Numerical analysis and experimental investigation on thermal bridge effect of vacuum insulation panel

Journal Pre-proofs Numerical analysis and experimental investigation on thermal bridge effect of vacuum insulation panel Shang Mao, Ankang Kan, Ning Wang PII: DOI: Reference:

S1359-4311(19)37441-1 https://doi.org/10.1016/j.applthermaleng.2020.114980 ATE 114980

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

28 October 2019 3 January 2020 20 January 2020

Please cite this article as: S. Mao, A. Kan, N. Wang, Numerical analysis and experimental investigation on thermal bridge effect of vacuum insulation panel, Applied Thermal Engineering (2020), doi: https://doi.org/ 10.1016/j.applthermaleng.2020.114980

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

© 2020 Elsevier Ltd. All rights reserved.

Numerical analysis and experimental investigation on thermal bridge effect of vacuum insulation panel Shang Mao1, Ankang Kan1, Ning Wang1 (1. Merchant Marine College, Shanghai Maritime University, 201306, Shanghai, P.R. China) Abstract: Vacuum insulation panel, composed of a core material and a barrier, is a very efficient thermal insulation material. Compared with conventional insulation materials, the vacuum insulation panel is proposed to achieve a better insulated performance. However, its thermal conductivity will be seriously increased and insulated performance will be significantly decreased since the additional heat is transferred through the barrier; that is called thermal bridge effect. This paper emphasized on effective thermal conductivity to evaluate the performance of vacuum insulation panel. Two criteria, i.e., the linear and point thermal transmittance are introduced to evaluate the comprehensive performance of vacuum insulation panel. A heat transfer model was used to analyze the thermal bridge. Then, a fast and effective method for measuring thermal bridge is presented, which is supported by numerical simulation analysis. The results indicated that thermal bridge not only could increase with the increasing of the mental foil (main aluminum) thickness, but also could exhibit higher heat losses with the reducing of thickness of the vacuum insulation panel. Overall, the effective thermal conductivity of vacuum insulation panel could increase by 110.8% when the barrier contains 10μm mental foil and the size of vacuum insulation panel is 300×300×10mm3. This research provides a reference for measuring the thermal bridge and could also disclose the quantitative

Corresponding Author: Ankang Kan. Email: [email protected] 1

behavior of physical parameters in thermal bridge. Key words: Vacuum insulation panel; Thermal bridge; Effective thermal conductivity; Numerical model; measurement method.

Nomenclature Symbols A

heat transfer area

(m2) (W·m-2·K-1)

e

external

eff

effective

g

gas

i

internal

h

surface heat transfer coefficient

l

VIP’ length (m)

ix

inlet in X direction

L

effective length (m)

l

linear

n

number of points

m

measurement

P

VIP’ perimeter (m)

ox

outlet in X direction

𝑄

heat flow (W)

p

panel

T

temperature (K)

pt

point

w

VIP’ width (m)

r

radiation

Φ

heat transfer per unit time (W)

s

solid

tb

through barrier

x

X direction

z

Z direction

Greek symbols Δ

difference (W·m-1·K-1)

λ

thermal conductivity

δ

thickness (m)

Abbreviation

ψ

thermal transmittance (W·m-1·K-1)

χ

thermal transmittance (W·K-1)

Al CFD GPHM IR LD NY PE PET SEM VIP

Subscript ax

air in X direction

ay

air in Y direction

b

barrier

bx

barrier in X direction

by

barrier in Y direction

c

core

cop

center of panel

cv

convection

aluminum computational fluid dynamics guarded hot plate meter Illuminator Radar low density nylon polyethylene polyethylene terephthalate scanning electron microscope vacuum insulation panel

1. Introduction To maintain the thermal comfort of buildings, buildings account for 40% of global energy consumption [1]. Hence, it is urge to develop new insulations to enhance the energy efficiency,

2

which also satisfies the demand of circular economy [2]. Vacuum insulation panel (VIP) provides an effective solution to reduce heat losses and improve energy efficiency in the building field. The center-of-panel thermal conductivity can be no more than 0.004W·m-1·K-1, which is only 1/6 or even 1/10 than those of conventional insulation materials [3]. The low thermal conductivity of VIP makes it possible to obtain low thickness when the same thermal resistance is achieved [4]. For this reason, they are gradually applied to various industries: buildings, cold chain, refrigerators, heating pipes, cold storage and so on [5-8]. Core material, barrier and necessary getter are the main components of VIP. The core materials are generally porous material and the barrier is usually multi-layered with polymers and Al layer. The polymer layers are used to heat sealing after evacuation and the Al-layers, either Al-foil or Almetallized layers are used to prevent air and vapor permeation from the atmosphere [9]. VIP has been studied by numerous researchers during the past few decades. Biswas et al. [10] proposed a composite foam insulation panel using low-cost core. They found that the thermal resistance is double that of foam panel. Lee et al. [11] found that the low thermal conductivity can be obtained by using low emissivity shields. They designed an artificial core employing high reflecting shields to decrease the center-of-panel thermal conductivity. Although VIP has a near adiabatic performance, there are still some questions that have not been clarified yet. The reason is serious edge heat losses in real applications, especially relating to thermal bridge effect. An empirical model dealing with the thermal bridge effect in constructions has been carried out by Isaia et al. [12]. The results indicated that the thermal transmittance can increase 50% when the thermal bridge effect is considered. Capozzoli et al. [13] presented a detailed analysis of the thermal bridge including the typical joint points of the

3

building envelope, and performed non-linear regression models for each thermal bridge. As expected, they found that the thermal bridge should be accurately considered when the thermal conductivity of the barrier is remarkable. Calculation of linear thermal transmittance model of VIP was established by Schwab et al. [14] and Tenpierik et al. [15]. Bianchi et al. [16] showed a methodology to investigate the thermal bridge through in-field assessments with IR thermography. In the study of Sprengard et al. [17], a numerical analysis was carried out by comparing different structures. For his study, a calculation method of linear thermal conductivity and the factors affecting the thermal bridge were found. Several investigations mentioned above have focused on the thermal bridge effect only from theoretical and numerical analysis. Lorenzati et al. [18] performed numerical analysis of different VIP assemblies, investigating thermal bridge effect on the geometry of the air joint between two adjacent panels. Brunner et al. [19] studied the thermal bridge effect of staggered, non-staggered and thick single VIP layer, and found staggered VIPs have a small thermal bridge than that of non-staggered configuration. Wakili et al. [20] proposed that the size of VIP is larger, the thermal bridge is lower and thermal insulation performance is better. Many universal conclusions from these research studies demonstrate the vital significance of considering the thermal bridge effect to assess VIP thermal performance correctly. However, these studies are only based on pure numerical methods. Furthermore, few studies have been conducted to investigate the influence of thermal bridge by means of experiments and the calculation method of thermal bridge has not been clearly proposed. In present paper, firstly, the reason of thermal bridge effect, effective thermal

4

transmittance and numerical model were introduced. The numerical resolutions of linear thermal transmittance ψl and the point thermal transmittance χpt were obtained. Secondly, the geometric model of VIP was drawn by CFD and boundary conditions were established by citing some references. And, the simulation was also performed by CFD software. In addition, experiments to measure the thermal bridge effect were designed and carried out by changing configurations of VIP. The measurement values were validated after numerical analysis. Thirdly, the influence factors of thermal bridge effect, such as the thickness of VIP, barrier’s thickness and barrier’s thermal conductivity were discussed. Finally, the conclusions are shown in section 6. Since both linear thermal transmittance and point thermal transmittance are very important for thermal bridge of VIP, this study used these performance indexes to evaluate the thermal bridge. In order to analyze the linear and point thermal transmittance of VIP, a heat transfer model and experiments were designed and carried out. The results have also been compared with published paper. After the validation, this method can be used to determine which behavior would reduce the thermal bridge.

2. Analysis and model 2.1 The thermal bridge effect What is thermal bridge effect? Generally speaking, the thermal bridge is the bridge of heat transmission. When heat is transferred from the high temperature to low temperature, some heat will be transferred through the edge rather than transferring through the thermal insulation material, and the heat flow is continuously transferred from the high temperature to low

5

temperature, thus thermal bridge is formed. The barrier must have a good characteristic to reduce the gas and vapor permeation. Generally speaking, a polymer and metal laminated film are employed for this purpose. At present, two main barriers are able to satisfy the air and vapor tightness criteria for long term performance. The SEM of each type is shown in Fig. 1.

Fig. 1. SEM images of barriers, (a) AF, (b)MF.

One, based on a laminated Al-foil(thickness 5 ～ 10μm), is called AF. A cover layer is added on the external side (10～100μm of PET) and a weld layer on the internal (20～100μm of PE/NY). The other is called MF, a multilayer membrane with metal-coated polymer films. MF is composed of metal-coated polymer films (20～50μm of PET with 20-100nm of Al), whose cover layer and weld layer are similar to that of AF barriers. Sometimes, these thin Al coating layers obtained by vacuum deposit on PET barriers, are not absolutely regular and contain a high density of defects (mainly pinholes) [21]. This effect can be attenuated by the superposition of several metal layers. The path length and tortuosity, therefore, are increased due to the molecule permeation [22]. If the VIP is infinite, heat is only transferred through the center of VIP and little heat is transferred along the VIP edge, which is called center-of-panel thermal conductivity. Actually, the assumption is not realistic. Near by the edge of VIP, heat flow is conducted through the

6

barrier. It means that there are additional heat losses by the barrier. The scheme is shown in Fig. 2. The thermal conductivity of Al is λAl=160W·m-1·K-1, which is five orders of magnitude higher than the core material conductivityλc≈0.004W·m-1·K-1. And the traditional polymer conductivity (PE, PET) λ≈0.1-0.5 W·m-1·K-1 is only two orders of magnitude higher than λcop. This difference explains why VIPs have a thermal bridge at the edge.

Fig. 2. Schematic diagram of thermal bridge effect.

2.2 Effective thermal conductivity The thermal performance of VIP can be determined by calculating effective thermal transmittance for single element or component. It depends on the size of the VIP and the thermal bridge effect. Heat is mainly transferred through the Al foil layer along the VIP edge due to its high thermal conductivity [23]. The thermal conductivity is the prevalent heat transmission in homogeneous materials. Therefore, the effective thermal conductivity of VIP, λeff, can be calculated by Eq. (1) considering the influence of thermal bridge [5]. 

Q

eff  A  T p

(1)

The central thermal conductivity of VIP consists of three parts: the solid thermal conductivity through core material, the residual gases thermal conductivity and radiation. The center-of-panel thermal conductivity of VIP could be evaluated [11]: 7

cop  s  g  r

(2)

In order to quantify the thermal bridge effect, three parameters were adopted: the linear thermal transmittance ψl, the point thermal transmittance χpt and the effective thermal conductivity λeff. The effective thermal conductivity λeff can be evaluated by using the following equation [23].

eff  cop 

 i

l

 P  p   j  p  n  p A

(3)

In fact, in engineering applications, there are two types of thermal bridge. One is linear thermal bridge, which occurs in the VIP joint. The other is point thermal bridge, which is localized thermal bridge whose influence is assessed by a point thermal transmittance. Hence, the heat losses caused by the thermal bridge effect can be obtained. The linear thermal transmittance ψl and point thermal transmittance χpt of VIP are important parameters to estimate the thermal bridge effect. The thermal bridge has been determined by means of Eq. (3), which could also be achieved by numerical simulations and the experimental measurement are concerned.

2.3 Numerical model A 3D numerical model was created, which is shown in Fig. 3, considering the several parameters that mainly influence thermal bridge.

8

Fig. 3. The analysis model of VIP thermal bridge effect. In fact, at a steady state, it can be defined as: 







 ix   ox   cv   tb  0

(4)

Here, Eq. (4) can be rewritten as:

b b

dTx dT  b b x dx x dx

 he Ti  Tx  dx  x  dx

c T  T  dx  0  x z

(5)

In order to simplify calculation without loss of accuracy, the assumption is made that the barrier is uniform and continuous, the barrier’s thickness and the thermal conductivity are constant. Both sides of Eq. (5) are divided by dx·δb·δp and the final equation adopted for the calculation was:

c d 2T  he   2  dx  b b b b p

 c h T  Tx  e Ti  b b b b p z 

(6)

 c h Tz  Ty  e Ti       b b b b p 

(7)

Similarly, it can be obtained as:

c d 2T  he   2 dy  b b b b p The boundary conditions are:

9

 x  0, Tx  Tbx x  w ,T  T p x ax    y  0, Ty  Tby  y  l ,T  T p z ay 

(8)

Combined Eqs. (6), (7) and (8) with the boundary conditions of the linear thermal conductivity ψl, the result is:

l 

1

  1 c  c he p hi p



p 

b b b b

(9)

hi  he

The linear thermal conductivity ψl has been obtained by means of Eq. (9), which depends on the VIP’s thickness, barrier’s thickness, core material’s thermal conductivity, barrier’s thermal conductivity, and surface convective heat transfer coefficient of VIP. The point thermal bridge has a higher point thermal transmittance than other places. The solution can be solved according to partial differential equation of heat conduction, assuming a steady state in the VIP.

b b

dTz dT  b b z dz z dz

0

(10)

z  dz

The boundary conditions are the internal and external temperature Ti and Te when it comes to z=0 and z=δp. The theoretical model of point thermal transmittance can be obtained based on the boundary conditions as:

 pt 

b b he hi l p wp

b  he  hi    p he hi   p

(11)

It is worth noting that the panel thickness and barrier properties were used to assess the value of the point thermal transmittance. Therefore, the effective thermal conductivity λeff of VIP is obtained:

10

eff  cop    cop 

P  p

A 2 l p  w p lpwp

  i

l

1



n  p A 1



c c hi p he p

j

 pt



p 

 b b  b b hi 



b b he hi b  he  hi    p he hi

(12)

he

3. Simulation analysis 3.1 Model and boundary conditions The thermal bridge occurred in VIP edge will never be neglected and it has a significant impact on the heat losses from above analysis. For this reason, a standard panel size 300mm×300mm was introduced for this analysis. The geometric model was carried out by a CFD software. CFD is a simulation technology used to simulate the flow of working fluids. Due to the regular shape and simple structure of the model, tetrahedral mesh was selected to construct grids. The accuracy of the simulation depends on, to a large extent, the number of meshing. The more the meshing is, the higher the accuracy of the simulation results are. Unfortunately, it also needs to take a long time to complete if there are more grids. Therefore, the 2.5mm grid was selected as simulation grids without loss of accuracy. The number of three types of grids is 506831, 1058620, 2231944, respectively. It is shown in Fig. 4.

Fig. 4. Simulation of grids model.

For the simulation of these models, the following are assumed: 1. The viscous dissipation of fluid is not considered. 11

2. The properties of air are considered independent of temperature and pressure. 3. It is assumed that the sides of VIP are insulated and no heat exchange between sides and air occurs. The energy equation was used to simulate after geometric models were created. VIP can be found on the market with different kinds of core materials, as well as different barriers. A glass fiber core material and a laminated Al-foil barrier were considered in this study. Some simplifications were necessary to make the simulation analysis faster and more feasible, without loss of the accuracy. Since the thermal conductivity of Al-foil is relatively high compared with the polymers, the barrier is simplified as a pure Al-foil of which the thermal conductivity λAl is 160W·m-1·K-1 and the thickness δAl is 10μm. For the boundary conditions, both sides are assigned to be adiabatic and the hot plate and cold plate are assumed to be constant temperatures. Te, Ti signify the temperature of hot plate and cold plate temperature, that is: Te=308K, Ti=288K, respectively, according to the VIP test standard ASTMC 518-2010 [24]. The steady state heat conduction equation is solved by a finite volume method, and a non-uniform grid is used near the thin Al-foil. The convective heat transfer coefficient of the barrier and the physical parameters of VIP are listed in Table. 1 and Table. 2 according to ISO-10077[25]. Tab. 1. Boundary conditions of simulation analysis. Type

Temperature/K

Surface heat transfer coefficient(W·m-2·K-1)

Exterior

288

25

Interior

308

7.7

Tab. 2. The properties of VIP.

Barrier

Type

Thermal conductivity(W·m-1·K-1)

Thickness

Al-foil

160.00

10μm

12

Core material

PET

0.20

40μm

PE

0.42

50μm

Stainless steel

16

100μm

Plastic barrier

0.38

100μm

Glass fiber

0.004

20mm

VIP

—

10-40mm

There are errors between simulation and experiments. The main reasons are as follows: firstly, the simplification of model. Secondly, the influence of grid precision and the algorithm; thirdly, the heat losses of the actual experiments.

3.2 Analysis Assumption has been made that the heat is transferred through VIP at a steady state. The temperature distribution of VIP without thermal bridge at a size of 300mm×20mm (Wp×δp) is shown in Fig. 5. Although the VIP barrier contains Al-foil, the temperature distribution in the center of VIP seems to be a one-dimensional heat transfer.

Fig. 5. Temperature distribution of VIP without thermal bridge.

Most of the heat will be transferred through the edge with the existence of gap and thermal bridge effect during installing. The temperature distribution of VIP with thermal bridge effect

13

is shown in Fig. 6. Noting that the heat losses will be seriously increased due to the thermal bridge effect. Fig. 6 indicated that the heat losses was improved with the joint and point of VIP in buildings, which owed to the higher thermal conductivity in these locations than that of center-of-panel.

Fig. 6. The simulation results of VIIP with thermal bridge.

4. Experimental system and procedure 4.1 Apparatus The effective thermal conductivity was measured to verify the simulation and theoretical analysis. A GHPM device was used to measure the thermal conductivity. It consists of a hot plate, two cold plates, a guarded hot plate and pressing load exerting components, as shown in Fig. 7. The hot plate of the apparatus is surrounded by guard plates to avoid heat losses from the hot plate to the surrounding environment [26]. The hot plate and cold plate are 300mm×300 mm. The measurement area, located in the center of plate, is 150×150mm. When stable conditions are built, the specific heat flow (average value over of measurement area, Am) is

14

obtained.

Fig. 7. Schematic diagram of GHPM.

When a VIP specimen is placed, the thermal conductivity of specimen in the measuring area is measured by Eq. (15) [26].

m 

Q  p 2 Am T

(13)

4.2 Measurement method When the thermal conductivity of VIP is measured by GHPM, the measured value is only the center-of-panel thermal conductivity. Therefore, the edge must be placed in the measuring area in order to measure the heat flow through the edge. Three types of specimens are manufactured to extract edge conduction from the differences in collected data. The total size of each specimen is 300mm×300mm according to the GHPM size. Thus, for the first setup, the type “A” is one specimen 300mm×300mm. For the second, two blocks of 300mm×150mm, that is type “B”. And for third, four blocks of 150mm×150mm specimens named type “C”, which

15

are located side by side. Three types specimens were used for measurement and three tests were carried out on each specimen. The values were averaged to determine the thermal conductivity of each specimen.

Fig. 8. Schematic diagram of thermal bridge measurement, (a) center-of-panel, (b) and (c) linear and point thermal transmittance, respectively.

Fig. 8(a) is the VIP without thermal bridge, that is, the thermal conductivity of this assembly represents the center-of-panel λcop. The determination of this quantity requires two specimens of 300mm×300mm. Each side of hot plate is placed a specimen. 

Q

 m  T  2 Am  cop  T  2 Am p p

cop 

Q  p 2 Am T

(14)

(15)

Fig. 8(b) represents a VIP with one joint. For this case, four VIPs at the size of 300mm×150mm are needed (two specimens on each side of the hot plate). The corresponding linear thermal transmittance ψl can be determined from the tested effective thermal conductivity. 

Q

 m  T  2 Am  cop  T  2 Am  l  2 Lm  T p p

(16)

Am      p  Lm m cop

(17)

l 

The difference between type B and type C is the cross joint in the VIP. Consequently, eight VIPs at the size of 150mm×150mm are needed to measure the additional heat losses caused by 16

thermal bridge (four specimens on each side of the hot plate). This case includes linear thermal transmittance ψl and point thermal transmittance χpt, which can be obtained from the tested effective thermal conductivity λm. 

Q

 m  T  2 Am  cop  T  2 Am  l  4 Lm  T  2  pt  T p p  pt 

Am

p



m

 cop   l  2 Lm

(18)

(19)

4.3 Measurement uncertainty The measurement uncertainty of VIP’ thermal conductivity has been investigated by Lorenzati et al. [27] on the basis of experimental analysis. They found that the uncertainty can be reduced to 3% when the mean temperature is close to the ambient temperature. Thus, the temperature of hot plate and cold plate is 308K and 288K (mean temperature 298K), respectively. To minimize uncertainty, a standard material needs to be measured before every measurement for calibration. The PT-100 is used as a temperature sensor to measure the thermal conductivity of VIP. What’s more, there are five temperature sensors in hot plate and cold plate, and four temperature sensors in guarded plate. To ensure the heat flow which transfers in the vertical direction, the guarded plate and hot plate are heated and maintained to the same temperature. The distribution of temperature sensors is shown in Fig. 9. The measurement uncertainty of sensors is shown in Table. 3. The uncertainty for the thickness and area of the VIP is 3% and 1%, respectively.

17

Fig. 9. The distribution of temperature sensors. Tab. 3. Measurement uncertainty for sensors. Type

Temperature(K)

Error

Thermocouple

PT-100

233-358

±0.18-±0.27K

Measure power

Shunt resistor

233-358

1.00%-1.47%

The uncertainty of measurement for each single test can be estimated, taking the actual boundary and measurement condition into consideration.

d m

m

2

  dA   m d  T    m d  p     m  m              T A   m  m  m    p m 2

 2   m d Q            Q m   

2

(20)

5. Results and discussion The center-of-panel thermal conductivity can be measured at mean temperature 298K. The linear thermal conductivity and point thermal conductivity obtained by experimental measurement and theoretical numerical analysis are tabulated in Table. 4. The linear thermal transmittance ψl and point thermal transmittance χpt can be calculated from Eqs. (20) and (22). Tab. 4. Comparison of experimental measurement and numerical analysis. (the thickness of Al is 10μm) Experiments Specimen thickness (mm) 10

λcop×10-3 5.1±0.1

Numerical analysis Δλ(%)

λeff×10-3

Ψl×10-3

χpt×10-3

11.5±0.3

42.4±0.1

2.4±0.1

18

106.8-110.8

Δλ(%) λeff×10-3

Ψl×10-3

χpt×10-3

10.6±0.3

40.9±0.1

2.1±0.1

98.4-94.9

15

5.3±0.1

11.0±0.3

37.2±0.1

2.3±0.1

106.0-110.1

10.5±0.3

35.6±0.1

1.9±0.1

93.1-96.6

20

4.9±0.1

10.8±0.3

37.7±0.1

2.3±0.1

106.4-110.6

10.6±0.3

30.8±0.1

1.8±0.1

95.4-99.2

25

5.2±0.1

10.5±0.3

28.3±0.1

2.2±0.1

100.5-104.5

9.9±0.3

25.8±0.1

1.6±0.1

87.9-95.4

30

5.2±0.1

10.4±0.3

24.7±0.1

2.1±0.1

110.7-115.4

9.4±0.3

22.3±0.1

1.5±0.1

901.-93.9

35

5.3±0.1

9.4±0.3

21.2±0.1

2.0±0.1

76.0-78.9

9.2±0.3

19.6±0.1

1.4±0.1

70.5-71.8

40

5.5±0.1

8.2±0.3

19.1±0.1

2.0±0.1

59.5-61.9

8.1±0.3

17.4±0.1

1.3±0.1

56.9-59.2

It is found from Table. 4 that the results of the effective thermal conductivity between the experiments and analysis are in close agreement and they clearly indicated that the numerical model is very reliable in terms of the results of experiments. Therefore, the thermal bridge effect can be obtained using Eqs. (9) and (11). The deviation between the effective thermal conductivity with thermal bridge and the center-of-panel thermal conductivity can be obtained from the Tab. 4. The maximal deviation is Δλ=110.8%, which indicated the edge heat losses will be seriously increased due to the existence of thermal bridge.

5.1 The influence of VIP thickness A vital influence on overall heat losses is the thickness of VIP. The linear thermal transmittance ψl of various thickness and comparison with previous results are shown in Fig. 10. There is a little deviation between the results appeared in the paper and experimental results of Brunner et al. [19] and Kovács et al. [28]. When the VIP thickness is 20mm and 40mm (see Fig. 10), the linear thermal conductivity has almost the same value, which also indicates the model is reliable. Calculations for determining thermal transmittance values have been carried out for 10mm to 40mm panels. When the thickness is 10mm, the linear thermal transmittance is 0.041W·m-1·K-1, while the thickness is 40mm, the linear thermal transmittance is 0.017W·m1·K-1.

Therefore, thin panels have higher thermal bridge effect and higher heat losses.

19

Fig. 10. Comparison of the linear thermal transmittance for present results and that of published papers.

For configuration and application of VIP, the corner is inevitable. The point thermal transmittance seems to be weak, but since the size of VIP would affect the point thermal conductivity, the point thermal conductivity cannot be neglected. The comparison of experimental and theoretical results with Wakili’s et al. [20] is illustrated in Fig. 11. The results indicated that further increase of thickness of VIP would contribute little on reduction of the point thermal transmittance, in this case higher thickness of VIP was not necessary.

Fig. 11. Comparison of the point thermal transmittance for present results and that of published papers.

20

5.2 The influence of barrier’s thickness The influence on thermal conductivity of the VIP is the material containing inorganic barrier layer and its thickness with the metal foil. The impact of the barrier’s thickness is shown in Fig. 12. The barrier foil generally shows the thickness from 5μm to 15μm. Though these layers are very thin, their impact on thermal bridge is notable. The ideal thermal conductivity of VIP should be around 0.005W·m-1·K-1, while the effective thermal conductivity (real) is around 0.014W·m-1·K-1 and 0.012W·m-1·K-1, respectively. When metal thickness is 15μm and the thickness of VIP is 10mm and 40mm. Therefore, the thermal bridge effect can be reduced by using metal foil barrier with small thickness and/or increasing VIP thickness.

Fig. 12. Effect of metal thickness on the thermal bridge, (a) linear thermal transmittance ψl, (b) point thermal transmittance χpt.

5.3 The influence of thermal conductivity of barrier The element of Al as a barrier layer is common, as it has great barrier of the material in vacuum laminate. All of the VIP’s films use Al as barrier layer. What’s more, the thermal conductivity of Al is 160W·m-1·K-1, and it’s nearly 160 times higher than that of plastic barrier. When it comes to plastic barrier, a considerable reduction of the thermal bridge effect could be

21

achieved even for thick barriers. In fact, the higher the thermal conductivity of the barrier layer is, the higher the thermal bridge effect is. Therefore, it is crucial to study the new low thermal conductivity barrier to reduce the thermal bridge effect. The influence of thermal conductivity of barrier on thermal bridge is shown in Fig. 13.

Fig. 13. Effect of barrier’s thermal conductivity λb on the thermal bridge, (a) the comparison between linear thermal transmittance ψl and previous literature, (b) point thermal transmittance χpt.

5.4 Economic analysis This measurement need three types specimens, i.e., type A, B, C and the tested device. The price of VIP with the thickness 20mm is 120-150¥/m2(nearly 15-19$/m2) according to the Chinese VIP market. In this experiment, 2 “A” panels, 4 “B” panels and 8 “C” panels are needed. The total area is 0.54 m2, which cost 80¥ (around 10$). The GPHM used in this experiment cost 81,000¥ (around 10000$). The total cost is around 10000$. Each test will spend 2h and it only takes 6h to measure the thermal bridge of the VIP. If the specimen is sent to the company for testing, the cost is only 1000¥ (around 100$). Thus, this method is fast and low-cost. 6. Conclusions Compared with conventional insulated materials, vacuum insulation panel not only could increase the thermal resistance of building envelope, but also could improve the energy 22

efficiency. However, it is still impossible to avoid the thermal bridge in practical utilization. This study used both linear thermal transmittance and point thermal transmittance as criteria to evaluate the thermal bridge based on a heat transfer model. According to the results, the conclusions are as follows: (1) The thermal bridge occurring in vacuum insulation panel have been investigated by both experiments and calculations for the same type barrier but different panels thickness. It was shown that the influence of the vacuum insulation panel thickness on the linear and point thermal transmittances caused by various of thermal bridge can be detected by numerical calculations and experiments. (2) Effects of mental foil on the thermal bridge of vacuum insulation panel were significantly different. The linear thermal transmittance increased which varies from 0.032W·m-1·K-1 to 0.065W·m-1·K-1 when the meatal foil thickness ranges from 5μm to 15μm and the vacuum insulation panel thickness is 10mm. While the change of point thermal transmittance was from 0.001W·K-1 to 0.003W·K-1 under the same conditions. Since the low mental foil thickness can provide high thermal performance and reduce thermal bridge, a new high barrier with thinner mental foil or without mental foil should be developed. (3) Higher thickness of vacuum insulation panel can contribute to low linear and point thermal transmittance as well as high thermal efficiency. The index of linear thermal transmittance decreased from 0.041 to 0.017W·m-1·K-1with the thickness varying between 10mm and 40mm. Hence, high-thickness is preferred in buildings envelope for high energy utilization efficiency. (4) Compared with an ideal insulation made of identical vacuum insulation panel, the

23

analysis performed in this work demonstrated that effective thermal conductivity λeff can increase up to 110.8% when the thermal bridge effect is considered, which means the heat losses can be sharply reduced by minimizing the thermal bridge effect. This study provided an experimental method for practical applications in measuring the thermal bridge of vacuum insulation panel in the future.

Acknowledge This work was financially supported by the National Natural Science Foundation of China (Grant No. 51679107). The authors would also like to render thankfulness to the Qingdao Kerui New Environmental Materials Groups Co., Ltd. for the materials supply. The article was supervised by Dr. Samuel Brunner of the Swiss Federal Materials Science and Technology Laboratory. The authors express their sincere thanks to him.

References

[1] P. Johansson, St. Geving, C.E. Hagentoft, B.P. Jelle, E. Rognvik, A.S. Kalagasidis, B. Time, Interior insulation retrofit of a historical brick wall using vacuum insulation panels: Hygrothermal numerical simulations and laboratory investigations, Build Environ. 79 (2014) 31-45. [2] R.W. Stahel, Circular economy, Nature, 531 (2016) 435-438. [3] M. Bouquerel, T. Duforestel, D. Baillis, et al. Heat transfer modeling in vacuum insulation panels containing nanoporous silica—A Review, Energy Build. 54 (2012) 320-336. [4] S.E. Kalnaes, B.P. Jelle, Vacuum insulation panel products: a state-of-the-art review and future research pathways, Appl Energy. 116 (2014) 355-375. [5] M. Alam, H. Singh, M.C. Limbachiya, Vacuum Insulation Panels (VIPs) for building construction 24

industry–A review of the contemporary developments and future directions, Appl Energy. 88 (2011) 3592-3602. [6] S. Verma, H. Singh, Vacuum insulation in cold chain equipment: A review, Energy procedia. 16 (2019) 232-241. [7] S. Thiessen, F.T. Knabben, C. Melo, J.M. Gonçalves, A study on the effectiveness of applying vacuum insulation panels in domestic refrigerators, Int. J. Refrig. 96 (2018) 10-16. [8] X.F. Xu, X.L. Zhang, S. Liu, Experimental study on cold storage box with nanocomposite phase change material and vacuum insulation panel, Int. J. Energy Res. 42 (2018) 4429-4438. [9] H. Jung, C.H. Jang, I.S. Yeo, T.H. Song. Investigation of gas permeation through Al-metallized film for vacuum insulation panels, Int. J. Heat Mass Trans. 56 (2013) 436-446. [10] K. Biswas, A. Desjarlais, D. Smith, J. Letts, J. Yao, T. Jiang, Development and thermal performance verification of composite insulation boards containing foam-encapsulated vacuum insulation panels, Appl Energy, 228 (2018) 1159-1172. [11] J. Lee, T.H. Song, Conduction/radiation combined heat transfer with contact resistance for application to vacuum insulation, Int. J. Heat Mass Trans. 129 (2019) 380–388. [12] F. Isaia, S. Fantucci, A. Capozzoli, M. Perino, Thermal bridge in vacuum insulation panels at building scale, Eng. Sus. 170 (2017) 47-60. [13] A. Capozzoli, A. Gorrino, V. Corrado. A building thermal bridges sensitivity analysis, Appl Energy. 107 (2013) 229-243 [14] H. Schwab, C. Stark, J. Wachtel, H.P. Ebert, J. Fricke, Thermal bridges in vacuum insulated building facades, J. Build Phys, 28 (2005) 345-356. [15] M. Tenpierik, H. Cauberg, Analytical models for calculating thermal bridge effects caused by thin high barrier envelopes around vacuum insulation panels, J. Build Phys. 30 (2007) 185-216. [16] F. Bianchi, A.L. Pisello, G. Baldinelli, F. Asdrubali. Infrared thermography assessment of thermal bridges in building envelope: experimental validation in a test room setup, Sus. 6 (2014) 7107-7120. [17] C. Sprengard, A.H. Holm, Numerical examination of thermal bridging effects at the edges of vacuum 25

insulation panels (VIP) in various constructions, Energy Build. 85 (2014) 638-643. [18] A. Lorenzati, S. Fantucci, A. Capozzoli, M. Perino, Experimental and numerical investigation of thermal bridging effects of jointed Vacuum Insulation Panels, Energy Build. 111 (2016) 164-175. [19] S. Brunner, T. Stahl, K.G. Wakili. Single and double layered vacuum insulation panels of same thickness in comparison. Building Enclosure Science & Technology Conference, BEST 3. April 2-4th 2012, Atlanta. [20] K.G. Wakili, T. Stahl, S. Brunner. Effective thermal conductivity of a staggered double layer of vacuum insulation panels, Energy Build. 43 (2011) 1241-1246. [21] A. Batarda, T. Duforestel, L. Flandinb, B. Yrieix, Modelling of long-term hygro-thermal behaviour of vacuum insulation panels, Energy Build, 173 (2018) 252–267. [22] Z.Y. Li, C.Y Zhu, X.P. Zhao, A theoretical and numerical study on the gas-contributed thermal conductivity in aerogel, Int. J. Heat Mass Trans, 108 (2017) 1982-1990. [23] K.G. Wakili, R. Bundi, B. Binder, Effective thermal conductivity of vacuum insulation panels, Build. Res. Inf. 32 (2004) 293–299. [24] ASTMC518-2010，Standard test method for steady-state thermal transmission properties by means of heat flow meter apparatus[S]. American Society for Testing and Materials. [25] ISO 10077-2:2012 “Thermal performance of windows, doors and shutters – Calculation of thermal transmittance – Part 2: Numerical methods for frames. [26] S. Sonnick, M. Meier, J. Ross-Jones, L. Erlbeck, I. Medina, H. Nirschl, M. Rädle, Correlation of pore size distribution with thermal conductivity of precipitated silica and experimental determination of the coupling effect, Appl Therm Eng. 150 (2019)1037-1045. [27] A. Lorenzati, S. Fantucci, A. Capozzoli, M. Perino, VIPs thermal conductivity measurement: test methods, limits and uncertainty, Energy Procedia. 78 (2015) 418–423. [28] Z. Kovács, S. Szanyi, I. Budai, Á. Lakatos, Laboratory Tests of High-Performance Thermal Insulations, Sustainability in Energy and Buildings. 163 (2019) 73-82. 26

27

Conflict of interest No conflict of interest exits in the submission of this manuscript, and manuscript is approved by all authors for publication.

28

Highlights 

A measurement method of thermal bridge for vacuum insulation panel was presented.



Model focusing on edge effect to predict thermal bridge was proposed.



Linear and point thermal transmittance were used to evaluate thermal bridge.



The thermal conductivity can increase 110% due to thermal bridge.

29