Calculating equation coefficients

Transcription

1 Solar Energy 1

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

3 The Sun Core temperature 8x10 6 to 40x10 6 K. Effective black body temperature is 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.

4 Energy from the sun Longwave radiation to space W Incoming solar energy W Reflected shortwave radiation W Atmospheric boundary Tidal energy W Geothermal energy W Earth s surface Formation of fossil fuels W Convection currents (wind and ocean waves) W Evaporation of water, heating of water & ice W Photosynthesis on land and sea W Direct conversion to heat W

5 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 thickness (equivalent to direct solar radiation at an altitude of 30 degrees). Atmosphere

6 Direct and diffuse radiation Solar radiation reaches the Earth as direct (from the Sun), as diffuse radiation after scattering in the atmosphere and as radiation reflected from surrounding objects. Only direct radiation can be focussed. The total radiation reaching a surface is the summation of the three components. On clear days around 90% of the total solar radiation is direct. On heavily overcast days 100% of the solar radiation is diffuse. ME922/927 Solar energy Solar Lecture - No. 6

7 Spectral distribution NASA/ASTM Standard Spectral Irradiance Wavelength (μm) (visible range) > 0.78 Fraction in range Energy in range (W/m 2 )

8 Short-wave radiation impacts

9 Passive utiulisation

10 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). ME922/927 Solar energy 10

11 Solar declination 21 March 21 December summer S hemisphere 21 June summer N hemisphere 21 September Declination D ay of the year ME922/927 Solar energy 11

12 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

13 Solar geometry Declination d = sin ( 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

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

15 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. ME922/927 Solar energy 15

16 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 ME922/927 Solar energy 16

17 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.

18 Short-wave radiation calculation Intensity of direct radiation on surface of inclination β: I dβ = I dh cos i β / sin β s Intensity of diffuse radiation on same surface ground reflected: I rβ = 0.5 [1- cos (90 β f )] (I dh + I fh ) r g where r g is the ground reflectance sky component: I sβ = 0.5 [1+ cos (90 - β f )] I fh assuming an isotropic diffuse sky i β - ω - angle between the incident beam and the surface normal vector surface-solar azimuth (= α s α f ) α f, β f - surface azimuth and inclination respectively α s, β s - solar azimuth and elevation respectively In practice the sky is not isotropic and so empirically-based models that correct for circumsolar and horizon brightening are employed: sky component: 2 Angle of incidence: i β I s β fh cos -1 I sin s I I cos( fh 2 gh cos( cos 90 β 2 f f (i ) β 1 1 )sin 3 s 90 β s I I fh 2 gh sin ) cos cos sin( 90 ) f 3 β f 2

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

20 Solar angle tables (altitude & azimuth) ME922/927 Solar energy 20

21 Solar tables (I dv & I dh ) ME922/927 Solar energy 21

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

23 Longwave Radiation Exchange 23

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

25 Internal long-wave radition = ε σ A = A

26 Internal long-wave radiation calculation

27 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.

28 External long-wave radiation