical and experimental modelling of an open oscillatoryheat pipe including gravity, Int. J. Therm. Sci. 43 (2) (2004) 113–119.

[9] R.T. Dobson, An open oscillatory heat pipe water pump, Appl. Therm. Eng. 25(4) (2005) 603–621.

[10] M. Rao, F. Lefèvre, S. Khandekar, J. Bonjour, Understanding transportmechanism of a self-sustained thermally driven oscillating two-phasesystem in a capillary tube, Int. J. Heat Mass Transf. 65 (2013) 451–459.

[11] M. Rao, F. Lefèvre, S. Khandekar, J. Bonjour, Heat and mass transfermechanisms of a self-sustained thermally driven oscillating liquid–vapourmeniscus, Int. J. Heat Mass Transf. 86 (2015) 519–530.

[12] M. Rao, F. Lefèvre, P.C. Czujko, S. Khandekar, J. Bonjour, Numerical andexperimental investigations of thermally induced oscillating flow inside acapillary tube, Int. J. Therm. Sci. 115 (2017) 29–42.

[13] S. Kato, K. Okuyama, T. Ichikawa, S. Mori, A single, straight-tube pulsating heatpipe (Examination of a mechanism for the enhancement of heat transport), Int.J. Heat Mass Transf. 64 (2013) 254–262.

[14] R. Ishida, Y. Youn, K. Muramatsu, K. Kohara, Y. Han, N. Shikazono, Heat transferand flow characteristics of thermally induced two-phase oscillating flow inmicro tubes, J. Therm. Sci. Technol. 11 (3) (2016) 1–16.

[15] M. Miura, T. Nagasaki, Y. Ito, Experimental investigation of heat transport withoscillating liquid column in pulsating heat pipe using forced oscillationsystem, Int. J. Heat Mass Transf. 106 (2017) 997–1004.