Performance evaluation method of solar-assisted
heat pump water heater
B.J. Huang
*, C.P. Lee
Department of Mechanical Engineering, National Taiwan University, Taipei 106, Taiwan
Received 18 April 2006; accepted 1 June 2006 Available online 4 August 2006
Abstract
The present study derives a simple linear correlation for the performance evaluation of different solar-assisted heat pump water heater (ISAHP). The correlation was derived from the principle of energy conservation with some simplifications. The correlation is then ver-ified using the long-term outdoor field test data of four different ISAHP. The problems of seasonal repeatability and method of data scattering were examined. From that, a standard performance test method is proposed. The test method suggests that only the measure-ment of instantaneous solar incident radiation on horizontal surface, ambient temperature, hot water temperature in the storage tank, total mass of water in the storage tank and total power input to the ISAHP are required. It is suggested to select the value of COP at Tf Ta,ave= 15°C as the characteristic COP for performance comparison of ISAHP. It is found from the test results that the same
per-formance correlation holds for ISAHP operating with single or dual energy source. Ó 2006 Elsevier Ltd. All rights reserved.
Keywords: Heat pump; Solar-assisted heat pump; Solar energy
1. Introduction
National Taiwan University has been devoted to the development of integral-type solar assisted heat pump water heater (ISAHP) since 1999. Several types of ISAHP with different structures were designed and tested. Some of them are commercialized as a domestic hot water heater (Fig. 1).
The ISAHP consists of a Rankine refrigeration cycle coupled with a solar collector that acts as an evaporator. The refrigerant is expanded inside the evaporator to absorb the ambient or solar energy. By a proper design of the Ran-kine refrigeration cycle (heat pump) and the collector for a specific operating condition, heat may be absorbed from, rather than rejected to, the ambient. That is, ISAHP can absorb heat from solar radiation and ambient air simulta-neously. ISAHP integrates the heat pump, solar collector and water storage tank together to come up with a single
unit that is easy to install. Huang and Chyng[1]first
pro-posed the design of an integral-type solar-assisted heat
pump water heater. Huang and Chyng[2]further studied
experimentally the instantaneous performance
characteris-tics of an ISAHP. Chyng et al.[3]also developed a method
of analysis for ISAHP. From the long-term test result,
Huang and Lee [4] found that the thermal performance
of an ISAHP varies with weather conditions.
ISAHP is now accepted in commercial market as a domestic water heater. How to evaluate the performance of different ISAHP using a commonly-trusted method becomes a problem to be resolved. The development of a test standard for ISAHP is thus very important.
Ito et al.[7]showed that the evaporator temperature and
the condenser temperature both influenced the COP and the compressor power, and he derived the correlation
between them. Hawlader et al.[8]found the COP of a solar
assisted heat pump decreased when the water temperature increased, and efficiency of the solar collector evaporator
also decreased. Morrison et al. [9]also indicated that the
instant COP of the air-source heat pump could be
1359-4311/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2006.06.005
*
Corresponding author. Tel.: +886 223 634 790; fax: +886 223 640 549. E-mail address:[email protected](B.J. Huang).
correlated in terms of the difference between the water tem-perature and the ambient temtem-perature. Although the daily overall coefficient of performance (COP) can be a perfor-mance index for an ISAHP, many factors may cause COP to vary. Both the ambient air temperature and solar radiation will affect the performance of ISAHP. The tem-perature of water inside the ISAHP changes hour by hour
and its initial temperature (make-up city water tempera-ture) varies season by season. Water temperature is another factor that affects the performance.
The present study intends to derive a long-term perfor-mance correlation using the outdoor test results collected from several types of ISAHP. From that, a performance test method of ISAHP may further conclude.
2. Test samples of ISAHP
Four samples of ISAHP with different designs were selected for the present study. All ISAHP used R134a
refrigerant. Table 1 shows the design feature. There are
three types of designs: type A, B and D. The main differ-ence is the mechanism of solar energy and ambient heat absorption in the evaporator. Type A (2, ISAHP-7) uses a direct-expansion type evaporator which directly
absorbs both solar and ambient heat as shown in Fig. 2.
The evaporator of type A consists of black fins to absorb incident solar radiation directly and ambient heat via free convection. The type D (ISAHP-5) is similar to type A but with a split evaporator and heat pipe enhancement
design [5] as shown in Fig. 3. The evaporator of type D
is set with a tilted angle 23°. The design of type B (ISAHP-8) uses a forced-convection evaporator with fan like a traditional heat exchanger and the intake air is pass-ing through a passage beneath the body case so that it is preheated by solar radiation incident upon the body surface.
The test of ISAHP is performed on daily total basis since it represents an overall efficiency. The test starts at 9:00 AM daily and terminates when water temperature
reaches 55°C. The water was mixed using a circulation
pump before water temperature measurement. Total energy consumption of the compressor was measured by a watt meter. The daily accumulated solar radiation Nomenclature
a, b, c, g constants defined in Eqs.(2) and (3)
A, B constants defined in Eq. (12)
Aeff effective evaporator or surface area (m2)
Cp specific heat of water (kJ/kg°C)
COP daily overall coefficient of ISAHP
Ht daily total horizontal solar radiation (J/m2)
Iave daily average incident solar radiation (W/m2)
Is instantaneous horizontal solar radiation (W/m2)
M total water mass in ISAHP (kg)
Rih symmetry factor of solar radiation pattern
defined in Eq.(21)
T temperature (°C)
Twf final water temperature (°C)
Twi initial water temperature (°C)
Tf daily mean water temperature (°C) = (Twi+
Twf)/2
t time (s)
ti starting time of ISAHP operation (s)
tf stop time of ISAHP operation (s)
Ua overall heat transfer coefficient from the
evapo-rator to ambient air (W/°C)
Ue time average of Ua(W/°C)
Wcomp daily total energy consumption of ISAHP (J)
wcomp instantaneous energy consumption of ISAHP
(W)
a solar absorption coefficient of the evaporator or
body surface of ISAHP
ae effective solar absorption coefficient of the
evap-orator or body surface of ISAHP
incident on ISAHP in horizontal position was measured by a pyranometer. T-type thermocouples were used to mea-sure water and ambient temperatures. Hot water is fully discharged and replaced with fresh city water at early morning before starting the ISAHP.
3. Derivation of performance correlation of ISAHP 3.1. ISAHP operating at single energy source from ambient air
The ISAHP absorbs energy from both solar radiation and ambient heat. In order to derive the performance cor-relation, we first try to derive a performance correlation for ISAHP operating at only one energy source (ambient heat). This corresponds to the condition of cloudy days or the performance of conventional air-source heat pump. The energy balance to ISAHP will result in the follow equation:
MCp
dTw
dt ¼ UaðTa TeÞ þ wcomp ð1Þ
where M is the mass of water storage (kg); Cpis the specific
heat of water (kJ/kg°C); t is time (s); Uais the overall heat
transfer coefficient from the evaporator to ambient air (W/
°C); Twis the water temperature in the storage tank; Tais
the ambient temperature (°C); Teis the evaporator
temper-ature (°C); wcompis the power input to the compressor (W).
The measurement of evaporator temperature Teusually
requires installing temperature probes at various locations of the evaporator and taking an average value. This is quite complicated and sometimes difficult to obtain an accurate result. Simplification is thus necessary.
We observed from many test results of ISAHP that
Ta Teand wcompare proportional to Tw Ta, as shown
inFig. 4for ISAHP-2 on one particular day. This implies that the following relations may hold:
Ta Te¼ aðTw TaÞ þ b; ð2Þ
wcomp¼ cðTw TaÞ þ g: ð3Þ
Substituting Eqs.(2) and (3)into Eq.(1) and taking
inte-gral, we obtain Z tf ti MCp dTw dt dt¼ Z tf ti UaðTa TeÞ dt þ Z tf ti wcompdt Rtf ti MCp dTw dt dt Rtf ti wcompdt ¼ Rtf ti aUaðTw TaÞ dt þ Rtf ti bUadt Rtf ti cðTw TaÞ dt þ Rtf ti gdt þ 1: Table 1
Specification of different ISAHP used in the present study
Type Model Evaporator design Water
storage (l)
Rated compressor input power (W) A ISAHP-2 Direct-expansion natural convection; (Fig. 2) direct absorption of solar radiation 115 150
D ISAHP-5 Direct-expansion natural convection; (Fig. 3) split evaporator; heat-pipe enhancement 240 600 A ISAHP-7 Direct-expansion natural convection; (Fig. 2) direct absorption of solar radiation 130 250
B ISAHP-8 Forced-convection with fan; intake air preheated by solar radiation 200 250
Fig. 2. Schematic diagram of type-A evaporator.
Assuming constant Cpand Ue, we obtain COPMCpðTwf TwiÞ Wcomp ¼ ðaUeÞðTwTa;aveÞ g þ bUe g c Tð wTa;aveÞ g þ 1 þ 1; ð4Þ Wcomp¼ Z tf ti wcompdt; ð5Þ Dt¼ tf ti; ð6Þ Tw¼ Z tf ti Twdt=Dt; ð7Þ Ta;ave¼ Z tf ti Tadt=Dt; ð8Þ Ue Rtf ti UaðTw TaÞ dt Rtf tiðTw TaÞ dt ¼ Rtf ti UaðTw TaÞ dt DtðTw Ta;aveÞ ; ð9Þ
where Ue is defined as the time average of Ua; Twf is the
final water temperature, Twi is the initial water
tempera-ture. It is seen from Fig. 4 that ðc=gÞ ðTw Ta;aveÞ is
much less than 1. Hence, it can be ignored and Eq. (4)
becomes COPMCpðTwf TwiÞ Wcomp ¼aUe g ðTw Ta;aveÞ þ bUe g þ 1 : ð10Þ
The time average water temperature Tw in Eq. (10)is
re-lated to the initial and final temperature. Twcan be taken
as the arithmetic mean of the initial and final water temper-atures for simplification, that is
Tf¼
Twiþ Twf
2 ffi Tw ð11Þ
Eq.(10)then becomes
COP¼ AðTf Ta;aveÞ þ B ð12Þ
where A and B are constants defined as
A¼aUe
g ; B¼
bUe
g þ 1: ð13Þ
Eq. (12) represents an approximate correlation for
ISAHP operating at cloudy days (single energy source). The condition for a cloudy day is defined as the average
solar radiation intensity Iave< 200 W/m2. It can be seen
from Figs. 5 and 4 that the test results for ISAHP-2 and
ISAHP-7 obey the relation of Eq.(12)very well. This
ver-ifies that Eq.(12)is the performance correlation for ISAHP
operating at cloudy days with Iave< 200 W/m2 (see also
Fig. 6).
To investigate the possibility of correlation variation in different test seasons, we used the test data collected in
dif-ferent seasons and plot the correlations again.Table 2
sum-marizes the results of ISAHP-2 operating at cloudy days
with Iave< 200 W/m2. It shows that the performance
corre-lation can be repeated with small errors.Table 2also
pre-sents the effect of the number of test data points on the performance correlation results. For the test in spring season (2003/3/1–2003/5/31) with 17 test points (days), the results is almost identical with the whole year test result (2002/1/1–2002/12/31) with 50 test points. The result of
Table 2indicates that the performance test result of ISAHP
ISAHP-2 (2002/5/15)
initial water temp: 25 ºC final temp: 55 ºC average solar radiation: 68.2W/m2
y = 2.9383x + 236.08 R2 = 0.9792 y = -0.3713x + 20.49 R2 = 0.9579 0.0 5.0 10.0 15.0 20.0 25.0 30.0 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 Tw-Ta, ºC Ta -T e ,ºC 200 250 300 350 400
compressor power input
w
comp
(W)
Fig. 4. ISAHP-2 outdoor test results.
ISAHP-2 (2002/1/1~2002/12/31) Iave< 200 W/m 2 y = -0.1204x + 3.8146 R2 = 0.869 0.0 0.5 1.0 1.5 2.0 2.5 3.0 5 10 15 20 25 Tf-Ta,ave (ºC) COP Experimental error: 5%
at cloudy days using the correlation, Eq.(12), is repeatable.
Table 3 presents the performance test results of different
ISAHP at Iave< 200 W/m
2
. The performance correlation is shown very well.
3.2. ISAHP operating at dual energy source from solar and ambient air
ISAHP is designed to absorb both solar and ambient energies simultaneously. For dual energy source operation,
the energy balance Eq.(1)needs to be modified as
MCp
dTw
dt ¼ aIsAeffþ UaðTa TeÞ þ wcomp; ð14Þ
where Aeffis the effective surface of ISAHP for absorbing
solar radiation, a is the solar absorption coefficient of the evaporator or body surface of ISAHP. Taking integration
of Eq. (14)from tito tfin a day, we obtain
MCpðTwf TwiÞ ¼ aeHtAeffþ UeDtðTa;ave Te;aveÞ þ Wcomp
ð15Þ Te;ave¼ Z tf ti Tedt=Dt ð16Þ aeHtAeff Z tf t1 aIsAeffdt ð17Þ
where Htis the accumulated solar radiation from tito tf.
It is seen that the first term aeHtAeff in the right hand
side of Eq. (15) represents the total solar radiation
absorbed by ISAHP, the second term UeDt(Ta,ave Te,ave)
represents the total energy absorbed from ambient air, the
last term Wcompis the total input energy of the compressor.
Similar to the derivation of Eq. (12), we obtain from Eq.
(15) COPMCpðTwf TwiÞ Wcomp ¼aeHtAeff Wcomp þaUe g ðTf Ta;aveÞ þ bUe g þ 1 : ð18Þ
The term aeHtAeff/Wcomp is the ratio of total absorbed
en-ergy to the compressor input enen-ergy. From field experience,
it can be assumed that aeHtAeff/Wcomp is a constant k.
Hence, Eq.(18)is simplified as
COP¼ CðTf Ta;aveÞ þ K; ð19Þ
where C¼aUe
g ; K¼
bUe
g þ 1 þ k: ð20Þ
Eq. (17) provides a simple performance correlation for
ISAHP operating with two energy sources. It is seen that
the form of Eq.(19)is the same as Eq.(12)that is for single
energy source operation. The simple linear correlation remains to be verified experimentally.
Fig. 7 shows the performance correlation of ISAHP-2
for Iave> 200 W/m2. The correlation is satisfactory, but
with some scattering. The data scattering inFig. 7showing
lower R2value in linear regression mainly results from the
variation of instantaneous solar radiation during a day. This phenomenon is similar to that occurs in the
perfor-mance test of solar hot water heater [6]. Chang et al. [6]
ISAHP-7(2003/4/1~2004/4/1) Iave< 200W/m 2 y = -0.0621x + 2.7504 R2 = 0.9117 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 5 10 15 20 25 30 Tf -Ta,ave (ºC) COP
Fig. 6. Test results of ISAHP-7 at cloudy days.
Table 2
Performance test results in different seasons (ISAHP-2) Test period Tf Ta,ave
range No. of test points Slope C Intercept K R2 -value 2002/1/1–2002/12/31 10–25 50 0.120 3.815 0.869 2003/3/1–2003/5/31 10–25 17 0.117 3.773 0.935 2003/7/1–2003/9/31 10–20 19 0.103 3.603 0.785 2003/11/1–2004/1/31 10–25 22 0.115 3.764 0.855 Table 3
Performance test results of different ISAHP at Iave< 200 W/m 2
Model Test period Tf Ta,averange No. of test points Slope C Intercept K R
2 -value ISAHP-5 2004/2/1–2004/6/30 12–22 19 0.099 3.541 0.914 ISAHP-7 2003/11/1–2004/6/30 15–27 23 0.075 3.467 0.890 ISAHP-8 2004/3/1–2004/4/30 13–21 17 0.068 2.871 0.856 ISAHP-2 (2002/1/1-2002/12/31) Iave>200W/m 2 y = -0.0806x + 3.2188 R2 = 0.716 0.0 0.5 1.0 1.5 2.0 2.5 3.0 5 10 15 20 Tf-Ta,ave (ºC) COP
used a solar radiation symmetrical parameter Rihwhich is defined as Rih¼ Rtm ti IsðtÞdt Rtf tmIsdt ; ð21Þ
where tm is the time at solar noon. Rih= 1 represents the
solar radiation energy is symmetrical to solar noon.
Rih> 1 stands for incident solar energy is higher in the
morning; Rih< 1 stands for solar energy is lower in the
morning. We screened the test data to satisfy the condition
0.7 < Rih< 1.5 and obtain a much better linear correlation
as shown inFig. 8.
To verify the applicability of the correlation to different ISAHP, we used performance data of another ISAHP (ISAHP-7) and repeat the data processing and obtain
Fig. 9which shows good correlation again.
To investigate the possibility of correlation variation in different test seasons, we used the test data collected in
dif-ferent seasons and plot the correlations again.Table 4
sum-marizes the results of ISAHP-2. It shows that the performance correlation can be repeated with small errors.
Table 4 also presents the effect of the number of test data points on the performance correlation results. For the test in summer (2003/8/1–2003/10/31) with 17 test points (days), the results is almost identical with the whole year test results (2002/1/1–2002/12/31) with 34 test
points. The result of Table 4 indicates that the
perfor-mance test of ISAHP using the correlation, Eq. (19), is
repeatable.
Table 5presents the performance test results of another
4 different ISAHP at Iave> 200 W/m2. The performance
correlation is shown very well again although the ISAHP consists of 3 different types of design (type A, B, D). ISAHP-8 absorbs solar energy indirectly. That is, the intake air is first preheated by solar energy before entering the evaporator. ISAHP-5 is a heat-pipe enhanced ISAHP with split and fanless evaporator design. The performance of both ISAHP still follows the performance correlation,
Eq. (19).
4. Method of standard performance test and evaluation of ISAHP
4.1. Standard performance test method
The above experimental results have shown that the
performance correlation of ISAHP, Eq. (19), is adequate
to correlate the thermal performance of different ISAHP.
ISAHP-2 (2002/1/1-2002/12/31) Iave>200W/m 2 0.7<R ih<1.5 y = -0.0603x + 3.0225 R2 = 0.8167 0.0 0.5 1.0 1.5 2.0 2.5 3.0 5 10 15 20 Tf-Ta,ave (ºC) COP
Fig. 8. Performance correlation of ISAHP-2 with Iave> 200 W/m2 and
0.7 < Rih< 1.5. ISAHP-7 (2003/4/1-2004/3/31) Iave>200W/m 2 0.7<R ih<1.5 y = -0.068x + 2.8727 R2 = 0.8326 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 5 10 15 20 25 Tf-Ta,ave (ºC) COP
Fig. 9. Performance correlation of ISAHP-7 with Iave> 200 W/m2 and
0.7 < Rih< 1.5.
Table 4
Performance test results in different seasons (ISAHP-2) for Iave> 200 W/m2, 0.7 < Rih< 1.5
Test period Tf Ta,averange No. of test points Slope C Intercept K R2-value
2002/1/1–2002/12/31 5–15 34 0.0603 3.0225 0.832
2003/4/1–2003/6/30 7–13 16 0.0514 2.9310 0.787
2003/8/1–2003/10/31 8–13 17 0.0611 2.9936 0.801
2003/11/1–2004/1/31 8–15 15 0.0734 3.1528 0.944
Table 5
Performance test results of different ISAHP (Iave> 200 W/m 2
, 0.7 < Rih< 1.5)
Model Test period Tf Ta,averange No. of test points Slope C Intercept K R
2
-value ISAHP absorbs heat from solar and ambient air (Iave> 200 W/m
2 ) ISAHP-2 2003/11/1–2004/1/31 8–15 15 0.073 3.153 0.944 ISAHP-5 2004/5/1–2004/7/31 4–15 17 0.133 4.233 0.823 ISAHP-7 2004/5/1–2004/7/31 6–13 15 0.065 2.935 0.952 ISAHP-8 2003/11/1–2004/6/30 6–15 11 0.032 2.939 0.878
Thus, a method of standard test for the thermal performance of ISAHP can be developed and used for the evaluation of different ISAHP. In order to obtain a consistent and repeatable result, the following test method is suggested:
1. items of measurement: instantaneous solar incident
radi-ation on horizontal surface Isand ambient temperature
Ta, hot water temperature in the storage tank Tw, total
mass of water in the storage tank and total power input
to the ISAHP Wcompare required. Three minutes
sam-pling time interval is suggested.
2. operation: the daily operation starts from 9 AM until the
water temperature reaches 55°C. Before 9 AM, the
water in the tank needs to be completely drawn off and replaced by makeup water. The initial and final
water temperatures, Twiand Twf, are measured at
begin-ning and end of the daily operation. Every water
tem-perature measurement requires a mixing before
measurement.
3. data analysis: the daily total solar radiation Htis
calcu-lated from instantaneous solar radiation data Is. Using
the measured instantaneous data on Twi, Twf, Ta, we
can calculate daily Tf, Ta,ave, Rih, Iaveand COP
accord-ing to Eqs.(8), (11), (19) and (21). Then, the results are
screened for Iave> 200 W/m2 and 0.7 < Rih< 1.5. It
suggests that the data covers the range 5 < Tf Ta,ave
< 15°C, with minimum number of total data points 10
for linear regression analysis using Eq.(19).
4. performance evaluation: using the two parameters C and K of the resultant performance correlation to evaluate the thermal performance of ISAHP.
4.2. Method of performance evaluation
From the performance correlation shown inFig. 10 for
Iave> 200 W/m2, the performance evaluation of different
ISAHP can be made on a common basis. Table 6 shows
the parameters of the performance correlation obtained for 4 different ISAHP. If the evaluation is based on the per-formance correlation curves, ISAHP-5 may be the best, ISAHP-8 is the next, ISAHP-3 is the third, and ISAHP-7 is the last. However, the slope of the performance curve of ISAHP-5 is rather high. This means that COP will
decrease more quickly with increasing Tf Ta,ave. In order
to simplify the performance evaluation, the COP at an
ade-quate value of Tf Ta,ave can be chosen for comparison.
Since Tf Ta,ave= 15°C represents a reasonable operating
condition for most ISAHP, we selected the value of COP at Tf Ta,ave= 15°C as the characteristic COP of a ISAHP
for comparison. The results shown inTable 7indicates that
ISAHP-8 is the best at Tf Ta,ave= 15°C among the 4
dif-ferent ISAHP. This is reasonable since the evaporator of ISAHP-8 is designed with a fan to provide forced convec-tion and the intake air is preheated by solar energy. Thus the heat transfer mechanism is better.
5. Discussion and conclusion
The present study derives a simple linear correlation for the performance evaluation of different ISAHP. The corre-lation was derived from the principle of energy conserva-tion with some simplificaconserva-tions. The correlaconserva-tion is then verified using the long-term outdoor field test data of 4 dif-ferent ISAHP. The problems of seasonal repeatability and method of data scattering were examined. The COP of
ISAHP is proportional to Tf Ta,ave in single or dual
energy source. The error of the determined COP is about
5% for the results screened for Iave> 200 W/m2 and
0.7 < Rih< 1.5. From that, a standard performance test
method is concluded. It is found from the test results that the performance correlation of ISAHP has the same form for operating with single or dual energy source.
The test method suggests that only the measurement of instantaneous solar incident radiation on horizontal
sur-face Is, ambient temperature Ta, hot water temperature in
the storage tank Tw, total mass of water in the storage tank
and total power input to the ISAHP, Wcomp, are required.
Thus, outdoor test using natural sunlight is feasible. It is
also suggested to select the value of COP at Tf Ta,ave=
15°C as the characteristic COP of a ISAHP for
Table 6
Parameters of the performance correlation for different ISAHP at Iave> 200 W/m2
Model ISAHP-2 ISAHP-7 ISAHP-8 ISAHP-5
Intercept K 3.0225 2.8728 2.9388 4.2329
Slope C 0.0603 0.0681 0.0316 0.1331
Table 7
Characteristic COP value for different ISAHP at different Tf Ta,ave
Tf Ta,ave(°C) ISAHP-2 ISAHP-7 ISAHP-5 ISAHP-8
5 2.72 2.53 3.57 2.78 10 2.42 2.19 2.90 2.62 15 2.12 1.85 2.24 2.46 Tf-Ta,ave (ºC) Iave>200W/m 2 0 1 2 3 4 0 5 10 15 20 COP ISAHP-5 ISAHP-2 ISAHP-7 ISAHP-8
performance comparison. This provides a simple tool for the performance evaluation of ISAHP.
Acknowledgement
The present study was supported by Energy Bureau, Ministry of Economic Affairs, Taiwan.
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