Power from the Sun Chapter9.docx

Power from the Sun Chapter9.docx

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PowerfromtheSunChapter9

9._________________________ConcentratingCollectors

Theopticalprincipleofareflectingparabola（asdiscussedinChapter8）isthatallraysoflightparalleltoitsaxisarereflectedtoapoint. Aparabolictroughissimplyalineartranslationofatwo-dimensionalparabolicreflectorwhere,asaresultofthelineartranslation,thefocalpointbecomesaline. Theseareoftencalledline-focusconcentrators. Aparabolicdish（paraboloid）,ontheotherhand,isformedbyrotatingtheparabolaaboutitsaxis;thefocusremainsapointandareoftencalledpoint-focusconcentrators. 

Ifareceiverismountedatthefocusofaparabolicreflector,thereflectedlightwillbeabsorbedandconvertedintoheat（ordirectlyintoelectricityaswithaconcentratingphotovoltaiccollector）. Thesetwoprincipalfunctions,reflectiontoapointoraline,andsubsequentabsorptionbyareceiver,constitutethebasicfunctionsofaparabolicconcentratingcollector. Theengineeringtaskistoconstructhardwarethatefficientlyexploitsthesecharacteristicsfortheusefulproductionofthermalorelectricalenergy. Theresultinghardwareistermedthecollectorsubsystem. Thischapterexaminesthebasicopticalandthermalconsiderationsthatinfluencereceiverdesignandwillemphasizethermalreceiversratherthanphotovoltaicreceivers.

Alsodiscussedhereisaninterestingtypeofconcentratorcalledacompoundparabolicconcentrator（CPC）. Thisisanon-imagingconcentratorthatconcentrateslightraysthatarenotnecessarilyparallelnoralignedwiththeaxisoftheconcentrator. 

∙Tocompletethissectionwedescribeengineeringprototypeconcentratorsthathavebeenconstructedandtested. Parabolicconcentratorsthatarenotcommercialproductswerechosenfordiscussion. Thisallowsfreediscussionwithoutconcernforrevealingproprietaryinformation. Inaddition,theprototypeconcentratorsdiscussedarerepresentativeoftheparabolicconcentratorsunderdevelopmentforcommercialuse,andconsiderabledesigninformationisavailable.

Performancedatafromsomeearlyprototypesarepresented. Thedevelopmentincludesthefollowingtopics:

∙ReceiverDesign

oReceiverSize

oReceiverHeatLoss

oReceiverSizeOptimization

∙CompoundParabolicConcentrators（CPC）

∙PrototypeParabolicTroughs

oSandiaPerformancePrototypeTrough

∙PrototypeParabolicDishes

oShenandoahDish

oJPLPDC1

∙OtherConcentratorConcepts

oFixed-MirrorSolarCollector（FMSC）

oMovingReflectorStationaryReceiver（SLATS）

oFixed-MirrorDistributedFocus（FMDF）（sphericalbowl）

∙PrototypePerformanceComparisons

Specialnotetothereader:

 Theprototypehardwaredescribedinthesectionsbelowrepresentsthestate-of-the-artinthe1970´sandearly1980´s. Forupdatesoncurrentstatusofsolarconcentratorhardware,thereaderisreferredtothewebsiteofTheSunLab（combinedeffortsofSandiaNationalLabsandtheNationalRenewableEnergyLaboratorywebsite:

  http:

//www.energylan.sandia.gov/sunlab/overview.htm andtheInternationalEnergyAgencywebsite:

 http:

//www.solarpaces.org/csp_technology.htm. Readersarealsoencouragedtoaccessthewebsitesofdifferenthardwaremanufacturers.

9.1   ReceiverDesign

Thejobofthereceiveristoabsorbasmuchoftheconcentratedsolarfluxaspossible,andconvertitintousableenergy（usuallythermalenergy）. Onceconvertedintothermalenergy,thisheatistransferredintoafluidofsometype（liquidorgas）,thattakestheheatawayfromthereceivertobeusedbythespecificapplication.

Thusfarwehaveconcentratedourattentiononreflectionofincidentsolarenergyandnotbeenconcernedwiththegeometryofthereceiver. Therearebasicallytwodifferenttypesofreceivers-theomnidirectionalreceiverandthefocalplanereceiver.

Ratherthandealincompletegeneralityandtalkaboutthemanypossibletypesofreceiversthatcouldfallintothesetwocategories,wediscussonlytwowidelyusedreceivers,thelinearomnidirectionalreceiverandthepointcavityreceiver. Thiswillnotartificiallylimittheapplicabilityofthedevelopmentofthefollowingparagraphsbutwillprovideanicefocustothediscussion.

Figure9.1isasphotographofalinearomnidirectionalreceiverusedwithparabolictroughs. Itconsistsofasteeltube（usuallywithaselectivecoating;seeChapter8）surroundedbyaglassenvelopetoreduceconvectionheatlosses. Asthename´omnidirectional´implies,thereceivercanacceptopticalinputfromanydirection.

Figure9.1 Linearomnidirectionalreceiver,（a）photographofoperationalreceiver;（b）sketchofreceiverassemblycross-section. CourtesyofSandiaNationalLaboratories.

Figure9.2isasketchofacavityreceiver. Thisisclearlynotanomnidirectionalreceiversincethelightmustenterthroughthecavityaperture（justinfrontoftheinnershieldforthisreceiver）tobeabsorbedonthecavitywalls（coiledtubesinthiscase）.

Figure9.2 Cavity（focalplane）receiver. CourtesyofSandiaNationalLaboratories.

Typically,theplaneofthecavityapertureisplacednearthefocusoftheparabolaandnormaltotheaxisoftheparabola. Thussuchareceiverissometimescalledafocalplanereceiver. Althoughthecavitycouldbelinearandthususedwithaparabolictrough,acavityreceiverismostcommonlyusedwithparabolicdishes. Figure9.3isaphotographofthissameparabolicdishcavityreceiver.

Figure9.3  PhotographlookingintothecavityapertureofthereceiverofFigure9.2.CourtesyofSandiaNationalLaboratories

9.1.1  ReceiverSize

OmnidirectionalReceivers-TheappropriatesizeforanomnidirectionalreceiverwasdevelopedinChapter8. ThediameterofatubereceiverisΔrasdefinedinEquation（8.44）（and2r1 asshowninFigure9.1b）. Areceiverofthissizeinterceptsallreflectedradiationwithinthestatisticalerrorlimitsdefinedbyn. Thisequationisreproducedhereasanaidtothereader.

                  （8.44）

wherepistheparabolicradius,nthenumberofstandarddeviations（i.e.definingthepercentofreflectedenergyintercepted）,andσtot theweightedstandarddeviationofthe beamspreadangleforallconcentratorerrors,asdevelopedinSection8.4anddefinedbyEquation（8.43）. 

Aswillbedescribedbelow,thevalueofn（i.e.thenumberofstandarddeviationsofbeamspreadinterceptedbyareceiverofsizeΔr）,isdeterminedinanoptimizationprocessbasedonbalancingtheamountofinterceptedradiationandamountofheatlossfromthereceiver. Putinsimplifiedterms,alargerreceiverwillcapturemorereflectedsolarradiation,butwillloosemoreheatduetoradiationandconduction.

CavityReceivers-Theappropriatesizeofthecavityopening（i.e.itsaperture）isdeterminedusingthesameopticalprinciplesusedinthedevelopmentofEquation（8.44）butthenprojectingthereflectedimageontothefocalplanewherethereceiveraperturewillbelocated.

IfthebeamspreadduetoerrorsissmallinFigure9.4,theanglesα andβ areapproximately90degrees. Thustheprojectionoftheimagewidthontothefocalplaneis

                      （9.1）

SubstitutionintoEquation（8.44）yields

                                     （9.2）

Figure9.4 Sizingofcavityapertureconsideringbeamspreadingduetoerrors.

SelectionofConcentratorRimAngle-Itisinterestingtostudytheimpactofreceivertypeonthepreferredconcentratorrimangle. Thewholeideaofaconcentratoristoreflectthelightenergyincidentonthecollectorapertureontoassmallareceiveraspossibleinordertominimizeheatloss.

Figure9.5isaplotoftherelativeconcentrationratiosforbothcavitiesandomnidirectionalreceiversasafunctionofrimangle. TheconcentrationratioforthetwoconceptsistheratioofthecollectorapertureareadividedbytheareaoftheimageatthereceiverasdefinedbyEquations（8.44）and（9.2）,respectively. Notethatthecurvefortheomnidirectionalreceiverincreasesuniformlyupto90degrees,whereasthecurveforthefocalplanereceiverincreasesuptoarimangleofabout45degreesandthendecreasesbecauseofthecosineψ terminthedenominatorsinEquations（9.9）and（9.10）.

Figure9.5 Variationofgeometricconcentrationratiowithrimangle.

Theimpactofthisphenomenonisthatmostconcentratorswithanomnidirectionalreceiverhaverimanglesnear90degrees. Ontheotherhand,concentratorswithfocalplanereceivershaverimanglesnear45degrees. Thecurvesshowonlytrendsforeachreceivertype,andtheirmagnituderelativetoeachotherasshowninFigure9.5isnotcorrect.

9.1.2  ReceiverHeatLoss

LinearOmnidirectionalReceivers-TheheatlossratefromalinearomnidirectionalreceiverofthetypeshowninFigure9.1isequaltotheheatlossratefromtheoutsidesurfaceoftheglasstube. Thiscanbecalculatedasthesumoftheconvectiontotheenvironmentfromtheglassenvelopeplustheradiationfromtheglassenvelopetothesurroundings.

                   （9.3）

where:

hg=convectiveheat-transfercoefficientatoutsidesurfaceofglass

            envelope（W/m2°C）

Ag=outsidesurfaceofglassenvelope（m2）

Tg=outsidesurfacetemperatureofglassenvelope（K）

Ta=ambienttemperature（K）

σΒ  =Stefan-Boltzmannconstant（5.6696×10-8W/m2K4）

ε g=emittanceoftheglass

Fga=radiationshapefactor

Ts=skytemperature（K）（typicallyassumedtobe6Kelvinslowerthanambienttemperature）（Treadwell,1976）

Ifallthevariablescanbeeval