DO Radiation Model Theory

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1、5.3.6.DiscreteOrdinates(DO)RadiationModelTheoryWhatisit?Thediscreteordinates(DO)radiationmodelsolvestheradiativetransferequation(RTE)forafinitenumberofdiscretesolidangles,eachassociatedwithavectordirectionSfixedintheglobalCartesiansystemxyz,,.Thefinenessoftheangulardiscretiza

2、tioniscontrolledbyyou.Howdoesitwork?TheDOmodeltransformsEquation5–17intoatransportequationforradiationintensityinthespatialcoordinatesxyz,,.TheDOmodelsolvesforasmanytransportequationsastherearedirectionsS.Thesolutionmethodisidenticaltothatusedforthefluidflowandenergyequations

3、.&')(assistheopticalthicknessoropacityofthemedium.InANSYSFLUENT:TwoimplementationsoftheDOmodel:uncoupledand(energy)coupled.Uncoupledimplementation:ItissequentialinnatureandusesaconservativevariantoftheDOmodelcalledthefinite-volumescheme,anditsextensiontounstructuredmeshes.In

4、thiscase,theequationsfortheenergyandradiationintensitiesaresolvedonebyone,assumingprevailingvaluesforothervariables.Coupledordinatesmethod(orCOMET):Thediscreteenergyandintensityequationsateachcellaresolvedsimultaneously,assumingthatspatialneighborsareknown.Theadvantagesofusingth

5、ecoupledapproachisthatitspeedsupapplicationsinvolvinghighopticalthicknessesand/orhighscatteringcoefficients.Suchapplicationsslowdownconvergencedrasticallywhenthesequentialapproachisused.5.3.6.1.TheDOModelEquationsTheDOmodelconsiderstheradiativetransferequation(RTE)inthedirectio

6、nSasafieldequation.Thus,Equation5–17iswrittenasANSYSFLUENTalsoallowsthemodelingofnon-grayradiationusingagray-bandmodel.TheRTEforthespectralintensityIrs,canbewrittenasHereisthewavelength,aisthespectralabsorptioncoefficient,andIistheblackbodybintensitygivenbythePlanckf

7、unction.Thescatteringcoefficient,thescatteringphasefunction,andtherefractiveindexnareassumedindependentofwavelength.Thenon-grayDOimplementationdividestheradiationspectrumintoNwavelengthbands,whichneednotbecontiguousorequalinextent.Thewavelengthintervalsaresuppliedbyyou,andcorres

8、pondtovaluesinvacuum(n).TheRTEisintegratedove