外文翻译-内燃机冷却风扇设计的新方法.docx
NewDesignMethodForEngineCoolingFanHuangHongbinzhengShiqinLiuShuyanYanWeige(SchoolofVehicularEngineering,BeijingInstituteifTechnology,Beijing100081)AbstractAimToputforwardatypeofmathmodelforoptimizingfan,stwistinglaw.MethUdSThismathmodelwasbasedonturbo-machineryeulerequalionsandcalculusofvariation,itwasconductedforoptimizingtheaerodynamicparametersalongthebladeheightofthefanandthemathmethodwasproducedfortheoptimizationoffan'stwistinglaw.Resultsthetype6102Qenginecoolingfanwasoptimizedbyuseofthismodel»andthecalculationdatawerecontrastedwiththoseofiso-reactioncoefficiencyflowtypeandfreevortexflowtype.Someproblemsexistinginlongbladecanbesolvedbyuseofabovemelhod.ConclusionThedesignparamtersneedn'tbedeterminedartificially,socalculatingresultsaremorerationaltoahighdegreethanthatfromothermethods.Keywords:coolingfan,twistinglaw,optimumdesignThedesignoffanhasbeenahardworkontheorientationofaerodynamicsbecauseoftheomlicatedflowthroughtheblades,sothefanhadbeendesignedbyuseofkaufantheory.Thislawbelievesthattheflowthroughthefanbladesisofone-dimension,theairflowparametersatthemeanbladediameteraretakenintoaccount,buttheflowthroughtherootandtipisnegative.Afterthat,fanwasprojectedaccordingtothesimplyradialbalanceequation.Numericalprecisionwasenhancedbyuseofcompletelyradialequilibriumequationandiso-reactionfactorOftwistinglawtodeterminetheair-flowparametersalongthebladeradialdirection,sotheflowlossesoftipandrootarelessentocertainextent.Inthispaper,theauthorsputforwardamathmodelforoptimizingairflowparameteralongbladeheightbyuseofeulerequationsandcalculusofvariation.1 .MATHMODELWhiletheminutematterGflowsaroundthebladewhichisformedbytwoneighboringflowsurfaces,accordingtoEulerCqUatiOn,fan'spowerisP=o；(v2ur2-vur)G(1)Whereistheangularvelocityofthefan,vluisthecircumferentialspeedatthefaninlet,v2uisthecircumferentialspeedatfanoutlet.rlisthefaninletradius,r2isIhefanoutletradius.Forthecaseofnon-guideblade,Eq.(l)becomesP=V2w2G(2)Wcsetuptherelationsbetweenrlandr2byuseoftheflowfunctionbasedoncontinuityofflow.Theflowfunctionisconstantalongtheflowsurface,andthethoroughfaresurfaceofflowpassageregionisconsideredasflowsurface.Thus,wehavethedefinitionoftheflowsurfaceG=2(3)SubstituteEq.(3)intoEq.(2).andintegralEq.(2),thenrP=2乃&LV2u2<i(4)WherePistheeffectivepowerofthefan,°istheflowfunctionoftheblade-tipThetheoreticalpowerPlisP2万'(v；/2)dpi(5)WherevpisthetheoreticalspeedcorrespondingtoPlForniEqs.(4)(5),thefanefficiencyis1oi2Gtln-v2r(6)WhererlandrO2areinternalandoutradiirespectivelyatthefan,sinletstretchingregion,q()isflowofstreamsperinle(bladeheight,GistheflowofmatterOnthebasisofEulerequations,thefan'spowerPhisK=叫Substitutethisequationintothefirstlawofthermodynamics2(%-M)+(匕-K)-2匕此=OWherevlistheabsolutespeedofthefaninlet,v2istheabsolutespeedofthefanoutlet,HlisIheinletenthalpyofthefan,H2isthecircumferentialspeedofthefanoutlet.Accordingtothespeedtriangleofcascade,substitutingtherelationsbetweenspeeds,wecanobtaintheenergyequationofrelativemotionwhilestaticentropyKeepsconstantMZ2=W；+2(H2l-Hl)-u+u；(9)Fromaboveequations,actualoutletspeedofhealinsulationthatfrictionexistsIsobtained暇=(%(%2一咳一"：-"；)"2,(10)WhereW2/isrelativespeedoffanoutletascommunalentropycourse,Wandw、arerelativespeedsofthefaninletandoutletrespectively,Vlisthecircumferentialspeedofthefaninlet,？isthestaticenthalpyofthefanoutletascommunalentropycourse,0)istheoutletspeedparameterofthefan,W；=2(HHJAccordingtothetriangleofspeedinthethree-dimensionspace,wehave»2“=“2_(02(%wR-wI÷w2)v2zV2/)'(U)HuangHongbinetal./NewDesignMerhodforEngineCoolingFanSubstitutingEq.(l1)intoEq.yields7f：占1叫；-Tf2(PA(Pl片-(1+夕2)吠+2-匕-匕严%d%(I2)ForthefanOfnon-guidcblade,vlf=vlr,vlr=0Accordingtoflowcontinuityqds= (中% 5% /Qdqqdr。=(p2v2rrf2r 2 /r2)dr(3)(14)where % =玖 /人，2 = "JWl 4 饮'he inlet speed factor , 2 is the outlet speed factor , x is inlet flow matter factors, ? is outlet flow matter factors, rr is inlet streamline radius, 2 诒 outlet StreamIine radius.Eq.(12) belongs to the extreme value problem with qualifications, it can be solved by use of Lagrangian multiplier, the Lagrangian function isF = 2 2lV,c2-rf2v1p -(1+ 炉)就 +a>2-v -巨产+ 4(%) + 4仇)寿/21-4仇)w/q -4伍)02%i石5(15)Where () and 4(%) are Iagrangian multipliersAccording to the relation of aerodynamics, the relationship of densities between inlet and outlet areThusP2 =自口 +伏+ 1）够/（2心）严1）总=（D阮+吟(16)(17)Where vl is inlet sound speed. % 依 OUHel sound speed.For the extreme value problem of Eq.(12),we make use of the Euler-Iagrangian equations5Fv2r7- = Rrf20 =0, a>GVifv2uSF2v2rqn1 C- =亏小2(r0)户2 一心 = °&喔*&%2;FG(8)F _ 2 忆。2.沙岩一/仆；,4 = 0,(9-M(T)=-4(%)P|vIr-4(G)"1vIr-0=0，%rfl%4色声）叱%/22 2詈会-4(")p2 -乙2。2(20)-/-%(%)。此一少1=0打GWhere(21)也=5vIp-(l+¾)w+2f/?-年-g严FromEq.(18)w
