Fundamentals of Salar Energy Utilization
(2 4'¡ - 5 2 1)

;  .

José- G.  e Martín
Energy Engineering Program
University o...
ACHAPTER 1. Exrzaterresu-iaisoiar Iiadiation

.  - h ~.  ,x
, A «, , 

'hg A§ug

/ Kn

Most of the radiation from the SLm ...
Surface

Egggçgstrial &digügn
Definition: 

 the intensity of radiation impinging on the Earth's
atmosphere,  i.  e.  .

=...
.iFnannaafgsomo
Í_ bemeirpressed  as

”Iá = Isc[ 1é"b. óâ3“cos (360n/365HZ Where n =  day of the year. )

. . . _.. ... .....
The area under the curve is just the solar constant

- .  g ? í
1,5¡ 511w.  
The shape of this curve is not very diñerent ...
Table.  Electromaggeüc Wave Spectrum'

 
   

 
 
 

 

 

  Time of Wate* ' Frequency/  3
(m) Z (Hz =  c 54)
: $717 -----...
Ultrasonic Waves . 
10 p_ _ ' 10
10 ' j ' 1

 
 

 
 

Fraction of Blackhody Radiant “Emery Between Zero and M' for Even
F...
CHAPTER 11: Solar radiation at Earth's surface '
( Reference:  Dufñe 8: Beckman)

Normally,  there is insuücient meteorolo...
12,. .

Attenugggn gf Eggiaggn in mgeAtmgs ghgg' 1 'i

-  111 _1 '  7

/ i
L1

1. X-rays are absorbed high in the ionosphe...
I (x)= ¡ (0)exz›(- udx)   '

0
oçnzlthidirzss
' u:  constant ( not so since air composition depends x) . 
(1) becomes '

v...
SQATFERING _
§gaggring pv ai;  mgleglçg;  À 12.3». 

[Rayiight scattering.   than air molecules.  E ñeld vibrates bound el...
f --$- conector
sun

(3-Dimensions) y

m
Collector on a horizontal surface)
co:  hour angle

conector

   
 

. É. . of
í
, w . 

f? , /  Equator
. a3 beem 

; JV ...
casõcoscp

or 0), : cas *Han ãan g5)

@ngm gf gay ;  Td / 
TF-LMÊExm, x2=Âcos '1(-tan&an<p) l
15° 1.5 «. 
lsfotezNearnorth...
., ... ...  _. ... ... .__. .. .  ., ... ... . _, 

_One has: : e_ e   '  . 
(pâsplagrütime =  standaÊdlísíê + E + 4 ( Let...
s men' dían

A meridian is a great circle passing _through the north and

south peles.  f
N f l I'

 ff, 
57_ 

norma¡ s; ...
ê = sun vector =  unit vector
pointing toward the sun

íê= sxi+syj+szk

Consider a rotation about Z axis

 

Ên-lomscpaieee
Projection of g Projection of

Sx on X' axis : Sxcosat ' S);  on Y" axis= sycosm
Sy on X' axis =  Sysinq) 5x on Y' mds= -S...
-. .._. ... ... .. .  .. _ .  _ . _.. . . 

' 1 0 É ' N
.  'a '
Rxwp( 0 cosa smp : l (l 

C034¡ 0 . .sina-n v - p. 
RQWF( ...
l.  Rotate Earth through angle co _

S' =  R:  ( -0) ) S ( co defined negative for positive rotation )
z. 

 

a_ v (cosa,...
., ,.. ... ... .-. ... ._. -«. ... ..



*II

Check : 

sind¡ O _cg§$ C058 CÚSLD
o 1 o .  _' cosô sina: 
cost# o sind) sin...
as

8'":  Rz m S"

easy siny 0 8x" sx”

&'SÍY¡ cusy o)(S u") =  'Egg-hj
Sz"'

Note: 
Sz" = Sz"'
Y axls through

4. Rotate ...
leads to

, s

Sz"" : sinõ sirup coss - sinõ caso sirzs cosy a
-i-casõ coscp coss Cosan» cosô sino sinscosy casco l
+cos6 ...
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Fund ener sol aer 1

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Fund ener sol aer 1

  1. 1. Fundamentals of Salar Energy Utilization (2 4'¡ - 5 2 1) ; . José- G. e Martín Energy Engineering Program University of Massachusetts - Lowell Fall, 1991 . 'v. -,. -_. q.
  2. 2. ACHAPTER 1. Exrzaterresu-iaisoiar Iiadiation . - h ~. ,x , A «, , 'hg A§ug / Kn Most of the radiation from the SLm is radiation of<O.3 to 3.0 The Suns energy comes from fusion - the Stan is like a fusion reactor using 'ravitaüonal conñnement. These are possible fusion reactions myolvíng hydrogen isotopes: 1H1 + 1H1 1D¡ + 1e° 1H1+1D2---->2He3 +7 a 11-11 +1'I°----› 2He4+y / The above have small cross-section) . ~' j “j i 'P . ~ Í i 1D? HDZ--í-a» zHeí* +an1 3.. .'2;7Mev f a x 1D? +1D2 ----B- 1T3 +1H1 + 4.03Mev / 1D¡ +1T3 2He4 + an¡ + 17.6Mev 1D? +2He3 2He4 +1H¡ + 18.3Mev he most important net process is: 4 hydrogen atoms ( 4 protons) combine : 't 'se Helium. Not necessarily according to the above reactions: instead. ¡rough Catalyst. tggnsig The intensity of beami of radiationtis cíeñned as the energy per unit 'ea per unit time Crossing a surface that is perpendicular to the direction 'the beam. i-imsepmgss'
  3. 3. Surface Egggçgstrial &digügn Definition: the intensity of radiation impinging on the Earth's atmosphere, i. e. . = sc_g_l_ar energy per unit time per' perpendicular to the radiation impinging on the Earth's atmosphere. ” : kw aii/ Á» / G 4%- LSx 1081931175844 _ 1 Astronomical Unit = 1.5x 103 km = mean earth-sun distance : energrfrom sun per unit time. :per unit area perpendicular to the radiation. in space at 1 Astrgngmical Unit. g_ “Jr, m _=1.94o cai/ cm2mm=1as3__vg mzbr :428 n21:: ( Space measurements have improved data overthat artrapolated from Earth measurements) ' Íac is the value of Io when the Earth is at its mean distance &om the Sun. V onfE rrtriRaiuwiime z The variation of the intensity of the radiation emitted by the Sun is i 1.5%. The variation of exiraterresu-ial radiation. (Ío). with time of the year is :3%. This isdue to the changing distance between the Earth and Sun. The variation is as follows: í. i-ZRLSQLIQQ
  4. 4. .iFnannaafgsomo Í_ bemeirpressed as ”Iá = Isc[ 1é"b. óâ3“cos (360n/365HZ Where n = day of the year. ) . . . _.. ... .._. .au. " 4/ " "E ' ( often, consider” (instant) The performance of certain solar energy devices like photovoltaic cells s dependem on wavelength as well. asáthe intenfityQ/ :af solar radiation. ,H , aii , wi . a . t. uv . For the analysis of these types of it is important to have a etailed description of the various wavelengths of solar radiation emitted by : ie Sun. The specual distribution of extraterreâtrial radatlon is as follows: W/ mzpm . 2 400 pectzral beem í wavelengthuljín um A i i- 3 Fri. Sep 1.- 1939 ,
  5. 5. The area under the curve is just the solar constant - . g ? í 1,5¡ 511w. The shape of this curve is not very diñerent from the speed-al distribution emitted by a' perfect black body radiatlon at 5762.12 For this reason. in many solar applications such as hearing or cooling, it is suñcien' to approximate the solar spectral distribution. by that of a. black body at 5762°K. (Black body radiation is discussed later) ( In text. "solar spectral irradiance in W/ cmziim : in terms of 'this quantity. E. 1' , if 1,5¡ Edil. g , E O M/ li V 'x Also. D1. the percentage of the solar constant associated with wavelengths shorter than 1. clearly, ' J. i Em DZ' ° X ¡rc - . Where JV , , . e _a/ w- f . à u' - 1se=1353W/ rpz__ . , * ~ Using the Table 1.3.1. one can obtain the amount of radiation in a desired range. i-4Fri. Sep1.19$
  6. 6. Table. Electromaggeüc Wave Spectrum' Time of Wate* ' Frequency/ 3 (m) Z (Hz = c 54) : $717 ------------------------- f” ______________ : g2: 10-16 ' Cosmic rays . 1024 1015 - 1023 10-14 A_ 1022 10'” = 1021 10'” Gamma rays ' 10°° 10'” r ' 1019 . Í ~1O g 18 r lAngsirom (A) XY rays « 10 10° E ' 1017 10's a 1015 e tnuavxoierizamanançoa- 102mm) 10'? › - 1015 1 Nlicron ( um) Visible light (O.4- O.711m) V 10's . 1014 10-5 Infrared ( heat) radiation (0.7--l00011m) 1013 10-4 12 l Fresnel 10 1 millimeterimm) « A lt. _ › 1011 10'” EBF 1 101° 10'1 SHE v 109 1 1 meter UHF , ' 108 10 VHF v 107 101 HF '1 Megacycle 106 LOS l kilometer (km) NIF o 105 104 LF 104 _ 5 3 ;0 VLF 1o s ' 2 . O _ lO l- 5 Fri. Sep 1.19%
  7. 7. Ultrasonic Waves . 10 p_ _ ' 10 10 ' j ' 1 Fraction of Blackhody Radiant “Emery Between Zero and M' for Even Fractional Increment $047 Hum: : 1T at ene 531W” , midpoint -i ______________________________________________________ __ 0 05 1880 16 0 10 2200 20 o 15 2450 23 o 2o 2680 5 0 25 2900 27 0 30 E3120 30 0 35 *3350 32 0 4o 3530 34 o 45 3830 37 0 50 41 10 39 0 55 4410 42 0 60 4,740 45 o 65 15130 49 0 70 5590 53 0 75 6150 5a . ... ... ... ... ... .. _. ._e. .--~. ._i_-. ... _-__. ___. .___. __-_. .__. .__. _-___. 0 a0 6860 64 0 55 7.850 73 0 90 9380 a5 0 95 12500 106 1 00 0° 163 l iÀÁÉÉÉiQSep 1. 1959
  8. 8. CHAPTER 11: Solar radiation at Earth's surface ' ( Reference: Dufñe 8: Beckman) Normally, there is insuücient meteorological information to accurately calculate ground intensity from the solar: constant. f ri 0551111119115: › “Íâaditaitignj Radiation received the sun without change in direction. Also eaueã* LLLDED or "n'1_1n; _1<: _c'_m radiation. This radiaüon is from the geometrical disc of the sun. ( Part that can be focused) - . Ibifuse Radiation whose direction has been change bylscattering _. .-_. _m. ._ _m_ atmosphere (Also called " '_'; .1(1'Note: ground surfaces also scatter sunhght) ' ' ' m = Path length ofbeam radiador: ~ wwe ' ~ 1 Path length a: sea level when sun is a: the zenith; › _ í o (Zenith: directly overrreadij¡ Atmosphere Í#- xnxx Earth V v: S: = angle _ pm» ------- 7'? ( "- . 1* m= %s _J_ = secB, - ' >(- For m<3 ) l cos 9, ° / › u-in-Lsepa-isas
  9. 9. 12,. . Attenugggn gf Eggiaggn in mgeAtmgs ghgg' 1 'i - 111 _1 ' 7 / i L1 1. X-rays are absorbed high in the ionosphere by nitrogen, oxyg/ en. etc. 2. Most ultraviolet is absorbed by ozone. (O51 2.5 um. a low value of extraterresuial radiation and strong “ absorption by CO2 and HzzO résults in little radiaiion reaching the surfacé (Also, greenhouse eifect E'. ' 431m5- 991v wavelenems bstwém 0-29. and_ 27.5191 EIFÀPÍÉÍEIÍFÊÊ in terrestrial applications. i - 1 aan-unem”. 1.41.1.. ., -" 5. @ter vapor absorbs certain hands of wavelengths _inqthejnfrared region 6. Additional absorpüon between 0.3 and 2.5 iimis caused_ by O2.03.CO7. . nara» ma. 7. In agdiüon to absorption by-Íabove there is scattenng by air molecules, water vapor. and zduâji. _ g. ; . .__V V VV_ _ »a »if . 1, _ , li__«“à Attenuation coeñicient- 1attenuation¡ nofbeam radiation IN, n** ' l um: # of absorptions / (tbm avera ; is : Êofscatters/ cmiravelled '(*1) (d) 11 paus + pe = attenuation coeñcient # of interactions / travelled 1 X I(x dx v: 4- Ear th # reacting in dx= I (x) partidas >< V , x-Êxmn-Lagyáezled = l(x)¡, idx reactions V d¡ (I): -Í (x)/ .L dx z. . _ . ii-ZMnnnSepILISBQ
  10. 10. I (x)= ¡ (0)exz›(- udx) ' 0 oçnzlthidirzss ' u: constant ( not so since air composition depends x) . (1) becomes ' v I (X)= I (O) e-#X X . . . ' - dx Monochramazzc transnusszan factor = 1'¡ : -: IlOí-L-: e L É¡ é 5X0) (X: wavelength, p. = fa) ) Note : x x X www» u-. dz uudx" ? Fe o x -. =e o e o TFTMsNÍMabaJ - Tm¡ : monochromatic transmission factor for scattering Tum): monochrornaüc transmission facto; .for absorptlon The T's can be defined for each type of scattenng or absorption: then the total 1: is found by multiplying together the T's for individual processes. ü-3Mon.5ej›11.A1989 (1)
  11. 11. SQATFERING _ §gaggring pv ai; mgleglçg; À 12.3». [Rayiight scattering. than air molecules. E ñeld vibrates bound electxor which radiate at the same frequency) '4 x* '7' talão-amam t q É for m=1. X is in um. baromletrlc' pressure = 760mm §çgttgñng frgm *ggsf rá¡ 43.75 V TdFIO-aooassx 4- . Íi o for m=1. 800 particles/ Àcm” at ground Sgagering from water mp0; 'tvht V Twfloxxomsxz r 'A' g for m=1 . 20 mm of precifaitable Watermamount' of vapor in theaair. colúr above observar) . . a t . For other conditions and including all three eñects 'fu-- x' 1 , x 4, fus; =[(raa)””°°(vw””°°(nz)”'z°]“ ' - " : transmittance for beam. radiaiion ai: wavelength À. . considering scattering only. Symbols: p= total pressure. mm d= dust partlciple concentration at ground ( partlcles/ cm3) í w: depth ofprecipitable water, mm m= air mass t " n= msimabsa= oisamü _ni »~ “À o-oxygen = ' i i w-water (Water vapor. strong absorpüontin infrared, Fig . 2.3.1 up to 2.3 ; im . Beyond 2.9 ; im HzO and CO2 absorb more than 95% . Below 0.29nm. aimos' complete absorption by ozone; between 0.29 and O.351.Lm. shown in Table 2.3.1) V lí 'ut-aimsepenses
  12. 12. f --$- conector sun (3-Dimensions) y m
  13. 13. Collector on a horizontal surface) co: hour angle conector . É. . of í , w . f? , / Equator . a3 beem ; JV a . ee , /97 . .a-w j, Other angles of interest are 62. the zenith angle, and , JL 4655-4? . um. .., .. . a= (90°-9z) i . - (s: The zenith angle can be calculated by putting s : O in Eq. (7) (i. e. 1.6.2). Thus ~ x r' cosa; ;sina sin. a + cosô'_cosíi$""ç'õ§ã¡ (9) Qalgulaiing me @e gfsuggise That is. ñnd (Ds. where_o)a= value of cn at sunrise. Sunrise ez: 90'. cos6z"= 'O' thus, from Eq. (9) sinõ singi- + cosô coszp cascos : O . IL-GFÍLSCpS. 1989
  14. 14. casõcoscp or 0), : cas *Han ãan g5) @ngm gf gay ; Td / TF-LMÊExm, x2=Âcos '1(-tan&an<p) l 15° 1.5 «. lsfotezNearnorth pole e = 90° tanq) -i eo - no solution; days never end in summer nights never end in winter Ai: equator cp: 0°. tan ozo, C05 '1((3)=90° Ta: 125:: 90 = 12 hours Determining the direction of diifuse radiation is much. more difficult than for beam radiation. We will consider this later. Solar time _a clock time Solar noon e clock noon ( Solar noon: sun directly overhead n l Clock noon: sun usually not quite directly overhead ) Two reasons why not ~ 1) Location not on standard meridian. for time zone ne E r particular location i ' 'z time zo L Lst =75°w , standard meridia: : ) Perturbations in the earth' s orbit and rotaüon which afect the osition of the sun in the sky. a - e w ' u-? msepa 1939_
  15. 15. ., ... ... _. ... ... .__. .. . ., ... ... . _, _One has: : e_ e ' . (pâsplagrütime = standaÊdlísíê + E + 4 ( Let - uoc ) (in minutes) where Let = longítudélmoflsftañdard m - or particular time; (zone in degrees west ) Lioc = longitude of location in question ( Longitude is measured in degrees east or west. up to 180° , from the standard . or prime meridian which passes through Greenwich. England) _ There are 24 hours/ 360° = 4 min/ degree E = the equation of time = correction for orbital and rotational perturba: . TW” E time Equatinn of time min. -15 ! On é) âzangie between equatorial diana and beam radiation 5 Approximate exprese1íon3f~eFô-~«~-~-~--v- a 'z V W*"N'"" _ . 284 É. lô= z°^-f*ss*““ô° 1 X Collectors ( tracking type specially) may face east or west of " due south" l1-8H1Scp8.19$
  16. 16. s men' dían A meridian is a great circle passing _through the north and south peles. f N f l I' ff, 57_ norma¡ s; :the deviation from the local 7¡ g rñeridian of the projectíon of the normal to the conector on: a horizontal surface. (m is negative in ñgure ) c 11-9FYL5Q8.19B9
  17. 17. ê = sun vector = unit vector pointing toward the sun íê= sxi+syj+szk Consider a rotation about Z axis Ên-lomscpaieee
  18. 18. Projection of g Projection of Sx on X' axis : Sxcosat ' S); on Y" axis= sycosm Sy on X' axis = Sysinq) 5x on Y' mds= -Sxcos(90°-q›) " l = -Sxsinqa 'Ihus sx: saccosqwsysmq; (12) Sy: Sycoso-Sxsincp (13 ) Also ' Sz"-= Sz ' (14 ) In matrix form S= Sx i+Sgj+Sz k 5x às( Su S2 (15) In the new coordinate system: 5X: SxcosqH-Sgsinq¡ . §'= 3M_ = -Sxsindrl-Sgcosà 52 S2 (16) Note: for a rotation by an angle q) about the Z axis, we had s- = R2 (ç ) 's“ (17) Where ' ' 60541 sina 0 R203): í- 81m cosa 0 : l p 0 0 1 (1 8) : rotation man-ix 'l For rotations about the X and Y axis. there are similar matrices: n-nmsepaisas t'
  19. 19. -. .._. ... ... .. . .. _ . _ . _.. . . ' 1 0 É ' N . 'a ' Rxwp( 0 cosa smp : l (l C034¡ 0 . .sina-n v - p. RQWF( 0 1 0 : l ptb? Sind¡ 0 cosa). ( We shall demonstrate the use of these maizrices by deriving Eq. ( '. e. , 2.5.2 in Dufñe and Beckman. ) First place the coordinate system on the North pole at high no01 with the X axis facing toward the Sun. . g (Summer time) Clearly, S= cosõ í+ sinõ k or equivalently, cosa s= í 9 j sinô ñ-12PYLScp8.1989
  20. 20. l. Rotate Earth through angle co _ S' = R: ( -0) ) S ( co defined negative for positive rotation ) z. a_ v (cosa, -sinw 0 C088 s' : sina: cosa: 0 0 o o 1) (SW) cosa cosa; = cosa sinw j l sinô 2. Rotate about Y axls through angle ( 90 -a ) S" = Ry ( 90- 42 )S' Note: cos(90-q›)= sinq› › sin(90-q›)= cosq› l1-l3FTLScp8. 1989
  21. 21. ., ,.. ... ... .-. ... ._. -«. ... .. *II Check : sind¡ O _cg§$ C058 CÚSLD o 1 o . _' cosô sina: cost# o sind) sinô cosa cosa: sinqu-cosçsínô sx: cosõsinm = SEI cosa coswcosç + sinõsinú sz' cosez = Sz" = cosã costa coscp + sinâ sirup . Which agrees vríth Eq. ^(9) of the notes (2.5.3 of the text) 11- 144115438. 1989
  22. 22. as 8'": Rz m S" easy siny 0 8x" sx” &'SÍY¡ cusy o)(S u") = 'Egg-hj Sz"' Note: Sz" = Sz"' Y axls through 4. Rotate Collector about
  23. 23. leads to , s Sz"" : sinõ sirup coss - sinõ caso sirzs cosy a -i-casõ coscp coss Cosan» cosô sino sinscosy casco l +cos6 sínssinysmm . _ (as Duñe and Beakman 2.5.2) Ignoring aunospherlc eñectsmultiplied by incident radiation intensity, gives the intensity reaching the Collector, per unit area, if the collector is flat. Consider diñerent cases: 1. Horizontal flat plate 2. Vertical. heading South 3. Tllted a. t an angle, aimed, south; 4. Seasonally tllted. flat plate _ 5. North-South Horizontal. East-West tracking 6. North-South Polar. East-West' backing 7. East-West Horizontal. North-South Tracking n-ismsepaisas _ , E

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