Textbook SWH
Textbook SWH
Textbook SWH
Disclaimer
This publication is distributed for informational purposes only and does not necessarily reflect the views of the Government of Canada nor constitute an endorsement of any commercial product or person. Neither Canada, nor its ministers, officers, employees and agents make any warranty in respect to this publication nor assume any liability arising out of this publication.
ISBN: 0-622-35674-8 Catalogue no.: M39-101/2003E-PDF Minister of Natural Resources Canada 2001 - 2004.
TABLE OF CONTENTS
1 SOLAR WATER HEATING BACKGROUND. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.1 Solar Water Heating Application Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.1.1 Service hot water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.1.2 Swimming pools. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
SWH.
2.7 Validation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.7.1 Domestic water heating validation compared with hourly model and monitored data . . . . 49 2.7.2 Swimming pool heating validation compared with hourly model and monitored data. . . . . 52
2.8 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
REFERENCES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
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Figure 1:
Evacuated Tube Solar Collector in Tibet, China.
Photo Credit: Alexandre Monarque
1.
Some of the text in this Background description comes from the following reference: Marbek Resources Consultants, Solar Water Heaters: A Buyers Guide, Report prepared for Energy, Mines and Resources Canada, 1986.
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In addition to the energy cost savings on water heating, there are several other benefits derived from using the suns energy to heat water. Most solar water heaters come with an additional water tank, which feeds the conventional hot water tank. Users benefit from the larger hot water storage capacity and the reduced likelihood of running out of hot water. Some solar water heaters do not require electricity to operate. For these systems, hot water supply is secure from power outages, as long as there is sufficient sunlight to operate the system. Solar water heating systems can also be used to directly heat swimming pool water, with the added benefit of extending the swimming season for outdoor pool applications.
Figure 2:
Solar Domestic Hot Water (Thermosiphon) System in Australia.
Photo Credit: The Australian Greenhouse Office
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Other common uses include providing process hot water for commercial and institutional applications, including multi-unit houses and apartment buildings, as depicted in Figure 3, housing developments as shown in Figure 4, and in schools, health centres, hospitals, office buildings, restaurants and hotels. Small commercial and industrial applications such as car washes, laundries and fish farms are other typical examples of service hot water. Figure 5 shows a solar water heating system at the Rosewall Creek Salmon Hatchery in British Columbia, Canada. 260 m unglazed solar collectors heat make-up water and help increase fingerlings production at the aquaculture facility. Storage tanks help regulate temperature of make-up water. This particular project had a five-year simple payback period. Solar water heating systems can also be used for large industrial loads and for providing energy to district heating networks. A number of large systems have been installed in northern Europe and other locations.
Figure 3:
Glazed Flat-Plate Solar Collectors Integrated into Multi-Unit Housing.
Photo Credit: Chromagen
Figure 4:
Housing Development, Kngsbacka, Sweden.
Photo Credit: Alpo Winberg/Solar Energy Association of Sweden
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Figure 5:
Solar Water Heating Project at a Salmon Hatchery, Canada. Photo Credit: Natural Resources Canada
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There is a strong demand for solar pool heating systems. In the United States, for example, the majority of solar collector sales are for unglazed panels for pool heating applications. When considering solar service hot water and swimming pool application markets, there are a number of factors that can help determine if a particular project has a reasonable market potential and chance for successful implementation. These factors include a large demand for hot water to reduce the relative importance of project fixed costs; high local energy costs; unreliable conventional energy supply; and/or a strong environmental interest by potential customers and other project stakeholders.
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Figure 7:
System Schematic for Typical Solar Domestic Water Heater.
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Figure 8:
System Schematic for Unglazed Flat-Plate Solar Collector.
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Vapour and Condensed Liquid within Heat Pipe Absorber Plate Heat Pipe
Figure 10:
System Schematic for Evacuated Tube Solar Collector.
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2. Hot water storage tank (not required in swimming pool applications and in some large commercial or industrial applications when there is a continuous service hot water flow); 3. Liquid handling unit, which includes a pump required to transfer the fluid from the solar collector to the hot water storage tank (except in thermosiphon systems where circulation is natural, and outdoor swimming pool applications where the existing filtration system pump is generally used); it also includes valves, strainers, and a thermal expansion tank; 4. Controller, which activates the circulator only when useable heat is available from the solar collectors (not required for thermosiphon systems or if a photovoltaic-powered circulator is used); 5. Freeze protection, required for use during cold weather operation, typically through the use in the solar loop of a special antifreeze heat transfer fluid with a low-toxicity. The solar collector fluid is separated from the hot water in the storage tank by a heat exchanger; and 6. Other features, mainly relating to safety, such as overheating protection, seasonal systems freeze protection or prevention against restart of a large system after a stagnation period. Typically, an existing conventional water heating system is used for back-up to the solar water heating system, with the exception that a back-up system is normally not required for most outdoor swimming pool applications.
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sensitivity of important financial indicators in relation to key technical and financial parameters. In general, the user works from top-down for each of the worksheets. This process can be repeated several times in order to help optimize the design of the solar water heating project from an energy use and cost standpoint.
This section describes the various algorithms used to calculate, on a month-by-month basis, the energy savings of solar water heating systems in RETScreen. A flowchart of the algorithms is shown in Figure 12. The behaviour of thermal systems is quite complex and changes from one instant to the next depending on available solar radiation, other meteorological variables such as ambient temperature, wind speed and relative humidity, and load. RETScreen does not do a detailed simulation of the systems behaviour. Instead, it uses simplified models which
SWH.15
enable the calculation of average energy savings on a monthly basis. There are essentially three models, which cover the basic applications considered by RETScreen:
Service water heating with storage, calculated with the f-Chart method; Service water heating without storage, calculated with the utilisability method; and Swimming pools, calculated by an ad-hoc method. There are two variants of the last model, addressing indoor and outdoor pools. All of the models share a number of common methods, for example to calculate cold water temperature, sky temperature, or the radiation incident upon the solar collector. These are described in Section 2.1. Another common feature of all models is that they need to calculate solar collector efficiency; this is dealt with in Section 2.2. Then, three sections which deal with the specifics of each application are described: Section 2.3 covers the f-Chart method, Section 2.4 the utilisability method, and Section 2.5 swimming pool calculations. Section 2.6 deals with auxiliary calculations (pumping power, solar fraction). A validation of the RETScreen Solar Water Heating Project Model is presented in Section 2.7. Because of the simplifications introduced in the models, the RETScreen Solar Water Heating Project Model has a few limitations. First, the process hot water model assumes that daily volumetric load is constant over the season of use. Second, except for swimming pool applications, the model is limited to the preheating of water; it does not consider standalone systems that provide 100% of the load. For service hot water systems without storage, only low solar fractions (and penetration levels) should be considered as it is assumed that all the energy collected is used. For swimming pools with no back-up heaters, results should be considered with caution if the solar fraction is lower than 70%. And third, sun tracking and solar concentrator systems currently cannot be evaluated with this model; neither can Integral Collector Storage (ICS) systems. However, for the majority of applications, these limitations are without consequence.
Figure 12:
Solar Water Heating Energy Model Flowchart.
Calculate environmental variables, including solar radiation in plane of collector [section 2.1]
Swimming pools
Calculate renewable energy delivered and auxiliary heating needs [section 2.5.8]
Other calculations: suggested collector area, pumping needs, etc. [section 2.6]
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Declination
The declination is the angular position of the sun at solar noon, with respect to the plane of the equator. Its value in degrees is given by Coopers equation:
(1)
where n is the day of year (i.e. n =1 for January 1, n =32 for February 1, etc.). Declination varies between -23.45 on December 21 and +23.45 on June 21.
(2)
where is the declination, calculated through equation (1), and is the latitude of the site, specified by the user.
2.
Solar time is the time based on the apparent motion of the sun across the sky. Solar noon corresponds to the moment when the sun is at its highest point in the sky.
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(3)
where Gsc is the solar constant equal to 1,367W/m 2, and all other variables have the same meaning as before. Before reaching the surface of the earth, radiation from the sun is attenuated by the atmosphere and the clouds. The ratio of solar radiation at the surface of the earth to extraterrestrial radiation is called the clearness index. Thus the monthly average clearness index, K T , is defined as:
(4)
where H is the monthly average daily solar radiation on a horizontal surface and H 0 is the monthly average extraterrestrial daily solar radiation on a horizontal surface. K T values depend on the location and the time of year considered; they are usually between 0.3 (for very overcast climates) and 0.8 (for very sunny locations).
(5)
The first term on the right-hand side of this equation represents solar radiation coming directly from the sun. It is the product of monthly average beam radiation H b times a purely geometrical factor, Rb , which depends only on collector orientation, site latitude,
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and time of year3. The second term represents the contribution of monthly average diffuse radiation, H d , which depends on the slope of the collector, . The last term represents reflection of radiation on the ground in front of the collector, and depends on the slope of the collector and on ground reflectivity, g . This latter value is assumed to be equal to 0.2 when the monthly average temperature is above 0C and 0.7 when it is below -5C; and to vary linearly with temperature between these two thresholds. Monthly average daily diffuse radiation is calculated from global radiation through the following formulae: for values of the sunset hour angle s less than 81.4:
(6)
(7)
(8)
3.
The derivation of Rb does not present any difficulty but has been left out of this section to avoid tedious mathematical developments, particularly when the solar azimuth is not zero. For details see Duffie and Beckman (1991) sections 2.19 and 2.20.
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(9)
where is the Stefan-Boltzmann constant (5.669x10-8 (W/m2)/K4). Sky radiation varies depending on the presence or absence of clouds as experienced in everyday life, clear nights tend to be colder and overcast nights are usually warmer. Clear sky long-wave radiation (i.e. in the absence of clouds) is computed using Swinbanks formula (Swinbank, 1963):
(10)
where Ta is the ambient temperature expressed in C. For cloudy (overcast) skies, the model assumes that clouds are at a temperature (Ta 5) and emit long wave radiation with an emittance of 0.96, that is, overcast sky radiation is computed as:
(11)
The actual sky radiation falls somewhere in-between the clear and the cloudy values. If c is the fraction of the sky covered by clouds, sky radiation may be approximated by:
(12)
To obtain a rough estimate of c over the month, the model establishes a correspondence between cloud amount and the fraction of monthly average daily radiation that is diffuse. A clear sky will lead to a diffuse fraction K d = H d H around 0.165; an overcast sky will lead to a diffuse fraction of 1. Hence,
(13)
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K d is calculated from the monthly average clearness index KT using the Collares-Pereira
and Rabl correlation (cited in Duffie and Beckman, 1991, note 11, p. 84), written for the average day of the month (i.e. assuming that the daily clearness index KT is equal to its monthly average value KT ):
(14)
Automatic calculation
Diffusion of heat in the ground obeys approximately the equation of heat:
(15)
where T stands for soil temperature, t stands for time, is the thermal diffusivity of soil (in m2/s), and z is the vertical distance. For a semi-infinite soil with a periodic fluctuation at the surface:
(16)
t = and z / is its where T0 is the amplitude of temperature fluctuation at the surface frequency for month i. The solution to equation (16), giving the temperature T(z,t) at a depth z and a time t, is simply:
(17)
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(18)
In other words, a seasonal (yearly) fluctuation of amplitude T at the surface will be felt at a depth z with an amplitude and with a delay t = z / . The RETScreen SWH Project Model assumes that cold water temperature is equal to soil temperature at an appropriate depth. The model takes = 0.52x10-6 m2/s (which corresponds to a dry heavy soil or a damp light soil, according to the 1991 ASHRAE Applications Handbook; see ASHRAE, 1991), and z =2m, the assumed depth at which water pipes are buried. This leads to:
(19)
(20)
(21)
This theoretical model was tuned up in light of experimental data for Toronto, Ontario, Canada (see Figure 13). It appeared that a factor of 0.35 would be better suited than 0.42 in equation (20), and a time lag of 1 month gives a better fit than a time lag of 2 months. The tune up is necessary and methodologically acceptable given the coarseness of the assumptions made in the model. The model above enables the calculation of water temperature for any month, with the following algorithm. Water temperature for month i is equal to the yearly average water temperature, plus 0.35 times the difference between ambient temperature and average temperature for month i-1. In addition, the model also limits water temperature to +1 in the winter (i.e. water does not freeze). Table 1 and Figure 13 compare measured and predicted water temperatures for Toronto and indicate that this simplified method of cold water temperature calculation is satisfactory, at least for this particular example.
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Month
T ambient
[C]
(calculated) [C] 3.5 2.4 2.6 4.4 6.9 9.0 10.9 11.9 11.6 10.2 8.0 5.9 7.30
T water
(measured) [C] 4.0 2.0 3.0 4.5 7.5 8.5 11.0 12.0 10.0 9.0 8.0 6.0 7.12
T water
1 2 3 4 5 6 7 8 9 10 11 12 Yearly average
-6.7 -6.1 -1.0 6.2 12.3 17.7 20.6 19.7 15.5 9.3 3.3 -3.5 7.28
Table 1: Tabular Comparison of Calculated and Measured Cold Water Temperatures for Toronto, Ontario, Canada.
25
20
15
10
0 1 -5 2 3 4 5 6 7 8 9 10 11 12
-10
Month
Figure 13:
Graphical Comparison of Calculated and Measured Cold Water Temperatures for Toronto, Ontario, Canada. [Hosatte, 1998].
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Manual calculation
A sinusoidal profile is generated from the minimum and maximum temperatures specified by the user, assuming the minimum is reached in February and the maximum in August in the Northern Hemisphere (the situation being reversed in the Southern Hemisphere). Hence the average soil (or cold water) temperature Ts is expressed as a function of minimum temperature Tmin , maximum temperature Tmax , and month number n as:
(22)
(23)
where C p is the heat capacitance of water (4,200 (J/kg)/C), its density (1kg/L), and Tc is the cold (mains) water temperature. Qload is prorated by the number of days the system is used per week.
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(24)
is the energy collected per unit collector area per unit time, F is the where Q coll R collectors heat removal factor, is the transmittance of the cover, is the shortwave absorptivity of the absorber, G is the global incident solar radiation on the collector, U L is the overall heat loss cfficient of the collector, and T is the temperature differential between the working fluid entering the collectors and outside.
Values of FR ( ) and FRU L are specified by the user or chosen by selecting a solar collector from the RETScreen Online Product Database. For both glazed and evacuated collectors, FR ( ) and FRU L are independent of wind. Generic values are also provided for glazed and evacuated collectors. Generic glazed collectors are provided with FR ( ) =0.68 and FRU L =4.90(W/m 2)/C. These values correspond to test results for ThermoDynamics collectors (Chandrashekar and Thevenard, 1995). Generic evacuated collectors are also provided with FR ( ) =0.58 and FRU L =0.7(W/m2)/C. These values correspond to a Fournelle evacuated tube collector (Philips technology; Hosatte, 1998).
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(25)
where is the longwave emissivity of the absorber, and irradiance. L is defined as:
(26)
where Lsky is the longwave sky irradiance (see Section 2.1.3) and expressed in C.
FR and FRU L are a function of the wind speed V incident upon the collector. The values of FR and FRU L , as well as their wind dependency, are specified by the user or chosen by selecting a collector from the RETScreen Online Product Database. The wind speed incident upon the collector is set to 20% of the free stream air velocity specified by the user (or copied from the weather database). The ratio / is set to 0.96.
Because of the scarcity of performance measurements for unglazed collectors, a generic unglazed collector is also defined as:
(27)
(28)
These values were obtained by averaging the performance of several collectors (NRCan, 1998).
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(29)
where G is the global solar radiation incident in the plane of the collector , is the shortwave absorptivity of the absorber, is the longwave emissivity of the absorber ( / is set to 0.96, as before), and L is the relative longwave sky irradiance. In the RETScreen algorithms, effective irradiance is substituted to irradiance in all equations involving the collector when an unglazed collector is used. The reader has to keep this in mind when encountering the developments of algorithms in Sections 2.3 and 2.4.
(30)
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For systems with storage, the situation is slightly different since the system may be able, in some cases, to compensate for the piping and tank losses by collecting and storing extra energy. Therefore, the load Qload ,tot used in the f-Chart method (see Section 2.3) is increased to include piping and tank losses:
(31)
(32)
(33)
is the modified collector heat removal factor, UL is the where Ac is the collector area, FR collector overall loss cfficient, Tref is an empirical reference temperature equal to 100C, Ta is the monthly average ambient temperature, L is the monthly total heating load, is the collectors monthly average transmittance-absorptance product, H T is the monthly
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average daily radiation incident on the collector surface per unit area, and N is the number of days in the month.
FR accounts for the effectiveness of the collector-storage heat exchanger (see Figure 14 for a / FR is a function of heat exchanger effectiveness (see diagram of the system). The ratio FR
Duffie and Beckman, 1991, section 10.2):
(34)
is the flow rate and C p is the specific heat. Subscripts c and min stand for collectorwhere m side and minimum of collector-side and tank-side of the heat exchanger.
Mixing valve Load Aux. storage tank
Collector
Collectorstorage exchanger
Storageload exchanger
Tempering loop
Figure 14:
Diagram of a Solar Domestic Hot Water System.
is equal to FR . If there is a heat exchanger, the model If there is no heat exchanger, FR assumes that the flow rates on both sides of the heat exchanger are the same. The specific heat of water is 4.2(kJ/kg)/C, and that of glycol is set to 3.85(kJ/kg)/C. Finally is equal to 140 m2s/kg; this value is computed the model assumes that the ratio Ac / m from ThermoDynamics collector test data (area 2.97m2, test flow rate 0.0214kg/s; Chandrashekar and Thevenard, 1995). X has to be corrected for both storage size and cold water temperature. The f-Chart method was developed with a standard storage capacity of 75litres of stored water per square meter of collector area. For other storage capacities X has to be multiplied by a correction factor X c / X defined by:
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(35)
This equation is valid for ratios of actual to standard storage capacities between 0.5 and 4. Finally, to account for the fluctuation of supply (mains) water temperature Tm and for the minimum acceptable hot water temperature Tw , both of which have an influence on the performance of the solar water heating system, X has to be multiplied by a correction factor X cc / X defined by:
(36)
where Ta is the monthly mean ambient temperature. The fraction f of the monthly total load supplied by the solar water heating system is given as a function of X and Y as:
(37)
There are some strict limitations on the range for which this formula is valid. However as shown in Figure 15, the surface described by equation (37) is fairly smooth, so extrapolation should not be a problem. If the formula predicts a value of f less than 0, a value of 0 is used; if f is greater than 1, a value of 1 is used.
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1.5
0.5
0.5 - 1 -0.5 - 0
X
Figure 15:
f-Chart Correlation.
16
18
(38)
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where Ti is the temperature of the working fluid entering the collector and all other variables have the same meaning as in equation (24). This makes it possible to define a critical irradiance level Gc which must be exceeded in order for solar energy collection to occur. Since the model is dealing with monthly averaged values, Gc is defined using monthly average transmittance-absorptance and monthly average daytime temperature Ta (assumed to be equal to the average temperature plus 5C) through:
(39)
Combining this definition with equation (24) leads to the following expression for the average daily energy Q collected during a given month:
(40)
where N is the number of days in the month, G is the hourly irradiance in the plane of the collector, and the + superscript denotes that only positive values of the quantity between brackets are considered. The monthly average daily utilisability , is defined as the sum for a month, over all hours and days, of the radiation incident upon the collector that is above the critical level, divided by the monthly radiation:
(41)
where H T is the monthly average daily irradiance in the plane of the collector. Substituting this definition into equation (40) leads to a simple formula for the monthly useful energy gain:
(42)
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The purpose of the utilisability method is to calculate from the collector orientation and the monthly radiation data entered by the user (or copied from the RETScreen Online Weather Database). The method correlates to the monthly average clearness index KT and two variables: a geometric factor R Rn and a dimensionless critical radiation level X c , as described hereafter.
2.4.2 Geometric factor R Rn R is the monthly ratio of radiation in the plane of the collector, H T , to that on a horizontal surface, H :
(43)
where H T is calculated as explained in Section 2.1.2. Rn is the ratio for the hour centered at noon of radiation on the tilted surface to that on a horizontal surface for an average day of the month. This is expressed through the following equation:
(44)
where rt , n is the ratio of hourly total to daily total radiation, for the hour centered around solar noon. rd , n is the ratio of hourly diffuse to daily diffuse radiation, also for the hour centered around solar noon. This formula is computed for an average day of month, i.e. a day with daily global radiation H equal to the monthly average daily global radiation H ; H d is the monthly average daily diffuse radiation for that average day (calculated through equation 14), is the slope of the collector, and g is the average ground albedo (see Section 2.1.2).
rt ,n is computed by the Collares-Pereira and Rabl equation (Duffie and Beckman, 1991,
ch. 2.13), written for solar noon:
(45)
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(46)
(47)
with s the sunset hour angle (see equation 2), expressed in radians. rd , n is computed by the Liu and Jordan equation, written for solar noon:
(48)
2.4.3 Dimensionless critical radiation level X c X c is defined as the ratio of the critical radiation level to the noon radiation level on the typical day of the month:
(49)
(50)
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with:
(51a)
(51b)
(51c)
With this, the amount of energy collected can be computed, as shown earlier in equation (42).
(52)
where N days is the number of days in the month and 86,400 is the number of seconds in a day.
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SOLAR COLLECTOR
Radiative losses
Conductive losses
Makeup losses
WATER MAKEUP
Figure 16:
Energy Gains and Losses in a Swimming Pool.
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Wind speed
Simulations show that if a pool cover (also called blanket) is used for part of the day and the monthly average wind speed is used for the simulation, evaporative losses are underestimated. This can be related to the fact that wind speed is usually much higher during the day (when the pool cover is off) than at night. Observations made for Toronto, ON; Montreal, QC; Phoenix, AZ; and Miami, FL roughly show that the maximum wind speed in the afternoon is twice the minimum wind speed at night. Consequently wind speed fluctuation during the day is modelled in RETScreen SWH Project Model by a sinusoidal function:
(53)
where Vh is the wind velocity at hour h, V is the average of the wind speed fluctuation, and h0 represents a time shift. The model assumes that the maximum wind speed occurs when the cover is off; averaging over the whole period with no cover leads to the following average value:
(54)
where N blanket is the number of hours per day the cover is on. Similarly, the average wind speed when the pool cover is on is:
(55)
Finally, wind speed is multiplied by the user-entered sheltering factor to account for reduction of wind speed due to natural obstacles around the pool.
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Relative humidity
Evaporation from the pool surface depends on the moisture contents of the air. In RETScreen, the calculation of evaporation cfficients is done using the humidity ratio of the air, rather than its relative humidity; this is because the humidity ratio (expressed in kg of water per kg of dry air) is usually much more constant during the day than the relative humidity, which varies not only with moisture contents but also with ambient temperature. The humidity ratio calculation is done according to formulae from ASHRAE Fundamentals (ASHRAE, 1997).
(56)
where Ap is the pool area, rb is the average reflectivity of water to beam radiation and rd is the average reflectivity of water to diffuse radiation. As before, H b and H d are the monthly average beam and diffuse radiation (see equations 6 to 8). The user-specified shading cfficient s applies only to the beam portion of radiation. A short mathematical development will explain how rb and rd are calculated. A ray of light entering water with an angle of incidence z will have an angle of refraction w in the water defined by Snells law (Duffie and Beckman, 1991, eq. 5.1.4; see Figure 17):
(57)
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where nair and nwater are the indices of refraction of air and water:
(58)
(59)
Figure 17:
Snells Law.
z
AIR
WATER
rb can be computed with the help of Fresnels laws for parallel and perpendicular components of reflected radiation (Duffie and Beckman, 1991, eqs. 5.1.1to 5.1.3):
(60)
(61)
(62)
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Once all calculations are made, it is apparent that rb is a function of z only. Figure 18 shows that rb can be safely approximated by:
(63)
1.2
1.0
water reflectivity
0.8
0.6
0.4
0.2
0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
cos(zenith angle)
Figure 18:
Reflectivity of Water as a Function of the Cosine of the Zenith Angle.
To account for the fact that the sun is lower on the horizon in the winter, a separate value of rb is computed for each month. The equation above is used with z calculated 2.5h from solar noon (the value 2.5h comes from Duffie and Beckman, 1991, p.244). Reflectivity to diffuse radiation is independent of sun position and is basically equal to the reflectivity calculated with an angle of incidence of 60 (Duffie and Beckman, 1991, p. 227). Using the exact equation, a value of rd =0.060 is found.
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(64)
where c is the absorptivity of the blanket, set to 0.4, and H is, as before, the monthly average global radiation on the horizontal.
(65)
and the passive solar gain is simply assumed to be equal to the sum of passive solar gains with and without cover, prorated by the number of hours the blanket is off during daytime:
(66)
Expressed per unit time, the passive solar gain rate is calculated according to equation (52):
(67)
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(68)
is the power (in W) dissipated as a result of evaporation of water from the where Q eva pool, he is a mass transfer cfficient, and Pv , sat and Pv , amb are the partial pressure of water vapour at saturation and for ambient conditions. The mass transfer cfficient he (in (W/m2)/Pa) is expressed as:
(69)
where V is the wind velocity at the pool surface, expressed in m/s. The partial pressure of water vapour at saturation, Pv , sat , is calculated with formulae from ASHRAE (1997). The partial pressure of water vapour for ambient conditions, Pv , amb , is calculated from the humidity ratio, also with formulae from ASHRAE (1997).
by: eva , in kg/s, is related to Q The rate of evaporation of water from the pool, m eva
(70)
where is the latent heat of vaporisation of water (2,454 kJ/kg). When the pool cover is on, it is assumed to cover 90% of the surface of the pool and therefore evaporation is reduced by 90%. When the pool cover is off, losses are multiplied by two to account for activity in the pool (Hahne and Kbler, 1994).
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(71)
is the rate of heat loss due to convective phenomena (in W), T is the pool where Q p con temperature, Ta is the ambient temperature, and the convective heat transfer cfficient hcon is expressed as:
(72)
(73)
where w is the emittance of water in the infrared (0.96), is the Stefan-Boltzmann constant (5.669x10-8 (W/m2)/K4), Tp is the pool temperature and Tsky is the sky temperature (see Section 2.1.3). In the presence of a blanket, assuming 90% of the pool is covered, radiative losses become:
(74)
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where c is the emissivity of the pool blanket. Depending on the cover material the emissivity can range from 0.3 to 0.9 (NRCan, 1998). A mean value of 0.4 is used. Combining the two previous equations with the amount of time the cover is on and the values of w and c mentioned above one obtains:
(75)
(76)
where is the water density (1,000 kg/m3) and V p is the pool volume. The pool volume is computed from the pool area assuming an average depth of 1.5m:
(77)
(78)
where Tc is the cold (mains) temperature (see Section 2.1.4) and C p is the heat capacitance of water (4,200 (J/kg)/C).
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(79)
2.5.8 Active solar gains are determined by the utilisability method (see Maximum possible active solar gains Q act Section 2.4), assuming the pool temperature is equal to its desired value. 2.5.9 Energy balance required to maintain the pool at the desired temperature is expressed The energy rate Q req as the sum of all losses minus the passive solar gains:
(80)
This energy has to come either from the backup heater, or from the solar collectors. The , is the minimum rate of energy actually delivered by the renewable energy system, Q dvd of the energy required and the energy delivered by the collectors:
(81)
If the solar energy collected is greater than the energy required by the pool, then the pool temperature will be greater than the desired pool temperature. This could translate into a lower energy requirement for the next month, however this is not taken into account by the model. The required to maintain the pool at the desired temperature is simply the auxiliary power Q aux difference between power requirements and power delivered by the renewable energy system:
(82)
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(83)
which is then solved for the collector area, Ac . This provides 12 monthly values of suggested solar collector area. Then: For service hot water, the model takes the smallest of the monthly values. For a system without storage this ensures that even for the sunniest month the renewable energy delivered does not exceed 15% of the load. For a system with storage, 100% of the load would be provided for the sunniest month, if the system could use all the energy available. However because systems with storage are less efficient (since they work at a higher temperature), the method will usually lead to smaller solar fractions, typically around 70% for the sunniest month. For swimming pools, the method above does not work since the load may be zero during the sunniest months. Therefore the model takes the average of the calculated monthly suggested solar collector areas over the season of use. The number of solar collectors is calculated as the suggested collector area divided by the area of an individual collector, rounded up to the nearest integer.
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(84)
where Ppump is the pumping power per collector area and N coll the number of hours per year the collector is in operation. A rough estimate of N coll is obtained through the following method: if the collector was running without losses whenever there is sunshine, it would collect . It actually collects Qdld (1 + f los ) where Qdld is the energy delivered to the system and f los is the fraction of solar energy lost to the environment through piping and tank. N coll is simply estimated as the ratio of these two quantities, times the number of daytime hours for the month, N daytime :
(85)
Comparison with simulation shows that the method above tends to overestimate the number of hours of collector operation. A corrective factor of 0.75 is applied to compensate for the overestimation.
2.7 Validation
Numerous experts have contributed to the development, testing and validation of the RETScreen Solar Water Heating Project Model. They include solar water heating modelling experts, cost engineering experts, greenhouse gas modelling specialists, financial analysis professionals, and ground station and satellite weather database scientists.
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2.7.1 Domestic water heating validation compared with hourly model and monitored data
This section presents two examples of the validations completed for domestic water heating applications. First, predictions of the RETScreen Solar Water Heating Project Model are compared to results from the WATSUN hourly simulation program. Then, model predictions are compared to data measured at 10 real solar water heating project sites.
Description
Glazed, 5 m2 60 degrees facing south Fully mixed, 0.4 m3 70% effectiveness Toronto, ON, Canada
RETScreen
24.34 19.64 8.02 1,874
WATSUN
24.79 19.73 8.01 1,800
Difference
-1.8% -0.5% 0.1% 4.1%
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3.0
2.5
2.0
1.5
1.0
0.5
0.0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Month
Load (GJ)
1.2 1.0 0.8 0.6 0.4 0.2 0.0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Month
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1.0
0.8
0.6
0.4
0.2
0.0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Month
150
100
50
0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Month
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2,500
2,000
1,500
1,000
500 500
1,000
1,500
2,000
2,500
3,000
Figure 20:
Comparison of RETScreen Predictions to Monitored Data for Guelph, Ontario, Canada.
2.7.2 Swimming pool heating validation compared with hourly model and monitored data
This section presents two examples of the validations completed for swimming pool heating applications. First, predictions of the RETScreen Solar Water Heating Project Model are compared to results from the ENERPOOL hourly simulation program. Then, model predictions are compared to data measured at a real solar pool heating project site.
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Description
48 m2 8h/day 27C 25 m2 May 1st September 30th Montreal, QC, Canada
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60 ENERPOOL RETScreen 50
40
30
20
10
Month
30 ENERPOOL RETScreen 25
20
15
10
Month
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35 ENERPOOL RETScreen
30
25
20
15
10
Month
10 9 8 ENERPOOL RETScreen
Month
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Description
1,200 m2 14h/day* 24C 650 m2 May 5th September 6th
Table 5: Swimming Pool Heating System Parameters for Mhringen, Germany (* = estimated).
Over the pools swimming season energy requirements are measured at 546 MWh and estimated at 528 MWh by RETScreen (-3%). Energy from the solar collectors is measured at 152 MWh with system efficiency around 38%; RETScreen predicts 173 MWh (+14%) and 44% efficiency, respectively. As for domestic water heating the errors in the estimates of RETScreen are well within the range required for pre-feasibility and feasibility analysis studies.
2.8 Summary
In this section the algorithms used by the RETScreen Solar Water Heating Project Model have been shown in detail. The tilted irradiance calculation algorithm, the calculation of environmental variables such as sky temperature, and the collector model are common to all applications. Energy delivered by hot water systems with storage is estimated with the f-Chart method. For systems without storage, the utilisability method is used. The same method is also used to estimate the amount of energy actively collected by pool systems; pool losses and passive solar gains are estimated through a separate algorithm. Comparison of the RETScreen model predictions to results of hourly simulation programs and to monitored data shows that the accuracy of the RETScreen Solar Water Heating Project Model is excellent in regards to the preparation of pre-feasibility studies, particularly given the fact that RETScreen only requires 12 points of data versus 8,760 points of data for most hourly simulation models.
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REFERENCES
ASHRAE, Applications Handbook, American Society of Heating, Refrigerating and AirConditioning Engineers, Inc., 1791 Tullie Circle, N.E., Atlanta, GA, 30329, USA, 1991. ASHRAE, Applications Handbook (SI) - Service Water Heating, American Society of Heating, Refrigerating, and Air- Conditioning Engineers, Inc., 1791 Tullie Circle, N.E., Atlanta, GA, 30329, USA, 1995. ASHRAE, Handbook - Fundamentals, SI Edition, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc., 1791 Tullie Circle, N.E., Atlanta, GA, 30329, USA, 1997. Carpenter, S. and Kokko, J., Estimating Hot Water Use in Existing Commercial Buildings, ASHRAE Transactions, Summer Meeting 1988, Ottawa, ON, Canada, 1988. Chandrashekar, M. and Thevenard, D., Comparison of WATSUN 13.1 Simulations with Solar Domestic Hot Water System Test Data from ORTECH/NSTF Revised Report, Watsun Simulation Laboratory, University of Waterloo, Waterloo, ON, Canada, N2L 3G1, 1995. Duffie, J.A. and Beckman, W.A., Solar Engineering of Thermal Processes, 2nd Edition, John Wiley & Sons, 1991. Enermodal, Monitoring Results for the Waterloo-Wellington S-2000 Program, Report Prepared by Enermodal Engineering Ltd., and Bodycote Ortech for Natural Resources Canada, Enermodal Engineering Ltd., 650 Riverbend Drive, Kitchener, ON, Canada, N2K 3S2, 1999. Hahne, E. and Kbler, R., Monitoring and Simulation of the Thermal Performance of Solar Heated Outdoor Swimming Pools, Solar Energy 53, l, pp. 9-19, 1994. Hosatte, P., Personal Communication, 1998. Marbek Resource Consultants, Solar Water Heaters: A Buyers Guide, Report Prepared for Energy, Mines and Resources Canada, 1986. NRCan, ENERPOOL Program, Version 2.0, 1998. Smith, C. C., Lf, G. and Jones, R., Measurement and Analysis of Evaporation from an Inactive Outdoor Swimming Pool, Solar Energy 53, 1, pp. 3-7, 1994. Soltau, H., Testing the Thermal Performance of Uncovered Solar Collectors, Solar Energy 49, 4, pp. 263-272, 1992. Swinbank, W. C., Long-Wave Radiation from Clear Skies, Quarterly J. Royal Meteorological Soc., 89 (1963) pp. 339-348, 1963. University of Waterloo, WATSUN Computer Program, Version 13.2, University of Waterloo, Waterloo, ON, Canada, N2L 3G1, 1994.
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