Shortwave solar radiation 1 Calculating equation coefficients - PowerPoint PPT Presentation

Shortwave solar radiation 1

Calculating equation coefficients Construction Conservation Equation Surface Conservation Equation Fluid Conservation Equation needs flow estimation needs radiation and convection estimation 2

The Sun  Core temperature 8x10 6 to 40x10 6 K.  Effective black body temperature of 6000 K.  Solar constant: extraterrestrial flux from the sun received on a unit area perpendicular to the direction of propagation – mean Sun/Earth distance value is 1353 W/m 2 .  Actual extraterrestial radiation varies with time of year as earth-sun distance varies. 3

Energy from the sun Incoming Longwave Reflected shortwave solar energy radiation to space radiation 175 . 10 15 W 122.5 . 10 15 W 52.5 . 10 15 W Atmospheric boundary Convection currents (wind and ocean waves) 368 . 10 12 W Tidal energy 3 . 10 12 W Evaporation of water, heating of water & ice Geothermal 40 . 10 15 W energy 32 . 10 12 W Photosynthesis on land and sea 98 . 10 12 W Earth’s surface Direct conversion to heat 82 . 10 15 W Formation of fossil fuels 13 . 10 6 W 4

Atmospheric interactions  The greater the distance that the radiation passes through the atmosphere, the greater is the frequency dependent scattering. Spectra at ground level are often referred to particular ‘air masses’.  Air Mass 1 is the thickness of the atmosphere vertically above sea level.  Air Mass 2 is double this 2 thickness (equivalent to 1 Atmosphere direct solar radiation at an altitude of 30 degrees). 30 ° 5

Direct and diffuse radiation  Solar radiation reaches the Earth directly from the Sun) and On clear days diffusely after scattering in the around 90% of atmosphere and reflected from the total solar surrounding objects. radiation is direct.  Only direct radiation can be focussed.  The total radiation reaching a On heavily surface is the summation of the overcast days direct, sky diffuse and reflected 100% of the solar components. radiation is diffuse. 6

Spectral distribution of short-wave solar radiation NASA/ASTM Standard Spectral Irradiance Wavelength (μm) 0 - 0.38 0.38 – 0.78 > 0.78 (visible range) Fraction in range 0.07 0.47 0.46 Energy in range (W/m 2 ) 95 640 618 7

Short-wave radiation impacts 8

Passive utiulisation 9

Location coordinates  latitude - angle N or S above or below equator.  longitude – angle E or W from prime meridian (Greenwich).  Longitude difference – angle from location to local time zone reference meridian (west –ve). 10

Solar declination 21 December 21 March summer S hemisphere 21 June summer N 21 September 30 hemisphere 20 10 Declination 0 -35 65 165 265 365 -10 -20 -30 D ay of the year 11

Solar time t s – t m = ± L diff /15 + (e t /60) + d s where, t s = solar time t m = local time L diff = longitude difference e t = equation of time d s = daylight saving time 12

Solar geometry  Declination d = 23.45 sin (280.1 + 0.9863 Y) where Y = year day number (January 1 =1, December 31 = 365)  Altitude β s = sin -1 [cos L cos d cos θ h + sin L sin d ] where L is site latitude, θ h is hour angle = 15 (12 – t s )  Azimuth α s = sin -1 [ cos d sin θ h / cos β s ]  Incidence angle i β = cos -1 [ sin β s cos (90-β f ) + cos β s cos ω sin (90-β f )] where ω = azimuth angle between sun and surface normal, β f = surface inclination angle 13

Solar radiation prediction (all W/m 2 ) I dn - direct normal or “beam” (pyrheliometer) I dh - direct horizontal I dh = I dn sinβ s known I fh - diffuse horizontal (pyranometer with shadow band) I gh - global horizontal (pyranometer or solarimeter) r g - ground reflectivity I dβ - direct radiation on a surface of inclination β f unknown I sβ - sky diffuse radiation incident on a surface of inclination β f I rβ - ground reflected radiation incident on a surface of inclination β f I gh = I dh +I fh = I dn sin β s + I fh Solar Altitude, β s Solar data for simulation: either: I gh and I fh or I dn and I fh 14

Solar radiation measurement  Pyranometer measures the total solar irradiance on a planar surface.  Pyrheliometer measures direct beam solar radiation by tracking the sun’s position throughout the day. 15

Solar radiation measurement  Shaded pyranometer measures diffuse solar irradiance on a (usually horizontal) surface.  The shade blocks direct radiation and some diffuse radiation (so need to adjust readings).  Integrated pyranometer measures both total and diffuse radiation on a (usually horizontal) surface.  Diffuse is calculated based on shading patterns from internal shades 16

Short-wave flow-paths A - reflected shortwave flux B - flux emission by convection and longwave radiation C - shortwave flux transmission to cause opaque surface insolation D - shortwave transmission to cause transparent surface insolation E - shortwave transmission to adjacent zone F - enclosure reflections G - shortwave loss H - solar energy penetration by transient conduction I - solar energy absorption prior to retransmission by the processes of B. 17

Short-wave radiation calculation i β - angle between the incident beam and the Intensity of direct radiation on surface of inclination β: surface normal vector I dβ = I dh cos i β / sin β s ω - surface-solar azimuth (= |α s − α f |) Intensity of diffuse radiation on same surface α f , β f - surface azimuth and ground reflected: I rβ = 0.5 [1- cos (90 – β f )] (I dh + I fh ) r g inclination respectively where r g is the ground reflectance α s , β s - solar azimuth and sky component: I sβ = 0.5 [1+ cos (90 - β f )] I fh elevation respectively assuming an isotropic diffuse sky In practice the sky is not isotropic and so empirically-based models that correct for circumsolar and horizon brightening are employed: sky component:         2     1 cos(90 β ) I β             3   I I f 1 1 fh sin f     s β fh 2  2  I  2          gh       2 I        fh      2 3  1 1 cos (i )sin 90 β    β s 2 I         gh   Angle of incidence:  -1         Numerical approach i cos sin cos( 90 ) cos cos sin( 90 ) β s f s f using 145 sky vault patches. 18

Surface-solar angles solar surface beam normal N ψ β f cross section β s surface inclined at plan view angle β f α f α s solar beam surface 3-D view i β normal ω solar beam S S β f 19

Solar angle tables (altitude & azimuth) 20

Solar tables (I dv & I dh ) 21

PV power output A simple model: Example 1 Example 1 Calculate the power output from a PV For the same situation calculate the panel at 60°C with 840 W/m 2 incident power output if the temperature was solar radiation if the same panel produces 30°C. β is again measured at 0.003 W/K 150 W at STC (1000W/m 2 & 25°C). β is measured at 0.003 W/K 22

Longwave Radiation Exchange 23

Calculating equation coefficients Construction Conservation Equation Surface Conservation Equation Fluid Conservation Equation needs flow estimation needs radiation and convection estimation 24

Internal long-wave radiation – calculation 25

Internal long-wave radition � � = ε σ A �→� = � A 26

Internal long-wave radiation – numerical method  Surfaces divided into finite elements and a unit hemisphere superimposed on each element.  Unit hemisphere’s surface divided into patches representing the radiosity field of the associated finite element.  ‘Energy rays’ are formed by connecting the centre point of the finite element and all surface patches.  Each ray is projected to determine an intersection with another surface.  At this intersection a surface response model is invoked to determine the energy absorption and the number and intensity of exit rays – these are continually added to the stack of rays queued for processing.  Ray processing is discontinued when the inherent energy level falls below a threshold.  The energy absorptions for each finite element are then summated as appropriate to give the final net longwave radiation exchanges for the enclosure. 27

External long-wave radiation 28