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Solar Energy 86 (2012) 1222–1231

A new dynamic test method for thermal performanceof all-glass evacuated solar air collectors

Li Xu a,b, Zhifeng Wang a,⇑, Guofeng Yuan a, Xing Li c, Yi Ruan c

a Key Laboratory of Solar Thermal Energy and Photovoltaic System of Chinese Academy of Sciences,

Institute of Electrical Engineering, Beijing 100190, Chinab Graduate University of the Chinese Academy of Sciences, Beijing 100049, China

c Himin Solar Energy Group Co., Ltd., Shandong 253000, China

Received 23 June 2011; received in revised form 14 November 2011; accepted 19 January 2012Available online 28 February 2012

Communicated by: Associate Editor Bibek Bandyopadhyay

Abstract

A new study on testing thermal performance of all-glass evacuated solar collectors with the air as heat transfer fluid under dynamicconditions outdoors has been developed. The model of this dynamic method was established with the energy balance analysis on solarcollectors of this type. Compared with the first order model under steady-state conditions, this model can characterize thermal efficiencyof solar collectors under more extensive conditions, reducing considerable operating time spent in waiting for the right test conditions.Through the derivation of the proposed model, it proved a strong relationship existed between this model and the first order model men-tioned above. The dynamic model projection for the outlet temperatures was in good agreement with the measured result.� 2012 Elsevier Ltd. All rights reserved.

Keywords: Solar air collector; Thermal performance; All-glass evacuated tube; Dynamic method

1. Introduction

A reliable and quick method to test thermal perfor-mance of solar collectors outdoors is needed by both solarcollector manufacturer and customer while the conven-tional steady state tests in standards such as the ASHRAE93-2003 (ASHRAE, 2003), EN 12579-2 (EN, 2006) andISO 9806-1 (ISO, 1994) commonly cost considerable timein terms of rigorous operational requirement, especiallyfor the test spots under unfavorable weather conditions.Several dynamic and quasi-dynamic methods have beenprovided to transcend limitations of steady state method.One paper (Fischer et al., 2004) presents an improvedapproach to outdoor performance testing of solar liquidcollectors under quasi-dynamic test conditions based on

0038-092X/$ - see front matter � 2012 Elsevier Ltd. All rights reserved.

doi:10.1016/j.solener.2012.01.015

⇑ Corresponding author. Tel.: +86 10 62520684; fax: +86 10 62587946.E-mail address: zhifeng@vip.sina.com (Z. Wang).

EN 12975-2 and compares three parameter identificationtools for it; A new procedure for testing solar flat plate col-lectors under unsteady weather conditions is developed andcompared with steady state ASHRAE 93 (Amer et al.,1999); Nine dynamic test methods for solar flat plate collec-tors are reviewed and compared based on both theoreticaland experimental evaluation (Nayak and Amer, 2000); Thepaper (Hou et al., 2005) provides a new method for mea-surement of solar collector time constant without adjustingthe inlet temperature to be equal to the ambient tempera-ture needed in ISO 9806-1; The uncertainties of the leastsquare and the weighted least square regression methodsin the quasi-dynamic according to EN 12975-2 are calcu-lated and validated (Kratzenberg et al., 2006).

However, these methods are based on flat-plate solar col-lector, while in China the tests for all-glass evacuated solarcollectors become more significant in view of the data thatthe production of all-glass evacuated tubes was estimated

Nomenclature

a1 algebraic constant, with reference to T� (W/(m2 K))

A algebraic constant, with reference to dTfo/ds (1/s))

Aa aperture area (m2)Aam heat loss area from glass tubes to the ambient

(m2)Ab effective aperture area for beam radiation (m2)Ad effective aperture area for diffuse irradiation

(m2)Af heat loss area from glass tubes to the fluid (m2)B algebraic constant, with reference to Tfo (K/s)cb specific heat capacity of the glass (J/(kg K))cf specific heat capacity of the air (J/(kg K))C algebraic constant, with reference to d Tfi/ds

(1/s)Cb thermal capacity of glass tubes (J/K)Cf thermal capacity of the air in glass tubes (J/K)D algebraic constant, with reference to Tfi (K/s)E algebraic constant, with reference to G

(J s/(K m2))Eb algebraic constant, with reference to Gb (J s/(K

m2))Ed algebraic constant, with reference to Gd

(J s/(K m2))F algebraic constant (K/s)FR collector heat removal factor (–)G global solar irradiance (W/m2)Gb beam irradiance (W/m2)Gd diffuse solar irradiance (W/m2)Khb(h) incident angle modifier for beam radiation (–)

Khd incident angle modifier for diffuse radiation (–)mb mass of glass (kg)mf mass of air in the tube (kg)_m mass flow rate of air (kg/s)Rbf overall heat transfer resistance from glass tubes

to the fluid (K/W)Rba overall heat transfer resistance from glass tubes

to the ambient (K/W)Ta ambient temperature (K)Tb glass tube temperature (K)Tf air temperature in the tube (K)Tfo collector outlet temperature (K)Tfo,initial temperature leaving collector at the beginning of

time constant test period (K)Tfo,t temperature of the heat transfer fluid leaving

collector at a specified time (K)Tfi collector inlet temperature (K)T� reduced temperature difference (m2 K/W)U overall heat loss coefficient of collector with ref-

erence to T� and Aa (W/(m2 K))Ubf overall heat loss coefficient from glass tubes to

the fluid (W/(m2 K))Uba overall heat loss coefficient from glass tubes to

the ambient (W/(m2 K))g collector thermal efficiency (–)g0 eta zero (g at T� = 0) (–)s time (s)(sa)en effective transmittance–absorptance product at

normal incidence (–)

L. Xu et al. / Solar Energy 86 (2012) 1222–1231 1223

to be more than 350 million tubes and this type solar collec-tor took an 95% share of the market in 2009 (Tang et al.,2011). Consequently, the efforts to make researches on all-glass evacuated solar collectors have been devoted in recentyears. For example, a simulation model and the transverseincidence angle modifier of the water-in-glass solar waterheater are presented (Budihardjo and Morrison, 2009);The comparative tests between flat plate and evacuated tubesolar collectors in stationary standard EN 12975-2 showthat only at low inlet temperature the output energy ofthe flat plate collector overcomes the one of evacuated tubecollector (Zambolin and Del Col, 2010); The thermal per-formance analysis on one single evacuated tube shows thesurface temperature of the absorbing coating is an impor-tant parameter (Ma et al., 2010).

For the areas where the solar irradiance is relativelypoor quality, the stringent requirements for solar sourcebeyond manual control make the days in a year reducedenormously for the reason that the thermal efficiency test,more often than not, is interrupted. The aim of this studyis to solve the problems caused by rigorous conditions

for testing the all-glass evacuated solar collectors in thesteady state method. Therefore, this dynamic method fortesting thermal efficiency of evacuated solar collectors out-doors is supposed to enlarge the test days in the whole yearby extending the range of solar irradiation limits.

Through the analysis on energy balance of all-glassevacuated solar air collector, this new dynamic method isproposed to effectively solve the difficulties brought aboutby severe operational limits for steady state test conditionsoutdoors, particularly due to uncontrollable weather con-ditions. For example, during one test period, the globalsolar irradiance is less than 790 W/m2 or varies more than±32 W/m2, or the diffuse solar irradiance is greater than20% of global solar irradiance. In these cases, the proposeddynamic method fills the role of characterizing thermal per-formance of solar collectors while the ASHRAE 93-2003does not work anymore, which saves actually operationaltime strikingly rather than expect the perfect weather.

Multiple linear regression (MLR) as the ordinary andconvenient math tool to identify parameters is applied tothe proposed dynamic model. Once these parameters for

Tf

Tb

GT

fi Tfo

(a)

Evacuated AreaInner Aluminum Tube

(b)

1224 L. Xu et al. / Solar Energy 86 (2012) 1222–1231

one type of solar air collector are obtained from the com-mon computer software of MLR, they can always beemployed to describe thermal performance of this typeunder different test conditions. Additionally, the time con-stant can be found in the predicted results obviously onaccount of the intrinsic thermal capability of a solar collec-tor, which means that the instantaneous change or shock inoperational conditions cannot take place in outlet temper-ature immediately.

Outer Glass Tube

Coated Inner Glass Tube

Fig. 2. All-glass evacuated solar air collector tube (a) schematic of oneevacuated tube (b) cross section of the tube.

2. Mathematical model

Before the establishment of mathematical model, thefollowing general assumptions will be made in the processof the energy balance analysis according to the heat trans-fer characteristics and the structural features of the all-glassevacuated solar air collector as shown in Fig. 1:

1. The tube-connection box of a solar collector is providedwith excellent insulation against its heat loss to thesurroundings.

2. The heat accumulation of inner aluminum tubes isignored.

3. The heat transfer processes among the different compo-nents of a solar collector are one dimensional.

4. The mass flowrate of the air through the collector shallbe standardized at one value within the variation of±2% for all data points.

5. During the test process, the incident angle shall be in thenear-normal incident range in which the incident anglemodifier varies by no more than ±2% from its value atnormal incidence by adjusting the rotating racket.

2.1. New dynamic model

Fig. 2 describes the input solar energy and output energyof one all-glass evacuated tube. In the new dynamic model,the global solar irradiance is separated into beam and dif-fuse portions in order to distinguish their influences onthermal performance of solar collectors. Additionally, theinner glass tube is assumed to own uniform temperature

Fig. 1. Schematic of all-glass evacuated solar air collector.

Tb. Thus, the energy balance equation for this glass tubeis expressed as

mbcbdT b

ds¼ F RðiaÞenKhbðhÞAaGb þ F RðiaÞenKhdAaGd

� Af Ubf ðT b � T f Þ � AamUbaðT b � T aÞ: ð1Þ

For the last term, the heat loss also includes the onefrom the outer glass tube to the ambient by converting itinto this form according to the relationship between outerand inner glass tube temperature (Liang et al., 2011), there-fore, the Uba is a coupled over heat loss coefficient.

Similarly, when the air in the glass tube is assumed toown uniform temperature Tf, the energy balance equationfor the air in glass tubes is expressed as

mf cfdT f

ds¼ Af U bf ðT b � T f Þ � _mcf ðT fo � T fiÞ: ð2Þ

According to the fifth assumption, Khb (h) and Khd

become constant. As a consequence, by definingFR(ia)enKhb(h)Aa = Ab and FR(ia)enKhdAa = Ad, and usingthe thermal resistance Rbf and Rba, Eqs. (1) and (2) aretreated to be simple mathematical expressions shown inEqs. (3) and (4), respectively.

CbdT b

ds¼ AbGb þ AdGd �

T b � T f

Rbf� T b � T a

Rbað3Þ

CfdT f

ds¼ T b � T f

Rbf� _mcf ðT fo � T fiÞ ð4Þ

Then, Eq. (4) is rearranged as

T b

Rbf¼ Cf

dT f

dsþ T f

Rbfþ _mcf ðT fo � T fiÞ: ð5Þ

Furthermore, Eq. (5) is differentiated with respect to s.

1

Rbf

dT b

ds¼ Cf

d2T f

ds2þ 1

Rbf

dT f

dsþ _mcf

dT fo

ds� dT fi

ds

� �ð6Þ

L. Xu et al. / Solar Energy 86 (2012) 1222–1231 1225

For the purpose of eliminating Tb in Eq. (3), Eqs. (5)and (6) are employed. Thus, the final combining expressionof the two energy balance equations is

CbCfd2T f

ds2þ CbRba þ Cf Rba þ Cf Rbf

Rbf Rba

dT f

dsþ T f

Rbf Rba

¼ AbGb þ AdGd

Rbf� Rba þ Rbf

Rbf Rba_mcf ðT fo � T fiÞ

� Cb _mcfdT fo

ds� dT fi

ds

� �þ T a

Rbf Rba: ð7Þ

When the outlet temperature Tfo is selected as the char-acteristic temperature of the air in the tube (Hou, 2005),Eq. (7) is changed into

1þ ðRbf þ RbaÞ _mcf

CbCf Rbf RbaT fo ¼ �

d2T fo

ds2

� 1þ _mcf Rbf

Cf Rbfþ Rbf þ Rba

CbRbf Rba

� �dT fo

ds

þ _mcf

Cf

dT fi

ds

þ ðRbf þ RbaÞ _mcf

CbCf Rbf RbaT fi

þ 1

CbCf Rbf RbaT a

þ Ab

CbCf RbfGb

þ Ad

CbCf RbfGd :

ð8Þ

As a consequence, the linear differential equation is

d2T fo

ds2þ A

dT fo

dsþ BT fo ¼ C

dT fi

dsþ DT fi þ EbGb þ EdGd

þ FT a: ð9Þ

Derived from Eq. (8), the coefficients are expressed inthe following equations.

A ¼ 1þ _mcf Rbf

Cf Rbfþ Rbf þ Rba

CbRbf Rbað10Þ

B ¼ 1þ ðRbf þ RbaÞ _mcf

CbCf Rbf Rbað11Þ

C ¼ _mcf

Cfð12Þ

D ¼ ðRbf þ RbaÞ _mcf

CbCf Rbf Rbað13Þ

Eb ¼Ab

CbCf Rbfð14Þ

Ed ¼Ad

CbCf Rbfð15Þ

F ¼ 1

CbCf Rbf Rbað16Þ

Obviously, D = B � F hence Eq. (9) is rearranged.

d2T fo

ds2þ A

dT fo

dsþ BðT fo � T fiÞ

¼ CdT fi

dsþ EbGb þ EdGd � F ðT fi � T aÞ ð17Þ

Eq. (17) is the basic dynamic mathematical model withthe parameters A, B, C, Eb, Ed and F, describing the ther-mal characteristics of the solar air collector, needed to beidentified with the experimental data.

2.2. Deduction of new model

The terms in Eq. (17), Tfo � Tfi and Tfi � Ta, indicatethat the new dynamic model has a special relationship withthe first order model recognized in steady state test for thethermal performance. Accordingly, the expression of Eq.(17) is rearranged again.

BðT fo � T fiÞ ¼ �d2T fo

ds2� A

dT fo

dsþ C

dT fi

dsþ EbGb

þ EdGd � F ðT fi � T aÞ ð18Þ

Mathematically, multiplying both sides of Eq. (18) bythe term

_mcf

BGAayields

_mcf

GAaðT fo�T fiÞ¼�

_mcf

BGAa

d2T fo

ds2þA

dT fo

ds�C

dT fi

ds

� �

þ _mcf

BGAaðEbGbþEdGdÞ�

_mcf

BGAaF ðT fi�T aÞ:

ð19ÞIn order to compare with the first order model in stan-

dards mentioned above, the global solar irradiance substi-tutes for beam irradiance and diffuse solar irradiance.

_mcf

GAaðT fo � T fiÞ ¼ �

_mcf

BGAa

d2T fo

ds2þ A

dT fo

ds� C

dT fi

ds

� �

þ E _mcf

BAa� F _mcf

BAa

ðT fi � T aÞG

ð20Þ

With the definitions in ISO 9806-1, the thermal efficiency

of a solar collector is expressed as g ¼ _mcf

GAaðT fo � T fiÞ and

reduced temperature difference as T � ¼ T fi�T a

G . As a conse-

quence, the thermal efficiency is given by

g ¼ � _mcf

BGAa

d2T fo

ds2þ A

dT fo

ds� C

dT fi

ds

� �þ E _mcf

BAa

� F _mcf

BAaT �: ð21Þ

On the assumption of ideal test conditions in the abso-lutely steady state, the inlet temperature is constant andthe output temperature keeps constant as well since allother influencing factors including solar irradianceand heat loss of the collector do not change, thereby the

1226 L. Xu et al. / Solar Energy 86 (2012) 1222–1231

differential terms in Eq. (18) disappear. In addition, by set-ting E _mcf =BAa ¼ g0 and F _mcf=BAa ¼ a1, Eq. (21) is finallyexpressed as

g ¼ g0 � a1T �: ð22Þ

Obviously, the deduction from Eqs. (17)–(22) provesthat a close relationship between the new model and thefirst order model exists although they are suitable for twodifferent test procedures.

2.3. Identification of model parameters

Both sides of Eq. (18) are divided by B and Gb so as tomake the new model turn into the standardized form ofmultiple linear equation.

T fo � T fi

Gb¼ Eb

B� 1

BGb

d2T fo

ds2� A

BGb

dT fo

dsþ C

BGb

dT fi

ds

þ EdGd

BGb� F

T fi � T a

BGbð23Þ

With the utilization of the basic numerical heat transfermethod, the terms dT 2

fo/ds2, dTfo/ds, and dTfi/ds are treatedwith the averaged-difference method. By choosing N

(N > 3) continuous recording points with the same timeinterval these differential terms become

d2T fo

ds2ðnÞ ¼ T foðnþ 1Þ þ T foðn� 1Þ � 2T foðnÞ

Ds2ð24Þ

dT fo

dsðnÞ ¼ T foðnþ 1Þ � T foðn� 1Þ

2Dsð25Þ

dT fi

dsðnÞ ¼ T fiðnþ 1Þ � T fiðn� 1Þ

2Dsð26Þ

where n = 2, . . .,N � 1.Consequently, with experimental data obtained from the

dynamic test procedure presented just below, the modelparameters in Eq. (23) will be identified by multiple linearregression tool.

3. Test procedure

In order to make a comparison between the steady statemethod and the dynamic one, the instrumentation andapparatus shown in Fig. 3 and Fig. 4 satisfy both therequirement of the steady state method mentioned in ASH-RAE 93-2003 and the needs for dynamic method such asdramatic variation in the air temperature at the collectorinlet.

3.1. Steady state test

According to the standard ASHRAE 93-2003, theinstantaneous thermal efficiency of a solar collector wascalculated as the ratio between the output power and theglobal solar irradiance as shown in Fig. 5. This standardrequires a minimum of 16 data points at four different inlet

temperatures to draw the thermal efficiency curve producedby using a least squares linear fit of the 16 data points.

For testing time constant of the solar air collector, aftersteady state conditions are achieved, the air collector isabruptly shielded from the sun light with an opaque cover.Then, the air temperatures at the inlet and outlet are con-tinuously monitored as a function of time until

T fo;t � T fi

T fo;initial � T fih0:30: ð27Þ

Time constant is the time t required for the quantity(Tfo,t � Tfi)/(Tfo,initial � Tfi) to change from 1.0 to 0.386.For the tested solar air collector, its time constant is465 s as shown in Fig. 6.

3.2. Dynamic test

The dynamic test procedure was implemented to obtainthe experiment data with two aims of the identification ofmodel parameters and the comparison with results calcu-lated from the regressed model. When the natural condi-tions did not cause fluctuations, the artificial adjustmentswere made to create some unsteady state conditions. Forexample, the inlet temperature varied sharply by control-ling the electrical heater, and solar irradiance abruptlybecame nearly zero through shielding the collector fromthe solar radiation. During all tests, the data were acquiredon 10-s intervals to capture transient conditions.

In case 1, as shown in Fig. 7 and Fig. 8, among this setof experimental data, there are five distinct periods catego-rized according to their impacts on testing the solar air col-lector. At the beginning, 10:30–10:57, it is suitable toperform the steady state test in the light of ASHRAE 93-2003. Unfortunately, from 10:58, albeit the global solarirradiance was at high value, all above 790 W/m2, the dif-fuse solar irradiance was greater than 20% of global solarirradiance, hence, the steady state conditions did not exitany more. Then, 11:48–12:13, as the electrical heater wasshut down, a sharp decrement in inlet temperature tookplace when the diffuse solar irradiance still constituted arelatively large percentage of the global solar irradiance.During the period from 12:14 to 13:17, the inlet tempera-ture was kept nearly constant again. At the last period,13:18–13:38, both of global solar irradiance and diffusesolar irradiance turned down expeditiously until Gd/Gwas close to 47%. In addition, the mass flow rate wasensured to be constant according to ASHRAE 93-2003 asshown in Fig. 9 by adjusting control valves. With thesemeasured data and the method to identify model parame-ters described above, Eq. (23) is regressed to

T fo � T fi ¼ 0:027Gb � 1:507d2T fo

ds2� 0:476

dT fo

ds

þ 2:561dT fi

dsþ 0:033Gd � 0:024ðT fi � T aÞ ð28Þ

Fig. 3. Schematic diagram of experimental set-up.

Fig. 4. Test facility of the solar air collector. 0.00 0.01 0.02 0.03 0.04 0.05 0.06

η=η0-U (tin-ta)/G

(tin-ta)/G (m2K/W)

Inst

anta

neou

s ef

ficie

ncy

η0=0.43

U=1.92 W/(m2K)

0.32

0.33

0.34

0.35

0.36

0.37

0.38

0.39

0.40

0.41

0.42

0.43

0.44

Fig. 5. Thermal efficiency curve of the solar air collector.

L. Xu et al. / Solar Energy 86 (2012) 1222–1231 1227

Case 2, as shown in Fig. 10, Fig. 11 and Fig. 12, is usedfor the comparison between the measured data and the pre-dicted ones calculated with Eq. (28). In reality, so perfectwere the weather conditions in Case 2 for the steady statetest in ASHRAE 93-2003, and also the mass flowrate ofthe air through the collector was controlled at one valuewithin the variation of ±2% during the whole period from11:42 to 13:30. However, at the time 13:10, the electricalheater was turned off immediately in order to producethe transient data in relation to the variation in inlettemperature.

Figs. 13–15 show the case 3, also applied to the com-parison, is composed of several diverse periods. Differentfrom both cases 1 and 2, the mass flow rate was no moreconstant since there was no manual control on it. Therelation between mass flow rate and the temperature, asshown in Figs. 14 and 15, illustrates that the approxi-mately ten percent deviation of mass flow rate from theinitial value was coincident with the variation in inlet tem-

0 200 400 600 800 1000 1200 1400 1600 1800

time (s)

t fo- t

fi ()

2

4

6

8

10

12

14

16

18

20

22

24

Fig. 6. Time constant of the solar air collector.

10:04 10:33 11:02 11:31 12:00 12:28 12:57 13:26 13:55150200250300350400450500550600650700750800850900950

1000

10:04 10:33 11:02 11:31 12:00 12:28 12:57 13:26 13:5515

20

25

30

35

40

45

50

G Gb Gd

Irrad

ianc

e (W

/m2 )

Gd/

G (%

)

Time

Fig. 7. Measured data for solar irradiance in Case 1.

10:04 10:33 11:02 11:31 12:00 12:28 12:57 13:26 13:55586062646668707274767880828486889092

10:04 10:33 11:02 11:31 12:00 12:28 12:57 13:26 13:55

16

17

18

19

20

21

22

Tfo Tfi

Tem

pera

ture

()

Tem

pera

ture

()

Ta

Time

Fig. 8. Measured data for ambient, inlet and outlet temperatures inCase 1.

10:04 10:33 11:02 11:31 12:00 12:28 12:57 13:26 13:55

Mas

s flo

wra

te (k

g/h)

170

171

172

173

174

175

176

177

178

Time

Fig. 9. Measured mass flow rate of the air through the solar collector inCase 1.

1228 L. Xu et al. / Solar Energy 86 (2012) 1222–1231

perature mainly because the density of the heated air fromabout 15 �C to 45 �C decreased and the power of induceddraft fan maintained almost constant. To start with,10:40–12:03, it was a steady state condition in view ofASHRAE 93-2003. In the subsequent period, throughturning on the electrical heater a severe rise in inlet tem-perature was followed with a relatively constant inlet tem-perature until the electrical heater was closed at 14:09,causing that a swift reduction in inlet temperature com-menced. During the period from 14:11 to the end, threestep changes in solar irradiance happened, with the resultthat both Gd and G equaled to near zero and the conse-

quent Gd/G was near 100% when the solar air collectorwas suddenly shaded with an opaque cover.

4. Results and discussion

The collector parameters obtained from test procedureCase 1 were presented in Eq. (28). As a consequence, thecalculation of the outlet temperature of the collector wasdone according to the inlet temperature, ambient tempera-

11:31 11:45 12:00 12:14 12:28 12:43 12:57 13:12 13:26 13:40100200300400500600700800900

10001100

11:31 11:45 12:00 12:14 12:28 12:43 12:57 13:12 13:26 13:4011.0

11.5

12.0

12.5

13.0

13.5

14.0

14.5

15.0

G Gb Gd

Irr

adia

nce

(W/m

2)

Gd/

G (%

)

Time

Fig. 10. Measured data for solar irradiance in Case 2.

11:31 11:45 12:00 12:14 12:28 12:43 12:57 13:12 13:26 13:40

50

60

70

80

90

11:31 11:45 12:00 12:14 12:28 12:43 12:57 13:12 13:26 13:4018.0

18.5

19.0

19.5

20.0

20.5

21.0

Tem

pera

ture

()

Tem

pera

ture

() Tfo

Tfi

Ta

Time

Fig. 11. Measured data for ambient, inlet and outlet temperatures inCase 2.

11:31 11:45 12:00 12:14 12:28 12:43 12:57 13:12 13:26 13:40

Time

Mas

s flo

wra

te (k

g/h)

170

171

172

173

174

175

176

177

Fig. 12. Measured mass flow rate of the air through the solar collector inCase 2.

10:48 12:00 13:12 14:24 15:36 16:48

10:48 12:00 13:12 14:24 15:36 16:48

0

20

40

60

80

100

G Gb Gd

Irrad

ianc

e (W

/m2 )

Time

Gd/

G (%

)

0

200

400

600

800

1000

1200

Fig. 13. Measured data for solar irradiance in Case 3.

L. Xu et al. / Solar Energy 86 (2012) 1222–1231 1229

ture, and solar irradiance. Subsequently, the output energyand the thermal efficiency of the collector throughout the

test period were computed with the predicted outlettemperature.

The iterative technique was employed to calculate thepredicted outlet temperature in order to get the differentialterms in Eq. (28) according to Eqs. (24)–(26), which meansthis process continued until the solution converged. Thesecalculated data needed to be smoothed for a better result.It was found that the measured outlet temperature laggedbehind the predicted one in Fig. 16a(1). From the peakof predicted data to that of the measured one, the timewas 460 s, which was quite close to the time tested constant

10:48 12:00 13:12 14:24 15:36 16:4810

20

30

40

50

60

70

80

10:48 12:00 13:12 14:24 15:36 16:4814

15

16

17

18

19

20

Tfo Tfi

Ta

Time

Tem

pera

ture

()

Tem

pera

ture

()

Fig. 14. Measured data for ambient, inlet and outlet temperatures in Case3.

10:48 12:00 13:12 14:24 15:36 16:48

Mas

s flo

wra

te (k

g/h)

Time

170

175

180

185

190

195

200

205

Fig. 15. Measured mass flow rate of the air through the solar collector inCase 3.

Out

let t

empe

ratu

re (

)O

utle

t tem

pera

ture

()

84

86

88

90

92

94

96

Time

Predicted Measured

11:31 11:45 12:00 12:14 12:28 12:43 12:57 13:12 13:26 13:40

10:48 12:00 13:12 14:24 15:36 16:48

20

30

40

50

60

70

80

Time

Predicted Measured

(a)

(b)

(c)

10:04 10:33 11:02 11:31 12:00 12:28 12:57 13:26 13:55

76

78

80

82

84

86

88

90

92

10:04 10:33 11:02 11:31 12:00 12:28 12:57 13:26 13:5578

80

82

84

86

88

90

92

Predicted Measured

Out

let t

empe

ratu

re(º

C)

(2)

(1)

Time

Out

let t

empe

ratu

re(º

C)

ig. 16. Comparison between predicted and measured outlet temperatures) Case 1, (b) Case 2 and (c) Case 3.

1230 L. Xu et al. / Solar Energy 86 (2012) 1222–1231

according to ASHRAE 93-2003 as shown in Fig. 6, hencethis gave a new way to understand the time constant of asolar collector. Moreover, when the whole predicted datawere moved backwards, namely a time-constant delay onpredicted outlet temperature, the two lines in Fig. 16a(2)almost coincided with each other.

In the light of the method of calculation detailed above,Cases 2 and 3 were treated to obtain the outlet temperatureas shown in Fig. 16b and c respectively. Accordingly, theresults from calculations of predicted and measured data

F(a

Table 1Comparison between predicted and measured calculations.

Case Test time(HH:MM)

Predicted output energy(kJ)

Measured output energy(kJ)

Solar energy(kJ)

Predicted efficiency(%)

Measured efficiency(%)

Error(%)

1 10:30–13:38 12,499 12,485 34,695 36.03 35.98 0.052 11:42–13:30 8352 8304 23,867 34.99 34.79 0.203 10:40–16:10 25,651 27,193 64,342 39.87 42.26 2.39

L. Xu et al. / Solar Energy 86 (2012) 1222–1231 1231

were listed in Table 1. It proved that the dynamic methodgave the accurate and reliable prediction for thermal per-formance of the solar air collectors. Although the resultin Case 3 was not as good as the case 2 due to unsteadymass flow rate during the whole test period, however, itshowed that this method gave the approximate outcomeenough to be applied to engineering projects.

5. Conclusions

A detailed study on the new dynamic method for testingthermal performance of solar air collectors based on thebasic theoretical knowledge of energy balance and theexperimental procedures. Through the mathematicaldeduction, the dynamic model was proved to have a closerelationship with the first order model in recognized stan-dards. Only simple mathematical tools such as MLR, iter-ation, and smooth were employed to predict outlettemperature, output energy and thermal efficiency of solarair collectors by means of measured data obtained readily.Without increasing any new measurement parameter, thenew method was suitable for the varying climate condi-tions. In comparison with the measured data and their cal-culating results, the minor errors, no more than 2.39%,mean that this method is reasonable and reliable. In addi-tion, another way to obtain the time constant was offeredthrough the same test procedure.

Consequently, less restriction in the test requirementssuggests this method offers more convenient and cheapertests, especially for places under unfavorable weather con-ditions. Additionally, this method is helpful for the design-ers to find out the output energy and thermal efficiency ofsolar air collectors according to the weather recourse.

Acknowledgment

This work has been supported by the National NaturalScience Foundation of China (No. 51106150) and Interna-tional S&T Cooperation Program of China (Grant No.

S2012ZR0139). Especially, we would like to thank LiXu’s Master Supervisor Prof. Haigeng Chen at Northeast-ern University, Shenyang, China for his positive guidance.

References

Amer, E.H., Nayak, J.K., et al., 1999. A new dynamic method for testingsolar flat-plate collectors under variable weather. Energy Conversionand Management 40 (8), 803–823.

ASHRAE 93-2003, 2003. Methods of Testing to Determine the ThermalPerformance of Solar Collectors.

Budihardjo, I., Morrison, G.L., 2009. Performance of water-in-glassevacuated tube solar water heaters. Solar Energy 83 (1), 49–56.

EN 12975-1, 2006. Thermal Solar Systems and Components – SolarCollectors – Part 1: General Requirements.

Fischer, S., Heidemann, W., et al., 2004. Collector test method underquasi-dynamic conditions according to the European Standard EN12975-2. Solar Energy 76 (1), 117–123.

Hou, H., 2005. Research on Dynamic Thermal Performance test Methodof Solar Collectors. PH.D. Thesis, Shanghai Jiao Tong University,Shanghai, China.

Hou, H.J., Wang, Z.F., et al., 2005. A new method for the measurement ofsolar collector time constant. Renewable Energy 30 (6), 855–865.

ISO 9806-1, 1994. Test Methods for Solar Collectors – Part 1: ThermalPerformance of Glazed Liquid Heating Collectors Including PressureDrop.

Kratzenberg, M.G., Beyer, H.G., et al., 2006. Uncertainty calculationapplied to different regression methods in the quasi-dynamic collectortest. Solar Energy 80 (11), 1453–1462.

Liang, R.B., Ma, L.D., et al., 2011. Theoretical and experimentalinvestigation of the filled-type evacuated tube solar collector with Utube. Solar Energy 85 (9), 1735–1744.

Ma, L.D., Lu, Z., et al., 2010. Thermal performance analysis of the glassevacuated tube solar collector with U-tube. Building and Environment45 (9), 1959–1967.

Nayak, J.K., Amer, E.H., 2000. Experimental and theoretical evaluationof dynamic test procedures for solar flat-plate collectors. Solar Energy69 (5), 377–401.

Tang, R., Yang, Y., et al., 2011. Comparative studies on thermalperformance of water-in-glass evacuated tube solar water heaters withdifferent collector tilt-angles. Solar Energy 85 (7), 1381–1389.

Zambolin, E., Del Col, D., 2010. Experimental analysis of thermalperformance of flat plate and evacuated tube solar collectors instationary standard and daily conditions. Solar Energy 84 (8), 1382–1396.