Review of Lecture 8 T - MIT OpenCourseWare · PDF...

.997 Copyright © Gang Chen, MI

or 2.99irect Solar/T

hermal to



hermal to

2

T

F

7 D

Electrical Energy Conversion

Review of Lecture 8

Solar spectra: AM0, AM1, AM1.5 etc. Definition of radiative properties Maximum efficiency of solar thermal engines Maximum achievable temperature

• Wavelength (frequency) selective surfaces

• Blackbody function

• Earth motion

••••

2

T

F

7 D


Contents of lecture 9

Solar hot water systems Maximum solar concentration Methods for concentration Nontracking and tracking

• Solar thermal-mechanical energy conversion

• EM wave calculation of surface properties

••••

1

2.997 Copyright ©

r 2.997 Direct S

cal Energy

ght ©

Chermal

ersion

g Chen, MI

r/Thermal to

ala

Gan

T

Fo

ola

Electri

Conversion

Solar Hot Water Systems

http://78.136.49.147/images/Solar%20Hot%20Water%20Heating %20Diagram.gif

How Much Area You Need? • 80 Gallon of Water • Start temperature Ti=15 oC • Hot water temperature Tf=60 oC

( )ifs TTmctJA −=•Δ•• η Energy Balance

hours/day5.5=Δt Specific heat c= 4180 J/kg.K Js=1000 W/m2

Thermal efficiency η=60%

A=5.1 m2

Gng

hen, MIT

or/T

to

Conv

Flat Panel Solar Hot Water Heaters

http://collector-solar.com/products/index.htm

2

Image by EERE.

Images removed due to copyright restrictions.Please also see:http://greennav.files.wordpress.com/2008/03/solar-panel.gif

http://www.mdelectric.ca/1_Pictures/GreenEnergies/GE-ViessmannCollector.jpg

Photo by szczel on Flickr.

Figure by MIT OpenCourseWare.

http://greennav.files.wordpress.com/2008/03/solar-panel.gif

http://www.mdelectric.ca/1_Pictures/Green%20Energies/GE-ViessmannCollector.jpg

http://www.mdelectric.ca/1_Pictures/Green%20Energies/GE-ViessmannCollector.jpg

http://www.flickr.com/photos/stefan-szczelkun/1639659393/

2.997 Copyrightang Ch

For 2.997 Direlar/T

hermal t

trical En

Conversion

97 Copyright © Gang C

97 Direct Solar/Thermal

nergy Conversion

© G

en, MIT

ct So

o

Elec

ergy

Evacuated Tube Technology

http://www.diytrade.com/china/4/products/1716424/All-Glass_Evacuated_Solar_Collector_Tube-SFVA.html

2.9

hen, MIT

For 2.9

to

Electrical E

Vacuum Tube Hot Water Heaters

Unpressurized Separate Tank Collector

3

Images removed due to copyright restrictions. Please see:

http://img.diytrade.com/cdimg/194777/1624552/0/1160536024/All-Glass_Evacuated_Solar_Collector_Tube-SFVA.jpg

http://img.diytrade.com/cdimg/194777/1624568/0/1160536058/All-Glass_Evacuated_Solar_Collector_Tube-SFVB.jpg

http://img.diytrade.com/cdimg/194777/1624573/0/1160536136/Metal-Glass_Evacuated_Solar_Collector_Tube-SFVC.jpg

Images removed due to copyright restrictions. Please see any photos of solar water heaters, such as:

http://image.made-in-china.com/2f0j00ferESMmCAVoH/Solar-Collector.jpg

http://image.made-in-china.com/2f0j00VBdtYnQhIaRE/Split-Pressurized-Solar-Water-Heater-CY-SP-24-.jpg







http://image.made-in-china.com/2f0j00ferESMmCAVoH/Solar-Collector.jpg



22.997 Copyright © Gang Chen, MIT

For .997 Direct Solar/Thermal to


Efficiency Estimation---Evacuated Tubes

Incoming Solar Radiation

sJL ••

Radiation Loss

( ) [iloss TLDQ = σπε

Thermal Efficiency

− ilossa DQQη

Din

Do

Absorbed Solar Radiation

ατ ••••= sia JLDQ

Qin Do =

4 4 ]a−Ts

⎛ πεσ T 4 4 ⎟⎞

⎜⎜ ]⎟[ατ Ta− −= = sQin Do JJs ⎝ ⎠s


For 2.997 Direct Solar/Thermal to


Efficiency Estimation---Flat Panel

Js

Ther

mal

Insu

latio

n

Air

Rair1

Ts

Rg Rair2

Tam

4 sTσ4

amTσ

Solar In

Tam

[ ]K/W38.0026.0

1010 3

1 AAAk

dR air

air = ×

≈= −

[ ]K/W00025.02.1103.0 3

AAAk

dR

g

g g =

×≈=

−

[ ]K/W2.05 11

2 AAhARair =≈=

Ri

d

[ ]K/W3.01.0103 2

AAAk

dR i

i i =

×≈=

−

4

.997 Copyright © Gang

.997 Direct Solar/Therm

l Energy Conversion




Efficiency Estimation---Flat Panel

Js

Ther

mal

Insu

latio

n

Air Thermal Efficiency

in

lossa

Q

QQ

−=

− =

ατ

η

[ ]

[ ] [ ]44

4

2

5.5 amsams

am i

ams

gair

am

TTATTA

TTAR

TT

R

−+−=

−+−

+ +

εσ

εσT Ts −Qloss 4=

Rair R s+1

1.7[Ts − Tam ] −πεσ [T 4 −T 4 ]

J J s a s s

2

Chen, MIT

For 2

al to

Electrica

Estimated and Experimental Results

http://www.enviro-friendly.com/images/NSW-Winter-Solar-Efficiency-graph.jpg

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

40 50 60 70 80

Ther

mal

Effi

cien

cy

Temperature (oC)

5

Courtesy of Hills Solar. Used with permission.

Copyright © Gang Ch

97 Direct Solar/Thermal t

nergy Conversion

2.

T

o

Total Renewable Capacity in 2007

, MIne o

79 .9r 2 9

FE e t i al c r c l E

Weiss et al., Solar Heat Worldwide, 2009 Ed.

7 Copyright © Gang

7 Direct Solar/Therma

ergy Conversion

, MI

o2.99

ChenT

F r 2.99

l to

Electrical En

Solar Heat Utilization

Weiss et al., Solar Heat Worldwide, 2009 Ed.

6

Courtesy of IEA-SHC. Used with permission.

Courtesy of IEA-SHC. Used with permission.

ectrical

rrec

Ene 32'

Sun

= 1.495 x 1011 m= 9.3 x 107 mi

1.7%

1.27 x 107 m7900 mi

EarthSolar constant= 1367 W/m2

= 433 Btu/ft2 hr= 4.92 MJ/m2 hr{Gsc

{Distance is

1.39 x 109 m8.64 x 105 mi

ht © G

t SolaR

r θs

Energm

y Balance

er4 π or 2 n J = 4πR2 J

irss e

With Concentration

CJ = σT 4 ≤ σT 4 e c s = Js

J s ⎛ R ⎞2

Cmax = =⎜ ⎟Je ⎝ r ⎠

1 = = 46,164

sin2 θs

ang CEarth Orbital ,

Maximum Concentration of Sun Light---2nd Law Limit

Maximum concentration

7



Image by Robert Simmon (NASA).

Sol

y Conve

Sun 147,300,000 km152,100,000 km

September equinoxSept 22/23

March equinoxMar 20/21

PerihelionJanuary 3

DecembersolsticeDec 21/22

June solsticeJun 21/22

AphelionJuly 4

ra

997 Copyright

or 2.997 Direct S

trical Energ

.997 CopyrighG

7 Dir

a

θs

θs

Φ

θs

rθsr

d/2D/2

D/2

F

Concavefocusingmirror

.99ica

l En

2.

© Gang Chen, MIT

F

olar/Thermal to

Elec

y Conversion

Maximum Concentration of Sun Light---2nd Law Limit

nindexrefractive 4

e nCJ =

maxC =

Inside a medium of σTc

2n

sin2 θ

Achieved C=56,000

Gleckman et al., Nature, 339, 198 (1989)

o MI

,neh2D Flat Panel

sin Φ cos Φ sin 2Φ = =

3D Concentration

Φ= 2

sin d r sθ

sin D =Φr

D

cos

2

d sinθ 2sinθs s

1C = = 107max 2sinθ1 s

C = max 4sin2 θs

8

Image removed due to copyright restrictionsPlease see Fig. 1a in Gleckman, Philip, JosephO'Gallagher, and Roland Winston. "Concentration ofSunlight to Solar-surface Levels Using Non-imaging Optics."Nature 339 (1989): 198-200.


7 Copyright © Gang Che

.997 Direct Solar/Thermal to

al Energy Conversion

θs

θs

Φ

θs

rθs

r

D/2

C = (D/2 π r sin θs = sin φ / sin θs1/π sin θs (1/π) Cmax

D/2

F

Concavefocusingmirror

n

r 2ric

.997 Copyright

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C

A'A

θ

B' B

Reflector profile

Edge ray Wave front W

String Method

2. al

2.99

,T

FoElec

Imaging Concentration to Cylinder

From Fig.4.3: R. Winston et al., Nonimaging Optics, Elsevier, 2005

ang Chen, MIT

For

olar/Thermal to

Electric

Conversion

Nonimaging Optics

' BBABAC +=+

AC =

BAAB ''=

θsin1

' ' ==

BB

AAC

2D Concentration to Flat Plate

3D Concentration

21 ⎟⎞

⎜⎛ =C

A' B '

AA'sinθ

Maximum when θ=θs⎝sinθ ⎠

9



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2D Concentration to Cylinder

Winston r Foand Hinter

rber

Energ cat iger, Solar y, 17, 255

ec (1975)

Courtesy of Elsevier, Inc., El http://www.sciencedirect.comUsed with permission.

Earth Orbital

Summer

997 Copyri

r 2.997 D.

gEquator

23.5o (22-24.5 o)

10

Winter

Images from Wikimedia Commons, http://commons.wikimedia.org

http://www.sciencedirect.com

http://commons.wikimedia.org

r/

onversi


For 2.997 Direct SolaThermal to

Electrical Energy C

on

Daily Insolation Variation Js

A At Noon: Q=JsA

A Q= JsAsinθ

θ

Js also varies due to path length

45o North Latitude http://www.eoearth.org/article/Daily_a nd_annual_cycles_of_temperature




Tracking

Js

A Q= JsAsinθ

θ

Q= JsA

θ

One Axis: Axis Along South-North Direction

11

Courtesy of Michael Pidwirny. Used with permission.

997 Copyright

For 2.997 Direct

ectrical Ener

ers

7 Copyright © Gang Ch

r 2.997 Direct Solar/Thermal t


ang Chen, MI

larrmal to

2.

© G

T

So/The

El

gy Conv ion

V-Trough • East-West Orientation, with

seasonal adjustment: 2.5-3 times

• South-North tracking

http://www.electricksolutions.com/cms/temp lates/electriksolutions/IMAGES/banner1.jpg Holland, Solar Energy, 13, 149 (1971)

2.99

en, MIT

Fo

o

Solar Thermal Energy Conversion ---Mechanical Systems

Handbook of Energy Efficiency and Renewable Energy

12

Courtesy of Elsevier, Inc., http://www.sciencedirect.com.Used with permission.

Images by EERE. Please also see Fig. 21-13 in Kreith, Frank, and D.Yogi Goswami. Handbook of Energy Efficiency and Renewable Energy.Boca Raton, FL: CRC Press, 2007.

http://www.sciencedirect.com


or 2.997 Direct Solar/Thermal to

trical Energy Conversion

2.997 Copyright © G

h

For 2.997 Direct Solar/Th


2.9

en, MIT

F Elec

Solar Trough

ang C en, MIT

ermal to

Solar Trough

13

Courtesy of Plataforma Solar de Almería. Used with permission.

Image removed due to copyright restrictions.Please see Fig. 5.16 in Kaltschmitt, Martin, Wolfgang Streicher, and Andreas Weise.Renewable Energy: Technology, Economics, and Environment. New York, NY: Springer, 2007.Also see any photo of a commercial HCE, such as Schott's PTR 70.

http://www.schottsolar.com/fileadmin/media/us/SCHOTT%20PTR%2070%20Receiver%20US.pdf

2.997 Copyright © Gang Chen






, MITSolar Trough with

Molten Salt Storage

Price, H. Lupfert, E.“Advances in Parabolic Trough Solar Power Technology”

From J. Karni

14

Courtesy of Jacob Karni. Used with permission.

Photos by EERE, Sandia National Labs.

Courtesy of Elsevier, Inc., http://www.sciencedirect.com. Used with permission.

Image removed due to copyright restrictions.Please see any photo of a linear Fresnel lenssystem, such as http://commons.wikimedia.org/wiki/File:Fresnel_reflectors_ausra.jpg http://i.i.com.com/cnwk.1d/i/ne/p/2007/910Ausra1_550x367.jpg

http://www.sciencedirect.com/

http://commons.wikimedia.org/wiki/File:Fresnel_reflectors_ausra.jpg

http://commons.wikimedia.org/wiki/File:Fresnel_reflectors_ausra.jpg

http://i.i.com.com/cnwk.1d/i/ne/p/2007/910Ausra1_550x367.jpg

http://i.i.com.com/cnwk.1d/i/ne/p/2007/910Ausra1_550x367.jpg


or 2.997 Direct Solar/Thermal t

rical Energy Conversion

97 Copyright © Gang Chen, MI


ectrical Energy Conversion

2.

en, MIT

F

o

Elect

Solar Trough: Concentration Ratio


2.9

T

F El


Solar Trough: Cost

15

Table removed due to copyright restrictions.Please see Table 2 in Price, Hank, et al."Advances in Parabolic Trough Solar Power Technology."Journal of Solar Energy Engineering 124 (May 2002): 109-125.

Table removed due to copyright restrictions.Please see Table 8 in Price, Hank, et al."Advances in Parabolic Trough Solar Power Technology."Journal of Solar Energy Engineering 124 (May 2002): 109-125.

opyriGang Chen,

97 Direct S/Thermal

rical Energy Con

ion

Copyright © Gang Chen,

2.997 Direct Solar/Thermal t

ectrical Energy Conversion

2.997 C ght ©

MIT

For 2.9

olar

to

Elect

vers

Trough Efficiency

“Assessment of Parabolic Trough and Power Tower Solar Technology Cost and Performance Forecasts” NREL, 2003

2.997

MIT

For

o

El

Trough Cost Breakdown


16

Copyright © Gang Chen

2.997 Direct Solar/Thermal to

ical Energy Conversion

2.997

, MIT

or

Heliostat / Power Tower

l c rFE e t




From J. Karni

17

Courtesy of Jacob Karni. Used with permission.

Photo by Koza1983 on Wikipedia.

Images by EERE and Sandia National Laboratory.

http://commons.wikimedia.org/wiki/File:PS20andPS10.jpg

yright © GChen, MIT

or 2.9

t Sohermal to

ectrical E

version

Copyright © Gang

Direct Solar/Therma

rgy Conversion

2.997 Cop

ang

F 97 Direc

lar/T

El

nergy Con

Heliostat Receiver


2.997

Chen, MIT

For 2.997

l to

Electrical Ene

Heliostat / Power Tower Cost


18

Images removed due to copyright restrictions.Please see Fig. 21-49. 21-51, and Table 21-9 in Kreith, Frank, and D.Yogi Goswami. Handbook of Energy Efficiency and Renewable Energy. Boca Raton, FL: CRC Press, 2007.

Image removed due to copyright restrictions. Please see Fig. 21-40 in Kreith, Frank, and D. Yogi Goswami.Handbook of Energy Efficiency and Renewable Energy.Boca Raton, FL: CRC Press, 2007.

pyrigGang Chen,

7 Direct S/Therm

cal Energy Convio

97 Copyright © Gang Chen,


trical Energy Conversion

.99or 2

o

27 Co

ht ©

MIT

F.99

olar

al t

Electri

ersn

Heliostat / Power Tower Efficiency


2.9

MIT

FElec

Dish

19

Photo from Wikimedia Commons, http://commons.wikimedia.org

http://commons.wikimedia.org/wiki/Main_Page

2.997

Ch

For 2.997 D

Thermal to

Electrical Energ

version

opyright © Gang Chen,

97 Direct Solar/Therm

rical Energy Conversio

ol

2.9

Copyright © Gang en, MIT

irect Sar/

y Con

Dish and Stirling Engine

Kaltschmitt, M.,Wolfgang, S. Wiese, A. “Renewable Energy, technology, Economics and Enviroment”

TDish and Stirling Engine

MI

aol t

n

7 C9 .r 2 9o

e tFE

clKaltschmitt, M.,Wolfgang, S. Wiese, A. “Renewable Energy, technology, Economics and Enviroment”

20

Images removed due to copyright restrictions.Please see Fig. 5.20, 5.21, and 5.22 in Kaltschmitt, Martin, Wolfgang Streicher,and Andreas Weise. Renewable Energy: Technology,Economics, and Environment. New York, NY: Springer, 2007.

Table removed due to copyright restrictions.Please see Table 5.10 in Kaltschmitt, Martin, Wolfgang Streicher,and Andreas Weise. Renewable Energy: Technology, Economics,and Environment. New York, NY: Springer, 2007.



hermal to

2

T

F

7 D


eJDH + ∂

∂ =

t

eρ=•∇ D

0=•∇ B

• Constitutive Relations

E --- Electric Field H --- Magnetic Field D --- Electric Displacement B --- Magnetic Induction Je --- Free Current Density

EM Waves

Maxwell Equations:

∂B∇ × E = −

∂t

∇ ×

D = ε E

B = μH

ε – Electric Permitivity μ – Magnetic permeability

EM Wave Propagation



Electrical Energy Conversion ⎤

⎢ ⎢ ⎣

⎡ ⎞ ⎜⎜ ⎝

⎛ •−−= kErE ˆexp),(

o o c

Ntit ω

Plane Wave Solution

⎢ ⎣

⎡ ⎛ = HrH exp),( ot

H

ω--- angular frequency k --- Wavevector

k̂ --- Unit Wavevector

N=n+iκ, Complex refractive index κ --- Extinction coefficient

• Poynting Vector (Energy Flux)

[ ]*Re 2 1)( HErS ×= πκα

4

inside A Medium

E•

k r ⎟⎟⎥

⎠⎥⎦

N k̂ • r ⎟⎟⎞⎤

⎜⎜ ⎝ co ⎠⎦

ωi− −t ⎥

= λo1 n −αxS = e E 2 k̂

2 μc Absorption

o Coefficient

21




EM Wave Reflection and Transmission at An Interface

Symbol Convention:

Field Going Out of Paper Field Going Into Paper

TM Wave = // Wave = p Wave E-Field In the Plane of Incidence:

H-Field In the Plane of Incidence:

TE Wave = Wave = s Wave

ki

Ei

Hi kr

Et

kt

θi θr

θt

n1

n2

Er

z

x

x n̂

• Snell Law

θi =θr

ti nn θθ sinsin 21 =

• Fresnel Coefficients

ti

ti

i

r

nn

nn

E

E r θθ θθ

coscos coscos

12

12

//

// // +

+− ==

t1i2

i1

i//

t//// cosncosn

cosn2E E

t θ+θ

θ ==

2

//// rR = // 1

2 // )cosRe(

)cosRe( tN

N

i

t

θ θτ =

• Reflectivity/transmissivity 2




Examples

Reflectivity as a function of the angle of incidence for a dielectric material with n=4 and for gold with N=10.8+i51.6.

0

0.2

0.4

0.6

0.8

1

0 20 40 60 80

REF

LEC

TIVI

TY

INCIDENT ANGLE

Gold (wavelength=10um, TM)

Dielectric material (n=4, TM)

Gold (wavelength=10um, TE)

Dielectric material (n=4, TE)

Brewster Angle

22

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2.997 Direct Solar/Thermal to Electrical Energy Conversion TechnologiesFall 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.

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