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1 Collector Energy Balance M.Fossa, Sust. En. Solar & Geo 1, UniGe - Pag. 19 / 95 Collector Energy Balance (I) = G direct + G diff = G a - = G a K (, ave ) G a = (τα) ave (, ave T fluid, ave ) = / h fluid, ave = / h fluid + T fluid, ave (1 + K / h fluid ) = G a ) F = h fluid / (K + h fluid ) Efficiency factor Glass cover G abs Flow rate m G T f useful Thermal fluid Insulation M.Fossa, Sust. En. Solar & Geo 1, UniGe - Pag. 20 / 95
2 Collector Energy Balance (II) = m c (T fi T fu A=WL da = Wdx,x da =,x (W dx) = (m A) c dt f,x m c L dt f,x / dx = being d[g a = -K dt f dt f = -1/K d[g a F /(m c L) dx = (-1/K ) d[g a / [G a dx=l (G a K (T f, u )) / (G a K (T f, i )) = exp [-F K /(m c Glass cover W y L G abs T F Therm. fluid T FU T FI Insulation Δx seful Mass flow rate m x m [kg/(s m 2 (per unit surface) M.Fossa, Sust. En. Solar & Geo 1, UniGe - Pag. 21 / 95 Collector Energy Balance (IIIa) (heat removal factor) Fattore di rimozione termica = / [G a = [m c (T out T in / [G a = (1/K )m c [K (T out T in ] / [G a = (1/K )m c [K (T out )-K (T in / [G a = (1/K )m c [ [G a -K (T in - [G a - K (T out ] / [G a = (1- [ [G a - K (T out / [G a -K (T in ]) (1/K )m c = (1-exp [-F K /(m c) (1/K )m c = (1 exp[-f K /(m c)(m c)/k M.Fossa, Sust. En. Solar & Geo 1, UniGe - Pag. 22 / 95
3 Collector Energy Balance (IIIb) (heat removal factor) Fattore di rimozione termica = / [G a is close to unity for high flow rates, high h, low K. It can be demonstrated that: = [1 exp(-f K /m c(m c)/k Hence: = [G a (Bliss Equation) Copertura vetrata G ass T FI T f T FU tile Fluido vettore Portata fluido m Isolante Termico (per unità di superficie) M.Fossa, Sust. En. Solar & Geo 1, UniGe - Pag. 23 / 95 Collector Energy Balance (IV) = [G a (Bliss equation) G a = (τα) E a = E inc, ave (τα) ave [J/m 2 day] (on a daily basis, monthly ave) Collector efficiency η is defined as: η = [G a / η ave = [E a, ave )Δτ] / E inc η = / (on a daily basis, monthly ave) E a = E inc (τα) ave G ass T f E inc = E T E T = Overall insolation on tilted surface T FI T FU tile m (per unit surface M.Fossa, Sust. En. Solar & Geo 1, UniGe - Pag. 24 / 95
4 Collector Efficiency (I) η ave = (τα) K [(T fluid, in / M.Fossa, Sust. En. Solar & Geo 1, UniGe - Pag. 25 / 95 Collector Efficiency (II) η= (τα) K [(T fluid, in / η η=a + bx Notice: 1) Sometimes (τα) is written as η 0 2) Sometimes η= a + b 1 x + b 2 x 2 1 τα Atan (K ) Iso Solar Energy Methods of Test for the Thermal Performance of Liquid Heating Collectors EN :2006 2:2006 Thermal solar systems and components Solar collectors Part 2: Test methods [(T fluid, in / ] M.Fossa, Sust. En. Solar & Geo 1, UniGe - Pag. 26 / 95
5 Collector Efficiency (III) EN Indoor Test The lamps capable of producing a mean irradiance over the collector aperture of at least 700 W/m 2. Values in the range 300 to 1000 W/m 2 can be used for special tests. The irradiance at a point on the collector aperture shall not differ from the mean irradiance over the aperture by more than ±15 % The spectral distribution of the simulated solar radiation shall be approximately equivalent to that of the solar spectrum at optical air mass 1.5 M.Fossa, Sust. En. Solar & Geo 1, UniGe - Pag. 27 / 95 Collector Efficiency (III) M.Fossa, Sust. En. Solar & Geo 1, UniGe - Pag. 28 / 95
6 Collector Efficiency (IV) Coeff. In efficiency expression, as measured at CSTB (France) MARQUES de CAPTEURS BUDERUS - Logasol SKS CLIPSOL - TGD Y1200 DE DIETRICH - Sol 1 GASOKOL - Enersol GKAN et GKAQ GIORDANO - C8 HI PHÖNIX - Infinity 21 SOLAHART - Solahart Ko SONNENKRAFT - SK500 (Solar Connexion) SUNMASTER - SK20 LM (New Point Products) VIESSMANN - Vitosol 100 S1,7 WAGNER - EURO C20 AR WEISHAUP - WTS-F ZENIT - Thermic Avis Technique CSTB 14-00/577 AT / /576 14/ / / / /575 14/ / / / / Coef. τ α CSTB 0,79 0,73 0,68 0,72 0,72 0,79 0,76 0,76 0,85 Coef. K W/m 2. C 4,89 4,26 3,82 3,86 4,36 4,80 4,76 3,78 4,17 4,34 3,34 2,75 3,62 M.Fossa, Sust. En. Solar & Geo 1, UniGe - Pag. 29 / 95 Collector Efficiency (V) Incidence angle effects on daily efficiency η ave =C θw, ave (τα N ) K [(T fluid, in / C θw =C(IAM(θ w )) IAM(θ w ) w M.Fossa, Sust. En. Solar & Geo 1, UniGe - Pag. 30 / 95
7 Collector Efficiency(VI) Reference Area Very important is to know Efficiency to which Area is referred to. A gross, A aperture, A absorber M.Fossa, Sust. En. Solar & Geo 1, UniGe - Pag. 31 / 95 Collector Efficiency(VIB) Reference Area M.Fossa, Sust. En. Solar & Geo 1, UniGe - Pag. 32 / 95
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