View
14
Download
0
Category
Preview:
Citation preview
97 Copyright © Gang Chen,
or 2.997 Direct Solar/Thermal to
Electrical Energy Conversio
n
Importance of Heat
2.9
MIT
F
Courtesy of Lawrence Livermore National Laboratory. Used with permission.
yright © Ga
Direct Solar/Ther
ergy Conversion
Gasoline100 kJ
10kJ 30kJ 35kJ
Parasiticheat losses Coolant Exhaust
9kJ10kJ
6kJ
Exhaust
.99
hen, MI
or 2.
o
27 Cop
ng C
T
F997
mal t
Electrical En
Vehicle Systems
• In US, transportation uses ~26% of total energy.
Coolant
Gasoline 100kJ
10kJ
30kJ 35kJ
9kJ
10kJ
6kJ Auxiliary
Driving
Mechanical losses
Parasitic heat losses Exhaust
Photo from Wikimedia Commons, http://commons.wikimedia.org
2.997 Copyright © Gang Chen, MIT
For 2.997 Direct Solar/Thermal to
Electrical Energy Conversio
n
Heating
TE Recovery
PVElectricity
Oil or Nat’l Gas
Entropy Thermal Power
Electrical Power
Heating
TE Recovery
PVElectricity
Oil orNat’l Gas
Oil orNat’l Gas
EntropyThermal Power
Electrical Power
Co-Generation in Residential Buildings
In US, residential and commercial buildings consume ~35% energy supply
Photo by bunchofpants on Flickr.
Image removed due to copyright restrictions.Please see any photo of the Honda freewattMicro-CHP system, such as http://www.hondanews.com/thumbnails/2007/4/3/13644_preview.jpg
Refrigeration &Refrigeration &AppliancesAppliances
2.997 Copyright ©
Gang Chen, MIT
For 2. 997 Direct Solar/T
hermal to
Ele ctrical Energy C
onversion
Industrial Waste Heat
Fig. ES.1 in Hemrick, James G., et al. "Refractories for Industrial Processing:Opportunities for Improved Energy Efficiency." DOE-EERE Industrial TechnologiesProgram, January 2005.
Photos by arbyreed and toennesen on Flickr.
.
, MI
2 997 Copyright © Gang Chen
T
For 2.997 Direct Solar/Thermal to
Electrical Energy Conversio
n
Renewable Heat Sources
Photos by Jon Sullivan at http://pdphoto.org/ and NASA.
2.997
ght © Gang Chen, M
IT
For 2.997 DSolar/T
hermal to
Electrical Energy C
onversion
Solar Thermal
http://www.treehugger.com/Solar-Thermal-Plant-photo.jpg
http://media.photobucket.com/
Images by Sandia National Laboratories and NREL.
Photos of solar hot water tubes removed due tocopyright restrictions. Please see, for example,http://image.made-in-china.com/2f0j00KeoavBGJycbN/
rpy iUnpressurized-Solar-Water-Heater-VERIOUS-.jpg
Co irect http://ns2.ugurpc.com/productsimages/solarevacuatedtube_202160.jpg
2.997 Copyright ©
Gang Chen, MIT
For 2.997 Direct Solar/T
hermal to
Electrical Energy C
onversion
Direct Energy Conversion COLD SIDE
HOT SIDE
Thermoelectrics
Thermophotovoltaicshttp://www.keelynet.com/tpvcell.jpg
Photovoltaics http://www.solareis.anl.gov/images/photos/Nrel_flatPV15539.jpg
Image removed due to copyright restrictions. Please see http://web.archive.org/web/20071011185223
/www.eneco.com/images/science-new.jpg
Image by Nadine Y. Barclay, USAF. Courtesy of John Kassakian. Used with permission.
2.997 Copyright © Gang Chen, MIT
For 2.997 Direct Solar/Thermal to
Electrical Energy Conversio
n
Solar Spectrum
0 0.5 0
200
400
600
1800 Te
rrest
rial S
olar
Spe
ctru
m (W
/m2 μ
m)
AM1.5 Solar Spectrum Energy Usable for Silicon PV Cells
Bandgap of Silicon (1.1 μm)
1600
1400
1200
1000
800
1 1.5 2 2.5 3 Wavelength (μm)
D rior gi
Cyp
n ms oiar
C
T/reh
© Ggna
S nolt oCcgye
er
ah
h0
2.997
t
en, MIT
For 2.997
re
l to
Electrical En
v0 2 4 6 8 10 12
Irradiance From Emitter
0 2 4 6 8 10 120
00
0.5
1.0
1.5
Selective Absorber
Emitter
TPV Cell
Thermal Management
0 0.5 1.0 1.5 2.0 2.5 3.0 0
Optical Concentrator
Emis
sivi
ty A
bsor
ptan
ce
Wavelength (μm)
Wavelength (μm)
Pow
er (W
/m2 μ
m)
Pow
er (W
/m2 μ
m)
(d)
(b)
Solar Thermophotovoltaics
Theoretical maximum efficiency: 85.4%; comparable to that of infinite number of multi-junction cells, but with only a single junction PV cell. Key Challenges: Selective surfaces absorbing solar radiation but re-emitting only in a narrow spectrum near the bandgap of photovoltaic cells, working at high temperatures.
1500 Solar Insolation 1000
500
Wavelength (μm)(a)
1.5E4 Absorber
1.0E4 5 10 15
1.5 0.5E4 (c) Selective Emitter
1.0
0.5
•
•
©
2.997 Copyright
Gang Chen, MIT
For 2.997 Direct Solar/T
hermal to
Electrical Energy C
onversion
Solar Thermoelectrics
0.0
5.0
10.0
15.0
20.0
25.0
30.0
0.5 1.0 1.5 2.0 2.5
EFFI
CIE
NC
Y (%
)
AVERAGE FIGURE OF MERIT ZT
700 C
400 C
150 C 200 C
T cold
=30 C
600 C 500 C
250 C
T hot
-T cold
(b)
• Low materials cost and low capital cost, potentially high efficiency. • Key Challenges: Develop materials with high thermoelectric figure of
merit; and selective surfaces that absorb solar radiation but do not re-radiative heat.
2.997 Copyright © Gang Chen, MIT
For 2.997 Direct Solar/Thermal to
Electrical Energy Conversio
n
1st Law of Thermodynamics
System Q W
Environment
Boundary
WQdt dE
WQdE
WQEE
&& −=
−=
−=−
δδ 121212
State Properties: Process Independent
Process Dependent Quantities
...Energy)(Internal +++= UPEKEE
]m-J/Korkg,-[J/KHeatSpecific 3
dT
duC =
Closed System Open System
Closed:
2.997 Copyright ©
Gang Chen, MIT
For 2.997 Direct Solar/T
hermal to
Electrical Energy C
onversion
2nd Law of Thermodynamics
)0(Sgen12 ≥+=− ∫ gen boundary
ST
QSS δ
∫ = 0dS
c
c
h
h
T
Q
T
Q −=0
Entropy Change State Properties
Entropy Transfer
Entropy Generation
Heat Reservoir Th
Heat Reservoir Tc
W
Qh
Qc
During a cycle:
No entropy generation
Maximum Efficiency (Carnot Efficiency)
h
c
h
ch
h T
T
Q
Q
W −=
− == 1η
Th=223 oC, Tc=23 oC, η=40% Th=5800 K, Tc=300 K, η=95% Thermal power plant η~40%, IC engines η~25%
2.997 Copyright ©
Gang Chen, MIT
For 2.997 Direct Solar/T
hermal to
Electrical Energy C
onversion
Microscopic Picture of Entropy
Ω= lnBkS Ω
= 1P
• For Isolated Systems • Microstate: a quantum mechanically allowed state
• A total of Ω microstate • Principle of equal probability:
each microstate is equally possible to be observed
kB=1.38x10-23 J/K ---Boltzmann constant
Boltzmann Principle
• Constant Temperature and Closed Systems
)/()( TkE BAeEP −=
• Constant Temperature But Open Systems
()( EAeEP −= μ --- chemical potential (driving force for mass diffusion); average energy needed to move a particle in/out off a system
Probability
−μ ) /(kBT)
2.997 Copyright ©
Gang Chen, MIT
For 2.997 Direct Solar/T
hermal to
Electrical Energy C
onversion
Maxwell distribution
A box of gas molecules
( )22 y
2 x vvv
2 1
zmE ++=
( ) ⎥ ⎥ ⎦
⎤
⎢ ⎢ ⎣
⎡ ++ =
Tk
mAP
B
z x 2
vvv exp)v,v,v(
22 y
2 x
zy
All Probability must normalize to one
( ) ⎥ ⎥ ⎦
⎤
⎢ ⎢ ⎣
⎡ ++ = ∫∫∫
∞
∞−
∞
∞−
∞
∞− Tk
mA
B
z
2 vvv
expdvdvdv1 22
y 2 x
zyx 2⎜⎜ ⎝
⎛ =A
( ) ⎢ ⎢ ⎣
⎡ ++ ⎟⎟ ⎠
⎞ ⎜⎜ ⎝
⎛ =
Tk
m
Tk
mP B
z
B x 2
vvv exp
2)v,v,v(
22 y
2 x
2/3
zy π Maxwell Distribution
⎞⎟⎟
3/ 2m
πkBT⎠
⎤⎥⎥⎦
2.997 Copyright ©
Gang Chen, MIT
For 2.997 Direct Solar/T
hermal to
Electrical Energy C
onversion
One molecule
∫=E
( ) ( ) ⎥⎦⎢
⎢ ⎣
⎡ ++ ++= ∫∫∫
∞
∞−
∞
∞−
∞
∞− Tk
mAmE
B
z z 2
vvv expvvv
2 1dvdvdv
22 y
2 x22
y 2 xzyx
TkE B2 3
=
Equipartition Principle: every quardratic term in microscopic energy contributes kBT/2.
meV26 /106.1
105.14
5.14300KJ/K1038.1
19
21-
23
= ×
× =
=××=
−
−
eVJ
J
TkB
Oxygen Atom at 300 K
How much Is kBT at room temperature
1067.116 300/1038.133k v 27
23 B
××
××× == −
− KJ
m
T
⎤⎥
-2110 J×
K= 220 m/s
kg
2.997 Copyright ©
Gang Chen, MIT
For 2.997 Direct Solar/T
hermal to
Electrical Energy C
onversion
Fermi-Dirac Distribution • From quantum mechanics
• Energy levels are quantized • Each quantum state can have
maximum one electron • Planck-Einstein Relation • Planck constant h=6.6x10-34 Js,
kh/p:Momentum :Energy
h==
==
λ
νhE
)2/( πh=h
• Consider one quantum state with an energy E at constant temperature T. The state can have zero electron (n=0) or one electron (n=1). What is the average number of electrons if one does many observations?
⎥ ⎦
⎤ ⎢ ⎣
⎡ ⎟⎟ ⎠
⎞ ⎜⎜ ⎝
⎛ −+⎟⎟
⎠
⎞ ⎜⎜ ⎝
⎛ == −−
= ∑ Tk
E
TkAAe
BB
TkE
n
B exp1exp1 )/()(
1,0
μμ
• Average number of electrons in the state
hω
r o97
t
2.9Copyr gi h © Gang mChen, M
IT
F2.997 Direct S
olar/Ther al to
Electrical Energy C
onversion
Fermi-Dirac Distribution
1exp
1)/()(
1,0 +⎟⎟ ⎠
⎞ ⎜⎜ ⎝
⎛ − == −−
= ∑
Tk E
Aenf
B
TkE
n
B
μ μ
• Average number of electrons in the state
Fermi-Dirac Distribution
0
0.2
0.4
0.6
0.8
1
-0.1 -0.05 0 0.05 0.1
FER
MI-D
IRA
C D
ISTR
IBU
TIO
N
E-μ (eV)
1000 K
300 K 100 K
At T=0K, μ is called Fermi level, Ef
F=1 for E<μ F=0 for E>μ
2.997 Copyright ©
Gang Chen, MIT
For 2.997 Direct Solar/T
hermal to
Electrical Energy C
onversion π )
Natural Frequency
1ν =2π
Energy of Mode E = ⎛⎜ n + 1 ⎞⎟hω n =
⎝ 2 ⎠ Basic vibrational energy quanta hν is called a phonon
Photons and Phonons From quantum mechanics
• EM waves are quantized, basic energy quanta is called a photon
• Photon has momentum • Planck-Einstein Relation • Each quantum state of photon (an
EM wave mode) can have only integral number of photons
h/p:Momentum :Energy h
==
=
λ
ωνhE
2/(Js;106.6 34 hh =×= − h
One Photon
Energy of a quantum state:
2 ⎠⎝ n 1 =⎟
⎞⎜⎛ += ωhnE
Zero point energyClassical Oscillator
M
Spring
M
K
•
=
hk
0,1,2...
•
0,1,2...
2.997 Copyright ©
Gang Chen, MIT
For 2.997 Direct Solar/T
hermal to
Electrical Energy C
onversion
Bose-Einstein Distribution
0
1
2
3
4
5
0 0.1 0.2 0.3 0.4 0.5
BO
SE-E
INST
EIN
DIS
TRIB
UTI
ON
FREQUENCY (X1014 Hz)
5000 K
1000 K
300 K
100 K
• Consider one quantum state in thermal equilibrium
)/()()( TkE n
BnAeEP μ−−=
1exp
1
−⎟⎟ ⎠
⎞ ⎜⎜ ⎝
⎛ − =
Tk E
f
B
μ
Average number of photons/phonons in one mode (quantum state)
Usually μ=0
• Bose-Einstein Distribution
2.997 Copyright ©
Gang Chen, MIT
For 2.997 Direct Solar/T
hermal to
Electrical Energy C
onversion
Heat Transfer Modes
Heat Conduction
Thot Tcold
• Fourier Law
L
[W]dx
dTkAQ −=&
[ ]2W/mT)-k( ∇=−= dx
dTkq&
• Heat Flux
Thermal Conductivity [W/m-K] Materials Property
y
x
yy
ux
uy
Ta
uuu
FluidFluidFluid
TwTx
x
uy
xx
uyx
uy
TaTa
w
Convection
• Newton’s law of cooling
( )aw TThAQ −=&
Convective Heat Transfer Coefficient [W/m2K] Flow dependent
• Natural Convection • Forced Convection
Thermal Radiation
Thot Tcold
• Stefan-Boltzmann Law for Blackbody
4TAQ σ=&
Stefan-Boltzmann Constant σ =5.67x10-8 W/m2K4
• Heat transfer
( )44 coldhot TTAFQ −= εσ&
Emissivity of two surfaces
View factor F=1 for two parallel plates
Cross-Sectional Area
2.997 Copyright ©
Gang Chen, MIT
For 2.997 Direct Solar/T
hermal to
Electrical Energy C
onversion
Heat Conduction
Heat Conduction
Thot Tcold
L
th
coldhotcoldhot
R
TT
L
TTkAQ −
= −
=&
1D, no heat generation
Thermal Resistance kA
LRth =
10-2
10-1
100
101
102
103
104
105
101 102 103
Ther
mal
con
duct
ivity
(W/m
K)
Temperature (K)
Quartz single crystal (// to c-axis)
Water (saturated)
Fused quartz
Ice
Steam (saturated)
Stainless steel (type 304)
Copper
Silicon
Diamond
Air (1 atm)
Helium (1 atm)
Thot Tcold Rth
Convection hA
Rth
1 =
Q&CurrentHeat
aG©
Cy
7 2.99 997
op right ng Chen, M
IT
Fo cr 2.
DirecgSt olar/T
hermal to
Eletric
al Ener y Conversio
n
Heat Conduction: Kinetic Picture
qx
x
Hot Cold
xvxτ
qx
x
Hot Cold
xvxτ
( ) ( ) τvxxτvxxx xx nEv
2 1nEv
2 1
+− −=
dx
dTk−=−=
−=)
=
dx dTC
3 τv
dx dT
dT dU
3 τv
dx d(Env-vq
2
2 x
xx τ
Λ= v 3 1 CkThermal Conductivity
• Energy per particle: E [J] • Number of particles per
unit volume: n [1/m3] • Average random
velocity of particles v • Average time between
collision of two particles τ---relaxation time
• Average distance travelled between collision Λ=vτ---Mean free path
• Volumetric specific heat
[ ]KdT
dUC 3m J=
cC ρ=
Density
q
Specific heat per unit mass
922.9
7 Copyright © Gang Chen, MIT
For .997 Direct Solar/Thermal to
Electrical Energy Conversio
n
Thermal Radiaton: Planck’s Law
Inside the Cavity EM Wave In Equilibrium at Temperature T
Perfectly Reflecting Wall at T Frequency ν
Angular Frequency ω=2πν Wavelength λ Wavevector magnitude k=2π/λ
νλ=c
Wavevector k=(kx,ky,kz) 222 zyx kkkcck ++==ω
ω(k): Dispersion relation (linear)
k
x xx
x x
xx x
Lnk
nL
2 2
,...2
,...,2
2,2
π
λλλ
=
=
Basic Relations
How much energy in the cavity?
( )
( )
( )TfL
dk
L
dk
L
dk
TfL
dk
L
dk
L
dk
TfU
z
z
y
y
x
x
z
z
y
y
x
x
n n nx y z
,)/2()/2()/2(
2
,)2/2()2/2()2/2(
2
,2
000
1 1 1
ωωπππ
ωωπππ
ωω
h
h
h
∫∫∫
∫∫∫
∑∑∑
∞
∞−
∞
∞−
∞
∞−
∞∞∞
∞
=
∞
=
∞
=
=
==
Two polarization
2.997 Copyright ©
Gang Chen, MIT
For 2.997 Direct Solar/T
hermal to
Electrical Energy C
onversion
Thermal Radiaton: Planck’s Law ( )
( )
( )
( )
( ) ( )
( ) ωω
ωωωω
ωπ ωωω
ωωπωωπ
πωωπ
ωωπ
du
dDTf
d c
TfV
U
c d
c TfV
dkkTfV
dkdkdkTfVU zyx
∫
∫
∫
∫
∫
∫ ∫ ∫
∞
∞
∞
∞
∞
∞
∞−
∞
∞−
∞
∞−
=
=
=
⎟ ⎠ ⎞
⎜ ⎝ ⎛
⎟ ⎠ ⎞
⎜ ⎝ ⎛ =
=
=
0
0
32
2
0
2
0 3
2
0 3
3
,
,
4,8 2
4,8 2
,8 2
h
h
h
h
h
D(ω)-density of states per unit volume per unit angular frequency interval
• Energy density per ω interval
( ) ( ) ( )
1exp
1 ,
32
3
−⎟⎟ ⎠
⎞ ⎜⎜ ⎝
⎛ =
=
Tk
c
DTfu
B
ωπ ω
ωωωω
h
h
h
Planck’s law
Solid Angle
dAp
2RdA
d p=Ω
whole space 4π
• Intensity: energy flux per unit solid angle
( ) ( ) 44 23
3
== c
cuI π ω
π ωω
h
Per unit wavelength interval
( ) ( ) 4 5 == λ π
λ ωωλ
c
d
dII h
Planck’s law
1
⎛ hω ⎞⎟⎟ −exp⎜⎜
⎝ 1
kBT⎠
1
exp⎜⎜⎛ 2πhc ⎟⎟
⎞−1
⎝ kBTλ ⎠
t
2.997 C Dopyright ©
oGang Chen, MIT
For 2.997irec S
lar/Thermal to
Electrical Energy Conversio
n
Thermal Radiaton: Planck’s Law
( ) ( )
1exp
1 4 22
3
−⎟⎟ ⎠
⎞ ⎜⎜ ⎝
⎛ =
=
Tk
c A
IAQ
B
ωπ ω
λπλ
h
h
&
Q&
Total
( ) 4
0
TAdQQ σλλ == ∫ ∞
&&
10-1
100
101
102
103
104
0 2 4 6 8 10
EMIS
SIVE
PO
WER
(W/c
m2 μ
m)
WAVELENGTH (μm)
5600 K
2800 K
1500 K
800 K
Emissive Power
Wien’s displacement law
mK2898max μλ =T
MIT OpenCourseWare http://ocw.mit.edu
2.997 Direct Solar/Thermal to Electrical Energy Conversion Technologies Fall 2009
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
Recommended