Numerical and experimental investigation of flat-plate pulsating heat pipes with extra branches in the evaporator section

International Journal of Heat and Mass Transfer 126 (2018) 431–441

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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Numerical and experimental investigation of flat-plate pulsating heat pipes with extra branches in the evaporator section Erfan Sedighi, Ali Amarloo, Behshad Shafii ⇑ Department of Mechanical Engineering, Sharif University of Technology, P.O. Box 11365-9567, Tehran, Iran

a r t i c l e

i n f o

Article history: Received 28 January 2018 Received in revised form 4 May 2018 Accepted 9 May 2018

Keywords: Flat-plate pulsating heat pipe Circulatory flow Additional bubble-pump Numerical simulation VOF

a b s t r a c t In addition to some approaches such as changing the working fluid or number of turns in a flat-plate pulsating heat pipe (FP-PHP), geometrical changes are also appealing for enhancing the thermal performance of this type of heat pipes. The main idea of this investigation is to increase heat transfer rate by increasing flow circulation of working fluid. By placing additional branches in the evaporator section, secondary bubble pumps were created which improved the circulation of fluid inside the FP-PHP. In order to investigate the impact of these additional branches, two similar four-turn aluminum FP-PHPs were fabricated. One of them was the conventional FP-PHP and the other had four additional branches and is named additional branch FP-PHP (AB-FP-PHP). Thermal performances of these two types of heat pipes were investigated at different filling ratios (40, 50, 60, and 70 percent) and heat inputs (from 40 to 200 W). Results showed that the thermal resistance of the AB-FP-PHP was 11–20% lower on average compared to the thermal resistance of the conventional FP-PHP at different examined filling ratios. Additionally, for heat inputs around 80 W and above, thermal performances of both devices were better at 50% filling ratio. Furthermore, flow visualization indicated that additional branches affect the flow regime and enhance flow circulation in PHPs. Also, a numerical procedure was conducted for the two-phase system before the experimental investigation to show the role of additional branches in achieving a better circulation of the working fluid. Ó 2018 Elsevier Ltd. All rights reserved.

1. Introduction Heat pipes are used in various applications due to their very high thermal conductance and reliability. Gaugler first proposed the idea of using these devices in 1942. However, the remarkable benefits of the heat pipe became known after its invention by Grover [1]. Since that time, several investigations have taken place in laboratorial and industrial studies. Indeed, many different ideas have been presented for the better performance of heat pipes. Heat pipes have been recently used in electronic applications by embedding these devices with microelectronic chips and racks due to their high thermal conductivity, high efficiency, and suitable working temperature for electronic devices [2–4]. From 1990, that the pulsating heat pipe (PHP) was invented by Akachi [5], several investigations were conducted on this novel heat transfer device due to its simple structure and absence of capillary wicks. PHPs are available in two forms: looped and unlooped. The looped version is more popular because of its ability ⇑ Corresponding author. E-mail address: [email protected] (B. Shafii). https://doi.org/10.1016/j.ijheatmasstransfer.2018.05.047 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.

to produce circulation of the working fluid [6]. Due to its structural simplicity, its operating mechanism is simple as well. Working fluid evaporates and increases the vapor pressure when the evaporator is heated. This results in the growth of bubbles in the evaporator. Enlarged bubbles push the liquid towards the condenser. Unlike the evaporator, the condenser cools down the working fluid resulting in the reduction of vapor pressure and shrinkage of vapor bubbles. The growth and shrinkage of bubbles result in an oscillating motion in pulsating heat pipes. The heat transfer from the evaporator to the condenser is of sensible form within liquid slugs and latent form in vapor bubbles [1]. However, Shafii et al. [7] showed that the majority of heat transfer in the looped and unlooped PHPs is of the sensible form. In order to have vapor plugs and liquid slugs and to make sure that the capillary forces (surface tensions) are more significant than gravitational forces, the magnitude of Bond number introduced in Eq. (1) should not be more than 2 [8].

Di ffi Bo ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi . r ðq  q Þ l g g

ð1Þ

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Nomenclature Bo D E F g k _ m P Q_ R T u v

Bond number inner diameter, m internal energy, J body force, N=m3 gravitational acceleration, m=s2 thermal conductivity, W=mK mass flow rate, kg=s pressure, Pa heat rate, W thermal resistance, K=W temperature, K internal energy, J velocity field, m=s

l

q r

viscosity, kg=ms density, kg=m3 surface tension, kg=s2

Subscripts c condenser e evaporator in input l liquid m measurement p, q phases r repeatability v vapor

Greek letters a volume fraction

This constraint ensures that the vapor bubbles remain confined within the capillary tubes. In this condition, discrete bubbles and liquid slugs will be sustained in a tube [8]. Numerous factors, including inner and outer conditions, can affect the heat pipe operation. During the experiments, factors such as filling ratio, tilt angle, initial pressure in the heat pipe, amount of body force (gravitational acceleration), amount of heat input, etc. can affect the results. Khandekar et al. [9] examined the effect of filling ratio on the operational characteristics of PHPs by using various working fluids in their experiments. They found that better thermal performance and self-sustained thermally driven pulsating action only occurs in the filling ratio range of 25–65% which depends on the type of working fluid. Mameli et al. [10] experimentally investigated the combined effect of inclination angle and filling ratio at different heat input levels on operation stability and thermal performance of a multi-turn PHP filled with FC-72. Their results showed that their PHP is too sensitive to gravity and its operation is unstable at high heat input levels. They found that unlike the vertical position, their PHP does not undergo any performance drop with respect to the heat input in the horizontal position. Gu et al. [11] investigated the effect of gravity on heat transfer characteristics by testing a flat plate PHP under a variety of gravity levels (1–2.5g and 0.02g). They claimed that both the orientation of the PHP and locations of the heated and cooled sections could affect heat transfer performance under normal and hyper-gravity conditions. However, their results showed that, unlike the normal and hypergravity conditions, the performance of a PHP under reduced gravity is almost independent of heater location. The working fluid has a great impact on the performance of the PHPs. Mohammadi et al. [12] fabricated a four-turn PHP and charged it with water and ferrofluid with two different concentrations to investigate the effect of the working fluid, filling ratio, orientation, heat input and magnetic field on the thermal performance of PHP. Their results showed that using Ferrofluid instead of distilled water results in the reduction of thermal resistance in all orientations due to the improvement of thermal conductivity, heat transfer area and evaporator active nucleation sites. Geometrical parameters are the essential factors that should be considered during designing pulsating heat pipes. Results of previous investigations showed that the increase of contact area between the liquid and inner surface of the evaporator results in better thermal performance [13]. Additionally, the results indicated that fluid circulation could enhance the thermal performance, stability, and predictability of the PHPs [13]. Hence, the

main purpose of the geometric design of PHPs is to induce fluid circulation. Using check valves is one of the most straightforward solutions. Accordingly, Bhuwakietkumjohn and Rittidech [14] used two check valves in their ten-turn PHP that utilized ethanol and silver Nano-ethanol mixture as working fluids to induce a unidirectional flow. They reported that the flow pattern changed from slug-plug and annular to a dispersed bubble flow in the case of using check valves. Since the use of check valve makes the PHP structure more complicated, some researchers tried other alternatives to induce fluid circulation in PHPs. Thompson et al. [15] integrated Tesla-type check valves (without any moving parts) into a multi-turn flat-plate PHP and found that circulation in the desired direction was improved and that this improvement increased with heat input. By using Tesla-valves, the thermal resistance of their PHP was reduced from 15% to 25% depending on heat input value. A similar investigation was performed by de Vries et al. [13] on a one-turn flat-plate PHP with two Tesla-valves. They reached an optimized form of the Tesla-valve with the aid of single-phase flow simulations for a variety of valves. Using the optimized valve, they found a 25% difference in velocity for different flow directions in the Tesla-valve channels. Ebrahimi et al. [16] developed oblique interconnecting channels in both the evaporator and condenser sections to increase flow resistance in one direction. Their results indicated that the performance of the PHP improved noticeably by interconnecting channels in a wide range of heat inputs and filling ratios. Using PHPs with multiple pipe diameters is another approach proposed by other investigators to induce higher flow resistance in a specified direction. Chien et al. [17] fabricated two types of PHPs with 16 parallel channels. One of them had a uniform cross-section and the other one had 16 alternative cross-section diameters. They claimed that the performance of both uniform and non-uniform PHPs increased with the inclination angle, but only the non-uniform type could be functional at the horizontal position. Additionally, Kwon and Kim [18] studied the effect of non-uniformity in the cross-section of a PHP by testing a dualdiameter one-turn PHP. They made various types of PHPs with various inner diameters and observed operational characteristics of PHPs under different input powers and inclination angles. They recorded a 45% reduction in thermal resistance by using dualdiameter PHP. They also achieved an optimum range of diameter difference where thermal performance enhancement was maximized. Tseng et al. [19] proposed a novel design for dualdiameter PHPs to be functional even for top heat mode. The presence of vapor bubbles has a significant effect on the displacement of the liquid slugs in PHPs. In other words, by the

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growth and shrinkage of vapor bubbles, the bulk of fluid is pumped within the tubes of a PHP. Using bubble pumps is not a new idea. Einstein’s refrigerator [20] is among the first users of this phenomenon. Yuan and Prosperetti [21] simulated the flow induced by the bubble pump effect in a finite tube covered with a heating element joining two liquid reservoirs by a one-dimensional model. They included viscosity and surface tension effects in their model and showed that the system was capable of producing pumping action even in the presence of an adverse pressure gradient or in the case of a single bubble. In this study a new idea in which additional branches in the evaporator are used to improve fluid circulation of the working fluid in a four-turn flat-plate PHP is studied. Hence, at first, analysis of the positive effect of additional branches on flow circulation was carried out numerically. Afterwards, two different kinds of flatplate PHPs were fabricated one of which had four additional branches in the evaporator section and the other was a conventional one. These devices were used to investigate the effect of additional branches on a multi-turn PHP both thermally and visually.

Cooling Bath

Condenser Rotameter

Vacuum Pump

Thermometer

Camera

Heater 2. Experimental setup and procedure Schematics related to the experimental setups (FP-PHPs) are shown in Fig. 1. One of which (Fig. 1(a)) is the FP-PHP that contains additional branches in the evaporator section (AB-FP-PHP) and the other (Fig. 1(b)) is the conventional FP-PHP created in a four-turn configuration. The location for visualizing the flow pattern in ABFP-PHP is also indicated in Fig. 1(a) with a dashed box. Dimensions and condenser and evaporator locations for both types of the pulsating heat pipes are also depicted in Fig. 1(a) and (b). The length of these external branches was chosen in a way that it only made less than 10% difference in total volume. These two types of FP-PHPs were made from Aluminum plates. A glass plate was used to visualize the flow pattern.

Condenser

86

100

80

228

214 267

346

10 10 (a)

100 148

(b)

80

Heater

Fig. 1. Schematics relating to the experimental setups: (a) experimental setup of the AB-FP-PHP and the region of visualization (dashed line), (b) experimental setup of the conventional FP-PHP.

Variac

Fig. 2. Image of the AB-FP-PHP with thermocouple locations (cross points) and the related required equipment.

In the flat-plate pulsating heat pipes, channels with rectangular cross sections and with the dimensions 2 mm  2 mm were made. By considering Eq. (1), with respect to the operating temperature range of methanol as working fluid, the selected dimension of the channels is suitable when compared to the critical hydraulic diameter (3.4 mm in 20 °C and 3.0 mm in 100 °C). The additional branches were placed in a way to induce a counter-clockwise (CCW) motion of the fluid. In fact, it was believed that the presence of additional branches (secondary bubble pumps) with a closed end as a part of the evaporator would permit the working fluid to move in the desired direction (CCW). Two flat aluminum plates with the dimensions 346 mm  148 mm  5 mm were used for manufacturing the FP-PHP and the ABFP-PHP. A washer and a silicon glue were utilized to seal the channels. A plate heater with the dimensions 100 mm  80 mm was used as the heat source in the evaporator section. To reduce the contact resistance, a thin layer of silicon paste (thermal paste) was placed between the heater and the plate. An AC power supply supplied the generated heat input. Also, the applied power was controlled by a clamp-meter that could monitor voltages and currents with 0:01 A and 0:1 V accuracy. Eight thermocouples were mounted on the evaporator and four thermocouples were attached to the condenser sections of each FPPHP. To measure the temperature, K-type thermocouples (with 0:5 °C accuracy) were utilized. Channels with the dimensions 2 mm  2 mm were engraved on the back of the aluminum plate which helped the thermocouples measure the liquid temperature at specified locations at a closer distance to the working fluid (1 mm). The ends of the thermocouples were soaked with silicon paste to increase heat conductance and reduce contact resistance. Additionally, in order to insulate the system from the surroundings, all parts of the device were covered with mineral wool with a thermal conductivity of 0:036 W=mK.

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In Fig. 2, the image of the AB-FP-PHP with thermocouple locations (cross points) and the utilized equipment are shown. It should be noted that identical points were selected for thermocouples’ locations in each of the PHPs. In order to cool the device, a block with the volume of 8  10  3 cm3 was used in which cooling water (provided by the cooling bath) with a temperature of 20  0:1 °C and a flow rate of 360 cm3 =min entered the condenser sections. The flow rate of cooling water was controlled and measured by a rotameter to achieve a similar condition for both FPPHPs at all the stages of the experimental tests. The remaining parts of the heat pipes were considered as adiabatic sections which constitute about 1000 mm of the length of the FP-PHPs. A CMOS high-frame (1200 frames per second) camera (Nikon1 J4) was used to observe the effect of additional branches in the evaporator section on the flow regime. Before starting each stage of the experiment, at first, the air was evacuated from the FP-PHPs to obtain a pressure of approximately 5 Pa, using a vacuum pump (Edwards-RV3), and then the operating fluid with a specific volume was introduced into them. Heating was started at 40 W and continued up to 200 W in 20 W steps. In each level, the amount of heating was kept constant until a steady-state condition was achieved. Due to limitation of construction and prevention of failure, the heat was increased until the average temperature of the evaporator reached 110 °C. To investigate the effect of an additional branch on the thermal performance of FP-PHPs, thermal resistance values of the AB-FPPHP and FP-PHP were measured and the results were compared. Comparison was performed at different filling ratios (40%, 50%, 60%, and 70%). 3. Uncertainty analysis In order to calculate thermal resistance values of the heat pipes in the experimental investigation, the average temperature of the evaporator and the condenser sections are calculated in steady state condition in two steps. First, the temporal averaging is performed over a sufficient time span for each thermocouple. Next, the local average temperatures of evaporator and condenser sections are calculated using Eqs. (2) and (3). Afterwards, thermal resistance can be calculated using Eq. (4).

1 T c ¼ 4 1 T e ¼ 8

4 X Ti

ð2Þ

i¼1 12 X Ti

ð3Þ

i¼5

uRt ¼

ð4Þ

In Eqs. (2)–(4), T i is the temperature of the i-th thermocouple, T c is the average temperature of the condenser, T e is the average temperature of the evaporator, Q_ in is the heat input, and R is the thermal resistance. Since each measurement equipment has a finite precision, collected data contain errors. The uncertainty of the equipment (uRm ) is calculated by [16]:

R ¼ RðT e ; T c ; Q_ in Þ "

@R  dT e @ T e

ð5Þ 2

 þ

@R  dT c @ T c

2

 þ

@R _ dQ in @ Q_ in

2 #1=2 ð6Þ

Since for each specific case, the experiments were repeated 3 times, the uncertainty of the repeatability of the experiments

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ðuRm Þ þ ðuRr Þ

ð7Þ

According to the above equations, maximum uncertainty calculated in thermal resistance is approximately 0.0361 K=W. 4. Numerical modeling Before the experimental investigation of the thermal characteristics of AB-FP-PHP, the idea proposed in this paper was numerically analyzed using the OpenFOAM [22] software. The effects of additional branches were examined using the volume of fluid (VOF) model for a 2-dimensional flow domain. In fact, the numerical simulation was not considered to precisely model the thermal performance of the heat pipe, but to show the effect of additional branches on the circulation of the working fluid. Therefore, the VOF model was used due to its relative simplicity and an easier analysis which could yield the desired results sooner. Full-scale simulations (2-dimensional) were carried out for each of the devices. Schematics in Fig. 3 illustrate the boundary conditions used in the numerical simulation for each type of the PHPs and Fig. 4 shows the meshing configuration used in this study. It has been attempted to choose heated walls with identical lengths in order to apply equal heat to both devices by applying equal heat fluxes. Only a part of the evaporator section, in which the additional branch meets the lower curve, has been depicted in Fig. 4 to show the applied mesh for the simulation. After examining several grid formations and time steps for the numerical problem grid and time independence check, a grid with 48,000 computational cells (for the AB-FP-PHP) and a time step of 0.0001 s were selected. To simulate heating and evaporation, a constant heat flux was defined at the wall boundaries of the evaporator section (q00 ¼ 5000; 7500; 10; 000 W=m2 ). A zero heat flux was defined as the boundary condition on the adiabatic section, assuming this section to be insulated. Furthermore, it was assumed that the walls of the condenser are maintained at a fixed temperature (20  C), for instance, by using a high flow rate of cooling water. In the VOF model, one set of Navier-Stokes equations are solved throughout the computational domain and used to track the motion of the different phases by defining the volume fraction of each phase. The VOF model relies on the fact that each cell in the domain is occupied by one phase or a combination of the two phases. Continuity, momentum, and energy equations used for the problem domain are all obtained from Ref. [23] which are respectively as follows.

1

T e  T c R¼ Q_ in

uRm ¼ dR ¼

(uRr ) should also be included. The total uncertainty (uRt ) is calculated using Eq. (7) [16].

qq



@ ! _ qp _ pq  m ðaq qq Þ þ r  ðaq qq v Þ ¼ m @t



ð8Þ

@ ! ! ! !! ! ! ðq v Þ þ r  ðq v v Þ ¼ rP þ r  ½lðr v þ r v T Þ þ q g þ F @t @ ! ðqEÞ þ r  ð v ðqE þ PÞÞ ¼ r  ½keff rT @t

ð9Þ

ð10Þ

The continuity equation should be solved for each of the two phases in which q is the intended phase and p is the other phase. Terms on the right side of Eq. (8) illustrate the mass transfer from either of the phases to the other and vice versa. The variable aq represents the volume fraction of phase q in a computational cell. In the current vapor-liquid two-phase system, the density and viscosity of each cell used in Eqs. (9) and (10) are given by

q ¼ at qt þ ð1  at Þql

ð11Þ

E. Sedighi et al. / International Journal of Heat and Mass Transfer 126 (2018) 431–441

435

Fig. 4. Meshing configuration.

Fig. 3. Boundary conditions used in the numerical simulation for each type of the PHPs.

l ¼ at lt þ ð1  at Þll

ð12Þ

! The surface normal ( n ) is defined as the gradient of aq and the surface curvature (k) is defined in terms of the divergence of the ^ ). unit normal (n

! n ¼ raq

ð13Þ

! ^ k ¼rn

ð14Þ

! The source term present in the momentum equation ( F ) is related to the pressure jump across the surface due to the effect of surface tension [23]. For a two-phase system, it can be formulated as

qk1 ra2 ð q1 þ q2 Þ 2

F ¼ r12 1

ð15Þ

q1 and q2 refer to the liquid and vapor phase, respectively and k1 is the curvature. The contact angle that the fluid makes with the wall is assumed to be constant. In this condition, the surface normal in the cells near the wall would also be constant. Therefore, by calculating the surface normal of cells adjacent to the wall, the local curvature of the fluid’s surface would be achieved. This curvature adjusts the body force term used in the momentum equation (Eq. (15)). In the energy equation, which is shared among the phases, E and T are used in an average mass form. While, the variable keff is utilized in the same form as overall viscosity and density for each cell (i.e. based on the volume fraction of each phase). When a conventional PHP in a closed-loop shape is used and the heat flux at the heating section is relatively high, the liquid slugs move from the heating section to the cooling section at a relatively high velocity. The inertia of the liquid slugs may be large enough so that the liquid slug can pass the cooling section and enter the next heating section. In this case, flow pattern in the PHP may also include circulatory flow in addition to oscillatory flow [8]. Additionally, the presence of asymmetry in the PHP devices can enhance the circulatory flow. As mentioned, researchers had previously tried to intentionally increase the asymmetry in devices to improve circulation by using check-valves, pipes with different diameters, interconnecting channels, etc. Therefore, our aim for modeling is concentrated on the effect of additional branches on flow circulation. 5. Numerical simulation results and discussion In order to calculate the thermal resistance, evaporator temperature was considered as the average amount of wall temperature all over the heating section. Furthermore, a temporal averaging was performed over a sufficient time span to obtain a single temperature which could be considered as the overall evaporator temperature for a specific amount of heat input to the PHP. Fig. 5 shows thermal resistances (Eq. (4)) of both FP-PHP and AB-FPPHP under three different heat input values. In order to have more consistency with experimental data, heat input values have been reported in Watts by assuming a (3-dimensional) structure for the simulated problem similar to the structure of the experimental

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0.015 Normal With Aditional Branch

Average thermal resistance/(K.m 2 .W -1 )

0.014 0.013 0.012 0.011 0.01 0.009 0.008 0.007 0.006 0.005 5000

7500

10000 -2

Heat Input/(W.m ) Fig. 5. Thermal resistance versus heating power.

Table 1 Numerically obtained initiation time for unidirectional circulation occurrence for different heat input. PHP device

FP-PHP AB-FP-PHP

Heat input 5000 W=m2

7500 W=m2

10,000 W=m2

Dominantly oscillatory behavior 11.6 s

Dominantly oscillatory behavior 8.2 s

24.7 s 3.5 s

setups. As it can be seen, thermal resistances decrease by increasing the heat input. This trend shows that the numerical simulation results are congruent with previous investigations in the field of PHP simulations [24]. Furthermore, this figure indicates that thermal resistance is lower for the AB-FP-PHP compared to FP-PHP for the intended range of heat input.

Recently, investigators had presented the occurrence of fluid circulation in their simulations after some time at relatively high levels of heat input [24]. Simulations in the present work showed that this type of circulation would not change after developing, but its direction is completely random. In other words, starting from the same initial condition, flow circulation in the PHP may be in either CW direction or CCW direction and there is no control on it. A similar condition for flow circulation was observed in the PHP with additional branches. However, the path of flow circulation in this device was predictable and was completely dependent on the position of the branches. For the proposed shape of the PHP (Fig. 1), results showed that the working fluid always circulates in a CCW direction. Unidirectional circulation of the working fluid was observed after a while for all three boundary conditions applied to the ABFP-PHP device and for the highest applied heat flux (q00 ¼ 10; 000 W=m2 ) to the FP-PHP device. For all three heat fluxes applied to the AB-FP-PHP device, the unidirectional CCW circulation was initiated before reaching t ¼ 12 s which was very earlier than the initiated time for constant circulation in the FP-PHP in the case of q00 ¼ 10; 000 W=m2 . However, for the two other applied heat fluxes to the FP-PHP device (q00 ¼ 5000 and 7500 W=m2 ), the working fluid did not show any sign of unidirectional circulation and the regime was dominantly oscillatory. Table 1 shows the numerically obtained initiation time for unidirectional circulation occurrence in both devices for different heat inputs. In addition, the amount of working fluid’s velocity within the PHP was compared between both of the devices. For the applied heat flux of q00 ¼ 10; 000 W=m2 , it was observed that the working fluid’s velocity in the AB-FP-PHP device reached up to 1.35 m/s, while the working fluid’s maximum velocity in the FP-PHP device was nearly 0.7 m/s. It should be noted that the mentioned flow velocities were obtained after achieving steady unidirectional circulation in each of the devices. Fig. 6 shows the unidirectional flow pattern obtained from numerical analysis in a specified area of the PHP due to the presence of additional branches, which is very similar to the unidirectional flow pattern observed in the experiment as shown in Fig. 8. As it can be seen, growth and collapse of vapor bubbles in this device occur in a manner that would produce a semisteady flow in the CCW direction. Additionally, Fig. 6 shows how returning fluid from the condenser flows into the additional branch. As a cooler fluid enters the additional branch, vapor bubbles with high temperature cool down and partially condense in

Fig. 6. Numerical results of morphological arrangement of the vapor and liquid phases in one of the branches under steady unidirectional circulation. (Dashed arrows are tagged with a single vapor plug and solid arrows are tagged with a single liquid slug.)

E. Sedighi et al. / International Journal of Heat and Mass Transfer 126 (2018) 431–441

437

Fig. 7. Numerical results of fluid circulation in the whole PHP setup at different times with q00 ¼ 10; 000 W=m2 ; (a): t = 3.6 s, (b): t = 3.7 s, (c): t = 3.8 s, (d): t = 3.9 s. (Solid arrows are tagged with a single vapor plug.)

that section. After entering the branch, the cooler fluid gets trapped in this section and due to the evaporation, increases the local pressure and eventually pushes the column of fluid

above itself which would create a fluid circulation. The same procedure happens in each of the additional branches which would result in a considerable circulation of the working fluid

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Fig. 8. Mixing behavior in the junction area.

Fig. 9. Refilling behavior as slug/plug flow.

90 in the expected (CCW) direction. Fig. 7 shows the fluid circulation in the whole PHP setup. It could be inferred from the results of the conducted simulations that using additional branches in a PHP leads to a stronger one-way circulation of the working fluid and eventually results in a reduction of the thermal resistance of the device.

Evaporator / Conventoinal FP-PHP Condenser / Conventoinal FP-PHP Evaporator / AB-FP-PHP Condenser / AB-FP-PHP

80

Temperature ( °C)

70

60

6. Flow visualization (experimental setup)

50

40

30 40W

60W

80W

100W

120W

20 0

2000

4000 6000 Time(Sec)

8000

10000

Fig. 10. Thermal variations for 50% filling ratio as a function of heat input in both FP-PHPs.

Images were captured from the area where the additional branch was connected to the AB-FP-PHP experimental setup (dashed rectangle on the evaporator section of Fig. 1(a)). Two main behaviors of flow were observed when the AB-FP-PHP was working. These two behaviors, which are mixing and refilling, are explained in the following sections. All the visualization images were captured for the AB-FP-PHP with filling ratio of 50%. Since one end of the branch was closed, generation and expansion of bubbles pushed up liquid slugs in the CCW direction and drew the circulated cold water into the branch simultaneously. Therefore, in the evaporator section, hot generated liquid slugs and vapor plugs were mixed with returning cold fluid from the condenser and pushed again to the condenser section in CCW circular motion which is shown in Fig. 8 as mixing behavior.

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Conventional FP-PHP 70% 60% 50% 40%

Average thermal resistance/(K.W -1)

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2

Conventional FP-PHP AB-FP-PHP

0.9

0.1

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

0

0 40

60

80

100 120 140 160 180 200 Heat Input/(W)

Fig. 11. Thermal resistance of FP-PHP at different filling ratios.

40

100 120 140 160 180 200 Heat Input/(W)

0.7 0.6 0.5 0.4 0.3 0.2

Conventional FP-PHP / 80 Watt AB-FP-PHP / 80 Watt Conventional FP-PHP / 120 Watt AB-FP-PHP / 120 Watt Conventional FP-PHP / 200 Watt AB-FP-PHP / 200 Watt

0.8 Average thermal resistance/(K.W -1 )

0.8

80

0.9 70% 60% 50% 40%

0.9

60

Fig. 13. Thermal resistance vs. heat input for both FP-PHPs in filling ratio of 50%.

AB-FP-PHP

1

Average thermal resistance/(K.W -1)

Filling Ratio: 50%

1

Average thermal resistance/(K.W -1 )

1

0.7 0.6 0.5 0.4 0.3 0.2 0.1

0.1

0 40

0 40

60

80

100 120 140 160 180 200 Heat Input/(W)

50 60 Filling Ratio/(%)

70

Fig. 14. Comparison between AB-FP-PHP and FP-PHP at different filling ratios and three heat inputs.

Fig. 12. Thermal resistance of AB-FP-PHP at various filling ratios.

7. Results of thermal investigation and discussion As a consequence of mixing behavior, a large portion of existing fluid in the additional branch was discharged upward towards the condenser section and due to the vacuum created in the branch, the returning cold fluid was again sucked into the branch and refilled it. The refilling process is shown in Fig. 9. These mixing and filling processes caused CCW flow recirculation in the AB-FPPHP. This refilling behavior was, to some degree, observed in the simulation results shown in Fig. 6.

The curve in Fig. 10 shows temperature variations of both FPPHP and AB-FP-PHP devices at 50% filling ratio as a function of time and heat input. Starting from the same condition (initial temperature) for both the PHPs, it can be seen that the temperature difference between the evaporator and condenser sections is always lower for the AB-FP-PHP. This shows that in all heat inputs, the thermal resistance of the AB-FP-PHP is less than that of FP-PHP.

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Thermal performance of heat pipes at different filling ratios was investigated. Figs. 11 and 12 demonstrate thermal performance at four different filling ratios for the FP-PHP and the AB-FP-PHP, respectively. The reduction of thermal resistance due to heat increase is visible in both figures. The main reason for this is that the rise of heat input changes the flow regime from slug–plug to annular flow which causes the working fluid to circulate faster [25]. The enhancement of fluid circulation as a result of heat increase was also observed in the visualizations. According to Figs. 11 and 12, for heat inputs in the range of 80 W and above, thermal performances of both devices were better at 50% filling ratio. However, for heat inputs in the low range (below 80 W), thermal performance of the FP-PHP was better at 70% filling ratio. It is observed by comparing the AB-FP-PHP and conventional FPPHP that the AB-FP-PHP demonstrates better performance at the optimum filling ratio for all applied heat inputs (Fig. 13). According to the recorded data, the thermal resistance for the AB-FP-PHP is 18% lower on average compared to the thermal resistance of the conventional FP-PHP at 50% filling ratio. Additionally, from Figs. 11 and 12, it can be seen that the thermal resistance of AB-FP-PHP is considerably better in low orders of heat input (especially for 40 W and 60 W). Presence of additional branches in the AB-FP-PHP expedites the flow circulation and further reduces the evaporator temperature in comparison to FP-PHP. However, this difference between the thermal resistances of the PHPs becomes less by an increase in heat input which is the result of fluid circulation formation in the FP-PHP in higher rates of heat input. Fig. 14 comparatively illustrates the variations in the thermal resistance of both devices relative to the filling ratio at three heat inputs (low (80 W), medium (120 W) and high (200 W)). It can be seen that nearly at all the filling ratios, thermal performance of ABFP-PHP is better compared to FP-PHP. According to the recorded data, the thermal resistance for the AB-FP-PHP is 14%, 11%, and 20% lower on average at 40%, 60%, and 70% filling ratio respectively. The better thermal performance of the AB-FP-PHP in comparison to the FP-PHP in all filling ratios shows that the additional branch could impose its positive effect in a wide range of operating conditions. The observations for moderate heating shows that at the low filling ratio (40%), a large portion of the branch is always filled by vapor bubbles, and also, at the high filling ratio (70%), liquid slugs always fill a large portion of the branch. This unbalanced distribution of vapor and liquid slugs in the branch can deteriorate the thermal performance of the device. However, the AB-FP-PHP still has a better thermal performance compared to FP-PHP. Hence, it is believed that the effectiveness of additional branches can be the highest when a proper amount of working fluid is chosen precisely. The additional branch installed for the AB-FP-PHP must be the reason for better thermal performance under various conditions. Its special geometry enhances the flow circulation by leading the growth of bubbles in a specified direction (CCW). Presence of many vapor plugs at low filling ratios and the small number of them at high filling ratios are the reasons for the unsatisfactory performance of conventional heat pipes at low and high filling ratios [26]. However, it was observed that this problem had a smaller impact on the thermal performance of AB-FP-PHP. Nevertheless, more studies need to be conducted to further investigate the effect of branch length, branch diameter, number of branches, and different filling ratios on the performance of AB-FP-PHP.

ondary bubble pumps. The idea proposed in this paper was first numerically analyzed and the effects of the additional branches were examined using the VOF model for a 2-dimensional flow domain. Afterwards, two aluminum prototypes with Pyrex glasses on top were fabricated for thermal performance comparison and flow visualization purposes. One of them was made with the conventional structure of pulsating heat pipes and the other one with extra branches (secondary bubble pumps) in the evaporator section. Thermal parameters such as temperature variations and thermal resistance were compared between these two systems. Main conclusions are expressed as follows: 1. Numerical simulations showed that the presence of additional branches could trigger and maintain a circulation of the working fluid in an expected direction while circulation in the ordinary PHP is completely random and would just occur at high levels of heat input. The results also showed that fluid returning from the condenser to the evaporator would partially flow into the additional branch and to an extent reduce the evaporator temperature. 2. By visualizing flow behavior in the AB-FP-PHP, it was observed that the additional branches directed the expansion of bubbles in the desired direction and caused the hot fluid from the branch to merge with the cold fluid returning from the condenser at the junction and in the branches. This mixing caused a temperature drop in the evaporator section and a general flow circulation in the system. 3. Temperature variations were compared between FP-PHP and AB-FP-PHP in the vertical position and at 50% filling ratio and it was observed that because of the flow circulation, the difference between evaporator and condenser temperatures in the AB-FP-PHP is lower in comparison to the FP-PHP. Furthermore, evaporator temperature in the AB-FP-PHP was always lower which shows better cooling ability in comparison to FP-PHP. 4. The effect of different filling ratios was examined and at 50% filling ratio, both devices had the best thermal performance. 5. Thermal performance of AB-FP-PHP was improved 14%, 18%, 11%, and 20% on average compared to FP-PHP at 40%, 50%, 60%, and 70% filling ratios respectively. Additionally, thermal performance of AB-FP-PHP was significantly better for the lower order of heat inputs due to the positive effect of additional branches on flow circulation. 6. As a result, it can be concluded that additional branches (secondary bubble pumps) improve the thermal performance of pulsating heat pipes in a wide range of filling ratios. However, further research should be conducted to understand the exact effect of different filling ratios as well as the effect of branch length, branch diameter, and number of branches on the performance of this type of pulsating heat pipes. Conflict of interest The authors declare that they have no conflict of interests regarding the publication of this paper. Acknowledgement We would like to express our gratitude to the Deputy for Research and Technology of Sharif University of Technology for supporting this research study.

8. Conclusion The impact of a new geometrical configuration in pulsating heat pipe structure was investigated. The designed geometrical shape contained additional branches in the evaporator section as sec-

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