Enhancing a vertical earth-to-air heat exchanger system using tubular phase change material

Journal of Cleaner Production 237 (2019) 117763

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Enhancing a vertical earth-to-air heat exchanger system using tubular phase change material Zhengxuan Liu a, b, Pengcheng Sun c, Shuisheng Li d, Zhun (Jerry) Yu a, b, *, Mohamed El Mankibi e, Letizia Roccamena e, Tingting Yang f, Guoqiang Zhang a, b a College of Civil Engineering, National Center for International Research Collaboration in Building Safety and Environment, Hunan University, Changsha, Hunan 410082, China b Collaborative Innovation Center of Building Energy Conservation & Environmental Control, Hunan, 412007, China c China State Construction Engineering Corporation Technical Center, Beijing 100029, China d China Construction Fifth Engineering Division Corporation Limited, Changsha, Hunan, 410004, China e ENTPE-University of Lyon, 3 rue Maurice Audin, Vaulx en Velin 69120, France f College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan, Hunan, 411105, China

a r t i c l e i n f o

a b s t r a c t :

Article history: Received 22 May 2019 Received in revised form 20 July 2019 Accepted 23 July 2019 Available online 24 July 2019

In this study, a new vertical earth-to-air heat exchanger (VEAHE) system coupled with tubular phase change material (PCM) components was proposed. The proposed system has smaller occupied areas and higher geothermal energy use efficiency than traditional EAHE systems. Moreover, the tubular PCM component enables the system's air temperature at the outlet to be more stable, thereby enhancing the system's thermal performance. In particular, the tubular components' simple geometry, easy fabrication, convenient assembling-disassembling and low-cost facilitate their usage in practical applications. To explore the system's thermal performance, an experimental set-up was established and its numerical model was developed. Then the model was verified through a comparison between the system's simulated and monitored air temperatures at the outlet. The verification produced acceptable results with the maximum absolute relative error of 1.33%. Based on this model, the influences of the tubular PCM component, tube depth, PCM conductivity and container length on the proposed system's thermal performance were investigated. Results indicated that the tubular PCM components can effectively reduce the VEAHE system's air temperature peak and fluctuation at the outlet, and increase its average cooling capacity. For the proposed system, as the tube depths increase from 12 to 24 m, the air temperature peak and fluctuation at the outlet decrease from 25.74
C and 3.59
C to 21.01
C and 0.62
C, respectively. Different thermal conductivity of PCM has almost same influences on the system's air temperature at the outlet as the container diameter is 50 mm. Such influences, however, become apparent and require to be considered as the container diameter increases to 150 mm. The air temperature fluctuation at the outlet decreases as the container lengths increase, and 12 m can be considered as an appropriate length for the proposed system. Additionally, the system's static payback period was calculated as 18.03 years. © 2019 Elsevier Ltd. All rights reserved.

Handling Editor: Jin-Kuk Kim Keywords: Vertical earth-to-air heat exchanger Geothermal energy Phase change material Tubular component Static payback period

1. Introduction Geothermal energy, as a cleaner and nearly emission-free alternative to fossil fuels (Balbay and Esen, 2010; Esen et al.,

* Corresponding author. College of Civil Engineering, National Center for International Research Collaboration in Building Safety and Environment, Hunan University, Changsha, Hunan, 410082, China. E-mail address: [email protected] (Z. Yu). https://doi.org/10.1016/j.jclepro.2019.117763 0959-6526/© 2019 Elsevier Ltd. All rights reserved.

2017), has been widely used to provide cooling/heating for various energy-saving systems applied in buildings (Esen and Yuksel, 2013; Yu et al., 2019; Zhang et al., 2019). Common utilization of geothermal energy includes the ground source heat pump (GSHP) and earth-to-air heat exchanger (EAHE) (Esen et al., 2007a, 2007c; Esen, 2000). In recent years, the earth-to-air heat exchanger (EAHE) system has been attracting considerable interest with advantages of lower operational costs and smaller environmental impacts (Mehdid et al., 2018; Rouag et al., 2018). The EAHE system could be applied to cool/heat the outdoor air before it was sent into

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Z. Liu et al. / Journal of Cleaner Production 237 (2019) 117763

Glossary

Symbols Cp T R m_ T r1 rP S h V ri d Dz Ct Ca Sy

Specific heat capacity, J/(kg K) Temperature, ºC Thermal resistance, ºC/W Mass flow rate, kg/s Average temperature, ºC Fixed radius, m Outermost radius of PCM, m Heat transfer area, m2 Heat transfer coefficient, W/(m2$ºC) Volume, m3 Inner radius of tube, m Tube wall thickness, m Height of divided volume, m Total cost, $ Cost of a conventional air-conditioner, $ Annual income produced of energy-saving, $

Greek letters Density, m3/kg 4 Heating or cooling rate, ºC/s l Thermal conductivity, W/(m$K)

r

a building due to the stable soil temperature at a given depth (Balbay and Esen, 2013), thereby reducing the building energy consumption. For instance, Tittelein et al. (2009) reported that, compared to a traditional ventilation system, the EAHE system could decrease the building energy consumption of 7 and 9 kWh/ m2 per year as the tube depths were 0.6 m and 2 m, respectively. Ascione et al. (2016) made a comparison between an EAHE system and a conventional mechanical ventilation system, and the results showed that the EAHE system could contribute to the building energy reduction of about 29% in winter and 36e46% in summer for the Mediterranean climate. The EAHE system has been proved as an effective cooling and heating technology for reducing building energy consumption. However, their practical limitations, such as large land occupation demands during construction (Soni et al., 2016), produce severe limitations on their successful applications, particularly in densely built areas. Moreover, in most existing studies the depth of the buried tubes was 2e4 m (Singh et al., 2018)) while, at this depth, the soil temperature tended to be affected by soil properties and environmental conditions such as ambient temperatures and rainfall. This could lead to a large variance of outlet air temperature of EAHE systems (Mustafa Omer, 2008), thereby decreasing the systems’ thermal performance. To address the above issue, a vertical EAHE system (i.e., VEAHE) with a U-tube was proposed in (Liu et al., 2019b, 2019c). In this VEHAE system, a small hole (less than 1 m2) was drilled for the bury of the U-tube and thus the land occupation was significantly reduced compared to the traditional EAHE systems. Moreover, the VEAHE system was designed with a depth of more than 15 m where the soil temperature was more stable than that of the shallow soil. Such soil temperatures were also closer to the required cold/heat source temperature of building ventilation systems (Xi et al., 2017; Zhou et al., 2016), leading to an improvement of energy utilization efficiency. The experimental results (Liu et al., 2019b) and numerical analysis (Liu et al., 2019d) have demonstrated the VEAHE system's effectiveness. However, subject to the outdoor air temperature variations and air velocity increases, the VEAHE

Subscripts i a s t I g j P k m

Node location Air Soil Tube Insulation Outermost soil Vertical direction node location Phase change material Number of selected data samples Number of soil column

Superscripts t Time t  Dt Previous time of the time t Abbreviations VEAHE Vertical earth-to-air heat exchanger PCM Phase change material EAHE Earth-to-air heat exchanger GSHP Ground source heat pump SHC Specific heat capacity SPP Static payback period

system could still have a large air temperature fluctuation at the outlet. For instance, such temperature fluctuations were 2.6
C and 3.8
C in summer for the system's air velocity of 1 and 2 m/s, respectively (Liu et al., 2019d), which is difficult to satisfy the requirements of the indoor human comfort. In this view, a VEAHE system coupled with macro-encapsulated phase change material (PCM) was proposed in (Liu et al., 2019a). In this system, three identical stainless-steel annular PCM containers were installed from the outlet to the depth of 3.6 m in the left leg of U-tube. The PCM could store cooling/heating energy and use it at a later time, and thus reduce the fluctuation of air temperatures at the outlet (Zhou et al., 2019a,b). The results showed that, for the air velocity of 1 m/s, the system's air temperature fluctuation and peak at the outlet were decreased by 0.8
C and 0.5
C, respectively. When the air velocity became 2 m/s, the decreasing of the air temperature fluctuation and peak at the outlet became 1.1
C and 1.0
C, respectively. The integration of annular PCM components into VEAHE systems has been demonstrated with more stable air temperatures at the outlet. However, its relatively complicated structure could add manufacture and installation difficulties as well as expenses, thereby significantly increasing the system's initial investment. For example, the economic analysis in (Liu et al., 2019a) indicated that the capital investment of the annular PCM components with a length of 3.6 m was $160.0 and the system's static payback period was calculated as 20.8 years. Note that the manufacture expenses of annular PCM components will be dramatically increased with the increase of component lengths. Such a large initial investment would prevent the proposed system from being adopted and generalized in practical applications. Indeed, the economic feasibility has been treated as an important criterion in choosing an energy efficient technology/system (Esen et al., 2006, 2007b). Therefore, it is highly desirable that an appropriate form of PCM macro-encapsulation can be designed and integrated into the VEAHE systems, with the goal of reducing manufacture expenses and improving the system's thermal performance. Indeed, different

Z. Liu et al. / Journal of Cleaner Production 237 (2019) 117763

forms of PCM macro-encapsulation have been proposed and applied in the building domain, such as rectangular, tubular and spherical. The application of these forms has been reviewed and compared in (Dadollahi and Mehrpooya, 2017; Esen and Ayhan, 1996; Esen et al., 1998; Liu et al., 2018; Zhou et al., 2019a,b). Among these forms, tubular PCM components, due to their simple geometry, easy fabrication, convenient assembling-disassembling and low-cost, have been widely used in solar energy systems (Arunkumar and Kabeel, 2017; Englmair et al., 2019), energy storage tanks (Zhang et al., 2014), and heat exchangers (Dubovsky et al., 2011). In this view, a new VEAHE system coupled with tubular PCM components was proposed in this paper. Specifically, a tubular PCM component was installed from the outlet to the bottom in the leftleg of the U-tube. PCM inside the tubular container can absorb and release the latent heat when its phase change process occurs (Zhou et al., 2018), which can reduce the fluctuation in the system's air temperature at the outlet as well as its peak. This paper aims at presenting an experimental and numerical study conducted on a new VEAHE system coupled with tubular PCM components. First, its experimental set-up was introduced. Then, the system's numerical model was developed using the MATLAB/Simulink platform, and the developed model was verified by the monitored data. Based on the verified model, the influences of the tubular PCM component, tube depth, PCM conductivity and container length on the system performance were investigated. Finally, the system's static payback period was also calculated.

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Fig. 1. The schematic diagram and detailed dimensions of the proposed system.

2. Experimental set-up The proposed system's schematic diagram and its detailed dimensions are indicated in Fig. 1. A stainless steel U-tube with an outer diameter of 219 mm was buried in a drilled hole. A bypass was designed at the U-tube's bottom for the drainage of condensate water. The left leg of the U-tube (from the outlet to the depth of 7.5 m) was insulated with polyurethane. A tubular PCM component was set in the center of the tube and its container was made up of stainless-steel with a length of 15.5. The selected PCM was paraffin due to its low cost, high chemical stability, no pollution for the environment etc. (Liu et al., 2018). The site pictures are shown in Fig. 2. The location of the experimental set-up was Changsha (Latitude/Longitude: N28º12'/E112º59'), China. The air and PCM temperature were tested, from October 8 to 9, 2017 by using PT100 temperature sensors with a permissible error ±0.15
C. An Agilent 34972A was utilized for experimental data measurement and collection. The sensors of from IT-1 to IT-14 set in the center of the tube are labeled as air temperatures in the tube, as shown in Fig. 3. The sensors of TPT-1 to TPT-6 are labeled as PCM temperatures located in the center of the tubular container. 3. Numerical model A numerical model was developed to examine the influences of the tubular PCM component. The model was segmented into three parts based on the structure of proposed system. Specifically, the first part (i.e., Part I) is from the inlet to the depth of 15.5 m on the U-tube's right leg. The second part (i.e., Part II) and third part (i.e., part III) are from the depth of 15.5 to 7.5 m and 7.5 m to the outlet on the U-tube's left leg, respectively. In this study, the model equations of each divided part were built and then solved in the MATLAB/Simulink environment. Through the MATLAB/Simulink platform, a block for each divided part was developed using the S-

Fig. 2. Site pictures: (a) Drilling hole and burying U-tube; (b) Tubular PCM component.

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Z. Liu et al. / Journal of Cleaner Production 237 (2019) 117763

are segmented into n layers for Part I, II and III. The soil along its radial direction was segmented into m columns. The PCM layer was segmented into (Nþ1) columns along the radial direction. The heat transfer governing equations of these different mediums for each divided unit can be established based on energy balance as follows (Bahrar et al., 2018):

8 9 8 9 8 9 > > > > > > > < Temperature > = > < Conduction =Convective > = > < Advection > = change rate ¼ þ transfers transfers > > > > > > > > > in unit in unit : ; > : ; > : in unit > ; (1) The temperature change rate (i.e., storage of energy) of the divided unit can be written as:

8 > > < Temperature change rate > > in unit :

9 > > = > > ;

¼ r  Cp  V 

dT dt

(2)

where r, Cp , V and T is the density, specific heat capacity (SHC), volume and temperature of the medium, respectively; t is time. The conduction transfers between the adjacent mediums can be written as:

8 > > < Conduction=Convective transfers > > in unit :

9 > > = > > ;

¼

Ti1  2Ti þ Tiþ1 R

(3)

where Ti1 , Ti and Tiþ1 is the node temperature at node i-1, i, and iþ1, R is the thermal resistance between adjacent nodes. The advection transfer concerns the flowing air, which represents the energy transported into an air node i from an adjacent air node i-1 along the flowing air direction, as follows: Fig. 3. Arrangement of temperature sensors.

Function. Then these blocks were linked by Simulink platform to predict the temperature variation of the mediums with the operation time. 3.1. Assumptions of the model The following assumptions can be made for the development of proposed system's model: C Air is incompressible and the influence of its humidity change on the heat transfer can be ignored. C The heat conduction between two adjacent layers along the vertical direction can be ignored. C The thermal interference between the U-tube's right and left leg can be ignored due to the minor influences between the neighbor legs as their interval distance is more than two times of the tube diameter (Shojaee and Malek, 2017). C The PCM is considered as homogeneous and isotropic. C The influence of the container is ignored because of its small wall thickness and high thermal conductivity.

3.2. Model equations The model of each divided part is regarded as a cylindrical coordinate system (Niu et al., 2015b). Accordingly, various mediums, including air, PCM, insulation, tube and soil, in the vertical direction

8 > > < Advection transfers > > : in unit

9 > > = > > ;

  ¼ m_  Cp  Ta;i1  Ta;i

(4)

where m_ the mass flow rate, Ta;i1 and Ta;i is the air temperature at node i and i-1, respectively. The mean temperature between two adjacent time (e.g., time tDt and t) was introduced as each divided unit temperature (i.e., T ¼ ðT t þ T tDt Þ=2, where T t and T tDt are the temperature of each divided unit at any time t and t-Dt (Bahrar et al., 2018; Stathopoulos et al., 2016)). The finite difference method is used to estimate the temperature derivative terms and the final form of the mathematical equations can be written a matrix formulation for each divided unit. The following section conducts the analysis for different mediums of each part. 3.2.1. Model equations of part I Part I has the same structure with the VEAHE without PCM studied in (Liu et al., 2019d). Thus they have the same mathematical equations, which can refer to (Liu et al., 2019d). 3.2.2. Model equations of part II In Part II model, the PCM model was segmented into (Nþ1) layers. For its (Nþ1)-th layer, a unidirectional heat conduction from it to the N-th layer was assumed to simplify the calculation without considering the heat exchange from another internal layer (Roccamena, 2017). To decrease the influence of this assumption, a fixed radius of r1 (1 mm) was assigned for the (Nþ1)-th layer. The

Z. Liu et al. / Journal of Cleaner Production 237 (2019) 117763

PCM from r1 to outermost (rP ) was segmented into N layers with the identical thickness. The nodal representation in Part II is illustrated in Fig. 4. 1) Air model in Part II

5

PCM, respectively; SP and ht are the heat exchange area and coefficient of between air and PCM, respectively; St and hP are the heat exchange area and coefficient of between air and tube, respectively; and hP are related to ri , rP and vm (Niu et al., 2015a), and vp is the 2 v mean air velocity in Part II, vm ¼ ðrr2i r 2 . Þ i

The heat transfer for the flowing air in Part II includes the energy delivered from the (j-1)-th to j-th layer, and the heat convection of the flowing air with both the tube and PCM 1. For each air unit (e.g., j-th layer) at t-Dt:

ra Ca VP;a 

  Dt 2 TPa;j  T t Pa;j dt

  ¼ Ca m_  TPa;j1  TPa;j     TP;1;j  TPa;j Tt;j  TPa;j þ þ RP;1;j Rt;j

For PCM 1: The heat transfer for PCM 1 in Part II includes the heat convection between PCM 1 and the flowing air, and the heat conduction between PCM 1 and 2. The temperature of PCM 1 for each divided layer (e.g., j-th) at t-Dt is counted as: Dt T t P;1;j ¼ 1 þ

(5) 

The Eq. (5) can be written as:

"

_ Ca mdt dt þ 2  ra Ca VP;a 2  ra Ca VP;a  Rt;j # _ dt Ca mdt þ  TPa;j1  TPa;j  2  ra Ca VP;a  RP;1;1 2  ra Ca VP;a

Dt T t Pa;j





¼ 1þ

dt dt  Tt;j   TP;1;j 2  ra Ca VP;a  Rt;j 2  ra Ca VP;a  RP;1;1 (6)

where Ca , ra , and m_ are the SHC, density and mass flow of the flowing air, respectively; TPa;j and TPa;j1 are the mean air temperDt ature between t-Dt and t; T t Pa;j is the air temperature in Part II at t-

Dt; TP;1;j is the mean PCM 1 temperature between t-Dt and t; VP;a is the divided air volume in Part II; Rt;j and RP;1;j are the thermal resistance between tube wall and air, and between air and PCM 1, respectively: Rt;j ¼

ri þ 12  d 1 1 ln þ ht St 2p  lt  Dz ri

RP;1;j ¼

1 1 rP ln þ hP SP 2p  lpcm  Dz rP  ðrP r1Þ  1 2N

(7)

(8)

where rP and lpcm are the radius and thermal conductivity of the

P

2) PCM model

1

!

RP;1;j

dt 1 dt  þ 2  rP CP;1;j VP;1;j RP;2;j 2  rP CP;1;j VP;1;j

 TP;1;j 

dt 1   2  rP CP;1;j VP;1;j RP;2;j

TP;2;j

dt 1   TPa;j 2  rP CP;1;j VP;1;j RP;1;j

(9)

where TP;2;j is the mean temperature of PCM 2 between t-Dt and t; VP;1;j , CP;1;j and rP is the divided volume, SHC, density of the PCM 1, respectively; and the CP;1;j varies with PCM temperature and can be obtained by DSC testing (Bahrar et al., 2018). For PCM k: The heat transfer for PCM k in Part II includes the heat conduction between PCM k and PCM (k-1), and between PCM k and PCM (kþ1). The temperature of PCM k for each divided layer (e.g., jth) at t-Dt is counted as: Dt T t P;k;j ¼ 1 þ

 

1

!

dt 1 dt  þ 2  rP CP;k;j VP;k;j RP;k;j 2  rP CP;k;j VP;k;j

RP;kþ1;j

 TP;k;j 

dt 1   TP;k1;j 2  rP CP;k;j VP;k;j RP;k;j

dt 1   TP;kþ1;j 2  rP CP;k;j VP;k;j RP;kþ1;j

(10)

where TP;k1;j , TP;k;j and TP;kþ1;j are the mean temperature of PCM (k-1), k, and (kþ1) between t-Dt and t; CP;k;j and VP;k;j is the SHC and divided volume of the PCM k, respectively. For PCM N:

Fig. 4. The nodal representation in Part II.

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Z. Liu et al. / Journal of Cleaner Production 237 (2019) 117763

The heat exchange for PCM N in Part II includes the heat conduction between PCM N and (N-1), and between PCM N and (Nþ1). The temperature of PCM N for each divided layer (e.g., j-th) at t-Dt is counted as:

tDt T s;i;j

dt 1 dt  þ 2  rP CP;N;j VP;N;j RP;N;j 2  rP CP;N;j VP;N;j ! 1 dt 1    TP;N1;j  TP;N;j  RP;Nþ1;j 2  rP CP;N;j VP;N;j RP;N;j

Dt T t P;N;j ¼ 1 þ

2  rP CP;Nþ1;j VP;Nþ1;j

dt 1 dt 1   Ts;i1;j   2  rs Cs Vs;i;j Rs;i;j 2  rs Cs Vs;i;j Rs;iþ1;j (14)

where TP;N1;j , TP;N;j and TP;Nþ1;j are the mean temperature of the PCM (N-1), N and (Nþ1) between t-Dt and t; CP;N;j and VP;N;j are the SHC and divided volume of the PCM N, respectively. For PCM (Nþ1): The heat exchange for PCM (Nþ1) in Part II includes the heat conduction between PCM (Nþ1) and N. The temperature of PCM (Nþ1) for each divided layer (e.g., j-th) at t-Dt is counted as:



!

 Ts;iþ1;j

(11)

dt

dt 1 dt 1 ¼ 1þ  þ  2  rs Cs Vs;i;j Rs;i;j 2  rs Cs Vs;i;j Rs;iþ1;j

 Ts;i;j 

dt 1    TP;Nþ1;j 2  rP CP;N;j VP;N;j RP;Nþ1;j

Dt T t P;Nþ1;j ¼ 1 þ

(iþ1). Thus, the temperature of the soil i for each divided layer (e.g., j-th layer) at t-Dt can be counted as:

1 RP;Nþ1;j

!  TP;Nþ1;j 

where Ts;i;j , Ts;i1;j and Ts;iþ1;j are the mean temperature of soil i, (i1) and (iþ1) between t-Dt and t, respectively; and for i ¼ 1, Ts;i1;j ¼ Tt;j ; and for i ¼ m, Ts;iþ1;j ¼ Tg;j , and Tg;j is the outermost soil temperature.

dt 1   TP;N;j 2  rP CP;Nþ1;j VP;Nþ1;j RP;Nþ1;j

(12)

where CP;Nþ1;j and VP;Nþ1;j are the SHC and divided volume of the PCM (Nþ1), respectively.

3.2.3. Model equations of part III The nodal representation in Part III are illustrated in Fig. 5.

3) Tube wall model

1) Air and PCM model

The heat transfer for the tube wall in Part II consists of the heat convection between the tube wall and flowing air, and the heat conduction between soil 1 and the tube wall. Thus, the temperature of the tube wall for each divided layer (e.g., j-th) at t-Dt is counted as:

The air and PCM model in Part III have almost identical equations comparing with the Part II, except for the initial air and PCM temperatures based on the tube depths.

Dt T t ¼ 1þ t;j



dt 1 dt 1  þ  2  rt Ct Vt;j Rt;j 2  rt Ct Vt;j Rs;1;j

2) Tube wall model

!  Tt;j

dt 1 dt 1   Ta;j    Ts;1;j 2  rt Ct Vt;j Rt;j 2  rt Ct Vt;j Rs;1;j (13)

Dt T t t;j

dt 1 dt 1 ¼ 1þ  þ  2  rt Ct Vt;j Rt;j 2  rt Ct Vt;j RI;j

!  Tt;j 

The heat transfer for the tube wall in Part III consists of the heat convection between the tube wall and air, and the heat conduction between the tube wall and insulation. Hence, the temperature of tube wall for each divided layer (e.g., the j-th) at t-Dt is counted as:

dt 1 dt 1   TPa;j    TI;j 2  rt Ct Vt;j Rt;j 2  rt Ct Vt;j RI;j

(15)

where Ct and rt is the SHC and density of the tube material, respectively;

where TI;j is the mean temperature of the insulation between t-Dt and t.

4) Soil model

3) Insulation model

The heat transfer for the soil i (i  2) in Part II includes the heat conduction between the soil (i-1) and i, and between soil i and

The heat transfer of the insulation in Part III consists of the heat conduction between the insulation and tube wall, and heat conduction between soil 1 and the insulation. Thus, the temperature of the

Z. Liu et al. / Journal of Cleaner Production 237 (2019) 117763

7

(g$ºC). DðTÞ is the corresponding data of the DSC testing curve at tested temperature of T ºC, mW =mg. 4 is the testing rate of heating/ cooling, ºC/s. The PCM's SHC is calculated and illustrated in Fig. 6. In the development of system model, the curve values of the SHC with the change in PCM temperatures were introduced by using an interpolation method based on the comparison of PCM temperature values between consecutive time steps (e.g., at t-Dt and t) (Bahrar et al., 2018; Stathopoulos et al., 2016). 4. Model verification Fig. 5. The nodal representation in Part III.

insulation for each divided layer (e.g., the j-th) at t-Dt is counted as: Dt T t I;j



dt 1 dt 1 ¼ 1þ    2  rI CI VI RPI;j 2  rI CI VI RPs;1;j

!  TI;j

dt 1 dt 1   Tt;j    TPs;1;j 2  rI CI VI RI;j 2  rI CI VI RPs;1;j (16)

where TPs;1;j is the mean temperature of soil 1 between t-Dt and t; VI , CI and rI is the divided volume, SHC and density of the insulation, respectively.

The soil model of Part III has the same heat transfer equations as Part II. 3.3. SHC treatment The SHC of selected PCM was obtained using the method of DSC measurement, with a cooling and heating rate of 1
C per minute (Kong et al., 2013) and Eq. (21) (Kheradmand et al., 2015, 2016).

DðTÞ 4

5. Results and discussion 5.1. Comparison of the system between with and without PCM

4) Soil model

CP ðTÞ ¼

The numerical model was verified against the experimental results. Fig. 7 indicates the variation of the air temperature at the outlet under the simulated and monitored conditions. It can be seen that the verification produced acceptable results. In particular, for the system's air temperature at the outlet, the maximum difference between the monitored and simulated results is 0.28
C, and the corresponding maximum absolute relative error is 1.33%. In addition, the mean outlet air temperature difference between simulated and measured results is less than 0.07
C. The results show that the model is accurate to explore the influences of the tubular PCM component.

(17)

where CP ðTÞ is the PCM's SHC at the tested temperature of T ºC, J/

Based on different mass flow rates, the air temperatures at the outlet of the VEAHE system with and without PCM were compared to analyze the influences of the tubular PCM component. For demonstration purposes, a typical outdoor weather condition of Changsha in summer (i.e., the outdoor temperature ranges from 25.28
C to 40.04
C on August 18th, 2017) was used as the air temperature at the inlet of the developed model, as illustrated in Fig. 8. The influences of the tubular PCM component on the VEAHE system's thermal performance were examined based on different mass flow rates (i.e., 0.024, 0.047, 0.094 and 0.141 m/s). The air temperatures at the outlet of the proposed system and the pure VEAHE system (i.e., without PCM) are shown in Fig. 9. As can be seen, the proposed system has a lower air temperature at the outlet

Fig. 6. The curves of SHC under heating/cooling testing condition.

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Z. Liu et al. / Journal of Cleaner Production 237 (2019) 117763

Fig. 7. The comparison of the simulated and experimental air temperatures at the outlet.

Fig. 8. The variation of outdoor air temperatures in this study.

Fig. 9. The air temperatures at the outlet of the proposed system and pure VEAHE system.

Z. Liu et al. / Journal of Cleaner Production 237 (2019) 117763

than the pure VEAHE system under the different mass flow rates. Specifically, for the proposed system, its peak temperatures are 22.35
C, 23.44
C, 25.13
C and 26.44
C under the mass flow rates of 0.024, 0.047, 0.094 and 0.141 m/s, respectively. Compared to the pure VEAHE system, the corresponding drops in peak temperatures are 0.74
C, 0.96
C, 1.11
C and 1.12
C. Meanwhile, it also can be seen that the proposed system has a smaller temperature fluctuation than the pure VEAHE system. Specifically, as the mass flow rates are 0.024, 0.047, 0.094 and 0.141 m/s, the temperature fluctuations are 1.26
C, 2.13
C, 3.39
C and 4.35
C for the proposed system, and 1.93
C, 2.95
C, 4.30
C and 5.25
C for the pure VEAHE system, respectively. Compared to the influence of the annular PCM component on the VEAHE system in (Liu et al., 2019a), the tubular PCM component has a larger drop in the air temperature fluctuation and peak at the outlet. For example, as the mass flow rate is 0.047 kg/s, the air temperature fluctuation drop at the outlet for the system with the tubular and annular PCM component is 0.82
C and 0.80
C, respectively. And the corresponding outlet air peak temperature drop is 0.96
C and 0.54
C. Note that the outdoor temperature ranges in this study (25.28
C to 40.04
C) is larger than that in (Liu et al., 2019a) (24.32
C to 38.17
C). These results show that the tubular PCM component integrated into the VEAHE system can effectively cut down the air temperature's peak and fluctuation at the outlet by the PCM's energy release and storage. Moreover, the mean cooling capacity of the proposed system during its operation is 208.25 W, 389.11 W, 684.70 W and 814.02 W under the mass flow rates of 0.024, 0.047, 0.094 and 0.141 m/s, respectively. The corresponding cooling capacity for the pure VEAHE system is 201.51 W, 370.62 W, 644.12 W and 764.90 W. This result indicates that the tubular PCM component can increase the corresponding mean cooling capacity of the VEAHE system by 2.89%, 4.53%, 5.67% and 5.58%, respectively. 5.2. The influences of different tube depths Four tube depths (i.e., 12, 16, 20 and 24 m) were considered to investigate its influences on the proposed system's air temperature at the outlet. The air temperatures at the outlet under different tube depths are shown in Fig. 10. As can be seen, the air temperature's peak and fluctuation at the outlet reduce with the increase of the tube depths. Specifically, as the tube depths are 12, 16, 20 and 24 m, the peak temperatures are 25.74
C, 23.20
C, 21.79
C and 21.01
C, respectively. The corresponding air temperature fluctuations at the outlet are 3.59
C, 1.98
C, 1.11
C and 0.62
C. This result can be explained by the fact that a larger tube depth enables more heat

9

exchange between air and deep soil. Therefore, a more stable and lower air temperature at the outlet can be acquired by increasing the tube depths, thereby improving the proposed system's performance. However, a larger tube depth will also result in a higher initial investment. Meanwhile, the difficulty in the system construction will be considerably increased, particularly for drilling the hole and burying the U-tube. From Fig. 10, it also can be seen that the air temperature's peak and fluctuations decrease at the outlet tends to reduce with the increase of tube depths. For example, the air temperature's peak and fluctuation at the outlet decreases by 2.54
C and 1.61
C with the increase of tube depth from 12 to 16 m, respectively. While the corresponding temperature decreases by 0.78
C and 0.49
C with the increase of tube depth from 16 to 20 m, respectively. In this view, there are technical and economic tradeoffs associated with the tube depth in the design stage in practical applications. Additionally, it should be noted that, as the system's air temperatures at the outlet will reduce with the increasing of the tube depth, a lower/higher phase change temperature of the PCM will be needed when a larger/smaller tube depth is adopted. For example, when 12 and 24 m are selected, the outlet air temperatures are 22.15e25.74
C and 20.38e21.00
C respectively, based on the model prediction. Thus, the corresponding phase change temperature of the PCM could be selected as 22.10e25.80
C and 20.30e21.00
C. 5.3. The influences of PCM thermal conductivity Different values of PCM thermal conductivity (i.e., 0.5, 1, 2, 4 and 8 W/(m K)) were utilized to analyze their influences on the system's air temperature at the outlet, based on the container diameters of 50 and 150 mm. The air temperatures at the outlet under different PCM thermal conductivity are shown in Fig. 11. As shown in Fig. 11(a), when the container diameter is 50 mm, PCM thermal conductivity has almost the same influences on the system's air temperature at the outlet. This indicates that its increasing is not an effective means for improving the system's performance as the container diameter is relatively small. As shown in Fig. 11(b), as the container diameter increases to 150 mm, this influence become apparent and requires to be considered. The main reason is that the PCM thermal resistances are related to PCM conductivity, lengths and diameters. For a small container diameter, the PCM thermal resistance is kept at a low level, and thus its increase has a small influence on the system's air temperature at the outlet. When the container diameter increases to 150 mm, its thermal resistance increases thereby enlarging the influences of PCM thermal

Fig. 10. The influences of the tube depths on air temperature at the outlet.

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Z. Liu et al. / Journal of Cleaner Production 237 (2019) 117763

Fig. 11(a). The influences of PCM thermal conductivity for 50 mm container diameter.

conductivity. However, such influences will be weakened with the increase of the PCM thermal conductivity. Specifically, the air temperature fluctuation at the outlet ranges from 0.75
C to 0.61
C and 0.61
C to 0.56
C when the thermal conductivity increases from 0.5 to 2 and 2e8 W/(m K), respectively. Similar studies are found in a VEAHE system (Liu et al., 2019d) and a VEAHE system integrated with annular PCM components (Liu et al., 2019a). In these two studies, the results also indicate that the thermal conductivity has a negligible effect on the system performance when the tube wall thickness and PCM thickness are relatively small, respectively. Therefore, the simple selection of PCM with high thermal conductivity is not an efficient means of improving the system performance in practical applications. 5.4. The influences of container lengths Six container lengths (i.e., 4, 6, 8, 10, 12 and 14 m) were considered to investigate the influences of container lengths on the system's air temperature at the outlet. The air temperatures at the outlet under different container lengths are shown in Fig. 12. As can be seen, the air temperature's peak and fluctuation at the outlet decrease with the increase of the container lengths. In particular, as the container lengths are 4, 6, 8, 10, 12 and 14 m, the air temperature fluctuations at the outlet are 2.73
C, 2.64
C, 2.54
C, 2.47
C, 2.37
C and 2.28
C, respectively. And the corresponding peak

temperatures are 24.09
C, 23.96
C, 23.81
C, 23.73
C, 23.64
C and 23.62
C. The main reason is that a larger container length can contain more PCM and thus provide more energy to adjust the air temperature variation in the tube, thereby leading to a smaller air temperature fluctuation at the outlet. It also can be seen that the air temperature peak decrease tends to reduce with the rise of the container lengths. In particular, a peak temperature drop of 0.02
C occurs when the container length increases from 12 to 14 m. Meanwhile, from Fig. 12, it can be seen that the average air temperatures at the outlet are 22.48
C, 22.42
C, 22.34
C, 22.31
C, 22.30
C and 22.33
C for the container lengths of 4, 6, 8, 10, 12 and 14 m, respectively. This result shows that the average air temperature at the outlet is the lowest as the container length is 12 m. Based on above analysis, 12 m can be considered as an appropriate container length for the proposed system. Similar results can be found in (Liu et al., 2019a, 2019d). Thus, obtaining a more stable air temperature at the outlet by simply increasing the PCM length may not be an effective method in practical applications, especially when the system's capital costs are considered. 5.5. Economic comparison between tubular and annular components To evaluate the proposed system's economic feasibility, the initial investment of the tubular component and the system's static

Fig. 11(b). The influences of PCM thermal conductivity for 150 mm container diameter.

Z. Liu et al. / Journal of Cleaner Production 237 (2019) 117763

11

Fig. 12. The influences of the container lengths.

payback period (SPP) were calculated and compared with those of the system integrated with annular components in (Liu et al., 2019a). As an important economic analysis method for evaluating a new system, SPP can be calculated as a ratio of the total initial investment of the proposed system to its yearly cost-saving from the energy savings by using the following equation (Mi et al., 2016):

SPP ¼

Ct  Ca Sy

(18)

where Ct is the total cost of the VEAHE system (i.e., $1313.9 (Liu et al., 2019b)) and the tubular PCM component (including both the container and PCM, with a total of $99.3, which is much lower than the cost of the annular PCM component with the same amount of PCM (i.e., $160.0) (Liu et al., 2019a)); Ca is the cost of a conventional air-conditioner, which can be assumed as $300 (Liu et al., 2019b); Sy is the annual income produced from the energy-saving comparing with a traditional air conditioning with a COP of 2.7 (Huang and Mauerhofer, 2016). According to the calculation method in (Liu et al., 2019b), the system's annual energy conservation for cooling can be calculated as 514.66 kWh as the air velocity was set at 2 m/s. Currently the electric rate is 0.12$/kWh in Changsha. Thus, the Sy of the proposed system was $61.76. Based on above analysis, the system's SPP can be calculated as 18.03 years, which is lower than the VEAHE system coupled with annular PCM components (i.e., 20.8 years (Liu et al., 2019a)). 6. Conclusions and future work This study proposes a new VEAHE system coupled with the tubular PCM component. Comparing with the traditional EAHE system, its main advantage includes smaller land occupation during construction, deeper buried tube depth for more efficient utilization of geothermal energy, more stable air temperatures at the outlet for improving the indoor thermal comfort and higher cooling capacity for reducing energy consumption. To evaluate the system's thermal feasibility, different experiments were conducted and a numerical model was developed. Then the model was verified through a comparison between the system's simulated and monitored air temperatures at the outlet. The verification produced acceptable results with the maximum absolute relative error of 1.33%. The verified model was used to study the influences of the tubular PCM component based on different air velocities. Also, the influences of tube depths, PCM conductivity and container lengths were analyzed. In addition, the

system's static payback period was also conducted and compared with the system coupled with annular PCM components. The tubular PCM component integrated into the VEAHE system can decrease its outlet air temperature's peak of 0.74
C, 0.96
C, 1.11
C and 1.12
C, and the corresponding temperature fluctuation of 0.67
C, 0.82
C, 0.91
C and 0.90
C as the mass flow rates are 0.024, 0.047, 0.094 and 0.141 m/s, respectively. Meanwhile, the tubular PCM component can increase the corresponding mean cooling capacity of the VEAHE system by 2.89%, 4.53%, 5.67% and 5.58%, respectively. The air temperature's peak and fluctuation at the outlet reduce with the increasing of tube depths. In view of the fact that a larger tube depth will result in a higher initial investment and construction difficulty, there are technical and economic trade-offs associated with the tube depth in practical applications. This study also revealed that different PCM thermal conductivity has almost the same influences on the system's air temperature at the outlet as the container diameter is 50 mm, thus the simple selection of PCM with high thermal conductivity is not an efficient means when the container diameter is relatively small. However, when the container diameter increases to 150 mm, such influences become apparent and require to be considered. The air temperature peak and fluctuation at the outlet reduce with the increase of container lengths, however, the decrease in air temperature peaks tends to reduce with the increasing of container lengths. In this study, 12 m can be considered as an appropriate container length for the proposed system. The proposed system's static payback period could be calculated as 18.03 years, which is shorter than the VEAHE system with annular PCM components. These results demonstrate the proposed system's feasibility and effectiveness. In our future work, the developed model will be coupled with a building model to explore the influences of the proposed system on building energy consumption in different areas. In addition, the combination between the proposed system and other energy-saving technologies/systems (e.g., night ventilation and PCM walls) will be explored to achieve the system's intermittent operation as well as better thermal performance.

Acknowledgements The authors gratefully acknowledge the support from the China Construction Fifth Engineering Division Corp., Ltd. (Project No. 201991370055).

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