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A Model to Determine Thermal Performance of a Non-ventilated Double Glazing Unit with PCM and Experimental Validation
Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 157 (2016) 293 – 300
IX International Conference on Computational Heat and Mass Transfer, ICCHMT2016
A Model to Determine Thermal Performance of A Non-ventilated Double Glazing Unit with PCM and Experimental Validation Changyu Liu, Yumeng Zheng, Dong Li*, Hanbing Qi, Xiaoyan Liu School of Architecture and Civil EngineeringˈNortheast Petroleum University, Fazhan Lu Street, Daqing 163318, China
Abstract Phase change material (PCM) applied in the double glazing unit can decrease energy consumption and improve indoor thermal comfort by improving its thermal energy storage capacity. In the present work, a model to determine thermal performance of a non-ventilated double glazing unit with PCM and experimental validation was developed. The result shows that the developed model in present work can solve the coupled heat transfer problem between phase change and solar heat transfer in the double glazing unit filled with PCM. © Published by by Elsevier Ltd.Ltd. This is an open access article under the CC BY-NC-ND license ©2016 2016The TheAuthors. Authors. Published Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICCHMT2016 Peer-review under responsibility of the organizing committee of ICCHMT2016 Keywords: PCM, double glazing units, thermal performance
1. Introduction The energy production from coal and fossil fuel is the preponderant factors for CO2 emission into the atmosphere, which is widely believed to be contributing to global warming [1, 2]. Building is one of the leading sectors of the energy consumption, and especially about 40% of total fossil energy per each year in China was consumed in building sector in the last five years [3, 4]. Glazing units are an indispensable part of a building, which provide passive solar gain and air ventilation, for example window system [5].
* Corresponding author. Tel.: 15164563872. E-mail address: [email protected] [email protected](D. Li)
1877-7058 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICCHMT2016
doi:10.1016/j.proeng.2016.08.369
294
Changyu Liu et al. / Procedia Engineering 157 (2016) 293 – 300
Nomenclature Ag1 , Ap1 , Ap 2 , Ag 2
solar absorptance of glass 1 layer, phase 1 layer, phase 2 layer and glass 2, -
F 3 J F 3ˈS
specific heat of glass and PCM, J/(kg·K)
)VN\ ) JURXQG
view factor between the glazing unit and the sky dome, between the glazing unit
, VRO , J S , S O S V , S J
and the surrounding surfaces, specific enthalpy of PCM, J/kg; convective heat transfer coefficient of the exterior surface of outer glass, inner surface of internal glass, W/(m2·K) solar radiation, radiative heat flux of coupled surface between outer glass and
N J N S N S O N S V
PCM, liquid–solid interface in the PCM region, coupled surface between internal glass and PCM, W/m2C thermal conductivity of glass and PCM, liquid PCM near to liquid–solid
/J /S /S /J
interface, thermal conductivity of solid PCM near to liquid–solid interface, W/(m·K) thickness of glass 1 layer, phase 1 layer, phase 2 layer and glass 2, m
+ KRXW KLQ
S (t ), QL
refractive index of glass, phase1 and 2 of PCM, thickness of liquid PCM, m; latent heat of PCM, J/kg
qrad , qrad , air , qrad , sky , qrad , ground
radiative heat exchange between exterior surface of outer glass with the outdoor
7 J 7 S 7 S 7J
environment, with the air, sky and ground of outer glass, W/m2 solar transmittance of glass 1 layer, phase 1 layer, phase 2 layer and glass 2, -
QJ Q S Q S
7 7UHI 7V 7O 7 J 7 S 7 S O 7 S V
Tout , Ta ,out , Tsky , Tin , Ta ,in
temperature, reference temperature, temperature that the phase of PCM starts to change from solid to liquid, PCM completely changed into liquid, K temperature of the coupled surface of outer glass, coupled surface of PCM, liquid PCM near to liquid–solid interface, solid PCM near to liquid–solid interface, K temperature of the exterior surface of outer glass, ambient, sky temperature, inner surface of internal glass, indoors air, K
Greek letters DJ DS DS
extinction coefficient of glass, phase1 and 2 of PCM, m-1
liquid fraction, -; a factor that splits the heat exchange with the sky dome between sky and air radiation,-
J S
density of glass and PCM, kg/m3 interface reflectance for surface between air and glass, for surface between phase 1 of PCM and glass, for surface between phase 1 and phase 2 of PCM, for surface between phase 2 of PCM and glass, time, s radiative source term, W/m3 surface emissivity of glass,Stefan–Boltzmann constant,-
ˈ ˈˈ
angle between the glazing unit and the ground,-
Subscript a con
air, convective
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Changyu Liu et al. / Procedia Engineering 157 (2016) 293 – 300
g, p in, out rad sol l, s
glass and PCM, inner surface and exterior surface, radiative, solar radiation intensity, liquid and solid PCM, -
An effective approach to increase the thermal storage capacity of glazing units is to incorporate phase change material (PCM) in the glazing structure [6-8]. The aim of the PCM-filled glazing unit concept is thus to absorb part of the solar radiation for thermal energy storage, while letting visible radiation enter the indoor environment for daylighting. Until now, a variety of numerical models of thermal energy storage solutions for the integration of PCM into glazing unit have been developed. In these models, the semi-transparent property and phase change of double glazing unit with PCM is considered, radiation and convective heat transfer of interior and outer surface with surroundings is also clearly illustrated, however for the interior radiation transfer, all models ignores the reflection of the interface between liquid PCM, solid PCM and glass, which leads to the unexpected error [9-11]. In the present study, a model to investigate the thermal performance of a PCM-filled double glazing unit was developed. The reliability of the model was also validated by the experimental data. 2. Physical and Mathematical Models 2.1. Geometric Description Fig. 1 shows the details of the modeling four layer glazing unit filled with PCM. As shown in Fig. 1, solar energy reaching the glazing unit surface is partly transmitted and partly reflected, and the remaining portion is absorbed by the four layer glass and the PCM layer. The heat transfer process with the combination of thermal radiation and convection takes place on the boundary of the exterior and the interior surface, respectively. The convection heat transfer process of air between two glasses is considered. The absorbed heat will be transmitted inward and or outward, by the processes of conduction, convection and radiation exchange. The long wave radiation of the glasses on both sides of air layer is considered. For a transparent layer, the effective transmittance as well as the front and back reflectance are quantified as the consequence of multiple reflections between the front and back surfaces, plus the effects of absorption through the layer.
Long wave radiation
Long wave radiation Thermal radiation
Conduction
T
out
glass 3
glass 4 in
Interface
Conduction
St
a ir Glass
T
air 2
RI0
phase 2
transmitted
Thermal convection
glass 2
0
phase 1
Convection
I
Solar radiation
air 1
Thermal convection
Convection
Solar radiation reflected
room
glass 1
ambient Solar radiation
PCM
b1 1
Glass
x
Fig.1. Double glazing unit filled with PCM
x1
b2 x2
2
b4
b3 x3
x4
x5
b5
x6
x7
Fig.2. Layout of double glazing unit filled with PCM
2.2. Governing Equations and Boundary Conditions Assumptions for the mathematical model have been listed as follows: (1) The heat transfer through the glazing unit is simplified to one-dimensional unsteady heat transfer process. (2) The convection within the PCM layer is neglected.
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Changyu Liu et al. / Procedia Engineering 157 (2016) 293 – 300
(3) The radiation exchange between the two glass surfaces facing the cavity filled with PCM is neglected too. And the PCM of both liquid state and solid state is highly non-transparent to the long-wave radiation. (4) The glass and PCM are considered to be thermally homogeneous and isotropic media, and the thermal properties of the materials are temperature independent. (5) The effect of absorption and scattering of the air layer is omitted. (6) The scattering effect of PCM is omitted. For the four layer glazing unit filled with PCM, the heat transfer is calculated in five regions as shown in Fig. 2, which are the outer glass layer 1, outer glass layer 4, internal glass layer 2, internal glass layer 3 and PCM layer in the middle. A one-dimensional unsteady energy equation for glass regions is given as Eq. (1a) and (1b). Eq. (1b) is applied to the node of the glass regions near the air layer, Eq. (1b) is applied to the other nodes of the glass regions. 7 7 (1a) NJ JFS J [ 7 7 (1b) NJ W JF S J [ 3 Where, τ is time (s). T is temperature (K). g and c p , g are density (kg/m ), specific heat (J/(kg·K)) of glass, respectively. k g and k g ,t are thermal conductivity and effective thermal conductivity of glass (W/m·K), respectively. is radiation source term (W/m3). The effective thermal conductivity in Eq. (1b) is calculated by (2a) N J W N J KD 1X (2b) KD NJ
+ 1X *U 3U 1 1 H Nu 0.073(Gr Pr) 3 ( ) 9
*U *U
(2c) (2d)
Where, ha is the convection heat transfer of the air interlayer (W/(m2·K)). H and δ are the facade height (m) and the thickness (m) of the air layer. Nu, Grδ , Pr are the Nusselt number, the Grashof number and the Prandtl number. The one-dimensional unsteady energy equation for PCM region is given as + 7 (3) S NS [ Where, H is the specific enthalpy of PCM (J/kg). p and k p are density (kg/m3), thermal conductivity (W/m·K) of PCM, respectively. The specific enthalpy of PCM in Eq. (3) is calculated by +
7
7
UHI
F3 SG7 4 /
ˈ7˘7V 7 7V 7 7 7 7 7V V
(4a) (4b) (4c)
(4d) ˈ7˚7 Where, Tref is the reference temperature (K). cP , p is specific heat (J/kg·K) of PCM. QL is the latent heat of PCM in the whole phase change process (J/kg). is the local liquid fraction in calculation region. 7V and 7O are the temperature that the phase of PCM starts to change from solid to liquid (K), and the temperature that the phase of PCM completely changes into liquid (K), respectively. The radiative source term for each layer is given as following. When the calculation node is in the glass 1 except for the last one, as shown in Fig.2, $ , (5a) J VRO /J When the calculation node is the last one in the glass 1, as shown in Fig.2,
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Changyu Liu et al. / Procedia Engineering 157 (2016) 293 – 300
$J , VRO 7[ 7[ /J When the calculation node is in the glass 2 except for the first one, as shown in Fig.2, 7 $ , J J VRO /J When the calculation node is the first one in the glass 2, as shown in Fig.2, 7 $ , J J VRO 7[ 7[ /J When the calculation node is in the phase 1 of PCM layer as shown in Fig.2,
7J 7J $S , VRO /S
When the calculation node is in the phase 2 of PCM layer as shown in Fig.2, 7 7 7 $ , J J S S VRO /S When the calculation node is in the glass 3 except for the last one, as shown in Fig.2, 7 7 7 7 $ , J J S S J VRO /J When the calculation node is the last one in the glass 3,as shown in Fig.2, 7 7 7 7 $ , J J S S J VRO 7[ 7[ /J When the calculation node is in the glass 4 except for the last one, as shown in Fig.2,
7J 7J 7S 7S 7J $J , VRO /J
(5b)
(5c)
(5d) (5e)
(5f)
(5g)
(5h) (5I)
When the calculation node is the last one in the glass 4, as shown in Fig.2, 7 7 7 7 7 $ , (5J) J J S S J J VRO 7[ 7[ /J Where, I sol is solar radiation (W/m2). Tg1 , Tg 2 , T p1 , Tp 2 , Tg 3 , Tg 4 are solar transmittance of glass 1 layer, glass 2 layer, phase 1 layer, phase 2 layer, glass 3 layer and glass 4 layer, respectively. Ag1 , Ag 2 , Ap1 , Ap 2 , Ag 3 , Ag 4 is solar absorptance of glass 1 layer, glass 2 layer, phase 1 layer, phase 2 layer, glass 3 layer, glass 4 layer, respectively. The transmittance and absorptance of the layer i are calculated by [12] L L H[S L /L (6a) 7 L L H[S L /L (1 i1 ) i 2 exp(2i Li ) Ai 1 i1 Ti 1 i1 i 2 exp(2i Li ) L
(6b)
Where i1 , i 2 are the entrance and exit interface of media i. ai and Li are the extinction coefficient and length of the media i. The interface reflectance of media i and j are calculated based on Fresnel’s relations [13-15]. L M
QL QM QL QM
(7)
Where, ni and n j are the refractive index of the media i and j. The mathematical boundary conditions for the calculation domain are given as following. In the exterior surface of outer glass is exposed to solar radiation, and the boundary condition at x=0 is given as 7 (8) NJ T UDG KRXW 7RXW 7D RXW [ Where, qrad is radiative heat exchange between exterior surface of outer glass with the outdoor environment (W/m2). hout qrad , Tout and Ta ,out are the convective heat transfer coefficient of the exterior surface of outer glass (W/m2·K), temperature of the exterior surface of outer glass (K), and ambient temperature (K), respectively. The radiation heat exchange with the outdoor environment is given by
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(9) TUDG T UDG DLU TUDG VN\ T UDG JURXQG Where qrad , air , qrad , sky and qrad , ground are radiation heat exchange with the air, sky and ground (W/m2), respectively. The radiation heat flux qrad , air , qrad , sky and qrad , ground are respectively given by [10] T UDG VN\ )VN\ 7RXW 7VN\
TUDGDLU )VN\ 7RXW 7DRXW
(10a)
(10b) (10c) Where, is the surface emissivity of glass. is the Stefan–Boltzmann constant. Fsky is the view factor between the glazing unit and the sky dome. Fground is the view factor between the glazing unit and the surrounding surfaces, and assuming that all the surfaces are at the same temperature. is a factor that splits the heat exchange with the sky dome between sky and air radiation. Tsky is the sky temperature (K). The parameter Fsky , Fground , , Tsky are respectively established by [10] FRV (11a) ) TUDG JURXQG )JURXQG 7RXW 7DRXW
VN\
)JURXQG
FRV FRV
(11b) (11c)
(11d) Where, is the angle between the glazing unit and the ground, for example, 90D for a vertical glazing unit). 7VN\ 7DRXW
3. Experiment and validation The measurements were conducted in the small-scale test facility consisting of units and rooms at Northeast Petroleum University in Daqing city, which is one of the representative cities of the cold area of China. As shown in Fig. 3, the test facility has the south-facing rooms with the internal dimension of 2.66 m × 1.46 m × 1.65 m (Height × Width × Depth). The glazing type used in the experiments was composed by four 4.5 mm glass panes with PCM
Fig. 3. Picture of the small-scale test facility
or air of 45 mm between them, and the thickness between the outer glass and internal glass is 145mm. One of the facade systems is filled with PCM (paraffin, RT27) and the other is filled with air. The surrounding external surfaces were built up of 100 mm insulation material (mineral wool). Temperatures were measured using thermocouples type K, and the solar radiation was measured using Jinzhou Sunshine/TBQ-4-5 solar spectral radiometer. The experimental data is measured with the experimental setup in two sunny early winter days on October 10-11, 2015. The solar radiation is depicted in Fig. 4a, and the outdoors and indoors temperatures with the double glazing facades filled with and without PCM are shown in Fig.4b. As show in Fig.4, the peak indoors temperature of the double glazing facades filled with PCM is 7ć lower than that of the facades without PCM in the sunrise time, while the indoors temperature of the double glazing facades filled with PCM is about 2–4ć higher than of the facades without PCM in the sunset time. The first reason for this phenomenon is that the PCM absorbs solar radiation and stores thermal energy during the sunrise while releases
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Changyu Liu et al. / Procedia Engineering 157 (2016) 293 – 300
thermal energy in the sunset time, and another one is that the PCM enhances its temperature. This results indicates that the double glazing facades filled with PCM can be used to mitigate the indoors temperature fluctuations. 60
800
a
outdoors indoors-PCM indoors-without PCM
50 Temperature,ć
Solar heat flux, W/m2
600 400 200
b
40 30 20 10
0 0
6
12
18
24 30 Time, h
36
42
0
48
0
6
12
18
24 30 Time, h
36
42
48
Fig. 4. Solar radiation and temperatures in the experiment (a: heat flux; b: temperatures)
The method was validated by the measured temperatures on internal surface of the double glazing facades in the experiments. The equations together with the boundary conditions are solved by using an explicit finite difference scheme. PCM region is divided into 15 equally spaced increments. Each glass sheet thickness is also divided into 5 equally spaced increments. The thermophysical properties of materials can be attained in Table 1.The extinction coefficient and refractive index of glass is 19 m-1 and 1.5 [34], respectively. The emissivity of the glass is 0.88 [26]. The refractive index of PCM is 1.3, and the extinction coefficients of solid and liquid PCM is 50 and 20 m-1, respectively [34]. The initial temperature of the domain is 15ć. The simulation was kept running until the solution becomes periodic, which needs two days to reach the periodic condition. The temperatures on the interior surfaces of the double glazing filled with PCM are shown in Fig. 5. Table 1. Thermophysical properties of materials Material Melting temperature( ć) Density(kg/m³) Thermal conductivity(W/m·K) Specific heat capacity(J/kgK) Latent heat(J/kg)
PCM[34]
-
25-28
1400
880
1.3
0.2 3110(solid) 4810(liquid) 184000
840 experimental numerical
60 Temperature,ć
Glass[34]
40 20 0 0
6
12
18
24 30 Time, h
36
42
48
Fig. 5. Numerical and experimental results of the double glazing façade filled with PCM
As shown in Fig. 5, during the early sunset time, the difference between numerical and the experimental results is big, while the numerical results have a good agreement with the experimental results in the sunrise time region. The reason is that the effect of initial temperature in the double glazing facades filled with PCM in the experimental is not omitted when heat conduction plays an important role in the heat transfer process, but which is omitted in the calculation because it can be reached the rational periodic condition. The above analysis shows that the mathematic
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Changyu Liu et al. / Procedia Engineering 157 (2016) 293 – 300
model and calculation procedure in present work can solve the coupled heat transfer problem between phase change and solar heat transfer in the double glazing facades filled with PCM. 4. Conclusions In present study, to investigate the thermal behavior of a PCM-filled double glazing unit, a coupled model of phase change, radiation and conduction process was built, which is on the basis of experimental validation. The following conclusions can be gained: 1) The mathematic model and calculation procedure in present work can solve the coupled heat transfer problem between phase change and solar heat transfer in the double glazing unit filled with PCM. 2) The difference of numerical results and experimental results is mainly from the effect of initial temperature in the double glazing facades filled with PCM in the experiment. Acknowledgements The financial support is provided by the National Science Foundation of China (NSFC) through Grant No. 51306031. References [1] Thalfeldt, M, and Pikas, E.J, 2013, Facade design principles for nearly zero energy buildings in a cold climate, J. Energy Build. 67, pp. 309– 321 [2] Erdem, C, and Young, C.H, 2014, Performance investigation of heat insulation solar glass for low-carbon buildings, J. Energy Convers. Manage, 88, pp. 834–841. [3] Zhou, D, and Zhao, C.Y, 2012, Review on thermal energy storage with phase change materials (PCMs) in building applications, J. Appl. Energy, 92, pp. 593–605. [4] Kong, X.F, and Lu, S.L, 2014, Numerical study on the thermal performance of building wall and roof incorporating phase change material panel for passive cooling application, J. Energy Build, 81, pp. 404–415. [5] Hilliaho, K, and Mäkitalo, E, 2015, Energy saving potential of glazed space: Sensitivity analysis, J. Energy Build, 99, pp. 87–97. [6] Pielichowska, K, and Pielichowski, K, 2014, Phase change materials for thermal energy storage, J. Prog. Mater. Sci, 65, pp. 67–123. [7] Silva, T, and Vicente, R, 2015, Development of a window shutter with phase change materials: Full scale outdoor experimental approach, J. Energy Build, 88, pp. 110–121. [8] Silva, T, and Vicente, R, 2015, Performance of a window shutter with phase change material under summer Mediterranean climate conditions, J. Appl. Therm. Eng, 84, pp. 246–256. [9] Zhong, K.C, and Li, S.H, 2015, Simulation study on dynamic heat transfer performance of PCM-filled glass window with different thermophysical parameters of phase change material, J. Energy Build, in press. [10] Goia, F, and Perino, M, 2012, A numerical model to evaluate the thermal behaviour of PCM glazing system configurations, J. Energy Build, 54, pp. 141–153. [11] Gowreesunker, B.L, and Stankovic, S.B, 2013, Experimental and numerical investigations of the optical and thermal aspects of a PCMglazed unit, J. Energy Build, 61, pp. 239–249. [12] Li, D, and Qi, H.B, 2015, Determined optical constants of liquid hydrocarbon fuel by a novel transmittance method, J. Optik, 126, pp. 834– 837. [13] Wang, F.Q, and Tan, J.Y, 2014, Thermal performance analysis of porous medium solar receiver with quartz window to minimize heat flux gradient, J. Sol. Energy, 108, pp. 348–359. [14] Wang, F.Q, and Shuai, Y, 2013, Researches on a new type of solar surface cladding reactor with concentration quartz window, J. Sol. Energy, 94, pp. 177–181. [15] Wang, F.Q, and Tan, J.Y, 2015, Effects of glass cover on heat flux distribution for tube receiver with parabolic trough collector system, J. Energy Convers. Manage, 90, pp. 47–52. [16] Ismail, K.A.R, and Salinas, C. T, 2008, Comparison between PCM filled glass windows and absorbing gas filled windows, J. Energy Build, 40, pp. 710–719.
ScienceDirect Procedia Engineering 157 (2016) 293 – 300
IX International Conference on Computational Heat and Mass Transfer, ICCHMT2016
A Model to Determine Thermal Performance of A Non-ventilated Double Glazing Unit with PCM and Experimental Validation Changyu Liu, Yumeng Zheng, Dong Li*, Hanbing Qi, Xiaoyan Liu School of Architecture and Civil EngineeringˈNortheast Petroleum University, Fazhan Lu Street, Daqing 163318, China
Abstract Phase change material (PCM) applied in the double glazing unit can decrease energy consumption and improve indoor thermal comfort by improving its thermal energy storage capacity. In the present work, a model to determine thermal performance of a non-ventilated double glazing unit with PCM and experimental validation was developed. The result shows that the developed model in present work can solve the coupled heat transfer problem between phase change and solar heat transfer in the double glazing unit filled with PCM. © Published by by Elsevier Ltd.Ltd. This is an open access article under the CC BY-NC-ND license ©2016 2016The TheAuthors. Authors. Published Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICCHMT2016 Peer-review under responsibility of the organizing committee of ICCHMT2016 Keywords: PCM, double glazing units, thermal performance
1. Introduction The energy production from coal and fossil fuel is the preponderant factors for CO2 emission into the atmosphere, which is widely believed to be contributing to global warming [1, 2]. Building is one of the leading sectors of the energy consumption, and especially about 40% of total fossil energy per each year in China was consumed in building sector in the last five years [3, 4]. Glazing units are an indispensable part of a building, which provide passive solar gain and air ventilation, for example window system [5].
* Corresponding author. Tel.: 15164563872. E-mail address: [email protected] [email protected](D. Li)
1877-7058 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICCHMT2016
doi:10.1016/j.proeng.2016.08.369
294
Changyu Liu et al. / Procedia Engineering 157 (2016) 293 – 300
Nomenclature Ag1 , Ap1 , Ap 2 , Ag 2
solar absorptance of glass 1 layer, phase 1 layer, phase 2 layer and glass 2, -
F 3 J F 3ˈS
specific heat of glass and PCM, J/(kg·K)
)VN\ ) JURXQG
view factor between the glazing unit and the sky dome, between the glazing unit
, VRO , J S , S O S V , S J
and the surrounding surfaces, specific enthalpy of PCM, J/kg; convective heat transfer coefficient of the exterior surface of outer glass, inner surface of internal glass, W/(m2·K) solar radiation, radiative heat flux of coupled surface between outer glass and
N J N S N S O N S V
PCM, liquid–solid interface in the PCM region, coupled surface between internal glass and PCM, W/m2C thermal conductivity of glass and PCM, liquid PCM near to liquid–solid
/J /S /S /J
interface, thermal conductivity of solid PCM near to liquid–solid interface, W/(m·K) thickness of glass 1 layer, phase 1 layer, phase 2 layer and glass 2, m
+ KRXW KLQ
S (t ), QL
refractive index of glass, phase1 and 2 of PCM, thickness of liquid PCM, m; latent heat of PCM, J/kg
qrad , qrad , air , qrad , sky , qrad , ground
radiative heat exchange between exterior surface of outer glass with the outdoor
7 J 7 S 7 S 7J
environment, with the air, sky and ground of outer glass, W/m2 solar transmittance of glass 1 layer, phase 1 layer, phase 2 layer and glass 2, -
QJ Q S Q S
7 7UHI 7V 7O 7 J 7 S 7 S O 7 S V
Tout , Ta ,out , Tsky , Tin , Ta ,in
temperature, reference temperature, temperature that the phase of PCM starts to change from solid to liquid, PCM completely changed into liquid, K temperature of the coupled surface of outer glass, coupled surface of PCM, liquid PCM near to liquid–solid interface, solid PCM near to liquid–solid interface, K temperature of the exterior surface of outer glass, ambient, sky temperature, inner surface of internal glass, indoors air, K
Greek letters DJ DS DS
extinction coefficient of glass, phase1 and 2 of PCM, m-1
liquid fraction, -; a factor that splits the heat exchange with the sky dome between sky and air radiation,-
J S
density of glass and PCM, kg/m3 interface reflectance for surface between air and glass, for surface between phase 1 of PCM and glass, for surface between phase 1 and phase 2 of PCM, for surface between phase 2 of PCM and glass, time, s radiative source term, W/m3 surface emissivity of glass,Stefan–Boltzmann constant,-
ˈ ˈˈ
angle between the glazing unit and the ground,-
Subscript a con
air, convective
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Changyu Liu et al. / Procedia Engineering 157 (2016) 293 – 300
g, p in, out rad sol l, s
glass and PCM, inner surface and exterior surface, radiative, solar radiation intensity, liquid and solid PCM, -
An effective approach to increase the thermal storage capacity of glazing units is to incorporate phase change material (PCM) in the glazing structure [6-8]. The aim of the PCM-filled glazing unit concept is thus to absorb part of the solar radiation for thermal energy storage, while letting visible radiation enter the indoor environment for daylighting. Until now, a variety of numerical models of thermal energy storage solutions for the integration of PCM into glazing unit have been developed. In these models, the semi-transparent property and phase change of double glazing unit with PCM is considered, radiation and convective heat transfer of interior and outer surface with surroundings is also clearly illustrated, however for the interior radiation transfer, all models ignores the reflection of the interface between liquid PCM, solid PCM and glass, which leads to the unexpected error [9-11]. In the present study, a model to investigate the thermal performance of a PCM-filled double glazing unit was developed. The reliability of the model was also validated by the experimental data. 2. Physical and Mathematical Models 2.1. Geometric Description Fig. 1 shows the details of the modeling four layer glazing unit filled with PCM. As shown in Fig. 1, solar energy reaching the glazing unit surface is partly transmitted and partly reflected, and the remaining portion is absorbed by the four layer glass and the PCM layer. The heat transfer process with the combination of thermal radiation and convection takes place on the boundary of the exterior and the interior surface, respectively. The convection heat transfer process of air between two glasses is considered. The absorbed heat will be transmitted inward and or outward, by the processes of conduction, convection and radiation exchange. The long wave radiation of the glasses on both sides of air layer is considered. For a transparent layer, the effective transmittance as well as the front and back reflectance are quantified as the consequence of multiple reflections between the front and back surfaces, plus the effects of absorption through the layer.
Long wave radiation
Long wave radiation Thermal radiation
Conduction
T
out
glass 3
glass 4 in
Interface
Conduction
St
a ir Glass
T
air 2
RI0
phase 2
transmitted
Thermal convection
glass 2
0
phase 1
Convection
I
Solar radiation
air 1
Thermal convection
Convection
Solar radiation reflected
room
glass 1
ambient Solar radiation
PCM
b1 1
Glass
x
Fig.1. Double glazing unit filled with PCM
x1
b2 x2
2
b4
b3 x3
x4
x5
b5
x6
x7
Fig.2. Layout of double glazing unit filled with PCM
2.2. Governing Equations and Boundary Conditions Assumptions for the mathematical model have been listed as follows: (1) The heat transfer through the glazing unit is simplified to one-dimensional unsteady heat transfer process. (2) The convection within the PCM layer is neglected.
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(3) The radiation exchange between the two glass surfaces facing the cavity filled with PCM is neglected too. And the PCM of both liquid state and solid state is highly non-transparent to the long-wave radiation. (4) The glass and PCM are considered to be thermally homogeneous and isotropic media, and the thermal properties of the materials are temperature independent. (5) The effect of absorption and scattering of the air layer is omitted. (6) The scattering effect of PCM is omitted. For the four layer glazing unit filled with PCM, the heat transfer is calculated in five regions as shown in Fig. 2, which are the outer glass layer 1, outer glass layer 4, internal glass layer 2, internal glass layer 3 and PCM layer in the middle. A one-dimensional unsteady energy equation for glass regions is given as Eq. (1a) and (1b). Eq. (1b) is applied to the node of the glass regions near the air layer, Eq. (1b) is applied to the other nodes of the glass regions. 7 7 (1a) NJ JFS J [ 7 7 (1b) NJ W JF S J [ 3 Where, τ is time (s). T is temperature (K). g and c p , g are density (kg/m ), specific heat (J/(kg·K)) of glass, respectively. k g and k g ,t are thermal conductivity and effective thermal conductivity of glass (W/m·K), respectively. is radiation source term (W/m3). The effective thermal conductivity in Eq. (1b) is calculated by (2a) N J W N J KD 1X (2b) KD NJ
+ 1X *U 3U 1 1 H Nu 0.073(Gr Pr) 3 ( ) 9
*U *U
(2c) (2d)
Where, ha is the convection heat transfer of the air interlayer (W/(m2·K)). H and δ are the facade height (m) and the thickness (m) of the air layer. Nu, Grδ , Pr are the Nusselt number, the Grashof number and the Prandtl number. The one-dimensional unsteady energy equation for PCM region is given as + 7 (3) S NS [ Where, H is the specific enthalpy of PCM (J/kg). p and k p are density (kg/m3), thermal conductivity (W/m·K) of PCM, respectively. The specific enthalpy of PCM in Eq. (3) is calculated by +
7
7
UHI
F3 SG7 4 /
ˈ7˘7V 7 7V 7 7 7 7 7V V
(4a) (4b) (4c)
(4d) ˈ7˚7 Where, Tref is the reference temperature (K). cP , p is specific heat (J/kg·K) of PCM. QL is the latent heat of PCM in the whole phase change process (J/kg). is the local liquid fraction in calculation region. 7V and 7O are the temperature that the phase of PCM starts to change from solid to liquid (K), and the temperature that the phase of PCM completely changes into liquid (K), respectively. The radiative source term for each layer is given as following. When the calculation node is in the glass 1 except for the last one, as shown in Fig.2, $ , (5a) J VRO /J When the calculation node is the last one in the glass 1, as shown in Fig.2,
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$J , VRO 7[ 7[ /J When the calculation node is in the glass 2 except for the first one, as shown in Fig.2, 7 $ , J J VRO /J When the calculation node is the first one in the glass 2, as shown in Fig.2, 7 $ , J J VRO 7[ 7[ /J When the calculation node is in the phase 1 of PCM layer as shown in Fig.2,
7J 7J $S , VRO /S
When the calculation node is in the phase 2 of PCM layer as shown in Fig.2, 7 7 7 $ , J J S S VRO /S When the calculation node is in the glass 3 except for the last one, as shown in Fig.2, 7 7 7 7 $ , J J S S J VRO /J When the calculation node is the last one in the glass 3,as shown in Fig.2, 7 7 7 7 $ , J J S S J VRO 7[ 7[ /J When the calculation node is in the glass 4 except for the last one, as shown in Fig.2,
7J 7J 7S 7S 7J $J , VRO /J
(5b)
(5c)
(5d) (5e)
(5f)
(5g)
(5h) (5I)
When the calculation node is the last one in the glass 4, as shown in Fig.2, 7 7 7 7 7 $ , (5J) J J S S J J VRO 7[ 7[ /J Where, I sol is solar radiation (W/m2). Tg1 , Tg 2 , T p1 , Tp 2 , Tg 3 , Tg 4 are solar transmittance of glass 1 layer, glass 2 layer, phase 1 layer, phase 2 layer, glass 3 layer and glass 4 layer, respectively. Ag1 , Ag 2 , Ap1 , Ap 2 , Ag 3 , Ag 4 is solar absorptance of glass 1 layer, glass 2 layer, phase 1 layer, phase 2 layer, glass 3 layer, glass 4 layer, respectively. The transmittance and absorptance of the layer i are calculated by [12] L L H[S L /L (6a) 7 L L H[S L /L (1 i1 ) i 2 exp(2i Li ) Ai 1 i1 Ti 1 i1 i 2 exp(2i Li ) L
(6b)
Where i1 , i 2 are the entrance and exit interface of media i. ai and Li are the extinction coefficient and length of the media i. The interface reflectance of media i and j are calculated based on Fresnel’s relations [13-15]. L M
QL QM QL QM
(7)
Where, ni and n j are the refractive index of the media i and j. The mathematical boundary conditions for the calculation domain are given as following. In the exterior surface of outer glass is exposed to solar radiation, and the boundary condition at x=0 is given as 7 (8) NJ T UDG KRXW 7RXW 7D RXW [ Where, qrad is radiative heat exchange between exterior surface of outer glass with the outdoor environment (W/m2). hout qrad , Tout and Ta ,out are the convective heat transfer coefficient of the exterior surface of outer glass (W/m2·K), temperature of the exterior surface of outer glass (K), and ambient temperature (K), respectively. The radiation heat exchange with the outdoor environment is given by
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(9) TUDG T UDG DLU TUDG VN\ T UDG JURXQG Where qrad , air , qrad , sky and qrad , ground are radiation heat exchange with the air, sky and ground (W/m2), respectively. The radiation heat flux qrad , air , qrad , sky and qrad , ground are respectively given by [10] T UDG VN\ )VN\ 7RXW 7VN\
TUDGDLU )VN\ 7RXW 7DRXW
(10a)
(10b) (10c) Where, is the surface emissivity of glass. is the Stefan–Boltzmann constant. Fsky is the view factor between the glazing unit and the sky dome. Fground is the view factor between the glazing unit and the surrounding surfaces, and assuming that all the surfaces are at the same temperature. is a factor that splits the heat exchange with the sky dome between sky and air radiation. Tsky is the sky temperature (K). The parameter Fsky , Fground , , Tsky are respectively established by [10] FRV (11a) ) TUDG JURXQG )JURXQG 7RXW 7DRXW
VN\
)JURXQG
FRV FRV
(11b) (11c)
(11d) Where, is the angle between the glazing unit and the ground, for example, 90D for a vertical glazing unit). 7VN\ 7DRXW
3. Experiment and validation The measurements were conducted in the small-scale test facility consisting of units and rooms at Northeast Petroleum University in Daqing city, which is one of the representative cities of the cold area of China. As shown in Fig. 3, the test facility has the south-facing rooms with the internal dimension of 2.66 m × 1.46 m × 1.65 m (Height × Width × Depth). The glazing type used in the experiments was composed by four 4.5 mm glass panes with PCM
Fig. 3. Picture of the small-scale test facility
or air of 45 mm between them, and the thickness between the outer glass and internal glass is 145mm. One of the facade systems is filled with PCM (paraffin, RT27) and the other is filled with air. The surrounding external surfaces were built up of 100 mm insulation material (mineral wool). Temperatures were measured using thermocouples type K, and the solar radiation was measured using Jinzhou Sunshine/TBQ-4-5 solar spectral radiometer. The experimental data is measured with the experimental setup in two sunny early winter days on October 10-11, 2015. The solar radiation is depicted in Fig. 4a, and the outdoors and indoors temperatures with the double glazing facades filled with and without PCM are shown in Fig.4b. As show in Fig.4, the peak indoors temperature of the double glazing facades filled with PCM is 7ć lower than that of the facades without PCM in the sunrise time, while the indoors temperature of the double glazing facades filled with PCM is about 2–4ć higher than of the facades without PCM in the sunset time. The first reason for this phenomenon is that the PCM absorbs solar radiation and stores thermal energy during the sunrise while releases
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thermal energy in the sunset time, and another one is that the PCM enhances its temperature. This results indicates that the double glazing facades filled with PCM can be used to mitigate the indoors temperature fluctuations. 60
800
a
outdoors indoors-PCM indoors-without PCM
50 Temperature,ć
Solar heat flux, W/m2
600 400 200
b
40 30 20 10
0 0
6
12
18
24 30 Time, h
36
42
0
48
0
6
12
18
24 30 Time, h
36
42
48
Fig. 4. Solar radiation and temperatures in the experiment (a: heat flux; b: temperatures)
The method was validated by the measured temperatures on internal surface of the double glazing facades in the experiments. The equations together with the boundary conditions are solved by using an explicit finite difference scheme. PCM region is divided into 15 equally spaced increments. Each glass sheet thickness is also divided into 5 equally spaced increments. The thermophysical properties of materials can be attained in Table 1.The extinction coefficient and refractive index of glass is 19 m-1 and 1.5 [34], respectively. The emissivity of the glass is 0.88 [26]. The refractive index of PCM is 1.3, and the extinction coefficients of solid and liquid PCM is 50 and 20 m-1, respectively [34]. The initial temperature of the domain is 15ć. The simulation was kept running until the solution becomes periodic, which needs two days to reach the periodic condition. The temperatures on the interior surfaces of the double glazing filled with PCM are shown in Fig. 5. Table 1. Thermophysical properties of materials Material Melting temperature( ć) Density(kg/m³) Thermal conductivity(W/m·K) Specific heat capacity(J/kgK) Latent heat(J/kg)
PCM[34]
-
25-28
1400
880
1.3
0.2 3110(solid) 4810(liquid) 184000
840 experimental numerical
60 Temperature,ć
Glass[34]
40 20 0 0
6
12
18
24 30 Time, h
36
42
48
Fig. 5. Numerical and experimental results of the double glazing façade filled with PCM
As shown in Fig. 5, during the early sunset time, the difference between numerical and the experimental results is big, while the numerical results have a good agreement with the experimental results in the sunrise time region. The reason is that the effect of initial temperature in the double glazing facades filled with PCM in the experimental is not omitted when heat conduction plays an important role in the heat transfer process, but which is omitted in the calculation because it can be reached the rational periodic condition. The above analysis shows that the mathematic
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model and calculation procedure in present work can solve the coupled heat transfer problem between phase change and solar heat transfer in the double glazing facades filled with PCM. 4. Conclusions In present study, to investigate the thermal behavior of a PCM-filled double glazing unit, a coupled model of phase change, radiation and conduction process was built, which is on the basis of experimental validation. The following conclusions can be gained: 1) The mathematic model and calculation procedure in present work can solve the coupled heat transfer problem between phase change and solar heat transfer in the double glazing unit filled with PCM. 2) The difference of numerical results and experimental results is mainly from the effect of initial temperature in the double glazing facades filled with PCM in the experiment. Acknowledgements The financial support is provided by the National Science Foundation of China (NSFC) through Grant No. 51306031. References [1] Thalfeldt, M, and Pikas, E.J, 2013, Facade design principles for nearly zero energy buildings in a cold climate, J. Energy Build. 67, pp. 309– 321 [2] Erdem, C, and Young, C.H, 2014, Performance investigation of heat insulation solar glass for low-carbon buildings, J. Energy Convers. Manage, 88, pp. 834–841. [3] Zhou, D, and Zhao, C.Y, 2012, Review on thermal energy storage with phase change materials (PCMs) in building applications, J. Appl. Energy, 92, pp. 593–605. [4] Kong, X.F, and Lu, S.L, 2014, Numerical study on the thermal performance of building wall and roof incorporating phase change material panel for passive cooling application, J. Energy Build, 81, pp. 404–415. [5] Hilliaho, K, and Mäkitalo, E, 2015, Energy saving potential of glazed space: Sensitivity analysis, J. Energy Build, 99, pp. 87–97. [6] Pielichowska, K, and Pielichowski, K, 2014, Phase change materials for thermal energy storage, J. Prog. Mater. Sci, 65, pp. 67–123. [7] Silva, T, and Vicente, R, 2015, Development of a window shutter with phase change materials: Full scale outdoor experimental approach, J. Energy Build, 88, pp. 110–121. [8] Silva, T, and Vicente, R, 2015, Performance of a window shutter with phase change material under summer Mediterranean climate conditions, J. Appl. Therm. Eng, 84, pp. 246–256. [9] Zhong, K.C, and Li, S.H, 2015, Simulation study on dynamic heat transfer performance of PCM-filled glass window with different thermophysical parameters of phase change material, J. Energy Build, in press. [10] Goia, F, and Perino, M, 2012, A numerical model to evaluate the thermal behaviour of PCM glazing system configurations, J. Energy Build, 54, pp. 141–153. [11] Gowreesunker, B.L, and Stankovic, S.B, 2013, Experimental and numerical investigations of the optical and thermal aspects of a PCMglazed unit, J. Energy Build, 61, pp. 239–249. [12] Li, D, and Qi, H.B, 2015, Determined optical constants of liquid hydrocarbon fuel by a novel transmittance method, J. Optik, 126, pp. 834– 837. [13] Wang, F.Q, and Tan, J.Y, 2014, Thermal performance analysis of porous medium solar receiver with quartz window to minimize heat flux gradient, J. Sol. Energy, 108, pp. 348–359. [14] Wang, F.Q, and Shuai, Y, 2013, Researches on a new type of solar surface cladding reactor with concentration quartz window, J. Sol. Energy, 94, pp. 177–181. [15] Wang, F.Q, and Tan, J.Y, 2015, Effects of glass cover on heat flux distribution for tube receiver with parabolic trough collector system, J. Energy Convers. Manage, 90, pp. 47–52. [16] Ismail, K.A.R, and Salinas, C. T, 2008, Comparison between PCM filled glass windows and absorbing gas filled windows, J. Energy Build, 40, pp. 710–719.