- Email: [email protected]
Development of design charts for solar cooling systems. Part II: Application of the cooling f-chart
Energy Conversion and Management 44 (2003) 341–355 www.elsevier.com/locate/enconman
Development of design charts for solar cooling systems. Part II: Application of the cooling f-chart Khalid A. Joudi *, Qussai J. Abdul-Ghafour Department of Mechanical Engineering, College of Engineering, University of Baghdad, Baghdad, Iraq Received 1 August 2001; accepted 26 December 2001
Abstract This work includes the evaluation of the solar contribution in solar cooling systems by the newly developed solar cooling design chart. The effect of collector area and storage volume on the solar fraction is well taken into account in the cooling design charts. The results of several experimental installations are compared with the present cooling f-chart predictions. The agreement is very good, which verifies the validity of design predictions by the new cooling f-chart. Changing the collector area in a solar cooling system has a similar effect on the solar fraction as that in a solar heating system. Storage volume appears to show an optimum in a solar cooling system with a marked influence on the solar contribution. The cooling f-chart may be used in equation form for design purposes. Design by solar cooling design charts is applicable for different building constructions, solar collector types, length of cooling season, location and meteorological conditions. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Cooling f-chart; Solar cooling system simulation; Solar cooling design charts
1. Introduction The design procedure for a solar heating and cooling system requires a computer simulation program for predicting the performance and sizing of each system component. In 1976, Klein et al. [1] developed a method for designing solar heating systems, which they called the f-chart method. They used TRNSYS [2] as a design tool for the solar heating system. The heating f-chart simplifies the designerÕs task in predicting the solar fraction.
*
Corresponding author.
0196-8904/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 1 9 6 - 8 9 0 4 ( 0 2 ) 0 0 0 4 4 - 4
342
K.A. Joudi, Q.J. Abdul-Ghafour / Energy Conversion and Management 44 (2003) 341–355
Nomenclature Ac f FR H T UL Xc Yc Greek a b e c d W ðsaÞ ðsaÞn
collector aperture area (m2 ) solar fraction heat removal factor daily solar radiation (kJ/m2 ) temperature (°C) collector loss coefficient (kJ/hr m2 °C) reference solar system energy loss/cooling load solar absorbed energy/cooling load symbols solar collector plate absorptance solar collector array tilt angle (degree) solar collector plate emittance collector azimuth angle (degree) solar fraction at ith VOLRATIO /solar fraction at minimum VOLRATIO ith VOLRATIO/minimum VOLRATIO monthly average daily transmittance––absorptance product transmittance––absorptance product at normal incidence angle
Subscripts amb ambient eq equation min minimum T on tilted surface Abbreviation COP coefficient of performance
An early model of a lithium bromide water cooler was used by Butz et al. [3] in the simulation of a solar air conditioning system. The chiller was modeled as operating at a constant COP. One of their conclusions was that the simulation could not be performed for new building designs. Also, it would be necessary to develop empirical correlations or other short cut methods for each particular system configuration. Blinn [4] introduced a method of modeling transient operation of the cooler. The relation became popular because of its capability in relating most absorption system parameters in dimensionless groups. Many solar houses were installed in the USA, Japan and other countries by the YAZAKI Company [5]. They included solar cooling and heating systems. Design simulation was performed by YAZAKIÕs SIGMA program. One of their recommendations for system storage sizing was that the storage capacity varies from 20 to 200 l/m2 of collector area and that there is no short cut approach for sizing the storage tank.
K.A. Joudi, Q.J. Abdul-Ghafour / Energy Conversion and Management 44 (2003) 341–355
343
In part I of this paper, a method for estimating the solar contribution for solar cooling systems was presented in the form of two design charts. The cooling f-chart and the minimum allowable storage size chart. The credibility of the cooling f-charts is established when agreement is obtained with published results of actual standing systems. This part of the paper is related to validation of the new solar cooling f-chart and the presentation of an integrated approach for designing solar cooling systems.
2. The cooling f-chart equation The simulation results, which are used in constructing the cooling f-chart, are compared with the cooling f-chart equation in Fig. 1a. The result is logically a straight line passing through the origin with a slope equal to 1. The resultant line in Fig. 1a is a straight line intersecting the y-axis at point (0, 0.02) with a slope equal to 0.958. The reason for this deviation is the distribution of the data points around the line. The data points can be divided into three regions as shown in Fig. 1b. The f-equations for these three regions, using the least squares fit, are: f ¼ 0:629feq þ 0:066 for f 6 0:13
ð1Þ
f ¼ 0:98feq
ð2Þ
for 0:13 < f < 0:8
f ¼ 0:896feq þ 0:0672 for f P 0:8
ð3Þ
The use of these cooling f-chart equations is easier in computer calculations than using the actual chart.
Fig. 1. Simulation results compared with cooling f-chart equation.
344
K.A. Joudi, Q.J. Abdul-Ghafour / Energy Conversion and Management 44 (2003) 341–355
3. Effect of collector area on system performance The fraction of cooling supplied by solar energy during each month for each collector area can be determined from the cooling f-chart as a function of the dimensionless parameters Xc and Yc , in which the collector area is implicitly included and directly proportional to these parameters. The simulation results of the Iraqi solar house, which are shown in Table 1, are taken as an example for expressing the effect of changing the collector area on system performance. A simple approach of using the cooling f-chart when estimating the system performance for more than one collector area is to construct a straight line through the origin and a point corresponding to a known collector area. Along this line, the meteorological conditions for the month and all the design parameters, except collector area, are fixed, i.e. the collector area becomes a scale factor. Fig. 2 shows such a line for July, and the fixed points are the values of Xc and Table 1 The effect of collector area on solar cooling system performance––Iraqi solar house Month May June July August September October Season average
Xc =Ac (m2 )
Yc =Ac (m2 )
f-fraction of load supplied by solar Ac ¼ 40 m2
Ac ¼ 80 m2
Ac ¼ 120 m2
Ac ¼ 160 m2
Ac ¼ 200 m2
Ac ¼ 240 m2
0.01154 0.009441 0.0086375 0.0098329 0.012416
0.005875 0.006308 0.005779 0.00625 0.00629
0.1504719 0.1721316 0.1636759 0.1686534 0.1560449
0.2330824 0.2754826 0.2589964 0.268682 0.2439622
0.3134812 0.3757015 0.3517687 0.3657258 0.3292478
0.391054 0.4721459 0.4414828 0.4591396 0.4111718
0.4653023 0.5642629 0.5276921 0.5483736 0.4891573
0.5358431 0.6515892 0.6100128 0.6329733 0.5627815
0.0086
0.0036
0.1149144
0.1625999
0.207201
0.2482722
0.2871583
0.3269939
0.154315
0.240468
0.323854
0.403878
0.480324
0.553366
Fig. 2. The effect of the collector area variation on the solar fraction for July.
K.A. Joudi, Q.J. Abdul-Ghafour / Energy Conversion and Management 44 (2003) 341–355
345
Yc corresponding to each collector area, starting from 40 to 240 m2 with 40 m2 increments (Table 1). On the other hand, for f ¼ 0:8 and f ¼ 1, the collector areas are found to be 343 and 475 m2 respectively. These values are obtained by solving the cooling f-chart equation iteratively for the collector area. This enables the designer to choose the proper collector area for the desired solar fraction. A similar approach can be used to draw different lines for other months. Each line can be defined as the collector area axis, and it can be scaled to facilitate the solar fraction versus collector area for each month as shown in Fig. 3. Fig. 4 shows the variation of average solar fraction with collector area during the cooling season. It is clear that the seasonal average solar fraction increases with increasing collector area, but this increment is of a decreasing order. Fig. 4 shows that 1100 m2 collector area is required to cover all the seasonal cooling demands for the Iraqi solar house. This result is similar to that for a solar heating system, as shown in Fig. 5 [1].
Fig. 3. Monthly average solar fraction variation with collector area for Iraqi solar house.
Fig. 4. Average seasonal solar fraction variation with collector area.
346
K.A. Joudi, Q.J. Abdul-Ghafour / Energy Conversion and Management 44 (2003) 341–355
Fig. 5. Season average heating load supplied by solar energy [1].
4. Effect of storage volume The cooling f-chart is designed for a minimum allowable storage size, which results in zero energy discarded. Fig. 6 shows the minimum allowable storage size related to the Yc values. The designer has to calculate the seasonal Yc value and then uses this value to estimate the minimum allowable storage size from Fig. 6. From the simulation results, two dimensionless groups are investigated. The first group is the ratio of the solar fraction fi (calculated for larger VOLRATIO) to the solar fraction fo (calculated for the minimum VOLRATIO). This ratio is named d, i.e.
Fig. 6. Optimum storage size selection for Qrel .
K.A. Joudi, Q.J. Abdul-Ghafour / Energy Conversion and Management 44 (2003) 341–355
347
Fig. 7. The effect of increasing storage volume size.
d¼
fi f for ith VOLRATIO ¼ fo f for min : VOLRATIO
ð4Þ
The second group, named W, is the ratio of the ith VOLRATIO to the minimum VOLRATIO, i.e. ith VOLRATIO ð5Þ min: VOLRATIO Fig. 7 shows the variation of d with W. The data points are scattered around the best fit curve, which is a polynomial found to be: W¼
d ¼ 0:438W þ 3:443W2 2:544W3 þ 0:531W4
ð6Þ
Increasing W means increasing the storage size. This causes a larger area for energy loss and a lower average tank temperature. A lower tank temperature means a reduced temperature differential for energy loss. The net effect was found to be an increase in the useful energy supplied by the solar collectors. However, the system will operate at a lower temperature, which necessities more auxiliary energy. Each change in the above parameters causes a significant change in the solar fraction. The relation shown in Fig. 7 is the cumulative effect on the solar fraction of all the parameters related to storage volume. The maximum value of d is obtained by equating the first derivative of Eq. (6) to zero. This value is d ¼ 1:2 at W ¼ 1:45. Therefore, the maximum theoretical value of the solar fraction is 1.2 times its value at minimum VOLRATIO when the value of VOLRATIO is increased to 1.45 times its minimum value.
5. The optimum collector orientation program Usually the collector array is fixed at a certain tilt angle b and azimuth angle c. The optimum orientation is not necessarily taken for maximum solar energy collection [6]. Also, it is a
348
K.A. Joudi, Q.J. Abdul-Ghafour / Energy Conversion and Management 44 (2003) 341–355
function of the cooling load. A computer program is arranged for calculating the daily radiation on a tilted surface. By taking the daily cooling load data, the optimum orientation can be defined as the angles b and c that maximize the ratio of the total incident radiation to the cooling load: SUM ¼
b X i¼a
ðHT Þi ðcooling loadÞi
ð7Þ
where a is the first summer month and b is the last summer month. The program strategy is to calculate the SUM value, starting with the horizontal at b ¼ 0. Then, the tilt angle is increased at 0.1° increments. At the same time, the collector azimuth angle c is increased from 30° east of south to 30° west of south, one degree at a time for each incremental step in b. The optimum orientation of the collector surface is obtained when the value of SUM reaches a maximum. The optimum collector orientation was found at b ¼ 14:6° due south and c ¼ 0. However, the actual value of c was 22:5° east of south for the Iraqi solar house due to the land condition. A difference, within 5%, in the solar fraction was found due to the orientation.
6. How to design a solar cooling system This section describes the integrated approach for designing a solar cooling system using the results of the design charts as a design tool. For simplicity, the designer must follow a number of steps, which are described below. 1. The building characteristics, location and weather conditions for the cooling months are introduced in the computer program for calculating the cooling load for each month. 2. The available data of hourly solar radiation on a horizontal surface and the cooling load data for each month are used to calculate the optimum orientation of the solar collectors (tilt angle and azimuth angle). 3. Calculate the value of ð saÞ=ðsaÞn for each cooling month. 4. The hourly weather data is used with the performance curves of the selected absorption chiller for estimating the daily average COP. 5. The performance data for the solar collector, FR ðsaÞn and FR UL , are taken from the manufacturerÕs data. These values are introduced for calculating the Xc and Yc values, keeping the collector area at unity in this step. 6. Select a number of collector areas and multiply each one by the Xc and Yc values of the previous step. 7. Use the cooling f-chart or the equation and estimate the f value corresponding to each pair of Xc and Yc values. 8. Use the storage size chart for estimating the minimum allowable storage size. 9. The final selection of the appropriate collector area and storage volume is left to the designerÕs choice taking into consideration the economic evaluation of his decision.
K.A. Joudi, Q.J. Abdul-Ghafour / Energy Conversion and Management 44 (2003) 341–355
349
Table 2 Comparison of results between cooling f-chart and experimental results for Iraqi solar house Month May June July August September October
H tilt (MJ/m2 ) 18.076 29.724 34.274 32.786 28.728 10.956
Tamb (°C) 29 34 36.5 36.5 33 28
Load (MJ) Cooling
Generator
– – – – – –
3.849 9.861 11.842 12.285 8.295 3.677
COP
Xc
Yc
fchart
factual
0.394 0.448 0.507 0.516 0.398 0.393
2.769 2.26 2.073 2.36 2.979 2.064
1.41 1.512 1.387 1.5 1.509 0.864
0.356 0.651 0.61 0.63 0.56 0.327
0.588 0.528 0.576 0.567 0.479 0.322
Project: Iraqi solar house; Location: Baghdad, Iraq; Latitude: 33.3° N; Tilt angle: 15.6°; Col. area: 243 m2 ; FR ðsaÞn : 0.771; FR UL : 15.25 kJ/hr m2 °C.
7. Comparison with published results 7.1. Iraqi solar house A description of this installation was detailed in part I. The results of the comparison are shown in Table 2 and graphically in Fig. 8. It is clear that the actual data and the estimated simulation results of the present program are compatible. The difference in June is rather larger than for other months. Ref. [7] reported that in 1984, the year in which the test was done, the weather was rather dusty during June, and the reduction of the incident solar radiation was significant. 7.2. YAZAKI’s solar house, Umeda, Japan The house was placed in operation in August 1974 with 143 m2 total floor area and occupied by four persons. The solar collector array is of 94.5 m2 effective area of the flat plate type with one glass pane and a selective surface (a ¼ 0:93, e ¼ 0:11). The collectors were tilted at 25° due south.
Fig. 8. Comparison of results between actual and estimated values of solar fraction for Iraqi solar house.
350
K.A. Joudi, Q.J. Abdul-Ghafour / Energy Conversion and Management 44 (2003) 341–355
Table 3 Comparison of results between cooling f-chart and experimental results for YAZAKI solar house Month
H tilt (MJ/m2 )
Tamb (°C)
Load (MJ)
COP
Xc
Yc
fchart
factual
0.47 0.53 0.52 0.4
5.099 3.765 6.035 12.967
2.0179 1.344 2.062 3.931
0.568 0.378 0.483 0.860
0.62 0.42 0.61 0.82
Cooling Generator July August September October
495 425 400 415
23.5 28 26 20
7560 10867 6615 2646
– – – –
Project: YAZAKI solar house; Location: Umeda, Japan; Latitude: 34.7° N; Tilt angle: 25°; Col. area: 95.5 m2 ; FR ðsaÞn : 0.771; FR UL : 15.25 kJ/hr m2 °C.
Fig. 9. Comparison of results between actual and estimated values of solar fraction for YAZAKI solar house.
The building was located at latitude 34.7° north in Umeda, Japan [8]. The performance results are compared with the present cooling f-chart as shown in Table 3 and graphically in Fig. 9. The agreement is good with more than the expected difference in September. 7.3. Ishibashi solar house, Umeda, Japan The house was placed in operation in July 1976 with 138 m2 total floor area and occupied by four persons [8]. The solar collector array is of 56.7 m2 effective area of the flat plate type with a single glass pane and a selective surface (a ¼ 0:93, e ¼ 0:11). The collectors were tilted at 22° from the horizontal and oriented at 50° due west due to the land condition. The building was placed 1.5 km away from the previous house [8]. The published results are compared with the present cooling f-chart results as given in Table 4 and shown in Fig. 10. The agreement is excellent. 7.4. Colorado state university solar house-I (1978) Table 5 summarizes the performance data of a residential scale installation on Colorado State University house I, as described by Duff et al. [9]. The collectors in this installation were of the
K.A. Joudi, Q.J. Abdul-Ghafour / Energy Conversion and Management 44 (2003) 341–355
351
Table 4 Comparison of results between cooling f-chart and experimental results for Ishibashi solar house Month July August September
H tilt (MJ/m2 ) 500 460 400
Tamb (°C)
Load (MJ)
28 28 24
Cooling
Generator
5805 5670 4725
– – –
COP
Xc
Yc
fchart
factual
0.57 0.58 0.51
5.173 7.900 8.510
2.197 3.017 2.900
0.645 0.725 0.62
0.7 0.71 0.62
Note: Collector azimuth angle 50° W; Project: Ishibashi solar house; Location: Umeda, Japan; Latitude: 34.7° N; Tilt angle: 22°; Col. area: 56.7 m2 ; FR ðsaÞn : 0.771; FR UL : 15.25 kJ/hr m2 °C.
Fig. 10. Comparison of results between actual and estimated values of solar fraction for Ishibashi solar house.
Table 5 Comparison of results between cooling f-chart and experimental results for Colorado State University solar house (I), 1978 Month
H tilt (MJ/m2 )
Tamb (°C)
Load (MJ) Cooling
Generator
August September
950 1386
21 16
– –
803 638
COP
Xc
Yc
fchart
factual
– –
0.388 0.58
0.7346 1.173
0.456 0.676
0.43 0.63
Project: Colorado State University; Location: Colorado, USA; Latitude: 38° N; Tilt angle: Col. area (evacuated tube collector): 39.9 m2 ; FR ðsaÞn : 0.79; FR UL : 7.308 kJ/hr m2 °C.
evacuated tube type with a flat absorber. The gross area was 75.2 m2 and an absorber area of 39.9 m2 . The reported FR ðsaÞ was 0.79 and FR UL was 7.308 kJ/hr m2 °C based on absorber area. Table 5 also shows the comparison between the actual data and present cooling f-chart. The agreement is very good.
352
K.A. Joudi, Q.J. Abdul-Ghafour / Energy Conversion and Management 44 (2003) 341–355
Table 6 Comparison of results between cooling f-chart and experimental results for Colorado State University solar house (I), 1983 Datea
H tilt (MJ/m2 )
Tamb (°C)
Load (MJ) Cooling
Generator
–
132
32.77
2257
–
COP
Xc
Yc
0.553
2.022
1.135
fchart
factual
0.478
0.52
2
Project: Colorado State University; Location: Colorado, USA; Latitude: 38° N; Col. area: 56 m ; FR ðsaÞn : 0.6; FR UL : 11.52 kJ/hr m2 °C. a Note: Results of 122 selected summer days.
7.5. Colorado state university solar house-I (1983) Two solar systems were used for operating the cooling system of this solar house. The first system used 56 m2 Miromit flat plate collectors with FR UL ¼ 11.52 kJ/hr m2 °C. The second system used 60 m2 Phillips evacuated tube collectors with FR ðsaÞn ¼ 0.52 and FR UL ¼ 6.68 kJ/ hr m2 °C [10]. The reported performance results are compared with the present cooling f-chart results and recorded in Table 6. There is only one point, which can be compared. Thus, no graphical presentation is given. The agreement is very good.
7.6. Kuwait institute solar office This office is occupied seven hours per day expect for Fridays and public holidays. More information was available for this project for comparison. The results for the solar fraction are given in Table 7. Fig. 11 shows, graphically, the comparison between the reported solar fraction and the predicted solar fraction from this work. The agreement is rather good for all the weekly data reported [11]. From these comparisons, it is found that the present cooling f-chart is applicable in estimating the solar fraction for solar cooling systems. The experimental results are for installed projects in different locations, different weather data and various collector types. The differences between the experimental and estimated solar fraction values are within a range of 1% to 15% for most of the reported data. Some odd points fall within 20%. One of the reasons for the larger deviation is the shortage in the information reported in the experimental data. Missing data, such as the weekly ð saÞ=ðsaÞn for the Kuwait Institute office had to be estimated from the reported monthly value. This is one example of why there may be differences. These estimates were made as accurately as possible. In general, the cooling f-chart appears to underestimate the solar fraction for all the installations reported above except for the Iraqi solar house. In this situation, it overestimates the cooling solar fraction. The reason behind this is thought to be due to the degradation in the actual solar cooling system for the year reported. The system was in operation for 4 years with untreated water in the collector system, which caused scale deposits. It is thought that in 1984, the year for which the data is given in Ref. [7], the system performance had actually declined from its design point.
K.A. Joudi, Q.J. Abdul-Ghafour / Energy Conversion and Management 44 (2003) 341–355
353
Table 7 Comparison of the results estimated from cooling f-chart with experimental results for Kuwait Institute solar office, 1985 Date (weekly data)
H tilt (MJ/m2 )
Tamb (°C)
18–23/5 25–30/5 1–6/6 8–13/6 22–27/6 29/6–4/7 6–11/7 13–18/7 20–25/7 27/7–1/8 3–8/8 10–15/8 17–22/8 31/8–5/9 7–12/9 14–19/9 21–26/9 28/9–3/10
23.54 25.71 21.57 21.99 26.21 23.15 22.77 29.47 35.04 31.18 33.48 34.92 35.57 34.05 32.42 31.38 30.32 30.04
36.7 37.4 36.2 37 38.3 39.1 39.8 41.5 40.7 39.5 41.9 41.1 41.38 38.7 38.9 36.5 35.2 36.7
Load (MJ) Cooling
Generator
10.24 8.809 8.64 8.63 11.64 11.11 11.57 12.35 10.39 12.51 12.416 10.314 12.75 11.03 11.1 10.85 10.724 10.56
– – – – – – – – – – – – – – – – – –
COP
Xc
Yc
fchart
factual
0.59 0.63 0.61 0.65 0.53 0.52 0.57 0.6 0.52 0.54 0.56 0.55 0.53 0.52 0.51 0.53 0.54 0.57
0.7 0.86 0.865 0.911 0.539 0.547 0.57 0.54 0.487 0.501 0.503 0.603 0.468 0.555 0.539 0.496 0.627 0.656
0.951 1.29 1.05 1.16 0.83 1.04 0.78 0.992 1.039 0.934 1.05 1.29 1 1.114 1.04 1.08 1.074 1.137
0.54 0.71 0.57 0.63 0.49 0.61 0.458 0.582 0.615 0.55 0.62 0.739 0.6 0.647 0.62 0.636 0.62 0.65
0.57 0.77 0.61 0.76 0.5 0.63 0.46 0.62 0.68 0.61 0.69 0.75 0.67 0.71 0.7 0.73 0.72 0.75
Project: Kuwait Institute; Location: Kuwait; Col. area: 300 m2 ; FR ðsaÞn : 0.771; FR UL : 15.25 kJ/hr m2 °C.
Fig. 11. Weekly comparison results between actual and estimated values of solar fraction for Kuwait solar office starting from 18–23/May to 28/Sep–3/Oct 1985.
8. Heating and cooling f-chart design The cooling f-chart reported in this work is an extension of the heating f-chart [1]. They are rather similar in trend and application. However, they are different in the construction up procedure. The main differences between the two f-charts are the following:
354
K.A. Joudi, Q.J. Abdul-Ghafour / Energy Conversion and Management 44 (2003) 341–355
1. The heat exchanger between the collector fluid loop and storage tank, which is used in solar heating system, is omitted in the solar cooling system. 2. The solar cooling f-chart parameters included the coefficient of performance of the lithium bromide-water absorption chiller. 3. The heat dissipated form the storage tank and piping are considered as an energy loss to the ambient. In designing the heating f-chart, the energy loss from piping is not included, and the energy loss from the storage tank is considered to be transferred to the heated space. 4. The technique used in designing the cooling f-chart is based on the minimum allowable storage size, causing zero discarded energy form the pressure relief valve, i.e. the storage volume to collector area ratio is variable, while the technique used in designing the heating f-chart is based on 75‘/m2 , storage volume to collector area ratio. The heating solar fraction needs a correction for other storage sizes.
9. Conclusions From the results obtained form this work, the following conclusions can be made: 1. The cooling f-chart can be recommended as a good method for predicting the solar fraction for solar cooling systems, for any type of building, collector, meteorological conditions and locations. 2. The cooling f-chart can be used for predicting the value of the monthly or average seasonal solar fraction. 3. The cooling f-chart can be used in equation form for computer design procedures for solar cooling systems. 4. Increasing the storage volume to collector area ratio to its optimum value results in increasing the solar fraction. The solar fraction reaches 1.2 times its minimum value when the storage volume reaches 1.45 times the minimum allowable value. 5. The cooling f-chart is designed for monthly values, but it can be used for weekly prediction with good agreement with actual systems.
References [1] Klein SA, Beckman WA, Duffie JA. Solar Heating Design the f Chart Method. New York: John Wiley and Sons, Inc; 1977. [2] TRNSYS. A transient system simulation program. Solar Energy Laboratory, University of Wisconsin, Madison, Engineering Experiment Station report 38–12. [3] Butz LW, Beckman WA, Duffie JA. Simulation of a solar heating and cooling system. Solar Energy 1974;16:129. [4] Blinn JC. Simulation of solar absorption air conditioning. MSc thesis in Chemical Engineering, University of Wisconsin, Madison, 1979. [5] Solar Heating and Cooling in Japan. Product and System Data Manual. Tech-in Notes, YAZAKI Company, 1980. [6] Duffie JA, Beckman WA. Solar engineering of thermal processes. New York: John Wiley and Sons; 1980. [7] AL-Karaghouli A, AL-Hamdani N, AL-Sinan W. Iraqi solar house cooling season performance evaluation. Solar Wind Technol 1989;6(1):29–40.
K.A. Joudi, Q.J. Abdul-Ghafour / Energy Conversion and Management 44 (2003) 341–355
355
[8] Ishibashi T, Yazaki S. The operation results of the Yazaki experimental solar house one and the Ishibashi solar house. American Section of International Solar Energy Society, Inc, 1978. [9] Duff WS, Conway TM, Lof GOG, Meredith DB, Pratt RB. Performance of residential solar heating and cooling system with flat plate and evacuated tubular collectors CSU house––I. Proceeding of the CCMS/ISES Conference on Performance of Solar Heating and Cooling Systems, NATO Committee on Challenges to Modern Society, CCMS report 85, 1978. p. 217. [10] Duff WS, Lof GOG. Comparison of eight solar heating, cooling and hot water systems in Colorado State University solar house I, Perth. Solar World Congress 1983;1:14–9. [11] Al-Shami HR. Performance results of solar absorption cooling installation. Technical Report 1908, Kuwait Institute for Scientific Research, 1985.
Development of design charts for solar cooling systems. Part II: Application of the cooling f-chart Khalid A. Joudi *, Qussai J. Abdul-Ghafour Department of Mechanical Engineering, College of Engineering, University of Baghdad, Baghdad, Iraq Received 1 August 2001; accepted 26 December 2001
Abstract This work includes the evaluation of the solar contribution in solar cooling systems by the newly developed solar cooling design chart. The effect of collector area and storage volume on the solar fraction is well taken into account in the cooling design charts. The results of several experimental installations are compared with the present cooling f-chart predictions. The agreement is very good, which verifies the validity of design predictions by the new cooling f-chart. Changing the collector area in a solar cooling system has a similar effect on the solar fraction as that in a solar heating system. Storage volume appears to show an optimum in a solar cooling system with a marked influence on the solar contribution. The cooling f-chart may be used in equation form for design purposes. Design by solar cooling design charts is applicable for different building constructions, solar collector types, length of cooling season, location and meteorological conditions. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Cooling f-chart; Solar cooling system simulation; Solar cooling design charts
1. Introduction The design procedure for a solar heating and cooling system requires a computer simulation program for predicting the performance and sizing of each system component. In 1976, Klein et al. [1] developed a method for designing solar heating systems, which they called the f-chart method. They used TRNSYS [2] as a design tool for the solar heating system. The heating f-chart simplifies the designerÕs task in predicting the solar fraction.
*
Corresponding author.
0196-8904/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 1 9 6 - 8 9 0 4 ( 0 2 ) 0 0 0 4 4 - 4
342
K.A. Joudi, Q.J. Abdul-Ghafour / Energy Conversion and Management 44 (2003) 341–355
Nomenclature Ac f FR H T UL Xc Yc Greek a b e c d W ðsaÞ ðsaÞn
collector aperture area (m2 ) solar fraction heat removal factor daily solar radiation (kJ/m2 ) temperature (°C) collector loss coefficient (kJ/hr m2 °C) reference solar system energy loss/cooling load solar absorbed energy/cooling load symbols solar collector plate absorptance solar collector array tilt angle (degree) solar collector plate emittance collector azimuth angle (degree) solar fraction at ith VOLRATIO /solar fraction at minimum VOLRATIO ith VOLRATIO/minimum VOLRATIO monthly average daily transmittance––absorptance product transmittance––absorptance product at normal incidence angle
Subscripts amb ambient eq equation min minimum T on tilted surface Abbreviation COP coefficient of performance
An early model of a lithium bromide water cooler was used by Butz et al. [3] in the simulation of a solar air conditioning system. The chiller was modeled as operating at a constant COP. One of their conclusions was that the simulation could not be performed for new building designs. Also, it would be necessary to develop empirical correlations or other short cut methods for each particular system configuration. Blinn [4] introduced a method of modeling transient operation of the cooler. The relation became popular because of its capability in relating most absorption system parameters in dimensionless groups. Many solar houses were installed in the USA, Japan and other countries by the YAZAKI Company [5]. They included solar cooling and heating systems. Design simulation was performed by YAZAKIÕs SIGMA program. One of their recommendations for system storage sizing was that the storage capacity varies from 20 to 200 l/m2 of collector area and that there is no short cut approach for sizing the storage tank.
K.A. Joudi, Q.J. Abdul-Ghafour / Energy Conversion and Management 44 (2003) 341–355
343
In part I of this paper, a method for estimating the solar contribution for solar cooling systems was presented in the form of two design charts. The cooling f-chart and the minimum allowable storage size chart. The credibility of the cooling f-charts is established when agreement is obtained with published results of actual standing systems. This part of the paper is related to validation of the new solar cooling f-chart and the presentation of an integrated approach for designing solar cooling systems.
2. The cooling f-chart equation The simulation results, which are used in constructing the cooling f-chart, are compared with the cooling f-chart equation in Fig. 1a. The result is logically a straight line passing through the origin with a slope equal to 1. The resultant line in Fig. 1a is a straight line intersecting the y-axis at point (0, 0.02) with a slope equal to 0.958. The reason for this deviation is the distribution of the data points around the line. The data points can be divided into three regions as shown in Fig. 1b. The f-equations for these three regions, using the least squares fit, are: f ¼ 0:629feq þ 0:066 for f 6 0:13
ð1Þ
f ¼ 0:98feq
ð2Þ
for 0:13 < f < 0:8
f ¼ 0:896feq þ 0:0672 for f P 0:8
ð3Þ
The use of these cooling f-chart equations is easier in computer calculations than using the actual chart.
Fig. 1. Simulation results compared with cooling f-chart equation.
344
K.A. Joudi, Q.J. Abdul-Ghafour / Energy Conversion and Management 44 (2003) 341–355
3. Effect of collector area on system performance The fraction of cooling supplied by solar energy during each month for each collector area can be determined from the cooling f-chart as a function of the dimensionless parameters Xc and Yc , in which the collector area is implicitly included and directly proportional to these parameters. The simulation results of the Iraqi solar house, which are shown in Table 1, are taken as an example for expressing the effect of changing the collector area on system performance. A simple approach of using the cooling f-chart when estimating the system performance for more than one collector area is to construct a straight line through the origin and a point corresponding to a known collector area. Along this line, the meteorological conditions for the month and all the design parameters, except collector area, are fixed, i.e. the collector area becomes a scale factor. Fig. 2 shows such a line for July, and the fixed points are the values of Xc and Table 1 The effect of collector area on solar cooling system performance––Iraqi solar house Month May June July August September October Season average
Xc =Ac (m2 )
Yc =Ac (m2 )
f-fraction of load supplied by solar Ac ¼ 40 m2
Ac ¼ 80 m2
Ac ¼ 120 m2
Ac ¼ 160 m2
Ac ¼ 200 m2
Ac ¼ 240 m2
0.01154 0.009441 0.0086375 0.0098329 0.012416
0.005875 0.006308 0.005779 0.00625 0.00629
0.1504719 0.1721316 0.1636759 0.1686534 0.1560449
0.2330824 0.2754826 0.2589964 0.268682 0.2439622
0.3134812 0.3757015 0.3517687 0.3657258 0.3292478
0.391054 0.4721459 0.4414828 0.4591396 0.4111718
0.4653023 0.5642629 0.5276921 0.5483736 0.4891573
0.5358431 0.6515892 0.6100128 0.6329733 0.5627815
0.0086
0.0036
0.1149144
0.1625999
0.207201
0.2482722
0.2871583
0.3269939
0.154315
0.240468
0.323854
0.403878
0.480324
0.553366
Fig. 2. The effect of the collector area variation on the solar fraction for July.
K.A. Joudi, Q.J. Abdul-Ghafour / Energy Conversion and Management 44 (2003) 341–355
345
Yc corresponding to each collector area, starting from 40 to 240 m2 with 40 m2 increments (Table 1). On the other hand, for f ¼ 0:8 and f ¼ 1, the collector areas are found to be 343 and 475 m2 respectively. These values are obtained by solving the cooling f-chart equation iteratively for the collector area. This enables the designer to choose the proper collector area for the desired solar fraction. A similar approach can be used to draw different lines for other months. Each line can be defined as the collector area axis, and it can be scaled to facilitate the solar fraction versus collector area for each month as shown in Fig. 3. Fig. 4 shows the variation of average solar fraction with collector area during the cooling season. It is clear that the seasonal average solar fraction increases with increasing collector area, but this increment is of a decreasing order. Fig. 4 shows that 1100 m2 collector area is required to cover all the seasonal cooling demands for the Iraqi solar house. This result is similar to that for a solar heating system, as shown in Fig. 5 [1].
Fig. 3. Monthly average solar fraction variation with collector area for Iraqi solar house.
Fig. 4. Average seasonal solar fraction variation with collector area.
346
K.A. Joudi, Q.J. Abdul-Ghafour / Energy Conversion and Management 44 (2003) 341–355
Fig. 5. Season average heating load supplied by solar energy [1].
4. Effect of storage volume The cooling f-chart is designed for a minimum allowable storage size, which results in zero energy discarded. Fig. 6 shows the minimum allowable storage size related to the Yc values. The designer has to calculate the seasonal Yc value and then uses this value to estimate the minimum allowable storage size from Fig. 6. From the simulation results, two dimensionless groups are investigated. The first group is the ratio of the solar fraction fi (calculated for larger VOLRATIO) to the solar fraction fo (calculated for the minimum VOLRATIO). This ratio is named d, i.e.
Fig. 6. Optimum storage size selection for Qrel .
K.A. Joudi, Q.J. Abdul-Ghafour / Energy Conversion and Management 44 (2003) 341–355
347
Fig. 7. The effect of increasing storage volume size.
d¼
fi f for ith VOLRATIO ¼ fo f for min : VOLRATIO
ð4Þ
The second group, named W, is the ratio of the ith VOLRATIO to the minimum VOLRATIO, i.e. ith VOLRATIO ð5Þ min: VOLRATIO Fig. 7 shows the variation of d with W. The data points are scattered around the best fit curve, which is a polynomial found to be: W¼
d ¼ 0:438W þ 3:443W2 2:544W3 þ 0:531W4
ð6Þ
Increasing W means increasing the storage size. This causes a larger area for energy loss and a lower average tank temperature. A lower tank temperature means a reduced temperature differential for energy loss. The net effect was found to be an increase in the useful energy supplied by the solar collectors. However, the system will operate at a lower temperature, which necessities more auxiliary energy. Each change in the above parameters causes a significant change in the solar fraction. The relation shown in Fig. 7 is the cumulative effect on the solar fraction of all the parameters related to storage volume. The maximum value of d is obtained by equating the first derivative of Eq. (6) to zero. This value is d ¼ 1:2 at W ¼ 1:45. Therefore, the maximum theoretical value of the solar fraction is 1.2 times its value at minimum VOLRATIO when the value of VOLRATIO is increased to 1.45 times its minimum value.
5. The optimum collector orientation program Usually the collector array is fixed at a certain tilt angle b and azimuth angle c. The optimum orientation is not necessarily taken for maximum solar energy collection [6]. Also, it is a
348
K.A. Joudi, Q.J. Abdul-Ghafour / Energy Conversion and Management 44 (2003) 341–355
function of the cooling load. A computer program is arranged for calculating the daily radiation on a tilted surface. By taking the daily cooling load data, the optimum orientation can be defined as the angles b and c that maximize the ratio of the total incident radiation to the cooling load: SUM ¼
b X i¼a
ðHT Þi ðcooling loadÞi
ð7Þ
where a is the first summer month and b is the last summer month. The program strategy is to calculate the SUM value, starting with the horizontal at b ¼ 0. Then, the tilt angle is increased at 0.1° increments. At the same time, the collector azimuth angle c is increased from 30° east of south to 30° west of south, one degree at a time for each incremental step in b. The optimum orientation of the collector surface is obtained when the value of SUM reaches a maximum. The optimum collector orientation was found at b ¼ 14:6° due south and c ¼ 0. However, the actual value of c was 22:5° east of south for the Iraqi solar house due to the land condition. A difference, within 5%, in the solar fraction was found due to the orientation.
6. How to design a solar cooling system This section describes the integrated approach for designing a solar cooling system using the results of the design charts as a design tool. For simplicity, the designer must follow a number of steps, which are described below. 1. The building characteristics, location and weather conditions for the cooling months are introduced in the computer program for calculating the cooling load for each month. 2. The available data of hourly solar radiation on a horizontal surface and the cooling load data for each month are used to calculate the optimum orientation of the solar collectors (tilt angle and azimuth angle). 3. Calculate the value of ð saÞ=ðsaÞn for each cooling month. 4. The hourly weather data is used with the performance curves of the selected absorption chiller for estimating the daily average COP. 5. The performance data for the solar collector, FR ðsaÞn and FR UL , are taken from the manufacturerÕs data. These values are introduced for calculating the Xc and Yc values, keeping the collector area at unity in this step. 6. Select a number of collector areas and multiply each one by the Xc and Yc values of the previous step. 7. Use the cooling f-chart or the equation and estimate the f value corresponding to each pair of Xc and Yc values. 8. Use the storage size chart for estimating the minimum allowable storage size. 9. The final selection of the appropriate collector area and storage volume is left to the designerÕs choice taking into consideration the economic evaluation of his decision.
K.A. Joudi, Q.J. Abdul-Ghafour / Energy Conversion and Management 44 (2003) 341–355
349
Table 2 Comparison of results between cooling f-chart and experimental results for Iraqi solar house Month May June July August September October
H tilt (MJ/m2 ) 18.076 29.724 34.274 32.786 28.728 10.956
Tamb (°C) 29 34 36.5 36.5 33 28
Load (MJ) Cooling
Generator
– – – – – –
3.849 9.861 11.842 12.285 8.295 3.677
COP
Xc
Yc
fchart
factual
0.394 0.448 0.507 0.516 0.398 0.393
2.769 2.26 2.073 2.36 2.979 2.064
1.41 1.512 1.387 1.5 1.509 0.864
0.356 0.651 0.61 0.63 0.56 0.327
0.588 0.528 0.576 0.567 0.479 0.322
Project: Iraqi solar house; Location: Baghdad, Iraq; Latitude: 33.3° N; Tilt angle: 15.6°; Col. area: 243 m2 ; FR ðsaÞn : 0.771; FR UL : 15.25 kJ/hr m2 °C.
7. Comparison with published results 7.1. Iraqi solar house A description of this installation was detailed in part I. The results of the comparison are shown in Table 2 and graphically in Fig. 8. It is clear that the actual data and the estimated simulation results of the present program are compatible. The difference in June is rather larger than for other months. Ref. [7] reported that in 1984, the year in which the test was done, the weather was rather dusty during June, and the reduction of the incident solar radiation was significant. 7.2. YAZAKI’s solar house, Umeda, Japan The house was placed in operation in August 1974 with 143 m2 total floor area and occupied by four persons. The solar collector array is of 94.5 m2 effective area of the flat plate type with one glass pane and a selective surface (a ¼ 0:93, e ¼ 0:11). The collectors were tilted at 25° due south.
Fig. 8. Comparison of results between actual and estimated values of solar fraction for Iraqi solar house.
350
K.A. Joudi, Q.J. Abdul-Ghafour / Energy Conversion and Management 44 (2003) 341–355
Table 3 Comparison of results between cooling f-chart and experimental results for YAZAKI solar house Month
H tilt (MJ/m2 )
Tamb (°C)
Load (MJ)
COP
Xc
Yc
fchart
factual
0.47 0.53 0.52 0.4
5.099 3.765 6.035 12.967
2.0179 1.344 2.062 3.931
0.568 0.378 0.483 0.860
0.62 0.42 0.61 0.82
Cooling Generator July August September October
495 425 400 415
23.5 28 26 20
7560 10867 6615 2646
– – – –
Project: YAZAKI solar house; Location: Umeda, Japan; Latitude: 34.7° N; Tilt angle: 25°; Col. area: 95.5 m2 ; FR ðsaÞn : 0.771; FR UL : 15.25 kJ/hr m2 °C.
Fig. 9. Comparison of results between actual and estimated values of solar fraction for YAZAKI solar house.
The building was located at latitude 34.7° north in Umeda, Japan [8]. The performance results are compared with the present cooling f-chart as shown in Table 3 and graphically in Fig. 9. The agreement is good with more than the expected difference in September. 7.3. Ishibashi solar house, Umeda, Japan The house was placed in operation in July 1976 with 138 m2 total floor area and occupied by four persons [8]. The solar collector array is of 56.7 m2 effective area of the flat plate type with a single glass pane and a selective surface (a ¼ 0:93, e ¼ 0:11). The collectors were tilted at 22° from the horizontal and oriented at 50° due west due to the land condition. The building was placed 1.5 km away from the previous house [8]. The published results are compared with the present cooling f-chart results as given in Table 4 and shown in Fig. 10. The agreement is excellent. 7.4. Colorado state university solar house-I (1978) Table 5 summarizes the performance data of a residential scale installation on Colorado State University house I, as described by Duff et al. [9]. The collectors in this installation were of the
K.A. Joudi, Q.J. Abdul-Ghafour / Energy Conversion and Management 44 (2003) 341–355
351
Table 4 Comparison of results between cooling f-chart and experimental results for Ishibashi solar house Month July August September
H tilt (MJ/m2 ) 500 460 400
Tamb (°C)
Load (MJ)
28 28 24
Cooling
Generator
5805 5670 4725
– – –
COP
Xc
Yc
fchart
factual
0.57 0.58 0.51
5.173 7.900 8.510
2.197 3.017 2.900
0.645 0.725 0.62
0.7 0.71 0.62
Note: Collector azimuth angle 50° W; Project: Ishibashi solar house; Location: Umeda, Japan; Latitude: 34.7° N; Tilt angle: 22°; Col. area: 56.7 m2 ; FR ðsaÞn : 0.771; FR UL : 15.25 kJ/hr m2 °C.
Fig. 10. Comparison of results between actual and estimated values of solar fraction for Ishibashi solar house.
Table 5 Comparison of results between cooling f-chart and experimental results for Colorado State University solar house (I), 1978 Month
H tilt (MJ/m2 )
Tamb (°C)
Load (MJ) Cooling
Generator
August September
950 1386
21 16
– –
803 638
COP
Xc
Yc
fchart
factual
– –
0.388 0.58
0.7346 1.173
0.456 0.676
0.43 0.63
Project: Colorado State University; Location: Colorado, USA; Latitude: 38° N; Tilt angle: Col. area (evacuated tube collector): 39.9 m2 ; FR ðsaÞn : 0.79; FR UL : 7.308 kJ/hr m2 °C.
evacuated tube type with a flat absorber. The gross area was 75.2 m2 and an absorber area of 39.9 m2 . The reported FR ðsaÞ was 0.79 and FR UL was 7.308 kJ/hr m2 °C based on absorber area. Table 5 also shows the comparison between the actual data and present cooling f-chart. The agreement is very good.
352
K.A. Joudi, Q.J. Abdul-Ghafour / Energy Conversion and Management 44 (2003) 341–355
Table 6 Comparison of results between cooling f-chart and experimental results for Colorado State University solar house (I), 1983 Datea
H tilt (MJ/m2 )
Tamb (°C)
Load (MJ) Cooling
Generator
–
132
32.77
2257
–
COP
Xc
Yc
0.553
2.022
1.135
fchart
factual
0.478
0.52
2
Project: Colorado State University; Location: Colorado, USA; Latitude: 38° N; Col. area: 56 m ; FR ðsaÞn : 0.6; FR UL : 11.52 kJ/hr m2 °C. a Note: Results of 122 selected summer days.
7.5. Colorado state university solar house-I (1983) Two solar systems were used for operating the cooling system of this solar house. The first system used 56 m2 Miromit flat plate collectors with FR UL ¼ 11.52 kJ/hr m2 °C. The second system used 60 m2 Phillips evacuated tube collectors with FR ðsaÞn ¼ 0.52 and FR UL ¼ 6.68 kJ/ hr m2 °C [10]. The reported performance results are compared with the present cooling f-chart results and recorded in Table 6. There is only one point, which can be compared. Thus, no graphical presentation is given. The agreement is very good.
7.6. Kuwait institute solar office This office is occupied seven hours per day expect for Fridays and public holidays. More information was available for this project for comparison. The results for the solar fraction are given in Table 7. Fig. 11 shows, graphically, the comparison between the reported solar fraction and the predicted solar fraction from this work. The agreement is rather good for all the weekly data reported [11]. From these comparisons, it is found that the present cooling f-chart is applicable in estimating the solar fraction for solar cooling systems. The experimental results are for installed projects in different locations, different weather data and various collector types. The differences between the experimental and estimated solar fraction values are within a range of 1% to 15% for most of the reported data. Some odd points fall within 20%. One of the reasons for the larger deviation is the shortage in the information reported in the experimental data. Missing data, such as the weekly ð saÞ=ðsaÞn for the Kuwait Institute office had to be estimated from the reported monthly value. This is one example of why there may be differences. These estimates were made as accurately as possible. In general, the cooling f-chart appears to underestimate the solar fraction for all the installations reported above except for the Iraqi solar house. In this situation, it overestimates the cooling solar fraction. The reason behind this is thought to be due to the degradation in the actual solar cooling system for the year reported. The system was in operation for 4 years with untreated water in the collector system, which caused scale deposits. It is thought that in 1984, the year for which the data is given in Ref. [7], the system performance had actually declined from its design point.
K.A. Joudi, Q.J. Abdul-Ghafour / Energy Conversion and Management 44 (2003) 341–355
353
Table 7 Comparison of the results estimated from cooling f-chart with experimental results for Kuwait Institute solar office, 1985 Date (weekly data)
H tilt (MJ/m2 )
Tamb (°C)
18–23/5 25–30/5 1–6/6 8–13/6 22–27/6 29/6–4/7 6–11/7 13–18/7 20–25/7 27/7–1/8 3–8/8 10–15/8 17–22/8 31/8–5/9 7–12/9 14–19/9 21–26/9 28/9–3/10
23.54 25.71 21.57 21.99 26.21 23.15 22.77 29.47 35.04 31.18 33.48 34.92 35.57 34.05 32.42 31.38 30.32 30.04
36.7 37.4 36.2 37 38.3 39.1 39.8 41.5 40.7 39.5 41.9 41.1 41.38 38.7 38.9 36.5 35.2 36.7
Load (MJ) Cooling
Generator
10.24 8.809 8.64 8.63 11.64 11.11 11.57 12.35 10.39 12.51 12.416 10.314 12.75 11.03 11.1 10.85 10.724 10.56
– – – – – – – – – – – – – – – – – –
COP
Xc
Yc
fchart
factual
0.59 0.63 0.61 0.65 0.53 0.52 0.57 0.6 0.52 0.54 0.56 0.55 0.53 0.52 0.51 0.53 0.54 0.57
0.7 0.86 0.865 0.911 0.539 0.547 0.57 0.54 0.487 0.501 0.503 0.603 0.468 0.555 0.539 0.496 0.627 0.656
0.951 1.29 1.05 1.16 0.83 1.04 0.78 0.992 1.039 0.934 1.05 1.29 1 1.114 1.04 1.08 1.074 1.137
0.54 0.71 0.57 0.63 0.49 0.61 0.458 0.582 0.615 0.55 0.62 0.739 0.6 0.647 0.62 0.636 0.62 0.65
0.57 0.77 0.61 0.76 0.5 0.63 0.46 0.62 0.68 0.61 0.69 0.75 0.67 0.71 0.7 0.73 0.72 0.75
Project: Kuwait Institute; Location: Kuwait; Col. area: 300 m2 ; FR ðsaÞn : 0.771; FR UL : 15.25 kJ/hr m2 °C.
Fig. 11. Weekly comparison results between actual and estimated values of solar fraction for Kuwait solar office starting from 18–23/May to 28/Sep–3/Oct 1985.
8. Heating and cooling f-chart design The cooling f-chart reported in this work is an extension of the heating f-chart [1]. They are rather similar in trend and application. However, they are different in the construction up procedure. The main differences between the two f-charts are the following:
354
K.A. Joudi, Q.J. Abdul-Ghafour / Energy Conversion and Management 44 (2003) 341–355
1. The heat exchanger between the collector fluid loop and storage tank, which is used in solar heating system, is omitted in the solar cooling system. 2. The solar cooling f-chart parameters included the coefficient of performance of the lithium bromide-water absorption chiller. 3. The heat dissipated form the storage tank and piping are considered as an energy loss to the ambient. In designing the heating f-chart, the energy loss from piping is not included, and the energy loss from the storage tank is considered to be transferred to the heated space. 4. The technique used in designing the cooling f-chart is based on the minimum allowable storage size, causing zero discarded energy form the pressure relief valve, i.e. the storage volume to collector area ratio is variable, while the technique used in designing the heating f-chart is based on 75‘/m2 , storage volume to collector area ratio. The heating solar fraction needs a correction for other storage sizes.
9. Conclusions From the results obtained form this work, the following conclusions can be made: 1. The cooling f-chart can be recommended as a good method for predicting the solar fraction for solar cooling systems, for any type of building, collector, meteorological conditions and locations. 2. The cooling f-chart can be used for predicting the value of the monthly or average seasonal solar fraction. 3. The cooling f-chart can be used in equation form for computer design procedures for solar cooling systems. 4. Increasing the storage volume to collector area ratio to its optimum value results in increasing the solar fraction. The solar fraction reaches 1.2 times its minimum value when the storage volume reaches 1.45 times the minimum allowable value. 5. The cooling f-chart is designed for monthly values, but it can be used for weekly prediction with good agreement with actual systems.
References [1] Klein SA, Beckman WA, Duffie JA. Solar Heating Design the f Chart Method. New York: John Wiley and Sons, Inc; 1977. [2] TRNSYS. A transient system simulation program. Solar Energy Laboratory, University of Wisconsin, Madison, Engineering Experiment Station report 38–12. [3] Butz LW, Beckman WA, Duffie JA. Simulation of a solar heating and cooling system. Solar Energy 1974;16:129. [4] Blinn JC. Simulation of solar absorption air conditioning. MSc thesis in Chemical Engineering, University of Wisconsin, Madison, 1979. [5] Solar Heating and Cooling in Japan. Product and System Data Manual. Tech-in Notes, YAZAKI Company, 1980. [6] Duffie JA, Beckman WA. Solar engineering of thermal processes. New York: John Wiley and Sons; 1980. [7] AL-Karaghouli A, AL-Hamdani N, AL-Sinan W. Iraqi solar house cooling season performance evaluation. Solar Wind Technol 1989;6(1):29–40.
K.A. Joudi, Q.J. Abdul-Ghafour / Energy Conversion and Management 44 (2003) 341–355
355
[8] Ishibashi T, Yazaki S. The operation results of the Yazaki experimental solar house one and the Ishibashi solar house. American Section of International Solar Energy Society, Inc, 1978. [9] Duff WS, Conway TM, Lof GOG, Meredith DB, Pratt RB. Performance of residential solar heating and cooling system with flat plate and evacuated tubular collectors CSU house––I. Proceeding of the CCMS/ISES Conference on Performance of Solar Heating and Cooling Systems, NATO Committee on Challenges to Modern Society, CCMS report 85, 1978. p. 217. [10] Duff WS, Lof GOG. Comparison of eight solar heating, cooling and hot water systems in Colorado State University solar house I, Perth. Solar World Congress 1983;1:14–9. [11] Al-Shami HR. Performance results of solar absorption cooling installation. Technical Report 1908, Kuwait Institute for Scientific Research, 1985.