Investigation on a mini-CPC hybrid solar thermoelectric generator unit

Renewable Energy 92 (2016) 83e94

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Renewable Energy journal homepage: www.elsevier.com/locate/renene

Investigation on a mini-CPC hybrid solar thermoelectric generator unit Y.J. Dai a, *, H.M. Hu a, T.S. Ge a, R.Z. Wang a, Per Kjellsen a, b a b

Institute of Refrigeration and Cryogenics, Research Center of Solar Power and Refrigeration, M.O.E, Shanghai Jiao Tong University, Shanghai, China Norwegian University of Science and Technology, Trondheim, Norway

a r t i c l e i n f o

a b s t r a c t

Article history: Received 31 August 2015 Received in revised form 20 January 2016 Accepted 20 January 2016 Available online xxx

A hybrid solar hot water and Bi2Te3-based thermoelectric generator (TEG) unit using a heat pipe evacuated tube collector with mini-compound parabolic concentrator (mini-CPC) is proposed. In this unit, the heat from the heat pipe evacuated tube solar collector is transferred to the hot side of TEG. Simultaneously, water cooling is used at the cold side to maintain the temperature difference. Electricity is generated by TEG and the remaining heat is transferred to water at the same time. This paper investigates how to convert excess solar heat into electricity more effectively. A mathematical model regarding this unit is developed and validated. It is found that the mini-CPC can significantly improve the electrical efficiency. The optimal thermal conductance of TEG is determined, which could make the best use of excess solar heat. The excess solar heat can be effectively converted into electricity when ZT of Bi2Te3 can be improved from 100
C to 200
C. Using TEG with ZT ¼ 1.0 and a geometrical concentrating ratio at 0.92, electrical and thermal efficiencies of this system are predicted to be 3.3% and 48.6% when solar radiation and water temperature are 800 Wm2 and 20
C, respectively. © 2016 Published by Elsevier Ltd.

Keywords: Solar hot water Thermoelectric generator Mini-CPC Efficiency

1. Introduction Increasing pressure from environment and energy crisis attracts the development of solar thermal technologies for industrial and domestic applications. Operation data in the USA show that water heating accounts for 20% of household energy use [1]. Flat plate solar collector and evacuated glass tube solar collector are commonly used for solar water heating system. In China, evacuated glass tube collector is more popularly used due to the improved thermal performance and low cost. Most of the evacuated glass tube solar collectors are nonconcentrating, and the operation temperature is normally low. Recently, low concentrating solar evacuated collector has been developed to be both cheaper and more compact. Li et al. [2] investigated thermal performance of evacuated collectors with 3 and 6 CPC reflectors. It is found that thermal efficiencies (hths) are as high as 51% and 54% by using 3 CPC and 6 CPC when water temperature (Tw) is 150
C. Pei et al. [3] compared the performances of solar evacuated collectors with and without mini-CPC. It is found that solar evacuated collector with mini-CPC has a higher thermal efficiency than that without mini-CPC at high water temperature.

* Corresponding author. E-mail address: [email protected] (Y.J. Dai). http://dx.doi.org/10.1016/j.renene.2016.01.060 0960-1481/© 2016 Published by Elsevier Ltd.

Zambolin [4] investigated the thermal performances of flat plate and evacuated tube solar collectors with external CPC reflectors. The efficiency curves in steady-state and quasi-dynamic methods are obtained. Kossyvakis et al. [5] modeled the solar thermoelectric generator using ANSYS workbench software. The computational results reveal that the performance can be significantly improved by optical concentrated configurations. The efficiencies of evacuated glass tube collectors with and without low concentrating CPC are normally above 50% and 60%, respectively, even if the water temperature is up to 90
C. The temperature range meets the operational requirement of thermoelectric generator (TEG). The combined technology of TEG and evacuated glass tube solar collector has received increasing attention. Chen et al. [6,7] proposed the concept of thermal concentration to obtain a large temperature drop across thermoelectric (TE) legs in a very cost-effective way. The experimental results showed that electrical efficiency (he) is around 4.6% with solar radiation (G) at 1000 Wm2 and cold-side temperature of 20
C. However, commercial TEG could not be employed in this system because the thermal concentration of the commercial TEG is not more than 10 [8], while in that system the thermal concentration is around 200 [7]. McEnaney et al. [9] also extended the concept of thermal concentration into concentrating solar TEG. The results showed that he can be 10% when geometric optical concentration ratio is 45 using skutterudite and Bi2Te3 materials. Lesage et al. [10] have

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Y.J. Dai et al. / Renewable Energy 92 (2016) 83e94

Nomenclature A C Cp D F F0 hfg K I L N m G Q P W R RL S T Z

area (m2) geometrical concentration ratio specific heat (J kg1 K1) diameter (mm) fin efficiency of straight fin collector efficiency factor heat of vaporization (J/kg) thermal conductance (W K1) electrical current (A) length (m) thermocouple number mass flow rate (kg /s) solar irradiance (W m2) energy (W) power (W) circumferential distance of the inner tube (m) thermal resistance (K W1) electrical resistance of external load (U) collected solar energy (W) Temperature (K) a2te =ðkte rte Þ (K1)

Greek symbols a Seebeck coefficient (V K1) & absorptance r electrical resistivity (U m) & density (kg m3) h heat transfer coefficient (W K1 m1) m dynamic viscosity (Pa s) h Efficiency k thermal conductivity (W m1 K1)

investigated the optimal load for peak power in solar TEG. They also proposed a normalized thermo-power theoretical evolution curve relative to load resistance. Some researchers investigated hybrid solar water and TEG system to harvest the heat released on the cold side of TEG. He et al. [11] developed a solar heat pipe TEG unit. The hot side of TEG is connected to the condenser section of the heat pipe and its cold side is cooled by water. This is a simple way to achieve thermal concentration. The commercial TEG can be used in this system. It is predicted that he is 1.62% and hth is 59.3% when G, Tw and ZT are 1000 Wm2, 25
C and around 1.0, respectively [11]. Lei et al. [12] extended the study [11] and designed a solar thermoelectric cogenerator which can produce electricity and heat simultaneously. From the previous studies, it can be known that the hybrid solar water and TEG systems are mainly non-concentrating unit, especially non-CPC unit. For domestic use, the required temperature of hot water is about 40
Ce50
C. The required area of solar collectors is generally designed for winter demand. Therefore, there will be excess heat in the solar water system in summer, especially for the systems with CPC components. It is worth to utilize the excess heat of solar evacuated collector in the summer by using the hybrid hot water and TEG system. Moreover, the produced electricity can be supplied to power grid using inverter or supplied to the electromagnetic anti-scaling instrument for hot water. In the present study, a hybrid solar hot water and TEG unit (SHTG) using heat pipe evacuated glass tube collector with miniCPC is proposed, which would be discussed in Section 2. In Section 3, mathematical model, including optical analysis and thermal analysis, is established. And the thermal conductance of TEG, leading to maximum electrical efficiency under given conditions, is

d q t ε

thickness (m) incident angle (
) Transmittance Emittance

Subscripts a ambient & acceptance b Bond c cold side C condensation section con contact resistance e electric power E evaporation section h hot side hp heat pipe i inner & inner tube in Inlet L loss & longitudinal projection l Liquid o outer & outer tube opt optimal out Outlet ref reflect s Sky sat saturation T transversal projection te thermoelectric element th thermal energy U useful energy v Vapor w water & wall

determined. In Section 4, limits of hot side temperature of TEG of SHTG are investigated. Effects of structure parameter and operating parameters, including Tw and G, are investigated. It is found that SHTG for TEG with optimal thermal conductance could effectively convert the excess solar heat into electricity without reducing thermal efficiency significantly at low solar radiation. The effect of the thermoelectric material is also investigated. The experimental validation is also described in Section 4. 2. Description of SHTG Fig. 1 shows the schematic diagram and photo of the proposed SHTG. It consists of a mini-CPC reflector, an evacuated glass tube, a heat pipe with fin, a Bi2Te3-based TEG and a water jacket. As shown in Fig. 1, the reflector's enclosures are fabricated using several acrylic molds based on CPC shape in order to ensure the optical performance. The CPC reflector is made of solar mirror film 1100 (3M Inc.) with a high reflectivity (href ¼ 0.95). As shown in Fig. 2, the fin is directly connected to the inner glass. The solar heat collected by the inner glass (which has the selective coating) can be directly transferred to the fin. The copper-water heat pipe is employed due to its suitable working temperature (298e573 K). The internal pressure at static state is 6.3 kPa. So the start-up temperature is about 35
C. The condenser section of the heat pipe is flattened and soldered to a copper plate in order to improve the heat transfer coefficient. The TEG is connected to copper plate using thermal grease to decrease thermal contact resistance. The other side of TEG is connected to water jacket in the similar way. The configuration gives a temperature difference between two sides of TEG in operation. So both heat and electricity can be produced. Table 1 and

Y.J. Dai et al. / Renewable Energy 92 (2016) 83e94

C¼

85

WCPC pDi

(1)

3. Mathematical model 3.1. Optical analysis In order to evaluate the performance of SHTG, a three dimensional ray tracing program Tracepro (Lambda Research Corporation, Littleton, MA) is employed to determine angular acceptance of mini-CPC reflector. The transversal projection angle of the rays is varied in steps of 10
from 70
to þ70
. As shown in Fig. 3, it can be noted that the longitudinal projection angle of the rays is changed from þ60
to 0
to þ60
in the whole day. So the longitudinal projection angle of the rays is varied in the steps of 10
from 0
to þ60
. The angular acceptance at a given incident angle can be calculated by Ref. [2]:

ha ðqÞ ¼ ha ð0; 0Þ

ha ðqT ; 0Þ ha ð0; qL Þ ha ð0; 0Þ ha ð0; 0Þ

(2)

Fig. 4 shows the variation of the angular acceptances at any given incident angle. It is noted that there exists a drop at qT ¼ ± 60
, because part of incident rays reflected by reflector cannot reach the absorber. It is also found that average ha is more than 84% at any given incident angle in the whole day. It indicates that ha can remain at a very high value without tracking system. 3.2. Thermal performance modeling One-dimensional analytical mathematical model of SHTG is established. The following assumptions have been made without losing significant accuracy:

Fig. 1. A general view of SHTG.

(1) Heat transfer is assumed to be steady state. (2) Thermal resistance along the heat pipe is neglected. (3) Thermal properties of selective coating are constant.

Fig. 2. Construction of heat pipe collector with mini-CPC.

West

θT

Fig. 2 show the specification and schematic of heat pipe evacuated glass tube solar collector with mini-CPC. The prototype of SHTG is mounted facing south and inclined at 30
from the horizon using a support. The angle of inclination for SHTG is nearly identical with latitude of Shanghai (latitude 31.14
) in order to obtain largest annual solar gain [13]. According to the study of Mills [14], the geometrical concentration ratio (C) can be defined as:

θ 30o

South

SHTG

North

East Fig. 3. Position of SHTG.

Table 1 The specification of heat pipe collector with mini-CPC. ai

εi

ao ¼ ε o

to

Do (mm)

Di (mm)

Ltube (m)

Lcpc (m)

Wcpc (mm)

0.86

0.10

0.80

0.90

47

58

1.75

1.75

136

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Y.J. Dai et al. / Renewable Energy 92 (2016) 83e94

the TEG, QU converts into electrical energy (P) by TEG and the remaining QU is absorbed by hot water. So QU contains electrical energy (P) and thermal energy (Qth). 3.2.1. Thermal loss coefficient It is found that QU can be expressed as [15]:

QU ¼ S  QL ¼ GCAi href ha to ai  QL

(1)

where G is the solar irradiance, C is the concentration ratio, Ai is the area of the inner glass tube and ai is the absorptance of the inner glass tube. The thermal loss can be expressed as [16]:

QL ¼ UL Ai ðTi  Ta Þ

(2)

where UL, Ti and Ta are the thermal loss coefficient, the temperature of the inner glass tube and the ambient temperature. Then, the thermal loss coefficient can be expressed as [16]:

UL ¼

1 Ai

1 1  þ hi;o Ai ho;a þ ho;s Ao

!1 (3)

where hi,o is the radiation heat transfer coefficient between the inner tube and outer glass tube. ho,a is the convection heat transfer coefficient between outer glass tube and ambient, and ho,s is the radiation heat transfer coefficient between outer glass tube and sky. Ao is the surface area of outer glass tube. hi,o can be expressed as [16]:

hi;o

Fig. 4. The optical results of mini-CPC: a) the illustration ray tracing program for the mini-CPC and b) variations of ha (0, qL) and ha (0, qT) with longitudinal projection angle and longitudinal projection angle.

(4) The Thomson effect of TEG is neglected. (5) Heat transfers of the air gap inside TEG module are neglected. Fig. 5 shows the thermal network of SHTG. The mini-CPC reflector concentrates solar energy onto the selective coating and then the thermal energy (S) is produced, which contains useful energy (QU) and thermal loss (QL). QU is the thermal energy absorbed on the hot side of TEG. Based on the energy balance for

  s Ti2 þ To2 ðTi þ To Þ   ¼ 1 þ Ai 1 1 εi Ao εo

(4)

where To is the temperature of outer glass tube. s is the StefaneBoltzmann constant. εi and εo are the emittances of the absorber tube and outer glass tube, respectively. ho,s can be expressed as [16]:

   2 2 To2 þ Tsky ho;s ¼ sεo To2 þ Tsky

(5)

where Tsky is the temperature of the sky, Tsky ¼ 0.0522T1:5 a . ho,a can be expressed as [16]:

ho;a ¼ 5:7 þ 3:8v

(6)

where v is the wind speed. As shown in Fig. 5, the energy balance of the outer glass tube can be expressed as:

   GCAi href ha ao þ hi;o Ai ðTi  To Þ ¼ Ao ho;s To  Tsky  þ ho;a ðTo  Ta Þ

(7)

where ao is the absorptance of the outer glass tube. Ti is assumed to be Th here, thus UL can be obtained from Eq. (3) to Eq. (7). 3.2.2. Useful efficiency As shown in Fig. 5, the useful energy contains the electric energy and thermal energy. It can be expressed as:

QU ¼ P þ Qth Fig. 5. Thermal network of SHTG.

(8)

As shown in Appendix B, the efficiency of useful energy, which is defined as useful efficiency (hU), can be expressed as:

Y.J. Dai et al. / Renewable Energy 92 (2016) 83e94

hU ¼

 QU U ¼ F 0 href ha ai to  L ðTh  Ta Þ GCAi GC

87

it is found that the ZT of commercial TEG available is around 0.59 at the room temperature, which is far less than that discussed in the previous studies (ZT ¼ 1) [12].

(9)

It is noted that C is WCPC/pDi, namely, 1/p for non-concentrating evacuated collector. F0 is the collector efficiency factor in Eq. (9). It can be expressed as [16]:



ate ¼



 2  0:004111Tm þ 2:84Tm  272:2  106

VK 1

 (14)

F0 ¼

1=UL

" W

1 WFUL

#

(10)

þ k Lbd þ Ltube Rhp

tanh½mW=2 mW=2

2  0:03767Tm þ 6:491 kte ¼ 6:954  105 Tm

ðUmÞ



WK 1 m1

 (16)

where Tm is (Th þ Tc)/2. The electrical power produced by TEG is [18]:

(11)

where m is expressed as:

sffiffiffiffiffiffiffiffiffiffiffiffiffiffi UL m¼ kfin dfin

 2  8:735  105 Tm þ 0:1241Tm  15:85  106

(15)

where W is the circumferential distance of the inner tube, Lb is the average length of the bond, Ltube is the length of the tube, F is the fin efficiency of straight fin and Rhp is the resistance from fin to hot side of TEG. W is about pDi/2. Rhp is the thermal resistance of the heat pipe. It is given in Appendix A. F can be expressed as [16]:

F¼



rte ¼

fin fin

P¼

nate ðTh  Tc Þ

(12)

nrte ALtete þ RL

 Lte  R2L ¼ n ate IðTh  Tc Þ  I 2 rte Ate

(17)

where RL is the electrical resistance of the external load. Thus, the electrical efficiency of SHTG is:

where kfin and dfin are the thermal conductivity and the thickness of the fin. The details of the derivation of the heat transfer model for this fin-type heat pipe are given in Appendix B.

he ¼

(1). Maximum electrical efficiency of SHTG

P GCAi

(18)

The energy balance equation of the hot side of TEG can be expressed as:

According to the study of solar thermoelectric generator from Chen [6,7], the optimal current (Iopt) or optimal load (RL,opt), leading to maximum electrical efficiency of the system, are found to be:

 Ate 1 Lte GCAi hU ¼ n ate ITh þ kte ðTh  Tc Þ  I 2 rte 2 Lte Ate

Iopt ¼ 

(13)

where n is the number of thermoelectric legs. Ate and Lte are the cross area and the length of TE legs. ate, kte and rte are the Seebeck coefficient, thermal conductivity and electrical resistivity of TE legs, respectively. In the present study, the TE legs are composed by the Bi2Te3-based TE material. The properties of the TE material are temperature dependent. Properties of Bi2Te3 are fitted in Fig. 6 based on the experimental data from Ferrotec Company [17]. And

ate ðTh  Tc Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Lte 1 þ ZTm rte Ate

(19)

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Lte 1 þ ZTm rte Ate

(20)

where Z ¼ a2te =ðkte rte Þ. We substitute Eq. (19) to Eq. (13) and it is found that:

0.7

21

ZT measured 2 ZT=α T/(kρ)

2.8

15

2.0

0.5

ZT

2.4

-1

18

-1

0.6

k/Wm K

210

α measured fit of α ρ measured fit of ρ k measured fit of k

RL;opt ¼

ρ/Ωm

S/VK

-1

220

1þ

0.4

200 12

190

280

320

360

400

440

1.6

1.2

0.3

0.2

280

T/K

320

360

T/K Fig. 6. Experimental data and fitted curve of properties of TE material.

400

440

88

Y.J. Dai et al. / Renewable Energy 92 (2016) 83e94

Input structure parameters and operation parameters

200

Guess Ti

190

Th / oC

Guess To Determine To using Eq.(7)

180

Calculate UL and ηu

170

Guess Tc

160

G=solar constant C=0.92 20

Calculate ηe and ηth Variable KTEG

40

60

80

100

o

Tw/ C Fixed KTEG Fig. 8. Variations of Th with Tw.

Determine Tc using Eq.(26)

Input KTEG

Find maximum ηe under Tis

Determine Tc using Eq.(22) Determine Th using Eq.(26)

Determine corresponding To, ηth, KTEG

of SHTG multiplied by the maximum electrical efficiency (hTEG) of TEG. It can be noted that the maximum he can be obtained at the KTEG and Iopt or RL,opt, respectively. (2) Thermal efficiency of SHTG. The energy balance on the cold side of TEG can be expressed as [18]:

Determine corresponding ηth and ηe

 Tc  Tw Ate 1 Lte ¼ n ate ITc þ kte ðTh  Tc Þ þ I 2 rte 2 Rw Lte Ate

Fig. 7. Flowchart of SHTG model.

, nkte Ate ¼ KTEG ¼ GCAi hU ðTh  Tc Þ Lte 3 2 ZTh 1 ZðTh  Tc Þ 4 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ 1     2 5 2 1 þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ 1 þ ZTm 1 þ ZTm

where Tw and Rw are the temperature of water and the thermal resistance between cold side and water, respectively. Rw is approximated to be 0.026 KW1 in this system [19]. The current of TEG is fixed to be Iopt, so Eq. (24) can be expressed as:

(21) Tc  Tw ¼ GCAi hU ð1  hTEG Þ Rw

where KTEG is the thermal conductance of TEG in SHTG. It is found that KTEG is related to the structure parameters of low concentrating solar evacuated collector such as Ai and C, and is also related to operating parameters including G and Tc. More importantly, some manufactures (Marlow, Ferrotec and Kryotherm) have already given the thermal conductance of TEG. So the suitable TEG can be directly obtained based on KTEG. So Eq. (13) can be expressed as:

Tc  Tw Rw

hth ¼

2.5

(26)

120 η 56

η

ZTh pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ1 1 þ ZTm 1

 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðTh  Tc Þ 1 þ ZTm  1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ¼ hU  hTEG Th 1 þ ZTm þ Tc =Th

∆T

100

(22)

(23)

where the electrical efficiency of SHTG is the useful efficiency (hU)

1.5

80

48

G=800Wm T =45 C

1.0

0.2

0.4

0.6

0.8

1.0

C Fig. 9. Variations of he, hTEG, hth and DT with C.

44

1.2

60

∆ T/ C

52 η /%

1 ZðTh  Tc Þ 2 A 2 1 þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ ZTm

2.0 /%

1þ

Substituting Eqs. (17), (19) and (21) to Eq. (18), the maximum electrical efficiency of SHTG can be expressed as:

he ¼ hU 

 GCAi ¼ hU ð1  hTEG Þ

η

η &η



(25)

Hence, the thermal efficiency of SHTG is defined as:

0 GCAi hU ¼ KTEG ðTh  Tc Þ@

(24)

Y.J. Dai et al. / Renewable Energy 92 (2016) 83e94 2.4

89

58

K η

0.70

57

η

2.1

55

η /%

η /%

0.65

K

/WK

56 1.8

1.5

0.60

53

G=800Wm C=0.92 10

20

30

40

54

1.2 52

50

T /C Fig. 10. Variations of KTEG, he and hth with Tw.

3.3. Solution The M language in MATLAB is adopted to establish the mathematic model described above. The flowchart of SHTG calculation is shown in Fig. 7. There are two kinds of calculation processes. One is to obtain maximum electrical efficiency based on variable KTEG, the other is to investigate the performance under fixed suitable KTEG at different solar irradiations and water temperatures. 4. Results and discussion As the two calculation processes discussed in Fig. 7, the calculation process based on variable KTEG is used to investigate limited Th of TEG, and effect of concentration ratio (C), operating parameters and ZT of TEG on the performance of SHTG under the maximum electrical efficiency condition of SHTG. The calculation process based on fixed KTEG is adopted to investigate performance of SHTG under different fixed KTEGs at different solar irradiations, which would be discussed in section 4.3. The reference value of solar irradiance is assumed to be 800 Wm2 for common data in Shanghai [20]. The experimental validation is discussed in section 4.6. Fig. 12. Variations of he and hth with G with respect to different KTEGs: a) he and b) hth.

4.1. Theoretical limits of hot side temperature of TEG There exists a temperature limit on the hot side of TEG to avoid melting of the solders, which are used to connect the TE legs to the electrical connector. Hence, it is important to predict the hot side temperature of TEG of SHTG in extreme condition.

Fig. 8 shows variations of Th with Tw in the extreme condition. The solar irradiance is set to be solar constant (assumed to be 1368 Wm2) [16]. It can be seen that Th increases with the increase

200

KTEG for constant ZT

1.0

K

1.5

η 0.8

0.8

KTEG for practical ZT

55

Th for constant ZT

160

η

Th for practical ZT

0.6

K

120

0.4

40

0.4

T =45 C

0.5

C=0.92

0.2 0

200

400

600

800

1000

G/Wm Fig. 11. Variations of KTEG, he and hth with G.

o

35

30

Tw=45 C

80

C=0.92 0

200

400

600

800

1000

0.2 1200

-2

G/Wm

Fig. 13. Variations of Th and KTEG for practical ZT and constant ZT with G.

KTEG/WK

o

Th/ C

45

η /%

1.0

0.6

η /%

/WK

-1

50

Y.J. Dai et al. / Renewable Energy 92 (2016) 83e94

2.0

constant ZT

pratical ZT

1.0

constant ZT

5

50

4

ηe/%

ηth/%

1.5

60

40

ηe/%

90

ZT=0.5 ZT=1.0 ZT=1.5

3

o

Tw=45 C

0.5

C=0.92 2

30 0

200

400

600

800

C=0.92 -2 G=800Wm

1000

-2

G/Wm

10

Fig. 14. Variations of he and hth for constant ZT and practical ZT with G.

20

30

40

50

o

Tw/ C
C

a)


C.

of Tw and the largest value of Th is 201 when Tw is 100 The commercial TEGs of some manufactures (Ferrotec, Marlow) can be operated steadily below 250
C, so SHTG can work steadily.

ZT=0.5 ZT=1.0 ZT=1.5

51.0

4.2. Effect of concentration ratio (C)

ηth/%

49.5

Fig. 9 shows the variations of he, hTEG, hth and DT with C when Tw is 45
C and G is set to be 800 W/m2. C increases from 0.32, which is non-concentrating system, to 1.12. The temperature of 45
C can meet the needs of domestic hot water [11]. Firstly, it is noted that hTEG increases from 1.8% to 2.5%. It agrees with the variation of DT with respect to the commercial TEG. It indicates that hTEG increases with the increase of C due to the increase of DT. Secondly, it is found that hth increases from 45.0% to 56.2%. It is because hU increases with the increase of C based on Eq. (9). Finally, he increases from 0.8% to 1.4%. It is noted that he increases by more than 50%. It is because both of hTEG and hU increase with the increase of C. It indicates that the low concentrating system can improve he significantly.

48.0

46.5

C=0.92 -2 G=800Wm 45.0

10

20

40

50

o

Tw/ C

4.3. Effects of operating parameters (Tw and G)

b) 180

ZT=0.5 ZT=1.0 ZT=1.5

175

170 o

Th/ C

The operating parameters (Tw and G) are variable in SHTG. Thus, the thermal conductance of TEG (KTEG) is variable along the process. As a result, it is important to investigate the effects of these operating parameters on KTEG. Fig. 10 shows the variations of KTEG, he and hth as Tw increases from 10
C to 50
C. he drops from 2.2% to 1.3% and hth drops from 57.4% to 53.8% in the process. It is noted that he drops by nearly 50%, while hth drops slightly. It indicates a high electrical efficiency in the process of heating water can be obtained without severely reducing thermal efficiency. It is also noted that KTEG increases slightly from 0.60 W/K to 0.71 W/K in this process. Thus, the impact of Tw on KTEG can be neglected in the process. Fig. 11 shows the variations of KTEG, he and hth with G. It is found that both he and hth increase with the increase of G, because hU increases with increasing of G according to Eq. (9). It is also noted that he increases more drastically than hth. KTEG increases from 0.15 WK1 to 0.85 WK1 when G increases from 100 Wm2 to 1000 Wm2. It implies that KTEG changes dramatically with G. However, variable KTEG could not be employed in SHTG in practice. Hence, the optimal value, KTEG, is selected based on the large solar irradiance and low solar irradiance in the following. Fig. 12 shows the effect of G on hth and he with respect to different KTEG including variable KTEG, summer KTEG, winter KTEG and

30

165

160

155

C=0.92 -2 G=800Wm 10

20

30

40

50

o

Tw/ C c) Fig. 15. Effect of ZT of TEG on performance of SHTG. a) Variations of he with Tw, b) Variations of hth with Tw and c) Variations of Th with Tw.

Y.J. Dai et al. / Renewable Energy 92 (2016) 83e94

91

Fig. 16. The experimental test system of SHTG.

nonTEG. Summer KTEG and winter KTEG are the KTEG based on high solar irradiance (1000 Wm2) and poor solar irradiance (100 Wm2), respectively. Variable KTEG is adopted on the basis of a variable solar irradiance, which leads to the largest electrical efficiency under different solar irradiances. NonTEG is just a solar evacuated heater without TEG. It is noted that hths for variable KTEG and nonTEG increase along with G due to the increase of hU shown in Eq. (9). hth for variable KTEG is 30%e40% lower than that for nonTEG. However, hth for summer KTEG increases firstly and then decreases as G further increases. So there exists a maximum value (60%) around 300 Wm2, which is caused by the variation of hU. As shown in Eq. (9), when G is low, hU can be improved by G. When G is high, the increase of hL and Th due to the increase of Ti leads to the decrease of hU. Moreover, hth for summer KTEG is close to that for nonTEG when G is at 300e500 Wm2, while hth for summer KTEG is close to that for variable KTEG when G is higher than 500 Wm2. Meanwhile, he for both variable KTEG and summer KTEG increase with G. However, he for summer KTEG is close to that for variable KTEG. Furthermore, it is found that hth for winter KTEG decreases with increasing of G due to small KTEG. Though he for winter KTEG is close to the maximum he at lower G level, hth for winter KTEG is far lower than that for nonTEG. It can be seen that the summer KTEG can be used in SHTG to fully use excess solar heat without reducing thermal efficiency when solar radiation is low. 4.4. Effect of temperature dependent properties of TE material Fig. 13 shows variations of Th and KTEG for practical ZT and

constant ZT (ZT ¼ 0.59) with G. It is noted that Th for constant ZT is higher than that for practical ZT, especially at large G. When G is 1000 Wm2, Th is 159
C and 192
C for practical and constant ZT, respectively. The reason is that ZT of traditional Bi2Te3 decreases with the increase of temperature. Further, KTEG for constant ZT is lower than that for practical ZT, especially at large G. Low Th can be kept in order to increase hU when KTEG is high at practical ZT. Thus, it is effective to increase ZT value at high temperature from 100
C to 200
C for Bi2Te3 TE material. Fig. 14 shows variations of he and hth for constant ZT and practical ZT with G. Similarly, he for constant ZT is higher than that for practical ZT while hth for constant ZT is lower than that for practical ZT, especially at high G. It indicates that TEG cannot effectively convert solar heat into electricity due to performance degradation of TE material at high temperature. 4.5. Effect of ZT of TEG ZT of TEG is the most important parameter to improve the performance of SHTG. Though practical ZT for traditional Bi2Te3 is temperature dependent, constant ZT with respect to different values is adopted to investigate its effect in a straightforward way. Fig. 15 shows the effect of ZT of TEG on the performance of SHTG under G and C is 800 Wm2 and 0.92, respectively. Recently, ZT values at 0.5, 1.0 and 1.5 refer to common, good and excellent TEGs, respectively. The TEG, whose ZT is 1.0, can be fabricated by nanocomposites Bi2Te3 TE material and it is available in some manufactures [21]. The TEG, of which ZT is 1.5, can be prepared at the

Table 2 Specification of the experimental apparatus. Apparatus

Specification

Production site

Parameter

TEG Thermostatic Side rheostat Temperature sensor Pyranometer Flowmeter

9500/127/060 B TZL-1015D BC1e25 W 10U PT1000 CM22, Kipp&Zonen LFS15

China China China Germany Netherlands China

L  W  H (mm): 39.7  39.7  4.1 Water temperature: 0e100 (oC) Accuracy:0.1U Accuracy: ±0.15
C Accuracy: ±1% Accuracy: ±2.5%

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Y.J. Dai et al. / Renewable Energy 92 (2016) 83e94

T =50 C

T =30 C

T =40 C

T =20 C

3.4

P for T =20 C

3.2

G/Wm-2

P for T =30 C

3.0 2.8

P/W

800

2.6 o

P for Tw=50 C

700

P for Tw=40 C

this testing system, various inlet water temperatures have been maintained by using a thermostatic waterbath (Poxiwar China) and the water is circulated using brushless DC pumps. The slide rheostat (0e10U, 0.1U) is employed as electrical load and connected with the TEG. The side rheostat is fixed at 3.2 U which is around the optimal value of load (Ropt). he and hth can be measured by:

. 2 RL ULoad P he ¼ ¼ GACPC GACPC

2.4

hth ¼ 0

1

2

3

4

5

6

7

t/min a)

2.0

65 simulation experiment

1.6

60

55 0.8 50

0.4

0.0

ηth/%

ηe/%

1.2

20

25

30

35 o Tw/ C

40

45

50

45

b) Fig. 17. Variations of experimental data and simulation data with Tws, a) experimental data for P at different Gs, b) variations of he and hth.

laboratory level. As shown in Fig. 15 a), it is noted that he increases distinctly with the increase of ZT, especially at the low ZT. For example, hes are 2.0%, 3.3% and 4.3% when ZTs are 0.5, 1.0 and 1.5 at Tw ¼ 20
C, respectively. It implied that the low ZT (ZT ¼ 0.5) value should be increased. It suggests that some commercial TE material should be improved by nanocrystallization and doping [21]. More importantly, hth could not decrease obviously with the increase of ZT. As shown in Fig. 15 b), hth is 46.0%, 45.0% and 44.3% when ZT is 0.5, 1.0 and 1.5 when Tw ¼ 50
C Fig. 15 c) shows the variations of Th with Tw under different ZTs. It can be seen that Th decreases with the increase of ZT and all of Ths are below 200
C. So in SHTG, high performance TEG can ensure that Th is lower than melting temperature of solders. 4.6. Experimental validation In order to validate the simulation analysis, experimental setup is established as shown in Fig. 16. Experiments are conducted to test the electrical and thermal performance of SHTG. The TEG of SHTG is 9500/127/060B from the Ferrotec Company (Hangzhou, China) and its thermal conductance is about 0.64 W/K, which is KTEG for this SHTG at 700 Wm2e800 Wm2 of solar irradiance. The specification, mount and inclination of SHTG are described in Section 2. In

Cp mw ðTout  Tin Þ GACPC

(27)

(28)

where ACPC is the area of the CPC, ULoad is the voltage of external load, RL is the resistance of the load, Cp is the specific heat of water, mw is the mass flow rate of water, Tin is the inlet water temperature and Tout is the outlet water temperature. Physical measurement parameters include the water temperature at inlet and outlet of SHTG, the ambient temperature, the flow rate of water, the incident solar irradiance and electrical power of SHTG. The temperature sensors (PT1000) were used to measure the water temperatures of the inlet and outlet, and ambient temperature. A pyranometer (CM22, Kipp&Zonen) was employed to measure the global irradiance on SHTG. The output voltage was measured by Keithley 2700 directly. The data of temperatures and solar irradiance were transmitted to a data logger (Keithley 2700) and then to computer for analysis shown in Fig. 16. The flowmeter (Rotameter) was employed to measure the water flow rate. The specification of the experimental apparatus is shown in Table 2. Fig. 17 shows the variations of experimental data and simulation data with Tws when G is around 750Wm2. From Fig. 17 a), the fluctuation of P is small under the variable G due to the thermal capacity of SHTG. It implies that continuous electricity can be produced. From Fig. 17 b), it can be seen that the results of the model agree with that of the experiment. The largest relative errors of he and hth are 4.5% and 6.0%, respectively. Further, he drops from 1.88% to 1.23% and hth drops from 56.7% to 47.1% when Tw increases from 20
C to 50
C. The he and hth are higher than that predicted by Miao et al. [12], because the mini-CPC and TEG with suitable KTEG are employed in the present study. Generally, the cost of thermoelectric generator module using in SHTG is about 4e5 $/piece. This data is from a Chinese largest online shop (Alibaba) or Amazon. The cost is very low compared to evacuated tube solar collectors ($830/m2) [22]. In AM1.5G and Tw ¼ 25
C, he is about 1.9%. As for this SHTG, P is about 4.5 W for one TEG. It indicates that the increased cost is about 1 $/W. This value is close to that for solar PV.

5. Conclusion A SHTG using heat pipe evacuated glass tube collector with mini-CPC has been presented in this study. The following conclusions can be obtained: (1) ha of mini-CPC is more than 80% from 70
to 70
without tracking system and the mini-CPC reflector can significantly improve he. (2) The optimal KTEG should be determined by high solar irradiance and is almost independent on the temperature of the

Y.J. Dai et al. / Renewable Energy 92 (2016) 83e94

hot water. SHTG with optimal KTEG can effectively convert the excess solar heat into electricity. (3) The excess solar heat can be effectively utilized if ZT of Bi2Te3 TE material at the temperature from 100
Ce200
C is improved to a great extent. (4) he and hth of SHTG are predicted to be 3.3% and 48.6% when C, ZT, G and Tw are 0.92, 1.0, 800 Wm2 and 20
C, respectively.

93

Appendix B. Derivation of heat transfer for fin-type heat pipe

Acknowledgments This work is supported by the National Science and Technology Support Project of China under the Contract No.2012BAA05B04. Appendix A. Thermal resistance of heat pipe

Rb

Rw,E

RE

RC

Rw,C

Rcon

Tb

Th Rhp Fig. 18. Thermal network of the heat pipe.

As shown in Fig. 18, thermal resistance of the heat pipe can be expressed as [23]:

Rhp ¼ Rw;E þ RE þ RC þ Rw;C þ Rcon

(29)

where Rw,E and Rw,C are the wall radial thermal resistances of evaporation and condensation sections. RE and RC are evaporation and condensation interfacial thermal resistances. Rcon is the contact resistance between the heat pipe and hot side of TEG. Rcon is assumed to be 0.02 W K1 [12]. The thermal resistance of the vapor flow is negligible.

Rw;E ¼

  ln Do;E Di;E 2pLE kw

1 pDi;E hE LE

(31)

RC ¼

1 pDi;C hC LC

(32)

  ln Do;C Di;C 2pLC kw

(33)

The evaporation and condensation heat transfer coefficients can be expressed as [24,25]:

" hE ¼ A

r21 ghfg k3l ml ðTw:E  Tsat:E ÞLE

#0:25 (34)

0:385 # " i L ½0:254ðcos qÞ  h E 0:108 A ¼ 0:997  0:334ðcos qÞ Di;E

"

Based on Fig. 2, the details of the unfolding fin are shown in Fig. 19. The half of the unfolding fin inside of the inner glass tube is selected due to symmetry.

(30)

RE ¼

Rw;C ¼

Fig. 19. The details of the unfolding fin.

r1 g cos qðr1  rv Þhfg k3l hC ¼ 0:943 ml ðTsat:C  Tw:C ÞLC

(35)

#0:25

where q is the incline angle for the SHTG

Fig. 20. Energy balance on the fin element.3

As shown in Fig. 20, the element balance on the fin element can be expressed as:

   SDx dT

 UL DxðT  Ta Þ þ  kfin d Ai dx x  

dT L   kfin d dx xþDx tube ¼0

(37)

The fin is directly connected with the inner glass tube of the evacuate tube. So the input thermal energy per unit of length due to solar energy is SDx/Ai. The corresponding output thermal energy per unit of length is ULDx (TTa).

Ai ¼ WLtube

(38)

W ¼ pDi

(39)

(36) (30


in this study).

Boundary conditions:

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Y.J. Dai et al. / Renewable Energy 92 (2016) 83e94

dT

¼0 dx x¼0

(40)

It is insulated when x ¼ 0 due to thermal symmetry.

Tjx¼W=2 ¼ Tb

[7]

(41)

The useful energy collected by fin can be expressed as:

QU ¼ F½S  UL Ai ðTb  Ta Þ F¼

[6]

[8] [9]

(42)

[10]

[11]

tanh½mW=2 mW=2

(43) [12]

The useful energy is transferred to the hot side of TEG. There exist two thermal resistances: one is the bond resistance, the other is the thermal resistance of the heat pipe. The useful energy can be expressed as:

QU ¼

Tb  Th Rb þ Rhp

(44)

[14]

[15]

Based on the Eq. (42) and Eq. (44), we can find that:

QU ¼ F 0 ½S  UL Ai ðTh  Ta Þ

[13]

(45)

[16] [17]

0

1=UL

"

F ¼ W

1 WFUL

#

(46)

þ kLb d þ Ltube Rhp

[18] [19]

fin

[20]

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