Performance comparison: Flat Collector vs Evacuated tube Collector,

and investment cost per usable Watt

Flat-plate collectors are better than the tubes, why?

How to interpret technical data:

The yield curve of a sensor is defined by the following equation:
n = n0 - a1 Ã— ((Tm - Text) / G) - a2 Ã— G Ã— ((Tm - Text) / G) Â²
where:
n is the collector efficiency;
n0 is the optical conversion factor (in%);
a1 coefficient of heat loss by conduction (W / mÂ². K);
a2 coefficient of heat loss by convection (W / mÂ². K Â²);
Tm the mean temperature sensor (Â° C);
Text outdoor temperature (Â° C);
G solar irradiance (W / mÂ²).
If DT = Tm - Text, the equation can be reduced as follows:
n = n0 - a1 Ã— (DT / G) - a2 Ã— G Ã— (DT / G) Â²

Ranges of values
L The optical factor n0
The optical factor (n0) varies depending on the nature of the sensor: take care, it is calculated based on its surface
Specifically, it is usually the surface of the sensor that can actually absorb solar energy.  For a flat collector, this surface area corresponds to the total surface areas minus the surface of the frame round the collector.  For a evacated tube collector, the surface is the area actually exposed tubes (the spaces between the tubes are not considered as functional (je crois quâ€™il y a une erreur ds le texte en francais).  The optical factor varies between 0.5 and 0.8.  It corresponds to the maximum yield of the sensor (when DT = 0).
The coefficient a1
Expressed in W / mÂ². K, the coefficient a1 is representative of conductive heat loss from the sensor.  It is the level of isolation of the sensor and the nature of the absorber, and varies greatly depending on the type of sensor:
sensor without glass, 20-25 and over;
Simple glass flat collector, 4 to 6 and more;
selective glass flat collector, 3 to 5;
evacuated tube lined with AL-N/AL, 2 to 3;
evacuated tube lined with SS-C/CU, 1 to 2.
The coefficient a2
Expressed in W / mÂ². K Â², the coefficient a2 is representative of heat loss through convection of the sensor.  It depends essentially on the quality of the absorber of the sensor and its nature, and varies widely depending on the type of collector:
Simple glass flat collector, 0.05 to 0.1 and more;
selective glass flat collector, 0.005 to 0.015;
evacuated tube lined wth AL-N/AL, from 0.006 to 0.010;
evacuated tube lined with SS-C/CU, 0.004 to 0.007.
Graphics representation
Suppose a sensor with K = 0.70, a1 = 3.5 a2 = 0.02:
n = 0.7 to 3.5 Ã— (DT / G) - 0.02 Ã— G Ã— (DT / G) Â².

Yield Graph:

Actual results
An overall area occupied by a sensor receives on average 1000 W per m2 when sky is clear.  What remains of it-in the end?
Calculation of final yield  against the overall area of the collector
Depending on whether one speaks of overall surface, surface entry, yields are obviously not the same.  When comparing two collectors, it is very important to verify that the features are provided on the same surface of reference: ie the area occupied collector!
The surface used by the testing standard is the surface wich actually collect the irradiation, i.e. the evacuated tube get much better score than flat tube as the surface between the tubes are not considered.
To change a coefficient expressed for an area to another factor, simply multiply by the area ratio:
Ncollector = Noverallt Ã— Soevrall / Scollector,
a1collector  = a1overall Ã— Soverall / Scollector
a2collector = a2overall Ã— Soverall / Scollector.

On the chart below are grouped both good and poor evacuated tubes collector, and good and poor flat collector. Yield is calculated against the overall surface of the collector:

Graph of the yield vs the temperature difference

The evacuated tubes collector yields are given on three more horizontal curves.

The flat collector are given by the four other curves. The steeper curves
represent flat collectors surface painted in black, not so good, the other 3 collector are coated with Tinox,

Comparison of evacuated tubes vs flat collectors:
If we compare the best evacuated tube with the best flat collector, we see that whatever the Delta T studied the flat collector still has a superior performance.

With a low delta T, i.e. low temperature heating (eg: Delta T 30 Â°):
we will compare for example the best flat collector with the black surface painted collector. There are 2 curves starting at the same point for a delta T of 0 Â° the green curve represent the Tinox coating technology whereas the other cuver represents the black painted technology (these 2 collectors are from the same manufacturer only the coating is deifferent).

So we have to Delta T 30 Â°:
the black painted yield is 45%. He Tinox coated is  Tinox is 50%.
the best collector gives 63%
If we push the analysis to the evacuated tube collector:
the best collector gives a 45% yield (same as the plane painted studied)
The worst gives 33%
Lets look at the overall picture:
starting with flat painted collector: its curve is very steep one might think to avoid this collector as its performance falls drastically in the high delta T.  It would be a serious mistake because it is precisely this behavior that will prevent summer overheating due to low demand (DHW only). It is the main reason why the old solar rarely cause maintenance problems.

If one takes into production with a single ECS collection surface low:
Study of a 55 Delta T (HDW with a 10 degree outside temperature and 65 Â° water temperature:
the flat painted collector gives 25%
the best flat collector (Tinox) is still 50%
For this application, the Tinox is the best choice.
One could argue endlessly, but choices must be done knowingly and depending on the applications.

Price per watt retrieved (a major factor when purchasing)
A very important criteria is the price per watt produced.

Calculation of Effective Yield:

Cost per watt calculation for an irradiation of 500W/m2.  (The sun gives between 0 and 1000W per m2)
Calculation of Effective Yield:
Starting formula
r = n0 - a1 x (DT / G) - a2 Ã— G Ã— (DT / G) Â²
The n0, a1 and a2 must be recalculated against the overall surface of the collector.
n0HT, a1HT, a2HT (multiply by the ratio of two areas: opening and overall)
Lets assume a delta of 30 Â° (house heating application)
R = effective n0HT - a1HT Ã— 0.06 - 0.06 Ã— a2HT Â²

Example of a low tier evacuated tube collector (sold under different brn names on the French market:
n0 = 0.74, a1 = 1071, a2 = 0.035
S HT = 2939, S Open: 1456
R = 0366 owner - (0.53 x 0.06) - 500 (0017 x 0.06 x Â²) = 0.30
Example of the Sunrain collector of our buying group
n0 = 0733; a1 = 1529, a2 = 0.0166
S HT = 5.0; S Open: 2.69
R = actual 0438 - (0914 x 0.06) - 500 (0.0099 x 0.06 x Â²) = 0366
Example of the GM Tinox collector of our purchasing group
n0 = 0751, a1 = 4.99, a2 = 00.0
S HT = 2.48; S Ouv: 2.25
R effective = 0.68 - (4.52 x 0.06) - 500 (0.000 x 0.06 x Â²) = 0408

Calculate Price HT Watt:

HT is the price per m2 of the sensor / effective power recovered
Price HT m2 / (500 x Reffective)
Example of our entry level evacuated tube collector present in many different names on the French market:
Price per m2 = 350 euro
Reffectif = 0.30
350 / (500 x 0.30) = 2.33 euros per Watt
Example of sensor Sunrain:
Price per m2 = 134 euro
Reffectif = 0.366
134 / (500 x 0366) = 0.73 euros per Watt
Example GM Tinox collector of our purchasing group :
Price per m2 = 109 euro with maximum discount on quantity (15%),
Reffectif = 0.408
109 / (500 x 0408) = 0.53 euros per watt, almost five times less expensive than the entry level evacuated tube collector.

For those who are not yet convinced, see:

Christoph Trinkl, Wilfried ZÃ¶rner, Claus Alt, Christian Stadle CENTRE OF EXCELLENCE FOR SOLAR ENGINEERING

by Heliodyne, Inc. â€¢ 4910 Seaport Avenue â€¢ Richmond, CA 94804 T: 510.237.9614 â€¢ F: 510.237.7018 â€¢ www.heliodyne.com