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I hereby declare that I did this work independently, using only the listed sources and aids.
Karlsruhe, May 2011
I want to thank Prof. Torsten Fransson, head of the Department of Energy Technology at the Roy- al Institute of Technology for giving me the possibility to do my Master thesis at his institute. The same gratitude goes to Prof Bauer, head of the Institut für Thermische Strömungsmaschinen at the Karlsruhe Institute of Technology for supervising my work from Germany.
My sincerest appreciation goes to my supervisor James Spelling who’s competence and helpful- ness were highly appreciated and made this work possible and fun. I am equally thankful to the head of the solar group, Dr. Björn Laumert for his guidance and advice throughout the project.
I additionally want to extend my thanks to my supervisor at the Institut für Thermische Strömungsmaschinen, Corina Höfler for her crucial help and useful suggestions during the writing and correction process.
Last but not least I want to express my gratitude to my parents whose mental and financial support gave me once again the opportunity to study six wonderful months abroad.
Tab
List of List of Nomen 1 Intr 2 Bac 2.1
2.2
2.3
2.4
2.5 3 Ela
3.1 3.2
3.3
le of Co
f Figures f Tables nclature roduction ..
ckground ..
Solar rad 2.1.1 D 2.1.2 C 2.1.3 S Concentr 2.2.1 P 2.2.2 L 2.2.3 D 2.2.4 S Conversi 2.3.1 T 2.3.2 T The poten 2.4.1 C The gas t aboration of The simu The hybr 3.2.1 T 3.2.2 T 3.2.3 T 3.2.4 T 3.2.5 O The comb
ontent
...
...
diation ...
Distribution a Concentration
olar radiatio rating Solar
arabolic trou Linear Fresne Dish design ..
olar tower p ion of heat to The Clausius The Joule-Br
ntial of CSP Cost analysis turbine in C f dynamic S ulation softw rid solar gas The heliostat The tower ....
The receiver . The gas turbi Other elemen bined cycle
...
...
...
and density n of solar ra on data ...
Power Syste ugh plant ....
el plant ...
...
power plants o electricity s-Rankine cy rayton Cycle P technology s of a CSP pl SP technolo System Mod ware TRNSY turbine cyc s field ...
...
...
ine ...
nts ...
...
...
...
...
of the solar adiation ...
...
ems ...
...
...
...
s ...
...
ycle ...
e ...
y and econom lant ...
ogy ...
dels...
YS ...
cle ...
...
...
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radiation ....
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mic aspects.
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i
iii vii viii
... 1
... 4
... 4
... 6
... 6
... 9
... 10
... 10
... 11
... 11
... 12
... 16
... 17
... 19
... 20
... 22
... 29
... 32
... 32
... 34
... 37
... 40
... 41
... 43
... 44
... 45
3.4 4 Cos
4.1
4.2
4.3 5 Mo
5.1 5.2 5.3 5.4
6 Res 6.1 6.2 6.3 6.4 7 Con 8 Ref Appen A.1
3.3.1 T 3.3.2 T 3.3.3 O Validatio st calculatio Cost func 4.1.1 T 4.1.2 T 4.1.3 T Cost func 4.2.1 T 4.2.2 T 4.2.3 T 4.2.4 T Data acqu odel optimiz
Multi-obj Evolution The Queu The optim 5.4.1 P 5.4.2 P sult of the o Evaluatio Results f Results f Variation nclusions an ferences ...
ndix ...
1 One TRNS
The heat reco The turbine ..
Other compo on of the mo ons ...
ctions for th The heliostat The receiver The power un
ctions for th The HRSG u The power un The condense The condensa uisition ove zation ...
jective optim nary algorith ueing Multi- mization set
rogram desc arameters ch optimization on of a multi for the hybri for the comb n of the fuel nd outlook . ...
...
SYS simulat
overy steam ...
nents ...
odels ...
...
he hybrid cyc s field ...
and the tow nit ...
he steam cyc nit ...
nit ...
er and coolin ate and feed
r TRNSYS . ...
mization ...
hms ...
-Objective O up ...
cription ...
hosen for th n ...
i-objective o d cycle ...
bined cycle ..
price and th ...
...
...
ion run ...
generator...
...
...
...
...
cle ...
...
wer ...
...
cle ...
...
...
ng tower ....
dwater pump ...
...
...
...
Optimizer ...
...
...
he optimizati ...
optimization ...
...
he heliostat c ...
...
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...
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...
...
...
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...
...
p ...
...
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...
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ion ...
...
n result ...
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costs ...
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... 47
... 49
... 49
... 50
... 54
... 54
... 54
... 55
... 55
... 56
... 56
... 57
... 58
... 59
... 59
... 63
... 63
... 68
... 70
... 74
... 74
... 75
... 77
... 77
... 80
... 86
... 89
... 93
... 95
... 99
... 99
iii
A.2 Correlation of different tower materials ... 101 A.3 Constants chosen for the optimization ... 101 A.4 The MATLAB functions ... 102
List of Figures
Figure 1.1: Scheme of a solar thermal tower power plant ... 1
Figure 2.1: Definition of absorber and aperture on a parabolic trough collector ... 5
Figure 2.2: Acceptence range of a line and a point focusing system ... 6
Figure 2.3: a) Theoretical achievable absorber temperature ... 8
Figure 2.4: Yearly Mean of Daily Irradiation in UV in the World ... 9
Figure 2.5: Parabolic Trough Principle ... 10
Figure 2.6: Parabolic Trough Principle ... 11
Figure 2.7: Dish/Stirling scheme ... 12
Figure 2.8: Central tower system ... 12
Figure 2.9: Open air receiver scheme ... 13
Figure 2.10: An external receiver (left) and a cavity receiver (right) ... 15
Figure 2.11: The ideal Carnot cycle ... 16
Figure 2.12: Theoretical total efficiency of a CSP system ... 17
Figure 2.13: The Clausius-Rankine Cycle in a T,s diagram ... 18
Figure 2.14: The Joule-Brayton Cycle in a T,s diagram ... 19
Figure 2.15: World primer energy demand ... 20
Figure 2.16: Online and planned CPS plants ... 22
Figure 2.17: Cost for the Solar Tres components in percent ... 23
Figure 2.18: LEC prediction for two different scenarios ... 25
Figure 2.19: Breakout of the LEC ... 25
Figure 2.20: Predicted Heliostats Cost Improvements... 27
Figure 2.21: Impact of innovations on solar LEC for the SCR system ... 31
Figure 3.1: The information flow for a TRNSYS Type ... 32
Figure 3.2: Scheme of the hybrid solar tower power plant cycle ... 35
Figure 3.3: The hybrid solar gas turbine cycle scheme and its model in TRNSYS ... 36
Figure 3.4: A Solar One Heliostat ... 37
Figure 3.5: the cosine effect on heliostats with different orientation ... 38
Figure 3.6: The field efficiency ... 39
Figure 3.7: The SOLGATE pressurized receiver ... 41
ii
Figure 3.8: The SGT 750 (left) and the SGT 400 (right) ... 43
Figure 3.9: The plant scheme for the combined cycle ... 45
Figure 3.10: The simulation model of the combined cycle in TRNSYS ... 46
Figure 3.11: Pinch point analysis for the SGT750 (upper figure) and SGT400 (lower figure) ... 48
Figure 3.12: T,s diagram for the hybrid cycle at full fuel supplement firing ... 51
Figure 3.13: T,s diagram for the hybrid cycle during solar preheating ... 52
Figure 3.14: T,s diagram for the combined cycle ... 52
Figure 3.15: Sankey diagram for the SGT 750 in the hybrid cycle ... 53
Figure 3.16: Sankey diagram for the SGT 400 in the hybrid cycle ... 53
Figure 4.1: Cost distribution for the hybrid cycle, with two different solarization sizes ... 60
Figure 4.2: Cost distribution for the combined cycle, with two different solarization sizes ... 60
Figure 5.1: Data flow between MATLAB and TRNSYS ... 63
Figure 5.2: Expected optima in a single objective optimization ... 64
Figure 5.3: Illustration of a general multi-objective optimization problem ... 65
Figure 5.4: General data flow in an EA ... 68
Figure 5.5: Solutions at the start of the optimization(left) and after termination (right) ... 69
Figure 5.6: Simplified data flow scheme during the optimization process ... 74
Figure 6.1: Typical POF for the analyzed cases ... 77
Figure 6.2: Breakup of the LEC ... 78
Figure 6.3: Progression of the solar share with increasing solar field size ... 79
Figure 6.4: Comparison of the initial gradient of Cinv and LEC ... 80
Figure 6.5: Solar share vs. LEC ... 81
Figure 6.6: Solar share vs. LEC ... 81
Figure 6.7: specific. CO2 emissions vs. LEC ... 83
Figure 6.8: Fraction of the total energy generation , with SGT 750 base load as reference ... 83
Figure 6.9: specific. CO2 emissions vs. LEC ... 84
Figure 6.10: Solar share vs. Investment costs ... 84
Figure 6.11: Solar share vs. heliostat area and tower height... 85
Figure 6.12: Total mirror area and solar share vs. receiver area ... 85
Figure 6.13: Solar share vs. LEC ... 87
Figure 6.14: specific CO2 emissions vs. Solar share... 87
Figure 6.15: Solar share vs. investment costs ... 88
Figure 6.16: Fraction of the total energy generation ... 88
Figure 6.17: Impact of the heliostat price on the LEC ... 90
Figure 6.18: Price development for natural gas during the last decade ... 91
Figure 6.19: Solar share vs. LEC for three fuel prices ... 91
Figure 6.20: Solar share vs. specific CO2 emissions for three fuel prices ... 92
iv
List of Tables
Table 2.1: List of the larger solar tower plants build to date ... 13
Table 2.2. Renewable power generation costs ... 24
Table 2.3: LEC calculated by the ECOSTAR report ... 24
Table 2.6: Results for 24h base load ... 30
Table 3.1: Used correlations for the Nusselt number... 40
Table 3.2: technical data of the used gas turbines... 43
Table 3.3: technical data of the used gas turbines... 47
Table 5.1: Selected variables and ranges ... 76
Table 5.2: Selected constants with values ... 101
Table 5.3: Variables for the combined cycle ... 76
Table 5.4: Constants for the combined cycle ... 76
Table 6.1: Analysis of two possible plant designs ... 82
Nomenclature
Abbreviations
CC Combined cycle
CRS Central receiver systems CSP Concentrated solar power
DLR Deutsches Zentrum Für Luft- und Raumfahrt (German Aerospace Department) DNI Direct normal irradiation
EA Evolutionary algorithm
ECOSTAR European Concentrated Solar Thermal Road-Mapping HRSG Heat recovery steam generator
HTF Hot temperature fluid LEC Levelized electric cost M&S Marshall and Swift Index
MMBTU One million British thermal units MOO Multi objective optimization MOP Multi objective problem NTU Number of transferred units O&M Operation and maintenance
OSMOSE OptimiSation Multi-Objectifs de Systemes Energetiques integres POF Pareto optimal front
PV Photovoltaic
REFOS Receiver for fossil-hybrid gas turbine systems SOLGATE Solar hybrid gas turbine electric power system SOO Single objective optimization
SOP Single objective problem
STEC Solar thermal electric component library
Symbol Unit Meaning
Latin symbols
A m2 Area
c - Concentration ratio
cp J/(kg K) Specific isobare heat capacity
C USD Cost
E0 W/m2 Solar constant
E kWh Energy, produced electricity
F N Force
h kJ/kg Enthalpy
h W/m2K Heat transfer coefficient
vi
Ib W/m2 Beam radiation
Kg/s Mass flow
n - Exponent
P / W Power
p bar Pressure
r m Radius
t s time
T K Temperature
m3/s Volumic flow rate
V m³ Volume
W Joule Work
Greek symbols
- Emissivity
- Heat exchanger efficiency
c - Carnot efficiency
- Optical losses
rad Acceptance angle
ρ kg/m³ Density
S W/m2K4 Stefan-Boltzmann constant
Π - Pressure ratio
Indices
abs Absorber
air Air
ap Aperture
aux Auxiliary
comb Combustion chamber
comp Compressor
cond Condenser
cw Cooling water
dp Pressure loss
eco Economizer
el Electric
evap Evaporation
evap Evaporator
fire Firing
helio Heliostats
max Maximum
min Minimum
net Net
rec Receiver
ref Reference
rel relative
sh Superheater
sol Solar
tower Tower
turb Turbine
1 Intro
1 I
For the The in erating itive re staged source genera nology So far, to now tions o of both Brayto centrat ature f stored steam a singl pressed temper
Figure (left) a
oduction
ntrodu
e short and m ncreased dem
g prices for c enewable en research a es, solar ther ation. In rec y, solar towe
, almost all w several pow
of solar towe h configurat on Cycle on
ted on the to fluid (HTF)
in a storage cycle to run le working f d air. For co rature.
e 1.1: Schem and in a Bra
ction
mid-term ou mand for fos conventiona nergy sourc and develop rmal power p
ent years, a er power pla work conce wer plants h er power pla tions is displ the right ha op of a towe
. In the Ran e tank or dir n the turbine fluid. The re ombustion in
me of a sola ayton Cycle
utlooks a red ssil resource al power plan
es. To mak pment are c
plants are n apart from th ants were in entrated on s have been su ants based on
layed in Fig and side. Su er were a rec nkine Cycle rectly passed e and genera
eceiver trans n the combu
ar thermal e configurat
duced grow es will there nts, eventua ke these ne critical. Con next to wind
he already f the focus of solar tower uccessfully in
n the Brayto gure 1.1 , the unlight is co ceiver absorb
this is usua d on to the s ator. The Bra sfers the hea ustion chamb
tower powe tion (right)
rate in the w efore be acco ally paving th ew technolog nsidering the parks the on fairly well e f research an systems bas nstalled [1].
on Cycle are e Rankine C ollected by m
bs the radiat ally a molte steam gener ayton Cycle at from the c ber, fuel is a
er plant in
worlds energ ompanied by he way for c gies ready f e potential nly possibili established p nd developm sed on the R In this work e investigate Cycle on the mirrors calle tion in order en salt or m rator where configuratio concentrated added to inc
a Rankine
gy demand i y further gr commerciall for deploym
of renewab ity for bulk parabolic tro ment.
Rankine Cyc k, different ed. The basic
left hand si ed heliostats r to heat a h metal. The he
it is transfer on is charac d sunlight to crease the tu
Cycle confi
1
s unlikely.
rowing op- ly compet- ment, early
ble energy electricity ough tech-
cle, and up configura- c principle de and the s and con-
ot temper- eat can be rred to the cterized by o the com- urbine inlet
iguration
Using a gas turbine in such central receiver systems has a number of consequences that can be critical for a deployment decision, when taking into account local geographic and politic re- strictions.
High operation temperatures. Substitution of the steam turbine cycle with a gas turbine driven cycle allows higher operating temperatures and therefore a higher efficiency of the power plant.
No cooling water. In an open Brayton cycle with air as heat transfer medium, waste heat can be discharged to the environment without additional cooling. Already installed con- centrating solar power (CSP) systems using a steam cycle have a high demand of cooling water. A resource that is particularly scarce in regions where the solar power plants are most beneficial, as e.g. in arid areas.
Hybrid configuration. In the absence of a storage device or for a quick response to varying solar input, a constant power output can only be achieved with supplemented fossil fuel burning. Although this cannot be an objective on the long term, it is an important instru- ment to minimise investment risks and boost the deployment of gas turbine driven power plants today.
Combined cycle. Due to the high gas turbine outlet temperatures, the integration of a com- bined cycle can further rise the efficiency whilst reducing the costs for the solar generated energy1. Apart from the combined cycle other promising options are the combination of a Brayton cycle with cogeneration, cooling or desalination.
The integration of a gas turbine in a CSP system has up to now only been tested in experimental power plant setups [2]. No plant on a commercial scale has been built yet. Therefore it is im- portant to have a broad knowledge of the thermodynamic potential and limits, as well as of the expected costs for investment and operation of the plant.
In this work two different gas turbine driven CSP plants were simulated, using the software tool TRNSYS. More precisely, a special model library, the TRNSYS Model Library for Solar Thermal Electric Components (STEC) developed by the German aerospace agency (DLR) is implemented.
The cycles are:
I. Hybrid gas turbine solar cycle II. Combined cycle
The hybrid cycle uses heat from concentrated solar radiation and from supplemented firing of fossil fuel to drive the gas turbine. The more heat is provided by radiation the less additional fuel is needed. The combined cycle also uses the hybrid system but adds a steam generation unit and a steam turbine, using the exhaust heat from the gas turbine.
1Cooling water would now be required for the steam cycle. However, the demand is considerably lower than in a pure Rankine based CSP.
1 Introduction 3
With the thermodynamic data from the models and a set of corresponding cost functions for each component in the cycles, predictions about the power plant performance will be derived. These include:
Overall investment costs: The sum of all costs accumulating during construction
Levelized electric costs (LEC): A figure that spreads all costs that accrue over the life- time of the plant divided by the annual electric output.
Solar Share: The percentage of electric power that comes from solar energy.
CO2 emissions: The amount of CO2 per kWh that is discharged to the environment In a next the step, an optimization was performed to find optimal configurations of the plant mod- els. As it is often the case for energy system optimization, problems are multi-objective. Highest efficiency is desired for minimal costs, or maximal power output for minimal CO2 emissions. The result is a trade-off curve which offers several equally valuable solutions.
In this work, a multi-objective evolutionary algorithm was used to perform the optimization and obtain a number of trade-off curves for the two plant configurations. Trends were analyzed for various cases.
2 B
In this by an o tion is tems is
2.1
To det physic itself a sion at layer, c 5670 K yieldin
where distanc extrate
with over th
Scatter tion po has to the air the atm dry da the sol es valu
Backgro
s chapter som overview of
analyzed. F s reviewed.
Solar r
termine the cal propertie
and its relati t a temperatu
called the ph K. The spec ng
is the em
ce 1.4
errestrial val
the radius he year at ar
ring process ower that re travel throu mass coeffi mosphere an ay. The high lar radiation ues of 2200
ound
me fundame f the CSP te Finally, the w
radiation
amount of s of the sun ive position
ure of aroun hotosphere.
cific power
missivity, 469 10 lue of E0, ca
of the sun. B ound 1.7%.
ses as well a eaches the su ugh the atmo icient (AM) nd the distan her the AM n that can be
⁄ to 2
entals requir chnology. T work accom
n
energy that nlight is nece to the earth nd 107 K and
Here, the su on its surfa
the Stefan- of the su lled the sola
Because of t It is measur
as absorption urface of the osphere and
. It is the qu ce that the li
coefficient, collected fl 2800 ⁄
red for solar The potentia mplished so f
can be obta essary. Thes h. The sun g d transfers it uns radiatio ace ps can be
6.24 -Boltzmann un to the ea ar constant.
the eccentric red by satell
1.353 2 n in the atm e earth. It d
the cloudine uotient of the
ight has to t the weaker luctuates wit in the most
r engineerin al in context
far in the fie
ained from s se in turn de generates its t with sever n resembles e calculated
4 10 constant an arth, the pow
city of the e ite to be [3]
21
mosphere def epends main ess of the sk e actual trav
ravel with th r is the irrad th time and t favorable r
ng are briefly to the actua eld of gas tur
solar radiati epend on the energy in th al different s a black bod d with the S
nd T the tem wer of the su
arth’s orbit,
fine the frac nly on the e ky. This dist elled distanc he sun in the diation. Ther location. On regions of th
ly described al global ene urbine driven
ion, knowle e properties he core by n processes to dy at a temp Stefan-Boltzm
mperature. D unlight redu
its value flu
ction of spec extent, which
tance is indi ce of the lig e zenith on a
refore, the f n a clear day he earth (see
d, followed ergy situa- n CSP sys-
dge of the of the sun nuclear fu- o the outer perature of mann law,
(2.1) Due to the uces to the
(2.2) uctuates
(2.3) cific radia-
h the light cated with ht through a clear and fraction of y, it reach- e also Fig-
2 Back
ure 2.4 effectiv erating the fol
Here, t sorber the fac fer coe
F Figure apertur sorber.
tion of collect coming imum diance Aabs⁄A c = 30 quence concen the acc range f
kground
4 and Figur ve the less h g temperatur
lowing simp
the aperture Aabs, where ctor that redu efficient.
Figure 2.1: D e 2.1 illustra
re of the co . Radiation o f the solar ra tor without
g radiation o temperature e can only Aap. To use t 0 are require e, the accept ntration qual ceptance ang
from which
re 2.16). Th heat it loses re and the a plified energ
e Aap is the e it is conve uces the bea
Definition o ates the geom
llector. In th outside the a adiation is n concentratio of 800 ⁄ e of 44 can
be obtained the solar rad ed, and an o tance angle o lity of the ra gle range of the receiver Receiver
e thermal c to the envir absorber area gy balance [4
area that th erted into us am solar radi
of absorber metry of a p his case the acceptance a necessary to on, e.g. a so , assuming n be reached d with sma diation in a c
order of ma of the system adiation dep f the receiver r will accep
onversion ta ronment. Th a. The useab 4]
he concentra seful heat re iation by
and apertu parabolic tr
receiver co angle cannot o increase th
o called flat g values for
d. Considera aller values
conventiona agnitude hig m is reduced pends on the
r. The highe pt radiation.
akes place i he heat losse
ble thermal
ator can use educed by lo the optical l
ure on a par ough collec nsists of an t be reflecte he maximum
plate collec 1 and ably higher
for and a al steam cycl gher for a ga
d. As it will e power dens er the concen For high co
in a collecto es rise propo power c
to focus the oses in the a
losses, h rep
rabolic trou tor. The con
evacuated g d on the rec m temperatur
ctor should 0, with temperature a higher co le, concentra as turbine c l be seen late sity distribut ntration, the ncentrations Concentrato
or, which is ortionally w can be dete
e radiation absorber itse presents the h
ugh collecto ncentrator d glass tube a ceiver. The c
re of the rec return 80%
equation (2 es with terre oncentration ation values cycle [5]. A er in section ution of the s smaller is th s it is theref or
5
s the more with its op-
rmined by
(2.4)
on the ab- elf. is
heat trans-
or [5]
defines the and the ab-
concentra- ceiver. If a
of the in- .4) a max- estrial irra- n ratio
of at least s a conse- n 2.1.2, the
source and he angular fore neces-
sary to sorber
2.1.1 Since t paralle pears o would tance f design sun’s i ena is Scatter lar ran well ab radiati ticles a values trating ceptan tem w energy
2.1.2 With t can be
o adjust this can only be
Distribu the sun has el but has a
on an angle be constant from the cen n of central r
image produ also called l ring in the a nges. In close
bove the rad on, CR. If s a slight haze of CR, the g system, be nce angle of
ith the same y gain from t
Figur Concent the help of a increased. T
Reduction operating t A better u tem
range in rel e achieved w
ution and d a finite dist slight diver of 16′. If th t. However, ntre increas receiver syst uces a hot sp
limb darken atmosphere o
e proximity diation of th scattering ef e can be obs beam radiat cause of a t = 4.65 m e angle , the the irridi
Line focu re 2.2: Acce tration of s additional de
This is motiv of the spec temperature utilization of
lation to the with beam ra
ensity of th ance from th rgence. The he sun was a
since the d es, the sun tems as need pot with high ning. The int
of the earth of the sun’s e remaining ffects increas
erved. This tion Ib conta too small ac mrad (=16‘) not all of th iance is high
using system ptence rang olar radiat evices such vated by the ific heat los s (Eq. (2.4) f the expens
e position of adiation and
he solar rad he earth (dse
geometric a lambertian density and t is slightly d ded in CSP t her radiative tensity decre results in an s disk, the ra g hemisphere
se due to hig leads to an ains shares, t cceptance an the losses e he CR is lo her for point
m
ge of a line tion
as mirrors o e following a ses at the in ive absorbe
f the sun. He a collector s
diation
e), its solar r expansion o n emitter, the the temperat darker at the tower plants e flux than t eases toward n additional adiation is or e of the sky gh cloud lay increase in t that usually ngle. For a p equal the va
st. Therefor t focusing th
Point focu and a point
or lenses, th aspects:
nput aperture r unit, reduc
ence, high te system using
radiation rea of the sun a e distribution
ture of a sta e edges. Thi s because the
he overall a ds the edges
radiation in rders of mag . This effect yers (cirrus)
the circumso cannot be c point focusin
lue of CR. I re the influe hen for a line
sing system t focusing sy
e irradiance
e of the rece cing the spe
emperatures g a tracking
aching the e as seen from n of the ang ar diminish is is importa
e central reg average. Thi
s by the fact nput from la
gnitude lowe t is called ci ), aerosols or olar radiatio collected by ng system w In a line foc ence of the C
e focusing sy
m
ystem [4]
e of the solar
eiver, resulti ecific costs o
s at the ab- device.
earth is not m earth ap-
gular range as the dis- ant for the gion of the s phenom- tor 2.5 [6].
rger angu- er, but still ircumsolar r dust par- on. At high
a concen- with an ac- cusing sys- CR on the ystem.
r radiation
ing in high of the sys-
2 Background 7
The possibility to oversize the collector system for an integration of a storage device If it would be possible to increase the concentration to any level, one would at some point reach higher temperatures than found on the sun’s surface, which is physically impossible2. Therefore, from a thermodynamic point of view, a limit to the concentration must exist. As seen above, a smaller receiver, resulting in a higher concentration ratio, leads to a smaller acceptance angle. If this angle is reduced further, losses will occur. This limit can be used to calculate the concentra- tion limit (see also [5]). A perfectly aligned collector transfers the radiated power PS-E to the re- ceiver
(2.5)
where TS is the temperature of the sun. Equation (2.1) applied on the receiver yields to the follow- ing radiation from the absorber to the sun
(2.6) Likewise it applies
→ (2.7)
With the earlier introduced concentration ratio c ⁄ and equation (2.7), the maxiumum for c can be expressed as
,
1 (2.8)
If is assumend to be 16′, the concentration maximum for a two-dimensional concentrator is
, 45000 (2.9)
For a one-dimensional or line concentrator it can be shown that the maximum concentration ratio is limited to
,
1 212 (2.10)
With an absorber temperature Tabs lower than TS, but without any heat gain (efficiency 0), the following concentration ratio c can be derived for a perfect concentrator
lim→ (2.11)
2 This situation would result in a heat flux from a colder to a hotter source, which is a violation of the second law of thermodynamics.
This c ture Ta
Figure tration can be receive
Figure tion ra tration With a efficien efficien the rec rises. T optical pointle would accura entire length.
trance.
ture gr centrat value.
onsideration
abs
e 2.3a shows n ratio. Even e reached. In
er concentra
e 2.3: a) Th atio b) colle n ratios [5]
an increasin ncy increase ncy. The re ceiver area i The achievab l accuracy o ess to adjust
be lost due acy for the sy
aperture. Op . The mirro . This is esp radients are tion ratio is
n and the as
s the theoret n with low c n Figure 2.3 ation ratios i
heoretical a ector efficie
g concentra es in accorda
ason is that is smaller th ble concentr of the system t the concent
to inaccurac ystem. Espe ptical errors r system th pecially impo
high, as it is a comprom
sumption of
tically achie concentration 3b the collec
s shown.
achievable a ency as a fu
tion ratio c, ance with th with a high han the radia ration ratio d m itself. In tration ratio cies. The hig ecially in mi s of the oute erefore prod ortant for th s the case fo mise of all re
f a black bo
evable absor n ratios rela ctor efficien
absorber te unction of te
, a higher ab he concentra
her c the co ation losses depends not
a mirror ar according t gher the con irror arrays er mirrors ha
duces a unif he design of
or gas turbin elated effect
ody leads to
rber tempera atively high ncy as a func
mperature emperature
bsorber tem ation ratio c.
nvective he , which incr t only on the rray with re to the solar a ncentration,
the acceptan ave a bigger form distrib
the receiver ne driven sol ts, but often
the maximu
ature as a fu theoretical a ction of tem
as a functi e for differe
perature can If Tabs is co at losses de rease as the e acceptance latively larg angle, since
the higher i nce angle is r impact due buted radian
r when temp lar plants. T
the econom
um absorber
unction of th absorber tem mperature fo
ion of the c ent absorbe
n be achieve onstant, c inc ecrease faste
absorber te e angle but a ge optical e
much of the is the require s not constan ue to the incr nce at the re
peratures and The choice o mic factors d
r tempera-
(2.12) he concen- mperatures or different
concentra- er concen-
ed, i.e. the creases the er, because emperature also on the rrors, it is e radiation ed level of nt over the reased run eceiver en-
d tempera- of the con- dictate this
2 Back
2.1.3 A cruc mation ing sy overvi ble inf in Euro
Radiat commo TRNSY al Sola to disti is gene data ha exact u ical ele represe for a w plants amoun ance. A with v is not t possib
kground
Solar ra cial element n about the i stems, beca ew about th frastructure ope, like Sp
Figur tion data is
on, a month YS, data file ar Radiation
inguish it fro erally less a as an accura up to 5%
ements, suc ents the ave worst case s based on th nt of aerosol
Although the ariations of taking into a
le.
adiation dat t for a reliab irradiance at ause only th he irradiance and high irr ain, Portuga
re 2.4: Year usually ava hly average d
es for a typi n Data Base o
om the earli accurate due
acy no bette [3]. The TM h as ambien erage values
cenario. Th his data. An ls in the atm e global effe 16% at som account the l
ta
ble solar pow t the desired he beam rad variation ar radiance are al and Greec
rly Mean of ailable for h daily total ra ical meteoro of the Unite er TMY dat to poorer in er than 10 MY2 are data
nt temperatu of many ye his has to be nother effect mosphere in t
ect is small, me places du
last 20 years
wer plant si d location. Th diation contr
round the w e the western ce.
f Daily Irra horizontal su adiation and ological year ed States are ta, taken from nstrument q
% or worse a sets of hou ure or wind ears, it is no e kept in mi t that might
the last deca it has been uring the last s, deviation
mulation is his is of par ributes to th world, measu n states of th
adiation in U urfaces as a
an hourly to r (TMY) der e available. T
m the years uality and c e, whereas re urly values o speeds for ot suitable f ind when di t reduce sim ades, having found that l t 25 years [9 to the actua
the availabi ticular impo he heat gain red by satell he US and t
UV in the W function of otal radiation rived from th The data set
1950-1975.
calibration st ecent measu of solar radia a one year p for simulatin imensioning mulation accu
g a direct im large local f 9]. Given the
l insolation
ility of deta ortance for c n. Figure 2.4
llite. Areas w the southern
World [7]
f time. Two n. In the sof he 1961-199
is known as Data from t tandards. M urements are
ation and m period. Sinc ng extreme g component
uracy is the mpacting on fluctuations
e fact that T at a certain
9
ailed infor- concentrat- 4 gives an with a usa- n countries
o types are ftware tool 90 Nation- s „TMY2“
this period Most of this e probably meteorolog-
ce the data conditions ts for CSP e changing the irradi- can occur, TMY2 data location is
2.2
In the genera focusin kilowa the com radiant ing to r
2.2.1 Parabo formed
ment.
If it is direct ture lim the sol density Parabo Energy are co costs f the LS which Figure Princi
Concen
following s ation is give ng systems.
atts for smal mbination o t intensity, C requirement
Parabol olic trough p
d like a para
The maximu s heated to o
evaporation mit and redu lar field dep y changes in olic trough p
y Generating nsidered as for the parab S-3 collector increased w e 2.5: Parab iple
ntrating
section a bri en. In genera CSP plants ll villages to f a heat stor CSP plants a ts and econo
ic trough p plants belong
abolic dish
um operatio over 400 n systems, ef uces heat los ending on w n the two-ph
plants have g Systems) a „proven bolic shape, r used in the wind loads to bolic Troug
Solar Po
ief overview al, it can be s can be des o grid conne rage device o
are ready fo omical aspec
plant g to the line
and concen an to co th cu ch T o ab T w ti ti ra in on temperatu decomposin ffectively eli sses and inve weather and
ase-flow in the highest plants in C technology“
further up sc e latest SEG o unacceptab
h
ower Syst
w over the d e distinguish signed for a ected applica or hybridiza or use in bas
cts.
e focusing sy ntrated on th nd 100 are or, used in th
oncentration hermodynam
uracy of the hronization The core elem
f the mirro bsorber and The steel tub which has th
ion. The stee ive layer to ange of the nfra-red rang ure is limite ng will occu
iminating th estment cost
time of day the absorber maturity of alifornia op
“ by projec caling is als GS plant had ble values.
tems
different typ hed between large powe ations with ation by runn
e load, as w
ystems. Radi he receiver.
achieved [1 he ANDASO n ration of mic limit, th
e tracking sy of the entir ment is the r rs. It contai
carries the H be is embod e function to el tube is us o guarantee
solar spectr ge to minim d by the HT ur. One way he need of a ts. However , difficulties r pipe.
f all CSP tec perating succ ct investors
o limited by d an increase
pes of CSP t n line focusi r range, star several hund ning the plan well as in pea
iation is coll Concentrati 10]. The EU OL 1 and 2 p
82 [11]. B his ratio is c
ystem, the o re system an receiver syst
ins a steel HTF.
died in an e o minimize sually coated
a high abs rum and a s mize the hea TF, which is y to overcom
HTF. This i r, due to inst s are impose
chnologies, w cessfully for
[12]. Howe y wind loads ed aperture f
technology ing systems
rting from o dred megaw nt on fossil f ak load mod
lected in the ion ratios b UROTROUG
plants in Sp Beside the t constrained b optical error
nd the resul tem in the li tube which
evacuated g losses due t d with a spe sorption ove small reflect at loss to th s usually a t me this limi increases the tationary con ed by heat tr
with the SE r over 30 ye ever, beside s. The advan
from 5.76m
for power and point only a few watts. With fuel at low de, accord-
e reflector, etween 30 GH collec- pain have a
theoretical by the ac- s, the syn- ltant costs.
near focus works as
glass tube, to convec- ecial selec- er a large tion in the e environ- hermo oil.
t is to use e tempera- nditions in ransfer and
EGS (Solar ears. They s the high ncement of
to 10.3m,
2 Back
2.2.2 Fresne one pa increas the Pla
isolate penden the sam regard ally de inal po mirror of view larmun field co
2.2.3 The so decent large r applica mirror making engine tor. A Figu
kground
Linear F el systems co arabolic conc se the conce ataforma So
ed by a glas nt of the emi me for all m ing controlli efocusing so osition with
s. On the ot w, which is ndo the adva ompared to
Dish des olar dish sys tralised syste range of dep
ation. Incom system, usu g dish syste e, converting A Brayton cy ure 2.6: Par
Fresnel pla onsist of sev centrator. Th entration rati
lar de Alme
s plate and ission, are a mirrors whic ing this is n ome mirrors time, makin ther side, on
why mirror antages of th parabolic tr
sign
stem is a po em, with ev ployment var ming radiatio ually measu ems the mos g it into mec ycle using a abolic Trou
nt
veral segmen his reduces t
io because b eria (PSA) re
the seconda more impor ch makes a
ot desirable, would not b ng a readjus ne servomoto rs are group he Fresnel sy
ough [13].
oint focusing very dish co
riations as in on is reflecte
ring betwee t efficient C chanical wor
turbine to e ugh Princip
nted mirrors the costs of bigger apert
eached a con Nova 171, m This an ac is so the r area.
er of alway range sure j unne es du ated the F ary receiver
rtant issue. T coupling to , because an be possible. A
stment nece or for each m ped in array
ystem lead t
g concentrat nverting sol ndividual po ed and conc en 50m2 -150 CSP technolo rk and final expand the w ple
s in close pr the mirrors, ures are pos ncentration atec BioSol i
mainly by a requires a h ccurate track
lved with a receiver, in Compared t f the Fresn ys receiving e thus the in
joints as nee ecessary. Wh ue to convec glass tube a Fresnel syste r. Therefore,
The angular one conjoin n adjustment
Additionally ssary. This mirror is not ys connected to a cost red
tor. Unlike lar radiation ower genera centrated to 0m2. Concen ogy [14]. Th lly to electri working flui
roximity to t , facilitates t ssible. The d ratio of 107 in Lorca ach
smaller diam higher quali king system.
a secondary creasing th to a parabol nel collector g radiation fr nstallation o eded in para hile in parab ction are su and radiatio em the hot , convection velocity of nt servomot t of the outp y, mirrors ca
would be ea t feasible fro d to one mot duction of ab
all the other n to electric ators or in a the power c ntration rati he heat is tra
c power in t id has also b
the ground, their handlin demonstratio 7. The test c
hieved a rat meter of the ity of the m Usually thi y concentrat he effective lic system, t r remains from the sam
of flexible h abolic plant bolic trough uppressed by on losses do
absorber pi n losses that f the tracking tor possible.
put power by an vary from asier for sin om an econo otor. Accord
bout 50% fo
r CSP syste power. Thi large scale conversion u ios can go u ransferred to the connecte been tested.
11
instead of ng and can on plant at ollector of tio of even e tubes [5].
mirrors and is problem tor around e absorber
the receiv- stationary, me angular high pres- s becomes hs the loss-
y a evacu- ominate, in
pe is only t are inde- g system is
. However y individu- m the nom- ngle driven
omic point ding to So-
or the solar
ems, it is a is allows a connected unit by the up to 4000, o a sterling ed genera-
Electrical
output 30 kW have a
2.2.4 This p are mir
which exchan capacit heliost bine at time op
3 This is Figure
Figure
in the curre W for the Bra
also been dem
Solar tow oint focusin rrors that tra
circulates th nger by the H
ty factor, w tat field enab
t the design peration.
s mainly beca e 2.7: Dish/S
e 2.8: Centr
ent dish/eng ayton system monstrated [
wer power ng system co
ack the sunl
hrough the HTF and pr while runnin bles the syst
point. This
ause of the mo Stirling sch
ral tower sy
gine prototyp ms under con
[15]. Problem e tr o o m v o a a p th o
plants oncentrates
ight around
tower. An a roduces elec
g the plant tem to feed enables ch
odular setup th heme
ystem
pes is about nsideration.
ms arise fro every dish ha
racking syst other hand, w one system, maintaining very beginni only very fe are in direct and it therefo penetration c
he efficiency opment and m
the sunlight two axes w Since all h do not app vidual hel ual parabo of central lower tha values of ed sunligh about 100 stats. Here attached pow ctric power.
at low inso energy into harging of th
hat also domin
t 25 kWe fo Smaller dis m the increa as its own po
tem that ca when an arr it never has individual u ing of their w experime concurrenc ore remains can be achiev
y to over 30 might help t
t with the he with a mirror heliostats ar proximate on liostat appro
ola. Thus, th l receiver s an that of p 500 to 1500 ht is sent to t m height, de e, the absorb wer cycle us Usually, a s olation level the storage he storage w
nates in PV po
r dish/Stirlin h/Stirling sy ased need fo ower conver an move the ray of many
s to shut do units. Dish s r commerci ental setups e to Photov to be seen i ved. Howev 0% seem to b
o boost furth
elp of so cal size of usua re located in ne single pa oximates a se
he achievab systems (CR parabolic di 0 in practice
the receiver epending on ber transfers ses the steam storage is inc ls or at nigh
tanks, while without a po
ower plants.
ng systems ystems of 5 or maintenan
rter and the e heavy un y units is con
own comple systems are ial introduc in place so voltaic (PV) if a noticeab ver, strong in be a promis her deploym
lled heliost ally 50m2 -1 n the same p arabola, but
egment of a ble concentr
RSs) is sig ish systems
[18]. The c r situated in n the numbe s the energy m generated ncluded to in ht-time. An
e still runnin ower drop du
and about to 10 kWe
nce since costs for a it. On the nnected to etely while still at the ction, with
far. They ) systems3, ble market ncreases in sing devel- ment [16].
tats. These 50m2 [17].
plane they each indi- an individ- ation ratio gnificantly , reaching concentrat-
a tower of er of helio- y to a HTF
d in a heat ncrease the oversized ng the tur- uring day-
2 Back
Table plant f be com Key c genera al temp dition, perform receive but als equally
kground
Table 2.
Power SSP EURE SUNS Solar CES MSEE/
THE SPP
TS Solar Cons Solg SierraSun
PS PS2 Solar
2.1 gives an feed electric mmercially o
component i ated heat flux
peratures de the materia mance cycle er fits best t so on perfor y developed
Open air r
.1: List of th r Plant P
PS ELIOS
HINE r One SA-1
/Cat B MIS P-5 SA
Two sular gate
n Tower 10 20
Tres
n overview al power int operated.
in the solariz x densities o emanding hi al must not es in the ran to a certain
rmance and d variations:
receiver
Figu
he larger so Power(MWe)
0.5 1 1 10
1 1 2.5
5 1 10 0.5 0.3 5 11 20 17
of the exist to the grid. S
zation proce of 0.3 – 4MW igh standard
only be able nge of minu plant, depen d costs requi
ure 2.9: Ope
olar tower p HTF Liquid Sod
Steam Steam Steam Steam Nitrat Sa Hitec Sa Steam Air Nitrat Sa Pressurized Pressurized Steam
Air Steam Molten s
ting tower p Solar Tres i
ess is the re W/m2 the re ds for the str e to absorb utes without nds very mu uirements. F
en air receiv
plants build Coun dium Spa m Ital m Japa
m US
m Spa alt US alt Fran m Rus
Spa alt US d Air Isra d Air Spa
m US
Spa m Spa salt Spa
plants. Today s planned to
eceiver. Beca ceiver must ructural desi
high peak f t damage ov uch on the c
our types o
ver scheme
d to date [19 ntry
ain ly an
S 19
ain S nce
sia ain
S 19
ael ain S ain ain
ain Under
y only the P o be the first
ause of the be able to c gn of the re flux densitie ver a long p connected po
f receivers
9], [20], [14]
Year 1981 1981 1982 982-1986
1982 1983 1984 1986 1993 995-1999
2001 2002 2009 2007 2009 r construction
PS10 and PS t power plan
concentratio cope with hi eceiver set [2 es but also e period. Whic
ower genera can be con
13
]
S20 power nt that will
on and the gh materi- 22]. In ad- endure fast
ch type of ation cycle nsidered as
A blower sucks ambient air through the porous absorber material, which is heated up from the concentrated radiation. The absorber can be made from metallic or ceramic material.
The hot air transfers the heat via an exchanger to the steam cycle. The use of air at ambi- ent pressure makes this design cheap and very easy to handle and maintain. Segments of the receiver can be replaced without pressure reduction if a modular layout is installed, giving the system a high operational availability. However, the low specific heat as well as the low pressure limit the heat transfer, requiring high air mass flows [5]. Figure 2.9 il- lustates the 200 kWth HiTRec-II open volumetric air receiver, tested at Plataforma Solar de Almería (PSA) in 2001. It worked with an inlet flux of up to 900 kW/m2 and an aver- age outlet air temperatures of up to 840°C with a peak outlet air temperatures of up to 950°C.
Closed air/helium receiver
To increase the transferable heat load, the air circulating through the receiver can be com- pressed. The concentrated solar radiation enters the receiver through a quartz window which has to withstand the high thermal loads and rapid temperature changes as well as the pressure difference to the environment with minimal reflection and absorption losses.
This type will be discussed in detail in chapter 3
Direct evaporation receiver
A directly evaporating absorber is for example implemented in the PS10 plant, working with a saturated steam cycle at 40bar and 250ºC. Although water has a much higher spe- cific heat capacity than air, water chemistry can result in problems when reaching very high temperatures. Therefore the heat flux to the receiver as well the pump performances have to be critically observed at all times. Failure to do so can lead to steam explosions if critical temperatures are exceeded. Another problem are the high costs for the storage of steam, when compared to molten salts [23].
Molten salt/metal receiver
Molten salt or metals offer a high heat transfer coefficient at a low temperature differ- ence. Their high thermal conductivity reduces the thermal stress for the absorber material.
Since the heat transfer occurs in a single-phase regime, the design of the receiver unit is less complex. An advantage is their high heat capacity at relatively low costs, making them an ideal medium for a heat storage implementation [23]. Molten sodium can be used for temperatures up to 880 combinded with an excellent thermal conductivity, leading to low absorber temperatures. As in air receivers, a heat exchanger is needed to transfer the heat to the steam cycle, increasing complexity and costs compared to direct evapora- tion systems. High temperature loads over a long period of time can lead to partial disso- ciation of the molten salts, resulting in fire hazards due to oxygen formation or toxic by- products like potassium nitrite. In steel pipes corrosion must be considered and is usually
2 Back
Two p ternal around termin the HT configu
A cavi ty. The trated the rec ty allo efficien
4 The fi receiver
kground
reduced by is pyropho
possibilities t design with d the tower.
ned by the m TF. Therefor uration base
Figure 2.
ity receiver t e effectivene in Figure 2.
ceiver is not ows to trap t ncy than the
figure illustrate
r system.
y special coa oric in air ab
to install the h the absorbe To minimiz maximum te
re, a system ed on a wate
.10: An exte tries to mini ess is determ
.104, where axially sym the solar rad e external ty
es a cavity de
atings for pip ove 140 [
e receiver on er in a 360 ze heat losse
mperature o m which uses er/steam med
ernal receiv imize heat lo mined by the
blue repres mmetrical, th diation more
pe.
esign from a d
ipe walls. Co [5].
n the tower degree arran es, the size i of the absorb s a molten s dia, which re
ver (left) an osses to the e angle unde ents the low he acceptanc
e effectively
dish collector
ontact with a
do exist: ex ngement all is reduced t ber tubes an alt or metal educes heat
d a cavity r environmen er which the west, and red ce angle is m y and conse
system. The
air must be a
xternally or ows for a c o a minimum nd the heat
HTF can b losses.
receiver (rig nt by placing receiver is i d the highes much smaller quently the
effect shown
avoided, sin
inside a cav circular heli m. The lim removal cap e build sma
ght) [24] [25 g the absorb
installed. Th st temperatu r. However receiver ha
is the same f
15
nce sodium
vity. A ex- iostat field mits are de-
pability of aller than a
5]
ber in cavi- his is illus- ures. Since
r, the cavi- as a higher
for a central
2.3
One o known cheap for CS Joule-B consist in a T-
At the release the tota
It can b any he input s ambien
5 The d generat
6 Parabo in [18]
Conve
f the major n and tested and reliable SP technolog Brayton cyc ts of two iso -s diagram.
upper temp ed. The cycl
al heat input
be shown th eat to mecha should be pr nt temperatu downside of th
ion, making c olic dishes are .
rsion of h
r advantages heat transfe e standard ap
gy, which w cle. Both are othermal and
perature TH, le efficiency t Qth that is
hat the Carno anical energ
rovided at a ure to achiev
his situation i compromises i e usually com
heat to el
s of solar p er cycles can
pplications f will be expla
e variations o d two isentro
Figure 2.11 , heat is add y C is indep converted to
ot cycle effi gy conversio a very high t ve a high co
s that power in terms of eff mbined with a S
lectricity
power tower n be used, th for the pow ained in the of the ideal C opic change
1: The idea ded to the f pendent of th
o work W w
iciency is eq on process
temperature onversion eff
equipment is ficiency and d Sterling cycle
y
r systems is hus enabling wer generatio
following, Carnot cycle s of state6. F
al Carnot cy fluid and at he working which can be
1
qual to the th [24]. As a c
whereas he ficiency. Ho
to date not ” desired power e. Detailed info
s the fact th g the system on5. The two are the Clau e. This is a r Figure 2.7 sh
ycle
the lower te fluid and de calculated a
heoretical m consequence eat removal owever, for t
off the shelf”
output inevita ormation abou
hat conventi m to be equi o most relev usius-Rankin reversible pr hows the Ca
emperature escrbes the f as
maximum eff e of this equ should occu the applicati
” for solar the able.
ut this cycle c
ional, well ipped with vant cycles ne and the rocess that arnot cycle
T0 heat is fraction of
(2.10)
ficiency of uation heat ur close to ion of heat
ermal power
can be found
2 Back
engine with in The pr
describ sion of plotted ratio c calcula can be perform the eff higher
Figure work a and an 2.3.1 The Cl It has b stood p cycle g 1→2 I
kground
es in CSP sy ncreasing tem roduct of bot
bes the perfo f mechanica d as a functi c and differe
ation the up e seen, there
mance can b ficiency. Th
is the theor
e 2.12: Theo as the funct n ideal selec The Cla lausius-Ran been used in power cycle goes through
sentropic pr
ystems it can mperature.
th efficienci
ormance of al power to e
on of the ab ent absorber per fluid tem e is an optim be achieved he higher the
retical conve
oretical tota tion of the u ctive or a bl ausius-Ran kine cycle c n power plan e. The worki
h the follow ressure rise b
n be seen in
ies
an ideal CSP electricity is bsorber temp r characteris mperature is mum temper . Even high e concentrat ersion efficie
al efficiency upper receiv
lack body c nkine cycle
can be consi nts for over ng medium ing state cha by the feed-w
n Figure 2.3b
P system tha s free of loss perature. Sev stics (selecti s assumed to
rature for e her temperatu
tion ratio, th ency.
y of a CSP s ver temper characterist
idered as the r 100 years,
is water, or anges which water pump
b that the ef
∙
at produces ses. In Figur veral graphs ive or black o be equal t ach concent ures result i he higher is
system for t ature for di tic of the ab
e most impo and is there
water vapor h are depicte
,
fficiency of
electricity, a re 2.12 the t s based on d k body type to the absorb
tration ratio in excessive
the optima
the generati ifferent con sorber [18]
ortant cycle efore a well- r. The ideali ed in Figure
a solar rece
assuming th total efficien different con e) are shown
ber tempera o where the e heat losses al temperatu
ion of mech ncentration
for power g -developed a ised Clausiu
2.13:
17
eiver drops
(2.11)
hat conver- ncy is ncentration n. For this ature. As it maximum s, reducing re and the
hanical ratios
generation.
and under- us-Rankine
