A proposed modified efficiency for thermosyphon solar heating systems

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A proposed modiﬁed eﬃciency for thermosyphon solar

heating systems

J.M. Chang

a,*

, J.S. Leu

a

, M.C. Shen

a

, B.J. Huang

b

a_{Department of Mechanical Engineering, Far East College, No. 49, Chung-Hwa Road, Hsin-Shih Town, Tainan County 744, Taiwan} b_{Department of Mechanical Engineering, National Taiwan University, Taipei 106, Taiwan}

Received 3 January 2003; received in revised form 18 December 2003; accepted 21 January 2004

Communicated by: Associate Editor Claudio Estrada-Gasca

Abstract

Conventionally, the overall performance rating of a thermosyphon solar water heater considers the thermal per-formance of the system during the energy-collecting phase and the system cooling loss during the cooling phase. However, this study suggests that the performance rating should also take the heat removal efficiency of the system during the system application phase into consideration. This study modifies the CNS 12557 B7276 test standard and employs a precise, on-line operation to derive the heat removal efficiency of a system. The thermal performance and heat removal efficiency of 12 systems with capacities in the range of 102–446 L are evaluated. An efficiency coefficient, g₀, is defined, which represents the synthesis of the characteristic thermal performance, g

s, and the characteristic heat

removal eﬃciency, g

R. The proposed modified efficiency coefficient is given by g0¼ gs gR, and represents the

quasi-overall performance of a solar heating system. The coeﬃcient provides an eﬀective measure of the amount of energy provided to the user from a system which collects and stores heat from solar radiation. According to prevailing reg-ulations in Taiwan, commercial solar heating products should have a value of g

s in excess of 0.5 in order to attract a

government subsidy. The proposed modified efficiency, g₀, is a more practical and representative indication of the actual thermal performance of a system, and accordingly, the present study suggests that the regulations should adopt a value of g₀P0:41 as the standard for qualification rather than the current criterion of g

sP0:5.

1. Introduction

It was suggested by Huang and Du (1991) that the overall performance rating of a thermosyphon solar water heater should include the thermal performance of the system during the energy-collecting phase and the system cooling loss during the cooling phase. As dis-cussed by Belessiotis and Mathioulakis (2002), Henden et al. (2002) and Kubler et al. (1988), the thermal per-formance of a system refers only to its perper-formance during the energy-collecting phase when solar radiation is incident upon the system collectors, i.e. it does not indicate the actual amount of useable energy that a user

will receive from the system. This amount of energy is determined by the mixing effects of the hot water in the storage tank and the cool charge water which flows into the storage tank during the system application phase. Knudsen (2002) investigated the influence of the storage tank volume upon the thermal performance of SDHW systems. His study emphasized the importance of system utilization from the consumer’s point of view, and established a relationship between the energy consumed by the user and the volume of the storage tank. How-ever, the heat removal efficiency of the storage tank during the hot water draw-off phase or the system application phase was not considered.

The heat removal eﬃciency of a system during its application phase is an important consideration when assessing the overall thermal performance of that system since it enables the direct evaluation of the energy which

*

Corresponding author. Fax: +886-6-5977921. E-mail address:[email protected](J.M. Chang).

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will be made available to the user. Various forms of draw-off tests exist which relate specifically to storage tanks. These include, but are not restricted to, ANSI/ ASRAE 94.2-1981 (1981), CNS 12557 B7276 (1989), DD ENV 12977-3 (2001) and JIS A 1426 (1995). How-ever, these test standards are inappropriate for ther-mosyphon solar water heaters with evacuated tube collectors or a number of flat-plate collectors because the volumes of such systems are far higher than the volumes of traditional storage tanks. Moreover, in Taiwan, thermosyphon solar water heaters typically comprise of one or two evacuated tube collectors, each with a volume of between 18 and 48 L. Furthermore, each of these collectors contains between 12 and 48 evacuated tubes plunged into the body of the storage tank, where each individual tube has a volume of be-tween 1.0 and 1.5 L. Therefore, it is difficult to perform a physical heat removal efficiency test on the storage tank in isolation since this would require the removal of the evacuated tubes, which would then leave many holes in the body of the storage tank.

To overcome these difficulties, the current study modifies the CNS test standard (1989) and uses an on-line operation (Chang, 2002) to conduct a heat removal efficiency test of the complete system including the storage tank and the collectors. An efficiency coefficient, g₀, is defined, which indicates the amount of energy made available to a user by a thermosyphon solar water heating system, and represents the synthesis of the

heating system’s thermal performance and its heat re-moval eﬃciency. In Taiwan, regulations state that pur-chasers of commercial solar heating systems with a thermal performance, g

s, in excess of 0.5 are eligible for

a government subsidy. However, the current study sug-gests that the proposed modified efficiency, g₀, provides a better evaluation of the practical performance of such systems than this thermal performance coefficient, and accordingly, proposes that the subsidy regulations should be re-specified in terms of g₀.

2. Experimental method

In order to obtain the modified efficiency of a system, this study first determines its thermal performance dur-ing the energy-collection phase and then assesses its heat removal efficiency during the application phase.

The test conditions to be established when deter-mining the thermal performance for a thermosyphon system were speciﬁed by Chang et al. (2003) as follows:

1. Ri should lie in the range 0:5 6 Ri61:6.

2. The daily eﬃciency test should extend for a period of 9 h, with symmetry about the solar noontime. 3. The total daily solar radiation should be HtP7 MJ/

m2_.

4. The daily mean wind speed during the period of the test should be vw63 m/s.

Nomenclature

Ac collector area, m2

Cp speciﬁc heat with constant pressure

condi-tion, kJ/(kg K)

Ht daily total irradiation upon collector slope,

MJ/(m2_day)

M total mass of water in a solar thermosyphon system, kg

_

md discharge ﬂow rate of storage tanks of a

system, L/min

Qu useful heat which users obtain from a system

in Eq. (4), kJ

Qt total heat which is collected in the storage

tank of a system by a collector in Eq. (5), kJ Ri a distribution factor of solar irradiation,

dimensionless

tf the time required to renovate one storage

volume by the given ﬂow rate, min Ta ambient temperature,°C

Ta mean ambient temperature,°C

Te discharge water temperature,°C

Ti initial mean tank temperature,°C

Tw cool charge water temperature,°C

Tw cool mean charge water temperature,°C

t95 student’s t statistic based on 95% coverage

Us coeﬃcient of overall system loss rate, MJ/

(m2_{K day)}

Vt volume of a system, L

vw daily mean wind speed during testing, m/s

Zxy correlation coeﬃcient of test data based on

regression analysis, dimensionless qw density of water, kg/m3

g₀ modiﬁed eﬃciency of a system, dimension-less

g_R heat removal eﬃciency of a system in Eq. (3), dimensionless

g

R characteristic heat removal eﬃciency of a

system in Eq. (9), dimensionless

gs daily system eﬃciency in Eq. (1),

dimen-sionless g

s system characteristic eﬃciency in Eq. (2),

dimensionless

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5. The range of operational parameters should be 0 6ðTi TaÞ=Ht62:5.

6. A minimum of 10 test points, each of which satisﬁes the above conditions, must be taken.

Huang and Du (1991) developed the daily system eﬃciency model shown below in Eq. (1), where a0

rep-resents the daily system eﬃciency for the case where the initial mean tank temperature Ti equals the mean

ambient temperature, Ta, and Us is the energy loss

coeﬃcient in the energy-collecting phase. The parame-ters a0 and Us are determined from a linear regression

analysis of Eq. (1). As shown in Eq. (2), the test results of a0 may be extrapolated to a point with a speciﬁed

M =Ac value. In his study of 1993, Huang ﬁrst deﬁned,

and then veriﬁed, the thermal performance, g s, as the

value of a0corrected at M=Ac¼ 75 kg/m2

gs¼ qnet Ht ¼ a0 Us Ti Ta Ht ð1Þ g_s ¼ a0jM =Ac¼75 ð2Þ

In accordance with the guidelines put forward by Chang (2002), the present research modified a CNS test standard (1989) and used an on-line operation to obtain the heat removal efficiency of the system. The configu-ration of the experimental apparatus adopted in the current study is shown in Fig. 1. A pump is employed to draw off hot water at the outlet of the system at a rate governed by a downstream flow meter. The combined pump and flow meter arrangement facilitates a simple simulation of the typical hot water flow rates that occur in practice when a user draws off water from the system. It is also noted that a second flow meter is installed at the system inlet. For each testing, the flow meters at the inlet and outlet sides of the system enable the charge and discharge flow rates which are the same during the

period of testing for general systems, and which are different during the period of testing for special systems with the regulation of the charge flow. The measure-ments of the discharge flow temperature, Te, the charge

ﬂow temperature, Tw, and the initial mean tank

tem-perature, Ti in Fig. 1 are used to calculate the heat

re-moval eﬃciency of the system.

The heat removal eﬃciency, g_R, is shown in Eq. (3), and is deﬁned as the ratio of the useful heat, Qu, to the

total heat, Qt, where the useful heat represents the heat

obtained from the system by the user, and the total heat indicates the heat which is accumulated by the system collectors from the solar radiation and then stored in the storage tank gR¼ Qu Qt ð3Þ where Qu¼ Z tf 0 _ mdqwCp½TeðtÞ TwðtÞ dt ð4Þ Qt¼ qwVtCpðTi TwÞ ð5Þ tf¼ Vt= _md ð6Þ Tw¼ Rtf 0 TwðtÞ dt tf ð7Þ g_R¼ Rtf 0ðTeðtÞ TwðtÞÞ dt Rtf 0ðTi TwðtÞÞ dt ð8Þ

In practice, Qu is always less than Qt because the

mixing of the cool charge water into a system with the hot water already within the system causes a portion of the total heat to remain within the system when the user draws oﬀ water from the tank. Hence, from Eq. (3) it can be seen that the heat removal eﬃciency, g_R, must always be less than 1. In Eq. (7), the parameter tf

de-notes the time required to renovate one storage volume by the given ﬂow rate during testing of the heat removal eﬃciency, while Tw represents the mean charge water

temperature at the inlet of the system during time tf. Eq.

(8) gives the heat removal eﬃciency of the system. It is noted that this equation represents the collation of Eqs. (3)–(7), and that it is expressed in terms of Te, Twand Ti.

The present study investigates the modified efficiency of the 12 different systems described in Table 1. Of these 12 systems, eight are of the flat-plate collector type with volumes of between 120 and 381 L, while the remainder incorporate one or two evacuated tube collectors and have volumes in the range 102–442 L. To carry out this investigation, CNS12557 B7276 (1989) is modified and an on-line operation of a complete system is used with the following test conditions:

Fig. 1. Conﬁguration of testing system used to evaluate the heat removal eﬃciency of thermosyphon systems.

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1. Mean radiation intensity is less than 100 W/m2_.

2. Mean ambient temperature range is 10 6 Ta635°C.

3. Gage pressure of cool water charge ﬂow at the inlet of a system is Pi60:3 atm.

4. Range of operational parameters is 0 6ðTi TwÞ=

_ md66:0.

5. At least 10 test points that satisfy the above testing conditions are taken.

Regarding the fourth condition above, the empirical model of the heat removal eﬃciency, g_R, is in the form of the logarithmic curve gR¼ a lnððTi TwÞ= _mdÞ þ b

established by Chang (2002). It is found that the value of gR remains constant other than within the interval of

1:0 6ðTi TwÞ= _md63:0, and that gR maintains a

vir-tually constant value as the value ofðTi TwÞ= _mdvaries

from 3.0 to 6.0. Hence, the characteristic heat removal eﬃciency, g

R, shown in Eq. (9) below, is deﬁned as the

value of gRatðTi TwÞ= _md¼ 2:0, i.e. the mean value in

the range of 1:0 6ðTi TwÞ= _md63:0

g

R¼ gRjðTiTwÞ= _md¼2:0 ð9Þ

The heat removal eﬃciency of each thermosyphon system in Table 1 is determined via the following pro-cedure: (1) determine the initial mean tank temperature, Tiwith the mixing of thermal stratiﬁcation in the storage

tank of a system, (2) establish a specific discharge flow rate of hot water in the range of 5–15 L/min, (3) use a PC-based data acquisition system to collect data relating to the charge flow temperature, Tw, and the discharge

ﬂow temperature, Te, once a minute during the testing

period, (4) use Eq. (8) to calculate the heat removal eﬃciency, g_R, as one system volume is discharged in a time interval of tf, (5) repeat steps 1–4 with diﬀerent

discharge ﬂow rates, _md, and temperature diﬀerences,

Ti Tw, until a minimum of 10 experimental results for

the heat removal eﬃciency have been obtained in order to construct an empirical model of the heat removal

efficiency, and (6) find characteristic heat removal effi-ciency, g

R, with the empirical model of heat removal

eﬃciency,

gR¼ a lnððTi TwÞ= _mdÞ þ b; at gR ¼ gRjðTiTwÞ= _md¼2:0

The resistance temperature detectors (RTD), preci-sion spectral pyranometers, wind speed meters and flow meters used for collecting data in the current test con-figuration were well calibrated by their respective stan-dard instruments. Table 3 presents the results of an uncertainty analysis of the various experimental mea-surements involved in determining the modified effi-ciency. The calculation of the uncertainty of a single parameter is based on the root-sum-square model pro-posed by Hayward (1977) with a 95% confidence inter-val. Meanwhile, the calculation of the combined uncertainty of several independent parameters is based on the root-sum-square model presented by Abernethy et al. (1983) with a 95% confidence intervalðt95¼ 2:0Þ, a

relative sensitivity factor of 1.0 for g

s, and a relative

sensitivity factor of 1.4 for g

R. The uncertainty of the

modified efficiency established in the present study is 11.8%, where the uncertainty of the thermal perfor-mance is 5.4% and the uncertainty of the characteristic heat removal efficiency is 6.4%.

3. Experimental results and veriﬁcation

In determining the modified efficiency of the ther-mosyphon solar heating system, this study first tested its thermal performance and its heat removal efficiency.

3.1. Test results and veriﬁcation of thermal performance

The thermal performance of 12 systems was tested in this study. The daily eﬃciencies of systems A, B, C and D are shown in Figs. 2–5, respectively. Applying linear Table 1

Details of the 12 systems used in the current evaluation of the criterion of modiﬁed eﬃciency

No. Systems Collector types of systems (collector area, m2₎ _{Types of storage tank} _{Volume of storage tank (L)}

1 A 48 Evacuated tubes (3.64) Closed, horizontal 442

2 B 2 Flat plates (3.8) Closed, horizontal 294

3 C 2 Flat plates (3.71) Closed, horizontal 287

4 D 1 Flat plates (1.89) Closed, horizontal 120

5 E 12 Evacuated tubes (1.36) Closed, horizontal 102

6 F 48 Evacuated tubes (3.64) Closed, horizontal 416

7 G 3 Flat plates (4.28) Open, horizontal 381

8 H 3 Flat plates (5.62) Open, horizontal 363

9 I 2 Flat plates (3.73) Open, horizontal 306

10 J 32 Evacuated tubes (2.42) Closed, inclined at 13°

to the horizontal

300

11 K 2 Flat plates (3.8) Closed, horizontal 297

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regression analysis to these results yields values which enable the calculation of the thermal performance of these systems. The results for g

spresented in Table 2 for

systems A, B, C and D indicate thermal performances of 0.604, 0.543, 0.532 and 0.462 respectively. The overall mean value of the system characteristic efficiency of the 12 systems is found to be 0.54. It is noted that the mean value of the system characteristic efficiency for the eight systems with flat-plate collectors is 0.51 and the mean value of the four systems with evacuated tube collectors is 0.59. Furthermore, Table 2 indicates that the data correlation for the thermal performance of the 12 sys-tems is very high, i.e. in the range of 0.945–0.993. The present results suggest that the criterion of thermal performance, g

s, used currently in subsidy regulations

should adopt a value of g

sP0:51 rather than the

pres-ent value of g

sP0:5, which was determined from a CNS

test standard (1989) 14 years ago. Note that the 2% in-crease in the thermal performance of the commercial systems indicates an improvement in the quality of such systems since that time.

3.2. Test results and veriﬁcation of heat removal eﬃciency

On-line operation of each of the 12 flat-plate collec-tor or evacuated tube colleccollec-tor systems presented in Table 1 was performed in order to evaluate the heat removal efficiency of each system. During the testing stage, discharge rates at the outlet of the storage tank were established in the range of 5–15 L/min to reflect the flow rates which typically occur in practical thermosy-phon solar heating system applications. The test results for the heat removal efficiency of systems A, B, C and D are presented in Figs. 6–9, respectively. The results re-veal that the heat removal efficiency of the system de-creases as the discharge flow rate inde-creases. This observation may be explained by considering the

0 0.5 1 1.5 2 2.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

number of screened data = 14 Vt = 442 kg; Ac = 3.643m2 Vt / Ac =121.33 kg/m2 t a i s=0.635−0.104(T−T)/H η ; 604 . 0 *₌ s η Daily efficiency ηs 987 . 0 = xy Z , / ) (Ti−Ta Ht K m 2 day/MJ

Fig. 2. Daily eﬃciency test results of system A with g s¼ 0:604. 0 0.5 1 1.5 2 2.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Vt = 294 kg; Ac = 3.802m Vt / Ac =77.33 kg/m t a i s=0.545−0.142(T−T)/H η ; 543 . 0 *₌ s η

number of screened data = 10

Daily efficiency ηs 2 2 991 . 0 = xy Z , / ) (Ti−Ta Ht K m 2_day/MJ

Fig. 3. Daily eﬃciency test results of system B with g s¼ 0:543. 0 0.5 1 1.5 2 2.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Vt = 287 kg; Ac = 3.705m Vt / Ac =77.544 kg/m t a i s=0.535−0.152(T−T)/H η ; 532 . 0 *₌ s η

Daily efficiency s 2 2 988 . 0 = xy Z , / ) (Ti−Ta Ht K m 2 day/MJ η

Fig. 4. Daily eﬃciency test results of system C with g s¼ 0:532. 0 0.5 1 1.5 2 2.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Vt = 120 kg; Ac = 1. 892m Vt / Ac =63. 155 k g/m t a i s=0.448−0.143(T−T)/H η ; 462 . 0 *₌ s η

Daily efficiency ηs 2 2 991 . 0 = xy Z , / ) (Ti−Ta Ht K m 2 day/MJ

Fig. 5. Daily eﬃciency test results of system D with g s¼ 0:462.

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thermal stratification within the storage tank which is formed by the cool charge water flowing into the system and the hot water which is already present in the system. During testing, this stratification is easily destroyed when the discharge flow rate is sufficiently high to induce strong water jets to enter the storage tank (Shah et al., 2001). Furthermore, it is noted that the heat removal efficiency increases with an increasing temperature dif-ference, Ti Tw. This trend is the result of a strong

thermal stratification effect for higher values of the temperature difference. Accordingly, Chang (2002)

de-ﬁned a new integral variable,ðTi TwÞ= _md, as an

oper-ational parameter to construct an empirical model of the heat removal eﬃciency, which had the form of a loga-rithmic curve.

From Table 2, it can be seen that the mean value of the heat removal efficiency for the 12 systems is 0.8, and that the data correlation coefficient is in the high range of 0.889–0.967. Therefore, the current experimental re-sults suggest that the criterion of heat removal efficiency, g

R, should adopt a value of gRP0:8. 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 6

Heat removal efficiency

, / ) (Ti Tw md • • − K.min.Liter ηR 79 . 0 ) / ) (( 062 . 0 − + = i w d R Ln T T m η 833 . 0 *₌ R η , Zxy=0.952, Vt=442 L

Fig. 6. Heat removal eﬃciency for system A with g R¼ 0:833. 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 6

η R 738 . 0 ) / ) (( 089 . 0 − + = i w •d R Ln T T m η 8 . 0 * ₌ R η , Zxy=0.928, Vt=294 L , / ) (Ti Tw md • − K.min./Liter

Fig. 7. Heat removal eﬃciency for system B with g R¼ 0:8. Table 2

Details of the thermal performance, characteristic heat removal efficiency and modified efficiency of the 12 systems

No. Systems System characteristic efficiency Characteristic heat removal efficiency Modified efficiency g0¼ gs gR g s Correlation coefficient Zxy g R Correlation coefficient Zxy 1 A 0.604 0.987 0.833 0.952 0.503 2 B 0.543 0.991 0.8 0.928 0.434 3 C 0.532 0.988 0.846 0.939 0.45 4 D 0.462 0.991 0.723 0.906 0.334 5 E 0.525 0.983 0.689 0.901 0.362 6 F 0.623 0.993 0.811 0.913 0.505 7 G 0.502 0.976 0.885 0.926 0.444 8 H 0.513 0.963 0.869 0.904 0.446 9 I 0.504 0.976 0.784 0.901 0.395 10 J 0.601 0.983 0.841 0.889 0.505 11 K 0.514 0.945 0.8 0.928 0.411 12 L 0.533 0.99 0.748 0.967 0.399 Range 0.462–0.623 0.945–0.993 0.689–0.885 0.889–0.967 0.334–0.505

Mean value 0.54, including ﬂat plate: 0.51; evacuated tube: 0.59 0.98 0.80 0.921 0.43, including ﬂat plate: 0.41; evacu-ated tube: 0.47

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3.3. Development of the criterion of modiﬁed eﬃciency

The characteristic thermal performance, g

s, and the

characteristic heat removal eﬃciency, g

R, of each of the

12 systems are presented in Table 2. The modified effi-ciency, g₀, proposed in the current study combines the thermal performance and the heat removal efficiency in the form g₀¼ g

s gR. The modiﬁed eﬃciency, g0,

rep-resents the quasi-overall performance of a system during its energy-collecting phase and system application phase. With a daily total radiation, Ht, upon the collector slope

of a system, g0 is an eﬀective means of evaluating the

amount of energy provided to a user from the solar radiation.

The modified efficiency of each of the 12 systems is shown in Table 2. The mean value of the modified

effi-ciency is shown to be 0.43, where the mean value of modified efficiency for the eight systems with flat-plate collectors is 0.41 and that of the four systems with evacuated tube collectors is 0.47. Therefore, the experi-mental results suggest that the criterion of modified efficiency, g₀, should be g₀P0:41. Furthermore, the mean value of 0.43 for the modified efficiency of the 12 systems indicates that users of domestic thermosyphon solar heating systems receive an average of 43% of the total solar energy, Ht, incident on the collectors of the

system.

4. Discussion

Heat loss in the storage tank of a system occurs if the value of the heat removal efficiency, g_R, is less than 1.0. There are two principal origins of heat loss during the testing process: (1) the thermal stratification of the cool charge water and the hot water in the system is de-stroyed by the cool charge water flow due to a poor storage tank design, and (2) the thickness of the storage tank insulation is insufficient to prevent heat from leaking out of the system. These two situations are also responsible for system cooling loss during the cooling stage of the application phase. Hence, the modified efficiency, g0, which is based on the characteristic heat

removal eﬃciency, g

R, for the application phase and the

cooling phase, and on the system characteristic eﬃ-ciency, g

s, for the energy-collecting phase represents the

quasi-overall performance of a system in a practical implementation. Moreover, the criterion of modified efficiency, i.e. g₀P0:41, which is established in the present study is credible because all of the experimental data relating to the testing of thermal performance and heat removal efficiency have been verified with a high data correlation coefficient in the range of 0.889–0.993 (as shown in Table 2) and with a reasonable uncertainty of 11.8% (as shown in Table 3).

Table 4 presents a comparison of the testing methods used to evaluate the thermal performance and heat re-moval efficiency in the current study with those adopted previously by other test standards. Regarding the testing of the thermal performance, it is noted that the current test results are virtually the same as those obtained from ISO 9459-2 (1995) under a test error of 9%. This simi-larity is explained by the fact that the testing conditions employed in both cases are the same other than the test time period and the wind speed limit. In the current study, the test time period was modified from the test time period specified in ISO 9459-2 (1995), i.e. from 6:00 AM to 6:00 PM. It was found that the test results for the thermal performance are unchanged if the coefficient of heat loss during the cooling phase (Huang and Du, 1991) does not exceed 2.5 W/°C. If this condition is not achieved, it is determined that the value of thermal

0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 6

ηR 788 . 0 ) / ) (( 083 . 0 − + = i w d R Ln T T m η 846 . 0 *₌ R η , Zxy=0.939, Vt=287 L , / ) (Ti Tw md

·

− K·min./Liter

Fig. 8. Heat removal eﬃciency for system C with g R¼ 0:846. 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 6

ηR 69 . 0 ) / ) (( 048 . 0 − + = i w •d R Ln T T m η 723 . 0 * ₌ R η , Zxy=0.906, Vt=120 L , / ) (T_i T_w md • − K.min./Liter

Fig. 9. Heat removal eﬃciency for system D with g R¼ 0:723.

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performance derived from ISO 9459-2 (1995) is 9% lower than the result obtained from the current study. The ISO 9459-2 (1995) standard speciﬁed a wind speed of vwP3 m/s. However, this is inappropriate for the

prevailing climate conditions in Taiwan, where wind speeds rarely exceed 3 m/s. In practice, the test time period and wind speed conditions specified in ISO 9459-2 should be modified to reflect the local climate within which the thermosyphon solar heating system is

situ-ated. Failing that, testing of the thermal performance could be performed from early morning to night, which conforms to the test time period speciﬁed in ISO 9459-2 (1995), and over an extended period of several months in order to maximize the possibility of collecting data, which conforms to the wind speed condition of vwP3

m/s. Regarding the testing of heat removal eﬃciency, no test methods exist to deal with a system which incor-porates evacuated tube collectors other than the test Table 3

Uncertainty analysis of experimental measurements for modiﬁed eﬃciency

Parameter Thermal performance

g

s¼ f ðTi TaÞ=Ht; vw

Characteristic heat removal eﬃciency

g R¼ f ðTi TwÞ= _md Modified efficiency g0¼ gs gR Accuracy error (%) Precision error (%) Uncertainty (%) Accuracy error (%) Precision error (%) Uncer-tainty(%) Temperature difference ±0.2 ±4.0 ±4.0 ±0.2 ±4.0 ±4.0 Solar irradiation intensity ±1.5 ±2.5 ±2.9 Wind speed ±2.0 ±1.0 ±2.2 Flow rate ±1.0 ±2.0 ±2.2 Total uncertainty ±5.4% ±6.4% ±11.8%

Note that the uncertainty of the modified efficiency established in the present study is 11.8%, where the uncertainty of the thermal performance is 5.4% and the uncertainty of the characteristic heat removal efficiency is 6.4%.

Notes: 1. The calculation of uncertainty of one parameter is based on the familiar root-sum-square model (Hayward, 1977) with the 95% conﬁdence interval. 2. The calculation of uncertainty of several independent parameters into a result is based on the familiar root-sum-square model (Abernethy et al., 1983) with the 95% conﬁdence intervalðt95¼ 2:0Þ, a relative sensitivity factor of 1.0 calculated for g

s and a relative sensitivity factor of 1.4 calculated for gR.

Table 4

Comparison of current test method with other test standards Test

conditions

The test method for thermal performance

The test method for heat removal eﬃciency

ISO 9459-2 Testing of this study ANSI/AS-RAE 94.2-1981 CNS B7276 DD ENV 12977-3 JIS A 1426 Testing of this study Total daily solar irradiation HtP8 MJ/ (m2_day) HtP7 MJ/ (m2_day) Test method for storage tanks only Test method for storage tanks only Test method for storage tanks only Test method for storage tanks only Test method with an on-line system operation for a whole sys-tem includ-ing storage tanks and collectors Range of operational parameters 0:2 6 ðTi TaÞ= Ht62:5 0 6ðTi TaÞ= Ht62:5 Test points Six points at least Ten points at

least Test time period 12 h from 6:00 AM to 6:00 PM 9 h from 7:30 AM to 4:30 PM Daily mean wind speed vwP3 m/s vw63 m/s A distribution factor of solar irradiation, Ri No 0:5 6 Ri61:6

Regarding the testing of the thermal performance, it is noted that the current test results are virtually the same as those obtained from ISO 9459-2 (1995) under a test error of 9%.

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method using an on-line system operation presented in this study. Moreover, the testing procedure of heat re-moval efficiency in the study is different from those of other test methods because the empirical model created in this study results in the difference of operational parameters and the on-line system operation presented in this study results in the difference of required test time.

5. Conclusions

The present study has evaluated the thermal perfor-mance and heat removal efficiency of 12 different types of thermosyphon solar water heating systems. A modi-fied efficiency coefficient, g0, has been defined in the form

of g0¼ gs gR, and represents the practical

quasi-overall performance of a system over the application phase, the cooling phase and the energy-collecting phase. The present results have suggested a criterion of modiﬁed eﬃciency of g0P0:41. Current regulations in

Taiwan stipulate that commercial thermosyphon solar heating systems should demonstrate a thermal eﬃciency, g

s, in excess of 0.5 in order to qualify for government

subsidy. However, based upon the experimental results presented in this study, it is the current authors’ belief that the proposed modified efficiency, g₀, provides a more representative measure of the performance of such systems. Accordingly, it is proposed that the criterion of modified efficiency, g0P0:41, should be adopted as the

standard for qualiﬁcation in this regulation.

Acknowledgements

The authors wish to acknowledge the support pro-vided to this study by the Energy Commission, Ministry of Economic Aﬀairs in Taiwan under contract nos. NEC 89-A, NEC 90-A and NEC 91-A.

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