solar radiation definitions incident solar...
Transcript of solar radiation definitions incident solar...
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Solar energy
solar radiation definitions incident solar energy
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Sun
closest star centre of our planetary system – solar system
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Sun
diameter 1 392 000 km 109 x larger than Earth weight 2 x 1030 kg 330 000 x greater than Earth
99,86 % weight of solar system consists of: 70 % hydrogen H, 28 % helium He, 2 % other elements
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Sun
origin of solar energy in nuclear reactions
nuclear fusion takes place inside the Sunat high temperatures 106 K and pressures 1010 MPasynthesis of hydrogen nuclei (H) → helium nuclei (He)
564 x 109 kg/s H transforms to 560 x 109 kg/s He mass difference 4 x 109 kg/s is radiated in the form of energy
E = m.c2
radiative power: 3,6 x 1026 W
specific radiated power (density): 6 x 107 W/m2
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Sun
core (to 23 % radius)temperature 106 K, X-ray radiation90 % of Sun’s energy generated
radiative zone (from 23 to 70 % radius)temperature falls down to 130 000 Kradiative energy transfer (fotons)
convective zone (from 70 to 100 % radius)lower density, convective energy transfer
photosphere (visible surface of Sun)temperature 5800 K, solar radiation
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Spectral density of radiative flux
Sun radiates as perfect black body with surface temperature 5800 K
spectral density of radiative solar flux (Planck’s law)1
5
212),(
Tk
ch
č echTE
[W/m2.m]
h = 6,6256 x 10-34 J.s Planck’s constantk = 1,3805 x 10-23 J/K Boltzmann’s constantc = 2,9979 x 108 m/s light velocity in vacuumT thermodynamic surface temperature [K]
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Planck’s law
Černý, M. (2008)wavelength
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Spectral density of radiative fluxVISUV NIR
UV: ultraviolet radiation 0,2 až 0,4 m
UVA (> 0,32 m), UVB, UVC (< 0,28 m)
VIS: visible radiation 0,40 to 0,75 m
NIR: near infrared radiation 0,75 až 5 m
black body 5800 K
wavelength [nm]
dens
ity of
radia
tivef
lux [W
/(m2 .n
m)]
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black body 5800 K
Solar energy irradiated
50 %41 %9 %
VISUV NIR
wavelength [nm]
dens
ity of
radia
tivef
lux [W
/(m2 .n
m)]
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Wien’s law
maximum of radiative flux – seeking the extreme of Planck’s function
28980),(max
TTEč
[m.K] Wien’s law
5800 K: max = 0,5 m
373 K: max = 7,8 m
black body 5800 K
wavelength [nm]
dens
ity of
radia
tivef
lux [W
/(m2 .n
m)]
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Propagation of solar energy
power spreads to larger area with increasing distance from Sun 0,5 x 10-9 of the irradiated Sun’s power is incident on Earth
radiative flux 1,7 x 1017 W solar „beams“ considered as parallel (32’)
Sun Earth
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Earth rotates around Sun
Sun
Earth
eliptic orbit (almost circular), Sun in one of focusses
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Radiative flux density out of atmosphere
solar radiative flux incident on area unit perpendicular to direction ofpropagation
changes during the year, variable distance Sun-Earth (eliptic orbit)change of distance 1,7 %, change of flux 3,3 %
value for mean distance Sun-Earth
solar constant Gsc = 1367 W/m2 (value from WRC, 1 %)
original measurements Ch. Abbot in mountains 1322 W/m2, todaysatellites
Merkur: 9040 W/m2 ... Neptun: 1,5 W/m2
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Radiative flux density out of atmosphere
1320
1340
1360
1380
1400
1420
0 50 100 150 200 250 300 350dny v roce
Gon
[W/m
2 ]
365
360cos033,01 nGG scon
day in the year
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Solar radiation passing the atmosphere
solar radiation enters the atmosphere (no definite boundary, exosphere continuosly fading to interplanetary space)
ionosphere (60 km)atmospheric gases O2, N2 absorb ultraviolet a x-ray radiation, becoming ionised
ozonosphere (20 až 30 km)ozon O3 absorbs rest of harmfull ultraviolet radiation (UVC)
troposphere (lowest layer, clouds)water vapor, CO2, dust, water droplets absorb infrared radiation
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Solar radiation passing the atmosphere
wavelength [nm]
dens
ity of
radia
tivef
lux [W
/(m2 .n
m)]
AM0: spectrum outside atm.
AM1: perpendicular pass
AM1,5: spektrum at 48°
AM2: spektrum at 60°
solar radiation: 0,3 to 3 m
outside atmosphere
sea level
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Annual balance
reflection from atmosphere 34 % absorption in atmosphere 19 % incident and absorbed by Earth surface 47 %
absorbed at surface
emitted back 14 % energy of environment
evaporation (oceans) 23 % water energy
convection, winds 10 % wind energy
biologic reactions, photosynthesis 1 ‰ energy of biomass
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Solar geometry
surface slope surface azimuth latitude
time, date time angel declination Sun height h Sun azimuth s
incidence angle
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Surface position
latitude convention: north (+), south (-)angle between plane of equator and a line connecting Earth centre and given place on Earth surface
51°
50°
49°
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Surface position
high difference between north andsouth in one country
Norway: 57 to 71°
Sweden: 55 to 68°
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Surface orientation
slope angle convention: horizontal 0°, vertical 90°angle between horizontal plane and surface plane
surface azimuth convention: east (-), west (+), south (0°)angle between projection of surface normal and local meridian (south)
J projection
normal
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Declination
21. june
22. december 23. september
21. march
-23.45°
+23.45°
0°
0°
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Declination
tilt angle of Earth’s axis due to precession movement during rotation angle between the line (connecting centres of Earth and Sun) and
equator plane latitude of place on Earth where in given day in the noon the Sun is in
zenith
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Calculation of declination
from calender date DD.MM.
from order of the day in the year n
1097,2998,0sin45,23 MMDD
365
284360sin45,23 n
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Calculation of declination
-30
-20
-10
0
10
20
30
0 50 100 150 200 250 300 350pořadí dne v roce
dekli
nace
[°]
equinoxsolstice
solstice
-23,45°
+23,45°
0° 0°
order of the day in a year
decli
natio
n [°]
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time (hour) angle
angle of virtual translation of Sun above local meridians due to Earthrotation, related to solar noon
Earth is rotating around its axis (360°) once for 24 hours→ translation of Sun by 15° over 1 hour
time angle is calculated from solar time ST
convention: before noon (-), after noon (+)
1215 ST
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Solar time ST
each timezone has a time related to local meridiantimezones of 1 h ~ meridians of 15°
CET: local solar time at meridian 15° east longitude
solar time: daily time defined from virtual translation of Sun
observer at reference meridian: local time = solar time observer out of reference meridian: local time solar time
shift up to 30 minnutes
example: solar noon Prague 14,4° 12:02Brno 16,6 ° 11:53Košice 21,2° 11:35
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Sun altitude h
angle between line connecting surface-Sun and horizontal
complement angle to 90°: zenith angle z
coscoscossinsinsin h
hz 90
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Air mass
ratio between mass of atmosphere passed by solar radiation to mass, which would be passed if Sun is in zenith
AM = 0 outside atmosphere
AM = 1 zenith h = 90°
AM = 1,5 z = 48° h = 42°
AM = 2 z = 60° h = 30°
hAM
z sin1
cos1
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Change of spectrum with air mass
h = 90° AM = 1,00h = 70° AM = 1,06h = 50° AM = 1,31h = 30° AM = 2,00h = 10° AM = 5,76
dens
ity of
radia
tivef
lux [W
/(m2 .n
m)]
wavelength [nm]
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Time of sunrise and sunset
sunrise / sunset: altitude angle = 0°
0coscoscossinsinsin h
tgtg arccos2,1
time angle of sunrise / sunset
theoretical period of sunshine = time between sunrise and sunset
15
2 2,1 t
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Azimuth of Sun s
angle between projection of line connecting surface-Sun and localmeridian (south)
convention: measured from southeast (-), west (+)
sincoscossin
hs
Sun
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Altitude and azimuth of Sun
source: solarpraxis
22. december
23. september21. march
21. june
J
S
V
Z
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Incidence angle
angle between line connecting surface-Sun and surface normal
shh cossincoscossincos
Sun
surfacenormal
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Solar radiation - definitions
solar irradiance G [W/m2] - radiative power incident at area unit, density of solar radiative flux
solar irradiation H [kWh/m2, J/m2] – density of radiative energy, integral of flux density per time period, e.g. hour, day, ...
2
1
.
dGH
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Solar radiation - definitions
direct solar radiation (index „b“, beam) – withoutscattering in atmosphereangle dependent, significant intensity in one direction
diffuse solar radiation (index „d“, diffuse) – scattered in atmosphereall-directions, isotropic: identical intesity in all direction
reflected solar radiation (index „r“, reflected) – reflectionfrom terrain, buildingsusual surfaces reflect diffusively – considered togetherwith diffuse radiation
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Solar radiation - definitions
source: solarpraxis
reflection from air molecules, dustparticles, ice crystals
reflection fromterrain
reflectedradiation
directradiation
diffuse radiation
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Solar radiation passing the atmosphere
direct normal solar irradiance (on surface perpendicular to directionof propagation) after passing atmosphere
ZGG onbn exp
Gon normal solar irradiance above atmosphereZ attenuation factor
91018,0)101(0015,2
)sin003,0(sin38076,94
5,02
vL
hh
h Sun altitudeLv elevation above sea-level [m]
[W/m2]
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Attenuation factor
how many times the clear atmosphere should be „heavier“, to havethe same transmissivity as the real polluted atmosphere
polluted means also water vapor not only dust, emissions, etc.
gives attenuation of solar flux when passing the real atmosphere
00
0
lnlnlnln
bn
bnn
GGGGZ
Gb0 direct irradiance after passing completely clearatmosphere (with Z = 1)
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Attenuation factor
5,03,752,751,9annualaverage
4,23,12,21,5XII.4,53,32,31,6XI.4,93,62,61,8X.5,34,02,92,1IX.5,74,33,32,3VIII.5,84,43,52,3VII.5,74,33,42,3VI.5,54,23,22,0V.5,34,02,91,9IV.4,73,52,51,8III.4,33,22,21,6II.4,13,12,11,5I.
industrialcitiescontrysidemountains
Average monthly values for Zfor locations with different environment
Monthsimplified:
mountains Z = 2
countryside Z = 3
cities Z = 4
industrial Z > 5
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Solar irradiance on general surface
total solar irradiance on generally sloped and oriented surface
rTdTbTT GGGG
directirradiance
diffuseirradiancefrom sky
diffusereflectedirradiance
diffusecharacter
[W/m2]
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Solar irradiance on general surface
direct solar irradiance on given surface
sky diffuse solar irradiance on given surface
reflected diffuse solar irradiance on given surface
zbbbnbT G
hGGG
coscos
sincoscos
ddT GG
2
cos1
dbgrT GGG
2cos1
[W/m2]
[W/m2]
[W/m2]
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Terrain reflectance (albedo)
ratio between reflected and incident solar irradiance
for calculations considered g = 0,2
usual surfaces 0,10 až 0,15
snow 0,90
Earth albedo (planet) 0,30 (average)
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Solar irradiance on horizontal plane
direct solar irradiance on horizontal plane
diffuse solar irradiance on horizontal plane
simplified model: 1/3 of solar radiatin „lost“ in atmosphere comes to horizontal plane (sin h) as a diffuse isotropic radiation
hGG bnb sin
hGGG bnond sin33,0
[W/m2]
[W/m2]
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Solar irradiation on general surface
theoretical daily solar irradiation, integration of irradiance on a plane from sunrise 1 to sunset 2
2
1
,,
dGH TthdayT
mean daily solarirradiance
t
thdayTmT
HG
,,
,
[kWh/(m2.day)]
[W/m2] HT,day,th
t
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Influence of slope
optimum slope: summer 20-30° winter 75-90° annual 35-45°
0
2
4
6
8
10
12
1 2 3 4 5 6 7 8 9 10 11 12měsíc
HT,
den,
teor [
kWh/
m2 .den
]
0° 30° 45° 75° 90°
0
2
4
6
8
10
12
1 2 3 4 5 6 7 8 9 10 11 12měsíc
HT,
den,
teor [
kWh/
m2 .den
]
0° 30° 45° 75° 90°
azimuth 0° (south) azimuth 45° (SW, SE)
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Solar irradiation of general surface
diffuse daily solar irradiation, integration of diffuse solar irradiance on a plane from sunrise 1 to sunset 2
2
1
,,
dGH dTdifdayT
HT,day,th
HT,day.dif
GT,m
tabelled in literature for given:slopes, azimuths, locations (attenuation factors)}
[kWh/(m2.day)]
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Real duration of sunshine
duration of direct solar radiation > 120 W/m2
i
iss ,
relative period of sunshine
t
sr
[h]
[-]
meteo-institute (CZ) presents the values for 22 locations
120 W/m2
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Real duration of sunshine
1 8101 8261 6911 899
30423635XII.
56485553XI.
116115108117X.
179188174190IX.
230233219238VIII.
270252238266VII.
258249226266VI.
232241207247V.
163185164187IV.
142149136157III.
88778290II.
46474653I.
BrnoHradec KrálovéČeské BudějovicePraha
Real duration of suhshine s [h]Month
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Real duration of sunshine in CZ
1400 – 1900 h/year
source: ČHMÚ
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Real duration of sunshine in Europe
> 2500 h
< 1200 h
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Total irradiation on given plane
daily solar irradiation
monthly solar irradiation
difdayTrthdayTrdayT HHH ,,,,, 1
dayTmonT HnH ,,
annual solar irradiation
XII
ImonTyearT HH ,,
[kWh/(m2.day)]
[kWh/(m2.mon)]
[kWh/(m2.year)]
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Annual solar irradiation in CZ
slope 30 až 45°, south orientation: 1000 až 1200 kWh/m2
slope 90°, south orientation: 750 až 900 kWh/m2
source: ČHMÚ
MJ/m2
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Optimum slope for Central Europe ?
southeast west
southeast - southwest
15-6
0°
slope
azimuth
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Solar energy: typical values
solar irradiance G (power)
clear sky 800 to 1000 W/m2
semibright 400 to 700 W/m2
overcast 100 to 300 W/m2
solar irradiation H (energy)
winter 3 kWh/(m2.day)
spring, autumn 5 kWh/(m2.day)
summer 8 kWh/(m2.day)