v32_187_199

7/31/2019 v32_187_199

1/13

Parabolic

Trough

ParabolicTrough

Superheater

(optional)

Backup

Power

Conversion

Unit (PCU)

ThermalStorage

Heat

Exchanger

Solar

Radiation(S)

Amb ie nt

Tem perature(Ta)

Wind

Veloc ity(Va)

InletTemperature

(Ti)

MassFlow(m)

BackupHeater Input

(Qu,bu)

Outlet

Temperature(To)

The rmalOutput to

PCU

(Ls)

ThermalInput from

Trough

(Qu,t)

StorageTemperature

(Ts)

ThermalStorage(Qstore)

StorageLoss (Qloss)

ScienceAsia 32 (2006):187-199

Solar Parabolic Trough Simulation and Application for

a Hybrid Power Plant in Thailand

Eron Jacobsona,b,c, Nipon Ketjoya*, Sukruedee Nathakaranakulea and Wattanapong Rakwichiana

a

School of Renewable Energy Technology, Naresuan University, Phitsanulok 65000 Thailand.b University of Washington Seattle, Washington 98101, USA.c Seattle Engineer at the Boeing Company, P. O. Box 3707, Seattle, Washington 98124, USA.

* Corresponding author, E-mail: [email protected]

Received 24 Dec 2004

Accepted 13 Jan 2006

ABSTRACT:The purpose of this research project was to develop a software simulation of a solar parabolic troughfor use in the design of a solar thermal power plant. In order to determine the optimum size of a parabolictrough to power a solar thermal power plant system in Thailand, a simulation is necessary to determine bothlong-term operating performance and short term local temperatures in the system. The simulation describedin this paper was created for this purpose. It can evaluate both water and high temperature oil as the heattransfer fluid (HTF), in addition to the ability to vary many of the operating parameters of the system. Thesimulation was created to be a tool to determine the optimum parameters for the parabolic trough as theprimary input to a power plant. It is necessary due to the many parameters that characterize a solar parabolictrough system, which must be considered when determining the output of the system. The simulation wasconstructed using methods from widely accepted reference materials and assumptions to the best ability.

KEYWORDS: System simulation, Solar parabolic trough, Solar thermal power plant, Optimum size, Heattransfer fluid.

doi: 10.2306/scienceasia1513-1874.2006.32.187

INTRODUCTION

The simulation described in this paper was createdto be used as a design tool for the BioSun project. Thegoal of the BioSun project is to develop a conceptdesign for a hybrid power plant system using a solarparabolic trough as the primary energy source with abackup system consisting of a biomass gasifier in

Thailand. These two energy sources will be used toprovide heat to a thermal storage system, which will in

turn be used to provide steam to drive a steam engineand 25 kW generators. This paper focuses on theconcept design for the parabolic trough as the primaryenergy source. The very basic schematic of theproposed hybrid system is shown in Fig 1.

The energy output of the parabolic trough depends

Fig 1. Simplified Block Diagram of Proposed Hybrid Power Plant.

7/31/2019 v32_187_199

2/13

188 ScienceAsiaScienceAsiaScienceAsiaScienceAsiaScienceAsia 32 (2006)32 (2006)32 (2006)32 (2006)32 (2006)

on many parameters including the solar radiation input,the size of the trough, and the heat transfer fluid (HTF).The equations describing the performance of aparabolic trough cannot be solved in a simple mannerto find the optimum parameters of a trough for a desiredenergy output; rather the equations describing theparabolic trough must be solved for each given set ofparameters and the resulting energy outputs comparedto find the optimum parameters. This would be atedious task if performed manually. Therefore it is

necessary to have a simulation tool to easily compareresults for given differing parameters. In order to findthe optimum parameters for the parabolic trough tomeet the demands of the BioSun system, a yearsimulation with hourly time step was constructed usingan iterative process with Excel macro environment,which allows the parameters of the trough to be changedand the output HTF temperature and productive energyoutput to be known.

Solar RadiationSolar RadiationSolar RadiationSolar RadiationSolar RadiationSilapakorn University of Thailand performed a study

to measure the total radiation for each province inThailand1. For a parabolic trough, only the direct solarradiation is of practical use. To isolate the portion of themeasured radiation that is diffuse and the portion ofthe radiation that is direct, the following steps werefollowed using Duffie and Beckman2. Given that thelatitude (f) of Phitsanulok is 16, 47 N, the Monthly

Average Extraterrestrial Radiation (Ho,bar

) was enteredinto the simulation as a lookup table using data fromDuffie and Beckman2. Next the Monthly AverageClearness Index (K

T,bar), the Sunset Hour (w

s), and the

Declination (d) were calculated for each day usingequations in Duffie and Beckman2. The fraction of themonthly average daily diffuse radiation and directradiation were estimated using equations in Duffie andBeckman2 (since w

s>81.4, and 0.3 K

T,bar0.8), and

were entered into a lookup table in the simulation. Thevalues for the Daily Direct Beam Radiation in Phitsanulokon a monthly average are listed in Table 1. The resultinghourly beam radiation data is the default input for thetrough for a given day of the year.

Optical PerformanceOptical PerformanceOptical PerformanceOptical PerformanceOptical Performance

Angle of IncidenceAngle of IncidenceAngle of IncidenceAngle of IncidenceAngle of IncidenceFor the case of the BioSun project in Thailand, a

single north-south axis rotational tracking trough waschosen to reduce the average angle of incidence overa yearly period. The Angle of Incidence () is given byreference2 in equation (1), while the Zenith Angle (

z) is

found by equation (2) for an east-to-west tracking(north-south axis) trough:

12 2 2 2cos (cos ( ) cos ( )* sin ( ))w = + (1)

cos cos( )* cos( )*cos( ) sin( )* sin( )wz = + (2)

Absorbance of Collector PipeAbsorbance of Collector PipeAbsorbance of Collector PipeAbsorbance of Collector PipeAbsorbance of Collector PipeThe surface absorbance of a collector is dependant

upon the angle of incidence of the solar ray to thatsurface. Since data is not typically available fordescribing the relationship of the ratio of angularabsorbance to normal absorbance, it is estimated inreference2 with equation (3) for angles of incidencebetween zero and 80:

-3 -4 2 -6 3 -8 41 2.0345e -1.990e 5.324e 4.799en

= + +

(3)where is in degreesThe final beam specular absorbance for the

absorber pipe is then found by multiplying the ratio ofequation (3) by the normal specular absorbancecoefficient of the collector material itself.

TTTTTransmittance, Reflection and Absorptance of aransmittance, Reflection and Absorptance of aransmittance, Reflection and Absorptance of aransmittance, Reflection and Absorptance of aransmittance, Reflection and Absorptance of aSingle Cover SystemSingle Cover SystemSingle Cover SystemSingle Cover SystemSingle Cover System

The glass of the absorber cover is assumed to be asmooth surface of partially transparent material.

Accordingly, the angle of refraction for the interfacebetween the glass cover and the air can be calculatedby equation (4) 2:

sin( )1 1sin( )2 2

n

n

= (4)

where: n1equals 1 (assumed refractive index of air),

n2

is the refractive index of the glass, 1

is (angle ofincidence), and

2is angle of refraction.

The perpendicular and parallel components of theunpolarized radiation passing from one medium (air)

to the next (glass) are described by equations (5) and(6)2:

Table 1. Monthly Average Daily Direct Radiation in Phitsanulok.

Monthly AMonthly AMonthly AMonthly AMonthly Average Daily Dirverage Daily Dirverage Daily Dirverage Daily Dirverage Daily Direct (beam) Radiation, Hect (beam) Radiation, Hect (beam) Radiation, Hect (beam) Radiation, Hect (beam) Radiation, Hb,barb,barb,barb,barb,bar

(MJ/m(MJ/m(MJ/m(MJ/m(MJ/m22222)))))

JJJJJ FFFFF MMMMM AAAAA MMMMM JJJJJ JJJJJ AAAAA SSSSS OOOOO NNNNN DDDDD AAAAAvgvgvgvgvg

Phitsanulok 9.6 11.0 12.4 13.3 14.1 13.5 10.9 13.8 10.1 9.6 9.5 9.8 11.5

7/31/2019 v32_187_199

3/13

ScienceAsiaScienceAsiaScienceAsiaScienceAsiaScienceAsia 32 (2006)32 (2006)32 (2006)32 (2006)32 (2006) 189

2sin ( - )2 1r2sin ( )

2 1

= +

(5)

2

2 1

22 1

tan ( - )r

tan ( )

=

+ (6)

For a one cover system as is assumed for the troughsimulation, the transmittance of the initiallyunpolarized radiation is the average transmittance ofthe perpendicular and parallel components as describedby equation (7) 2:

(1 - r ) (1 - r ) *r

(1 r ) (1 r )

= + + +

(7)

Absorption by GlazingAbsorption by GlazingAbsorption by GlazingAbsorption by GlazingAbsorption by GlazingThe amount of radiation transmitted through a

partially transparent medium (glass) is described byequation (8) 2. The remaining portion of the radiationis that absorbed by the medium. This is described asglazing.

*exp

cos2

I K Ltransmitteda

Iincident

= =

(8)

where Kis extinction coefficient of glass, and L is

thickness of glass cover.

Optical Properties of the Cover SystemOptical Properties of the Cover SystemOptical Properties of the Cover SystemOptical Properties of the Cover SystemOptical Properties of the Cover SystemReference2 suggests that the transmittance,

reflectance and absorptance of a one cover system canbe simplified into equation (9) for practical collectorcover applications.

=

a*

r(9)

Intercept FactorIntercept FactorIntercept FactorIntercept FactorIntercept Factor

The intercept factor for a linear imagingconcentrator (as is the case for the parabolic trough)is the fraction of the reflected radiation that is incidenton the absorbing surface of the receiver. For a receiverof large enough diameter, the fraction of the reflectedradiation is 1.0. For a perfect linear imagingconcentrator, the diameter (D

=1) of the cylindrical

receiver for an Intercept Factor () equals to 1.0, whichis described by equation (10) 2. For a non-perfectimaging concentrator (defects in the surface of thereflector), the diameter (D

=1) is described by (11) 2:

( )sin 0.267*1 sin( )D w

r

== (10)

( )

( )

8 *1tan2

16 * 1

f wr

f w

=

(10a)

sin(0.267 / 2)*1 sin( )

dD wr

+== (11)

where w is width of the aperture,fis the focal lengthof the aperture, and

dis the dispersion angle.

For the simulation, the trough is assumed to beimperfect, meaning that the dispersion angle is greaterthan zero. The intercept factor was thus chosen for thesimulation as described in equations (12) 2:

o

o o

1 if D D

D /D if D D

= 1

= 1 = 1

=

< (12)

where D=1

is given by equation (11).It is worthwhile to note that using the proportion

Do/D

=1for the intercept factor is very conservative for

the second case of equation (12) since the distributionof the radiation is theoretically a normal distribution.

Overall Optical EfficiencyOverall Optical EfficiencyOverall Optical EfficiencyOverall Optical EfficiencyOverall Optical EfficiencyThe overall optical efficiency is the combination of

the efficiencies from the cover transmission, collectorabsorptance, and the primary mirror reflectivity. Thisis shown in equation (13) 2:

( ) * * *o e = (13)

where eis specular reflectivity of mirror.

Incident Angle ModifierIncident Angle ModifierIncident Angle ModifierIncident Angle ModifierIncident Angle ModifierThe effects of errors in the concentrating contours,

tracking errors, and errors in displacement of receiversfrom the focus all lead to enlarged or shifted images andaffect the intercept factor. These errors can beaccounted for by using biaxial incidence angle

modifiers. However, it is very specific for each collector,so in this study the LS3 specification is assumed to beused in Thailand. The simulation has included suggestedIncident Angle Modifiers from reference2 (K()

Duf) and

that suggested for the LS3 design from reference3

(K()LS3

). The modifiers are given in equation (14) and(15):

( )

4

21 0.078043 * 0.58047 *330.950559 * 0.069092 *

KLS

= +

+ (14)

where is in radians.

7/31/2019 v32_187_199

4/13


( ) 5 21 6.74 *

6 3 8 41.64 * 2.51 *

K EDUF

E E

=

+ (15)

where is in degrees.

However, there is a difference in the application ofthese two incidence angle modifiers. Equation (15) isto be applied to the Overall Optical Efficiency (

o())

where it is a function of the angle of incidence2. Equation(14) is to be applied to the Overall Optical Efficiencyas a constant where it is evaluated at the normal3. Bothof these calculations are made as shown in equations(16) and (17) and the smallest Modified OpticalCoefficient (

o,mod()) is used in the simulation.

o,mod

() = K()LS3

*o(0) (16)

o,mod() = K()Duf*o() (17)

End Effect CorrectionEnd Effect CorrectionEnd Effect CorrectionEnd Effect CorrectionEnd Effect CorrectionThe End Effect Correction for receivers of the same

length as the reflectors is given by equation (18):

( )2

( ) 1 * 1 * tan( )248*

af l

f

= +

(18)

Absorbed Radiat ionAbsorbed RadiationAbsorbed Radiat ionAbsorbed RadiationAbsorbed Radiation

With all of the modifiers taken into account, theAbsorbed Radiat ion (S) or the actual amount ofradiation on the receiver is calculated by equation (19):

S = Ib*

o,mod() * () * cos (19)

Thermal Performance and LossesThermal Performance and LossesThermal Performance and LossesThermal Performance and LossesThermal Performance and LossesThe thermal losses for a parabolic trough system

are from convection and radiation from the absorbertube to ambient, and conduction from the absorbertube to the trough supporting structure itself. For the

simulation, it was assumed that conduction from theabsorber tube to the support structure is zero. It wasalso assumed that the cylindrical receiver is coveredwith a glass cover for the total distance of the trough.These assumptions were based on practicalapplications, but they may be areas for futureimprovement to the simulation.

Heat Loss by RadiationHeat Loss by RadiationHeat Loss by RadiationHeat Loss by RadiationHeat Loss by RadiationThere are two radiation coefficients that are

necessary to be calculated for a system with a glasscover. The first coefficient is that for radiation from the

absorber pipe (receiver) to the cover. This coefficientis given in equation (20):

2 2( )*( )*, (1 )*(1 ) 1

*12

T T T T r c r chr r c Dc orF Dr c c

+ +=

+ + (20)

where Tr is temperature of the receiver (absorberpipe), Tcis temperature of the cover,

ris emittance of

the receiver (absorber pipe), c

is emittance of thecover, D

ois receiver outer diameter,D

cis cover diameter

(small thickness assumed), F12

is view factor betweenthe receiver and the cover (assumed to be 1),and isStefan Boltzman constant which 5.67E-8 .

As reference2 described, this equation has theassumptions that the surfaces are gray, are diffuse orspecular-diffuse, are uniform in temperature and haveuniform incident energy over the surface. As can benoted from equation (20), the temperature of the

receiver and the temperature of the cover must beknown to calculate this coefficient. The simulationattempts a logical estimate at the average receivertemperature for the length of the evaluation by equation(20a). This logical estimate is then refined by a seconditeration of the evaluation length.

( )*0.25* *

*

a D lc evalT T Sr in m Cp

= +

(20a)

where leval

is evaluation length of the trough.

The temperature of the cover is assumed in thesimulation to be 20% of the difference between thereceiver temperature and ambient greater than theambient as described in equation (20a). The covertemperature is later checked in the simulation and asecond iteration of the thermal losses is performedusing the adjusted cover temperature.

Tc= 0.2 * (T

r- T

a) + T

a(20b)

The second coefficient is radiation coefficientbetween the cover and the ambient air. This coefficientis described by equation (21):

hr,c-a = 4** c * Tloc3

(21)where Tloc

is average (local) temperature betweenthe cover and the ambient air = 0.5 * (T

c+ T

a), and

cis

emittance of the cover.

Convection to AmbientConvection to AmbientConvection to AmbientConvection to AmbientConvection to AmbientThe convection to ambient is a bit more complicated

due to the fact that the fluid dynamics may call for alaminar or turbulent flow over the cover pipe dependingon the calculated Reynolds Number (Re). The governingequation for the convection coefficient is described inequation (22), but the Nusselt Number (Nu) can be

defined by two equations (22a) and (22b) as shown inreference2,4,5. The simulation incorporates equations

7/31/2019 v32_187_199

5/13


(22a) and (22b) in an if-then statement after evaluatingthe Reynolds Number (Re) in equation (22c).

*Nu ka ahwDc

= (22)

0.530.4 0.54 * ReNu a= + for 0.1< Rea < 1000(22a)

0.60.3*ReNua a= for 1000 < Rea< 50,000(22b)

* *Re

V Dca aa

a

= (22c)

where kais thermal conductivity of air,

ais density

of air, Vais velocity of air,

ais kinematic viscosity of air,

and Dcis cover diameter.

The characteristics of air ka

, a

, and a are

dependent on the air temperature. Therefore, thesimulation incorporated these characteristics from areference2 appendix into a lookup table to be evaluatedon a basis of a linear interpolation on the airtemperature.

Overall Loss CoefOverall Loss CoefOverall Loss CoefOverall Loss CoefOverall Loss Coefficient and Cover Tficient and Cover Tficient and Cover Tficient and Cover Tficient and Cover TemperaturemperaturemperaturemperaturemperatureeeeeThe Overall Loss Coefficient combines the thermal

losses into one coefficient. For the assumption that thearea between the cover and the receiver (absorberpipe) is a stagnant quantity of air, the coefficient on aper length basis is calculated by equation (23):

11

( )* ,,

DoUL h h D hw c r r cr c a

= + + (23)

The Cover Temperature (Tc) is evaluated by

performing an energy balance on the cover thusgenerating equation (24):

* * *( )*, ,

* *( ), ,

D h T D h h T o r r c r c wr c a aTc

D h D h ho r r c c wr c a

+ + =+ +

(24)

A second iteration of the thermal losses and OverallLoss Coefficient is performed in the simulation with theadjusted cover temperature. This iteration was foundto provide acceptable accuracy for the Overall LossCoefficient; additional iterations were deemedunnecessary.

Heat THeat THeat THeat THeat Transfer to Fluidransfer to Fluidransfer to Fluidransfer to Fluidransfer to FluidThe heat transfer from the receiver pipe to the fluid

(water or HTF) must be characterized by turbulent or

laminar flow conditions. Accordingly, the simulationevaluates the Reynolds Number of the fluid (Re

f) of

equation (25a) and uses an if-then statement betweenequations (25) (for turbulent flow) and (26) (for laminarflow) to calculate the Nusselt Number of the fluid (Nu

f)5.

The Heat Transfer Coefficient to the fluid (hf) is then

evaluated by equation (27):

( )

( )

18 *Re *Pr *

231.07 12.7 * 8 * Pr 1

n

f uf f fNuf uw

ff

= +

(25)

for Ref

> 2200

4 *Re

* *

mf

D ui f

=(25a)

2

0.79* ln(Re 1.64)ff

=

(25b)

Nuf

= 3.7 for Ref

< 2200 (26)

*Nu kf f

hf Di

= (27)

where Prf

is Prandlt Number of the fluid, f is

kinematic viscosity of the heat transfer fluid, w

iskinematic viscosity of water at atmospheric conditions,m is mass flow of fluid, D

iis receiver inner diameter, and

n1is 0.11.

For the case laminar flow (Ref< 2200), a fullydeveloped hydrodynamic and thermal profile wasassumed. The Nusselt Number of the fluid was chosento be 3.7 for the case of a constant wall temperaturerather than the 4.4 for a constant heat flux. This choicewas made because it results in a more conservative heattransfer coefficient although the theoreticalperformance of a solar collector lies somewherebetween a constant temperature condition and aconstant heat flux condition.

The characteristics of the fluid and water w ,

f, k

f,

andPrfare dependent on the water and oil temperatures.Therefore, the simulation incorporated thesecharacteristics from a reference4 appendix and fromreference6 into lookup tables to be evaluated by linearinterpolation based on the water and VP1 oiltemperatures respectively. Unless later noted, for thefirst iteration for the evaluation of the troughperformance, these characteristics are evaluated at thefluid inlet temperature.

Overall Heat TOverall Heat TOverall Heat TOverall Heat TOverall Heat Transfer Coefransfer Coefransfer Coefransfer Coefransfer Coefficient and Factorsficient and Factorsficient and Factorsficient and Factorsficient and FactorsThe Overall Heat Transfer Coefficient (U

o) is the

coefficient for heat transfer from the surroundings tothe fluid, based on the outer diameter of the receiver

7/31/2019 v32_187_199

6/13


Calculate HeatLoss Coef to

Ambient - Check(First Iteration)

Re-calculate HeatLoss Coef to

Ambient (2ndIteration)

Calculate HeatTransfer

Coefficient to HTF

AirCharacteristic

Data (Cp,k,etc)

HTFCharacteristic

Data

(Cp,k,etc)

TfmEst.

Calculate UsefulGain and Temp.

Out or Length

TrmEst.

Calculate Tfm andTrm for 2nd

Iteration.

2nd It.2nd It.

1st It.1st It.

Tin Tout2nd It.

1st It.

Tin

pipe. This is given in reference2 as equation (28):

1

* ln1

* 2

DoDoDD ioUo

U h D kiL f

= + +

(28)

where k is thermal conductivity of receiver pipe.It is convenient to define a Collector Efficiency

Factor (F) at this point by equation (29):

'UoFUL

= (29)

The Collector Flow Factor (F) is then described inequation (30):

* * * '

" * 1 exp' * * ' *

m CF A U Fp rR L

F F A U F m Cr pL

= = (30)

where Cpis the specific heat of the fluid,A

ris the

area of the receiver (Do* l*n), l is length of receiver per

module, n is number of modules.The specific heat of the HTF (C

p) is dependent on

the HTF temperature. Therefore, the simulationincorporated these characteristics from a reference4

appendix and reference6 into a lookup table to beevaluated by linear interpolation based on the fluid

temperature.The Useful Energy Gain (Q

u) is then calculated as

described in reference2 with equation (31):

* * * *( )ArQ F A S U T T u a aiR LAa

=

(31)

where Aais area of the aperture ((a-a

o)*l), a is the

width of the aperture, aois width of aperture shaded by

the receiver, and Tiis fluid inlet temperature.

First and Second IterationsFirst and Second IterationsFirst and Second IterationsFirst and Second IterationsFirst and Second IterationsThe collector performance is dependant on the

overall loss coefficient and the internal heat transfercoefficient to the heat transfer media. Both of thesecharacteristics are a function of temperature, whichrequires that they are based on an estimate in the firstiteration. The estimate for the heat transfer coefficientis calculated using the temperature into the trough forthe first iteration. The estimate for the mean receivertemperature for the first iteration is calculated byequation (32).

0.25 * *,1 *

AaT T Sirm st C mp= +

(32)

A second iteration is then performed for eachevaluation length of the trough using the performancefactors calculated in the first iteration in order to refinethese estimates. The mean fluid temperature (T

fm) is

calculated by equation (33), and the properties of theheat transfer fluid are then evaluated at thistemperature.

*(1 ")*

Q Au cT T Finfm F UR L

= + (33)

The mean receiver temperature is calculated byequation (34).

*(1 )*

Q Au cT T Frm in RF UR L

= + (34)

The iteration process is shown in Fig 2. The seconditeration of the simulation refines the calculatedperformance and useful gain of the trough.

Fig 2. Iteration Process for Trough Performance Evaluation.

7/31/2019 v32_187_199

7/13


L1 = ? L2 = ?

T,sat T,satT,in T=? T=?T,sat

L3 = L -

L1 - L2L4 = Lsup

Section 1 Section 2 Section 3

Section 4

Heat water to

saturation

temperature.

Vaporize water. Superheat steam

(normal trough

section).

Superheat steam

(Superheater

trough section).

T=?

*Separator *Separator

*The separator may be in the first or second position depending on

vaporizing conditions. There is only one separator.

Water as the heat transfer media makes the rather

simple calculations up to this point much morecomplicated. This has to do with the phase changefrom liquid to gas that water goes through upon heatingto temperatures in a parabolic trough application, andthe property changes that occur during the phasechanges (Fig 3).

First Section Evaluation: Heating the WFirst Section Evaluation: Heating the WFirst Section Evaluation: Heating the WFirst Section Evaluation: Heating the WFirst Section Evaluation: Heating the Water toater toater toater toater toSaturation TSaturation TSaturation TSaturation TSaturation Temperaturemperaturemperaturemperaturemperatureeeee

In this section, the output temperature is knownrather than the length of heating. For this reason,equations (30) and (31), which depend on the lengthof heating for evaluation, could not be used. Since thelength of the trough to heat the fluid temperature to thesaturation temperature is not known, different meansmust be used to calculate the useful gain. The strategyadopted in the simulation is to use equation (35) fromreference2 which calculates the useful gain per meterbased on the fluid temperature. The average fluidtemperature (T

fm) for this section of the trough can be

assumed to be the average between the inlet fluidtemperature and the saturation temperature. Theaverage receiver temperature (T

rm) is estimated as the

average fluid temperature for the first iteration.

' ' * * * *( )A Aa rq F S U T T u aL fL Aa

=

(35)

where

2

T TsatinTfm

+ =

(35a)

Tin

is temperature of the water into the trough, Tsat

is saturation temperature of the water at the Pin, P

inis

pressure at inlet.The characteristics of the fluid T

satis dependent on

the water pressure. Therefore, the simulation

incorporated these characteristics from a reference3

appendix into a lookup table to be evaluated by linearinterpolation based on the water pressure.

The section of the parabolic trough which serves toheat the water to its saturation temperature may havelaminar and/or turbulent flow. The Nusselt Numberand therefore the heat transfer coefficient of a turbulentfluid can be much higher than those for a laminar fluid.So it is not enough to take the Nusselt Number at theaverage temperature (T

f) of the section because this

may represent the characteristic flow for only slightlymore than half the length. Instead, the simulationevaluates the Reynolds number at both the inlettemperature and saturation temperature to check forlaminar and turbulent flow. If both are found to beturbulent or if both are found to be laminar, thenequation (25) or (26) can be applied using the averageReynolds Number and Prandtl Number. If both laminarand turbulent flow exists, then equation (36) is appliedto get a better estimate of the average Nusselt Number4.Fig 4 describes the flow characteristics of concern.

Re Re Re Re2200 22003.7*

Re Re Re Re0.11( 8)*Re *Pr

, ,* *

2 31.07 12.7* ( 8)*(Pr 1),

satinNuave

sat satin inf

turbave turbave

f wturb ave

= +

+

(36)

( )2

0.79* ln(Re 1.64),

fturb ave

= (36a)

whereRe Re2200

Re , 2

satturb ave

+

= , (36b)

Fig 3. Evaluation Sections of Parabolic Trough Using Water as the HTF.

Evaluation of the Parabolic TEvaluation of the Parabolic TEvaluation of the Parabolic TEvaluation of the Parabolic TEvaluation of the Parabolic TrrrrroughoughoughoughoughWWWWWater as the Heat Tater as the Heat Tater as the Heat Tater as the Heat Tater as the Heat Transfer Fluidransfer Fluidransfer Fluidransfer Fluidransfer Fluid

7/31/2019 v32_187_199

8/13


Tin

Rein

Prin

Tout

Reout

Prout

Laminar Turbulent

Retrans =2200, Prtrans

L lam L turb

L eval

Pr Pr2200Pr, 2

satturb ave

+ =

, (36c)

Re2200

is 2200 (turbulent flow beginning), Resat

isReynolds Number at saturation temperature, Re

inis

Reynolds Number at inlet temperature, Pr2200

is PrandtlNumber at Re equal to 2200, Pr

satis Prandtl Number at

saturation temperature, isaverage of viscosity ofwaterat T

inand T

sat,and

wis viscosity of water at T

rm

Using equation (37), the length to heat the water tosaturation (L

sat) is calculated.

*( )*

'

C mpL T Tsat sat in

qu

= (37)

For the second iteration of this section, the meanreceiver temperature (T

rm) is calculated using equation

(38) and the characteristics from the first iteration:

( )ln1' *2

D Do iT T Qrm ufm h k

f

= + +

(38)

Second Section Evaluation: VSecond Section Evaluation: VSecond Section Evaluation: VSecond Section Evaluation: VSecond Section Evaluation: Vaporizing the Waporizing the Waporizing the Waporizing the Waporizing the WaterateraterateraterThe second section for evaluating water as the heat

transfer media in the parabolic trough is very similar tothe first section in that the length of evaluation is not

necessarily known, but the energy to vaporize the water(h

fg) being based only on the pressure of the water is

found using linear interpolation through a lookup tablefrom reference2. The assumption made here is that thevaporization of the water in the receiver is a constantpressure process. The length to boil (L

b) is then

calculated by equation (39):

*

'

h mfg

Lb Qu

= (39)

where Qu is useful gain per meter.

The quality of the steam (x) is then calculated byequation (40):

L Lsep satx

Lb

= (40)

whereL

sep= l * n

sep, (40a)

nsep

is the number of the module that the separatorfollows. If the length to saturation (L

sat) is greater than

the length to the separator (Lsep), then the quality of thesteam is zero.

The separator is assumed to be adiabatic in thesimulation so that all the steam that enters also exits.This assumption is not conservative and may be an areafor future improvement to the simulation. The massflow out of the separator (m

s) is calculated by equation

(41):*sm x m= (41)

The enthalpy of the steam as it enters the separator,or if there is no separator present, as it leaves thetrough without being superheated (h

wo,2), is calculated

by equation (42):

,2 *wo f fgh h x h= + (42)

where hg

is the enthalpy of liquid water at thesaturation temperature.

For the second iteration of this section, the meanreceiver temperature (T

rm) is calculated using equation

(43) and the characteristics from the first iteration:

( )ln1' *2

D Do iT T Qrm ufm h k

f

= + +

(43)

ThirThirThirThirThird Evaluation Section: Superd Evaluation Section: Superd Evaluation Section: Superd Evaluation Section: Superd Evaluation Section: Superheating the Steam inheating the Steam inheating the Steam inheating the Steam inheating the Steam inthe Northe Northe Northe Northe Normal Tmal Tmal Tmal Tmal Trrrrroughoughoughoughough

The evaluation length of superheating in the normaltrough (L

e,w) can be defined by two means. If a

superheating section of normal trough exists after theseparator, then the length is defined by equation (44),

and the mass flow for evaluation is the mass flow outof the separator (m

s).

Fig 4. Transition of Flow as a Fluid Temperature Increases.

7/31/2019 v32_187_199

9/13


L1 = L/3 L2 = L/3

To1 = ? To2 = ?T,in To3 = ToH = ?

L3 = L/3

Section 1 Section 2 Section 3

,L L Le w sep= (44)

where L= n* l . (44a)

If the water is fully vaporized before the separator,then the superheating evaluation length for the normal

trough is defined by equation (45). This equation isapplicable if there is a superheating section of theregular trough or not.

,L L Le w b= (45)

The average temperature of the receiver (Trm

) forthe first iteration is calculated using equation (32) asdescribed in section 4.

The enthalpy of the water out of this section (hwo3

)is given by equation (46):

3

Quh hgwo ms= + (46)

Fourth Evaluation Section: Superheating the Steam inFourth Evaluation Section: Superheating the Steam inFourth Evaluation Section: Superheating the Steam inFourth Evaluation Section: Superheating the Steam inFourth Evaluation Section: Superheating the Steam inthe Superheater Sectionthe Superheater Sectionthe Superheater Sectionthe Superheater Sectionthe Superheater Section

The Superheater Section is a physically larger sizesection of the parabolic trough, which requires its ownfull analysis of the optical characteristics described inSection 3 using the geometry of the larger trough. Thesimulation incorporates this analysis and evaluates theSuperheater Section similar to the previous sections.The input steam may be at one of two conditions: ifthere is no superheating of the steam in the regular

section of the trough, then the input steam will besaturated vapor, if there is superheating in the regularsection of the trough, then the steam will be at theoutput conditions of the third section. Since the likelygain for the steam in this section at a higher temperatureis less than if the steam were at the saturationtemperature, equation (47) is used to estimate the meanreceiver temperature (T

rm) for the first iteration if the

input steam has been superheated. If the steam issaturated vapor, then equation (32) is used. This isaccomplished through an if-then statement.

0.05* *,1 *AaT T Sirm st C mp

= + (47)

Oil as the Heat TOil as the Heat TOil as the Heat TOil as the Heat TOil as the Heat Transfer Fluidransfer Fluidransfer Fluidransfer Fluidransfer FluidThe simulation divides the parabolic trough into

three sections to evaluate oil as the HTF. The input forthe second and third section is simply the output fromthe first and second section, respectively. It was deemedappropriate to use only three sections to evaluate thetrough because of the iterative nature of the simulation(Fig 5).

With oil as the heat transfer fluid, the equations ofSection 4 need very little modification. It is only worthy

to note that the evaluation length for this analysis isgiven by equation (48).

*, 3

l nLe H = (48)

Once the useful gain for the trough is calculated,

the temperature out of the oil (ToH) is calculated byequation (49).

*

QuT TioH m Cp= +

(49)

The output enthalpy of the oil (hoH

) is then evaluatedby interpolating from the lookup table of the oilproperties.

EfEfEfEfEfficiency of the Parabolic Tficiency of the Parabolic Tficiency of the Parabolic Tficiency of the Parabolic Tficiency of the Parabolic TrrrrroughoughoughoughoughThe efficiency of the parabolic trough is the amount

of useful gain from the parabolic trough divided by the

amount of energy input to the parabolic trough area.It is calculated by the simulation in equation (50).

,

*

Qu tottrough I Aadirect

= (50)

where Qu,tot

is the total useful gain for the trough forone hour, I

direct= the direct beam radiation for one hour,

andAa= the area of the aperture/reflector.

Output to Thermal Storage and EfficienciesOutput to Thermal Storage and EfficienciesOutput to Thermal Storage and EfficienciesOutput to Thermal Storage and EfficienciesOutput to Thermal Storage and EfficienciesFor the simulation, the trough is assumed to provide

heat to a thermal storage system. The advantage ofhaving a thermal storage system is that it can store thethermal energy generated during the peak radiationhours for later use when solar radiation is unavailable.The simulation assumes that there is a backup heatingsystem to keep the thermal storage at a certain minimumtemperature in the event that the solar energy input isnot adequate to do so. The thermal storage system isused to power a steam engine and generator or PowerConversion Unit (PCU) via a thermal water loop. Thisload may be constant or may have a distinct hourly load

profile.

Thermal StorageThermal StorageThermal StorageThermal StorageThermal StorageThe simulation models the thermal storage as an

unstratified thermal storage tank as described inreference2. The storage tank temperature change isevaluated on an hourly basis corresponding to the

Fig 5. Evaluation Sections Using Oil as the HTF.

7/31/2019 v32_187_199

10/13


Parabolic

Trough

Parabolic

Trough

Superheater

(optional)

PCU

Backup

Thermal

Storage

To

Ts

Qu,bu

LsQu,t

Qstore

Qloss

Fig 6. Basic Thermal Analysis of Thermal Storage.

simulation of the parabolic trough. The governingequation is described in equation (51).

, ,*( ) ( ) *( )

Q Q Lst u t u buT Ts smCp UA T T s s s a

+ + = +

(51)

where Tsisthe initial temperature of the storage

media, Ts+ = the temperature of the storage media after

one hour, (mCp)

sis mass times the specific heat of the

storage media, t is one hour, Qu,t

is thermal input fromthe parabolic trough, Q

u,buis thermal input from the

backup heater, Lsis the thermal output to the PCU,

(UA)s is loss-coefficient-area product of the storagesystem, and Tais ambient temperature.

Parabolic TParabolic TParabolic TParabolic TParabolic Trrrrrough Inputough Inputough Inputough Inputough InputIf the temperature of the heat transfer fluid from

the parabolic trough is above the initial temperature ofthe storage media, the thermal input from the parabolictrough (Q

u,t) is defined by equation (52). If the

temperature of the HTF is below the initial temperatureof the storage media, the HTF is incapable of providingthermal input.

( )*,Q m h hu t totif= (52)where h

tiis the enthalpy of the HTF out of the

trough, hto

is the enthalpy of the HTF at Ts, andm

fis mass

flow of the HTF out of the trough.

Output to PCUOutput to PCUOutput to PCUOutput to PCUOutput to PCUThe thermal output to the PCU per hour is calculated

by equation (53).

3600*gen

lLsEpcu

= (53)

wheregenlis the load on the generator per hour, and

Epcu

is efficiency of the PCU at load.

Backup Heater InputBackup Heater InputBackup Heater InputBackup Heater InputBackup Heater InputThe Backup System is used to keep the temperature

of the storage media at the temperature set point. If theparabolic trough cannot provide enough input to thethermal storage, the input is defined by equation (54):

( )*( ) ( ) *( ),,Q T T mC L UA T T s p s s s s as setu bu

= + + (54)

where Ts,set

is the temperature set-point of thethermal storage.

Solar FractionSolar FractionSolar FractionSolar FractionSolar FractionThe solar fraction is the amount of input to the

system that is from solar energy compared to the totalinput to the system. It is defined for one day by equation(55).

,

, ,

Qu tSF

Qu Qt u bu

=+ (55)

Use of the Simulation as a Sizing TUse of the Simulation as a Sizing TUse of the Simulation as a Sizing TUse of the Simulation as a Sizing TUse of the Simulation as a Sizing Tooloolooloolool

The solar parabolic trough power plantspecification for the simulation is shown in Table 2.

Comparison of WComparison of WComparison of WComparison of WComparison of Water and VP1 Oil for Maximumater and VP1 Oil for Maximumater and VP1 Oil for Maximumater and VP1 Oil for Maximumater and VP1 Oil for MaximumClear Sky RadiationClear Sky RadiationClear Sky RadiationClear Sky RadiationClear Sky Radiation

In order to demonstrate the capability of thesimulation, an evaluation was performed for a 96 meterparabolic trough with characteristics similar to the LS3design from reference7. The length of 96 meters waschosen because it is twice the size of the existing troughat the School for Renewable Energy Technology (SERT),and is one proposed size for the BioSun project. The

load on the PCU was considered to be a constant 25 kWand the efficiency of the PCU to be a constant 40%. The

7/31/2019 v32_187_199

11/13


Table 2. Input for the simulation.

Solar TSolar TSolar TSolar TSolar Trrrrrough Concentratorough Concentratorough Concentratorough Concentratorough Concentrator

Width (w) [m] 5.77Module length (l) [m] 6Focal length (f) [m] 1.71

Gap width (ao) [m] 0.1Specific reflectance (rs) 0.9Number of modules (n) 16Incident angle modifier K() LS3Dispersion angle (D) [degree] 0.1Solar Trough ReceiverCover diameter (D

c) [m] 0.09

Receiver inner diameter (Di) [m] 0.05

Receiver outer diameter (Do) [m] 0.07

Absorber length (l) [m] 12.5Thermal conductivity (k

a) [W/m.C] 47.6

Receiver emittance (r) 0.91

Cover emittance (c) 0.88

Cover thickness (L) [m] 0.0025

Cover extinction coefficient (K) [m-1] 32Specular absorbance (

n) 0.93

Cover refractive index (n2) 1.526

Heating fluid (Water = 1, HTF = 2) 1Superheater Section ConcentratorSuperheater width (w s) [m] 5.77Superheater module length (l) [m] 20/40Superheater focal length (f s) [m] 1.71Number of superheater modules (n s) 2Superheater specific reflectance (rs s) 0.9Superheater incident angle modifier K(),s LS3Dispersion angle (D) [degree] 0.1Superheater Section ReceiverSuperheater cover diameter (D

c,s) [m] 0.15

Superheater receiver inner diameter (Di,s) [m] 0.08Superheater receiver outer diameter (D

o,s) [m] 0.1

Superheater absorber length (l,s) [m] 6Superheater thermal conductivity (k

a,s) [W/m.C] 47.6

Superheater receiver emittance (r,s) 0.91

Superheater cover emittance (c,s) 0.88

Superheater cover thickness (L,s) [m] 0.0025Superheater cover extinction coefficient (K,s) [m -1] 32Superheater specular absorbance (

n,s) 0.93

Superheater cover refractive index (n2,s) 1.526

Superheater after which module? 0OtherLatitude (Phitsanulok Province) [degree] 16.75Day of the year (n) 116

Ambient ConditionsTemperature (T

a) [K] 298

Wind Velocity (Va) [m/s] 5

Fluid ConditionsInlet Temperature (T

i) [K] 323

Mass flow (m) [kg/s] 0.07Inlet pressure (P

i) [MPa] 1

Separator after which module? (n,sep) 16Thermal StorageMass of storage media (ms) [kg] 1,000Set point temperature of storage (T

s) [K] 498

Loss coefficient area product (UA)s

[W/K] 10Engine/Power Conversion Unit (PCU)Daily constant load on generator (gen

l) [kW] 25

Efficiency of PCU (Epcu) 0.5

trough was evaluated with both water and oil as theHTF, but with slightly different parameters includingthermal storage mass and a Superheater trough sectionlength.

WWWWWater Output for a Maximum Clear Skyater Output for a Maximum Clear Skyater Output for a Maximum Clear Skyater Output for a Maximum Clear Skyater Output for a Maximum Clear Sky

Radiation InputRadiation InputRadiation InputRadiation InputRadiation InputThis evaluation was performed with two lengths ofa Superheater section with optical characteristics similarto the LS3 design, 20 and 40 meters, in order toinvestigate if a greater length of trough is possible toproduce superheated steam. The mass of the thermalstorage (m

s) was found to be inconsequential because

the parabolic trough was not able to provide enoughenergy to charge the thermal storage. Fig 7 and Fig 8show the temperatures and energy inputs of the system.

As would be expected, the trend shows that a largerSolar Fraction (SF) can be achieved with a longer

Superheater section. However, the length of the regulartrough section is the parameter that is more responsiblefor the energy output of the trough, because this dictateshow much water is vaporized. If the amount of waterthat is vaporized and is able to be superheated is small,the temperature output will be high, but the energyoutput will be low. Therefore, the mass flow out of theseparator and the placement of the separator are veryimportant characteristics to study when using thesimulation. These considerations must be taken intoaccount when deciding the final size of the troughsections.

VP1 Oil Output for a Maximum Clear SkyVP1 Oil Output for a Maximum Clear SkyVP1 Oil Output for a Maximum Clear SkyVP1 Oil Output for a Maximum Clear SkyVP1 Oil Output for a Maximum Clear SkyRadiation InputRadiation InputRadiation InputRadiation InputRadiation Input

This evaluation was performed with two differentarbitrary but realistic masses of thermal storage, 4,000and 6, 000 kg. The VP1 thermal oil was not evaluatedwith a Superheater section because the oil has amaximum temperature of 415 Celsius. Fig 9 and Fig 10show the temperatures and energy inputs of the system.

The thermal storage mass plays a significant role forthis evaluation because the parabolic trough is able to

produce enough energy to charge the thermal storage.As can be seen from the results, a larger storage massequates to a larger solar fraction. This is because thetemperature of the storage increases slower with alarger mass, and the amount of energy input from thetrough depends on the temperature difference betweenthe oil and the thermal storage.

CONCLUSION

The simulation described in this paper was createdto be a tool to determine the optimum parameters for

a parabolic trough as the primary input to a hybridpower plant. This simulation tool is necessary due to

7/31/2019 v32_187_199

12/13


0

100

200

300

400

500

600

700

800

900

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour

Temperature(K)

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

45,000

Energy(kJ/h)

Temp of Steam Temp of Storage Energy from B ackup Energy from Trough

Temperature an d Ene rgy with 9 6 Meter Wa ter Oil Trough with Storage Mass of 4 ,000 k g, SF = 47.2%

Other Conditions: M ass

Flow = 0.31 PCU

Efficiency = 40%

Pressure in = 1 M p a

0

100

200

300

400

500

600

700

800

900

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour

Temperature(K)

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

18,000

Energy(kJ/h)

Temp of Steam Temp of Storage Energy from Backup Energy from Trough

Temperature and Energy with 96 Me te r Wate r Trough with 40 Me ter Supe rheater, SF = 2 2.7%

Other Conditions:

Mass Flow = 0.08 PCU

Efficiency = 4 0%

Pressure in = 1 M p a

Storage M ass

Inconsequential

0

100

200

300

400

500

600

700

800

900

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour

Temper

ature(K)

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

18,000

Energy(kJ/h)


Temperature and Energy with 96 M ete r Wate r Trough with 20 M e ter Supe rheater, SF = 1 9.8%

Other C onditions:M ass Flow = 0.08 PCU

Efficiency = 40 %

Pressure in = 1 Mp a

Storage M ass

Inconsequential

Fig 7. Water Output 1 for Maximum Clear Sky Radiation.

Fig 8. Water Output 2 for Maximum Clear Sky Radiation.

Fig 9. VP1 Oil Output 1 for Maximum Clear Sky Radiation.

7/31/2019 v32_187_199

13/13


0

100

200

300

400

500

600

700

800

900

1,000

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour

Temperat

ure(K)

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

45,000

50,000

Energy(kJ/h


Temperature and Energ y with 96 Met er Wate r Oil Trough with Storage Mass of 6,000 k g, SF = 47.2%

Other Cond ition s:

M ass Flow = 0.31 PCU

Efficiency = 40%

Pres sure in = 1 Mp a

the many parameters that characterize the system thatmust be considered when determining the output ofthe system. It was constructed using methods fromwidely accepted reference materials and assumptionsto the best ability. However, it should prove useful as atool for approximately sizing a parabolic trough for ahybrid power plant or for building block to morecomplex simulations.

The result of this study gives guidance for thepossible use of parabolic trough application for the

BioSun project. However, the detail study of eachcomponent is needed for the final decision of thesystem. Further studies should include a dynamicsimulation for the parabolic trough and a model for thepower plant in order to predict the system behaviorunder climate of Thailand.

Fig 10. VP1 Oil Output 2 for Maximum Clear Sky Radiation.

REFERENCES

1. Department of Energy Development and Promotion andSilapakorn University (1999) Solar Energy Map of Thailand,Jirangrath Printing, Bangkok.

2. Duffie JA and Beckman A (1991) Solar Engineering of ThermalProcesses, 2nd Edition, John Wiley & Sons Inc.

3. Platforma Solara de Alemaria. (1998) Solar Thermal ElectricityGeneration.

4. Cengel YA and Turner RH (2001) Fundamentals of Thermal-Fluid Sciences McGraw-Hill.

5. Thepa S, Kirtikara K, Hirunlabh J and Khedari J (1999)

Improving indoor conditions of a Thai-style mushroomhouse by means of an evaporative cooler and continuousventilation, Renewable Energy 1717171717, 359-3693.

6. Therminol VP-1. (1999) Technical Service Bulletin 7239115B,Solutia Inc.

7. Odeh SD, Morrison GL and Behnia M (1996) Thermal Analysisof Parabolic Trough Solar Collectors for Electric Power Generation,School of Mechanical and Manufacturing Engineering,University of New South Wales, Sydney, Australia.

v32_187_199

Documents