Applied Energy 106 (2013) 287–300

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Applied Energy

journal homepage: www.elsevier .com/locate /apenergy

Modeling and co-simulation of a parabolic trough solar plantfor industrial process heat

0306-2619/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.apenergy.2013.01.069

⇑ Corresponding author. Tel.: +351 966341445.E-mail address: ricardosilva@ual.es (R. Silva).

R. Silva a,⇑, M. Pérez a, A. Fernández-Garcia b

a CIESOL Centro Mixto Universidad de Almería – CIEMAT, Almería 04120, Spainb CIEMAT – Plataforma Solar de Almería, Ctra. Senés, km 4, E04200 Tabernas, Almería, Spain

h i g h l i g h t s

" A tri-dimensional dynamic complex model of a parabolic-trough collector is proposed." The collector model was validated with experimental data and agrees very well." An innovative co-simulation integration environment for PTC plants is developed." Co-simulations with complex dynamic and simplified stationary models were compared." Co-simulations for a reference solar industrial process heat scenario are presented.

a r t i c l e i n f o

Article history:Received 24 June 2012Received in revised form 14 January 2013Accepted 16 January 2013Available online 27 February 2013

Keywords:Parabolic-trough collectorsProcess heatCo-simulationTISCModelicaTRNSYS

a b s t r a c t

In the present paper a tri-dimensional non-linear dynamic thermohydraulic model of a parabolic troughcollector was developed in the high-level acausal object-oriented language Modelica and coupled to asolar industrial process heat plant modeled in TRNSYS. The integration is performed in an innovativeco-simulation environment based on the TLK interconnect software connector middleware. A discreteMonte Carlo ray-tracing model was developed in SolTrace to compute the solar radiation heterogeneouslocal concentration ratio in the parabolic trough collector absorber outer surface. The obtained resultsshow that the efficiency predicted by the model agrees well with experimental data with a root meansquare error of 1.2%. The dynamic performance was validated with experimental data from the Acurexsolar field, located at the Plataforma Solar de Almeria, South-East Spain, and presents a good agreement.An optimization of the IST collector mass flow rate was performed based on the minimization of anenergy loss cost function showing an optimal mass flow rate of 0.22 kg/s m2. A parametric analysisshowed the influence on collector efficiency of several design properties, such as the absorber emittanceand absorptance. Different parabolic trough solar field model structures were compared showing that,from a thermal point of view, the one-dimensional model performs close to the bi-dimensional. Co-simulations conducted on a reference industrial process heat scenario on a South European climate showan annual solar fraction of 67% for a solar plant consisting on a solar field of 1000 m2, with thermal energystorage, coupled to a continuous industrial thermal demand of 100 kW.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Co-simulation is an innovative simulation concept that consistson coupling distributed parallel simulation tools in an integratedenvironment that manages the data flow and synchronization be-tween them [1–3]. This modeling and simulation philosophy ex-plores the synergies of combining different tools in a cooperativeway, hence allowing the development of more complex overallmodels in a shorter time. In spite of these advantages there are still

at present no known studies of co-simulation applied to parabolictrough solar plants.

The classical parabolic trough solar plant annual simulationapproach typically relies on simplified stationary collector mod-els that are built from empiric efficiency data. This type of ap-proach, however, has a major drawback in the fact that it doesnot model many important physical phenomena that occur inthe collector, such as the dynamic effects, e.g. time constantand transport delay, fluid velocity and wind speed influence onefficiency. Furthermore, it does not contemplate specific solarfield geometry in detail, such as the row and series bi-dimensional distribution, typically considering the entire solar

Nomenclature

Aa absorber cross-sectional area, m2

Ac collector aperture area, m2

Af fluid cross-sectional area, m2

Ag glass envelope cross-sectional area, m2

Al fluid lateral area, m2

Cf thermo-hydraulic cost functionCp fluid specific heat capacity at constant pressure, J kg�1 -

K�1

D absorber tube internal diameter, mDe absorber tube external diameter, mDg glass tube internal diameter, mDge glass tube external diameter, mdq infinitesimal heat transfer, Wdx differential of the x-coordinate, mdh differential of the h-coordinate, radEi absolute error of collector efficiency for an individual

test point, %Emax maximum absolute error of collector efficiency for an

individual test point, %Et transient energy accumulation rate on infinitesimal

fluid element, Wf friction factorfbs fraction of collector aperture area shadedGb normal direct solar irradiance, W m�2

haf heat convection coefficient between fluid and absorber,W m�2 K�1

hgc heat convection coefficient between glass envelope andambient, W m�2 K�1

ka absorber thermal conductivity, W m�1 K�1

kf fluid thermal conductivity, W m�1 K�1

Ko dust, misalignment, and imperfections optical coeffi-cient

Kh incidence angle modifier coefficientL tube length, mLp spacing between parallel rows, m_m mass flow rate, kg s�1

N total number of test pointsNp number of collector in parallelNs number of collector in seriesNuD Nusselt number of the interior fluidNuDGC Nusselt number of the exterior windpi inlet pressure, PaPi internal tube perimeter, mpo outlet pressure, PaPr Prandtl number_QL collector total thermal losses to environment, W_QH collector hydraulic power consumed, Wq12,conv heat flow rate exchanged by convection between fluid

and absorber, Wq2,cond heat transfer by conduction in the absorber, Wq2,irr irradiance absorbed in the absorber, Wq21,conv heat flow rate exchanged by convection between absor-

ber and fluid, Wq23,rad heat flow rate by radiation between absorber and glass

envelope, W

q3,irr irradiance absorbed in the glass envelope, Wq3a,conv heat flow rate by convection from glass envelope to

ambient, Wq3s,rad heat flow rate by radiation from glass envelope to sky,

Wqe,in fluid element inlet enthalpy flow rate, Wqe,out fluid element outlet enthalpy flow rate, WRaD Rayleigh numberReD Reynolds numberT1 fluid average temperature, KT2 absorber average temperature, KT3 glass envelope temperature, KTa absorber temperature, KTamb ambient temperature, KTf fluid temperature, KTm fluid average temperature, KTs sky temperature, KV fluid infinitesimal element volume, m3

Vf fluid velocity, m s�1

W aperture width, mXi vector of test conditions for point ia thermal diffusivity of annular air, m2 s�1

ag glass tube absorptanceao absorber absorptanceao absorber absorptanceb collector slope, radDT average fluid temperature above ambient temperature,

Ke absolute roughness, mea absorber emittanceeGt glass tube emittancegexp measured efficiency at test point, %gmodel model predicted efficiency at test point, %h incidence angle, radm kinematic viscosity, m2 s�1

q fluid density, kg m�3

qo mirror reflectanceso glass envelope transmittance

AbbreviationsDAE differential algebraic equationsFDM finite difference methodFVM finite volume methodIST industrial solar technologyLCR local concentration ratioMCRT Monte Carlo ray tracingNEP new energy partnersODE ordinary differential equationPDE partial differential equationPSA Plataforma Solar de AlmeriaPTC parabolic-trough collectorRMSE root mean square errorSHC solar heating and coolingSIPH solar industrial process heatTISC TLK inter software connector

288 R. Silva et al. / Applied Energy 106 (2013) 287–300

field area to be concentrated in a unique algebraic equation. Onthe other hand, the studies that address parabolic trough collec-tor modeling in detail are mostly limited to short-term simula-tion, not having the necessary integration level to performannual plant simulations. Forristal et al. [4] developed a stea-dy-state parabolic trough collector (PTC) model based on energybalances and constitutive relationships. He et al. [5] developed a

finite volume method PTC model coupled with a Monte Carloray-tracing method. Padilla et al. [6] developed a one dimen-sional numerical model of a PTC. Yebra et al. [7] developed aone dimensional finite volume method PTC model with direct-steam generation using an experimentally identified heat losscurve. Camacho et al. [8] developed a one dimensional dynamicmodel coupled with an experimentally identified heat loss curve.

Absorber Glass Envelope

FluidTa

T3

Tf

Concentrator

Fig. 1. Temperatures in a cross-section of the parabolic trough collector.

R. Silva et al. / Applied Energy 106 (2013) 287–300 289

In the present paper an innovative environment to perform an-nual co-simulation of parabolic trough process heat plants coupledwith complex collector models is proposed. A tri-dimensional dy-namic non-linear model of a parabolic trough collector is devel-oped in Modelica and coupled with a solar industrial processheat plant in TRNSYS. The integration is performed in a co-simula-tion environment based on the TISC software middleware fromTLK. A discrete Monte Carlo ray-tracing model was developed inSolTrace to compute the solar radiation heterogeneous local con-centration ratio on the absorber outer surface.

Industrial process heat in the medium temperature range (100–250 �C) has been identified as a very promising and unexploredsector for solar thermal energy, mainly due to the enormous sizethat this market represents [9–12]. In EU countries, the industrialsector represents the biggest share of the total energy consump-tion, at an average of 30% of the total primary energy consumption,[9]. The largest part of these energetic requirements comes in theform of heat below 250 �C where the use of solar energy is a suit-able option, [13,14]. Studies performed by Vannoni et al. [13] with-in the frame of Task 33 of the International Energy Agency SHC andSolarPACES task IV have identified several European potential sec-tors for solar industrial process heat (SIPH). Among them are theplastics, textile, food, paper, chemistry, and surface treatmentsindustry. Schweiger et al. [15] identified the most relevant poten-tial industrial sectors for SIPH for the regions of Spain and Portugal.Another more recent study of Schweiger et al. [16] evaluated thepotential of thermal solar energy for the industrial sector in Spain.In spite of the enormous potential of SIPH, there are at present veryfew solar process heat plants. Vannoni et al. [13] reported only 90operating solar process heat plants worldwide, corresponding to avery small fraction of the total solar thermal available. This lack ofdissemination is attributed to some remaining barriers, such ascomplex solar system integration, insufficient design guidelines,and economical constraints, [17]. There are at present solar ther-mal collector technology available to supply thermal energy toindustrial processes [18–20]. Within the frame of Task 33/IV ofIEA/SolarPACES, Weiss et al. [21] developed a survey on availableconcentrating and non-concentrating solar collector technologies,focusing on their operating temperature, estimated costs, and stateof development. Kalogirou et al. [22] compared the thermal perfor-mance and economical revenue of several medium-temperatureconcentrating and non-concentrating solar collectors at differenttemperature levels. The results of this study showed that thesmall-sized parabolic-trough collectors achieve the highest eco-nomical revenue to supply heat between 120 �C and 200 �C. Theseconclusions are further corroborated by the results obtained by Rif-felmann et al. [23], which in a comparison between flat plate, vac-uum tube with compound parabolic concentrator and parabolictroughs also concluded that the parabolic troughs are the most costeffective, on the 80–200 �C temperature range. Small sized para-bolic troughs are single-axis tracking linear concentrating collec-tors that are based on the same basic physical principles as theirlarge-sized counterparts, but are optimized to supply he particularthermal demands on the 100–250 �C temperature range. This tech-nology has evolved on the past recent years increasing its presencein the solar thermal energy scenario. The main emphasis on PTCdevelopment has been placed on optimizing the cost-efficiency ra-tio, weight, modularity, durability and operation and maintenancecosts [24–29]. Some examples of recent small-sized parabolic-troughs are the CAPSOL collector developed at the Plataforma Solarde Almeria, Spain, [30,31], and the NEP collector, from New EnergyPartners, [32]. Other examples are the collectors from Abengoa So-lar, previously made by Industrial Solar Technology (IST), the SOL-ITEM collector from SOLITEM Gmbh, and PARASOL from AEE,INTEC. A survey on parabolic trough collectors available and theirapplications is presented in [33,34].

2. Parabolic trough collector model

2.1. Introduction

Parabolic trough solar collectors are constituted by a parabolicreflector that concentrates the parallel incoming solar direct radi-ation on an absorber cylindrical tube, which is typically coveredwith a selective coating to reduce radiation losses to the environ-ment. A fluid circulates in the absorber tube interior and extractsa fraction of the energy absorbed in the form of heat. A cylindricalglass envelope concentric to the absorber tube is used to reducethe thermal losses by convection to ambient. A tracking systemmoves the collector to ensure that the parabola axis faces thesun. Fig. 1 shows the collector main components.

The parabolic trough collector plays a key-role in the overallperformance of the solar plant, and thus particular detail was de-voted to its modeling. Therefore a complex tri-dimensional dy-namic non-linear thermohydraulic parabolic trough collectormodel is proposed. The implementation was performed in thehigh-level acausal language Modelica to explore its powerful dif-ferential algebraic solving capabilities and object-oriented fea-tures. The proposed model is constituted by three coupled sub-models: an optical model, a thermal model and a hydraulic model.

2.2. Optical model

The parabolic trough collector optical model was developed inthe SolTrace software from NREL [35,36] which is based on aMonte Carlo ray tracing method. The Monte Carlo ray tracing is astatistical method that consists on following the path of a seriesof randomly generated rays through a set of optical elements,[37,38]. The main objective pursued with this approach is to calcu-late the radiation flux angular local concentration ratio in the ab-sorber surface to establish more detailed boundary conditions forthe thermal model. A pillbox approximation was considered forthe sun shape, with a half-angle of 4.6 mrad. The elements consid-ered in the optical analysis were the parabolic trough concentrator,the absorber tube and the glass envelope. The interaction of therays with the elements is considered to be reflective, in the caseof the concentrator and the absorber tube, and refractive in thecase of the glass envelope. The number of ray intersections usedwas approximately 1 � 105. Fig. 2 shows the results of the ray trac-ing method applied to the IST collector (only 50 rays are presentedin the figure to ease the display).

The number of ray intersections in the different elements allowscalculating the solar radiation flux superficial distribution and thusthe local concentration ratio. Fig. 3 shows the local concentrationratio (LCR) distribution obtained for half of the absorber perimeter,for the ACUREX and the IST parabolic trough collectors. A maxi-mum local concentration ratio of LCR = 39 and LCR = 43 are ob-tained at an angular position of a = 120� and a = 110� for the IST

Fig. 2. Monte Carlo ray-tracing model of the IST parabolic trough collector inSolTrace.

20 40 60 80 100 120 140 1600

10

20

30

40

50

Angle [º]

Loca

l Con

cent

ratio

n R

atio ACUREX

IST

Fig. 3. Local concentration ratio angular distribution in the absorber outer surface.

q12conv(x,t)

qe,out(x,t)

qe,in(x,t)

Tf(x,t)

dx

Fig. 4. Energy fluxes on an infinitesimal fluid element.

290 R. Silva et al. / Applied Energy 106 (2013) 287–300

and ACUREX collector respectively. This difference is justified bythe fact that the IST and ACUREX collectors have different focallengths and geometry and therefore concentrate the incoming di-rect solar irradiance on different relative angular locations. TheLCR approaches a unitary value in the absorber top position sincein that section the absorber receives mainly non-concentrated so-lar radiation. By varying the intensity of the incident solar radia-tion it was observed that the LCR distribution remainsapproximately constant.

2.3. Thermal model

2.3.1. FluidThe fluid temperature evolution along the longitudinal direc-

tion and in time is modeled by performing an energy balance toan infinitesimal fluid element. Some initial assumptions are madeto simplify the problem while retaining the most important phys-ical phenomena. The flow is considered one-dimensional due tothe predominance of the velocity vector in the longitudinal direc-tion, in comparison with radial and angular direction. Fluid is con-sidered incompressible, which is a good assumption for liquids[39]. Axial conduction in the fluid is ignored since the fluid conduc-tivity is very low. Hydraulic and thermal entrance effects are not

considered since there is a pipe section before the fluid reachesthe collectors and the tube diameter is small in comparison withthe tube length. The energy balance fluxes for a cylindrical infini-tesimal fluid element are shown in Fig. 4.

The fluid model is developed by performing an energy balanceto all the fluxes on a fluid infinitesimal control volume, as shownin the following equation,

_Etðx; tÞ ¼ _qe;inðx; tÞ � _qe;outðx; tÞ þ _q12 convðx; tÞ ð1Þ

The transient energy term represents the rate of accumulation ofenergy in the infinitesimal volume, and is given by the equation,

_Etðx; tÞ ¼ qVCp@Tf ðx; tÞ

@t¼ qAf Cp

@Tf ðx; tÞ@t

dx ð2Þ

where q is the density, V is the infinitesimal element volume, Cp isthe specific heat at constant pressure, Tf, is the fluid element tem-perature, Af is the fluid cross-section and dx is the infinitesimal ele-ment length. The balance of enthalpy terms is given by the firstorder differential of enthalpy in the x-axis direction,

_qe;inðx; tÞ � _qe;outðx; tÞ ¼ � _mCp@Tf ðx; tÞ@x

dx ð3Þ

where _m represents the mass flow rate. The convection between thefluid element and the surrounding absorber tube infinitesimal sur-face _q12;conv is given by the following equation,

_q12 convðx; h; tÞ ¼ hAlðTs � T1Þ ¼ haf AlðTaðh; tÞ � Tf ðx; tÞÞ ð4Þ

where haf represents the heat transfer coefficient between the ab-sorber and the fluid, Al represents the surface section infinitesimalheat exchange area, Ta is the absorber element temperature and Ts

is the surface temperature. The surface area may be replaced bythe following equation, where dh represents the infinitesimal angle,

Al ¼D2

dhdx ð5Þ

This results in the following equation for the heat transfer betweenthe surface section and the fluid element by convection,

_q12 convðx; h; tÞ ¼ hafD2ðTaðh; tÞ � Tf ðx; tÞÞdhdx ð6Þ

The total heat transfer by convection for a given fluid element in aposition x is the integral of all the infinitesimal heat fluxes along theangular direction and is given by,

_q12 convðx; tÞ ¼Z 2p

0haf

D2ðTaðh; tÞ � Tf ðx; tÞÞdhdx ð7Þ

The energy balance in the fluid element is obtained by adding all theterms, and dividing the expression by dx resulting in the followingequation,

R. Silva et al. / Applied Energy 106 (2013) 287–300 291

Af qCp@Tf ðx; tÞ

@t¼Z 2p

0haf

D2ðTaðh; tÞ � Tf ðx; tÞÞdh� _mCp

@Tf ðx; tÞ@x

ð8Þ

which represents a non-linear first order transient partial differen-tial equation (PDE) with variable coefficients. The convection coef-ficients are obtained from heat transfer correlations considering aforced internal fluid flow on a tube with a constant heat flux. Theconstant flux approximation is supported by the fact that parabolictrough collectors typically operate at large Reynolds to increase theturbulence on the fluid flow, and at these regimes turbulent diffu-sion helps to reduce spatial temperature gradients on fluid and ab-sorber tube, therefore creating a more homogeneous heat transfer.The effect of heterogeneous heat flux in the fluid flow of single-phase fluid flow may be more relevant at small Reynolds numberswhen free convection starts to play an important role. Moreover,the constant heat flux consideration maintains the problem numer-ically efficient to allow performing dynamic simulations at anaffordable computational cost.

The Nusselt number of the fluid inside the absorber tube, NuD isdefined by the following equation:

NuD ¼hDkf¼ haf D

kfð9Þ

where D is the tube diameter and Kf is the thermal conductivity ofthe fluid. In the laminar flow case NuD is a constant, valid for ReD<2300

NuD ¼ 4:36 ð10Þ

In the turbulent flow case NuD is given by the Gnielinski correlation,[40,41].

NuD ¼f=8ðReD � 1000ÞPr

1þ 12:7ðf=8Þ0:5ðPr2=3 � 1Þð11Þ

This correlation is valid for 0.5 < Pr < 2000 and 3000 < ReD < 2 � 106

where Pr is the Prandtl number, ReD is the Reynolds number, and allproperties are evaluated at the fluid mean temperature Tm. f is thefriction factor and is calculated by the following equation, whichis valid for smooth pipes, transitional rough range, and fully roughflow [39],

1f 1=2 ¼ �2:0 log

e=d3:7þ 2:51

Redf 1=2

� �ð12Þ

2.3.2. AbsorberThe absorber model is developed by performing an energy bal-

ance to an infinitesimal element in angular coordinates. The radialthermal gradient is not considered since the absorber thickness is

θ

Ta( ,t)θ

Absorber node

Fluid

q2cond( ,t)θ

q2irr( ,t)θq23rad( ,t)θ

q23conv( ,t)θ

q21conv( ,t)θ

θ=0

θ π=

dθ

Fig. 5. Fluid temperature discretization along the longitudinal direction.

small and the conductivity of the absorber material (typicallystainless steel or carbon steel) is high. Longitudinal heat conduc-tion is not considered due to fact that the edges of the collectorare well insulated. A distributed heterogeneous concentrated solarradiation boundary condition is considered in the absorber outersurface. Fig. 5 shows the energy fluxes and temperatures discreti-zation on the absorber tube.

The transient accumulation term is given by,

_Etðh; tÞ ¼ qVCp@Taðh; tÞ

@t¼ q

Aa

pLCp

@Taðh; tÞ@t

dh2

ð13Þ

where Aa is the absorber cross-sectional area. The heat transfer byconvection for a given absorber element in position h is the integralthe infinitesimal heat fluxes along the longitudinal direction and isgiven by,

_q21 convðh; tÞ ¼Z L

0haf

D2ðTaðh; tÞ � Tf ðx; tÞÞdxdh ð14Þ

The gain by solar radiation _q2 irr is given by

_q2 irrðh; tÞ ¼ q0s0a0K0KhðhÞ cosðhÞGbðtÞLCRðhÞDe

2Lð1� fbsÞdh ð15Þ

where Ko represents the effects of the intercept factor, dust, mis-alignment, and tracking errors, Kh is the incidence angle modifier,Gb is the normal direct irradiance, h is the incidence angle, LCR isthe local concentration ratio, q0 is the mirror reflectance,T0 is theglass envelope transmittance and a0 is the absorber absorptance.fbs is the fraction of collector aperture area that is shaded by adja-cent rows and is calculated by Eq. (36), presented latter in the textin the solar field model. The heat transfer by radiation from the ab-sorber tube to the glass envelope is obtained by considering twolong cylindrical gray diffuse surfaces and is given by the expression,

_q23 radðh; tÞ ¼ðDe=2ÞLrðTaðh; tÞ4 � T3ðtÞ4Þdh

1eaþ 1�eGt

eGt

DeDg

ð16Þ

where De and Dg represent the absorber outer diameter and glasstube inner diameter respectively, eGt and ea represent the glass tubeand absorber emittance respectively, and T3 is the glass envelopetemperature. The absorber emittance temperature dependence isconsidered and was approximated by a fit of experimental data pro-vided by the manufacturer at different temperatures.

The heat transfer due to natural convection between the absor-ber and the glass cover may be approximated by the followingexpression, from [42],

_q23 convðh; tÞ ¼Lkeff

ln Dg

De

� � ðTaðh; tÞ � T3ðtÞÞdh ð17Þ

where keff is the effective thermal conductivity and is given by,

keff

k¼ 0:386

Pr0:861þ Pr

� �14

Ra�c� �1=4 ð18Þ

where k represents the fluid conductivity and Ra�c is the Rayleighnumber multiplied by a geometric correction factor for concenter-ing cylinders and is given by,

Ra�c ¼ln Dg

De

� �h i4

L3 D�3

5e þ D

�35

g

� �5 RaL ð19Þ

which is valid for the range 1026 Ra�c 6 10 and where RaL is given

by,

RaL ¼gbðT2 � T3ÞððDg � DeÞ=2Þ3

mað20Þ

292 R. Silva et al. / Applied Energy 106 (2013) 287–300

The thermal angular conduction inside the absorber is given by,

_q2 condðh; tÞ ¼ kL@2Taðh; tÞ

@h2 ððDe=2Þ � ðD=2ÞÞdh ð21Þ

The final equation is obtained adding all the terms and dividing bydh.

qAa

2pLCp

@Taðh; tÞ@t

¼ q0s0a0K0KhðhÞ cosðhÞGbðtÞLCRðhÞDe

2L

�Z L

0haf

D2ðTaðh; tÞ � Tf ðx; tÞÞdx

� ðDe=2ÞLrðTaðh; tÞ4 � T3ðtÞ4Þ1eaþ 1�eGt

eGt

DeDg

� Lkeff

ln Dg

De

� ��ðTaðh; tÞ � T3ðtÞÞ þ ððDe=2Þ � ðD=2ÞÞkL

� @2Taðh; tÞ@h2 ð22Þ

which represents a non-linear transient second order partial differ-ential equation (PDE) with variable coefficients. Since the equationis second order on space and first order in time, two boundary con-ditions and one initial condition are required for the integration.The initial condition is the absorber temperature at the instantt = 0. The boundary conditions can be obtained by taking in consid-eration that in normal operating conditions, disregarding possibleoptical misalignments, the direct solar radiation is on the collectorfocal line and thus the heat transfer problem possesses angularsymmetry. Mathematically this is equivalent to impose a tempera-ture gradient of zero at the vertical and bottom nodes, and can beexpressed by the following conditions,

@Taðh; tÞ@h

�h¼0¼ @Taðh; tÞ

@h

�h¼p¼ 0 ð23Þ

2.3.3. Glass envelopeThe glass envelope model is obtained by performing an energy

balance. The glass is considered to be isothermal and the heattransfer is assumed to occur in the radial direction. The heat con-duction resistance is not considered since the glass thickness isvery small. The accumulation term is given by the expression,

_EtðtÞ ¼ qVCpdTðtÞ

dt¼ qLAgCp

dT3ðtÞdt

ð24Þ

where Ag is the glass envelope cross-sectional area. The heat trans-fer by convection to the ambient _q3a conv can be approximated bynatural convection at low wind speeds, or by forced convectionfor high wind speeds, and its general expression is given by,

_q3a convðtÞ ¼ hgcpDgeLðT3ðtÞ � TambðtÞÞ ð25Þ

where Dge is the glass tube outer diameter. In case of natural con-vection, the Nusselt number from the glass tube to the ambient,NuDgc, is given by the following equations from [40,41],

NuDgc ¼ 0:60þ 0:387Ra1=6D

1þ 0:559Pr3a

� � 916

� �8=27

0BBB@

1CCCA

2

ð26Þ

where Pr3a is the Prandtl number at the average temperature be-tween T3 and Tamb and RaD represents the Rayleigh number, given by,

RaD �gbðT3 � TambÞD3

ge

m3aa3að27Þ

which is valid for RaD < 1012. In case of forced convection NuDgc isgiven by the Eq. (28) from Zhukauskas [40], which is valid for0.7 < Pr < 500 and 1 < ReD < 106.

NuDgc ¼ CRemD Prn Pr

Prs

� �1=4

ð28Þ

where constants C, m and n can be found on [40]. For typical windspeeds the boundary layer formed in the outer surface is laminar forstandard glass tube diameters of small parabolic trough collectors.The external wind speed affects the Reynolds number and the con-stants C and m.

The absorbed solar radiation in the glass tube _q3 irr is also takenin consideration and it is given by,

_q3 irrðtÞ ¼ GbðtÞ cosðhÞAcq0agð1� fbsÞ ð29Þ

where ag is the glass envelop absorptance. Radiation from the glasstube to sky _q3s rad can be approximated by the following equation,

_q3s radðtÞ ¼ rpDgeLeGtðT43ðtÞ � T4

s ðtÞÞ ð30Þ

where Ts is the sky temperature. Adding all the equations gives thefinal equation,

LAgqCpdT3ðtÞ

dt¼ hgcpDgeLðT3ðtÞ � TambðtÞÞ þ GbðtÞ

� cosðhÞAcq0ag � rpDgeLeGt T43ðtÞ � T4

s ðtÞ� �

�Z 2p

0

ðDe=2ÞLrðTaðh; tÞ4 � T3ðtÞ4Þ1eaþ 1�eGt

eGt

DeDg

dh

�Z 2p

0

Lkeff

ln Dg

De

� � ðTaðh; tÞ � T3ðtÞÞdh ð31Þ

which is a first order non-linear transient ODE with variablecoefficients.

2.4. Hydraulic model

A hydraulic model is used to compute the pressure drop evolu-tion along the collector. The pressure distribution is given by,

pðx; tÞ ¼ piðtÞ � hf ðx; tÞqg ð32Þ

where pi is the inlet pressure, g is the gravity acceleration constant,hf represents the head loss and is given by,

hf ðx; tÞ ¼fxD

V2f ðtÞ2g

ð33Þ

where f represents the Darcy friction factor given by Eq. (12), x isthe longitudinal position and Vf is the fluid velocity. In a row of col-lectors the connecting tube internal diameter should be the samethat the absorber tube internal diameter and mismatches shouldnot occur. However due to different standardizations in some casesthere are small mismatches. A sensitivity analysis was performed tostudy the impact of possible diameter mismatches on total pressurelosses. The results show that for a 20% diameter mismatch the pres-sure loss due to diameter expansion and contraction represents2.7% and 3.6% of the friction losses respectively, and hence are con-sidered negligible.

2.5. Implementation

The parabolic-trough collector model was implemented on thehigh-level non-causal object-oriented language Modelica [43]due its capability to handle differential algebraic equations (DAE)systems. Finite difference methods were used to integrate the fluidand absorber PDEs by substituting the spatial derivatives by finitedifference approximations, therefore converting the PDE problemson a set of ODE equations. The time integration of the resulting sys-tems of ODE was performed with the hybrid variable-step solverDASSL from [44]. In cases where the collector fluid is water,

50 100 150 200 250 3000

0.2

0.4

0.6

0.8

1

Tf−Tamb [ºC]

Effic

ienc

y

ExperimentalModel

Fig. 6. Experimental and theoretical efficiency points comparison.

R. Silva et al. / Applied Energy 106 (2013) 287–300 293

properties are obtained from the IAPWS97 international standard,and in the case of thermal oil the properties are calculated byexternal functions.

2.6. Parabolic trough model validation and sensitivity analysis

2.6.1. Thermal efficiencyThe parabolic trough theoretical collector model developed in

this work was validated by comparing the experimental efficiencypoints measured by Dudley et al. during the IST testing (presentedin the Sandia report [45]) with the individual efficiency points pre-dicted by our model at the same conditions. The calculus of the er-ror is performed by executing simulations of the model instationary state at the same individual conditions of each mea-sured experimental point (direct irradiance, mass flow rate, inlettemperature, wind speed, and ambient temperature), and compar-ing the efficiency of each individual point predicted by this modelwith the efficiency of each individual point measured experimen-tally by Dudley et al. [45]. The value of the individual error of a testpoint is given by,

Ei ¼ gmodelðXiÞ � gexpðXiÞ with i ¼ 1; . . . N ð34Þ

where gexp is the experimental efficiency measured at the condi-tions Xi (direct irradiance, inlet temperature, ambient temperature,mass flow rate, wind speed), gmodel is the theoretical efficiency pre-dicted by the model at the same conditions, and N is the total num-ber of test points.

The maximum absolute error is obtained by the followingexpression,

Emax ¼ maxðEiÞ ð35Þ

And the root mean square error is calculated by the followingequation,

RMSE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPNi¼1ðgmodelðXiÞ � gexpðXiÞÞ2

N

sð36Þ

Table 1 shows the characterization data of the IST collector [45].To include additional optical effects such as the intercept factor

[50], tracking system inaccuracy, misalignment, and dust accumu-lation on the reflector and glass envelope, a combined optical losscoefficient of Ko = 0.9 was considered. Fig. 6 shows the comparisonresults obtained including the uncertainty on experimentalmeasurements.

The results show a very good agreement between the efficiencypredicted by the theoretical model and the experimental data. The

Table 1IST parabolic-trough collector data, from [45].

Parameter

Collector aperture area 13.2 m2

Geometric concentration ratio 14.36Rim angle 70�Focal length 76.2 cmCollector aperture 2.3 mCollector length (module) 6.1 mAbsorber material SteelReceiver surface treatment Selective black nickelAbsorber inner diameter 0.0476 mAbsorber outer diameter 0.0510 mReflector surface Silvered acrylicMirror reflectance 0.93Glass envelope transmittance 0.96Glass envelope diameter 0.075 mAbsorber absorptance 0.97Absorber emittance @100 �C 0.14Absorber emittance @300 �C 0.30

model presents a maximum absolute error of 2.02%, and a rootmean square error of 1.2%. All the efficiency points predicted bythe model are within the uncertainty in experimental data, whichvaries between 1.95% and 2.93%. It can also be observed that thecurvature of the efficiency predicted by the model agrees very wellwith the experimental curvature, for the entire range of tempera-tures considered, and thus validates the thermal losses modelproposed.

2.6.2. Absorber emittanceParametric studies were performed to evaluate the influence of

the absorber emittance on the collector thermal performance.Fig. 7 shows the effect of varying the absorber emittance between60% and 140% of its nominal value. Increasing the absorber emit-tance substantially increases the thermal losses by radiation tothe environment and thus reduces the collector thermal efficiency.This effect is more pronounced at high temperatures because radi-ation losses depend on the difference in temperatures to a power offour. Fig. 7 shows that at a temperature differential between thefluid and ambient of 180 �C a reduction of the emittance to 60%of its nominal value increases the efficiency in roughly 2%.

2.6.3. Absorber absorptanceThe absorptance quantifies the fraction of the incident radiation

on the absorber that is absorbed in the form of heat. Parametricstudies were performed to assess the influence on the collectorthermal efficiency of the absorber absorptance.

Fig. 8 shows that by reducing the absorber absorptance the col-lector thermal efficiency is reduced at all temperatures due to a de-crease in optical efficiency. By reducing the absorptance in 40% ofits nominal value the efficiency is decreased by roughly 30%, at allfluid temperatures.

0 20 40 60 80 100 120 140 160 180

0.66

0.68

0.7

0.72

0.74

0.76

Tf−Tamb [ºC]

Effic

ienc

y 0.6ε0.8εε1.2ε1.4ε

Fig. 7. Sensitivity analysis of absorber emittance influence on thermal efficiency.

0 20 40 60 80 100 120 140 160 180

0.4

0.5

0.6

0.7

0.8

Tf−Tamb [ºC]

Effic

ienc

y 0.9αnom

0.8αnom

0.7αnom

0.6αnom

αnom

Fig. 8. Influence of absorber absorptance on thermal efficiency.

0.1 0.15 0.2 0.25 0.3 0.350

200

400

600

800

1000

Mass Flow Rate [kg/s.m2]

Tota

l Los

ses

[W]

Tf=150ºC

Tf=200ºC

Tf=100ºC

Tf=50ºC

Fig. 10. Variation of the optimal mass flow rate with fluid temperature.

294 R. Silva et al. / Applied Energy 106 (2013) 287–300

2.7. Mass flow rate optimization

A thermohydraulic analysis was conducted to optimize the col-lector mass flow rate. Both the fluid temperature and the directirradiance were kept constant at values of Tf = 20 �C andGb = 1000 W/m2 respectively. The mass flow rate affects the inter-nal heat transfer coefficient by forced convection and as a resultinfluences the collector overall thermal efficiency. The optimiza-tion cost function considered consists in the sum of thermal andhydraulic losses and is given by the following expression,

Cf ¼ _Q L þ _Q H ð37Þ

where _QL represent the thermal losses to environment and _QH is thehydraulic power necessary to circulate the heat transfer fluid in thecollector tube.

Based on that criterion an optimal mass flow rate of approxi-mately 0.22 kg/s m2 was obtained. This flow rate corresponds toa ReD of 1.3 � 104, placing the flow inside the turbulent regime. Be-yond that value the increase on hydraulic losses overcomes thereduction of thermal losses, as it can be seen in Fig. 9. Optical lossesdo not depend on temperature, or mass flow rate, and therefore donot influence the optimum mass flow rate relative point location.

It can also be observed in Fig. 10 that the optimum mass flowrate point is approximately constant with the fluid temperature.Another important conclusion drawn from this analysis is thatthe combined losses variation is small for a large range of massflow rates, being almost constant for flow rates above 0.2 kg/s m2. This fact suggests that the mass flow rate can be used asthe manipulated variable for control purposes without sacrificingsignificantly the collector efficiency. However, mass flow rates inthe laminar regime are not recommended since they do not guar-antee that all the sections of the tube are being effectively cooled,due to insufficient heat diffusion, which could cause high temper-ature gradients and give origin to considerable thermal stresses onthe absorber tube. The optimal flow rate strongly depends on the

0.1 0.15 0.2 0.25 0.3 0.350

100

200

300

400

Mass Flow Rate [kg/s.m2]

Loss

es [W

]

Thermal LossesHydraulic LossesTotal Losses

Fig. 9. Mass flow rate optimization based on thermal and hydraulic losses.

inner tube diameters and thermal properties of the collector andis therefore different for each manufacturer.

The proposed methodology is based on optimizing the thermo-hydraulic efficiency of the solar collector by minimizing the ther-mal plus hydraulic losses. Nevertheless, other design criteria maybe relevant depending on the application. For example if the collec-tor rows maximum length is restricted, due to geometric con-straints in the solar field layout, one could try to maximize thecollector input–output temperature differential by using the mini-mum acceptable mass flow rate, therefore minimizing the neces-sary row length for a given solar field temperature differential.

3. Solar field model

3.1. Introduction

Parabolic trough collector solar fields may be arranged on dif-ferent possible configurations. The direct return is the most com-monly used configuration for small solar fields. It uses lesspiping, allowing it to save piping costs and to minimize thermallosses. However in this configuration each row has a different in-let–outlet piping length which causes it to be hydraulically unbal-anced. To balance the flow, balancing valves may be installed in theentrance of each row, or the piping diameters may be properlydimensioned to compensate for the length differences. Any ofthese solutions represents however an increase on the pressurelosses and hence larger parasitic costs. The reverse return configu-ration has an intrinsically more balanced arrangement and there-fore has less hydraulic losses. However the additional piping onthe outlet section represents an increase on thermal losses, whichcan reach an important level if the fluid working temperature ishigh. The final configuration choice between each one the configu-ration should be based on a techno-economic criterion, consideringthe particular requirements of the field and thermal application.

3.2. Model

The solar field model was developed in the high-level acausallanguage Modelica pursuing an object-oriented modeling philoso-phy. In this approach every collector and pipe is represented by anindividual object instantiated from a general class. Both paralleland series number of collectors are explicitly parameterized to al-low subsequent optimization studies on the field configuration. Asimplified model of the shadowing effect between adjacent rowswas also implemented. The fraction of the collector aperture areathat is shaded was considered to be one-dimensional and is calcu-lated by,

fbs ¼max 1� Lp cosðbÞW

;0� �

ð38Þ

Tin Tout

Fig. 11. One-dimensional model of the solar field.

1 2 3 4 50

0.5

1

1.5

2

2.5

3

Flow Rate [L/s]

Pres

sure

Dro

p [b

ar] Ns=10

Ns=15Ns=20Ns=25

Fig. 13. Pressure drop on a small parabolic trough collector row.

Table 3Thermal losses on piping as a percentage of useful power at Tf = 150 �C.

Parameter U = 1 W/m2 K U = 5 W/m2 K U = 10 W/m2 K

Losses inlet piping (%) 0.07 0.35 0.71Losses middle piping (%) 0.06 0.30 0.61Losses outlet piping (%) 0.17 0.83 1.67Total losses (%) 0.30 1.49 2.90

R. Silva et al. / Applied Energy 106 (2013) 287–300 295

where Lp is the distance between rows, W is the collector aperturewidth, and b is the collector slope.

Two solar field model structures, a one-dimensional and a bi-dimensional model were developed. In the one-dimensional modelonly the temperature distribution along the longitudinal directionis considered, and as a result the differences between rows are ig-nored. The advantages of this model are that it is faster and has alower computational cost. The main disadvantage is that it isstrongly based on the assumption that the field is hydraulicallybalanced, i.e. that all the rows have the same mass flow rate (seeFig. 11).

A bi-dimensional solar field model considers all the collectorsand piping on the solar field. It provides a more extensive descrip-tion of the field, modeling the thermal performance distributionmore in detail. In this model structure the thermal losses on the in-let, outlet, and interior connecting piping are included. It allowsstudying the effect of distributed phenomena such as partial fieldshading, local dust, or unbalanced mass flow rate distribution.The main drawback is that it requires more computational effortdue to its complexity.

A comparison between the thermal efficiency calculated withone-dimensional and bi-dimensional model structures was per-formed. From a thermal point of view the main difference betweenthese two model structures, is that in the one-dimensional modelthe inlet and outlet connection piping thermal losses are ignored.The solar field consists on 6 � 6 parabolic trough collectors fromthe IST company. Table 2 shows the difference in the solar fieldthermal efficiency calculated with the two models for differentpiping overall losses coefficient. A distance between rows ofL = 7 m, corresponding approximately to three times the collectoraperture width, was considered (see Fig. 12).

The difference between the thermal efficiency calculated withthe two model structures increases with the increase of the pipingoverall loss due to the increase in the thermal losses on the solarfield inlet and outlet piping. The overall error of not consideringthe bi-dimensional effects on the thermal efficiency is 1.51%, forpiping with an overall heat transfer coefficient of U = 10 W/m2 K.This value reduces to 0.2% for piping with U = 1 W/m2 K.

Tin Tout

Fig. 12. Bi-dimensional model of the solar field.

Table 2Solar field efficiency with one-dimensional and bi-dimensional model for Tf = 150 �C.

Model U = 1 W/m2 K U = 5 W/m2 K U = 10 W/m2 K

One dimensional (%) 68.78 68.71 68.60Bi-dimensional (%) 68.58 67.90 67.09Difference (%) 0.20 0.81 1.51

3.3. Pressure losses

The pressure losses on a row of small parabolic troughs wereanalyzed for various mass flow rates. In Fig. 13 we can observe thatthe pressure drop evolution with the mass flow rate presents theexpected approximately quadratic tendency. For a loop consistingof 20 small parabolic trough collectors in series at a flow rate of4 l/s, the pressure drop is approximately1.3 bar, which representsan hydraulic power loss of 0.5 kW, corresponding roughly to 0.3%of the useful output thermal power.

3.4. Thermal losses on piping

Thermal losses on piping may represent an important influenceon the performance of a parabolic trough solar field depending onthe piping insulation and the fluid working temperature. In Table 3we can observe the total thermal losses on the piping at a fluidtemperature of Tf = 150 �C, and three piping thermal insulationlevels.

For a global heat transfer coefficient of 1 W/m2 K the total ther-mal losses represent a decrease of 0.3% on the solar field outputthermal power. Decreasing the insulation level for a value ofU = 10 W/m2 K increases the thermal losses to approximately2.9%.The largest fraction of the thermal losses occurs at the solarfield outlet piping where the fluid temperatures are higher.

4. Solar field experimental validation

4.1. Solar field description

The parabolic trough solar field dynamic model was validatedwith experimental data obtained from the ACUREX solar field, lo-cated at the Plataforma Solar de Almeria, southern Spain. This solarfield is composed by 480 small parabolic trough collectors, ACU-REX model 3001, East–West oriented, adding a total area of2674 m2, and the working fluid is Santotherm 55 thermal oil. TheACUREX collector properties data may be obtained from [8,46,47](see Table 4).

9 10 11 12860

880

900

920

940

960

980

1000

Local Ti

Irrad

ianc

e [W

/m2 ]

Fig. 14. Direct solar irradiance and flow rate

10 10.5 11 11.5 12 1

180

200

220

240

260

Local

Tem

pera

ture

[ºC

]

Fig. 15. Comparison between simulated a

10 10.5 11 11.5 12 1200

400

600

800

1000

1200

Local

Use

ful P

ower

[kW

]

Fig. 16. Comparison between simulate

Table 4ACUREX parabolic-trough collector and solar field data, from [20,28].

Parameter

Collector model ACUREX 3001Concentration ratio 18.32Rim angle 90�Focal length 0.46 mCollector aperture 1.83 mCollector length 3.05 mAbsorber diameter 0.0318Absorber tube thickness 0.002 mGlass tube diameter 0.056 mGlass tube thickness 0.002 mSpecular reflectance 0.91Glass tube transmittance 0.93Absorber absorptance 0.90Absorber emittance @300 �C 0.27Solar field location PSA, SpainSolar field orientation East–WestSolar field area 2674 m2

Total number of collectors 480Number of loops 10Groups per loop 4Collectors per group 12Distance between rows 5 m

296 R. Silva et al. / Applied Energy 106 (2013) 287–300

4.2. Experimental conditions

The experiment was conducted during a spring day with vari-able direct irradiance due to intermittent meteorological circum-stances, to guarantee dynamic operating conditions. Fig. 14shows the direct solar irradiance and the volumetric flow rate evo-lution during the experiment. The experimental data was obtainedfrom experiments performed by Camacho et al. [8].

4.3. Model validation

Fig. 15 shows the simulated and experimental outlet tempera-ture of the solar field. Optical efficiency was calibrated to best fitthe experimental data. The model presents a good agreement withthe experimental data during both steady-state and unsteady-stateperiods with a small root mean square error of RMSE = 2.09 �C anda maximum absolute error of 8.64 �C. The maximum error occursduring the start-up stage due to the uncertainty on the initial tem-peratures of the central nodes of the solar field. Both the time con-stant and the transport delay are well captured by the model.

Fig. 16 shows the comparison between the experimental andsimulated useful thermal output power. The output power varies

13 14 15 16me [h]

0

5

10

15

Flow

Rat

e [l/

s]conditions during the experiment day.

2.5 13 13.5 14 14.5 15Time [h]

Tout ModelTout ExperimentalTin Experimental

nd experimental outlet temperature.

2.5 13 13.5 14 14.5 15 Time [h]

ModelExperimental

d and experimental output power.

Type 109

Data Reader andRadiation Processor

Type 950 Type 4c Type 6

Solar Field(TISC Interface)

Stratified Storage Tank Auxiliary Heater

Variable Speed Pump Variable Speed PumpTime Dependent ForcingFunction

Time Dependent ForcingFunction

Type 110 Type 14h Type 110 Type 14h

Fig. 17. Block diagram of solar plant model in Trnsys.

R. Silva et al. / Applied Energy 106 (2013) 287–300 297

between approximately 300 kW at sunrise and 1 MW at the middleof the day. The modeled and experimental output powers present agood agreement during the whole experiment.

Fig. 18. Co-simulation environment diagram.

5. Solar plant model

The solar plant model was implemented in TRNSYS [48] to al-low performing annual dynamic simulations for different geo-graphical locations. The global plant model is constituted by aparabolic trough solar field, which is coupled to Modelica withType 950 TISC interface. A thermally stratified energy storage is in-cluded to allow the use of larger solar field areas and higher solarfractions, by accumulating the excess of thermal energy in periodsof high direct solar radiation to use in periods of low solar irradi-ance, and is modeled with TRNSYS type 4. An auxiliary heater isused to guarantee the required output power and the necessarytemperature level in periods where there is not sufficient energyavailable from solar sources, and is modeled with TRNSYS type 6.An industrial application load profile is included and modeled witha set of equations that simulate the enthalpy differential and out-put temperature for a given thermal load. Two variable speed cir-culation pumps are added to the primary and secondary circuits

Fig. 19. Co-simulation integrat

and modeled with type 110. An irradiance and data reader proces-sor was coupled to the model to compute the direct irradiance,ambient temperature and incidence and slope angles, based ontypical meteorological years and astronomical algorithms, mod-eled with type 109. In Fig. 17 we can observe the diagram of thesolar plant model in TRNSYS. The simulations in TRNSYS were con-ducted with a time step of one hour for a time frame of one year.

6. Co-simulation environment

Distributed or cooperative simulation (co-simulation) is anemerging new advanced concept where different simulations are

ion environment diagram.

Trigger3600 s

Connection"Modelica"

SYNC

RealScalar"Tout"

RealScalar"mout"

RealScalar"Qu"

"ambie...ScalarReal

"beam_...ScalarReal

"incide...ScalarReal

"slope_...ScalarReal

"t_in_c...ScalarReal

"m_coll...ScalarReal

Solar Field

Fig. 20. Modelica co-simulation interface to TISC.

298 R. Silva et al. / Applied Energy 106 (2013) 287–300

run on a distributed way, communicating and sharing data amongthem. These different simulation tools are externally coupled,allowing them to work cooperatively on solving more complexmodeling problems. In this study the TISC TLK software connectormiddleware co-simulation environment [49] was used. This mid-dleware is constituted by a simulation server that manages andsynchronizes the communication between various simulation cli-ents, where different models run in parallel. The dataflow, commu-nications, and platform are presented in Fig. 18.

The Modelica language is a very powerful tool that allows thedevelopment of differential–algebraic equations models in a non-causal object-oriented philosophy. These features make Modelicaan interesting choice to create detailed dynamic solar collectorand solar field models that can capture more closely the underlyingphysics, such as the thermal efficiency, pressure drop, time con-stant and transport delay. Trnsys is a transient simulation programbased on a block-oriented philosophy with a very complete set oflibraries for solar thermal energy, including an extensive meteoro-logical database. These features make it a powerful environment todevelop global system models and to perform annual system sim-ulations. By exploring the synergies of these two simulation tools,and using them together in a cooperative way, a more completeand complex global model of a solar plant may be addressed. A dia-gram of the implemented co-simulation platform is presented inFig. 19.

The synchronization with the co-simulation server is made witha time step of a few minutes due to the dynamics of the solar col-lector model. The variables exchanged with the TISC server are thesolar field inlet temperature, outlet temperature, mass flow rate,direct irradiance, ambient temperature, incidence angle and slopeangle. A large number of structural parameters were included inthe solar field model to adjust the computational effort required

during the co-simulations. Fig. 20 shows the TISC interface inDymola.

7. Co-simulations

7.1. Industrial process heat application

Annual co-simulations were performed on the TISC environ-ment to analyze the influence of key plant design parameters, suchas the solar field area, on the plant global performance, on a refer-ence industrial process heat application scenario.

7.2. Performance of parabolic trough solar plant

The performance of the parabolic trough solar plant in the basescenario of Table 5 for different demands is presented in Fig. 21.The solar fraction increases with area, presenting an asymptoticaltendency to constant value at large solar field areas due to the de-crease of the solar field thermal efficiency. For a 100 kW industrialprocess heat application an increase of the solar field area from500 m2 to 1000 m2 increases the solar fraction from 45% to 67%.

In a continuous thermal load profile, by using thermal storage,the solar field may be substantially oversized to supply exceedingthermal energy that can be stored during the day for use during thenight.

7.3. Stationary and dynamic model

The annual performance predicted by the stationary simplifiedempiric model proposed by Dudley et al. (given by Eq. (39)) wascompared with the performance predicted by the dynamic

Table 6Annual results with stationary and dynamic model.

Parameter Simplifiedstationarymodel (%)

Dynamiccomplexmodel (%)

Difference(%)

Solar fraction 61.90 62.56 0.66Field efficiency 45.93 48.97 3.04

Table 5Industrial process heat case scenario.

Parameter

Plant location Almeria, SpainType of collectors Parabolic troughCollector ISTProcess temperature 150 �CTemperature differential 50 �CCapacity 100 kWDemand profile ContinuousSolar field area ParameterSolar field orientation N–SDeposit volume 100 m3

Type of deposit Thermally stratifiedBackup fuel Natural gasBoiler efficiency 80%

0 200 400 600 800 1000 1200 1400 16000

102030405060708090

Solar Field Area [m2]

Sola

r Fra

ctio

n [%

]

Ql=100 kWQl=150 kW

Ql=200 kW

Ql=50 kW

Fig. 21. Solar fraction as a function of solar field area.

R. Silva et al. / Applied Energy 106 (2013) 287–300 299

complex model developed in this work, for the reference scenarioconditions presented on Table 5, with a solar field of 12 � 12 par-abolic trough IST collectors.

g ¼ 0:762� 0:00006836DT � 0:1468DTGb� 0:001672

DT2

Gbð39Þ

The stationary and dynamic models present an annual solar frac-tion of 61.90% and 62.56% and a solar field efficiency of 45.93%and 48.97% respectively. The difference of not taking in

1 2 3 4 5 60

20

40

60

80

100

Mo

Sola

r Fra

ctio

n [%

]

Fig. 22. Comparison of monthly solar fractio

consideration the dynamic effects is hence 0.66% and 3.04% forthe annual solar fraction and solar field efficiency respectively(see Table 6).

Fig. 22 shows the monthly solar fraction calculated with thetwo models. The largest difference between the two models is5.1% and 7.0% on the monthly solar fraction and solar field effi-ciency respectively. It can be observed that the largest differencesbetween the two models occur at the spring and winter monthswhere there are more solar irradiation transient periods that occurdue to intermittent clouding (see Fig. 22).

8. Conclusions

A tri-dimensional non-linear thermohydraulic dynamic modelof a parabolic trough collector with heterogeneous radiationboundary conditions was developed in Modelica and coupled to asolar industrial process heat plant developed in TRNSYS.

The stationary thermal efficiency predicted by the proposedcollector model was compared with experimental data and agreeswell with a RMSE of 1.2%. The dynamic evolution of the outlettemperature of the solar field model was compared with experi-mental data for a day with intermittent radiation and mass flowrate conditions showing a good agreement with a RMSE of2.09 �C.

A sensitivity analysis showed that the collector absorber emit-tance has a significant influence on thermal performance, and areduction of 60% of its nominal value increases the thermal effi-ciency of the collector in 2% at a fluid temperature of 200 �C.

A thermohydraulic mass flow rate optimization was performedon the IST parabolic trough collector suggesting an optimum massflow rate of 0.22 kg/s m2.

A comparison of one-dimensional and bi-dimensional solar fieldmodel structures showed that from a thermal point of view, thetwo models perform closely, presenting a difference on the thermalefficiency between 0.2% and 1.5%, for piping with an overall heattransfer coefficient of 1 W/m2 K and 10 W/m2 K respectively, at areference fluid temperature of 150 �C.

Stationary and dynamic solar field models were comparedregarding the predicted annual performance, showing that theinclusion of dynamic effects causes a maximum deviation of 5%and 7% on the monthly solar fraction and solar field efficiencyrespectively, and the largest differences occur on the months withless direct radiation where more transient solar radiation condi-tions occur due to intermittent clouding.

Co-simulations for a reference scenario in southern Spainshowed that a parabolic-trough solar plant constituted by a solarfield of 1000 m2 with a storage volume of 100 m3 coupled to anindustrial continuous application demanding 100 kW at 150 �C,obtained an annual solar fraction of 67% with a solar field thermalefficiency of 44%.

7 8 9 10 11 12nths

StationaryDynamic

n with stationary and dynamic models.

300 R. Silva et al. / Applied Energy 106 (2013) 287–300

Acknowledgments

This work has been supported by the Consejería de Economía,Innovación and Ciencia de la Junta de Andalucía thanks to the FED-ER funds, through the excellence Project P10-RNM-5927, and co-fi-nanced by the European Social Fund (ESF) through the HumanPotential Operational Programme/POPH. The authors would alsolike to thank the comments by Prof. Manuel Berenguel of Univer-sity of Almeria, Prof. Eduardo Zarza and Dr. Loreto Valenzuela ofPlataforma Solar de Almeria, CIEMAT.

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