Numerical and experimental investigation of pulsating heat pipes with corrugated configuration

Applied Thermal Engineering 102 (2016) 158–166

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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Research Paper

Numerical and experimental investigation of pulsating heat pipes with corrugated configuration Jiansheng Wang, He Ma, Qiang Zhu ⇑, Yiwei Dong, Kaihong Yue Key Laboratory of Efficient Utilization of Low and Medium Grade Energy, MOE, School of Mechanical Engineering, Tianjin University, Tianjin 300072, PR China

h i g h l i g h t s
An improved pulsating heat pipe with corrugated configuration is proposed.
The flow pattern observed from numerical and experimental method is compared.
The start-up time is reduced up to 28.96% with corrugated configuration in evaporation section.
The thermal resistance is reduced up to 37.57% with corrugated configuration in evaporation section.

a r t i c l e

i n f o

Article history: Received 28 December 2015 Revised 20 March 2016 Accepted 31 March 2016 Available online 5 April 2016 Keywords: Pulsating heat pipe Numerical simulation Experimental analysis Corrugated configuration

a b s t r a c t A single loop pulsating heat pipe with corrugated configuration in evaporation, adiabatic, and condensation section is numerically and experimentally investigated in present work. The investigation is carried out under the condition of varying input power ranged from 5 W to 40 W and filling ratio ranged from 30% to 60%. In the numerical investigation, VOF model is used to probe the feature of two-phase flow inside the single loop pulsating heat pipe. The present numerical results such as vapor–liquid flow pattern and variation trend of the thermal resistance show a good consistency with those of the experiments. It’s found that the pulsating heat pipe with corrugated configuration in evaporation section has the best performance of start-up and heat transfer of present considered cases. The results show 28.96% decrease in start-up time and 37.57% in thermal resistance due to the application of corrugated configuration, which presents a remarkable improvement in the overall performance of pulsating heat pipe. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction In the last decade, increasing demand for the heat transfer device with higher efficiency has been appears in engineering application such as electronic cooling. Pulsating heat pipe (PHP) is an efficient heat transfer device which was first proposed by Akachi [1] in the 1990s. Typically, PHP consists of evaporation, adiabatic and condensation section [2–4]. Due to the temperature and pressure difference established inside the PHP, heat is transferred by an action of pulsation or circulation of the working fluid [5–8]. To understand the thermo-hydrodynamic behavior of PHP, numerous investigations have been conducted. It has been found that the features of PHP depend on the structure parameters, physical properties of working fluid and operation conditions [2,9–12]. The flow patterns, such as bubble flow, slug flow, and semi-

⇑ Corresponding author. E-mail addresses: [email protected] (J. Wang), [email protected] (Q. Zhu). http://dx.doi.org/10.1016/j.applthermaleng.2016.03.163 1359-4311/Ó 2016 Elsevier Ltd. All rights reserved.

annular/annular flow were observed by visual methods [6–7,13–14]. In the process of start-up of PHP, the sudden and the gradual are two common types [15]. Changing the geometrical structure of PHP has been proved to be a significant approach to enhance heat transfer performance of PHP. Due to the function of extending heat-transfer surface and thinning the boundary layer, the corrugated surface was an effective way to improve the heat transfer efficiency in practical applications [16]. Dizaji et al. [17] compared several arrangements of convex and concave corrugated tube in a double pipe heat exchanger. They found that the use of corrugated tubes was advantageous to increase the Nusselt number of heat exchanger in comparison with that of smooth one. The heat exchanger with a concave corrugated outer tube and a convex corrugated inner tube performed the best heat transfer efficiency. Moawed et al. [18] used a sinusoidal-shaped inner tube in a pipe heat exchanger, and investigated the effect of the sinusoidal pipe on the heat transfer characteristics and pressure drop. Compared with the smooth

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Nomenclature Cp E F FR L p Q R Sh Sm T t ~ v

specific heat, J/(kg K) internal energy, kJ/kg interface volumetric force, N/m3 filling ratio length, m pressure, Pa input power, W thermal resistance, K/W latent heat source term due to phase change, kg/(m3 s) mass source term due to phase change, W/m3 temperature, K time, s velocity vector, m/s

Greek symbols a volume fraction l dynamic viscosity, kg/(m s)

tube, an up to 93% and 130% increase were achieved in heat transfer performance and friction factor, respectively. In addition, their results showed that the dimensionless exergy loss decreased with the increase of amplitude of the sinusoidal pipe. As mentioned above, the corrugated configuration structure has been widely used in the heat exchanger devices. So far as the authors know, a few available data of corrugated configurations were applied in PHP. Therefore, the objective of present work is to investigate the effect of corrugated structure on the characteristics of PHP with corrugated configuration in different sections. Both experimental and numerical investigations on PHP with corrugated configuration are conducted.

q r k

j gR gt

density, kg/m3 surface tension coefficient, N/m thermal conductivity W/(m K) surface curvature, 1/m the efficiency of thermal performance the efficiency of start-up

Subscripts a adiabatic c condenser e evaporator eff effective ex experimental l liquid nu numerical sat saturation v vapor

ing power varies from 5 W to 40 W by regulating the output voltage of transformer. As shown in Fig. 1, six T-type thermo-couples, labeled as Te1, Te2 for evaporation section, Ta1, Ta2 for adiabatic section, and Tc1, Tc2 for condensation section are attached at the outer wall of the PHP. The real-time temperature data is recorded by Agilent 34970A and then connected to a computer for scanning every 5 s. The experimental thermal resistance Rex of PHP is calculated as follows

Rex ¼ ðT e  T c Þ=Q

ð1Þ

where T e and T c is the average temperature of evaporation and condensation section, respectively, Q stands for the input heating power.

2. Experiment description 3. Physical and mathematical model The experimental apparatus of present work is shown in Fig. 1. The evaporation, adiabatic and condensation section are equal in length of 50 mm. For the purpose of visualization, the pulsating heat pipe is made of quartz glass with the inner diameter of 3.8 mm and outer diameter of 6 mm. The inner diameter of present pulsating heat pipe is small enough so that the working fluid water, will distribute itself naturally in the form of liquid–vapor slugs. The pulsating heat pipe apparatus is fixed in the vertical orientation with bottom-heating pattern. The surface of evaporation section is wrapped with heating wire of diameter 0.4 mm. The condensation section is immersed in a water cooler. The inlet temperature of water cooler maintains 25 °C and a constant mass flow rate at 4.77 g/s is set as well. In order to probe the influence of corrugated configuration on the performance of pulsating heat pipe, three testing PHPs are manufactured. The corrugated configuration is adopted in evaporation, adiabatic and condensation section of three testing loops, namely test 1, test 2 and test 3, and detailed geometries are shown in Fig. 2. For the comparison of present PHP with corrugated configuration with regular PHP (without corrugated configuration), a regular PHP is manufactured as well. All the experiment conditions of testing PHPs such as the inner and outer diameter, the heating and cooling condition, and the filling ratio are consistent with that of the regular PHP. The present PHPs are firstly evacuated to 0.084 MPa by a vacuum pump, and then filled the pipe with water through injection inlet as shown in Fig. 1 by a syringe. In present investigation, the filling ratios of PHPs are set to be 30%, 40%, 50% and 60%. The heat-

3.1. Physical model In numerical investigation, a two-dimensional single loop PHP is modeled. The geometric structure of PHP adopted in numerical simulation is same as that of the experimental apparatus. To keep consistent with the experimental condition, the boundary condition in evaporation section is constant heat flux which depends on the input power. The condensation section of PHP is convective boundary condition, and the other parts of PHP are treated as adiabatic. For obtaining the initial two-phase distribution of working fluid, the temperature of 25 °C and subatmospheric pressure are assumed to be initial conditions in numerical simulation. The k–epsilon viscous model and standard wall function are adopted as well. The SIMPLE algorithm is performed for pressure–velocity coupling. The second-order upwind method is adopted for the momentum equation. The Geo-Reconstruct discretization method is performed for volume fraction. The contact angles of water and quartz glass is 20°. 3.2. Mathematical model and governing equations The volume of fluid (VOF) model is adopted to simulate two immiscible free-surface fluids by solving one set of momentum equations in present numerical simulation. To track the interface between two phases, the definition of volume fraction av and al is necessary, where subscripts v and l represents vapor and liquid, respectively. In present numerical process, liquid water is defined

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Fig. 1. Schematic of the experimental setup.

Fig. 2. Three testing pipes and the parameters of corrugated configuration.

as the primary phase and water vapor is treated as the secondary one. The liquid phase is incompressible, and the vapor phase is compressible. The properties of working fluid such as thermal conductivity, specific heat and density, are assumed to be constant. The volume fraction in each computational mesh meets the following relationship

av þ al ¼ 1

ð2Þ

The governing equations are described, respectively. Continuity equations for each phase

@ al S v Þ ¼ m;l þ r  ðal ~ @t ql @ av S v Þ ¼ m;v þ r  ðav ~ @t qv

ð3Þ ð4Þ

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Sm;l and Sm;v is the source terms of mass transfer of liquid and vapor phase, which are used to calculate the mass transfer during evaporation and condensation process and expressed as [19,20]:

( Sm;l ¼ Sm;v ¼

sat 0:1al ql j TT j T P T sat T sat

sat 0:1av qv j TT j T sat ( TT sat 0:1al ql j T sat j

T < T sat T P T sat

sat 0:1av qv j TT j T < T sat T sat

ð5Þ ð6Þ

where T sat stands for the saturation temperature. Momentum equation:

! @ ðq~ v Þ þ r  ðq~ v~ v Þ ¼ rp þ r½lðr~ v T Þ þ q~g þ F @t

ð7Þ

The continuum surface force (CSF) model proposed by Brackbill et al. [21] is used to calculate the surface tension of the phase inter! action. The forces acting in the fluid F in Eq. (7) is treated as a source term that can be express as

F¼

X

rij

ai qi jj raj þ aj qj ji rai 1 ðqi þ qj Þ 2

ð8Þ

where r is the surface tension coefficient, ji is the surface curvature defined as

ji ¼ jrDaaii j.

Energy equation

@ ðqEÞ þ r  ½~ v ðqE þ pÞ ¼ r  ðkeff rTÞ þ Sh @t

ð9Þ

where keff is the effective thermal conductivity, E is the internal energy defined by saturation temperature T sat and specific heat C p

E¼

al ql C p;l ðT  T sat Þ þ av qv C p;v ðT  T sat Þ al ql þ av qv

ð10Þ

Sh is the energy source term and calculated by

Sh ¼ hLH Sm;l ¼ hLH Sm;v

ð11Þ

In a liquid–vapor two-phase system, the fluid properties in the above equations are determined as volume averaged variables of each phase

q ¼ al ql þ av qv k ¼ al kl þ av kv l ¼ al ll þ av lv

Fig. 3. Comparison between experiment and simulation of regular PHP at 5 W of, filling ratio = 50% (a) experiment; and (b) numerical simulation.

ð12Þ

The thermal resistance Rnu is

Rnu ¼ ðT e  T c Þ=Q

ð13Þ

where T e , T c is the overall average temperature of the evaporation and condensation section. 4. Results and discussion 4.1. Temperature oscillation characteristics Fig. 3 shows the temperature variation of regular PHP recorded by experiment and simulation at 5 W input power and filling ratio of 50%. As shown in Fig. 3(a), the temperature rise slowly and accompanying with slight oscillation, which indicates that the PHP does not start up at low input power condition. Actually, the working fluid is observed to be an up-and-down oscillation pattern with slight amplitude. However, the temperature variation of numerical simulation presents a clear trend that the temperature firstly rises and suddenly drops after reaching a peak as shown in Fig. 3(b). The moment with the abrupt change of temperature is generally considered the start up signal of PHP [15]. The deviation of experiment and numerical simulation may be attributed to the inconsistency of initial vacuum condition between the numerical simulation and the experiment. In contrast, the temper-

Fig. 4. Temperature fluctuation of regular PHP at 10 W, filling ratio = 50% by experiment.

ature at evaporation section derived from the numerical simulation is higher than that derived from the experiment, which results from the heat loss of evaporation section in experiment.

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Fig. 5. Temperature fluctuation of regular PHP at 20 W, filling ratio = 50% by experiment.

Fig. 7. Temperature fluctuation of regular PHP at 40 W, filling ratio = 50% by experiment.

visualization experiment. The input power is kept at 20 W, and filling ratio is 50%. It can be found that the flow patterns derived from the numerical simulation are in good agreement with that from the experiment. In Fig. 8(a), bubble A appears in evaporation section as heat flux is continuously added, and similar flow pattern can be observed in experiment (bubble a). Meantime, longer vapor slug B is also visually found in experiment (vapor b). Other types of gas–liquid two-phase flow such as vapor C and c in the corrugated section, plug D and d in the smooth section in Fig. 8(b), vapor E and e in elbow section, and bubble-plug flow F and f in Fig. 8(c) are observed both in numerical and experiment investigation. Therefore, the numerical simulation of present work is credible. In addition, it can be found that movement of the bubbles induces the flow disturbance inside the loop as shown with the contours of vector around vapors near the corrugated wall. 4.3. Start-up time of PHPs

Fig. 6. Temperature fluctuation of regular PHP at 30 W, filling ratio = 50% by experiment.

The temperature oscillation frequency and amplitude will augment with the increase of heating power [22,23]. As shown in Figs. 4 and 5 obtained from experimental records, an obvious variation of temperature occurs in all sections. At input power of 10 W, the sudden change follows closely the temperature increase. It means that the heat provided in evaporation section makes the temperature of working fluid inside PHP raised till the gas–liquid two-phase oscillating flow is induced. In contrast, the temperature shows an obvious variation at input power of 20 W. The temperature variation between adjacent tubes is alternate, which means the flow direction of working fluid inside PHP changes alternately as well. With the increase of input power, the temperature oscillation is reinforced as shown in Figs. 6 and 7. The frequency and amplitude of temperature variation can be observed. It manifests that more vapor plugs grow in evaporation section and the flow pattern varies from semi-annular flow to annular flow. 4.2. Overview of flow behavior Fig. 8 shows the comparison of bubble behaviors and distributions of three PHPs between the numerical simulation and the

The start-up time in experiment at different input powers and filling ratios for regular PHP and three tested PHPs are compared as shown in Fig. 9. It is obvious that test 1 shows a great advantage in start-up time compared with that of regular PHP, which may be attributed to two reasons. One is the corrugated wall in evaporation section extends the heat-transfer area, which is helpful for improving heat transfer, and other is that the uneven surface contributes to the growth of boiling cores, which results in the growth of bubbles in evaporation section. The increase of pressure around the bubbles leads to the hot working fluid pushed upwards, thereby PHP starts to running. Comparing the results of four PHPs, it is noteworthy that the PHP with corrugated configuration in adiabatic section has the poorest start-up performance at higher input power. The start-up process of PHP with corrugated configuration in condensation section is the longest at lower filling ration and input power, which results from the fact that the condensation enhancement of the working fluid leads the increase of liquid slug and then the reduction of driving force inside PHP. When the working fluid flows through the adiabatic section where no external heat is loaded, the uneven surface will increase the friction that doesn’t contribute to the improvement of heat transfer. At lower filling ration and input power, corrugated configuration in adiabatic section contributes the fluctuation of liquid slug, which is helpful for the starting of PHP and the start-up time is reduced. The influence of corrugated configuration in evaporation section on

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gt ¼

ttest1  tregular  100% t regular

163

ð14Þ

The results show that the pulsating heat pipe with corrugated configuration in evaporation section is helpful to accelerate the start-up, which can reduce by up to 28.96%. 4.4. Thermal performance Thermal resistances of present PHPs obtained from experimental and numerical investigation are compared as shown in Fig. 10 at the filling ratio of 50% and 60%. It can be found that the deviation exists between numerical and experimental results, the deviation decreases with the augment of the input power. As mentioned above, the heat loss from evaporation and adiabatic section is uncertain but non-negligible in visually experiment, which leads the deviation between the numerical and experimental result. With the increase of input power supplied on loop, the proportion of the heat loss reduces gradually, which results in the reduction of the deviation. The qualitative consistency of numerical and experimental result proves the reliability of present numerical investigation. Fig. 11 shows the thermal resistance of present PHPs obtained from experiment. Obviously, thermal resistance decreases with the increment of input power, which indicates that the heat transfer performance of PHPs is improved. Test 1, corrugated wall adopted in evaporation, has the lower thermal resistance compared with other considered PHPs especially at lower input power. Table 2 shows the comparison of thermal resistance of test 1 and regular PHP, and the efficiency of thermal performance gR is defined by following formula:

gR ¼

Fig. 8. Comparison between visualization and simulation (a) flow behavior of test 1; (b) flow behavior of test 2; and (c) flow behavior of test 3.

start-up time is shown. Table 1 shows the comparison of start-up time of test 1 and regular PHP. The efficiency of start-up gt , is defined as

Rtest1  Rregular  100% Rregular

ð15Þ

The results show that the thermal resistance of PHP is reduced by up to 37.57% under certain conditions. It indicates that the heat transfer improvement of PHP in evaporation section helps the reduction of thermal resistance, which is especially true under the condition of lower input power. It can be seen from the table that gR decreases with the increase of the input power. Because at higher input power, the proportion of heat transfer enhancement derived from the decrease of the corrugated configuration, which results in the reduction portion of the thermal resistance of PHPs wears off. At the present considered filling ratios, PHPs with the corrugated configuration in evaporation section have the minimum thermal resistance. Thus the corrugated configuration in evaporation section has great advantages in thermal performance. The reason is that the evaporation of working fluid inside PHP is the source of driving force for the running of PHP. Improving the heat transfer performance of evaporation section has the most significant influence on the improvement of PHP performance. Similarly, the improvement of heat transfer in condensation section with corrugated configuration is helpful to reduce the thermal resistance of PHP. Unlike the PHP with corrugated configuration in evaporation section, as shown in Fig. 11, the PHP with corrugated configuration in condensation section has higher thermal resistance, which results from the decisive role of evaporation section in the running of PHP. It’s worth noting that the PHP with corrugated configuration in adiabatic section has the lower thermal resistance at lower input power and filling ratio than that of regular PHP and the PHP with corrugated configuration in condensation section, which results from the fluctuation of liquid slug in adiabatic section. The fluctuation of liquid slug promotes the motion of liquid slug inside PHP. However, with the increase of input power and filling ratio, the heat loss proportion in adiabatic section augments, which results in the increase of thermal resistance of PHP.

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Fig. 9. Comparison of the start-up time at different input powers and filling ratios (a) Fr30 (b) Fr40 (c) Fr50 and (d) Fr60.

Table 1 Comparison on start-up time of test 1 and regular PHP. Q (W)

ttest1 (s)

10 15 20 25 30 35 40

FR = 30% 189.00 122.00 90.60 80.40 80.10 65.50 62.30

10 15 20 25 30 35 40

FR = 50% 174.26 107.68 74.63 71.47 62.10 58.13 47.02

ttest1 (s)

tregular (s)

gt

(%)

233.90 167.00 112.07 94.50 98.50 78.60 67.08

19.20 26.95 19.16 14.92 18.68 16.67 7.13

FR = 40% 177.80 116.83 95.13 79.15 75.18 61.59 55.01

249.20 160.45 125.24 106.46 102.67 72.50 62.10

28.65 27.19 24.04 25.65 26.87 15.05 11.42

233.86 151.57 90.13 89.00 86.83 69.28 57.20

25.49 28.96 17.20 19.70 28.48 16.09 17.80

FR = 60% 157.30 84.50 78.57 68.99 62.20 55.50 49.30

210.80 113.17 103.29 96.71 81.35 70.86 62.08

25.38 25.33 23.93 28.66 23.54 21.68 20.59

t regular (s)

gt

(%)

Fig. 10. Thermal resistance comparison between simulation and experiment.

5. Conclusions The performance of three type single loop PHP with different corrugated configuration is investigated by experimental and numerical methods, and compared with a regular one. The thermal resistance and flow visualization of present considered PHPs are studied. The conclusions are summarized as follows

(1) The results of present numerical simulation such as the flow patterns and thermal resistance show consistencies with that of experiment, which indicates that present numerical method is reliable.

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Fig. 11. Thermal resistance comparison at different input powers and filling ratios (a) Fr30; (b) Fr40; (c) Fr50; and (d) Fr60.

Table 2 Comparison on thermal resistance of test 1 and regular PHP. Q (W)

Rtest1 (°C/W)

Rregular (°C/W)

gR (%)

Rtest1 (°C/W)

Rregular (°C/W)

(%)

gR

5 10 15 20 25 30 35 40

FR = 30% 9.45 7.10 4.87 3.50 3.21 2.85 2.66 2.44

11.78 9.13 6.14 4.27 3.52 3.16 2.87 2.57

19.78 22.23 20.68 18.03 8.81 9.81 7.32 5.06

FR = 40% 7.71 6.95 4.56 3.66 3.16 3.09 2.93 2.51

12.35 9.06 5.81 4.15 3.33 3.29 3.07 2.76

37.57 23.29 21.52 11.81 5.11 6.08 4.56 9.06

5 10 15 20 25 30 35 40

FR = 50% 7.30 6.60 3.93 3.32 3.15 2.85 2.76 2.69

11.29 8.62 5.06 4.14 3.56 3.47 3.32 2.92

35.34 23.43 22.33 19.81 11.52 18.10 16.87 7.88

FR = 60% 8.12 5.26 4.06 3.52 3.12 2.89 2.88 2.73

9.39 6.40 4.64 4.13 3.69 3.41 3.29 2.91

13.53 17.81 12.50 14.77 15.48 15.25 12.46 6.19

(2) There is a deviation between the results such as the variation of temperature and the thermal resistance obtained from the numerical and experimental method, which is attributed to the heat loss of experimental apparatus and the inconsistency of initial condition between two methods.

(3) The corrugated configuration in evaporation section of PHP is proved to have a better performance of start-up and heat transfer than that of the regular one. The corrugated surface in adiabatic section has contributed to the motion of liquid slug at lower filling ration and input power. (4) The corrugated configuration in evaporation and condensation section improves the heat transfer, which results in the reduction of thermal resistance of PHP. Therefore, the corrugated configuration can be applied in practical engineering. It is suggested that further investigation should be conducted on the detail structures of corrugated configuration.

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