Solar Efficiency
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Solar water heater performance is often presented as a graph, or set of three performance variables. Values may be provided based on gross area, aperture area or absorber area. In Europe, aperture or absorber is often used, in the US, gross area is often used. It doesn't really matter which values is used, as long as you use the correct value. ie. Don't use absorber area when using performance values based on gross area.
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To adjust from one to the other, multiply by the size difference.
ie. Absorber area = 0.6m2, gross area = 1.1m2. If performance variables are provided for gross area, multiply by 1.83 (1.1/0.6 = 1.83) to obtain absorber area values. The smaller the area used, the higher the performance variable values.
The three performance variables for the AP solar collector as provided by the SPF testing laboratory in Switzerland (SPF report C632LPEN) are as follows (for metric calculations - absorber area):
Conversion Factor: h0 = 0.717
Loss Coefficient: a1 = 1.52 W/(m2K)
Loss Coefficient: a2 = 0.0085 W/(m2K2)
As well as the three performance variables shown above, insolation level (G) in Watts/m2, ambient temperatures (Ta) and average manifold temperature (Tm) must be know. These values give the value x, also sometimes presented as T*m, used in the formula below.
How to use the formula?
Based on the ambient temperature, average manifold temperature and insolation level firstly calculate the value for x.
Eg. At 2:00pm, the ambient temperature is 25oC (77oF), and the average water temp [(Tin+Tex)/2] is 50oC (122oF). The insolation level is 800Watts/m2 (252Btu/ft2).
x = (50-25)/800 = 0.03125
Now enter all the values into the formula:
h(x) = 0.717 - (1.52*0.03125) - (0.0085*800*0.03125*0.03125)
h(x) = 0.717 - 0.0475 - 0.0066 = 0.663
The solar conversion efficiency for that specific point in time and set of environmental conditions is 66.3%. That is: 66.3% of the energy provided by the sun is actually used to heat the water.
Based on the assumption that those three environmental factors (G, Tm and Ta) are stable for a period of one hour, then 800 x 0.663 = 530.4 Watts of energy per m2 of absorber area will be used to heat the water (168Btu/ft2)
530.4Watts is equivalent to 456kcal, which could heat 100L of water by 4.56oC (20 Gallons by 10.9oF)
Below is a graph showing the performance curves for the AP solar water heater at three different insolation levels, from 0 to 80oC Delta-T. In most cases the Delta-T values will be in the range of 20-50oC, with higher values present for high temperature heating such a for absorption cooling applications, or during very cold weather. As can be seen conversion efficiency is highly dependent on solar insolation levels, with higher insolation yielding greater levels of solar conversion.
In reality ambient temperature will fluctuate, and the manifold temperature will gradually increase as the water is heated. Furthermore insolation levels may fluctuate with intermittent cloud cover. In order to more accurately calculate energy output per day/month/year a more complete set of environmental data must be considered and many (hourly) performance calculations throughout the day taken. Your local ApricusTM distributor can provide estimates of average monthly and annual performance, heat output and thus solar contribution for your location.
One factor which is not considered in the straight performance calculations outlined above, is the affect of transversal IAM values (Incidence Angle Modifier) on solar collector output throughout the day. Please read the following section to learn more about IAM |
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Understanding IAM
IAM is an acronym for Incidence Angle Modifier and is simply a numeric value with refers to the amount of available solar radiation striking the absorber of the collector. A value of 1 is achieved when the collector is perpendicular to the suns rays, and therefore receiving maximum radiation.
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A solar collector that is mounted on a device to track the sun from sunrise to sunset (as commonly use in PV applications) will maintain a IAM value of 1 throughout the day, as the collector is always facing the sun. A collector that is installed at a fixed angle (generally equal to the location's latitude), will experience decreased radiation levels (IAM value < 1) in the morning and afternoon when the sun is not perpendicular to the absorber surface.
For most solar water heaters currently on the market, IAM is not an important consideration when comparing performance. This is because flat plate collectors, evacuated tube collector with a flat absorber, or those that using reflective panels usually have a fairly similar set of transversal and longitudinal IAM values. The value of most concern for fixed angle collectors is transversal IAM, as this reflects the solar radiation throughout the day. Longitudinal IAM is useful when looking at installation angle, and the changes in heat output throughout the year as angle of the sun above the horizon changes between winter and summer.
The longitudinal and transversal IAM values for the AP solar collector are as follows:
0 0o 10o 20o 30o 40o 50o 60o 70o 80o 90o
Kq (longitudinal) 1.0 0 0 0 0 0.93 0 0 0 0.0
Kq (transversal) 1.0 1.02 1.08 1.18 1.37 1.4 1.34 1.24 0.95 0.0
SPF report C632LPEN)
Note: 1o = 4minutes of time. So 1hour = 15o
The following graph displays the transversal IAM values for the AP model, a leading flat-plate and leading evacuated tube reflective panel solar water heater.
As can be seen, the AP solar water heater has a curve which is quite different to the other two solar water heaters. This is due to the cylindrical absorber area, which passively tracks the sun throughout the day. At 40-50o there is no light lost between the tubes, and no tube overlap, hence a peak in relative performance. This is ideal, as during this period (mid morning through mid afternoon) solar isolation levels are quite highest. The peak at 70o provided by the ET-reflect is of little benefit as this angle corresponds to early morning or late afternoon when solar insolation levels are very low. The flat plate collector's IAM values drop away from 1 as the angle increases, and as such solar conversion efficiency is only at peak levels at midday.
In order to accurately assess these values, they must be cosine adjusted, to account for the change in solar radiation levels on a given surface area as the sun passes across the sky each day.
Cosine Adjusted Transversal IAM Values (IAM Adjustment)
Because of the round shape of the solar tubes, the absorber passively tracks the sun from 40o either side of midday (9:20am to 2:40pm). The cosine adjusted IAM values confirm this, as the collector maintains a value of ~1 up until 40o, beyond which the tubes start to overlap and the relative surface area decreases. Flat plate collectors, and other collectors with flat absorbers display a fairly standard bell curve, only peaking at midday. |
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To understand how the tubes passively track the sun throughout the day, refer to the diagram to the left.
When looking at the tubes from above (0o) each tube's surface is clearly visible, and therefore exposed to the maximum amount of sunlight. At this angle however some light is lost between the tubes, and therefore because this is used as a reference point for the IAM value of 1, when the gaps close up, the IAM value with actually increase (a greater % of light shining on the collector is actually being absorbed). |
When the sun reaches an angle of 40o which correlates to 2h 40min before or after midday, the solar tubes are still fully visible with no gaps between, and no overlap. It is at this point that the pure IAM values reach their peak. The tubes are exposed to all the sunlight shining towards them, and all the tubes are still perpendicular to the sun. This is why even at this point the cosine adjusted IAM is still 1.
As the angle increases, the tubes start to overlap, shading each other. They are still facing the sun, but the actual surface area of absorber exposed to the sunlight is reduced. Only a small amount of sunlight falls beyond 40o (early morning and late afternoon), and so this decrease in surface area has minimal influence on the total daily energy output of the collector.
IAM Adjustment
When calculating the heat output of a collector, the cosine adjusted IAM value should therefore be included in the formula.
Heat Output = Performance x Cosine Adjusted IAM value x Insolation x Absorber Surface Area
Example:
Performance = 66.3%
Cos Adj IAM at 30o = 1.02
Insolation = 800 Watts/m2
Absorber Surface Area = 2.4m2
Heat Output = 0.663 x 1.02 x 800 x 2.4 = 1298.4Watts
So the collector will provide 1298.4 Watts of heat output.
Simplifying IAM Adjustment Calculations
The calculation completed above is only for a specific point in time, and does not give an indication of the the actual performance over an entire day. Using performance modeling software, hour by hour calculations can be made taking into consideration average daily temperature changes, cold water temperatures, hours of sunlight, solar insolation levels in addition to collector performance variables and cosine adjusted IAM values. Monthly and annual average performance values may therefore be estimated.
To complete a simple single day calculation for the purpose of comparing collector performance, an average IAM value can be use, along with an average Watt/m2 value. Although this won't give a completely accurate indication of the heat output for the day, it allows a comparison between the two collector to be made.
As the majority of useful solar radiation falls during the middle 6-7hours of the day, an average of the IAM values during this period can be used. If 1 hour corresponds to 15o then 7 hours corresponds to 50o either side of midday. The average cosine adjusted IAM for the AP solar collector for this period is 1, and a flat plate collector is 0.83 (see table here). These factors can therefore be used in the performance formula. See the following section for more details.
Putting it all together
How do I compare the performance of different collectors?
When comparing collectors, it is better to use efficiency values from the normal operating range rather than peak efficiency levels, as this will better represent average annual performance. The "normal operating range" refers to the normal Delta-T range (Tm - Ta) that the collector is exposed to. For domestic water heating an average value of 30-40oC is common.
Every region has different ambient temperatures and different insolation levels, but for the purpose of a comparison we can use a "standard" set of environmental conditions.
In a moderate climate, an "average" intermittently clouded day in Spring can provide an insolation level of 3.5kWh/m2/day. The solar radiation distribution throughout the day from sunrise to sunset is displayed in the following graph.
It can be seen that 90% of the radiation falls between 9:00am and 4:00pm with an average insolation level during this period of 400W/m2.
We now have a full set of factors in order to do a comparison:
1. Insolation Level = 400Watts/m2 (G)
2. (Tm-Ta) = 35K
3. (Tm-Ta)/G = 0.0875(x)
3. Apricus AP:
- Performance variables: h0 = 0.717, a1 = 1.52, a2 = 0.0085 (SPF)
- IAM adjustment = 1.0(M)
4. Leading Flat Plate:
- Performance variables: h0 = 0.8, a1 = 2.99, a2 = 0.023 (SPF)
- IAM adjustment = 0.83 (M)
Remember the formula from earlier? To the end we just need to add the IAM adjustment (M).
The calculations for the two collectors are therefore as follows.
AP: Performance = 0.717 - (1.52 x 0.1) - (0.0085 x 400 x 0.0875 x 0.0875) x 1.0= 53.9%
FP: Performance = 0.8 - (2.99 x 0.1) - (0.023 x 400 x 0.0875 x 0.0875) x 0.83 = 35.8%
Given the set of variables used, the AP solar collector provides 33.6% greater heat output for a given absorber area.
The same calculation can be completed with other collectors using performance variables and IAM values
SPA: Active Closed Loop Solar Water Heating Systems
Closed Loop Solar Heating Systems are suitable for single and multible solar heating application systems,e.g.domestic solar water heating,solar water heating hot tub,solar swimming pool heating or solar space heating systems.The Closed Loop Solar Systems are suitable for areas with questionable water quality and all climate conditions.The Closed Loop Solar Heating Systems are the preferred option for extremely cold areas.
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1.Collector |
2.Collector Sensor |
3.Manual Air Valve |
4.Hot Water to Taps |
5.Tempering Valve |
6.Collcetor Return |
7.Check Valve |
8.Hose Bibs For Filling And Flushing |
9.Expansion Tank |
10.Air Scoop & Air Vent |
11.Circulating Pump With Flanges Or Couplings |
12.Pressure Relief Valve |
13.Pressure Gauge |
14.Collector Supply |
15.Heat Exchange Coil |
16.Solar Hot Water Tank |
17.Immersion Heater |
18.USDT 2001 Controller |
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Operation
- The controller(18) will switch on the pump when the temperature at the collector sensor TC is higher than the return temperature TR by at least the pre selected(delta T)amount.
- The pump circulates a heat transfer liquid around the loop.
- Heat from the collector is transferred to the domestic water through the heat exchange coil in the tank.
- With the pump running,if delta T is not met,the pump will switch odd.
- When a present tank temperature is reached at Tmax,the controller switches off the pump.
- The check valve(non-return valve)prevents heat from the tank fising towards the collectors should the tank be warmer(e.g.at night).
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