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Oscillating Characteristics of Slug Flow in Oscillating Heat Pipes

Shibin Liang Ian Wark Research Institute ,University of South Australia, Adelaide, South Australia 5062

Self-sustainable oscillating motions of the slug flow in oscillating heat pipes have been investigated in the paper. A mass-spring model in the adiabatic section of the heat pipe under the exciting sources in its evaporator and condenser is applied to describe the oscillating characteristics of the two-phase flow in the serpentine capillary channels of the heat pipe. The effects of geometry of channels, properties of working fluid, capillary force, heating power, and gravity on the oscillating motions of the working fluids in the heat pipes were examined. Thermoacoustic theory is applied to calculate heat transport through the adiabatic section of the heat pipes. The experimental investigation of a prototype of the oscillating heat pipe was conducted. Numerical and experimental results relevant to the heat transport capability of the heat pipe were analyzed and compared. Oscillating motions of vapor bubbles and liquid slugs may dramatically enhance heat and mass transfer in the capillary channels of the heat pipes. For each capillary channel of the heat pipe, large quantities of heat will be transferred radially and hence transported axially. Recirculation of the working fluid, especially in short liquid plugs, may significantly improve the heat transport capability of the heat pipe.

Nomenclature A cross sectional tube area, m2 Cf friction factor Cpl liquid specific heat, J/kg K D (d) tube diameter (I.D.), m G mass flux rate, kg/sm2 g gravity acceleration, m/s2 h heat transfer coefficient, W/Km2 hlv latent heat, J/kg K gas spring constant L length, m m mass, kg p pressure, N/m2 P perimeter, m Pr Prandtl number q’’ or q wall heat flux, W/m2 Re Reynolds number r radial coordinate, m s entropy per unit mass, J/kg T temperature, K or °C t time, s u liquid plug velocity, m/s V bubble volume, m3 W work flux or acoustic power, w x quality z axial coordinate or distance along the tube (channel), m ∆ h length of liquid plugs between evaporator and condenser, m ∇ T temperature gradient, K/ m or °C/ m

9th AIAA/ASME Joint Thermophysics and Heat Transfer Conference5 - 8 June 2006, San Francisco, California

AIAA 2006-3416

Copyright © 2006 by shibin liang. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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∆ z length of adiabatic section, m Greek α contact angle, degree β thermal expansion coefficient

θ tilt angle, degree σ surface tension, N/m ρ density, kg/m3 µ viscosity, Pa S

φ filled ratio

δ thermal penetration depth, m κ ratio of specific heat λ thermal conductivity, W/Km γ thermal diffusivity, m2/s

ζ tidal displacement, m

ω angular frequency, rad/s

Subscript a adiabatic section ave. averaging c condenser cold condenser side e evaporator f pressure drop hot evaporator side i ith liquid plug or vapor bubble l liquid m average value n total number of liquid plugs v vapor sat saturation Superscript

averaging

I. Introduction t is well known that the oscillatory flow of fluid in the capillary channels or microchannels may enhance heat and mass transfer in their axial directions. Kurzweg [1] examined the enhanced conduction of heat transfer via a sinusoidal oscillatory flow through circular tubes that connect two fluid reservoirs maintained at different

temperatures. The significant enhancement of heat transfer is a radial temperature gradient produced by the fluid oscillations that largely depend on time. As a result, large quantities of heat will be transferred radially and hence transported axially. Graham et al. [2] studied the motion of fluid droplets in capillary tubes, subject to the action of a mean pressure gradient and an oscillatory body force. For large droplets, enhancement in the bulk flow rate is observed when the drop capillary number is small and the oscillatory force is strong. The enhancement is also associated with increased droplet deformation in the presence of oscillatory force. Thomas et al. [3] analyzed the separation of species in the fluid in the tubes oscillating with no net flow from one reservoir to the other. The species proceeds to move in a zigzag fashion down the tube, giving it a higher transport than by pure molecular diffusing with no net flow between the two reservoirs. Sophisticated thermoacoustic theories [4, 5] have demonstrated some insights to the enhanced heat transfer of an oscillating gas flow in thermoacoustic engines and refrigerators. A comprehensive understanding of enhanced heat transfer of the oscillating motions of the working fluid has led to an innovative development of thermoacoustic devices [5, 6]. Over the years, many researchers have reported that the bubble-train flow in capillaries is very effective in increasing the heat and mass transfer rates compared to a single-phase flow. Radial mixing was found to increase with Reynolds number, but rapidly increased with decrease in slug

I

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length. A similar study showed that radial heat transfer in a solid-liquid slug flow system exhibits increased heat transfer rates with the increase in flow rates and decrease in slug length [7].

An oscillating heat pipe (OHP), as shown in Figure 1, may be an excellent and unimaginable example of the enhancement of heat and mass transfer of an oscillatory slug flow in its capillary channels. Owing to its simple/miniature structure, low construction fees, and high efficiency, many researchers have investigated this heat transfer device experimentally as well as theoretically. The results reported by Vasiliev [8] showed that the thermal resistance of a flat aluminum multi-channel pulsating heat pipe (700 mm x 70 mm x 7 mm) with Propane as its working fluid can reach as low as 0.05 K/W. Xu and Liang et al. [9] conducted experimental studies of flat pulsating heat pipes with HFC-134a as its working fluid. The thermal resistance of the heat pipe reached the remarkable values of 0.03-0.05 K/W when positioned vertically with the heater at the bottom. Cai et al.[10] conducted an experimental investigation of a 12-turn open loop pulsating heat pipe, in which the water was used as a working fluid. The heat pipe worked horizontally and achieved the thermal resistance of 0.05 K/W.

Differing from a conventional heat pipe, an oscillating heat pipe has no wick structure and the pressure difference between its evaporator and condenser is imperative, thus it must be maintained at a certain or critical value to guarantee a self-sustaining oscillation of liquid plugs and vapor bubbles inside the channels of the heat pipe. Similar to charging a conventional heat pipe, the inner space of an oscillating heat pipe is filled with a working fluid to a certain filled ratio to form a saturated liquid -vapor mixture under a vacuum state. As the oscillating heat pipe operates , the saturated temperature and pressure of the liquid-vapor mixture varies at different locations in the heat pipe, i.e., its evaporator, condenser and adiabatic sections. We can assume that there is a temperature gradient between the evaporator and condenser of the heat pipe. It then becomes obvious that when the evaporator is heated, the saturated temperature of the working fluid inside the evaporator will increase and the corresponding saturated pressure will rise as well. Furthermore, the saturated liquid at this section will be superheated before vapor generation can take place at the surface of the channel wall. Once a vapor bubble forms in the superheated liquid, its growth rate becomes very high, especially in a small, restricted space, as shown in Figure 2. This explosive formation of vapor is often a source of instability since it is accompanied by a sharp local increase in the static pressure, which may reduce, stop, or even reverse the flow in the upstream section of the channel. Intensified thin film evaporation in the thin film surrounding the vapor bubble may also contribute to the explosive boiling. Hetstroni et al. [11] conducted an interesting experimental investigation of explosive boiling of water in microchannels. The study presented that under certain flow and heat transfer conditions, explosive boiling occurs in microchannels. The investigation showed strong dependence of the heat transfer coefficient on vapor quality. Balasubramanian and Kandlikar [12] observed that the highest velocity of the liquid-vapor interface is 3.5 m/s in a set of six parallel rectangular microchannels, each with 333 micron in hydraulic diameter. For the cooling section of the oscillating heat pipe, when the vapor bubbles are cooled, they will collapse and form condensed thin liquid film on the inner channel wall. Instability of the condensed thin liquid film in the capillary channel may exist as well. The saturated temperature of the vapor-liquid mixture is determined by the cooling surface area, wall temperature and heat transfer coefficient in the condenser section. The corresponding saturated pressure is dependent upon the saturated temperature of the vapor-liquid mixture. If the saturated liquid in the condenser section is cooled further, a subcooled liquid may appear in this area. A more complicated heat and mass transport process exists in the adiabatic section of the oscillating heat pipe, because a net vapor transport, like in a conventional heat pipe, is once again not available. A suitable description of heat and mass transfer of the slug flow of the working fluid in the adiabatic section of the heat pipe becomes a key component in the better understanding of the oscillating heat pipe. A mass-spring model [13] may be used to describe the oscillating motions of vapor bubbles and liquid slugs inside the section. Enhanced heat and mass transfer of the oscillatory flow of the working fluid in the heat pipe should be taken into account. This process of the oscillating bubble-train flow is a typical non-equilibrium and transient heat transfer process.

Figure 1. Closed loop oscillating heat pipe

Figure 2. Vapor bubbles generation in the evaporator of an OHP

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Based on the analysis above, we can conclude that there exist some oscillating/fluctuating pressure sources or driving forces such as explosive boiling inside the oscillating heat pipe while it is heated or cooled. Barbosa and Hewitt [14] presented a thermodynamic nonequilibrium slug flow model to describe boiling heat transfer characteristics in heated channels. The mechanism behind the heat transfer coefficient enhancement is the existence of thermodynamic nonequilibrium slug flow, i.e., a type of slug flow in which rapid bubble growth in subcooled boiling leads to the formation of Taylor bubbles separated by slugs of subcooled liquid. For vapor bubbles and liquid slugs in the adiabatic section of the heat pipe, Liang et al. [13] applied a mass-spring model to describe the oscillating motions of the slug flow in the section. No heating and cooling were considered. The effects of isentropic and is othermal bulk modulus, tube diameters, fluid structure, pressure distribution, gravity, and surface tension on the velocity, pressure and displacement of the mixture of vapor bubbles and liquid slugs were discussed. Khandekar and Groll [15] illustrated flow patterns of the slug flow in a closed loop channel. A random circulation of the slug flow of the working fluid was observed in their experiment. Wang and Nishio [16] presented a numerical model to simulate the heat transport characteristics of the oscillating heat pipe. In their experimental and numerical results, the variable saturated temperatures of the vapor-liquid mixture of the working fluid along the serpentine channels of the heat pipe agreed well.

In this investigation, a theoretical model to simulate the oscillating characteristics of the two-phase flow in the capillaries of the oscillating heat pipes is developed. Based on the simulation results, the enhancement of heat and mass transfer of the oscillating motions of the slug flow of the working fluid in the heat pipes, particularly in its adiabatic section, will be analyzed and discussed. A five-turn closed loop oscillating heat pipe is fabricated and tested as well. Numerical and experimental results for the heat transport of the heat pipe are also compared.

II. Modeling The transient/two-phase fluid flow and heat

transport in an oscillating heat pipe is so complicated that some assumptions for its theoretical modeling are necessary. The following major assumptions are made to simplify the heat transport and two-phase flow in the heat pipe. (1). A stable slug flow structure of the working fluid exists in the adiabatic section of the heat pipe. (2). Vapor is an ideal gas and is in saturated states. (3). Averaging wall temperatures are used for the evaporator and condenser. (4). Condensing heat transfer resistance is small enough to be neglected. (5). Lengths and numbers of vapor bubbles and liquid plugs in each channel of the heat pipe are the same. (6). One-dimensional fluid flow model is applied to the vapor bubbles and liquid plugs. A. Pressure distribution along the capillary channels of the oscillating heat pipe

Since the two-phase flow inside the serpentine capillary tube/channel of the two-phase heat transfer device, as shown in Figure 1, is in saturated states, the saturated pressure of the slug flow of the working fluid in the evaporator will increase when it is heated. Simultaneously, the saturated pressure of the slug flow in the condenser will reduce when it is cooled. Therefore, along the serpentine capillary tube/channel (i.e., defined as z direction), the pressure distribution of the slug flow can be approximately illustrated by Figure 3. The shape of the pressure distribution may be sinusoidal, but the exact profile of the pressure distribution mainly depends on the local saturated temperatures of the working fluid along the serpentine channel of the heat pipe. As we know, if such a pressure distribution of the two-phase flow exists inside a tube or channel, a self-sustainable oscillating motion of the slug flow may occur inside the tube or channel under a pressure difference between its two ends [13]. For the two-phase heat transfer device, the geometry of the capillary channel, heat flux, working fluids, orientations (i.e., gravity), and filled ratio determine the oscillation and thermal characteristics of the slug flow inside the capillary channel of the device. In Figure 4, a physical model used for the numerical simulation of the slug flow inside the oscillating heat pipe is partially shown. It is assumed that there are (n) liquid plugs and (n-1) vapor bubbles within the total length of the heat pipe. B. Heat transfer coefficient calculation in the evaporator section

(a)

(b)

Figure 3. Pressure distribution of slug flow along the serpentine channel of the OHP

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If the boiling heat transfer in the capillary tubes of the evaporator is considered as a superposition of nucleation and forced convection, the well-known Chen correlation for the boiling heat transfer coefficient of saturated convective boiling can be used. The convective transfer is expressed as a function of the two-phase Reynolds number after Lockhart -Martinelli, and the nucleation transfer is obtained from the nucleate boiling correlation of Forster and Zuber. The Chen correlation [17] can be expressed as

( )[ ] ( )[ ] MPTPPTTh

ch lwsatlsatw

vlvl

lpll 75.024.024.024.029.05.0

49.045.079.0

00122.0 −−

=

ρµσ

ρλ

+4.08.0 PrRe023.0 ll

l

D

λ

(1) where

( ) ( ) 117.16 Re1056.21Re−−×+= tptpM (2)

( )[ ] 25.1ReRe ttltp xF= (3)

l

lDxG

µ)1(

Re−

= (4)

F(xtt) is an empirical factor associated with Re l and Chen concluded that

78.15.0 )1()( −+= tttt xxF (5)

where xtt is the turbulent-turbulent Martinelli parameter. It can be given by

1.05.09.01

−=

v

l

l

vtt x

xxµµ

ρρ

(6)

When the filled ratio of the working fluid in the capillary tube of the heat transfer device is φ , the average density

ρ and quality x for the overall working fluid can be expressed as

v

v xρ

ρρφ

⋅−= and

lv

xxρρρ−

+=11

(7)

When a heat flux q ′′ is applied to the evaporator of the heat transfer device, the average quality x of the working fluid in the evaporator is given by the following equation

lv

et

hGA

qLPx

⋅⋅

⋅⋅=

'',

(8)

where ρ⋅= uG , u is the average velocity of the working fluid in the evaporator of the heat transfer device. Lt,e is the length of one U-turn tube of the evaporator.

When the heat transfer coefficient (h) of the two-phase flow in the capillary tube of the evaporator is determined by equations above, based on the heat transfer equation in the evaporator side with the known heat flux and outside wall temperature, the saturated temperature and pressure of the working fluid inside can be calculated.

Figure 4. Physical model of pressure inside an oscillating heat pipe (There are 29 of vapor bubbles and 30 of liquid plugs for the total length of the heat pipe)

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C. Multiple mass-spring model in the adiabatic section [13] Between the evaporator and condenser of the two-phase heat transfer device, there is an adiabatic section. A

typical slug flow pattern of the working fluid exists inside the capillary tube of the adiabatic section of the device or vapor bubbles and liquid slugs in the section consist of a bubble-train flow. If vapor bubbles of the slug flow are considered to act as gas springs and liquid slugs are considered to act as mass pistons, a multiple mass-spring model can be used to describe the oscillating motions of the slug flow in the adiabatic section of the heat transfer device. Liquid inside the liquid slugs is incompressible, but gas inside the vapor bubbles is compressible. Vapor pressure in one vapor bubble includes two components: the average pressure and the oscillating pressure. If the vapor-liquid mixture of the working fluid is in saturated states, the corresponding vapor temperature will consist of two parts: the average and oscillating temperatures. The oscillating pressures inside vapor bubbles are caused by the volume changes of bubbles and can be expressed by the gas spring constants. Therefore, the motion of one liquid plug (i) can be described by using Newton’s second law as follows

θsin)()( 1112

2

gzzKzzKAPAPdt

zdm iiiiiifii

ii −−−−−∆−∆= +−− (9)

For liquid slugs (1) to (n) in the adiabatic section of the OHP, the equation above is applied to establish the following coupled equations.

( )

( )

===

−−−∆−∆==

−−−−−∆−∆==

−−−∆−∆==

−

+−−

dtdz

udtdz

udtdz

u

gzzKAPAPdt

dum

dtzd

m

gzzKzzKAPAPdt

dum

dtzd

m

gzzKAPApdt

dum

dtzd

m

nn

ii

nnnfnnn

nn

n

iiiiiifiii

ii

i

f

,,,,

sin

sin)()(

sin

11

12

2

1112

2

211111

121

2

1

LL

M

M

θ

θ

θ

(10)

The displacements zi and velocities ui of the liquid slug (i) are calculated by solving these coupled equations in a Runge-Kutta numerical scheme. The time step used in the numerical simulation is 5.0×10-5 s. The initial velocity conditions of liquid plugs are set to zero. The temperature and pressure of vapor in the adiabatic section of the heat pipe can be derived from the following heat transfer analysis of the oscillating slug flow of the working fluid in the heat pipe. D. Heat transfer analysis of the oscillating slug flow in the adi abatic section

In the adiabatic section of the oscillating heat pipe, vapor bubbles and liquid slugs form an oscillating slug flow in its capillary channels. The oscillating characteristics of vapor bubbles and liquid plugs in the slug flow play a very important role in the heat and mass transfer between the evaporator and the condenser of the heat pipe. The transfer mechanism can be described by a laminar heat conduction model in which the radial variation in velocity and temperature produces an effective axial transport of heat orders -of-magnitude larger than that in the absence of oscillations.

The temperature T of the working fluid in the adiabatic section of the oscillating heat pipe can be expressed as follows:

tjm eTTT ω

r

1+= (11)

where the mean fluid temperature Tm(z) is independent of r and to be the same as that of the channel wall of the heat pipe.

To calculate the oscillating fluid temperature T1, the general equation of heat transfer of the vapor bubbles/liquid plugs is given below

∂∂

+∂∂

+

∂∂

+

∂∂

∂∂

=∂∂

+∂∂

+∂∂

zv

ru

zT

rT

rrrr

sv

zs

uts

T2

1)( 2

2 µλρ (12)

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Oscillating motions of vapor bubbles and liquid slugs controlled by the unsteady N-S equations in the capillary tubes of the heat pipe cause an intense variation of velocity of the flow field which causes diffusions of heat and mass transfer to enhance significantly. Actually, the convective flow of entropy, conduction of heat in the radial direction of capillary tube and generation of entropy (e.g., viscosity) of the oscillating working fluid in the oscillating heat pipe dominate heat transfer capability in the two-phase heat transfer device. Keeping only first-order terms, and neglecting thermal conduction along z, Eq. (12) becomes

21

2

11 rT

zs

usjT mmm ∂

∂=

∂∂

+ λωρr

(13)

To express s in terms of p and T, we write

dpdTT

cdp

TdT

Ts

dpps

dTTs

ds

p

pp

Tp

ρβρ

ρ−=

∂∂

+

∂∂

=

∂∂

+

∂∂

=

2

1 (14)

or

( ) ( ) 111 // pTTcs mmp ρβ−= (15)

Substituting Eqs. (14) and (15) into Eq. (13) yields a differential equation for the unknown function T1(r),

1121

2

1 uTcpTjdr

TdTcj mpmmpm ∇−=− ρβωλωρ

rr (16)

in terms of the given quantit ies p1, u1 and mT∇ , to be solved subject to the certain boundary conditions.

For a single and long fluid volume such as liquid plugs or vapor bubbles in the adiabatic section of the oscillating heat pipe, variations with z are not negligible. If we are neglecting ordinary thermal conductivity in the z direction, the only way that heat can be transported along z is by the hydrodynamic transport of entropy, carried by the oscillatory velocity. The total heat flux Q by vapor bubbles or liquid plugs through the capillary tubes in the adiabatic section of the heat pipe can be described by the thermoacoustic theory and is given below by Swift [4]

( )141

11 −Γ−= ssmk upTPQ βδ (17)

and crit

m

TT

∇∇

=Γ (18)

where critT∇ is the critical mean-temperature gradient in the adiabatic section of the heat pipe and can be expressed

below

s

pm

sm

crit ucpT

T1

1

ρβω

=∇ (19)

where P is the perimeter of the capilla ry tube and kδ is a thermal penetration depth (i.e. ωγδ /2=k ). γ is the

thermal diffusivity of the working fluid in the section (i.e. pmcρλγ /= , where λ is the fluid’s thermal

conductivity). Tm is the average temperature of fluid in the section. ω is the angular frequency of the oscillating

slug flow. su1 and sp1 are the velocity and pressure oscillating amplitudes of the oscillating slug flow, respectively.

Tm β may be equal to 1.0 for ideal gases. The thermal expansion coefficient β may be negligible while the fluid is

in liquid state. If the temperatures of the evaporator and condenser of the heat pipe are Te and Tc, respectively, and the length of the adiabatic section of the heat pipe is ∆ z, the mean-temperature gradient mT∇ is expressed as

ZTT

T cem ∆

−=∇ (20)

For a liquid plug, the equation (17) can be described by the following expression:

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mpmk TcPQ ∇−= 2

41 ωζρδ (21)

where ωζ /1su= is the tidal displacement of the liquid plug.

The total work flux W, i.e., the acoustic power generated particularly by the vapor bubbles in the capillary tubes of the adiabatic section of the heat pipe, can be described in the following equation by Swift [4]

( ) ( )141 2

1

2

−Γ∆= s

pm

mk p

cT

zPWρ

ωβδ (22)

The theoretical analysis above assumes that the fluid flow in capillary or microchannel is one-dimensional. The typical velocity profiles, i.e., local recirculation of liquid, inside a short liquid plug of the bubble-train flow in the adiabatic section of the heat transfer device are shown in Figure 5. The radial movement of fluid parcels tends to make the extra convective mixing of fluid possible. By adding an oscillating motion into the two-dimensional slug flow, the fluid diffusion will occur not only by conduction but also by convection. Compared to one-dimensional slug flow, such an oscillating two-phase flow, especially when a recirculation flow occurs in liquid plugs, may produce further enhancement of apparent diffusion for heat and mass transfer along the axial direction of the channel.

III. Experimental Study of a Five -Turn Oscillating Heat Pipe

In order to verify our theoretical modeling related to oscillating heat pipes, a prototype of five-turn closed loop oscillating heat pipe was fabricated and tested. The detail sizes of the heat pipe are shown in Figure 6. It was made by a copper tube with an inner diameter of 3.0 mm. In its adiabatic section, through six glass tubes with the same inner diameter of the copper tube, the oscillating motions of the slug flow of the working fluid inside the oscillating heat pipe can be observed. The experimental set-up for the the heat pipe is shown in Figure 7. Two aluminum cold plates were tightly clamped onto both sides of the condenser section of the heat pipe. An electrical flat heater was mounted onto the evaporator of the heat pipe. Twelve T-type thermocouples were embedded to measure the surface temperature distribution on the different points of the heat pipe. These thermocouples were connected to a USB data

Figure 5 Recirculation in a liquid plug in the capillary tube/channel of an OHP

Figure 7 Experimental set-up for the oscillating heat pipe

Figure 6 A five -turn closed loop oscillating heat pipe

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acquisition system to record the measured temperatures. OmegaThermal 200 conductive paste had been applied to reduce the contact resistance between the resistor and heat pipe. An AC power supply was connected to the flat resistor and its voltage and current were recorded simultaneously. The power input was controlled by a variac. The flat resistor was insulated by fiberglass to protect heat losses to the environment. Heat losses to the environment by the working heat pipe were closely approximated (less than 0.5 percent) versus operating temperature or free convection. When heat was removed by two aluminum cold blocks, the heat pipe was placed in a vertical position with the heater at the bottom. Contact resistance at the cold plate/heat pipe external wall surface was reduced by applying OmegaThermal 200 conductive paste between them. Cooling water was pumped through the cold plates from a Julabo cooling bath (F12). Ethanol was chosen as the working fluid of the heat pipe and the charging filled ratio was 0.53 for the testing prototype. The temperature variation between the evaporator and condenser of the heat pipe with its power input was studied as the baseline experiment.

IV. Results and Discussion

A. Comparison of heating power transport The physical model shown in Figure 4 has been applied for the numerical simulation of oscillating heat pipes.

For the prototype heat pipe shown in Figure 6, which is working vertically with the heater at the bottom, 29 vapor bubbles and 30 liquid plugs have been assumed to exist along its total length. The working fluid charged in the heat pipe is Ethanol with a filled ratio of 0.53. The lengths of these vapor bubbles and liquid plugs in the adiabatic section of the heat pipe are dependent on the filled ratio of the working fluid in the heat pipe. Combining the pressure distribution of the working fluid inside the heat pipe with the boiling heat transfer in its evaporator, as described in Section 2, the oscillating motions of the slug flow of the working fluid in the heat pipe have been simulated. In the current model, the condensed film in the condenser section of the heat pipe is neglected. When the heat flux in the evaporator was chosen as 4.0 w/cm2 and the temperature difference between the evaporator and condenser of the prototype heat pipe was 30 °C, the oscillating characteristics of the slug flow of the working fluid were simulated. Figure 8(a) illustrates the variations of velocity of one liquid plug in the adiabatic section of the heat pipe. Figure 8(b) shows the pressure fluctuation of its neighboring vapor bubble. The boiling heat transfer coefficient in the evaporator of the heat pipe is shown in Figure 8(c). The oscillating characteristics of the boiling heat transfer coefficient may be considered as the driving force of the oscillating motions of the slug flow of the working fluid in the heat pipe. Based on the oscillating velocity and pressure results, as shown in Figure 8(a) and (b), the average heating power transported by the liquid plugs in the adiabatic section of the heat pipe can be calculated using Eq. (20). The thermoacoustic power generated by the vapor bubbles in the adiabatic section of the heat pipes can be obtained by Eq. (21). The work flux calculation from the Eq. (21)

has shown that the acoustic power generation by vapor bubbles is too insignificant to be considered. Experimental and numerical results for the heat transport of the heat pipe are compared in Figure 9. The difference between the experimental and numerical results may result from the one-dimensional assumption for Eqs. (20) and (21). Equations (20) and (21) were derived from the one-dimensional fluid flow model, which may only be acceptable for a long liquid plug or vapor bubble. Actually, the typical flow pattern in one short liquid plug in the capillary tube of the heat pipe can be depicted as shown in Figure 5. Under an oscillating motion state, such a fluid flow structure will enhance heat and mass transfer significantly. The local liquid convection caused by the recirculation of liquid in the radial direction of the capillary tube of the heat pipe could make an additional noteworthy contribution to enhance heat and mass transfer in the axial direction of its capillary tube. B. Effect of gravity

Experimental results already shown that oscillating heat pipes can work well in any orientation [8, 9]. The effect of gravity on the performance of the oscillating heat pipe has been simulated by using the same physical and mathematical models discussed above. The inner diameter of the capillary tube of the five-turn heat pipe is chosen as 2.0 mm. The heat flux at the evaporator of the heat pipe is fixed to be 2.0 w/cm2. Ethanol is still used as the working fluid with a filled ratio of 0.6 in the heat pipe. The length of the adiabatic section of the heat pipe is as long as 0.15 m. The lengths of the evaporator and condenser of the heat pipe are 0.15 and 0.3 m, respectively. Three different working orientations of the oscillating heat pipe, i.e. horizontal and vertical, with the heater at either the bottom or top, have been studied. The simulation results are illustrated in Figure 10, and 11. The modeling results have shown that the oscillating heat pipe can work well in any orientation. Under the presence of gravity, i.e., the damping of gravity waves, the oscillating motion of the slug flow in the heat pipe becomes more stable. Another interesting phenomenon is that there is a unidirectional movement of the working fluid while the heat pipe is working vertically with the heater either at the bottom or top. In a horizontal position, the unidirectional motion of the slug flow of the working fluid becomes weak and even disappears. This means that an open loop oscillating heat pipe may work horizontally. Xu et al. [9] and Cai et al. [10] reported the similar results in their experiments. The

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simulating results also show that the heat transport capability of the heat pipe, which works in different orientations, cannot be changed much. C. Effect of capillary tubing diameters

The inner diameter of the capillary tube in the oscillating heat pipe plays an important role in the operation of the heat pipe. First, the stable slug flow structure of vapor bubbles and liquid plugs that forms in the capillary tubes of the oscillating heat pipe extremely depends on the inner diameter of the capillary tubing used. An annular flow may easily be built up in a tube with a larger inner diameter. If this occurs, enhanced heat and mass transfer of the oscillating two-phase flow of the working fluid in the heat pipe will break down. That should be avoided in practice. Secondly, and most importantly, the intensified enhancement of heat and mass transfer in the axial direction of the capillary tube of the heat pipe is dominated by the inner diameter of the tube. If the inner diameter of the capillary tube used in the oscillating heat pipe is too big, the effect of the enhanced heat and mass transfer in the heat pipe may diminish. The radial heat and mass transfer of the working fluid increases with the decrease of the inner diameter of the capillary tubes. Theoretically, the inner diameter of the capillary tube should be the order of the thermal penetration depth of vapor and liquid of the working fluid in the oscillating heat pipe. The values of the thermal penetration depth for vapor and liquid of Ethanol are around 0.1 mm. The further reduction of the diameter of the capillary tube will lead to the increasing friction loss of the working fluid in the capillary tube, though the drag loss of oscillating vapor bubbles is too small to be considered. Figure 12 shows the simulation results based on different inner diameters of the capillary tubes used in the oscillating heat pipe. Decreasing the hydraulic diameter of the capillary channels of the heat pipes from 2.0 mm to 1.25 mm may slightly reduce the tidal displacement of the oscillating motions of its working fluid. D. Effect of capillary force/contact angles

As we know, the main reason for the formation of a slug flow of the working fluid in the capillary channels of an oscillating heat pipe, especially in its adiabatic section, is the existence of its capillary force. As discussed above, a strong capillary force will help to establish a stable slug flow structure of the working fluid in the heat pipe. This is essential for the oscillating heat pipe to work properly. It is completely different from a conventional heat pipe, where capillary force is a driving force for its fluid flow and heat transfer. However, for the hydrodynamic flow of the liquid plugs in the capillary tube of the oscillating heat pipe, the capillary force adds an extra drag force to the working fluid flow. Figure 13 shows the simulation results for an oscillating heat pipe charging with Ethanol. The variation of the different capillary forces is mainly determined by the different contact angles, i.e., advancing (dry) and receding (wet) contact angles, of the working fluid. The less difference between the advancing and receding angles of the working fluid, the lower flow resistance caused by the capillary forces.

-3

-2

-1

0

1

2

3

4

4 4.2 4.4 4.6 4.8 5

time (s)

velo

city

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/s)

(a) velocity variations vs. time

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ssure

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(b) pressure variations vs. time

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hea

t tra

nsf

er c

oef

ficie

nt (

w/k

m2)

(c) heat transfer coefficient variations vs. time

Figure 8 Oscillating characters of liquid plug and vapor bubble in the adiabatic section of the heat pipe (tubing diameter = 3.0 mm ; Te-Tc=30 °C; αwet = 22 ° and αdry = 42 °; heat flux = 4.0 w/cm2)

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E. Effect of different working fluids

Choosing a suitable working fluid for an oscillating heat pipe is becoming an important factor in guaranteeing that the heat pipe works well. Unfortunately, at the present, it is not clear which properties of the working fluid will essentially affect the performance of the heat pipe, although the high values of (dP/dT)sat, viscosity, latent heat, thermal conductivity, isentropic/isothermal bulk modulus, density, specific heat, surface tension, and saturated temperature/pressure have been investigated. Further theoretical analysis and more experimental evidences both are needed to be demonstrated and verified. HFC134a and water were chosen as two more working fluids to study the performance of the oscillating heat pipe theoretically. Simulation results have been compared with the results obtained by using Ethanol, as shown in Figure 14. The oscillating heat pipes charged with HFC134a and water as their working fluids showed higher boiling heat transfer coefficients in their evaporators. The oscillating frequencies of vapor bubbles and liquid plugs in the capillary channels of the heat pipes charged with HFC134a and water are much higher than that charged

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hea

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nsf

er c

oef

ficie

nt (

W/s

m2 )

horizontalbottom heatingtop heating

Figure 10 Heat transfer coefficient variations in the evaporator vs., time (tubing diameter=2.0 mm; Te-Tc=40 °C; αwet = 22 ° and αdry = 42 °; heat flux = 2.0 w/cm2)

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er t

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numerical

Figure 9 Total heat power transport through the adiabatic section of the heat pipe

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2.0 mm1.5 mm1.25 mm

Figure 12 Effects of tube diameter on liquid plugs velocity vs., time (vertical with heater at the bottom; Te-Tc=40 °C; αwet = 22 ° and αdry = 42 °; 6.0=φ ; heat flux=2.0 w/cm2)

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Figure 11 Velocity variations of liquid plugs in adiabatic section vs., time

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/s)

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Figure 13 Effects of capillary force on liquid plugs velocity vs., time (vertical with heater at the bottom ;tubing diameter = 1.0 mm; Te-Tc=30 °C; 6.0=φ ;

heat flux = 2.0 w/cm2)

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with Ethanol. These may conclude that the heat pipe charged with HFC134a or water has the better thermal performance. The similar results were reported by other researchers in their experiments [9, 10].

V. Conclusion

The paper presented a theoretical model for predicting the self-sustainable oscillating motions of the two-phase flow in the serpentine capillary channels of oscillating heat pipes. A mass-spring model for the slug flow in the adiabatic section of the heat pipe plus the exciting pressure sources in its evaporator demonstrated the working mechanism of the heat pipe. Enhanced heat and mass transfer of the oscillatory slug flow of the working fluid in the capillary channels of the heat pipe was analyzed by the thermoacoustic theory. Experimental and theoretical results for the heat transport of the prototype of oscillating heat pipe were compared. The main conclusions arising from this work are as follows: A.The slug flow in the capillary channels of the oscillating heat pipe plays a paramount role in the proper operation of the heat pipe. The hydraulic diameter of channels, surface tension, and contact angles of the working fluid determine a stable slug flow in the heat pipe. Both the structure of the slug flow of vapor bubbles and liquid plugs in the capillary channels of the adiabatic section of the heat pipe and the exciting pressure sources in its evaporator provide self-sustainable oscillating motions of the working fluid in the oscillating heat pipe. B.Gravity influences the performance of the oscillating heat pipe. Decreasing the hydraulic diameter of the capillary channels of the heat pipe may slightly reduce the tidal displacement of the oscillating motions of its working fluid. Capillary force makes an extra contribution to the moving resistance of the liquid plugs in the heat pipe. The oscillating heat pipes charged with HFC134a and water as their working fluids have higher boiling heat transfer coefficients in their evaporators than that charged with Ethanol. The oscillating frequencies of vapor bubbles and liquid plugs in the capillary channels of the heat pipes charged with HFC134a and water are much higher than that charged with Ethanol. C.The oscillatory slug flow of liquid plugs and vapor bubbles in the capillary channels of the oscillating heat pipe enhance heat and mass transfer of the working fluid from its evaporator to condenser. For each capillary channel of the heat pipe, large quantities of heat will be transferred radially and hence transported axially. The radial heat and mass transfer of the working fluid increases with the decrease of the inner diameter of the capillary tubes. Recirculation of the working fluid, especially in short liquid plugs, may significantly enhance the heat transport of the oscillating heat pipe due to its convective flow in the radial direction of capillary channels of the heat pipe. D.Experimental and numerical results showed the one-dimensional thermoacoustic model/theory, which can be applied to calculate the axial heat transport of the oscillating heat pipe. A two-dimensional model, particularly for the heat transport of liquid recirculation in short liquid plugs, requires to be developed.

Acknowledgement

The author would like to thank Dr. Bud Peterson and Dr. Bill Ma for support to complete the work.

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(a) heat transfer coefficient variations vs. time (b) velocity variations vs. time

Figure 14. Effect of working fluids on the performance of the OHP (vertical with heater at the bottom; tubing diameter = 2.0 mm; αwet = 22 ° and αdry = 42 °; 6.0=φ ; heat flux = 2.0 w/cm2)

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