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.
To adjust from one to the other, multiply by the size difference.
ie. If absorber area = 0.6m2 & gross area = 1.1m2 then
(1.1/0.6 = 1.83), so multiply the performance factorsby
1.83 to convert from gross to absorber.
The three performance variables for the Diyi solar collector
as provided by the SPF
testing laboratory in Switzerland (SPF report C632LPEN)
are as follows (for metric calculations, based on 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.
(other slightly different forms of this formula
are used, but provide the same result)
How to use the formula?
Based on the ambient temperature, average manifold temperature
and insolation level, firstly calculate the value for X.
Eg. At 2:40pm; ambient temperature of 25oC (77oF);
average water temp [(Tinlet+Texit)/2]
of 50oC (122oF); insolation level
of 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*0.031252)
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
Diyi solar collector 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. Except
for when the delta-t is zero, conversion efficiency is 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
Diyi 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
or longitudinal IAM values (Incidence Angle Modifier). Considering
IAM is important as for Diyi solar collectors it accounts
for as much as an additional 25% in total daily heat output
values. Please read the following
section to learn more about IAM.
