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Research ArticleRay Tracing Study of Optical Characteristics of the Solar Imagein the Receiver for a Thermal Solar Parabolic Dish Collector

Saša R Pavlovic and Velimir P Stefanovic

Faculty of Mechanical Engineering Department of Energetics and Process Technique University of Nis Nis Serbia

Correspondence should be addressed to Sasa R Pavlovic saledocagmailcom

Received 15 June 2015 Revised 2 September 2015 Accepted 27 September 2015

Academic Editor Santanu Bandyopadhyay

Copyright copy 2015 S R Pavlovic and V P Stefanovic This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

This study presents the geometric aspects of the focal image for a solar parabolic concentrator (SPC) using the ray tracing techniqueto establish parameters that allow the designation of the most suitable geometry for coupling the SPC to absorber-receiver Theefficient conversion of solar radiation into heat at these temperature levels requires a use of concentrating solar collectors In thispaper detailed optical design of the solar parabolic dish concentrator is presented The system has diameter 119863 = 3800mm andfocal distance 119891 = 2260mm The parabolic dish of the solar system consists of 11 curvilinear trapezoidal reflective petals For theconstruction of the solar collectors mild steel-sheet and square pipe were used as the shell support for the reflecting surfaces Thispaper presents optical simulations of the parabolic solar concentrator unit using the ray tracing software TraceProThe total flux onthe receiver and the distribution of irradiance for absorbing flux on center and periphery receiver are given The goal of this paperis to present the optical design of a low-tech solar concentrator that can be used as a potentially low cost tool for laboratory scaleresearch on the medium-temperature thermal processes cooling industrial processes polygeneration systems and so forth

1 Introduction and Survey of Literature

This paper presents the numerical results of the optimizationof the solar image in a receiver for a fixed absorber in asolar parabolic concentrator which was a project supportedby the Ministry of Education Science and TechnologicalDevelopment of Republic of Serbia The device which isused to transform solar energy to heat refers to a solarcollector Solar thermal collectors have been widely usedto concentrate solar radiation and convert it into medium-high-temperature thermal processes In addition the listof possible alternative applications of this technology isgrowing due to the problems of oil dependency and globalwarming They can be designed as various devices includingsolar cooker [1] solar hydrogen production [2 3] andDish Stirling system of harvest electricity [4 5] The maintypes of concentrating collectors are parabolic dish parabolictrough power tower a Fresnel collector with mirror or lensand stationary concentrating collectors The ideal opticalconfiguration for the solar parabolic thermal concentrator isa parabolic mirror The parabolic mirror is very expensive

to fabricate and its cost escalates rapidly with increase ofaperture area The parabolic mirror can be designed withlarge number of elementary components known as reflectingpetals or facets Usually reflecting petals are made from glassand their thickness is from 07 to 10mm Traditionally theoptical analysis of radiation concentrators has been carriedout by means of computer ray-trace programs Recently aninteresting analytical solution for the optical performance ofparabolic dish reflectors with flat receivers was presented byOrsquoNeill and Hudson [6] Their method for calculating theoptical performance is fast and accurate but assumes thatthe radiation source is a uniform disk Saleh Ali et al [7]have presented a study that aims to develop a 3D static solarconcentrator that can be used as a low cost and low energysubstituteTheir goal was to design solar concentrator for theproduction of portable hot water in rural India They usedray tracing software for evaluation of the optical performanceof a static 3D Elliptical Hyperboloid Concentrator (EHC)Optimization of the concentrator profile and geometry iscarried out to improve the overall performance of the systemKaushika and Reddy [8] used satellite dish of 2405m in

Hindawi Publishing CorporationJournal of Solar EnergyVolume 2015 Article ID 326536 10 pageshttpdxdoiorg1011552015326536

2 Journal of Solar Energy

diameter with aluminium frame as a reflector to reduce theweight of the structure and the cost of the solar system Intheir solar system the average temperature of water vaporwas 300∘C when the absorber was placed at the focal pointThe cost of their system was US$ 950 El Ouederni et al[9] were testing parabolic concentrator of 22m in diameterwith reflecting coefficient 085 Average temperature in theirsystem was 380∘C Rafeeu and Ab Kadir [10] have presentedsimple exercise in designing building and testing smalllaboratory scale parabolic concentrators They made twodishes from acrylonitrile butadiene styrene and one fromstainless steel Three experimental models with various geo-metrical sizes and diameters were used to analyze the effectof geometry on a solar irradiation Liu et al [11] presenteda procedure to design a facet concentrator for a laboratoryscale research on medium-temperature thermal processesThe facet concentrator approximates a parabolic surface witha number of flat square facets supported by a parabolic frameand having two edges perpendicular to the concentratoraxis Authors [12] presented a physical and mathematicalmodel of the new offset type parabolic concentrator and anumerical procedure for predicting its optical performancesAlso the process of design and optical ray tracing analysisof a low cost solar concentrator for medium-temperatureapplications is presented This study develops and applies anew mathematical model for estimating the intercept factorof the solar concentrator based on its geometry and opticalbehaviour Pavlovic et al [13] developed mathematical modelof solar parabolic dish concentrator based on square flat facetsapplied to polygeneration system The authors developedoptimization algorithm for search of optimal geometricoptical and cost parameters They have applied Monte Carloray tracing methodology which is used for analysis of theoptical performance of the concentrator and to identify theset of geometric concentrator parameters that allow for fluxcharacteristics suitable for medium- and high-temperatureapplications in trigeneration and polygeneration systems A164-facet concentrator will deliver up to 815 kW of radiativepower over 15 cm radius disk located in the focal planeTheirsystem had an average concentration ratio exceeding 100Hasnat et al [14] presented two prototype parabolic dishesDunn et al [15] investigated experimental evaluation ofammonia receiver geometries with a 9m2 dish concentratorThe 20m2 dish is mirrored with around 2000 flat mirrortile facets arranged in concentric rings on a parabolic fiberglass support structure Size of mirror facets is from 5 cmto 10 cm Johnston et al [16] analyzed optical performanceof spherical reflecting elements for use with parabolic dishconcentrators This concentrator consists of 54 triangularmirrors The effective rim angle of the dish is 46∘ The 54units are composed of nine separate panel shapes each of theshapes is duplicated six times The focal length of system is131m

The decision to make solar parabolic concentrator with11 petals is based on large number of design concepts thatare realized in the world This concept already proved tobe useful in solar techniques especially in production ofheat and electrical energy as well as in trigeneration andpolygeneration systems

Thebasic idea behind this research is to startwith primaryconcept of solar parabolic concentrator which will generatefrom 10 to 25 kW in polygeneration systems Only withemployment of parabolic concentrating systems it is possibleto obtain high temperatures in range from 200∘C to 800∘Cand high optical and thermal efficiency of concentrating solarcollectors

2 Geometrical Model of the Solar ParabolicConcentrator and Receiver

The design of the solar parabolic thermal concentrator andoperation are presented Optical design is based on parabolicdish with 11 curvilinear trapezoidal petals Solar dish con-centrators are generally concentrators that concentrate solarenergy in a small area known as focal point Dimensions ofreflecting surfaces in solar dish concentrator are determinedby desired power at maximum levels of insolation andefficiency of collector conversion

The ray tracing technique is implemented in a softwaretool that allows the modelling of the propagation of lightin objects of different media This modelling requires thecreation of solid models either by the same software orby any computer aided design (CAD) software Once inthe optical modelling software portions of the rays of thelight source propagate in the flow of light in accordancewith the properties assigned to the relevant objects whichmay be absorption reflection transmission fluorescenceand diffusion The sources and components of the lightrays adhering to various performance criteria involvingthe system parameters result in simulation of the spatialand angular distribution uniformity intensity and spectralcharacteristics of the system Mathematical representation ofparabolic concentrator is paraboloid that can be representedas a surface obtained by rotating parabola around axis Math-ematical equations for the parabolic dish solar concentratorin Cartesian and cylindrical coordinate systems are definedas

1199092

+ 1199102

= 4119891119911 119911 =1199032

4119891 (1)

where are 119909 and 119910 are coordinates in aperture plane and119911 is distance from vertex measured along the line parallelwith the paraboloid axis of symmetry 119891 is focal length ofparaboloid that is distance from the vertex to the focus alongthe paraboloid axis of symmetry The relationship betweenthe focal length and the diameter of parabolic dish is knownas the relative aperture and it defines shape of the paraboloidand position of focal point The shape of paraboloid can bealso defined by rim angle 120595rim Usually paraboloids that areused in solar collectors have rim angles from 10 degrees upto 90 degrees The relationship between the relative apertureand the rim angle is given by

119891

119863=

1

4 tan (120595rim2) (2)

The paraboloid with small rim angles has the focal point andreceiver at large distance from the surface of concentrator

Journal of Solar Energy 3

The paraboloid with rim angle smaller than 50∘ (120595rim =

456) is used for cavity receivers while paraboloids with largerim angles are most appropriate for the external volumetricreceivers (central receiver solar systems) 119891119863 = 059 119891119863= 059 is focusdiameter ratiomdashratios of focal distance todiameter of aperture reflector Increasing the ratio 119891119889

reduces the rim angle Paraboloid with marginal angle isa little curved and its focal point and the receiver must befar from the surface of the concentrator Paraboloid with rimangle of less than 50∘ is used when reflective radiation passesinto the cavity of the receiver while the paraboloids with largeedge angles are most suitable for external receivers

The geometric concentration ratio can be defined as thearea of the collector aperture119860app divided by the surface areaof the receiver 119860 rec and can be calculated by

CR119892= (sin2120579

119886)minus1

= 119860119888119860119903

minus1

=

119860app

119860 rec (3)

The designed solar parabolic concentrator has geometricconcentration ratio CR

119892= 100

21 Parameters Design of Solar Parabolic ConcentratorMechanical design of the solar parabolic concentrator isdone in 3D design software CATIA Dassault Systemes USAParabolic shape of solar concentrator is obtained by entering119909 and 119910 coordinates for selected points For calculationof necessary points that define parabola public domainsoftware Parabola Calculator 20 [17] is used The calculatedcoordinates (119909 and 119910) for designed parabola are shown inTable 1 The calculated values are performed for 22 points inthe parabola curve The equation for parabola is

119910 =1199092

1

+ 1199092

2

4119891=

1199092

9040 (4)

Geometrical model of solar parabolic concentrator isparametrically designed from calculated coordinates andit is shown in Figure 1(a) Selected model of solar dishconcentrator with 11 petals requires very precise definition ofparameters during geometrical modelling of system Resultsobtained by optical analysis of solar concentration systemare very much dependent on the selected method of theCAD model generation Figure 2 represents the rear sideof solar parabolic dish collector and geometrical model ofconstruction of paraboloid curve with 11 petalsliefs Thegeometrical parameters from Mathematica is exported inCATIA software and have built 3D CAD model

Figures 3(a) and 3(b) show the profile of spiral absorbertube andwhole assembly of solar parabolic dish collectorwithreceiver in their focus

A truncated paraboloid of revolution (circularparaboloid) is obtained by rotating the parabola segmentabout its axis (Figure 4) Consider a concentrator consistingof 11 trapezoidal reflective petals of identical nonoverlappingtrapezoidal segments 3D model of trapezoidal reflectivepetal of solar parabolic concentrator is presented in Figure 4The outer diameter of corrugated pipe is119863

119890= 122mm inner

diameter is 119863119894= 93mm and thickness of wall pipes is 119904 =

025mm Figure 5 shows the paraboloidal liefpetal of solar

Table 1 Coordinates of designed parabola

119883 (cm) minus1900 minus1583 minus1266 minus9500 minus6333 minus3167 00119884 (cm) 399 277 1778 997 443 112 00119883 (cm) 3167 6333 9500 1266 1583 1900 mdash119884 (cm) 112 443 997 1778 277 399 mdash

Table 2 Design parameters of solar parabolic concentrator

Parameters Numerical value Unit

Aperture radius 1198771

02 [m]

Radius of smaller hole 1198772

19 [m]

Gross collector area 119860gross 1182 [m2]

The cross section of the openingparabola 119860proj

989 [m2]

A sheltered area of the concentrator119860 shadow

0126 [m2]

The effective area of theconcentrator 119860ef = 119860proj minus 119860 shadow

9764 [m2]

Receiver diameter 040 [m]

Shape of receiverDirectly irradiatedcorrugated spiral

thermal absorber pipemdash

Depth of the concentrator 0399 [m]

Focal length 226 [m]

1205951

6 [∘]

1205952

456 [∘]

paraboloidal concentrator systemThe front side of the petalsis reflective surface with coefficient of reflectance of 90(mirrored specular reflectance surface)

1198771is aperture radius of absorber while 119877

2is aperture

radius of solar dish concentratorreflector The small hole isconstructive approach

Detailed design parameters of solar parabolic concentra-tor are given in Table 2

Receiver-absorber is placed in focal area where reflectedradiation from solar concentrator is collected In the processof designing parabolic solar concentrators one always seeksfor the minimum size of the receiver With small receiver sizeone can reduce heat losses as well as cost of whole systemAlso small receiver size provides increase of absorbed flux onthe surface of receiver This is the way of obtaining greaterefficiency in conversion of solar radiation to heat In oursystem receiver-absorber is Archimedean spiral corrugatedpipe type with diameter of 400mm It is shown in Figure 6

In this paper only optical properties of receiver areanalyzed In our further research we plan to model allnecessary details of receiverrsquos geometry which are importantfor conversion of solar energy into heat of fluid that is usedfor transfer energy


(a)

(b)

Figure 1 (a) Parabola Calculator 20 [17] (b) Paraboloid generated fromMathematica Wolfram software

Figure 2 Mirrored segmented parabolic dish concentrator

3 Numerical Simulations and Ray TracingStudies to Determine the OpticalCharacteristics of the Solar Image

For optical ray tracing analysis of solar parabolicthermal concentrator software TracePro Lamda ResearchCorporation USA is used Simulations have been performed

using the technique of ray tracing to describe the behaviourof parabolic dish solar concentrators and such simulationshave been used to study the behaviour of such concentratorsin nonimaging optics however there is no such studyor simulation of ray tracing type to describe parabolicsolar concentrators In TracePro all material propertiesare assigned 11 trapezoidal reflective petals are defined


(a) (b)

Figure 3 3D CADmodel of thermal solar concentration system and sinusoidal profile of corrugated pipe of spiral absorber

dtarget

Focal plane

z

r

1205951

R2

1205952

f

R1

Figure 4 Schematic of truncated parabola

Silvered mirrored parabolic segment (3mm)

PMMA Poly(methyl methacrylate)

Figure 5 Trapezoidal reflective petal of solar parabolic concentra-tor

as standard mirrors with reflective coating Reflectioncoefficient was 95 Receiver was cylinder with diameter400mm placed on 2075mm from vertex of parabolicdish (optimal focal distance from vertex of parabolic solarconcentrator) Absorbing surface was defined as perfect

Concentratedsolar radiation

from solarparabolic

concentrator

Figure 6 Solar cavity receiver-spiral corrugated pipe type of solarabsorber

absorber After definition of geometry of solar parabolicconcentrator radiation source was defined Radiation sourcewas circular with diameter the same as diameter of parabolicdish (3800mm) Radiation source was placed 2000mmfrom vertex of parabolic dish and had circular grid patternfor generating 119401 rays for Monte Carlo ray tracingSpatial profile of generated rays was uniform and angularprofile was solar radiation Input parameter for opticalanalysis is solar irradiance 800Wm2 Experiential valuefor solar irradiation for town of Nis in Serbia is between750Wm2 and 900Wm2 Optical system for solar parabolicconcentrator with traced rays is given in Figure 7

Temperature of the spiral absorber pipe-stagnation sur-face temperature is about 680∘C Detailed heat transfer anal-ysis of this solar spiral heat pipe absorber will be presented inmy other future papers

Optical analysis is done by generating and calculatingMonte Carlo ray trace for 119401 ray From all emitted raysonly 103029 rays reached absorber surface of which 82 of


(a)

199885

193664

187443

181221

175minus0212788

minus0141152

minus00695158

000212016

00737562

minus0214976

minus0142975

minus00709747

000102603

00730267

0145027

Y

Z

X

2

(b)

Figure 7 (a) Ray tracing model of solar parabolic concentrator with traced rays (b) Ray tracing model of solar spiral heat pipe with housingSolTrace optical software tool NREL USA

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

times104

(Wm

2 )

200 150 100 50 0 minus50 minus100 minus150 minus200

200

150

100

50

0

minus50

minus100

minus150

minus200

Y(m

m)

X (mm)Irradiance min 41093e minus 008Wm2

total flux 60017W 83268 incident raysmax 13315e + 005Wm2 ave 64115Wm2

Total-irradiance map for absorbed flux

Local coordinates14 spiral |NAUO114 spiral imp surface 0

Figure 8 Irradiance map for absorbed flux on spiral receiver (solarfocal image)

emitted rays are absorbed on receiver Calculated irradiancefor absorbed rays on receiver is from 4109 sdot 10

minus8Wm2to 1331 sdot 10

5Wm2 Total calculated flux on receiver was

60017W In Figure 8 total irradiance map for absorbed fluxon receiver is shown When the sunlight shines on the solarcollector including the direct and scattered radiation thereare three conditions affecting the absorption properties ofthe solar collector (1) direct solar radiation absorbed directlyby the solar collector and the light energy after the specularreflection (2) the light energy of the scatter solar radiationafter the diffuse and specular reflection (3) the light energyof the direct solar radiation after the diffuse reflection Theslope of incident light is different in different latitude andtime

Figure 9 represents path sun rays from the source tothe concentration of absorbing surface corrugated profile ofabsorber tube receiver

We take city of Nis (Laboratory for Solar Thermal Engi-neering) as an example Nis is located in southeast Serbialongitude 4330∘ north latitude and 2190∘ east longitudeSolar Parabolic Dish concentrator (Figure 9(b)) is trackingthe sun with motorized slewing drive solar tracking systemsin two axes azimuth and elevation (dual axis solar trackingprecision system)

The influences of absorption rate for the sinusoidalcorrugated absorber plate by aspect ratio and the slope ofincident light are plotted in Figure 10 From the optical pointof view the time of light reflection absorption increaseswith the aspect ratio which causes the absorption rateof the absorber plate to increase Particularly the absorp-tion rate is close to 1 when the aspect ratio tends toinfinity


Grid source 1

Y

XZ

Grid source 1

Y

XZ A

120582

(a)

(b)

Figure 9 (a) Schematic diagram of optical path shinning on the sinusoidal corrugated pipe absorber (b) Dual axis solar tracking systemwith slew drives and gear motor boxes

Figure 10 right shows ray tracing model radiation con-trol volume grid (1000 elements) for part of corrugatedpipe

Figure 10 shows control volume grid (1000 elements) forpart of corrugated pipe small part from all spiral corrugatedabsorber this figure presented incident solar flux in controlvolumemdashsmall control volumemdash3 wrinkles-folds

According to the boundary conditions the optical prop-erties can be obtained after many simulation calculationswhich is called the ray tracing method [11]

Volume radiation flux distribution (incident andabsorbed flux at the wall surface of profiles) softwareTracePro generated this bmp file

Figure 11 shows distribution of incident and absorbedsolar hear flux at the corrugated surfaces of spiral thermalabsorber

Figure 12 shows scattered model for reflection of inci-dence angle for solar parabolic dish concentrator with11 curvilinear trapezoidal reflective petals In general thereflectance of a surface increases with angle of incidence Butfor a mirror the reflectance is already very high when AOI =0∘ It cannot increase much moreThis is why the peak BRDFdoes not changewithAOIHowever the reflectance of a blacksurface increases with AOI no matter how black the surfaceis

4 Conclusions

This paper presents optical analysis of the solar parabolicconcentrator using the ray tracing software TracePro Onecan see that results obtained from optical design of solarparabolic concentrator are satisfactory Total flux in focalarea is good Irradiance distribution for absorbed flux isrelatively uniform for small area for absorber A detailedsimulation and analysis were conducted to evaluate theabsorption rate of sinusoidal corrugated absorber pipe Asa next step various analysis and simulations of the modelare considered Among others are variation of number ofpetals size of petals and shape of petals Optimizationmethodology is not the topic of this work Here it is onlyshown that the application of the Monte Carlo method canbe performed to determine optimal parameters for obtainingthe maximum value of total solar flux density and aver-age irradiance-solar radiant energy at the spiral corrugatedabsorber

The significance of this work is primarily in finding theoptimal parameters of the geometric and optical parametersin the concentrator and receiverabsorber of concentrationradiation The main objective of this work is to find theoptimal parameters in order to develop a prototype of a solarparabolic concentrator aspects of polygeneration systems


Y

X

(a)

DN Codice tubo(tube code)

Superfice lineicainterna (inner linear

Superfice lineicaesterna (outer linear

10

12

12

15

20

25

32

S

Di De

TFA38TFA12

TFG12N

TFA40

TFA34-TFG15NTFA25-TFG20NTFA32-TFG25N

93

132

120

158

197

265

330

122

168

158

200

250

330

410

025

03

03

03

03

03

035

00407

00565

00540

00702

00912

01313

01757

00429

00591

00568

00730

00942

01345

01799

00890

01730

01500

02480

03830

07000

10464

38998400998400

1299840099840012998400998400

349984009984001998400998400

1 149984009984001 12998400998400

Volume lineico(linear volume)

(Lm)

Spessore

S (mm)(thickness)

Fil

(threadconnessione

connection)

De(mm)

Di(mm) surface) (m2m) surface) (m2m)

(b)Figure 10 (a) Ray tracing and radiation control volume grid (1000 elements) for part of corrugated pipe (b) Spiral corrugated one coil heatabsorber from total 13 coils

Volume flux map-spiraltxtUsing incident flux

0000644202

0000608413

0000572624

0000536835

0000501046

0000465257

0000429468

0000393679

000035789

0000322101

0000286312

0000250523

0000214734

0000178945

0000143156

0000107367

71578e minus 005

35789e minus 005

0

(W)

6

5

4

3

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

157

156

155

154

153

152

151

150

149

148

147

146

145

144

143

Volume flux map-spiraltxtUsing absorbed flux

0000608413

0000572624

0000536835

0000501046

0000465257

0000429468

0000393679

000035789

0000322101

0000286312

0000250523

0000214734

0000178945

0000143156

0000107367

71578e minus 005

35789e minus 005

0

(W)

6

5

4

3

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

157

156

155

154

153

152

151

150

149

148

147

146

145

144

143

Figure 11 Volume radiation flux distribution (incident and absorbed flux)

production of heating cooling and electricity using solarenergy in Southeastern Europe

Nomenclature

Latin Symbols

119860 Area in [m]119886 Facets height in [m]

119909 Coordinate at the119883 direction119910 Coordinate at the 119884 direction119911 Coordinate at the 119885 direction119860pp Collector 119904 aperture surface [m2]119860119903 Receiver aperture surface [m2]

119889target Diameter of receiver surface [m]CR119892 Average geometric concentration ratio [minus]

119891 Focal length [m]


Scatter distribution (BRDF)for various angles of incidence (sample mirror)

10 20 30 40 50 60 70 80 900120579 (from surface normal)

0001

001

01

1

10

100

1000

BRD

F (1

sr)

AOI = 70degAOI = 60degAOI = 50deg

AOI = 40degAOI = 30degAOI = 20degAOI = 10deg

Figure 12 ABg giving the BRDF as a function of incidence angle

1198660 Incident direct solar flux in [Wmminus2]

119868 Total radiative intensity in [Wmminus2 srminus1] Radiative power in [kW]119902 Radiative flux in [Wmminus2]119902 Average radiative flux in [Wmminus2]

119877 119903 Radius in [m]119903 Position vector [minus]120578119888 Collection efficiency [minus]

120579 Incident angle in [∘

]

120595rim Rim angle in [∘

]

120601 120593 Azimuthal angle in [∘

]

120574 Constant

Greek Symbols

120573 Facet tilt angle rad limb darkening parameter120575 120576 Small positive number120588 Density of the fluid in [kgmminus3]

Subscripts

cs Circumsolarffc Flat-facet concentratorsun Corresponding to sun disk

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This paper is done within the research framework of researchprojects III42006 Research and Development of Energy andEnvironmentally Highly Effective Polygeneration SystemsBased on Renewable Energy Resources Project is financed

by Ministry of Education Science and Technological Devel-opment of Republic of Serbia The authors would like toacknowledge the help provided by the Lambda ResearchCorporation by allowing the use of the TracePro software forthe PhD research of Sasa R Pavlovic

References

[1] A A Badran I A Yousef N K Joudeh R A Hamad HHalawa andH K Hassouneh ldquoPortable solar cooker and waterheaterrdquo Energy Conversion and Management vol 51 no 8 pp1605ndash1609 2010

[2] A S Joshi I Dincer and B V Reddy ldquoSolar hydrogen pro-duction a comparative performance assessmentrdquo InternationalJournal of Hydrogen Energy vol 36 no 17 pp 11246ndash11257 2011

[3] P Furler J R Scheffe and A Steinfeld ldquoSyngas production bysimultaneous splitting ofH

2

OandCO2

via ceria redox reactionsin a high-temperature solar reactorrdquo Energy amp EnvironmentalScience vol 5 no 3 pp 6098ndash6103 2012

[4] T Mancini P Heller B Butler et al ldquoDish-stirling systems anoverview of development and statusrdquo Journal of Solar EnergyEngineering vol 125 no 2 pp 135ndash151 2003

[5] D Mills ldquoAdvances in solar thermal electricity technologyrdquoSolar Energy vol 76 no 1ndash3 pp 19ndash31 2004

[6] M J OrsquoNeill and S L Hudson ldquoOptical analysis of paraboloidalsolar concentratorsrdquo in Proceedings of the Annual Meeting USSection of International Solar Energy Society vol 21 pp 855ndash862 Denver Colo USA August 1978

[7] I M Saleh Ali T S OrsquoDonovan K S Reddy and T K MallickldquoAn optical analysis of a static 3-D solar concentratorrdquo SolarEnergy vol 88 pp 57ndash70 2013

[8] NDKaushika andK S Reddy ldquoPerformance of a low cost solarparaboloidal dish steam generating systemrdquo Energy Conversionamp Management vol 41 no 7 pp 713ndash726 2000

[9] A R El Ouederni M Ben Salah F Askri and F AlouildquoExperimental study of a parabolic solar concentratorrdquo Revuedes Energies Renouvelables vol 12 no 3 pp 395ndash404 2009

[10] Y Rafeeu and M Z A Ab Kadir ldquoThermal performance ofparabolic concentrators under Malaysian environment a casestudyrdquo Renewable and Sustainable Energy Reviews vol 16 no 6pp 3826ndash3835 2012

[11] Z Liu J Lapp and W Lipinski ldquoOptical design of a flat-facetsolar concentratorrdquo Solar Energy vol 86 no 6 pp 1962ndash19662012

[12] S Pavlovic D Vasiljevic V Stefanovic Z Stamenkovic andS Ayed ldquoOptical model and numerical simulation of the newoffset type parabolic concentrator with two types of solarreceiversrdquo Facta Universitatis Series Mechanical Engineeringvol 13 no 2 pp 169ndash180 UDC 5352 2015

[13] S R Pavlovic V P Stefanovic and S H Suljkovic ldquoOpticalmodeling of a solar dish thermal concentrator based on squareflat facetsrdquoThermal Science vol 18 no 3 pp 989ndash998 2014

[14] A Hasnat P Ahmed M Rahman and K A Khan ldquoNumericalanalysis for thermal design of a paraboloidal solar concentratingcollectorrdquo International Journal of Natural Sciences vol 1 no 3pp 68ndash74 2011

[15] RDunnK Lovegrove G Burgess and J Pye ldquoAn experimentalstudy of ammonia receiver geometries for dish concentratorsrdquoJournal of Solar Energy EngineeringmdashTransactions of the ASMEvol 134 no 4 Article ID 041007 2012


[16] G Johnston K Lovegrove and A Luzzi ldquoOptical performanceof spherical reflecting elements for use with paraboloidal dishconcentratorsrdquo Solar Energy vol 74 no 2 pp 133ndash140 2003

[17] httpmscirtripodcomparabola

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High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


diameter with aluminium frame as a reflector to reduce theweight of the structure and the cost of the solar system Intheir solar system the average temperature of water vaporwas 300∘C when the absorber was placed at the focal pointThe cost of their system was US$ 950 El Ouederni et al[9] were testing parabolic concentrator of 22m in diameterwith reflecting coefficient 085 Average temperature in theirsystem was 380∘C Rafeeu and Ab Kadir [10] have presentedsimple exercise in designing building and testing smalllaboratory scale parabolic concentrators They made twodishes from acrylonitrile butadiene styrene and one fromstainless steel Three experimental models with various geo-metrical sizes and diameters were used to analyze the effectof geometry on a solar irradiation Liu et al [11] presenteda procedure to design a facet concentrator for a laboratoryscale research on medium-temperature thermal processesThe facet concentrator approximates a parabolic surface witha number of flat square facets supported by a parabolic frameand having two edges perpendicular to the concentratoraxis Authors [12] presented a physical and mathematicalmodel of the new offset type parabolic concentrator and anumerical procedure for predicting its optical performancesAlso the process of design and optical ray tracing analysisof a low cost solar concentrator for medium-temperatureapplications is presented This study develops and applies anew mathematical model for estimating the intercept factorof the solar concentrator based on its geometry and opticalbehaviour Pavlovic et al [13] developed mathematical modelof solar parabolic dish concentrator based on square flat facetsapplied to polygeneration system The authors developedoptimization algorithm for search of optimal geometricoptical and cost parameters They have applied Monte Carloray tracing methodology which is used for analysis of theoptical performance of the concentrator and to identify theset of geometric concentrator parameters that allow for fluxcharacteristics suitable for medium- and high-temperatureapplications in trigeneration and polygeneration systems A164-facet concentrator will deliver up to 815 kW of radiativepower over 15 cm radius disk located in the focal planeTheirsystem had an average concentration ratio exceeding 100Hasnat et al [14] presented two prototype parabolic dishesDunn et al [15] investigated experimental evaluation ofammonia receiver geometries with a 9m2 dish concentratorThe 20m2 dish is mirrored with around 2000 flat mirrortile facets arranged in concentric rings on a parabolic fiberglass support structure Size of mirror facets is from 5 cmto 10 cm Johnston et al [16] analyzed optical performanceof spherical reflecting elements for use with parabolic dishconcentrators This concentrator consists of 54 triangularmirrors The effective rim angle of the dish is 46∘ The 54units are composed of nine separate panel shapes each of theshapes is duplicated six times The focal length of system is131m

The decision to make solar parabolic concentrator with11 petals is based on large number of design concepts thatare realized in the world This concept already proved tobe useful in solar techniques especially in production ofheat and electrical energy as well as in trigeneration andpolygeneration systems

Thebasic idea behind this research is to startwith primaryconcept of solar parabolic concentrator which will generatefrom 10 to 25 kW in polygeneration systems Only withemployment of parabolic concentrating systems it is possibleto obtain high temperatures in range from 200∘C to 800∘Cand high optical and thermal efficiency of concentrating solarcollectors

2 Geometrical Model of the Solar ParabolicConcentrator and Receiver

The design of the solar parabolic thermal concentrator andoperation are presented Optical design is based on parabolicdish with 11 curvilinear trapezoidal petals Solar dish con-centrators are generally concentrators that concentrate solarenergy in a small area known as focal point Dimensions ofreflecting surfaces in solar dish concentrator are determinedby desired power at maximum levels of insolation andefficiency of collector conversion

The ray tracing technique is implemented in a softwaretool that allows the modelling of the propagation of lightin objects of different media This modelling requires thecreation of solid models either by the same software orby any computer aided design (CAD) software Once inthe optical modelling software portions of the rays of thelight source propagate in the flow of light in accordancewith the properties assigned to the relevant objects whichmay be absorption reflection transmission fluorescenceand diffusion The sources and components of the lightrays adhering to various performance criteria involvingthe system parameters result in simulation of the spatialand angular distribution uniformity intensity and spectralcharacteristics of the system Mathematical representation ofparabolic concentrator is paraboloid that can be representedas a surface obtained by rotating parabola around axis Math-ematical equations for the parabolic dish solar concentratorin Cartesian and cylindrical coordinate systems are definedas

1199092

+ 1199102

= 4119891119911 119911 =1199032

4119891 (1)

where are 119909 and 119910 are coordinates in aperture plane and119911 is distance from vertex measured along the line parallelwith the paraboloid axis of symmetry 119891 is focal length ofparaboloid that is distance from the vertex to the focus alongthe paraboloid axis of symmetry The relationship betweenthe focal length and the diameter of parabolic dish is knownas the relative aperture and it defines shape of the paraboloidand position of focal point The shape of paraboloid can bealso defined by rim angle 120595rim Usually paraboloids that areused in solar collectors have rim angles from 10 degrees upto 90 degrees The relationship between the relative apertureand the rim angle is given by

119891

119863=

1

4 tan (120595rim2) (2)

The paraboloid with small rim angles has the focal point andreceiver at large distance from the surface of concentrator






CR119892= (sin2120579

119886)minus1

= 119860119888119860119903

minus1

=

119860app

119860 rec (3)


119892= 100


119910 =1199092

1

+ 1199092

2

4119891=

1199092

9040 (4)




119890= 122mm inner








02 [m]


19 [m]



989 [m2]


0126 [m2]


9764 [m2]






1205951

6 [∘]

1205952

456 [∘]



2is aperture






(a)

(b)







(a) (b)


dtarget

Focal plane

z

r

1205951

R2

1205952

f

R1







from solarparabolic

concentrator






(a)

199885

193664

187443

181221

175minus0212788

minus0141152

minus00695158

000212016

00737562

minus0214976

minus0142975

minus00709747

000102603

00730267

0145027

Y

Z

X

2

(b)


14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

times104

(Wm

2 )


200

150

100

50

0

minus50

minus100

minus150

minus200

Y(m

m)














Grid source 1

Y

XZ

Grid source 1

Y

XZ A

120582

(a)

(b)








4 Conclusions




Y

X

(a)




10

12

12

15

20

25

32

S

Di De

TFA38TFA12

TFG12N

TFA40


93

132

120

158

197

265

330

122

168

158

200

250

330

410

025

03

03

03

03

03

035

00407

00565

00540

00702

00912

01313

01757

00429

00591

00568

00730

00942

01345

01799

00890

01730

01500

02480

03830

07000

10464

38998400998400

1299840099840012998400998400

349984009984001998400998400

1 149984009984001 12998400998400


(Lm)

Spessore

S (mm)(thickness)

Fil

(threadconnessione

connection)

De(mm)




0000644202

0000608413

0000572624

0000536835

0000501046

0000465257

0000429468

0000393679

000035789

0000322101

0000286312

0000250523

0000214734

0000178945

0000143156

0000107367

71578e minus 005

35789e minus 005

0

(W)

6

5

4

3

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

157

156

155

154

153

152

151

150

149

148

147

146

145

144

143


0000608413

0000572624

0000536835

0000501046

0000465257

0000429468

0000393679

000035789

0000322101

0000286312

0000250523

0000214734

0000178945

0000143156

0000107367

71578e minus 005

35789e minus 005

0

(W)

6

5

4

3

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

157

156

155

154

153

152

151

150

149

148

147

146

145

144

143



Nomenclature

Latin Symbols








0001

001

01

1

10

100

1000

BRD

F (1

sr)








]


]


]

120574 Constant

Greek Symbols


Subscripts




Acknowledgments



References




2

OandCO2





















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of






















CR119892= (sin2120579

119886)minus1

= 119860119888119860119903

minus1

=

119860app

119860 rec (3)


119892= 100


119910 =1199092

1

+ 1199092

2

4119891=

1199092

9040 (4)




119890= 122mm inner








02 [m]


19 [m]



989 [m2]


0126 [m2]


9764 [m2]






1205951

6 [∘]

1205952

456 [∘]



2is aperture






(a)

(b)







(a) (b)


dtarget

Focal plane

z

r

1205951

R2

1205952

f

R1







from solarparabolic

concentrator






(a)

199885

193664

187443

181221

175minus0212788

minus0141152

minus00695158

000212016

00737562

minus0214976

minus0142975

minus00709747

000102603

00730267

0145027

Y

Z

X

2

(b)


14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

times104

(Wm

2 )


200

150

100

50

0

minus50

minus100

minus150

minus200

Y(m

m)














Grid source 1

Y

XZ

Grid source 1

Y

XZ A

120582

(a)

(b)








4 Conclusions




Y

X

(a)




10

12

12

15

20

25

32

S

Di De

TFA38TFA12

TFG12N

TFA40


93

132

120

158

197

265

330

122

168

158

200

250

330

410

025

03

03

03

03

03

035

00407

00565

00540

00702

00912

01313

01757

00429

00591

00568

00730

00942

01345

01799

00890

01730

01500

02480

03830

07000

10464

38998400998400

1299840099840012998400998400

349984009984001998400998400

1 149984009984001 12998400998400


(Lm)

Spessore

S (mm)(thickness)

Fil

(threadconnessione

connection)

De(mm)




0000644202

0000608413

0000572624

0000536835

0000501046

0000465257

0000429468

0000393679

000035789

0000322101

0000286312

0000250523

0000214734

0000178945

0000143156

0000107367

71578e minus 005

35789e minus 005

0

(W)

6

5

4

3

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

157

156

155

154

153

152

151

150

149

148

147

146

145

144

143


0000608413

0000572624

0000536835

0000501046

0000465257

0000429468

0000393679

000035789

0000322101

0000286312

0000250523

0000214734

0000178945

0000143156

0000107367

71578e minus 005

35789e minus 005

0

(W)

6

5

4

3

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

157

156

155

154

153

152

151

150

149

148

147

146

145

144

143



Nomenclature

Latin Symbols








0001

001

01

1

10

100

1000

BRD

F (1

sr)








]


]


]

120574 Constant

Greek Symbols


Subscripts




Acknowledgments



References




2

OandCO2





















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















(a)

(b)







(a) (b)


dtarget

Focal plane

z

r

1205951

R2

1205952

f

R1







from solarparabolic

concentrator






(a)

199885

193664

187443

181221

175minus0212788

minus0141152

minus00695158

000212016

00737562

minus0214976

minus0142975

minus00709747

000102603

00730267

0145027

Y

Z

X

2

(b)


14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

times104

(Wm

2 )


200

150

100

50

0

minus50

minus100

minus150

minus200

Y(m

m)














Grid source 1

Y

XZ

Grid source 1

Y

XZ A

120582

(a)

(b)








4 Conclusions




Y

X

(a)




10

12

12

15

20

25

32

S

Di De

TFA38TFA12

TFG12N

TFA40


93

132

120

158

197

265

330

122

168

158

200

250

330

410

025

03

03

03

03

03

035

00407

00565

00540

00702

00912

01313

01757

00429

00591

00568

00730

00942

01345

01799

00890

01730

01500

02480

03830

07000

10464

38998400998400

1299840099840012998400998400

349984009984001998400998400

1 149984009984001 12998400998400


(Lm)

Spessore

S (mm)(thickness)

Fil

(threadconnessione

connection)

De(mm)




0000644202

0000608413

0000572624

0000536835

0000501046

0000465257

0000429468

0000393679

000035789

0000322101

0000286312

0000250523

0000214734

0000178945

0000143156

0000107367

71578e minus 005

35789e minus 005

0

(W)

6

5

4

3

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

157

156

155

154

153

152

151

150

149

148

147

146

145

144

143


0000608413

0000572624

0000536835

0000501046

0000465257

0000429468

0000393679

000035789

0000322101

0000286312

0000250523

0000214734

0000178945

0000143156

0000107367

71578e minus 005

35789e minus 005

0

(W)

6

5

4

3

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

157

156

155

154

153

152

151

150

149

148

147

146

145

144

143



Nomenclature

Latin Symbols








0001

001

01

1

10

100

1000

BRD

F (1

sr)








]


]


]

120574 Constant

Greek Symbols


Subscripts




Acknowledgments



References




2

OandCO2





















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















(a) (b)


dtarget

Focal plane

z

r

1205951

R2

1205952

f

R1







from solarparabolic

concentrator






(a)

199885

193664

187443

181221

175minus0212788

minus0141152

minus00695158

000212016

00737562

minus0214976

minus0142975

minus00709747

000102603

00730267

0145027

Y

Z

X

2

(b)


14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

times104

(Wm

2 )


200

150

100

50

0

minus50

minus100

minus150

minus200

Y(m

m)














Grid source 1

Y

XZ

Grid source 1

Y

XZ A

120582

(a)

(b)








4 Conclusions




Y

X

(a)




10

12

12

15

20

25

32

S

Di De

TFA38TFA12

TFG12N

TFA40


93

132

120

158

197

265

330

122

168

158

200

250

330

410

025

03

03

03

03

03

035

00407

00565

00540

00702

00912

01313

01757

00429

00591

00568

00730

00942

01345

01799

00890

01730

01500

02480

03830

07000

10464

38998400998400

1299840099840012998400998400

349984009984001998400998400

1 149984009984001 12998400998400


(Lm)

Spessore

S (mm)(thickness)

Fil

(threadconnessione

connection)

De(mm)




0000644202

0000608413

0000572624

0000536835

0000501046

0000465257

0000429468

0000393679

000035789

0000322101

0000286312

0000250523

0000214734

0000178945

0000143156

0000107367

71578e minus 005

35789e minus 005

0

(W)

6

5

4

3

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

157

156

155

154

153

152

151

150

149

148

147

146

145

144

143


0000608413

0000572624

0000536835

0000501046

0000465257

0000429468

0000393679

000035789

0000322101

0000286312

0000250523

0000214734

0000178945

0000143156

0000107367

71578e minus 005

35789e minus 005

0

(W)

6

5

4

3

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

157

156

155

154

153

152

151

150

149

148

147

146

145

144

143



Nomenclature

Latin Symbols








0001

001

01

1

10

100

1000

BRD

F (1

sr)








]


]


]

120574 Constant

Greek Symbols


Subscripts




Acknowledgments



References




2

OandCO2





















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















(a)

199885

193664

187443

181221

175minus0212788

minus0141152

minus00695158

000212016

00737562

minus0214976

minus0142975

minus00709747

000102603

00730267

0145027

Y

Z

X

2

(b)


14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

times104

(Wm

2 )


200

150

100

50

0

minus50

minus100

minus150

minus200

Y(m

m)














Grid source 1

Y

XZ

Grid source 1

Y

XZ A

120582

(a)

(b)








4 Conclusions




Y

X

(a)




10

12

12

15

20

25

32

S

Di De

TFA38TFA12

TFG12N

TFA40


93

132

120

158

197

265

330

122

168

158

200

250

330

410

025

03

03

03

03

03

035

00407

00565

00540

00702

00912

01313

01757

00429

00591

00568

00730

00942

01345

01799

00890

01730

01500

02480

03830

07000

10464

38998400998400

1299840099840012998400998400

349984009984001998400998400

1 149984009984001 12998400998400


(Lm)

Spessore

S (mm)(thickness)

Fil

(threadconnessione

connection)

De(mm)




0000644202

0000608413

0000572624

0000536835

0000501046

0000465257

0000429468

0000393679

000035789

0000322101

0000286312

0000250523

0000214734

0000178945

0000143156

0000107367

71578e minus 005

35789e minus 005

0

(W)

6

5

4

3

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

157

156

155

154

153

152

151

150

149

148

147

146

145

144

143


0000608413

0000572624

0000536835

0000501046

0000465257

0000429468

0000393679

000035789

0000322101

0000286312

0000250523

0000214734

0000178945

0000143156

0000107367

71578e minus 005

35789e minus 005

0

(W)

6

5

4

3

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

157

156

155

154

153

152

151

150

149

148

147

146

145

144

143



Nomenclature

Latin Symbols








0001

001

01

1

10

100

1000

BRD

F (1

sr)








]


]


]

120574 Constant

Greek Symbols


Subscripts




Acknowledgments



References




2

OandCO2





















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















Grid source 1

Y

XZ

Grid source 1

Y

XZ A

120582

(a)

(b)








4 Conclusions




Y

X

(a)




10

12

12

15

20

25

32

S

Di De

TFA38TFA12

TFG12N

TFA40


93

132

120

158

197

265

330

122

168

158

200

250

330

410

025

03

03

03

03

03

035

00407

00565

00540

00702

00912

01313

01757

00429

00591

00568

00730

00942

01345

01799

00890

01730

01500

02480

03830

07000

10464

38998400998400

1299840099840012998400998400

349984009984001998400998400

1 149984009984001 12998400998400


(Lm)

Spessore

S (mm)(thickness)

Fil

(threadconnessione

connection)

De(mm)




0000644202

0000608413

0000572624

0000536835

0000501046

0000465257

0000429468

0000393679

000035789

0000322101

0000286312

0000250523

0000214734

0000178945

0000143156

0000107367

71578e minus 005

35789e minus 005

0

(W)

6

5

4

3

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

157

156

155

154

153

152

151

150

149

148

147

146

145

144

143


0000608413

0000572624

0000536835

0000501046

0000465257

0000429468

0000393679

000035789

0000322101

0000286312

0000250523

0000214734

0000178945

0000143156

0000107367

71578e minus 005

35789e minus 005

0

(W)

6

5

4

3

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

157

156

155

154

153

152

151

150

149

148

147

146

145

144

143



Nomenclature

Latin Symbols








0001

001

01

1

10

100

1000

BRD

F (1

sr)








]


]


]

120574 Constant

Greek Symbols


Subscripts




Acknowledgments



References




2

OandCO2





















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















Y

X

(a)




10

12

12

15

20

25

32

S

Di De

TFA38TFA12

TFG12N

TFA40


93

132

120

158

197

265

330

122

168

158

200

250

330

410

025

03

03

03

03

03

035

00407

00565

00540

00702

00912

01313

01757

00429

00591

00568

00730

00942

01345

01799

00890

01730

01500

02480

03830

07000

10464

38998400998400

1299840099840012998400998400

349984009984001998400998400

1 149984009984001 12998400998400


(Lm)

Spessore

S (mm)(thickness)

Fil

(threadconnessione

connection)

De(mm)




0000644202

0000608413

0000572624

0000536835

0000501046

0000465257

0000429468

0000393679

000035789

0000322101

0000286312

0000250523

0000214734

0000178945

0000143156

0000107367

71578e minus 005

35789e minus 005

0

(W)

6

5

4

3

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

157

156

155

154

153

152

151

150

149

148

147

146

145

144

143


0000608413

0000572624

0000536835

0000501046

0000465257

0000429468

0000393679

000035789

0000322101

0000286312

0000250523

0000214734

0000178945

0000143156

0000107367

71578e minus 005

35789e minus 005

0

(W)

6

5

4

3

2

1

0

minus1

minus2

minus3

minus4

minus5

minus6

157

156

155

154

153

152

151

150

149

148

147

146

145

144

143



Nomenclature

Latin Symbols








0001

001

01

1

10

100

1000

BRD

F (1

sr)








]


]


]

120574 Constant

Greek Symbols


Subscripts




Acknowledgments



References




2

OandCO2





















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of




















0001

001

01

1

10

100

1000

BRD

F (1

sr)








]


]


]

120574 Constant

Greek Symbols


Subscripts




Acknowledgments



References




2

OandCO2





















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of
























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of

















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