Solar Radiation PDF

SOLAR RADIATION Part 1 https://www.pveducation.org J. A. Duffie, W. A. Beckman. Solar Engineering of Thermal Processes. J. Wiley and Sons. https://onlinelibrary.wiley.com/doi/epub/10.1002/9781119540328  SolarL’ENERGIA...

SOLAR RADIATION Part 1 https://www.pveducation.org J. A. Duffie, W. A. Beckman. Solar Engineering of Thermal Processes. J. Wiley and Sons. https://onlinelibrary.wiley.com/doi/epub/10.1002/9781119540328  SolarL’ENERGIA Energy SOLARE MAIN ADVANTAGES Primary source of energy for life on Earth Greater than human energy needs (in less than one hour, an amount of energy equal to the annual world consumption arrives on Earth) Free Widespread throughout the planet Inexhaustible Low environmental impact DISADVANTAGES Variable randomly Generally not "in phase" with the needs Low power density (in terms of W/m2) Its exploitation involves the use of "expensive" technologies Non-standard design (depends on local conditions) SUN STRUCTURE SUN STRUCTURE D = 1.39 x 109 m  ELEMENTS IN THE SUN Elemento % volume % massa Idrogeno 92,100 73,46 Elio 7,800 24,85 Ossigeno 0,061 0,77 Carbonio 0.030 0,29 Azoto 0,0084 0,09 Neon 0,0076 0,12 Ferro 0,0037 0,16 Silicio 0,0031 0,07 Magnesio 0,0024 0,05 Zolfo 0,0015 0,02 Resto 0,0015 0,10 92.1 7.8 5760 K  1 1 H H The positron reacts with its antiparticle electron, canceling neutrino itself out with the 1 emission of two H rays γ 2 H 3 He 1 1 H H 4 He sun earth  EARTH-SUN DISTANCE RADIATED POWER Radiative flux received from the Earth Solar constant 1367 W/m2 Sphere surface Average flux on the earth surface 1367/4=342 W/m2 NUCLEAR FUSION REACTION Every second Mass flow rate consumed in the reaction Power Speed of light in a vacuum Average distance Earth-Sun Travel time of solar radiation Solar constant average distance between Sun and Earth radius of the Sun HEAT FLUX REFERRED TO THE UNITARY SUN AREA Apparent surface temperature of a blackbody EMISSIVE POWER OF A BLACKBODY  EARTH MOTIONS The Earth moves in three ways. First, it turns around its polar axis; one turn takes 24 hours. Then it moves along its orbit around the Sun; one full revolution takes 1 year. Third: its polar axis changes direction very slowly, just like a spinning top. This effect is called precession and one full turn lasts almost 26,000 years.  EARTH MOVEMENTS Earth rotates on its axis as it revolves around the Sun VARIATION OF NORMAL EXTRATERRESTRIAL RADIATION [W m-2] Radiation outside the atmosphere The solar constant Gsc is the solar energy incident in the unit of time on a unitary surface disposed normally to the rays, in the absence of the atmosphere, at the average distance between the Sun and the Earth. The most reliable value is 1367 W/m2. Due to the eccentricity of the Earth's orbit, the distance between the Sun and the Earth varies throughout the year. The square of the ratio (average distance / distance on the generic day n of the year) is given by:  360n  r = 1 + 0,033 cos   365  It has a minimum value in the summer months and a maximum in the winter months with a variation that does not exceed 3.3%. The solar power incident on a unitary area of a surface normal to the rays outside the atmosphere is given by the product (Gsc r ). PIANETA PLANET Solar normal Radiazione solare normale [W m -2 ] irradiance Media Average Perielio Perihelion Aphelion Afelio Mercurio 9116,4 14447,5 6271,1 Venere 2611,0 2626,4 2575,7 Terra 1366,1 1412,5 1321,7 Marte 588,6 715,9 491,7 Giove 50,5 55,7 45,9 Saturno 15,04 16,76 13,53 Urano 3,72 4,11 3,37 Nettuno 1,510 1,515 1,507 Plutone 0,878 1,571 0,560 EXTRA-ATMOSPHERIC SOLAR SPECTRUM Planck Law for a blackbody  solar spectrum WRC blackbody 5777 K solar spectrum Wien Law GLOBAL EMISSIVE POWER Most radiation between 380 and 3000 nm 50% in the visible range IRRADIANCE ON HORIZONTAL PLANE IRRADIANCE ON INCLINED PLANE Anthropogenic Greenhouse Effect 235 235 -2 Energy I flussi fluxes radiante di energia are expressed -2 W m in W min sono espressi 107 Flusso 235 Flusso 342 Flusso radiante radiante riflesso solare medio infrarosso incidente emesso verso riflesso da lo spazio nubi, aerosol emesso e atmosfera dall’atmosfera 40 Finestra 30 atmosferica 165 77 Gas serra assorbito 67 dall’atmosfera latente 350 324 24 78 riflesso dalla superficie emesso Flusso dalle 30 radiante superficie atmosferico 168 390 convezione 324 assorbito dalla evaporazione assorbito dalla superficie superficie RADIATIVEENERGIA BILANCIO ENERGY RADIANTE BALANCE EARTH TERRA --SPAZIO SPACE RADIATION CROSSING THE ATMOSPHERE Sunlight Absorption of solar radiation and isotropic re- irradiation in the infrared O3 between 0.15 and 0.4 m H2O between 0.8 and 2 m Infrared CO2 between 2.5 and 4.5 m radiation Dispersion of solar radiation (a) Rayleigh dispersion, (b) Mie dispersion, (c) reflection  RADIATION CROSSING THE ATMOSPHERE Air Mass limit value AM = Not correct for zenith angle > 80° AIR MASS atmosphere [km] e HS ≥ 20° RADIATION CROSSING THE ATMOSPHERE Air Mass exp ( −0, 0001184  z ) AM = z altitudine in [m] →(96,AM −1,634 Air Mass sin h + 0,5057 080 − = h) 1/sin(h) AM = AM0 = 0 Limite sup. dell'atmosfera assorbente e n(h) = 1/s AM = AM1 = 1 AM Angolo di altezza solare h Orizzonte locale ~ 10 0 km Superficie Terrestre Air Mass vs. Altitude and solar height exp ( −0, 0001184  z ) AM = −1,634 sin HS + 0,5057 ( 96,080 − HS ) z altitudine in [m]; HS angolo di altezza solare in [ ] Altitude above sea level Solar height HS Comparison equations for Air Mass calculation exp ( −0, 0001184  z ) AM = −1,634 sin HS + 0,5057 ( 96, 080 − HS ) 1 − z 10000 AM = sin HS z altitudine in [m]; HS angolo di altezza solare in [ ] Altitude above sea level Solar height HS SUNLIGHT CROSSING THE ATMOSPHERE direct diffuse reflected concrete terrain roof tiles green grass gravel dry grass bitumen fields and plants Uptake of direct and diffuse radiation SOLAR SPECTRUM: EXTRATERRESTRIAL AND AM=1 Direct Radiation SOLAR SPECTRUM: EXTRATERRESTRIAL AND AT VARYING AM Direct Radiation  extra-terrestrial irradiance: limit of atmosphere diffuse direct global irradiance (with clear sky): 1000 W/m2 Solar radiation spectrum in a clear atmosphere [W m-2 μm-1] 1400 globale diretta diffusa 1200 radiazione monocromatica [W/m mm] 2 1000 800 600 400 200 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 [μm] lunghezza d'onda [mm] The direct component dominates over the diffuse one Solar radiation spectrum in a turbid atmosphere [W m-2 μm-1] 1400 globale diretta diffusa radiazione monocromatica [W/m mm] 1200 2 1000 800 600 400 200 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 [μm] lunghezza d'onda [m m] High turbidity on a clear day. From the quantitative point of view, direct and diffuse radiation are equivalent, but from the spectral point of view, the direct one is richer in the longer wavelengths, while the diffuse one is reacher in the blue tones. SUNLIGHT CROSSING THE ATMOSPHERE Estimate of ground irradiance  SUNLIGHT CROSSING THE ATMOSPHERE Estimate of ground irradiance: direct component  SUNLIGHT CROSSING THE ATMOSPHERE Estimate of ground irradiance: diffuse component reciprocal relationship of the view factors View factor Fraction of the sky seen from the receiving surface  SUNLIGHT CROSSING THE ATMOSPHERE Estimate of ground irradiance: diffuse component Not Visible View factor visible sky Fraction of the sky seen from the receiving surface HYPOTHESIS: perfectly isotropic diffuse radiation  SUNLIGHT CROSSING THE ATMOSPHERE Estimate of ground irradiance: reflected component View factor Fraction of the ground seen from the receiving surface SUNLIGHT CROSSING THE ATMOSPHERE Estimate of ground irradiance  DIFFUSE IRRADIATION WITH CLEAR SKY (Liu & Jordan, 1960) In order to calculate, in clear sky conditions, the diffuse irradiance on the horizontal plane we can use the relationship by Liu & Jordan (1960), by computing the ratio Per calcolare, sempre in condizioni di cielo sereno, l’irradianza diffusa su piano orizzontale, si può utilizzare Per calcolare, sempre in condizioni di cielo sereno, l’irradianza diffusa su piano orizzontale, si può utilizzare la relazione di Liu & Jordan (1960), per calcolare  d = Gd / G0 = Id / I0 , rapporto tra l’irradianza G (o la relazione di Liu & Jordan (1960), per calcolare  d = Gd / G0 = Id / I0 , rapporto tra l’irradianza G (o l’irradiazione oraria I ) diffusa su piano orizzontale e l’irradianza (o irradiazione oraria) extratmosferica: where Gd is diffuse l’irradiazione orariairradiance I ) diffusaonsuthe horizontal piano plane, orizzontale eG 0 is irradiance l’irradianza outside theoraria) (o irradiazione atmosphere, I is hourly extratmosferica: irradiation G  d = d = 0,271 G − 0,294  b G0d = d = 0,271 − 0,294  b G0 Esempio: calcolare l’irradianza globale (diretta + diffusa) su superficie orizzontale a Padova (Lat.: 45°24’ = Esempio: calcolare l’irradianza globale (diretta + diffusa) su superficie orizzontale a Padova (Lat.: 45°24’ = 45,40°, praticamente al livello medio-mare), alle 12:00 TSV (AH = 0) nel giorno del solstizio d’estate (21 45,40°, praticamente al livello medio-mare), alle 12:00 TSV (AH = 0) nel giorno del solstizio d’estate (21 giugno: n = 172; δ = +23,45°), in condizioni di cielo sereno e atmosfera standard, con visibilità 23 km. giugno: n = 172; δ = +23,45°), in condizioni di cielo sereno e atmosfera standard, con visibilità 23 km. HS = arcsin(sin LAT  sin + cos LAT  cos   cos AH) = 68,05 HS = arcsin(sin LAT  sin + cos LAT  cos   cos AH) = 68,05 HS = 90 +  − LA T = 90 + 23,45 − 45,4 = 68,05 HS = 90 +  − LA T = 90 + 23,45 − 45,4 = 68,05  −0,3872  AM = 1 / sin HS = 1,078;  b = 0,1248 + 0,7493exp   = 0,6184;  −0,3872   d = 0,271 − 0,294  b = 0,0892 AM = 1 / sin HS = 1,078;  b = 0,1248 + 0,7493exp sin68,05    sin68,05 = 0,6184;  d = 0,271 − 0,294  b = 0,0892    360 + n G0 n = Gsc (1 + 0,0333cos 360) =+1367 n  0,9672 = 1322 Wm ; G0-2= G0 n cos(90 − HS) = 1226 Wm -2 -2 G0 n = Gsc (1 + 0,0333cos 365 ) = 1367  0,9672 = 1322 Wm ; G0 = G0 n cos(90 − HS) = 1226 Wm-2 365 Gb = G0  b = 1226  0,6184 = 758 Wm-2 ; Gd -2= G0  d = 1226  0,0892 = 109 Wm-2 ; G =-2 758 + 109 = 867 Wm-2 Gb = G0  b = 1226  0,6184 = 758 Wm ; Gd = G0  d = 1226  0,0892 = 109 Wm ; G = 758 + 109 = 867 Wm-2 DIFFUSE SOLAR RADIATION: Correlation by Erbs et al. Horizontal Surface The ratio of diffuse radiation Idh to global radiation Ih is related to the clearness index kT (kT= Ih /Ih0). Correlazione di Erbs et al: 𝐼I𝑑ℎ d = 1 − 0, 09kT per kT  0, 22 𝐼Iℎ 𝐼I𝑑ℎd = 0,9511 − 0,1604kT + 4,388kT2 − 𝐼Iℎ − 16, 638kT3 + 12,336kT4 per 0, 22  kT  0,80 𝐼I𝑑ℎd = 0,165 per kT  0,8 𝐼Iℎ DIFFUSE SOLAR RADIATION: HOURLY VALUES MEASURED IN PADOVA Correlation by Erbs et al. 1.1 Err< - U Err > U 1 The diffuse radiation - U < Err < U fraction to the global 0.9 Rain radiation 0.8 Erbs et al. Diffuse Fraction (k) Idh / Ih 0.7 is a function of the 𝐼𝑑ℎ 0.6 clearness index (indice di 𝐼ℎ 0.5 \ soleggiamento orario 0.4 reale) 0.3 kT = Ih /Ih0 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Clearness Index (kt)  EARTH MOVEMENTS Earth rotates on its axis as it revolves around the Sun Eccentricity of the Earth's orbit: 0,017 Earth's orbital period: 365,25 days Earth's rotation period: 23,93 hours Earth's equatorial diameter: 12756 km Sun's equatorial diameter: 1392530 km Period of rotation of the sun: between 26,8 and 35 days (equator – poles) Mass ratio sun/earth: 332948,34  prime meridian meridian of P (Greenwich) parallel of P latitude of P equator longitude of P  Geographic coordinates same parallel same meridian same latitude same longitude Parallels run from east to west and never intersect with each other. Meridians run from north to south and intersect at the north and south poles.  Equatorial coordinates a) latitude  and longitude  b) declination angle  and hour angle   SUN’S POSITION The declination of the sun is the angle between the equator and a line drawn from the centre of the Earth to the centre of the sun. https://www.pveducation.org/pvcdrom/properties-of-sunlight/declination-angle The hour angle is the difference between the longitude of P (fixed) and the longitude of S (variable during the day)  = P - S zero at noon, negative in the morning, positive in the afternoon  SUN’S POSITION The declination angle does not depend from P but it depends on S and thus on time The hour angle depends on P and it is the same for all the points laying on the same meridian as P  VARIATION OF DECLINATION ANGLE sign - Solstice: The sun reaches the maximum or minimum declination angle Equinox: The sun is located at the zenith of the equator. Declination angle is zero VARIATION OF DECLINATION ANGLE Equation by Keplero  DECLINATION ANGLE – SPENCER EQUATION Per Forilthe calcolo della declinazione calculation  una of declination  ,relazione alternativa a different equationalla formula is the di Keplero, Spencer equation più precisa(1971), (errore more precise