M. Miura, T. Nagasaki, Y. Ito, “Experimental investigation of heat transport with

oscillating liquid column in pulsating heat pipe using forced oscillation system”,

International Journal of Heat and Mass Transfer, 106, pp.997-1004 (Mar 2017)(Elsevier)

Experimental investigation of heat transport with oscillating liquidcolumn in pulsating heat pipe using forced oscillation system

⇑ Corresponding author.E-mail address: miura.m.ah@m.titech.ac.jp (M. Miura).

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

a Tokyo Institute of Technology, Department of Energy Sciences, 4259-G3-33 Nagatsuta-cho, Midori-ku, Yokohama 226-8502, Japanb Tokyo Institute of Technology, Department of Mechanical Engineering, 4259-G3-33 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:Pulsating heat pipeSensible heatLatent heatLiquid filmVapor-mass fluctuation

To clarify the detailed heat-transport mechanism of a pulsating heat pipe, an experimental study wasconducted using a forced oscillation system. A liquid column was oscillated in a channel for a single-component (liquid ethanol and vapor ethanol) system and a two-component (liquid ethanol and air) sys-tem. In the single-component system, the sensible heat transport due to the oscillating flow and thelatent heat transport due to the phase change occurred simultaneously because the gas phase consistedof only working-fluid vapor. In the two-component system, only sensible heat transport occurred,because the gas phase consisted of air at the atmospheric pressure. The effective thermal conductivityof the latent heat transport was determined according to the difference in effective thermal conductivitybetween the single-component system and the two-component system. The effective thermal conductiv-ity of the sensible heat transport increased monotonically as the oscillation center moved to the heatingsection under the same amplitude and frequency. On the other hand, the effective thermal conductivityof the latent heat transport increased as the oscillation center moved to the cooling section under thesame amplitude and frequency until the tip of the oscillating liquid column reached the heating section.The vapor-mass fluctuation was estimated according to the measurement of the vapor-pressure fluctua-tion in the single-component system. The results show that the liquid film formed by the oscillating liq-uid column played an important role in the mechanism of the latent heat transport. They also show thatthe direct-contact condensation from the working-fluid vapor to the tip of the liquid column occurredwhen the liquid column moved from the cooling section to the heating section.

1. Introduction

Small and highly efficient heat-transport devices are needed tocool semiconductor chips with the increase in the power dissipa-tion. Heat pipes are among these heat-transport devices. Amongthe various types of heat pipes, wick heat pipes and ther-mosyphons are typically used [1]. These heat pipes use the latentheat of the evaporation and condensation of the working fluid forheat transport. Pulsating heat pipes (PHPs), which were originallyproposed by Akachi et al. [2], have a different heat-transport mech-anism from conventional heat pipes such as wick heat pipes andthermosyphons and have attracted considerable attention as anew type of high-performance and simple-structure heat-transport device [3]. A PHP consists of a single meandering capil-lary tube between a heating section and cooling section, as shownin Fig. 1(a). The tube is evacuated and partially filled with working

fluid. Several liquid columns are formed by surface tension. Thepressure difference between the heating section and cooling sec-tion causes the oscillation of the liquid columns.

PHPs have been widely investigated, ranging from fundamentalstudies for understanding the operating mechanism to appliedstudies for improving the heat-transport performance. Because thispaper focuses on the heat-transport mechanism, the fundamentalstudies are surveyed as follows. To observe the behavior of theworking fluid in the tube, numerous experimental studies usingtransparent glass tubes have been conducted. In a visualizationexperiment using a glass tube, Hosoda et al. [4] and Nishio et al.[5] observed the vapor-liquid two-phase flow in the tube using ahigh-speed video camera. They observed simple periodic flow pat-terns at a high filling ratio of the working fluid and estimated thelatent heat-transport rate with the phase change of the workingfluid according to the fluctuation of the length of the vapor plug.Shafii et al. [6] proposed a simple mathematical model for the flowof liquid slugs and vapor plugs in PHPs. They assumed that theevaporation and condensation heat-transfer coefficients were

(b) One-turn PHP. (c) Straightened one-turn PHP.

Forced oscillate

Liquid column is oscillated forcedly.

(d) Half-turn PHP with forced oscillation.

Heating section

Cooling section

(a) Usual PHP.

Cut Straighten

Working-fluid liquidGas

Bellows OscillatorLiquid column oscillates self-exitedly.

Fig. 1. Schematic of the experimental method used in the present study.

Nomenclature

A cross section (m2)f oscillation frequency (Hz)k thermal conductivity (W/m�K)m mass (kg)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)

Greekc specific-heat ratio (–)H dimensionless wall temperature (–)

Subscriptad adiabatic changeav averagec centercond heat conductionE electrical input power of heatereff effectivesat saturatedt tip of liquid columnw channel wall

constant. Zhang et al. [7] improved the model proposed by Shafiiet al. [6]. The improved model includes an analysis of thin-filmevaporation and condensation. Shafii et al. [6] and Zhang et al.[7] reported that the heat transfer in PHPs is mainly due to sensibleheat transport. Dobson [8,9] studied the mechanism of a PHP withopen ends using a simple model that considers the effect of the liq-uid film. In this model, the thickness of the liquid film and theheat-transfer coefficient of the phase change are regarded as con-stants. Das et al. [10] presented experimental data for a simplePHP comprising a capillary tube connected to a reservoir and pro-posed a film evaporation-condensation model to account for thetwo-phase equilibrium at the vapor-liquid interface. They com-pared experimental results with numerical results based on thefilm evaporation-condensation model. In addition, Nikolayev [11]applied the film evaporation-condensation model to simulate amulti-turn PHP. Rao et al. [12,13] reported data obtained withthe improved experimental setup that was originally proposedby Das et al. The tube was fully transparent to observe the motionof the entire liquid film. This enabled an understanding of the com-plex liquid-film evaporation and condensation. Kato et al. [14]experimentally investigated heat transport in a PHP of a singlestraight tube with a liquid reservoir at the cooling section. Theycharacterized the heat-transport mechanism by three factors: (a)the latent heat transport caused by the condensation on the liquidfilm, (b) the heat diffusion induced by the oscillating liquid col-umn, and (c) the liquid exchange between the heat-transport tubeand the liquid reservoir. In addition, Nagasaki et al. [15] reportedthe relationship between the vapor-pressure fluctuations andliquid-column oscillation in the case of a straight-channel PHPwith the cooling section at the center of the channel and the heat-ing sections at the both ends of the channel. This is the simplestsingle-turn PHP, as shown in Fig. 1(c).

As mentioned in the previous paragraph, although severalstudies have been conducted with both experimental and numer-ical approaches, the operating mechanism and heat-transport

mechanism of PHPs have not been sufficiently clarified [16]. Thisis because PHPs have complex thermal hydraulic phenomenadespite their simple structure. Zhang et al. [17] mentioned the rel-ative magnitude of the sensible heat transport and latent heattransport as one of the unresolved issues affecting the performanceof PHPs. Here, the sensible heat transport is based on convectiveheat transfer between the wall and the working fluid; that is, theoscillating working fluid receives heat from the channel wall inthe heating section and releases heat to the channel wall in thecooling section. The latent heat transport is based on the phasechange of the working fluid, such as evaporation mainly in theheating section and condensation mainly in the cooling section.Understanding the roles of the sensible heat and the latent heathelps to clarify the details of the heat-transport mechanism, selectthe optimum working fluid, and obtain guidelines for the improve-ment of the heat-transport performance. However, only a fewstudies have reported the contribution of the sensible heat andlatent heat in the heat transport of PHPs. It was reported that thesensible heat transport is the majority of the overall heat transportin PHPs by an experimental study [5] and numerical studies [6,7].This means that the contribution of the latent heat to the heattransport of PHPs is small and that the role of the evaporationand the condensation of the working fluid is mainly to oscillatethe liquid slugs. On the other hand, it was mentioned that the con-tribution of the latent heat to the overall heat transport depends onthe flow patterns [18]. It was suggested that the latent heat trans-port plays a significant role under an annular flow. This suggeststhe possibility that the long liquid film between the heating sectionand the cooling section observed in later studies [10,12–14] plays asignificant role in the latent heat transport. As previously men-tioned, the contribution of the sensible heat transport and latentheat transport in PHPs has not yet been clearly clarified. Therefore,further experimental studies are needed in order to clarify the rolesof the sensible heat and latent heat in the heat transport of PHPsunder various conditions.

In this paper, the contribution of the sensible heat transport andlatent heat transport in oscillating working fluid was evaluatedexperimentally by oscillating the liquid column in a channel hav-ing a heating section and cooling section, as shown in Fig. 1(d).The sensible heat transport and latent heat transport were esti-mated by a comparison with the single-component system, wherethey occur simultaneously, and the two-component system, whereonly the sensible heat transport occurs. Using a forced oscillationsystem made it possible to clarify the parameter dependence ofthe sensible heat transport and latent heat transport. For example,the relationship between the latent heat transport and the oscilla-tion frequency was clarified. In addition, the phase-change behav-ior of the working fluid was understood according to the vapor-mass fluctuation estimated using the measured vapor-pressurefluctuation.

2. Experimental setup and procedures

Fig. 2 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 for visualizingthe movement of the working-fluid in the channel. The channelin the heating section (length 50 mm) was heated with cartridgeheaters. The channel in the adiabatic section (length 50 mm) waspressed against Bakelite block. The channel in the cooling section(length 60 mm) was cooled by cooling water, and the temperaturewas maintained at �30 �C. The wall temperatures were measuredby T-type thermocouples with a wire diameter of 0.1 mm at adepth of 0.5 mm from the outer surface. The position xwas definedas the distance measured from the end of the heating sectiontoward the cooling section. A vapor chamber (volume 5.6 cm3)was connected to the channel at the end of the heating section inorder to make the compression ratio of gas as small as that inactual PHPs. The vapor chamber was heated with a tape heaterwound on the outer surface of the chamber in order to prevent

Working-fluid vapor in the single-component systeAir in the two-component system

x

Pressure transducer

Heater

Vapor Chamber

Copper platewith a square chan

50 50Heatingsection

Adiabaticsection

[ : Thermocouple]

4

3 Square channel

H1 H2 H3 H4 HA A1 A2 A3 AC C

xt

Valve

Fig. 2. Experime

working-fluid vapor from condensing in the vapor chamber. Thegas pressure was measured at the end of the vapor chamber. Thegas temperature was measured at the center of vapor chamber.The oscillator, which was composed of a piston-crank mechanism,was connected to the channel at the end of the cooling section viabellows. It oscillated working fluid sinusoidally in the channel. Theposition of the tip of the liquid column (i.e., the vapor-liquid inter-face), which is denoted as xt, was measured using images capturedby a high-speed video camera. The oscillation amplitude 2S wasdefined as the difference between the maximum and minimumvalues of xt. The oscillation center xc was defined as the averageof the maximum and minimum values of xt.

The working fluid in the channel was oscillated sinusoidallyunder two conditions: the ‘‘single-component system” and ‘‘two-component system,” in order to experimentally evaluate the sensi-ble heat transport and latent heat transport. In the single-component system, the channel was initially evacuated after thevalve at the end of chamber was closed, and then the working fluidwas charged. Ethanol degassed by boiling was used as the workingfluid. In the single-component system, sensible heat transport andlatent heat transport occurred simultaneously because the gasphase consisted of only the working-fluid vapor. This system corre-sponds to the thermal hydraulic phenomena in actual PHPs. In thetwo-component system, the working fluid was charged under theatmospheric pressure after the valve at the end of the chamberwas opened, and then the valve was closed after the working fluidwas charged. In the two-component system, only sensible heattransport occurred, because the gas phase consisted of air at theatmospheric pressure; the latent heat transport was negligible.

The experiments were conducted under various oscillation cen-ters of the tip of the liquid column and oscillation frequencies. Themeasurements of the temperature and vapor pressure and the cap-ture of images by the high-speed video camera were synchronizedby using a trigger signal. The heat loss to the ambient environmentwas previously estimated from the difference between the heaterinput power and the heat-transport rate without filling the work-

m /Liquid column

Transparentpolycarbonate platenel

60Coolingsection

Workingfluid

Vacuumpump

Piston-crankmechanism

[Unit: mm]

Bellows

1 C2 C3 C4

ntal setup.

ing fluid in the channel. In this case, the heat transport was onlydue to the heat conduction at the wall, and the heat-transport ratewas estimated according to the wall temperature gradient in theadiabatic section. The total heat-transport rate was calculated bysubtracting the estimated heat loss from the heater input power.

3. Experimental results and discussion

3.1. Wall-temperature distribution

Fig. 3 shows the wall-temperature distributions in the single-component and two-component systems under the same condi-tions of the heater input power QE, oscillation amplitude 2S, oscil-lation center xc, and the oscillation frequency f. As shown in Fig. 3,the results obtained in vacuum show the wall-temperature distri-bution without the working fluid. The heat transport was only dueto the heat conduction along the copper channel wall. The heating-section temperature in the two-component system was lower thanthat in the vacuum because the oscillating working fluid conductedsensible heat transport. Here, sensible heat transport means thatthe oscillating working fluid receives heat in the heating section,moves to the cooling section, and then releases heat in the coolingsection. The heating-section temperature in the single-componentsystem was lower than that in the two-component system: that is,the single-component system had a higher heat-transport perfor-mance than the two-component system. This is because both sen-sible heat transport and latent heat transport occurred in thesingle-component system, whereas only sensible heat transportoccurred in the two-component system. Here, latent heat transportmeans that the working fluid receives heat in the heating sectionand a part of the adiabatic section as evaporation heat, flows tothe cooling section, and then releases heat in the cooling sectionand a part of the adiabatic section as condensation heat. In Fig. 3,the time average of the vapor pressure, Pav, in the single-component system and the saturated temperature for the pressure,Tsat (Pav), are shown. The saturated temperature is also shown bythe horizontal dashed line. The working fluid evaporates in theregion of the channel wall where Tw > Tsat, and the working-fluidvapor condenses in the region of the channel wall where Tw < Tsat.According to Fig. 3, it was found that both the evaporation and con-densation occurred in the adiabatic section.

Fig. 3. Wall-temperature distribution.

Fig. 4(a) shows the wall-temperature distributions in the adia-batic section. The oscillation condition in Fig. 4(a) was the sameas that in Fig. 3. To clarify the difference in the wall-temperaturedistribution between the single-component and two-componentsystems, the dimensionless wall temperature was defined by usingthe temperatures at the both ends of the adiabatic section, asfollows:

HðxÞ ¼ TðxÞ � TAC

THA � TAC; ð1Þ

where THA is the temperature at the boundary between the heatingsection and the adiabatic section, and TAC is the temperature at theboundary between the adiabatic section and the cooling section.The dashed line in Fig. 4(a) shows the wall-temperature distributionfor the heat conduction along the copper channel wall. The dimen-sionless wall-temperature distribution in the single-componentsystem was convex upward compared with that of the wall heatconduction. This is because the channel wall in the adiabatic sectionwas mainly heated by the condensation of vapor that was generatedby the evaporation of a liquid film in the heating section that wasformed with the movement of the liquid column from the heatingsection to the cooling section. In this oscillation condition, the chan-nel wall in the adiabatic section was also partially cooled by theevaporation of the liquid film. However, the area of the adiabaticsection where the evaporation occurred was smaller than thatwhere the condensation occurred because the position of the chan-nel wall in the adiabatic section at Tw = Tsat was closer to the heatingsection. Consequently, the channel wall in the adiabatic section wasmainly heated by the condensation. The heat transported from theheating section to the adiabatic section by the working-fluid phasechange was transported from the adiabatic section to the coolingsection by the sensible heat transport of the oscillated liquid col-umn. In this way, the adiabatic section plays an important role inthe increase of heat transport by the phase change. In addition, itwas found by using the high-speed video camera that the liquid filmwas formed on the channel wall between the position where theliquid column entered the heating section most deeply and theposition where the liquid column receded to the cooling sectionmost deeply. Consequently, the length of the liquid film was nearlyequal to the oscillation amplitude. Such a liquid film was alsoobserved in previous studies [10,12–14]. On the other hand, thedimensionless wall-temperature distribution in the two-component system was convex downward compared with that ofthe wall heat conduction. This is because the channel wall wascooled by the liquid-column oscillation with sensible heat transport(i.e., the dream pipe effect [19,20]).

Fig. 4(b) shows the dimensionless wall-temperature distribu-tions in the adiabatic section for various oscillation centers in thesingle-component system. The dashed line in Fig. 4(b) is the sameas that in Fig. 4(a). The dimensionless wall-temperature distribu-tions changed as the oscillation center varied. At xc = 69.2 mm,i.e., closer to the heating section, the dimensionless wall-temperature distribution was overall convex upward comparedwith that of the wall heat conduction. This suggests that the chan-nel wall was heated by the condensation of the working-fluidvapor, as discussed in the previous paragraph. On the other hand,the conditions at xc = 80.1 and 90.7 mm were closer to the coolingsection. In these conditions, the dimensionless wall-temperaturedistribution was convex downward in the region of the adiabaticsection closer to the heating section and convex upward in theregion of the adiabatic section closer to the cooing section com-pared with that of the wall heat conduction. This suggests thatthe channel wall closer to the heating section was cooled by theevaporation of the working-fluid liquid film and the channel wallcloser to the cooling section was heated by the condensation ofthe working-fluid vapor. The boundary between the evaporation

Fig. 4. Dimensionless wall temperature.

Fig. 5. Relationship between the effective thermal conductivity and the oscillationcenter.

and the condensation is discussed in detail in Section 3.4 withrespect to the measurement of the working-fluid vapor pressure.The dimensionless wall-temperature distributions in the two-component system were convex downward compared with thatof the wall heat conduction for all oscillation centers. In contrastto the single-component system, the dimensionless wall-temperature distributions in the two-component system did notchange significantly.

3.2. Effective thermal conductivity

The heat-transport performance was evaluated according to therate of the heat transport from the heating section to the coolingsection and the temperature difference between the heating sec-tion and cooling section. In this study, the heat-transport perfor-mance was estimated by using the effective thermal conductivityof the oscillating working fluid, which is defined as

keff ¼ ðQ total � Q condÞ � LeffA � DT ; ð2Þ

where Qtotal is the total heat-transport rate, Qcond is the heat-transport rate caused by heat conduction through the channel wall,Leff is the effective length of the heat pipe (the distance betweenposition H3 in the heating section and position C2 in the coolingsection, as shown in Fig. 2), A is the cross section of the channel,and DT is the temperature difference between thermocouple H3in the heating section and thermocouple C2 in the cooling section.The heat-transport rate caused by heat conduction through thechannel wall was estimated according to the wall temperature gra-dient in the adiabatic section:

Q cond ¼ AwkwTHA � TAC

Lad; ð3Þ

where Aw is the cross section of the channel wall, kw is the thermalconductivity of the channel wall, and Lad is the length of the adia-batic section. The effective thermal conductivity of the latent heattransport keff,latent was defined by Eq. (4) as the difference betweenthe effective thermal conductivity in the single-component system,keff,single, where both sensible heat transport and latent heat trans-port occurred, and that in the two-component system, keff,two,where only sensible heat transport occurred.

keff;latent ¼ keff;single � keff;two ð4ÞHere, there is a possibility that the process of the latent heat trans-port affects the sensible heat transport in the single-component

system. For example, as was discussed according to Fig. 4(a), thecondensation to the liquid film of the adiabatic section enhancesthe sensible heat transport of the liquid column. However, it wasdifficult to evaluate the effects of the latent heat transport on thesensible heat transport in the single-component system precisely.Consequently, the effective thermal conductivity of the latent heattransport, keff,latent, signifies how much the effective thermal con-ductivity in the single-component system increases owing to thephase change of the working fluid as compared with the effectivethermal conductivity of the sensible heat transport in the two-component system under the same oscillation conditions.

Fig. 5 shows the relationship between the oscillation center andthe effective thermal conductivity for the single-component sys-tem and two-component system under the same conditions ofthe heater input power QE, oscillation amplitude 2S, and oscillationfrequency f. In addition, Fig. 5 also shows the relationship betweenthe oscillation center and the effective thermal conductivity of thelatent heat transport calculated by Eq. (4). Because the oscillationamplitude was fixed, the tip of the liquid column oscillated inthe region closer to the cooling section as the oscillation centerxc increased. In the two-component system, i.e., sensible heat

Fig. 7. Relationship between the effective thermal conductivity and the oscillationamplitude.

transport, the effective thermal conductivity keff,two decreased asthe oscillation center moved to the cooling section, because theshorter residence time of the liquid column in the heating sectionreduced the heat exchange between the channel wall and the liq-uid column. On the other hand, in the latent heat transport, theeffective thermal conductivity keff,latent increased as the oscillationcenter moved to the cooling section until xc reached �80 mm. Thisis because the cooling section exposed to the working-fluid vaporbecame longer, and the condensation was enhanced. However,for xc > 80 mm, the effective thermal conductivity of latent heattransport decreased as the oscillation center xc increased, becausethe tip of the liquid column did not reach the heating section. Theeffective thermal conductivity in the single-component system,which corresponds to actual PHPs, was maximized when the oscil-lation center was close to the adiabatic section center. This indi-cates that the heat-transport rate of actual PHPs is maximized ata working-fluid filling ratio of �50% when the heating sectionand cooling section are equal in length.

Fig. 6 shows the relationship between the effective thermal con-ductivities and the oscillation frequency under the same oscillationamplitude and oscillation center. In each experiment run, the oscil-lation centers were altered under a fixed oscillation frequency, asshown in Fig. 5, and it was difficult to adjust the oscillation centerxc precisely to a specified position. Consequently, the effectivethermal conductivities at xc = 75 mm, shown in Fig. 6, was esti-mated by using linear interpolation for the oscillation centers. Inthe two-component system, i.e., sensible heat transport, the effec-tive thermal conductivity increased monotonically as the oscilla-tion frequency increased. This is because the heat exchange ofthe liquid column in heating section and cooling section per unittime increased as the oscillation frequency increased. On the otherhand, in the latent heat transport, the effective thermal conductiv-ity decreased monotonically as the oscillation frequency increased.This is because the fast movement of the vapor-liquid interface at ahigh oscillation frequency makes the liquid film remaining on thechannel thicker [21,22], resulting in the lower heat transfer coeffi-cients of vaporization and condensation. Consequently, the effec-tive thermal conductivity of the latent heat transport decreases.In the oscillation conditions of this experiment, the average ofthe liquid film thickness was estimated to be 70 lm(f = 1.34 Hz)–99 lm (f = 3.02 Hz) according to the correlation[22]. The measurement of the liquid film thickness formed withthe liquid column oscillation should be conducted in the future.

Fig. 6. Relationship between the effective thermal conductivity and the oscillationfrequency.

Fig. 7 shows the relationship between the effective thermal con-ductivities and the oscillation amplitude under the same oscilla-tion frequency and oscillation center. In the latent heat transport,the effective thermal conductivity increased monotonically as theoscillation amplitude became larger, because the liquid film thatcontributed the evaporation and condensation became longer. Inthe two-component system, i.e., the sensible heat transport, theeffective thermal conductivity increased as the oscillation ampli-tude became larger, because the liquid column more deeplyentered the heating and cooling sections.

3.3. Vapor-pressure fluctuations

Fig. 8 shows the fluctuation of the vapor pressure P and theposition of the tip of the liquid column xt in the single-component system for a heat-transport rate of Qtotal = 2.78W, anoscillation amplitude of 2S = 73.1 mm, an oscillation center ofxc = 90.7 mm, and an oscillation frequency of f = 1.81 Hz. The tipof the liquid column was located in the heating section forxt � 50 mm, in the adiabatic section for 50 mm � xt � 100 mm,and in the cooling section for xt � 100 mm. Fig. 8 shows thefluctuation of adiabatic pressure Pad, which was calculatedtheoretically by assuming the adiabatic compression and expan-sion of the vapor by the oscillation of the liquid column, on thebasis of the following equation:

PadðtÞ ¼ PavVc

VðtÞ� �c

; ð5Þ

where Pav is the time average of the vapor pressure P, V is the vaporvolume, Vc is the vapor volume when the tip of the liquid column isat the oscillation center, and c is the specific-heat ratio of theworking-fluid vapor.

As seen in Fig. 8, the oscillation amplitude of the measuredvapor pressure Pwas larger than that of adiabatic pressure Pad. Thisindicates the effect of the phase change of the working fluid. Thevapor pressure P was lower than the adiabatic pressure Pad whenthe tip of the liquid column moved in the cooling section. Thisshows that the condensation of the working-fluid vapor was pre-dominant because the cooling section was exposed to the vapor.On the other hand, the vapor pressure P was higher than the adia-batic pressure Pad when the tip of the liquid column moved in the

Fig. 8. Vapor-pressure fluctuation.

adiabatic section and the heating section. This shows that theevaporation of the working fluid was predominant because the liq-uid column covered the cooling section and suppressed the con-densation of the working-fluid vapor while evaporation occurredcontinuously from the liquid film in the heating section.

3.4. Vapor-mass fluctuations

The fluctuations of the vapor pressure indicate the effects ofboth the vapor compression/expansion with the liquid-columnoscillation and the evaporation/condensation of the working-fluidphase change, as discussed in the previous section. Fig. 9 showsthe fluctuations of the vapor mass, which was calculated by assum-ing that the working-fluid vapor was an ideal gas with

m ¼ PVRT

; ð6Þ

where P is the measured vapor pressure, V is the vapor volume, R isthe gas constant of the working-fluid vapor, and T is the tempera-ture of the vapor measured at the center of the vapor chamber.The vapor-mass fluctuation estimated by Eq. (6) is the netvapor-mass fluctuation when the evaporation and the condensationoccur simultaneously. The saturated position xsat, shown in Fig. 9,denotes the position where the local channel wall temperature Twis equal to the saturated temperature for the working-fluid vaporpressure Tsat (P). The saturated temperature was calculated accord-

0

5

10

15

2

2.1

2.2

2.3

2.4

2.5

0 0.2 0.4 0.6 0.8 1

x

Vap

or m

assm

, mg

Time t , s

50

0

100

150

Posi

tion

x, m

m

xt

xc

m

mav

xsat

(a) xc = 90.7 mm.

Fig. 9. Vapor-mas

ing to the vapor pressure shown in Fig. 8. The working fluid evapo-rates in the region of x < xsat (Tw > Tsat) and condenses in the regionof x > xsat (Tw < Tsat).

Fig. 9(a) shows the vapor-mass fluctuation for xc = 90.7 mm cor-responding to Fig. 8. The vapor mass decreased when the liquidcolumnmoved from the heating section to the cooling section. Thisis because the exposure of the liquid film in the cooling section tothe working-fluid vapor caused the condensation of the working-fluid vapor to the liquid film, as shown in Fig. 10(a). On the otherhand, the vapor mass increased when the liquid column movedfrom the cooling section to the heating section, as shown inFig. 9(a). This is because the condensation of the working-fluidvapor was suppressed, as the cooling section that contributed tothe condensation of the working-fluid vapor was covered withthe liquid column, while the liquid film at the heating section con-tinued to evaporate.

Fig. 9(b) shows the vapor-mass fluctuation in the case wherethe oscillation center was closer to the heating section than thatshown in Fig. 9(a), i.e., the tip of the liquid column deeply enteredthe heating section. The vapor mass increased when the liquid col-umn moved from the cooling section to the heating section anddecreased when it moved from the heating section to the coolingsection, as shown in Fig. 9(a). On the other hand, Fig. 9(b) showsthat the vapor-mass fluctuation exhibited a peculiar behaviorwhen the tip of the liquid column was in the heating section (i.e.,xt � 50 mm). The vapor mass began to decrease when xt was smal-ler than xsat. This is because the liquid film in the heating sectionthat contributed to the evaporation was covered with the liquidcolumn, and the working-fluid vapor condensed to the tip of liquidcolumn, as shown in Fig. 10(b). This condensation is called direct-contact condensation hereinafter. When the liquid column movedfrom the cooling section to the heating section, the cold liquid waspushed out from the center to the tip of the liquid column. Thispromoted the direct-contact condensation at the tip of liquid col-umn. The decrease of vapor mass with the direct-contact conden-sation became remarkable as the oscillation center xc decreased,that is, the tip of the liquid column entered the heating sectiondeeply. This is because the evaporation of the liquid film was sup-pressed as the residence time of the tip of the liquid column thatcovered the heating section increased. The working-fluid vapormass increased again when the tip of the liquid column movedfrom the heating section to the cooling section. This is becausethe evaporating liquid film was formed again in the heating sectionwhen the liquid column moved from the heating section to thecooling section.

0

5

10

15

2.7

2.8

2.9

3

3.1

3.2

0 0.2 0.4 0.6 0.8 1

x

Vap

or m

assm

, mg

Time t , s

50

0

100

150

Posi

tion

x, m

m

(b) xc = 69.2 mm.

xtxc

m

mav

xsat

The effect of directcontact condensation

s fluctuation.

(a) Film condensation. (b) Direct contact condensation.

Direct contactcondensation

Evaporation issuppressed.

Evaporation

Heating section Adiabatic section

Liquid film

The liquid columnmoves from theadiabatic section tothe heating section.

The liquid columnmoves from theadiabatic section tothe cooling section.

Liquid film

Adiabatic section Cooling section

Vapor flow Condensation

Liquid column

Fig. 10. Relationship between the liquid-column movement and the phase change of the working fluid.

4. Conclusions

The contribution of the sensible heat transport and latent heattransport in an oscillating working fluid was experimentally inves-tigated. In addition, the vapor-mass fluctuation was estimated bymeasuring the vapor-pressure fluctuation in a single-componentsystem. The following conclusions were drawn.

1. The wall-temperature distribution in adiabatic section of thesingle-component system was convex upward compared withthat of only the wall heat conduction. This shows that theworking-fluid vapor condensed on the channel wall in the adi-abatic section. On the other hand, the wall-temperature distri-bution in the two-component system in the adiabatic sectionwas convex downward compared with that of only the wallheat conduction. This shows that the channel wall in the adia-batic section was cooled by the liquid-column oscillation withsensible heat transport.

2. The effective thermal conductivity in the single-component sys-tem was maximized when the oscillation center was close tothe center of the adiabatic section. This indicates that theheat-transport rate of actual PHPs is maximized at a working-fluid filling ratio of �50% when the heating section and coolingsection are equal in length. The effective thermal conductivityof the sensible heat transport increased monotonically as theoscillation center moved to the heating section under the sameoscillation amplitude and oscillation frequency. On the otherhand, the effective thermal conductivity of the latent heattransport increased as the oscillation center moved to the cool-ing section until the tip of liquid column reached the heatingsection.

3. The effective thermal conductivity of sensible heat transportincreased monotonically as the oscillation frequency increasedunder the same oscillation center and oscillation amplitude.On the other hand, the effective thermal conductivity of latentheat transport decreased as the oscillation frequency increased.This is because the thickness of the liquid film that evaporated inthe heating section increased as the liquid columnmoved faster.

4. The oscillation amplitude of the measured vapor pressure is lar-ger than that of the adiabatic pressure that assumes adiabaticchange of the vapor, because of the effects of the evaporationand condensation of the working fluid. The relationshipbetween the vapor pressure and the position of the tip of theliquid column shows that the liquid film played an importantrole in the latent heat transport. The vapor-mass fluctuationwas estimated according to the measured vapor-pressure fluc-tuation. The results indicate that direct-contact condensationfrom the vapor to the tip of the liquid column occurred whenthe tip of the liquid column moved from the cooling sectionto the heating section.

Conflict of interest

None declared.

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