thermal heat pump system

Applied Energy 190 (2017) 960–980

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Performance study of heat-pipe solar photovoltaic/thermal heat pump system Hongbing Chen a, Lei Zhang a, Pengfei Jie b,⇑, Yaxuan Xiong a, Peng Xu a, Huixing Zhai a a b

Beijing University of Civil Engineering and Architecture, Beijing 100044, PR China School of Mechanical Engineering, Beijing Institute of Petrochemical Technology, Beijing 102617, PR China

h i g h l i g h t s
The testing device of HPS PV/T heat pump system was established by a finished product of PV panel.
A detailed mathematical model of heat pump was established to investigate the performance of each component.
The dynamic and static method was combined to solve the mathematical model of HPS PV/T heat pump system.
The HPS PV/T heat pump system was optimized by the mathematical model.
The influence of six factors on the performance of HPS PV/T heat pump system was analyzed.

a r t i c l e

i n f o

Article history: Received 8 October 2016 Received in revised form 12 December 2016 Accepted 27 December 2016

Keywords: PV/T Heat pump Heat pipe COP

a b s t r a c t A heat-pipe solar (HPS) photovoltaic/thermal (PV/T) heat pump system, combining HPS PV/T collector with heat pump, is proposed in this paper. The HPS PV/T collector integrates heat pipes with PV panel, which can simultaneously generate electricity and thermal energy. The extracted heat from HPS PV/T collector can be used by heat pump, and then the photoelectric conversion efficiency is substantially improved because of the low temperature of PV cells. A mathematical model of the system is established in this paper. The model consists of a dynamic distributed parameter model of the HPS PV/T collection system and a quasi-steady state distributed parameter model of the heat pump. The mathematical model is validated by testing data, and the dynamic performance of the HPS PV/T heat pump system is discussed based on the validated model. Using the mathematical model, a reasonable accuracy in predicting the system’s dynamic performance with a relative error within ±15.0% can be obtained. The capacity of heat pump and the number of HPS collectors are optimized to improve the system performance based on the mathematical model. Six working modes are proposed and discussed to investigate the effect of solar radiation, ambient temperature, supply water temperature in condenser, PV packing factor, heat pipe pitch and PV backboard absorptivity on system performance by the validated model. It is found that the increase of solar radiation, ambient temperature and PV backboard absorptivity leads to the increase of the coefficient of performance based on thermal (COPth) of HPS PV/T heat pump system, while the increase of supply water temperature in condenser, PV packing factor and heat pipe pitch leads to the decrease of COPth. Furthermore, the increase of solar radiation and packing factor leads to the increase of the advanced coefficient of performance based on both thermal and electrical performances (COPPV/T), while the COPPV/T decreases as the ambient temperature, supply water temperature in condenser and heat pipe pitch increase. The PV backboard absorptivity has little influence on the COPPV/T of HPS PV/T heat pump system. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Shortwave radiation can be converted to electricity using photovoltaic (PV) technology. However, the photoelectric conversion ⇑ Corresponding author. E-mail address: [email protected] (P. Jie). http://dx.doi.org/10.1016/j.apenergy.2016.12.145 0306-2619/Ó 2017 Elsevier Ltd. All rights reserved.

efficiency is only 5–20% [1]. It is found that the photoelectric conversion efficiency is dependant on the temperature of PV cells [2–4]. When the PV cells’ temperature is higher than 25 °C, the temperature increase of every 1 °C results in the reduction of power generation efficiency by 0.5% [5,6]. It is also observed that the extracted heat from PV panel could be employed for use by photovoltaic/thermal (PV/T) technology [7]. Moreover, the

H. Chen et al. / Applied Energy 190 (2017) 960–980

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Nomenclature Parameters A area, m2 Bo boiling coefficient c specific heat capacity, J/(kgK) D diameter, m De equivalent diameter, m h enthalpy, J/kg H height, m G solar radiation intensity, W/m2 k thermal conductivity, W/m2 L length, m m mass flow, kg/s M mass, kg N power, W Nu Nusselt number P pressure, Pa Pr Prandtl number Q heat exchange, W q heat flow, W/m2 r latent heat of vaporization, kJ/kg R thermal resistance, (m2K)/W re reflectivity Re Reynolds number T temperature, °C t time, s u flow velocity, m/s v mass flow per unit area, kg/(m2s)

Greek letters a absorptivity; heat transfer coefficient, W/(m2K) c PV packing factor d thickness, m e emissivity g efficiency h installation angle l coefficient of kinetic viscosity, Ns/m2 n porosity of the wick q density, kg/m3 r Stefan-Boltzman constant, W/(m2K4) t transmissivity v dryness

photoelectric conversion efficiency could be improved due to the reduction of PV cells temperature. But it’s difficult to make full use of the extracted heat because of the intermittency of solar energy and low collector efficiency of PV panel. Therefore, various PV/T panels have been put forward in previous studies, including air-cooled PV/T panel [8–16], water-cooled PV/T panel [17–26], direct-expansion PV/T panel [27–32], heat-pipe solar (HPS) PV/T panel [33–38] and HPS PV/T heat pump system [39–43]. The simplest method to cool down PV cells is air-cooled PV/T panel by natural or mechanical ventilation [8–16]. However, the natural ventilation method is restricted by weather conditions, and the mechanical ventilation method has a high cost. In addition, the increase of photoelectric conversion efficiency for this structure is poor due to the limited cooling effect. Alternatively, a circulating water channel could also be used to extract heat from PV panel [17]. The cooling effect of this method is better than that of air-cooled panel, but the inner structure of PV cells could be destroyed in cold weather conditions due to the freeze of water

Subscripts a air Al aluminum sheet b backboard; boil c condenser, condensation co collector cr refrigerant in condenser cri critical cw water in condenser cap capillary com compressor e evaporator, evaporation ex exergy efficiency exp experimental value ele electrical eq equivalent ei heat conduction silica gel ew water in evaporator hpeva evaporation section of heat pipe hpcon condensation section of heat pipe in thermal insulation material i in; inlet g glass cover l liquid o out; outlet ov overall efficiency pv PV panel pv/t photovoltaic/thermal r refrigerant R reference sat saturation sh superheated sim simulation value sp sing phase th thermal tp two phase; traditional thermal power generation tw tube wall v vapor w water wm water in manifold wt water in storage tank wick liquid wick of heat pipe

pipe on the backboard of PV panel. A more advanced PV/T structure is direct-expansion PV/T panel. Evaporation coils are placed beneath PV panel so that the refrigerant can pass through it [27]. The PV cells in this structure can be cooled down to a very low temperature, leading to higher photoelectric conversion efficiency and better utilization of the extracted heat. But this structure has some inherent problems, such as a mass use of copper coils and gas tightness. As for the heat-pipe solar (HPS) PV/T structure, heat pipes are integrated with PV panel so that PV cells can be cooled down to a relatively low temperature. In addition, the freeze of water pipes can be avoided by using heat pipes. Pei et al. [34] designed a novel HPS PV/T system and developed a dynamic model to predict the performance of this system. The results indicated that the thermal efficiency was 41.9% and the electrical efficiency was 9.4%. Zhang et al. [35] established a simulation model of the HPS PV/T system using TRNSYS. The tank volume of the HPS PV/T system was optimized, the electric power generation was also calculated and the

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tilt angle of the HPS PV/T collector was optimized based on the model. When the HPS PV/T panel is combined with heat pump, the extracted heat can be fully utilized just like direct-expansion PV/T panel. Moreover, the HPS PV/T heat pump system not only has advantages of the above structures, but also avoids disadvantages that the above structures may occur. Zhang et al. [39] studied the dynamic performance of a HPS PV/T heat pump system. They established a mathematic model integrated the transient processes of solar transmission, heat transfer, fluid flow and photovoltaic power generation appropriately. It was concluded that the HPS PV/T heat pump system could harvest significant amount of solar heat and electricity, thus improving the solar thermal and electrical efficiencies. Fu [40] constructed a testing rig of a HPS PV/T heat pump system. Energy and exergy analyses were conducted to investigate the overall system performance and the optimum operation mode. A dynamic model of the HPS PV/T heat pump system was presented. Using this model, the dynamic parameters were predicted and analyzed under different intensities of solar irradiation, and the instantaneous system performance was also simulated and studied. Previous researches on HPS PV/T heat pump system have achieved prominent results. Many mathematical models and/or testing rigs were established to predict and investigate the system performance. Some performance evaluation methods were also presented in the previous researches. However, for those studies, the dynamic mathematical models of heat pump are quite simple and difficult to provide more accurate prediction of system performance, and the stability is poor as well. Meanwhile, they provide little investigation and discussion on the optimization of the HPS PV/T heat pump system and the influence of affecting factors such as solar radiation, ambient temperature, supply water temperature in condenser, PV packing factor, PV backboard absorptivity and

heat pipe pitch etc on system performance. In this paper, a relatively more detailed mathematical model of the HPS PV/T heat pump is established, which makes it possible to provide a more accurate prediction of the state parameters of refrigerant and water at the inlet and outlet of each component of heat pump, compressor power and system performance as well. The optimization of HPS PV/T heat pump system and the discussion on the influence of affecting factors on system performance are also presented in this paper. In addition, an advanced method that combines the quasi-steady state method and the dynamic method is used to solve the mathematical model of HPS PV/T heat pump system in this paper. 2. System descriptions The HPS PV/T heat pump system consists of a HPS PV/T collection system and a heat pump system. The HPS PV/T collection system includes water-storage tank, circulating pump and HPS PV/T collector. The experimental set-up of HPS PV/T collector and heat pump is shown in Fig. 1. The HPS PV/T collector is mainly made up of PV panel, heat pipes, aluminum sheet and manifold. Fig. 2 shows the cross-section view of HPS PV/T collector. A piece of YL200P-23b PV panel (including PV cells and backboard) with an area of 1310 mm  990 mm is chosen as the base panel, which has a nominal power of 195.0 W. The PV backboard is made of white Tedlar-Polyester-Tedlar (TPT), and the PV packing factor is 0.9. Table 1 shows the parameters of heat pipes. The evaporation section of heat pipes are adhered onto the back surface of PV panel by heat conduction silica gel for good thermal conductance. In order to enhance heat transfer effect, the evaporation sections are tightly partial-wrapped by aluminum sheet under precise pressure control to provide a good contact between aluminum sheet

(a) HPS PV/T collector

(b) Heat pump

Fig. 1. Pictures of testing rig.

Fig. 2. Cross-section view of the HPS PV/T collector.

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H. Chen et al. / Applied Energy 190 (2017) 960–980 Table 1 Parameters of heat pipes.

Table 2 List of testing instruments.

Item

Parameter

Shell material Liquid working medium Filling depth of working medium Length of condensation section Length of evaporation section External diameter of condensation section External diameter of evaporation section

Copper Water 25 mm 60 mm 1000 mm 14 mm 8 mm

and heat pipes, and the aluminum sheet is adhered onto the back surface of PV panel by heat conduction silica gel as well. The condensation sections are inserted into the manifold and the distance between every two adjacent heat pipes is 75 mm. A low-iron tempered glass plate is provided as the front glazing for collector, which permits sunlight penetration but prevents heat loss as well as the entry of dust particles and rain. Finally, a sponge rubber thermal insulation board is pasted onto the back surface of aluminum sheet. When solar radiation reaches PV panel, most of the radiation is absorbed by PV cells and backboard. Part of the radiation is converted to electricity and the rest is eventually converted to thermal energy. The thermal energy is transferred to the evaporation section of heat pipes through the backboard of PV panel and aluminum sheet. Then the working fluid in heat pipes evaporates and migrates to the condensation section. Finally, the working fluid vapor is condensed and releases heat at the condensation section, and the thermal energy is transferred to circulating water in the manifold. The water pump is installed between water-storage tank and manifold for water circulation. The storage capacity of waterstorage tank is 200L. The HPS PV/T collector is combined with heat pump through evaporator. The diagrammatic sketch of HPS PV/T heat pump system is presented in Fig. 3. A house-hold Danfoss SC10G compressor is used. The evaporator and condenser are plate heat exchangers. The inner diameter of capillary is 1 mm and the length is 1.6 m. R134a is used as the refrigerant. A thermostatic waterbath, where cold

Item

Model

Number

Testing accuracy

Pyranometer Electromagnetic flow meter Platinum resistance temperature sensor Pressure transducer Power meter Data collecting instrument

TBQ-2-B SE115MM WZP-01

1 2 10

±2.0% ±0.5% ±0.5%

KZY-K HP9800 Agilent34972A

4 1 1

±0.5% ±1.0% –

water could be heated and/or hot water could be cooled down as demand, is connected to the condenser. The testing instruments are listed in Table 2. 3. Methodology 3.1. The mathematical model of HPS PV/T collection system The mathematical model of HPS PV/T collection system consists of six main equations: energy balance equation of glass cover, energy balance equation of PV panel, energy balance equation of aluminum sheet, energy balance equation of heat pipes, energy balance equation of manifold, energy balance equation of waterstorage tank. In this study, some assumptions are made as follows: (1) The heat loss of water pipe is neglected. (2) The pressure drop of water circulation is neglected. (3) A mean temperature is assumed across each layer of the HPS PV/T collector. 3.1.1. Energy balance equation of glass cover In Eq. (1), the left side represents internal energy variation of glass cover, while the right side represents convective heat transfer with air, radiation heat transfer with sky, total heat transfer with PV panel and total solar radiation, respectively.

Fig. 3. Diagram of the HPS PV/T heat pump system.

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qg cg dg

@T g ¼ aa ðT a  T g Þ þ asky ðT sky  T g Þ þ ag;pv ðT pv  T g Þ þ Gag @t ð1Þ

The temperature of sky can be expressed as T sky ¼ 0:0552T a1:5 [34]. The heat transfer coefficients can be calculated as follows [42,44]:

aa ¼ 2:8 þ 3ua


ð2Þ 

asky ¼ eg r T 2sky  T 2g ðT sky  T g Þ


ð3Þ



ag;pv ¼ r T 2pv þ T 2g ðT pv þ T g Þ   c 1c NuK a  þ þ 1=epv  cð1=eg  1Þ 1=eb  ð1  cÞð1=eg  1Þ H

where hAl;a is the heat transfer coefficient between aluminum sheet and ambient air, with aAl;a ¼ ain þ kin =din ; j can be expressed as j ¼ Apv ;Al =AAl . 3.1.4. Energy balance equation of heat pipes (1) Energy balance equation of the evaporation section of heat pipes In Eq. (11), the left side represents internal energy variation of evaporation section, while the right side represents heat transfer with condensation section, heat conduction with PV panel and heat conduction with aluminum sheet, respectively.

Mhpev a cp

@T hpev a ðT hpcon  T hpev a Þ Ahpev a;pv þ ðT pv  T hpev a Þ ¼ @t Rei Rhpev a;hpcon þ ðT Al  T hpev a Þ

ð4Þ where packing factor can be expressed as c ¼ Apv =Aco . Nusselt number Nu can be calculated by Eq. (5) [44]:

 Nu ¼ 1 þ 1:1446 1 

1708 Gr  Pr  cos h

þ ð5Þ

where ‘‘+” indicates that only positive value is used. If the value is negative, use zero. 3.1.2. Energy balance equation of PV panel In Eq. (6), the left side represents variation of internal energy of PV panel, while the right side represents solar radiation absorbed by PV panel, total heat transfer with glass cover, heat conduction with evaporation section of heat pipes and heat conduction with aluminum sheet, respectively.

@T pv 1 ¼ Gðsg aÞpv þ ag;pv ðT g  T pv Þ þ k ðT hpev a  T pv Þ Rei @t 1 þ ð1  kÞ ðT pv  T Al Þ  Epv ð6Þ Rei

qpv cpv dpv

where Rei is the thermal resistance of heat conduction silica gel; Epv is the power output power per unit area; k can be expressed as k ¼ Ahpev a;pv =Aco . Rei can be obtained by Eq. (7):

Rei ¼ dei =kei

ð7Þ

ð8Þ

where gR is the reference efficiency of PV panel at reference operating temperature, T n = 25 °C; bpv is the temperature coefficient; ðsg aÞpv is the effective absorptivity. ðsg aÞpv can be expressed as Eq. (9) [45]:

ðsg aÞpv ¼ sg apv =ð1  ð1  apv Þreg Þ

ð9Þ

3.1.3. Energy balance equation of aluminum sheet In Eq. (10), the left side represents variation of internal energy of aluminum sheet, while the right side represents heat conduction with PV panel, total heat transfer with ambient environment through insulation layer and heat conduction with evaporation section of heat pipe, respectively.

qAl cAl dAl

@T Al 1 1 ¼ j ðT pv  T Al Þ þ aAl;a ðT a  T Al Þ þ ð1  jÞ Rei Rei @t  ðT hpev a  T Al Þ

ð10Þ

ð11Þ

(2) Energy balance equation of heat pipe condensation section In Eq. (12), the left side represents internal energy variation of condensation section, while the right side represents heat transfer with evaporation section and convective heat transfer with water in manifold, respectively.

Mhpcon cp

@T hpcon ¼ ðT hpev a  T hpcon Þ=Rhpev a;hpcon @t þ Awm;hpcon awm;hpcon ðT wm  T hpcon Þ

ð12Þ

where Rhpev a;hpcon is the thermal resistance between evaporation section and condensation section of heat pipes. It can be expressed as follows [34]:

Rhpev a;hpcon ¼ Rhpev a;wick þ Rhpev a þ Rhpcon Rhpev a;wick ¼ Rhpev a ¼ Rhpcon ¼

lnðDo;wick =Di;wick Þ 2pLhpev a kwick 2

pDhpev a;i Lhpev a ahpev a;i 1

pDhpcon;i Lhpcon ahpcon;i

ð13Þ ð14Þ

ð15Þ

ð16Þ

K wick is the thermal conductivity of liquid wick. It can be expressed as follows:

Epv can be expressed by Eq. (8):

Epv ¼ Gðsg aÞpv cgR ½1  bpv ðT pv  T n Þ

ðAAl  AAl;pv Þ Rei

kwick ¼

kl ½ðkl þ ktw Þ  ð1  nwick Þðkl  ktw Þ ðkl þ ktw Þ þ ð1  nwick Þðkl  ktw Þ

ð17Þ

The heat transfer coefficients, ahpev a;i and ahpcon;i , can be calculated as follows [44]:

ahpev a;i ¼ kl =dwick " # 3 g sin h  ql ðql  qv Þkl r ll DT d Lhpcon

ahpcon;i ¼ 1:13

ð18Þ ð19Þ

where DT d is the temperature difference between tube wall and liquid. The heat convection coefficient between water and condensation section of heat pipes can be expressed as Eq. (20) [44]:

aw;hpcon ¼

kw CRen Prm ðPr1 =Prs Þ1=4 Dhpcon;o

ð20Þ

where Pr 1 and Pr s are the Prandtl number calculated by tube wall temperature and liquid, respectively. When Pr 6 10, m = 0.37. When Pr > 10, m = 0.36. The value of C and n can be seen as Table 3.

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H. Chen et al. / Applied Energy 190 (2017) 960–980 Table 3 The value of C and n. Re

C

n

1  40 40  1  103 1  103  2  105 2  105  1  106

0.75 0.51 0.26 0.076

0.4 0.5 0.6 0.7

3.1.5. Energy balance equation of manifold In Eq. (21), the left side represents internal energy variation of water and energy difference between inlet and outlet water, while the right side represents heat transfer with ambient environment and convective heat transfer with condensation section of heat pipes respectively.

@T wm M wm cw þ mw cw ðT wm;o  T wm;i Þ @t ¼ ðT a  T wm Þ=Ra;wb þ Awm;hpcon hwm;hpcon ðT hpcon  T wm Þ

ð21Þ

3.1.6. Energy balance equation of water-storage tank In Eq. (22), the left side represents internal energy variation of water in the tank, while the right side represents heat transfer with ambient environment, energy difference between inlet and outlet water of tank and energy difference between inlet and outlet water of evaporator, respectively.

M wt cw

@T wt ¼ ðT a  T wt Þ=Ra;wt þ mw cw ðT wt;o  T wt;i Þ @t  mw cw ðT ew;i  T ew:o Þ

ð22Þ

3.1.7. Discretization of energy balance equations The mathematical model of HPS PV/T collection system consists of Eqs. (1), (6), and (10)–(22). These equations can be discretized using Newton’s backward interpolation formula. For glass cover,

qg cg dg

T gkþ1

 Dt

T kg

kþ1 . T hpcon  T khpcon
kþ1 Rhpev a;hpcon ¼ T hpev a  T kþ1 hpcon Dt
 kþ1 þ Awm;hpcon hwm;hpcon T kþ1 wm  T hpcon

Mhpcon cp



 kþ1  T kþ1  T kþ1 þ asky T sky ¼ aa T kþ1 a g g
 kþ1 þ Gkþ1 ag þ ag;pv T kþ1 pv  T g

For manifold,


 T kþ1  T kwm kþ1 þ mw cw T wm;o Mwm cw wm  T kþ1 wm;i Dt
.
 kþ1  T kþ1 Ra;wm þ Awm;hpcon awm;hpcon T kþ1 ¼ T kþ1 a wm hpcon  T wm For water-storage tank,

Mwt cw

ð23Þ

ð29Þ

3.2. The mathematical model of heat pump A quasi-steady state mathematical model of heat pump is established. Physical properties parameters of R134a are calculated. The compressor model is established by graphic method based on the compressor specifications provided by manufacture. The capillary model is established by the mass equation of refrigerant flow rate. A distributed parameter mathematical model of evaporator and condenser are established as well. 3.2.1. Calculation of physical properties parameters of R134a Vapor pressure and saturation temperature can be calculated as follows [46]:

  2200:9809 Psat ¼ exp 21:51297  246:61 þ T sat

ð30Þ

 T sat ¼

 2200:9809  246:61 ln Psat  21:51297

ð31Þ

hl ¼ 200; 000 þ 1335:29T l þ 1:7065T 2l þ 7:6741  103 T l

ð32Þ

Saturated vapor enthalpy can be calculated by Eq. (33) [46]:

hsat ¼ 398; 503 þ 606:163T sat  1:05644T 2sat  1:82426  102 T 3sat ð33Þ Superheated vapor enthalpy can be calculated as follows [46]:

DT sh ¼ T sh  T sat ð24Þ

ð34Þ


hsh ¼ ðhsat  149048Þ 1 þ 3:48186  103 DT sh þ 1:6886  106 DT 2sh þ 9:2642  106 DT sh T sat  7:698  108 DT 2sh T sat  þ 1:7070  107 DT sh T 2sat  1:2130  109 DT 2sh T 2sat þ 149048

ð25Þ

For heat pipes, k
. T kþ1 hpev a  T hpev a kþ1 M hpev a cp  T kþ1 ¼ T hpcon Rhpev a;hpcon hpev a Dt
A hpev a;pv kþ1 þ T pkþ1 v  T hpev a Rei
 ðA  A Al Al;pv Þ kþ1 kþ1 þ T Al  T hpev a Rei

k
.
 T kþ1 kþ1 kþ1 wt  T wt ¼ T akþ1  T wt Ra;wt þ mw cw T kþ1 wt;o  T wt;i D
t 

kþ1  T kþ1  mw cw T ew;i ew;o

For aluminum sheet,


 T kþ1  T kAl 1
kþ1 qAl cAl dAl Al T  T kþ1 ¼j þ aAl;a T akþ1  T kþ1 Al Al Rei pv Dt  1
kþ1 kþ1 T hpev a  T Al þ ð1  jÞ Rei

ð28Þ

Liquid enthalpy can be calculated by Eq. (32) [46]:

For PV panel,


 T kþ1  T kpv qpv cpv dpv pv  T kþ1 ¼ Gkþ1 ðsg aÞpv þ ag;pv T kþ1 g pv Dt  1
kþ1 T hpev a  T pkþ1 þ ð1  kÞ þk v Rei  1
kþ1  Epkþ1 T  T kþ1  v pv Rei Al

ð27Þ

ð35Þ Liquid density can be calculated as follows [47]:

TR ¼

T l þ 273:15 T cri þ 273:15


ql ¼ qc þ 4:37673  12:06501T R þ 15:45013T 2R  7:4495T 3R  ðql;b  qc Þ ð26Þ

ð36Þ  ð37Þ

Saturated vapor density can be calculated by Eq. (38) [46]:

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qv ¼

1

 2669 exp 12:45 þ 273:15þT sat  1:013 þ 0:00167T 2sat  9:25  106  3:21  107 T 3sat

Q r ¼ aDLDT m

Liquid kinetic viscosity can be calculated by Eq. (39) [46]:


¼ exp 0:295701  0:0012885=

ð38Þ

ð44Þ

Saturated vapor kinetic viscosity can be calculated by Eq. (40) [46]:

where e is the coefficient of heat leakage, e = 0.9 [48]; DT m is the logarithmic mean temperature difference; a is the heat transfer coefficient between refrigerant side and water side; ar and aw are the convective heat transfer coefficients at refrigerant side and water side, respectively. DT m can be calculated by Eq. (45):

lv ¼ 0:32671 þ 0:003457T  1:1836  105 T 2 þ 1:3599  108 T 3

DT m ¼

ll

T l þ 2:7941  106 T l  2:9630  109 T 2l



ð39Þ

ð40Þ

ðT r;i  T w;o Þ  ðT r;o  T w;i Þ ln½ðT r;i  T w;o Þ=ðT r;o  T w;i Þ

ð45Þ

h can be calculated by Eq. (46) 3.2.2. Energy balance equation of condenser For this quasi-steady state distributed parameter mathematical model, the condenser is divided into three phase regions, including superheated region, two-phase region and supercooled region, as shown in Fig. 4. The heat transfer coefficients are calculated in different regions. In this study, some assumptions are made as follows: (1) (2) (3) (4) (5)

The flow in plate exchanger is unidimensional. The pressure drop is neglected. The phase change is uniform. Thermal resistance of plate is neglected in the condenser. The values of flow velocity and heat transfer coefficient are constant in the same phase region. (6) The phase change from liquid to vapor of refrigerant in the two-phase region is gradual and approximately linear, so the average degree of dryness is set to be 0.5 when calculating the physical properties parameters in the two-phase region [48]. Convection heat transfer equation in the refrigerant side can be expressed as Eq. (41):

Q r ¼ mr ðhr;i  hr;o Þ

ð42Þ

Energy balance equation on both sides of the plate can be expressed by Eq. (43):

Q c ¼ eQ r

1

þ

ar

1



ð46Þ

aw

hr and hw can be calculated according to the convective heat transfer coefficient of single phase fluid and that of two phase fluid. Convective heat transfer coefficient of single phase fluid can be obtained as follows [43]:

asp ¼

ksp  0:023Re0:8 Pr0:3 De

Re ¼ v De=l

ð47Þ ð48Þ

Convective heat transfer coefficient of two phase fluid can be obtained as follows [43]:

atp ¼

ktp 0:33  4:118Re0:4 eq Pr De

Reeq ¼ v eq De=l

ð49Þ ð50Þ

0

v eq

!0:5 1 q l A ¼ v @1  x þ x

qg

ð51Þ

ð41Þ

Convection heat transfer equation of the water side can be expressed as Eq. (42):

Q c ¼ mw;c cw ðT w;o  T w;i Þ



h¼1

ð43Þ

Micro region heat transfer equation can be expressed by Eq. (44):

3.2.3. Heat balance equation of evaporator The mathematical model of evaporator is basically the same as that of condenser. The convective heat transfer coefficient can be calculated by Eq. (52) [49]:

atp ¼ 1:926

ktp 0:33 0:3 0:5 Pr Boeq Re Reeq De

ð52Þ

where ktp is the conductivity of refrigerant in two-phase region; De is the equivalent diameter between adjacent plate in evaporator; Pr and Re are the Prandtl number and Reynolds number of refrigerant

Fig. 4. Schematic diagram of condenser model.

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H. Chen et al. / Applied Energy 190 (2017) 960–980

in evaporator; Reeq and Boeq are the equivalent Reynolds number and equivalent Boiling number. Equivalent Boiling number can be expressed as:

Boeq ¼ q=ðv eq hv Þ

ð53Þ

where q is the average heat flow; hv is the enthalpy of vaporization. 3.2.4. Energy and mass balance equation of compressor The graphical method is adopted to establish the compressor model. The equation of compressor power and refrigerant mass flow are derived according to the performance curve of compressor provided by manufacturer [50]. The equations can be expressed as follows: Equation of compressor power can be expressed by Eq. (54):

N ¼ 0:1163T c T e  32:132T e  29:078T c þ 8245:4

ð54Þ

Equation of refrigerant mass flow can be expressed by Eq. (55):

mr ¼ 0:00009T c T 2e  0:021T 2e  0:0468T c T e þ 11:3975T e þ 5:9758T c  1500:94

ð55Þ

where the temperature range of application for the above equation is 15 °C to 20 °C for evaporation and 25–65 °C for condensation. The error between manufacturer’s value and the value calculated by the derived equation keeps less than ±3%. The results need to be corrected when the equations are used in real situation, as shown below [51]:



mcom

  V the ¼ 1 þ FV  1  mr V act

Ncom ¼

M r  Dhisenact N M  Dhisenthe

ð56Þ

ð57Þ

3.2.5. Mass balance equation of refrigerant at the capillary Capillary is used as the throttling device in the testing rig. Fu’s [40] method is used and modified according to the testing data in this paper. The mathematical model of capillary can be expressed by Eq. (58):

ð58Þ

where DSH is the degree of superheat of refrigerant at evaporator outlet; C 1 –C 5 are constants, with C 1 = 0.936548, C 2 = 2.498028, C 3 = 0.4159, C 4 = 0.84066, C 5 = 0.018751. 3.3. System performance evaluation The main performance evaluation indexes include heat output power, thermal efficiency, electrical output power, electrical efficiency, overall energy efficiency, exergy efficiency, COPth and COP PV=T . The heat output power can be expressed by Eq. (59):

Q th ¼ mw cw ðT w;o  T w;i Þ

R tkþ1 tk gele ¼ R tkþ1 tk

Q ele dt

ð62Þ

Aco cG dt

The overall energy efficiency can be expressed by Eq. (63):

R tkþ1 tk gov ¼ R tkþ1 tk

Q th þ Q ele dt

ð63Þ

Aco G þ Ncom dt

The exergy efficiency is defined as the ratio of PV/T panel converted exergy energy (thermal exergy energy and electrical exergy energy) to total exergy energy (solar radiation exergy energy and compressor electrical exergy energy), as expressed by Eq. (64) [52]:

R tkþ1

gex ¼

Exth þ Exele dt tk R tkþ1 Exsun þ ExN dt tk

R tkþ1

Q th ð1  T sky =T hp;ev a Þ þ Q ele dt t ¼ R ktkþ1 ð1  T a =T sun ÞGAco þ Ncom dt tk

ð64Þ

The coefficient of performance based on thermal can be calculated by Eq. (65):

R tkþ1 t

k COP th ¼ R tkþ1

tk

Q c dt

Ncom dt

ð65Þ

The advanced coefficient of performance based on both thermal and electrical performances can be calculated by Eq. (66):

R tkþ1 COP PV=T ¼

tk

. Q c þ Q ele gtp dt R tkþ1 Ncom dt t

ð66Þ

k

where F V is the volume correction factor, with F V = 0.75; V the and V act are the theoretical and actual suction specific volumes, respectively; Dhisenact and Dhisenmap are the theoretical and actual isentropic enthalpy differences, respectively.

2 3 mr;cap ¼ C 1 DCcap;i LCcap T Cc 4 10C 5 DSH

The electrical efficiency can be expressed by Eq. (62):

ð59Þ

where gtp is the traditional thermal power generation coefficient, and gtp = 0.38[52] 4. Program algorithm The dynamic and quasi-steady state methods are combined to solve the model of HPS PV/T heat pump system. The dynamic method is used to solve the model of HPS PV/T collection system, while the quasi-steady state method is used to solve the model of heat pump system during the time step. When solving the mathematical model of HPS PV/T collection system, Newton’s backward interpolation formula is used to discretize the energy balance equations, then solve the simultaneous equations to obtain the temperature of each component at time t + Dt based on time t. When solving the mathematical model of heat pump system, it is considered that the operation of heat pump system is in quasisteady state within the time step Dt. The parameters of heat pump, including the inlet and outlet state parameters of refrigerant and water, compressor power and refrigerant flow rate, are solved by assuming the initial values of evaporation temperature and compression factor of compressor. The instantaneous boundary conditions, such as solar radiation, ambient temperature and flow rate of circulating water, are directly acquired from the experimental data. Heat loss in pipes during water circulation is neglected. Based on these data, the discrete energy balance equations are solved together. Fig. 5 shows the program flow chart for the HPS PV/T heat pump system. The detailed solving process is shown as follows:

The thermal efficiency can be expressed by Eq. (60):

R tkþ1 tk gth ¼ R tkþ1 tk

Q th dt

GAco dt

ð60Þ

The electrical output power can be expressed by Eq. (61):

Q ele ¼ Epv Aco c

ð61Þ

(1) Input the initial conditions and weather conditions. The initial conditions include temperature of each component, and the weather conditions include solar radiation intensity, ambient temperature, etc. (2) Solve the simultaneously energy balance equations of six components.

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Fig. 5. Program flow chart for the HPS PV/T heat pump system.

(3) Assume the evaporation temperature. According to the performance parameters provided by manufacturers, the maximum value of evaporation temperature is equal to that of the inlet water temperature of evaporator, while the minimum value is 15 °C. (4) Solve the evaporator model and output the outlet parameters of evaporator such as outlet water temperature, outlet refrigerant temperature and enthalpy, evaporation heat exchange (Q e ). (5) Assume the compression factor of compressor. The outlet parameters of refrigerant in evaporator are used as the inlet parameters of compressor. (6) Solve the compressor model and output outlet parameters, refrigerant mass flow and compressor power. (7) The outlet parameters of refrigerant in compressor are used as the inlet parameters of condenser. Solve the condenser model and output the outlet parameters of condenser such as outlet water temperature, outlet refrigerant temperature and enthalpy, condensation heat exchange (Q c ).

(8) Judge if the assumption of compression factor is tenable according to the energy conservation equation (Q c ¼ Q e þ N com ). If the assumption is tenable, then carry out next step, or else go to (8) and re-assume the compression factor. (9) Solve the capillary model and output the refrigerant mass flow in capillary (mr;cap ). (10) If the assumption of evaporation temperature is tenable, then carry out next step, or else go to step (8) and reassume the evaporation temperature. (11) Compute the performance evaluation index. If the program reaches the end, go to step (12), or else go to step (2). (12) Program end. 5. Results and discussion The experiment is carried out in Beijing University of Civil Engineering and Architecture, a university in the north of China (116.3°E, 39.9°N). The solar collector is installed to be south-

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facing with a tilt angle of 30°. The experiment commences at 8:30 a.m. and concludes at 16:30 p.m. (August 12, 2015) with the data collection interval of 10 min. The mean solar radiation intensity and ambient temperature are 656 W/m2 and 37 °C, respectively. The initial ambient temperature is 30.5 °C. The initial water temperature in the tank is 24.8 °C. During the experiment, the water flow rates in evaporator and condenser are both set to be 6 L/min. The inlet water temperature in condenser is 40 °C. Fig. 6 shows the solar radiation and ambient temperature during the experiment. Six working modes are proposed and discussed to investigate the effect of solar radiation, ambient temperature, supply water temperature in condenser, packing factor, heat pipe pitch and PV backboard absorptivity on system performance.

Fig. 7 shows the variation of heat output power and thermal efficiency. It is found that the heat output power increases with the increasing solar radiation before 12:30 p.m. and it reaches the maximum value (380.6 W) at about 12:30 p.m. Then the heat output power decreases with the decreasing solar radiation in the afternoon. The average heat output power is 291.4 W during the testing. The thermal efficiency is also influenced by solar radiation. It increases in the early morning and remains nearly unchanged in the noon. Finally it increases significantly after 14:30 p.m. The thermal efficiency, with an average of 35.4%, varies between 17.0% and 61.3%. The reason for the significant increase of thermal efficiency can be explained as follows. The solar radiation decreases rapidly in the afternoon, but the ambient temperature is high at about 38 °C (shown in Fig. 6), so the temperature of PV panel remains about 40 °C (shown in Fig. 8) because of less heat loss from PV panel. Meanwhile, since the heat output obtained from PV panel cannot meet the demand of heat pump, it starts to absorb the heat, which is originally stored in water, for heat supply to heat pump. So the water temperature in water-storage tank decreases gradually (shown in Fig. 8). Since both water temperature and PV panel temperature decrease and the temperature difference fluctuates slightly, the heat obtained from PV panel reduces slightly. The sharp decrease of solar radiation and the slight decrease of heat obtain from PV panel lead to the sharp increase of thermal efficiency in the later afternoon. The relative

5.1. Model validation The time step is set as 10 min. The relative error (RE) is used to identify the discrepancy between simulation results and testing data, as shown in Eq. (67):

X exp  X sim  100% X exp

ð67Þ

where X sim and X exp are the values of simulation results and testing data, respectively.

G

Ta

900

42

Solar radiation/(W/m2)

800

40

700 600

38

500

36

400 300

34

200

32

100 0 08:30

09:30

10:30

11:30

12:30

13:30

14:30

15:30

Time Fig. 6. Solar radiation and ambient temperature.

Fig. 7. Variation of heat output power and thermal efficiency.

30 16:30

Ambient temperature/( )

RE ¼

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Fig. 8. Variation of PV panel temperature and water temperature in the tank.

Fig. 9. Variation of electrical output power and efficiency.

errors of thermal power, thermal efficiency, water temperature in the tank and temperature of PV panel are 10.4% to 6.9%, 9.0– 2.9%, 5.5% to 0% and 8.8% to 7.7%, respectively. The simulation results are in good accordance with the experimental values. Fig. 9 presents the variation of electrical output power and efficiency during the testing. The electrical output power gradually increases before 9:00 a.m. Then it fluctuates slightly until 15:30 p.m. Finally, it decreases significantly. The electrical output power, with an average of 88.5 W, varies between 57.8 W and 99.2 W. The electrical efficiency decreases in the morning and increases in the afternoon, with a minimum value of 8.8% at 12:30 p.m. The trend of PV panel temperature is opposite to that of electrical efficiency, the reason can be explained as that the PV panel temperature and the internal resistance of PV cells increase with the increasing solar radiation, as a result, the photoelectric conversion efficiency decreases. In addition, the reason for little fluctuation of electrical output power between 9:30 a.m. and 15:30 p.m. is that the solar radiation increases in the morning and decreases in the afternoon while the electrical efficiency has an opposite trend to solar radiation, decreasing in the morning and increasing in the afternoon. Therefore, the electrical output power, which is equal to the product of solar radiation, electrical efficiency and PV cells area, shows little fluctuation during the period of time. The relative errors of electrical output power and electrical efficiency are 8.0% to 11.45% and 14.9% to 15%, respectively. The simulation results are in good accordance with the experimental values. The heat pump performance, such as condensation capacity, compressor power, thermal and advanced coefficient of perfor-

mance (COPth and COPPV/T), is presented in Fig. 10. It is obvious that condensation capacity, compressor power, COPth and COPPV/T all decrease slightly. The average condensation capacity and compressor power are 1152.9 W and 416.7 W, respectively. The average COPth and COPPV/T are 2.77 and 3.23, respectively. Since the heat gain from PV panel cannot meet the demand of heat pump, it starts to absorb the heat from water, which is originally stored in circulating water. Consequently, it leads to the decrease of evaporation temperature. As a result, the compressor power decreases according to Eqs. (54) and (55). The reason for the decrease of COPth and COPPV/T is that the decrease of condensation capacity in percentage is more than that of compressor power. The relative errors of condensation capacity, compressor power, COPth and COPPV/T are 7.8% to 3.8%, 12.3% to 5.9%, 1.6–8.6%, 1.2% to 7.3%, respectively. The simulation results are in good accordance with the experimental values. It can be observed from Fig. 10 that the COPth and COPPV/T are lower than the expected values, and the reason is that the color of backboard is white leading to lower absorptivity compared with dark color backboard. The coefficient of performance can be improved by using a dark color backboard with high absorptivity and decreasing the packing factor at the same time. 5.2. Influence of different factors on system performance As is shown in the above analysis, the COP ranged from 2.68 to 2.91, which is at a relatively low level. The heat pump system is optimized by increasing the number of solar collector to three and replacing the heat pump with a larger capacity one correspon-

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Fig. 10. Variation of condensation capacity, compressor power and coefficient of performance.

dently. Three collectors are connected in series. A larger capacity compressor Panasonic 6RS114EAA41 is used. The equations of compressor power and refrigerant mass flow are also derived according to the performance curve of the compressor in compressor specifications provided by manufacturer as follows. Equation of compressor power can be expressed by Eq. (68):

N ¼ 0:1637T e T c þ 1:2699T e  0:1274T c þ 35:3

ð68Þ

Equation of refrigerant mass flow can be expressed by Eq. (69):

mr ¼ 0:0023T e T c  5:702T e þ 5:422T c þ 102:9

ð69Þ

Three external factors and three structural factors are involved for the numerical study. The external factors include solar radiation, ambient temperature and supply water temperature in condenser. The structural factors include packing factor, heat pipe pitch and PV backboard absorptivity. The influence of external factors on system performance is studied under condition A, B and C, while the influence of structural factors on system performance is studied under condition D, E and F. The operating parameters of condition A, B and C are listed in Table 4, and those of condition D, E and F are listed in Table 5. The geometrical parameters are as follows: PV panel: Aco = 1.25, c = 0.8, h = 30°, n = 3. Tank: Mwt = 120L, mw = 6 L/min.

Table 4 Operating parameters of condition A, B and C. Condition

Solar radiation (W/m2)

Ambient temperature (°C)

Supply water temperature in condenser (°C)

A

350 500 650 800

35

40

B

650

20, 25, 30, 35

40

C

650

35

35, 40, 45, 55

Evaporator: De = 0.07 m, Le = 0.3 m. Condenser: Dc = 0.07 m, Lc = 0.4 m, mw,c = 6 L/min. Capillary: Lcap = 0.48 m, Dcap,i = 1 mm. 5.2.1. Influence of solar radiation on system performance Figs. 11 and 12 show the influence of solar radiation on thermal and electrical performances, overall energy efficiency and exergy efficiency. The heat output power and electrical output power exhibit a nearly linear increase with the increasing solar radiation, while the thermal efficiency, electrical efficiency, overall energy efficiency and exergy efficiency exhibit a decreasing trend. It can be observed that when the solar radiation increases by 100 W/m2, the heat and electrical output powers increase by 62.9 W and 11.9 W, while the thermal efficiency, electrical efficiency, overall energy efficiency and exergy efficiency decrease by 6.6%, 1.1%, 3.4% and 1.0%, respectively. The temperature of PV panel increases with the increasing solar radiation, so the heat loss of HPS collector to ambient environment increases, leading to the decrease of thermal efficiency. At the same time, the increase of PV panel temperature improves the internal resistance of PV cells, leading to the decrease of electrical efficiency accordingly. Both overall energy and exergy efficiencies decrease with the decreasing thermal and electrical efficiencies. Fig. 13 shows the influence of solar radiation on condensation capacity, compressor power and coefficient of performance (COPth and COPPV/T). It can be observed that the condensation capacity, compressor power and coefficient of performance increase with the increasing solar radiation. When the solar radiation increases by 100 W/m2, the condensation capacity, compressor power, COPth and COPPV/T increase by 27.5 W, 1.93 W, 0.05 and 0.12, respectively. The temperature of circulating water increases with the increasing solar radiation, and the evaporation temperature increases as well. Since the evaporator could provide more heat for the system, the condensation capacity increases consequently. In addition, the increasing evaporation temperature leads to the increase of refrigerant mass flow rate to keep a relative stable superheat degree at the evaporator outlet, so that the compressor power increases

Table 5 Operating parameters of condition D, E and F. Condition

PV packing factor

PV backboard absorptivity

PV cell absorptivity

Heat pipe pitch (mm)

D E F

0.5, 0.65, 0.8, 0.9 0.8 0.8

0.8 0.5, 0.65, 0.8, 0.9 0.8

0.95 0.95 0.95

75 75 65, 75, 90, 110

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Fig. 11. Variation of thermal performance and overall efficiency with solar radiation.

Fig. 12. Variation of electrical performance and exergy efficiency with solar radiation.

Fig. 13. Variation of heat pump system performance with solar radiation.

due to the increasing refrigerant flow rate. However, since the condensation capacity increases more in percentage than compressor power, the COPth and COPPV/T still increase in the end.

5.2.2. Influence of ambient temperature on system performance Figs. 14 and 15 show the influence of ambient temperature on thermal and electrical performances, overall energy efficiency

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Fig. 14. Variation of thermal performance and overall efficiency with ambient temperature.

Fig. 15. Variation of electrical performance and exergy efficiency with ambient temperature.

and exergy efficiency. It can be found that the heat output power, thermal efficiency and overall efficiency exhibit nearly linear increase, while the electrical output, electrical efficiency and exergy efficiency exhibit nearly linear decrease with the increasing ambient temperature. When the ambient temperature increases by 5 °C, the heat output power, thermal efficiency and overall efficiency increase by 42.0 W, 1.60% and 0.60%, while the electrical output power, electrical efficiency and exergy efficiency decrease by 25.5 W, 1.15% and 0.75%, respectively. The heat loss of HPS PV/T collector decreases with the increasing ambient temperature, which leads to the increase of PV cells temperature, heat output power, thermal efficiency and internal resistance of PV cells. The increase of internal resistance of PV cells leads to the decrease of electrical output power and efficiency. The reason for the increasing overall energy efficiency is that the increase of thermal efficiency is greater than the decrease of electrical efficiency. Similarly, since the decrease of thermal exergy is greater than the increase of electrical exergy, the exergy efficiency decreases as well [53]. Fig. 16 shows the influence of ambient temperature on condensation capacity, compressor power, COPth and COPPV/T. As can be seen in Fig. 16, the condensation capacity and COPth increase, while the COPPV/T decreases with the increasing ambient temperature, but the compressor power varies slightly all the time. When the ambient temperature increases by 5 °C, the condensation capacity

and COPth increase by 46.5 W and 0.10, while the COPPV/T decreases by 0.10. The circulating water temperature and evaporation temperature increase with the increasing ambient temperature. Therefore, the refrigerant absorbs more heat from circulating water, leading to the increase of condensation capacity and COPth. The COPPV/T is found to be decreasing according to Eq. (66). 5.2.3. Influence of supply water temperature in condenser on system performance Figs. 17 and 18 show the influence of supply water temperature in condenser on thermal and electrical performances, overall energy efficiency and exergy efficiency. It is found that the supply water temperature in condenser has little influence on thermal and electrical performances, overall energy efficiency and exergy efficiency. As can be seen in Figs. 17 and 18, the heat output power, thermal efficiency, electrical power, electrical efficiency and exergy efficiency vary slightly with the supply water temperature in condenser. Moreover, the overall energy efficiency decreases from 36.2% to 34.8% when the supply water temperature in condenser increases from 30 °C to 45 °C. The condensation temperature increases with the increasing supply water temperature in condenser. Meanwhile, the evaporation temperature increases slightly due to the adjustment of refrigerant mass flow. The rise of evaporation temperature impacts slightly on PV panel temperature after transferring through circulating water and heat pipes. Therefore,

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Fig. 16. Variation of heat pump performance with ambient temperature.

Fig. 17. Variation of thermal performance and overall efficiency with supply water temperature in condenser.

Fig. 18. Variation of electrical performance and exergy efficiency with supply water temperature in condenser.

the increase of supply water temperature in condenser has a little influence on thermal and electrical performances of system. The overall energy efficiency and exergy efficiency increase slightly due to the increase of compressor power.

Fig. 19 presents the influence of supply water temperature in condenser on condensation capacity, compressor power, COPth and COPPV/T. As is shown in Fig. 19, the condensation capacity and compressor power increase, while the COPth and COPPV/T

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Fig. 19. Variation of heat pump performance with supply water temperature in condenser.

decrease with the increasing supply water temperature in condenser. When the supply water temperature in condenser increases by 5 °C, the condensation capacity and compressor power increase by 37.5 W and 36.5 W respectively, while COPth and COPPV/T decrease by 0.25 and 0.35, respectively. The increase of supply water temperature in condenser leads to the increase of condensation temperature and evaporation temperature. As a result, the condensation capacity and compressor power increase. Since the increase of compressor power in percentage is more than that of condensation capacity, the COPth and COPPV/T decrease with the increasing supply water temperature in condenser. 5.2.4. Influence of packing factor on system performance Figs. 20 and 21 show the influence of packing factor on thermal and electrical performances, overall energy efficiency and exergy efficiency. It’s obvious that the thermal output power and efficiency decrease, while the electrical output power and efficiency, overall energy efficiency and exergy efficiency increase with the increasing packing factor. When the packing factor increases by 0.15, the heat output power and thermal efficiency decrease by 19.4 W and 0.70%, while the electrical output power, electrical efficiency, overall energy efficiency and exergy efficiency increase by 43.8 W, 0.53%, 0.93% and 1.65%, respectively. Since the absorptivity of PV cells is lower than that of backboard, the heat gain from solar

radiation by PV/T collector and the temperature of PV panel decrease with the increasing packing factor. As a result, the heat output power and thermal efficiency decrease, while the electrical efficiency increases. It is obvious that the electrical output power increases with the increasing packing factor, and the overall energy efficiency and exergy efficiency increase as well for the reason that the increase of electrical output power is greater than the decrease of heat output power. The influence of packing factor on condensation capacity, compressor power, COPth and COPPV/T is presented in Fig. 22. It can be found that the condensation capacity, compressor power and COPth decrease, while the COPPV/T increases with the increasing packing factor. When the packing factor increases by 0.15, the condensation capacity, compressor power and COPth decrease by 8.0 W, 0.55 W and 0.017 respectively, while the COPPV/T increases by 0.26. As is shown in Fig. 20, the heat output power decreases with the increasing packing factor, leading to the decrease of condensation capacity, compressor power and COPth. The electrical output power significantly increases with the increasing packing factor. So the COPPV/T also increases according to Eq. (66). 5.2.5. Influence of heat pipe pitch on system performance Figs. 23 and 24 present the influence of heat pipe pitch on thermal and electrical performances, overall energy efficiency and

Fig. 20. Variation of thermal performance and overall efficiency with packing factor.

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Fig. 21. Variation of electrical performance and exergy efficiency with packing factor.

Fig. 22. Variation of heat pump performance with packing factor.

Fig. 23. Variation of thermal performance and overall efficiency with heat pipe pitch.

exergy efficiency. It was found that the heat output power, thermal efficiency, electrical output power, electrical efficiency, overall energy efficiency and exergy efficiency show a downward trend with the increasing heat pipe pitch. The heat output power, ther-

mal efficiency and overall energy efficiency increase significantly by 27.1 W, 1.05%, 1.0% and 0.75%, while the electrical output power, electrical efficiency and exergy efficiency increase slightly by 3.1 W, 0.18% and 0.18, when the heat pipe pitch increases by

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Fig. 24. Variation of electrical performance and exergy efficiency with heat pipe pitch.

Fig. 25. Variation of heat pump performance with heat pipe pitch.

5 mm. Less heat is absorbed by heat pipes with the increasing heat pipe pitch, which leads to the increase of PV panel temperature. As a result, the photoelectric conversion efficiency decreases due to the increasing internal resistance of PV cells. Therefore, all the performance parameters decrease with the increasing heat pipe pitch. The influence of heat pipe pitch on condensation capacity, compressor power, COPth and COPPV/T is shown in Fig. 25. There is also a downward trend for condensation capacity, compressor power, COPth and COPPV/T as the heat pipe pitch increases. When the heat pipe pitch is 65 mm, the condensation capacity, compressor power, COPth and COPPV/T are 1763.7 W, 414.2 W, 4.26 and 5.43, respectively. When the heat pipe pitch increases to 110 mm, the above parameters decrease to 1658.7 W, 406.7 W, 4.08 and 5.10, respectively. As the heat pipe pitch decreases by 5 mm, the condensation capacity, compressor power, COPth and COPPV/T decrease by 11.6 W, 0.85 W, 0.02 and 0.04, respectively. From the previous analysis, it can be seen that the heat output power decreases with the increasing heat pipe pitch, leading to the decrease of circulating water temperature. Moreover, the evaporation and condensation temperatures decrease with the decreasing circulating water temperature. As a result, the condensation capacity, compressor power and COPth decrease. Since the electrical output power also decreases, the COPPV/T decreases as well.

5.2.6. Influence of PV backboard absorptivity on system performance Figs. 26 and 27 show the variation of thermal and electrical performances, overall energy efficiency and exergy efficiency with different PV backboard absorptivity. It can be found that when the PV backboard absorptivity increases by 0.15, the heat output power and thermal efficiency increase by 25.5 W and 0.96%, while the electrical power and efficiency decrease by 8.7 W and 0.50%, respectively. While the overall energy and exergy efficiencies remain nearly unchanged and keep at around 35.0% and 10.2%. The PV panel temperature increases with the increasing PV backboard absorptivity. Moreover, the heat output power and thermal efficiency increase, while the electrical output power and electrical efficiency decrease due to the increasing internal resistance of PV cells. The overall energy efficiency and exergy efficiency remain nearly unchanged since the increase of heat output power offsets the decrease of electrical output power. Fig. 28 shows the variation of condensation capacity, compressor power, COPth and COPPV/T with different PV backboard absorptivity. It can be found that when the PV backboard absorptivity increases by 0.15, the condensation capacity, compressor power and COPth increase by 11.1 W, 0.80 W and 0.03, respectively, while the COPPV/T decreases by 0.03. The increase of heat output power mainly leads to the increase of COPth. The decrease of electrical output power mainly leads to the decrease of COPPV/T according to Eq.(66).

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Fig. 26. Variation of thermal performance and overall efficiency with PV backboard absorptivity.

Fig. 27. Variation of electrical performance and exergy efficiency with PV backboard absorptivity.

Fig. 28. Variation of heat pump performance with PV backboard absorptivity.

6. Conclusions A numerical and experimental study on the performance of a HPS PV/T heat pump system is carried out in this paper. A testing rig of the HPS PV/T heat pump system is constructed. A mathematical model, including a dynamic distributed parameter model of

the HPS PV/T collection system and a quasi-steady state distributed parameter model of the heat pump system, is presented to assess the performance of HPS PV/T heat pump system. The mathematical model is validated with the testing data. The capacity of heat pump and the number of solar collectors are optimized based on the validated model. Six working modes are proposed and

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discussed to investigate the influence of three external factors and three structure factors on energy performance of the HPS PV/T heat pump system based on the validated model. The conclusions can be drawn as follows:

National Natural Science Foundation of China (51206004) and Beijing Municipal Key Lab of HVAC (KF201004).

(1) The simulation results agree well with the testing data with a relative error within ±15%. The mathematical model can accurately predict the performance of HPS PV/T heat pump system. (2) The COPth and COPPV/T of the HPS PV/T heat pump system increase with the increasing solar radiation. When the solar radiation increases by 100 W, the COPth and COPPV/T increase by 0.05 and 0.12. The heat output power and electrical output power increase, while the thermal efficiency, electrical efficiency, overall energy efficiency and exergy efficiency decrease with the increasing solar radiation. (3) The increase of ambient temperature results in the increase of COPth but the decrease of COPPV/T. When the ambient temperature increases by 5 °C, the COPth increases by 0.08, while the COPPV/T decreases by 0.09. The heat output power, thermal efficiency and overall efficiency increase, while the electrical output power, electrical efficiency and exergy efficiency decrease with the increasing ambient temperature. (4) The supply water temperature in condenser influences the COPth and COPPV/T significantly. When the supply water temperature in condenser increases by 5 °C, the COPth and COPPV/T decrease by 0.25 and 0.35, respectively. But the supply water temperature in condenser has little impact on the electrical performance of HPS PV/T heat pump system. (5) The increase of packing factor results in the decrease of COPth but the increase of COPPV/T. When the packing factor increases by 0.15, the COPth decreases by 0.017 and the COPPV/T increases by 0.26. The heat output power and thermal efficiency decrease, while the electrical output power and efficiency increase with the increasing packing factor. (6) The COPth and COPPV/T decrease with the increasing heat pipe pitch. When the heat pipe pitch increases by 5 mm, the COPth and COPPV/T decrease by 0.02 and 0.04, respectively. The other performance parameters, such as heat output power, thermal efficiency, electrical output power, electrical efficiency, overall energy efficiency and exergy efficiency, also decrease with the increasing heat pipe pitch. (7) The increase of PV backboard absorptivity leads to the increase of COPth but the decrease of COPPV/T. When the PV backboard absorptivity increases by 0.15, the COPth increases by 0.03 while the COPPV/T decreases by 0.03. The heat output power, thermal efficiency and overall energy efficiency increase, while the electrical output power, electrical efficiency and exergy efficiency decrease with the increasing PV backboard absorptivity.

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The HPS PV/T heat pump system, which can produce thermal and electrical energy simultaneously, is more suitable to be used in individual small houses or low-rise buildings due to the limited energy supply capacity caused by the limited roof area and PV/T panel area. The size of HPS PV/T panel and the capacity of HPS PV/T heat pump system can be optimized according to the real energy demands, and the study in this paper could provide a reference for the optimization and design of the HPS PV/T heat pump system for real applications.

Acknowledgements The work of this paper is fully supported by Projects of National Key Research and Development Program (2016YFC0700104),

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