Numerical investigation on integrated thermal management via liquid convection and phase change in packed bed of spherical low melting point metal macrocapsules

International Journal of Heat and Mass Transfer 150 (2020) 119366

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

Numerical investigation on integrated thermal management via liquid convection and phase change in packed bed of spherical low melting point metal macrocapsules Jian-Ye Gao a,c,d, Xu-Dong Zhang a,b,d, Jun-Heng Fu a,b,d, Xiao-Hu Yang f, Jing Liu a,b,c,d,e,∗ a

CAS Key Laboratory of Cryogenics, Technical Institute of Physics and Chemistry, Beijing 100190, China School of Future Technology, University of Chinese Academy of Sciences, Beijing 100049, China School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China d Beijing Key Laboratory of Cryo-Biomedical Engineering, Beijing 100190, China e Department of Biomedical Engineering, School of Medicine, Tsinghua University, Beijing 100084, China f Science and Technology on Thermal Energy and Power Laboratory, Wuhan Second Ship Design and Research Institute, Wuhan 430205, China b c

a r t i c l e

i n f o

Article history: Received 26 August 2019 Revised 25 December 2019 Accepted 10 January 2020

Keywords: Phase change macrocapsule Low melting point metal Laminar flow Composite thermal management Porous media Numerical investigation

a b s t r a c t This paper is dedicated to investigate the integrated cooling modality that the spherical low melting point metal (LMPM) macrocapsules were introduced and filled as phase change material (PCM) into a convective cooling heat sink. The fluid-solid heat transfer process coupled with phase change in the packed bed was numerically calculated based on the local thermal non-equilibrium theory and the effective specific heat capacity model which were validated in advance by conceptual experiments. The thermal management ability of composite heat sink packed with spherical LMPM-PCM macrocapsules under typical operating conditions has been revealed. In addition, the influences of different stacking patterns of LMPM particles, particle diameter and inlet velocity on the heat transfer enhancement in the packed bed were comprehensively investigated, respectively. It is found that compared with convective cooling heat sink alone, the composite heat sink filled with LMPM-PCM macrocapsules presents excellent thermal management performance. The temperature increment of heat source in the pulse heat load is reduced by 73.4%, which fully demonstrates the advantages of filling spherical particles. Besides, the Orthoclinal Stacking method achieves the largest volumetric heat transfer coefficient among different stacking patterns of equal-diameter spherical LMPM-PCM macrocapsules. What is more, the plateau duration of the solidification is gradually shortened with the decreasing diameter of the spherical LMPM-PCM macrocapsules and the increasing inlet velocity, which is advantageous for the system to quickly rehabilitate to normal operating temperatures during the de-pulse stage. Overall, this novel integrated cooling modality is proven to be a powerful and practical way to sustain extreme thermal management challenge. © 2020 Elsevier Ltd. All rights reserved.

1. Introduction Recent interest in combinatorial heat transfer science [1,2] has grown intensively and various type of innovation designs have been proposed and studied. As conventional thermal management schemes have reached their practical application limit and become impractical for the severe and complex thermal management conditions, reasonable combinations of different heat transfer methods have been discussed and demonstrated. Among them, the integrated thermal management of convective cooling and phase

∗ Corresponding author at: CAS Key Laboratory of Cryogenics, Technical Institute of Physics and Chemistry, Beijing 100190, China. E-mail address: [email protected] (J. Liu).

https://doi.org/10.1016/j.ijheatmasstransfer.2020.119366 0017-9310/© 2020 Elsevier Ltd. All rights reserved.

change has recently attracted numerous attentions in the fields of energy storage [3,4], solar photovoltaic power generation [5–7], electronic circuits [8,9] and battery thermal management [10–14]. Conventionally, the integrated thermal management can be divided into two categories based on whether the heat transfer fluid is in direct contact with the PCMs. For the PCM thermal management combined with series or parallel convection cooling system [2,15–17], the PCMs are mainly used for thermal buffering without directly contacting with the fluid. Some typical hybrid PCM thermal managements are reported as follows. Huang et al. [18] studied the natural convection in an internally finned PCM heat sink for the thermal management of photovoltaics. Ling et al. [19] and Peng et al. [20] designed hybrid thermal management systems integrating PCM with air cooling to solve the overheating of lithium

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Nomenclature Ac cp C dp De fe h hv H k l L Nc p P Pr qn qp ReD S t tn tp T Ta Tb,max Tf,out Tin Tm u u uphysical w

sectional area (m2 ) specific heat capacity (J/kg/°C) inertial drag coefficient particle diameter (mm) equivalent dimension (m) friction factor area heat transfer coefficient (W/m2 /°C) volumetric heat transfer coefficient (W/m3 /°C) latent heat (J/kg) thermal conductivity (W/m/°C) sectional length (m) length of packed bed (m) coordination number pressure (Pa) sectional perimeter (m) Prandtl number normal heat flux (W/cm2 ) pulse heat flux (W/cm2 ) Reynolds number source term vector time (s) normal working time (s) pulse time (s) temperature (°C) ambient temperature (°C) maximum temperature of heat source (°C) temperature of outlet fluid (°C) temperature of inlet fluid (°C) melting point (°C) velocity vector (m/s) superficial velocity (m/s) physical velocity (m/s) sectional width (m)

Greek symbols 1/α viscous drag coefficient β liquid fraction εm mean voidage λ thermal conductivity (W/m/°C) μ dynamic viscosity (kg/m/s) ρ density (kg/m3 ) Subscript f fluid s solid l liquid Abbreviations HS heat sink LMPM low melting point metal NPCM nano phase change material PCM phase change material

ion batteries. Sahoo et al. [21] reported a hybrid PCM-based air cooling system experimentally to meet the requirement of power surge effect in electronics equipment. The hybrid PCM thermal management combined with air cooling systems may represent the simplest and cheapest approach, however, its performance is limited by the poor cooling capacity of air. Considering the high thermal conductivity and heat capacity of coolant in liquid cooling system, some novel PCM thermal management systems based on liquid cooling are introduced and integrated. Kim et al. [22] experimentally evaluated a PCM-based

compact cascade cooling system, which facilitates cooling through heat circulation without the additional energy required to circulate cooling fluids, but the reduced enhancement was observed in PCMs with low thermal conductivity during successive heatingcooling cycles. To maintain the temperature rise and difference of lithiumion battery module within a desirable range, An et al. [23] designed a novel thermal management system based on paraffin/expanded graphite composite PCM coupled with liquid cooling. In addition, liquid cooling enhanced by compact structures such as cooling plates [24] and cooling mini-channels [25] are coupled with the PCM thermal management. Nevertheless, the performance the hybrid thermal management coupled with liquid cooling, is mainly restricted by the inherently low thermal conductivity of PCMs. For another integrated thermal management of convective cooling and phase change, the PCM is nanoencapsulated or microencapsulated to maintain the shape during melting and solidification process, and then added into the heat transfer fluid to increase the thermal conductivity and the thermal energy storage capacity of the fluid [26–30]. Benefiting from the large specific surface area of nano/micro capsule, the performance of this integrated thermal management is superior to the former. However, the latent heat storage density of nano/micro capsule is greatly reduced due to the large volume ratio of the encapsulation shell or support structure [31], which hampers the use of these composited systems especially in the situations where there exist ultra-high thermal shocks. What is more, there are serious stresses on the shell of nano/micro capsule induced by the volume changes during melting and solidification of the PCM, resulting in the inevitable leakage of capsules [32]. Nowadays, the integrated thermal management based on the PCM macrocapsules and convective cooling has become a research focus. As PCM macrocapsules are packed into the heat sink and the heat transfer fluid contact with the PCM macrocapsules directly, the heat transfer area is effectively increased. Regin et al. [33] numerically analyzed the behavior of a packed bed latent heat thermal energy storage system using spherical PCM macrocapsules filled with paraffin wax. Benefiting from the larger specific surface of packed bed, the charging and discharging rate are significantly improved. Besides, the effects of conduction and outside convection of spherical PCM macrocapsules on the thermal storage performance were investigated by Lee et al. [34]. Yang et al. [35] reported a solar storage packed bed using three kinds of spherical PCM macrocapsules. The PCM capsules made of polycarbonate spheres were packed in a cylindrical tank based on the melting temperature of PCM. The energy and exergy performances of the multiple-type packed bed were revealed better than single-type packed bed. In fact, the thermal management performance of the PCM capsules packed bed is still limited due to the inherently low thermal conductivity of PCMs. Yu and He [36] first reported on a novel shape-remodeled PCM macrocapsule for thermal energy storage, which can be dynamically and repeatably remodeled as needed to a complicated shape with large-scale deformation. Expanded graphite was added to improve the thermal conductivity of octadecanol. This study is significant and the results are valuable, opening the way for further development of elastic PCM capsule applications in energy storage systems. As described in [36], the EBiInSn-silicone composites show great thermal and mechanical properties, the preparation method is similarly adopted and improved in the present work. The above analysis has indicated that the integrated performance of PCM thermal management and convection cooling is still limited due to the inherently low thermal conductivity of PCMs and the poor cooling capacity of coolant, which restricts the wide use of these composited system especially in the situations where there exist ultra-high thermal shocks. As a class of newly emerging

J.-Y. Gao, X.-D. Zhang and J.-H. Fu et al. / International Journal of Heat and Mass Transfer 150 (2020) 119366

high-performance phase change material, low melting point liquid metals, which own high thermal conductivity and thermal capacity inherently, show excellent performance in heat extraction and transport [37–39]. Up till now, little is known in the combinatorial utilization of liquid cooling and LMPM-PCM macrocapsules in packed bed units against thermal shock. The present work is dedicated to study the performance of composite convective cooling heat sink packed with the spherical LMPM-PCM macrocapsules. Benefiting from the larger heat exchange specific surface of packed bed and higher thermal conductivity and thermal capacity of LMPM-PCM, the integrated heat management system is used to cope with the transient peak load of continuously working heat source. The rest of paper is organized as follows. Firstly, the preparation spherical LMPM-PCM macrocapsules was introduced and a series of relevant characterizations were performed. Then a simplified 3D numerical model was developed to reveal the phase change and convection process in the packed bed of spherical LMPM-PCM macrocapsules, and it was validated through comparing with the experimental data. Finally, the reinforce mechanism of spherical LMPM-PCM macrocapsules on the convective heat transfer was revealed, the effect of different stacking patterns of spherical LMPM-PCM macrocapsules and single parameter of inlet velocity, particle size on the convection heat transfer in the packed bed were also investigated. 2. Experimental section 2.1. Materials The eutectic Bi31.6 In48.8 Sn19.6 alloy (EBiInSn) was composed of 31.6 wt% bismuth, 48.8 wt% indium and 19.6 wt% tin, which were supplied by Zhuzhou Keneng New Material Co. Ltd. These metals were mixed together by the given proportion at 200 °C in vacuum drying oven for 4 h to prepare EBiInSn [36]. The silicone of Ecoflex 00-30, supplied from Smooth-On, was selected as the main component of the macrocapsule shell, considering its excellent elastic properties. 2.2. Preparation of spherical LMPM-PCM macrocapsules The spherical LMPM-PCM macrocapsules were composed of two parts, as the macrocapsule core was prepared by spherical EBiInSn particles with diameter of 3 mm by the physical method of foundry grinding, and the macrocapsule shell, which helps spherical EBiInSn particles keep their shape when melted during the experiment, was prepared by the EBiInSn-silicone composites. The preparation process of the spherical LMPM-PCM macrocapsules was shown in Fig. 1. As the preparation of macrocapsule shell is crucial, the preparation process of macrocapsule shell is described and characterized in detail as follow. At first, 20 ml E-BiInSn and 40 ml Ecoflex 00-30 A were mixed and stirred for 30 min in a water bath at 70 °C. The speed of the mechanical stirrer was set as 10 0 0 r/min. And then, 20 ml E-BiInSn and 40 ml Ecoflex 00-30 B were mixed and stirred in the same way. After the temperature of mixtures was reduced to room temperature, taking 10 ml of each of the above mixtures and stirring at the speed of 100 r/min for 5 min. In order to reduce the viscosity of the silicone of Ecoflex 00-30, 10 ml n-hexane was added into the mixtures, which can significantly improve the fluidity of the silicone and is easy to volatilize during vacuum drying. The spherical EBiInSn particles were arranged on a copper mesh with size of 2 mm and the copper mesh was put on the rectangular vessel for recycling the coating materials and keeping particles in suspension. And then, the EBiInSn-silicone composites diluted with n-hexane were poured on the surface of the spherical EBiInSn

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Table 1 Thermophysical properties of the macrocapsule shell. Thermal conductivity Test k (W/(m°C))

Thermal diffusivity a × 106 (m2 /s)

Volumetric heat capacity cp (MJ/(m3 °C))

1 2 3

0.4528 0.4556 0.4547

1.437 1.426 1.429

0.6508 0.6496 0.6497

particles. Finally, both the copper mesh and rectangular container were placed in a vacuum drying oven at 40 °C for 12 h. 2.3. Characterization of the macrocapsule The density of the microscope shell was measured by the weighing method. The density value was obtained through averaging the results of three samples. The average density of the microscope shell is 3.296 g/cm3 . The thermophysical properties of the microscope shell, such as thermal conductivity, thermal diffusivity and volumetric heat capacity, were tested by transient plane source method (TPS, 2500S, Hot Disk). Both the two samples were prepared with diameter of 30 mm and height of 10 mm at each test. The tests were repeated three times and the results were shown in Table 1. The average thermal conductivity of the microscope shell is 0.65 W/(m°C), which is close to the thermal conductivity of water. And the average heat capacity is 1.430 MJ/(m3 °C), which is about one third of water. The average thermal diffusivity of the microscope shell is 0.454 mm2 /s, 3.2 times that of water approximately. Besides, the micro-morphology of the EBiInSn-silicone composites was observed using a field emission environmental scanning electron microscope (ESEM, QUANTA FEG 250, FEI) and was shown in Fig. 2. As illustrated in Fig. 2(c), the elemental distribution of EBiInSn-silicone composites in the section was obtained from the energy dispersive spectrometry (EDS, 6853-H, HORIBA). The solid-liquid phase change behavior of macrocapsule shell was characterized using differential scanning calorimetry (DSC, 200F3Maia, NETZSCH). Samples were heated at 10 °C/min in the temperature range of -100 °C to 100 °C. What is more, the thermal stability of the composites was evaluated by thermal gravimetric analysis (TGA, STA449C, Netzsch) and the heating rate was set as 10 °C/min from 30 °C to 900 °C. As illustrated in Fig. 3(a), there are two distinct peaks of the melting-freezing DSC curves of macrocapsule shell, which represents the two components respectively. In Fig. 3(b), TG and DTG curves of EBiInSn-silicone composites diluted with n-hexane and without n-hexane were compared. It can be seen from the figure that the curves of EBiInSn-silicone composites diluted with n-hexane and without n-hexane almost coincided, indicating that the n-hexane was fully volatile during the vacuum drying. The tensile property of macrocapsule shell was measured by a spring testing machine (ZQ-21B-1, Zhiqu, Dongguan). As illustrated in Fig. 4, the elastic parameters of the macrocapsule shell sample are Young’s modulus of 435.5 kPa and fracture strain of 580%. In order to characterize the thermal stability of the prepared spherical LMPM-PCM macrocapsules, the macrocapsules were arranged on a copper mesh firstly, and the copper mesh was heated by a heating device with temperature control module. Fig. 5(a) shows an optical photo of the macrocapsule array when the temperature rose to 110 °C, the K-type thermocouple was arranged between the heating platform and the copper mesh. In addition, the far-infrared thermograph imaging system (FLIR SC620, FLIR Systems Inc) was used to demonstrate the temperature distribution of the macrocapsule array visually, as shown in Fig. 5(b). As can be seen from Fig. 5(b), the internal temperatures of spherical LMPMPCM macrocapsules were higher than the melting point. However,

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Fig. 1. The preparation process of the spherical LMPM-PCM macrocapsules.

Fig. 2. The morphology of EBiInSn-silicone composites: (a) micro-morphology using ESEM, scale bar is 100 μm; (b) optical photo of EBiInSn-silicone composites; (c) the elemental distribution of EBiInSn-silicone composites in the section by EDS, scale bar is 10 μm.

they can still maintain their original shape when the heating temperature is 110 °C, which is a powerful proof of that the spherical LMPM-PCM macrocapsules have been successfully manufactured. 3. Determination of calculation model 3.1. Physical model The spherical metal macrocapsules, whose melting point is below 200 °C, are packed in the copper channel as phase change materials. And the fluid can flow in the void formed by the spherical LMPM-PCM macrocapsules. Then the gratings are arranged at both ends of the copper channel, which not only allows fluid to flow through, but also functions to fix spherical LMPM-PCM macrocapsules. Water is selected as the working fluid in present study due

to its easy access, low cost, and stability. When heat transferred from the heat source to the copper channel, the temperatures of fluid and spherical LMPM-PCM macrocapsules in the packed bed are increased. In regular working stage, the heat generated by the heat source is mainly carried away by the coolant, and the phase change process of spherical LMPM-PCM macrocapsules does not undergo. When encountering a pulsed thermal shock, the spherical LMPM-PCM macrocapsules absorb heat and couple with the phase change process. LMPM-PCM can be selected according to the different temperature control applications. The physical model is schematically shown in Fig. 6. In this study, the following assumptions are employed for calculating melting-freezing process of PCM: (1) Flow is laminar flow; (2) The natural convection during the melting-freezing process can be neglected, due to the high thermal conductivity of LMPM-

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Fig. 3. Thermal properties of macrocapsule shell: (a) the melting-freezing DSC curves of macrocapsule shell; (b) TG and DTG curves of EBiInSn-silicone composites diluted with n-hexane and without n-hexane.

Fig. 6. Schematic diagram of physical model.

much smaller than that of the capsule core; (5) PCM is homogeneous and isotropic. 3.2. Mathematical model and computational methods

Fig. 4. The mechanical property of macrocapsule shell.

In order to reveal the phase change and convection process in the packed bed of spherical LMPM-PCM macrocapsules, the model of isotropic homogeneous porous medium is adopted, and the three dimensional equations for mass, momentum, and energy are as follows. Continuity equation:

∂ ρf + ∇ · ( ρf u ) = 0 ∂t PCM [40]; (3) Volumetric expansion of the spherical LMPM-PCM macrocapsules can be neglected; (4) The thermal resistance of the macrocapsule shell can be ignored, considering that the thermal conductivity of the macrocapsule shell is close to that of the cooling fluid water, and the thickness of the capsule membrane is

(1)

Momentum equation:

∂ ( ρf u ) + ∇ · ( ρf u  u ) = ∇ p ∂t    2 T +∇ · μ ∇u + ( ∇u ) − δ ( ∇ · u ) + S 3

(2)

Fig. 5. The thermal stability of spherical LMPM-PAM macrocapsules: (a) heating device with temperature control system and digital display device with K-type thermocouple; (b) the far-infrared thermograph imaging of macrocapsules.

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The S in Eq. (2) is the source term vector of momentum exchange between liquid and solid phases, used to describe the effect of porous media on viscosity and inertial of fluid.

μ

S=−

α

u+



1 C ρf |u|u 2

(3)

The friction factor given by Aerov and Tojec is used to define the viscous drag coefficient (1/α ) and inertial drag coefficient (C) of fluid flow in non-sintered porous media regions [41], i.e. 3 dp  p εm 36.4 = + 0.45 Ree ( 1 − ε m ) 3 ρf u 2 L

fe =

(Ree < 20 0 0)

2 ρf u d p 3 μf ( 1 − ε )

Ree =

(4) (5)

According to Eqs. (4) and (5), one has: 2

α

= 163.8

C=

λ = (1 − β )λs + βλl

(17)

cp1 =

1 

ρ

0 T −Ts Tl −Ts

1

( 1 − ε m )2 εm 3 dp 2

(7) (8)

where ρ f is the fluid density, μf is the dynamic viscosity of the fluid, ε m is the voidage of the media defined as the ratio of the volume occupied by the fluid to the total volume, dp is particle diameter, |u| is the superficial velocity, |u| = εm uphysical , and uphysical is the actual fluid velocity. Considering the difference between the thermal conductivities of water and the spherical LMPM-PCM macrocapsules, the local thermal non–equilibrium model is used to describe the heat transfer in the packed bed. Dual energy equations for describing the heat transfer in packed bed layer are as follows. Porous media:

∂ (ρ cp1 T ) = (1 − εm )∇ · (λ∇ T ) − hv (T − Tf ) ∂t

(9)

Fluid:

∂ (ρf cp2 Tf ) + (u · ∇ )(ρf cp2 Tf ) = εm ∇ · (λf ∇ Tf ) + hv (T − Tf ) (10) ∂t The volumetric heat transfer coefficient (hv ) is calculated with the following correlation developed by Hwang et al. [42]:

6h ( 1 − εm ) dp

1 − β )ρs cp1,s + βρl cp1,l



+L

∂ αm ∂T

1 βρl − (1 − β )ρs 2 (1 − β )ρs + βρl

β=

2.7 ( 1 − εm ) εm 3 dp

hv =

(16)

(6)

According to Eqs. (3) and (6), we get:

1

ρ = (1 − β )ρs + βρl

αm =

( 1 − εm ) (1 − ε ) = 163.8 μf u + 1.35 3 m ρf u2 3 d2 L εm εm dp p

p

In order to describe the melting and solidification process of LMPM-PCM particles, the equivalent heat capacity method is adopted in this paper. The natural convection during the melting process could be neglected, due to the high thermal conductivity of LMPM, which leads to that the thermal conduction dominates the phase change process [40].

, , ,

T ≤ Ts Ts < T < Tl T ≥ Tl

(18)

(19)

(20)

The phase change and heat transfer process in the packed bed of spherical LMPM-PCM macrocapsules are solved numerically through CFD software Fluent. The solution equations mentioned above are discretized with the second order implicit scheme, and the pressure-velocity coupling is solved through the SIMPLE algorithm. In order to ensure calculation accuracy, the convergence residual for continuity equation is set as 10−13 and the convergence residual for momentum equation and dual energy equations are set as 10−15 respectively. 4. Grid independence analysis and model validation 4.1. Grid and time step independence analysis Before the simulation calculation, we first verified the grid size and time independence. The thermophysical properties of working fluid, LMPM and structural materials are listed in Table 2. The maximum temperature of the heat source and the average temperature of outlet fluid at the middle of the normal working stage are used as the comparison evaluation results. The total number of grids is set to 6.0×104 , 12.5×104 , 12.5×104 , 50×104 , 75×104 , respectively. The time step in the normal working stage is set to 2 s, 1 s, and 0.5 s, respectively. The results of independence study of grid size and time step are listed in Table 3.

(11)

Here, the h in Eq. (11) is the heat transfer coefficient of per unit area, which can be well predicted using the equation given by Achenbach [43], i.e.

hDe

Nu =

λ



=

1−

dp De





Re0D.61 P r 1/3 100 < ReD < 2 × 104



(12)

The Reynolds and Prandtl numbers in Eq. (12) are expressed as follows:

ReD = Pr =

u De

ν

μf cp2 λf

(13) (14)

where u is the the superficial velocity, De is the equivalent dimension of a rectangular cross-section channel, as the cross-section length is l and the width is w, De can be defined as following [44]:

De =

4Ac 4w · l = P 2 (w + l )

(15)

Fig. 7. Variations of average temperature of outlet fluid and maximum temperature of heat source with total grid number.

J.-Y. Gao, X.-D. Zhang and J.-H. Fu et al. / International Journal of Heat and Mass Transfer 150 (2020) 119366

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Table 2 Thermophysical properties of working fluid, LMPM and structural materials [38]. Material

Density ρ (kg/m3 )

Heat capacity cp (J/kg°C)

Thermal conductivity k (W/m°C)

Melting point Tm (°C)

Latent heat H (J/kg)

Water EBiInSn Copper

997 8043

4179 270a 297b 381

0.606 19.2a 14.5b 387.6

0 60.2

27900

-

-

a b

8978

At 25°C. At 80°C.

Table 3 Independence study of grid size and time step. Grid number (×104 )

Time step (s) Tf,out (°C)

6.0 12.5 25 50 75

Tb,max (°C)

2

1

0.5

2

1

0.5

26.028 26.027 26.037 26.030 26.032

26.03 26.031 26.032 26.030 26.032

26.034 26.028 26.032 26.030 26.032

30.628 30.638 30.665 30.639 30.64

30.636 30.649 30.653 30.638 30.639

30.649 30.638 30.651 30.638 30.639

Fig. 7 shows the variations of average temperature of outlet fluid and maximum temperature of heat source with total grid number, which intuitively illustrate the impact of grid and time steps on calculation accuracy. The red solid line in Fig. 7 represents the maximum temperature of heat source (Tb,max ), and black solid line represents average temperature of outlet fluid (Tf,out ) at the middle of the normal working stage. The results show that the grid 50×104 and time step of 1 s is accurate enough for the current problem. As is known, the normal working stage is mainly convective heat transfer without phase change process, the phase transition occurs when encountering the heat pulse. In order to improve computational efficiency, the time step is set up to 0.1 s without affecting the calculation accuracy. 4.2. Model validation The experimental platform shown in Fig. 8 was built to verify the reliability of the established model. The test section is a copper pipe with a length of 50 mm, outer diameter of 11 mm and the wall thickness of 1.5 mm, respectively. Copper grids were used at both ends of the copper pipe to secure the spherical LMPM-PCM macrocapsules filled in the test section. EBiInSn was selected as the packed particles, and its physical parameters were shown in Table 2. The diameter of spherical parti-

Fig. 8. Equilateral axial diagram of experimental apparatus.

Fig. 9. Gird and computational domain.

cles is 3 mm, and the voidage was measured to be 0.3019, according to Eq. (11), the heat transfer area per unit volume was calculated 1396.2 m2 /m3 . Three temperature measurement points were attached at the middle position along the axial direction of the test section surface and at the equidistant position of 15 mm (10 mm, 25 mm and 40 mm from the fluid inlet end). The calibrated T-type thermocouples were used to monitor the temperature, and Agilent 34970 was used as data acquisition to collect temperature and time information. Flexible electric heating film (30 mm ∗ 40 mm, 21 ) was wrapped on the copper pipe surface in the middle of the test section. Then the rubber insulation cotton, of which thermal conductivity is 0.034 W/(m°C), is wrapped on the surface of the whole test section. Submersible pump with rated voltage of 12 V and rated flow of 10 L/min was used to pump fluid, powered by a regulated voltage source. The system stability was detected and the test started after the temperature was stable. In order to simulate the heat flow in the normal working stage, the voltage between the electrodes of the electrically heated film was adjusted to 14.7 V, the heat flux density was 1 W/cm2 , and the operation was 90 s. For the pulse working stage, the regulation voltage was set to 40.4 V, and the heat flux reached to 7.5 W/cm2 , working for 60 s. Then adjust the voltage to 14.7 V, that is, the de-pulse stage. The test section was selected as the calculation area, and the calculation region was meshed by the structured mesh as shown in Fig. 9. The purple region in Fig. 9(a) was set as the heat flow boundary with a length of 30 mm, and the green and yellow regions were set as adiabatic boundary, each length is 10 mm. The green area in Fig. 9(b) was set as the adiabatic boundary and the brown area was set as the fluid outlet boundary. The yellow area in Fig. 9(c) was set as the adiabatic boundary, and the blue area was set as the velocity inlet boundary. The total number of test section meshes is 2.97×106 , the first boundary layer thickness is 0.015, and the boundary layer growth rate is set to 1.2. Fig. 10 shows the comparison between the experimental test results and the numerical simulation results. As shown in the Fig. 10, the solid black line represents the numerical calculation results,

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Fig. 10. The comparison between the experimental test results and the numerical simulation results.

and the blue semi-solid triangle represents the experimental test results. From the Fig. 10, the trend of the temperature curves is consistent. However, the maximum error is 18.72% based on the Celsius scale, which occurrs in the depulse phase. As can be found that, it is relatively difficult to strictly keep the temperature of inlet fluid constant during the verification experiment. As the fluid circulates in the pipeline, the temperature of inlet fluid gradually increases. However, in order to simplify the numerical model the temperature of the inlet fluid is set to constant, which leads to experimental results higher than the numerical simulations during the depulse phase. In summary, the error is within the allowable range and the model is verified to be reliable. 5. Results and discussion The research is carried out for a typical case, and the thermal condition is summarized in Table 4. 5.1. Influence of the spherical LMPM-PCM macrocapsules and heat flux The temperature response curve of convective cooling heat sink (black curve) under typical working condition in the three stages of conventional heat load, pulse heat load and de-pulse heat load is shown in Fig. 11. In the conventional heat load (0 - 60 s, qn = 1.0 W/cm2 ), the average temperature of heat source rises exponentially and reaches a stable value of 48.2 °C. At 60 s, the heat flux suddenly rises to 10 W/cm2 , the heat source temperature rises rapidly in the form of a new index and reaches a maximum temperature at the end of the heat pulse, Tmax = 183.2 °C at 65 s. After that, the heat flux returns to the normal value, and then the average temperature of heat source decreases exponentially and tends to a stable value eventually.

Fig. 11. Effect of spherical LMPM-PCM macrocapsules on the temperature response of convective cooling heat sink

It can be concluded from the Fig. 11 that for a single convection cooling heat sink, the average temperature of heat source rises rapidly during the heat pulse phase, exceeding the allowable critical temperature, as a result, the single convection cooling heat sink has failed. Based on this, the spherical LMPM-PCM macrocapsules are filled in the convection cooling heat sink as PCM, which not only can increase the heat capacity of the whole system by using its own phase change, but also can enhance the heat exchange to cope with the temperature swell caused by the heat pulse. The blue curve in Fig. 11 reveals the temperature response of the convection cooling heat sink filled with the spherical LMPMPCM macrocapsules. Similarly, the temperature of the composite heat sink will also increase exponentially during the conventional heat load stage. Because of the addition of spherical LMPM-PCM macrocapsules, which lead to large heat transfer area, the heat transfer in the composite heat sink is enhanced. As a result, the average temperature of heat source rises faster when compared with the single convection cooling heat sink. Besides, the temperature at the final stabilization is lower than that of the single convection cooling heat sink, because the heat capacity of the cooling fluid is also increased by adding LMPM-PCM to the fluid. During the pulse heat load (60 - 65 s, qp = 10 W/cm2 ), the average temperature of heat source initially increases exponentially until reaching the melting point, and then it increases linearly with time. The average temperature of heat source reaches the highest (Tmax = 66.5 °C at 65 s) after the heat pulse. The temperature increment of heat source during the pulse heat load is reduced by 73.4% compared with the convection cooling heat sink filled without the spherical LMPM-PCM macrocapsules. In the de-pulse phase, the average temperature of the heat source first drops to the melting point of the spherical LMPM-PCM macrocapsules, and then the temperature remains at the melting point in a short time. After the spherical LMPM-PCM macrocapsules are completely solidified, the average temperature of the heat

Table 4 Thermal condition of a typical case. Parameter Normal heat flux qn Normal working time tn Pulse heat flux qp Pulse time tp

Value 2

1.0 W/cm 60 s 10.0 W/cm2 5s

Parameter

Value

Ambient temperature Ta Fluid inlet temperature Tin Particle size dp Convective cooling heat sink

20 °C 25 °C 4 mm 30 mm∗ 30 mm∗ 15 mm

J.-Y. Gao, X.-D. Zhang and J.-H. Fu et al. / International Journal of Heat and Mass Transfer 150 (2020) 119366

Fig. 12. The variation of the average temperature of the heat_flux surface with working time under different heat fluxes in normal working stage.

source surface is rapidly reduced to a normal temperature exponentially. The effect of heat flux in the normal working stage on the heat sink temperature response is shown in Fig. 12. The dotted line in the figure is the response curve when unfilled spherical LMPMPCM macrocapsules. It can be seen from the figure that during the normal working stage, both the average temperature of the heat source and the time required for stabilization increase with the heat flux increase. Nevertheless, the time required for the average temperature of the heat source surface to reach a stable value decreases as the heat flux increases in the de-pulse phase. In the normal working and de-pulse stages, the steady temperature value of the heat source increases by 23.21 °C for each 1 W/cm2 increase of the heat flux. The solid line is the response curve when filling spherical LMPM-PCM macrocapsules. It can be seen from the figure that the change rule of the average temperature of heat source is the same as which without the spherical LMPM-PCM macrocapsules filled during the normal working stage. During the heat pulse phase, the duration of the quasi-linear growth of the heat source temperature increases as the heat flow increases. Besides, the duration of solidification of the spherical LMPM-PCM macrocapsules similarly increases as the heat flow increases during the de-pulse phase. In the normal working and de-pulse stages, the steady temperature value of the heat source increases by 5.64 °C for each 1 W/cm2 increase of the heat flux. The temperature increment is reduced by 85.7% compared to the convection cooling heat sink filled without the spherical LMPM-PCM macrocapsules, which fully demonstrates the advantages of filling spherical particles. When the pulse heat flow maintains constant and the heat flow in the normal working stage reaches 4 W/cm2 , the maximum mean temperature of the heat source is 69.15 °C, which is lower than the critical working temperature, indicating that the composite heat sink can still effectively cope with this condition. The composite heat sink will be optimized in subsequent studies to explore the maximum conventional working heat flow and pulsed heat flow that the composite heat sink can handle. As shown in Fig. 13 the average temperature of the outlet fluid varies with the different heat fluxes in normal working stage. What is more, the average temperature of the outlet fluid increases as the heat flow increases in whole working stage. The average temperature of outlet fluid of the convective heat sink is drawn in dotted lines in Fig. 13. In the normal working and

9

Fig. 13. The variation of the average temperature of the outlet fluid with working time under different heat fluxes in normal working stage.

de-pulse stages, the steady temperature value of the outlet fluid increases by 5.99 °C for each 1 W/cm2 increase of the heat flux. During the heat pulse stage, the temperature increment is varied from 20.70 °C to 13.81 °C when the heat flow varies from 1 W/cm2 to 4 W/cm2 , the larger the heat flux, the higher the average temperature of the outlet fluid at the end of the heat pulse. However, the steady temperature value of the outlet fluid in the normal working and de-pulse stages increases by 1.03 °C for each 1 W/cm2 increase of the heat flux for the convective heat sink packed with spherical LMPM-PCM macrocapsules (solid lines in Fig. 13). The temperature increment of outlet fluid is reduced by 82.8% compared with the convection cooling heat sink. During the heat pulse stage, the temperature increment is varied from 5.07 °C to 2.70 °C when the heat flow changes from 1 W/cm2 to 4 W/cm2 , which is a good proof of the advantages of filling spherical LMPMPCM macrocapsules. As illustrated in Figs. 12 and 13, the average temperature of the outlet water is lower than 63 °C but the temperature of the heat source is higher than the boiling point of water for the simple convective heat sink, which indicates that there are large temperature differences between the heat source and heat transfer fluid under different heat fluxes. In actual condition, the large heat transfer temperature differences may lead to local boiling of water in convective heat sink. In order to avoid this phenomenon, the heat flux should be further reduced for the simple convective heat sink. As a result, the simple convection thermal management fails to deal with the typical thermal condition mentioned before. For the composite convective heat sink, both of the maximum temperatures of heat source and outlet fluid are effectively controlled below the boiling point of water. The heat transfer fluid in composite heat sink can work normally. However, it is worth noting that the temperatures of heat source and water should keep under 100 °C when exploring the maximum heat flux that the composite heat sink can handle. 5.2. Different stacking patterns Different stacking patterns of spherical LMPM-PCM macrocapsules with equal-diameter are visually illustrated in Fig. 14, such as cubic stacking, orthoclinal stacking, rhombohedral stacking I and II, and wedge tetrahedron stacking. In this section, the effect of different stacking patterns on the voidage of packed bed was an-

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Fig. 14. Model diagrams of different stacking patterns of equal-diameter spherical LMPM-PCM macrocapsules. (a) Cubic stacking; (b) Orthoclinal stacking; (c) Rhombohedral stacking Ⅰ; (d) Wedge tetrahedron stacking; (d) Rhombohedral stacking Ⅱ. Table 5 Coordination number and voidage of regularly arranged equal-diameter spheres. Arrangement mode

Coordination number Nc

Accumulation rate 1-ε m (%)

Cubic stacking

6

π 6

47.64

Orthoclinal stacking

8

π · √2 6

39.54

Rhombohedral stacking Ⅰ

12

π · √2 6

Wedge tetrahedron stacking

10

π · ( √2 6

30.19

Rhombohedral stacking Ⅱ

12

π · √2 6

25.95

alyzed at first, and then the effect of voidage on the volumetric heat transfer coefficient was revealed, laying theory foundation for the voidage selection in the subsequent single parameter researches. The coordination number and the voidage of regularly arranged equal-diameter spherical LMPM-PCM macrocapsules in different stacking patterns are listed in Table 5. The voidage of the arrangement mode of cubic stacking is larger than any other arrangement modes in Table 5. Rhombohedral stacking I and II shows the same coordination number, which leads to the same accumulation rate and voidage. In the previous verification experiment, the voidage of the spherical LMPM particle packed bed was 0.3019, which shows the same accumulation rate as the wedge tetrahedron stacking method. In essence, different packing methods will result in different voidages in the packed bed, which affect the thermal management performance of the composite heat sink. According to Eq. (11), the heat transfer area per unit volume gradually decreases as the voidage increases. When the inlet velocity remains constant and the voidage increases, the superficial velocity gradually increases, resulting in a gradual increase of Reynolds number, and then the area heat transfer coefficient increases according to Eq. (12). As the volumetric heat transfer coefficient is the product of the area heat transfer coefficient and the heat transfer area per unit volume, which eventually leads to the inflection point in the volumetric heat transfer coefficient and voidage curve. The volumetric heat transfer coefficient varied with voidage is intuitively illustrated in Fig. 15. As can be seen, the volumetric heat transfer coefficient of Orthoclinal stacking method is the largest among different stacking patterns of equal-diameter spherical particles, when ε m = 0.3954, hv = 39.1×104 W/(m3 K). In order to further explore the performance of the composite heat sink, the voidage of packed bed is set as 0.3954 in subsequent numerical studies.

3

Voidage ε m (%)

25.95

2

)2 3

2

Fig. 15. Curve of the volumetric heat transfer coefficient varied with voidage.

5.3. Influence of flow rate The variation of the average temperature of the heat source with the working time under different inlet flow rates is illustrated in Fig. 16. The average temperature of the heat source gradually decreases throughout the working time as the flow rate increases, and the duration of the de-pulse stage also becomes shorter. When the flow rate increases, the volume convective heat transfer coefficient becomes larger, the heat exchange between the fluid and the spherical LMPM-PCM macrocapsules is enhanced, and the heat taken away increases, resulting in a decrease in the temperature of the heat source surface. Interestingly, when the flow rate is set to

J.-Y. Gao, X.-D. Zhang and J.-H. Fu et al. / International Journal of Heat and Mass Transfer 150 (2020) 119366

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It can be known from Eq. (12) that the area heat transfer coefficient decreases as the particle size increases; from Eq. (11), the heat exchange area per unit volume is inversely proportional to the particle diameter. As the particle diameter increases, the heat transfer area per unit volume decreases. The volumetric heat transfer coefficient is the product of the area heat transfer coefficient and the heat exchange area per unit volume. Therefore, as the particle diameter increases, the volumetric heat transfer coefficient decreases, and the heat transfer between the fluid and the spherical LMPM-PCM macrocapsules is weakened, resulting in an increase in the temperature of the heat source. As can be seen from the inset of Fig. 17, the plateau duration of the solidification is gradually shortened when the diameter of the particles decreases, which is advantageous for the system to quickly respond to normal operating temperatures in the de-pulse stage.

Fig. 16. The variation of the average temperature of the heat source surface with working time under different inlet flow rates.

0 m/s, the average temperature of heat source increases linearly in the conventional heat load, the growth rate is 0.508 °C/s. However, the average temperature of heat source decreases first in exponential form and then increases during the de-pulse stage, the growth rate is 0.06 °C/s. The simulation is meaningful when the inlet flow rates is set to 0 m/s, which can simulate the condition as the pump stops working abnormally. As can be seen from the inset, in the heat pulse phase, the average temperature of heat source reaches 90.8 °C, and the composite heat sink can still achieve the temperature control effect, but this situation should be avoided as much as possible when the system is working. 5.4. Influence of spherical LMPM-PCM macrocapsules size The variation of the average temperature of the heat source surface with working time under different particle size is shown in Fig. 17. As can be seen from the figure, as along with increase of the diameter of the spherical LMPM-PCM macrocapsules, the average temperature of the heat source surface gradually increases, and in addition, the time required for the de-pulse phase to return to the normal working temperature increases.

Fig. 17. The variation of the average temperature of the heat source surface with working time under different particle size.

6. Conclusions In this study, the spherical LMPM-PCM macrocapsules were introduced and filled into a convective cooling heat sink as PCM. The fluid-solid heat transfer process coupled with phase change in the packed bed was numerically calculated based on the local thermal non-equilibrium theory and the effective specific heat capacity model. The thermal management ability of composite heat sink packed with microencapsulated LMPM-PCM was studied and compared with the single convective cooling heat sink. In addition, the influences of different stacking patterns of LMPM particles, particle diameter and inlet velocity on the heat transfer enhancement in the packed bed were comprehensively investigated, respectively. Several major conclusions can be obtained as: (1) Compared with convective cooling heat sink, the composite heat sink filled with LMPM-PCM particles presents excellent thermal management performance. The temperature increment of heat source during the pulse heat load is reduced by 73.4%. Furthermore, the steady temperature increments of heat source and outlet fluid are reduced by 85.7% and 82.8% respectively both in the normal working and de-pulse stages for each 1 W/cm2 increase of the heat flux. (2) The volumetric heat transfer coefficient changes parabolically as the voidage increases. Besides, the volumetric heat transfer coefficient of Orthoclinal stacking method is the largest among different stacking patterns of equal-diameter spherical particles, when ε m = 0.3954, hv = 39.1×104 W/(m3 °C). (3) The average temperature of the heat source gradually decreases as the flow rate increases and the duration of the de-pulse stage also becomes shorter. In addition, the condition that the pump stops working abnormally was studied when the flow rate was set to 0 m/s. The average temperature of heat source increases linearly at the rate of 0.508 °C/s in the normal working stage. Moreover, the average temperature decreases at first in exponential form and then increases at the rate of 0.06 °C/s during the de-pulse stage. In the heat pulse phase, the maximum average temperature of heat source reaches 90.8 °C, and the composite heat sink can still achieve the temperature control performance, but this situation should be avoided as much as possible. (4) As the diameter of the spherical LMPM-PCM macrocapsules decreases, the average temperature of the heat source gradually decreases, and the time required for the de-pulse phase to return to the normal working temperature also decreases. What is more, the plateau duration of the solidification is gradually shortened, which is advantageous for the system

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to quickly rehabilitate to normal operating temperatures in the de-pulse stage. Declaration of Competing Interest We confirm that there is no conflict of interest in this research. CRediT authorship contribution statement Jian-Ye Gao: Investigation, Writing - review & editing. Xu-Dong Zhang: Methodology. Jun-Heng Fu: Conceptualization. Xiao-Hu Yang: Writing - review & editing. Jing Liu: Supervision. Acknowledgments This work was supported by the National Natural Science Foundation of China Key Project (91748206), and the Frontier Project of the Chinese Academy of Sciences and Dean’s Research Funding. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.ijheatmasstransfer. 2019.119292. References [1] R.J. McGlen, R. Jachuck, S. Lin, Integrated thermal management techniques for high power electronic devices, Appl. Therm. Eng. 24 (8-9) (2004) 1143–1156. [2] X.H. Yang, J. Liu, Liquid metal enabled combinatorial heat transfer science: toward unconventional extreme cooling, Front. Energy 12 (2) (2017) 259–275. [3] L. Mishra, A. Sinha, R. Gupta, Recent developments in latent heat energy storage systems using phase phange materials (PCMs)—a review, in: Green Build. Sustain. Eng., 2019, pp. 25–37. [4] A.K. Pandey, M.S. Hossain, V.V. Tyagi, N. Abd Rahim, J.A.L. Selvaraj, A. Sari, Novel approaches and recent developments on potential applications of phase change materials in solar energy, Renew. Sustain. Energy Rev. 82 (2018) 281–323. [5] S. Jakhar, M.S. Soni, N. Gakkhar, Historical and recent development of concentrating photovoltaic cooling technologies, Renew. Sustain. Energy Rev. 60 (2016) 41–59. [6] N. Choubineh, H. Jannesari, A. Kasaeian, Experimental study of the effect of using phase change materials on the performance of an air-cooled photovoltaic system, Renew. Sustain. Energy Rev. 101 (2019) 103–111. [7] T. Ma, J. Zhao, Z. Li, Mathematical modelling and sensitivity analysis of solar photovoltaic panel integrated with phase change material, Appl. Energy 228 (2018) 1147–1158. [8] M. Jaworski, Thermal performance of heat spreader for electronics cooling with incorporated phase change material, Appl. Therm. Eng. 35 (2012) 212–219. [9] J. Maxa, A. Novikov, M. Nowottnick, Thermal peak management using organic phase change materials for latent heat storage in electronic applications, Materials 11 (1) (2017) 1–15. [10] Y. Xie, J. Tang, S. Shi, Y. Xing, H. Wu, Z. Hu, D. Wen, Experimental and numerical investigation on integrated thermal management for lithium-ion battery pack with composite phase change materials, Energy Convers. Manag. 154 (2017) 562–575. [11] Z. Tian, W. Gan, X. Zhang, B. Gu, L. Yang, Investigation on an integrated thermal management system with battery cooling and motor waste heat recovery for electric vehicle, Appl. Therm. Eng. 136 (2018) 16–27. [12] S. Wilke, B. Schweitzer, S. Khateeb, S. Al-Hallaj, Preventing thermal runaway propagation in lithium ion battery packs using a phase change composite material: an experimental study, J. Power Sources 340 (2017) 51–59. [13] Z.Y. Jiang, Z.G. Qu, Lithium–ion battery thermal management using heat pipe and phase change material during discharge–charge cycle: A comprehensive numerical study, Appl. Energy 242 (2019) 378–392. [14] Z.G. Qu, W.Q. Li, W.Q. Tao, Numerical model of the passive thermal management system for high-power lithium ion battery by using porous metal foam saturated with phase change material, Int. J. Hydrog. Energy 39 (8) (2014) 3904–3913. [15] Y.C. Weng, H.P. Cho, C.C. Chang, S.L. Chen, Heat pipe with PCM for electronic cooling, Appl. Energy 88 (5) (2011) 1825–1833. [16] M.S. Naghavi, K.S. Ong, M. Mehrali, I.A. Badruddin, H.S.C. Metselaar, A state-of-the-art review on hybrid heat pipe latent heat storage systems, Energy Convers. Manag. 105 (2015) 1178–1204. [17] X.H. Yang, S.C. Tan, Z.Z. He, J. Liu, Finned heat pipe assisted low melting point metal PCM heat sink against extremely high power thermal shock, Energy Conv. Manag. 160 (2018) 467–476.

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