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1、NewDesignMethodForEngineCoolingFanHuangHongbinzhengShiqinLiuShuyanYanWeige(SchoolofVehicularEngineering,BeijingInstituteifTechnology,Beijing100081)AbstractAimToputforwardatypeofmathmodelforoptimizingfan,stwistinglaw.MethUdSThismathmodelwasbasedonturbo-machineryeulerequalionsandcalculusofvariation,it
2、wasconductedforoptimizingtheaerodynamicparametersalongthebladeheightofthefanandthemathmethodwasproducedfortheoptimizationoffanstwistinglaw.Resultsthetype6102Qenginecoolingfanwasoptimizedbyuseofthismodelandthecalculationdatawerecontrastedwiththoseofiso-reactioncoefficiencyflowtypeandfreevortexflowtyp
3、e.Someproblemsexistinginlongbladecanbesolvedbyuseofabovemelhod.ConclusionThedesignparamtersneedntbedeterminedartificially,socalculatingresultsaremorerationaltoahighdegreethanthatfromothermethods.Keywords:coolingfan,twistinglaw,optimumdesignThedesignoffanhasbeenahardworkontheorientationofaerodynamics
4、becauseoftheomlicatedflowthroughtheblades,sothefanhadbeendesignedbyuseofkaufantheory.Thislawbelievesthattheflowthroughthefanbladesisofone-dimension,theairflowparametersatthemeanbladediameteraretakenintoaccount,buttheflowthroughtherootandtipisnegative.Afterthat,fanwasprojectedaccordingtothesimplyradi
5、albalanceequation.Numericalprecisionwasenhancedbyuseofcompletelyradialequilibriumequationandiso-reactionfactorOftwistinglawtodeterminetheair-flowparametersalongthebladeradialdirection,sotheflowlossesoftipandrootarelessentocertainextent.Inthispaper,theauthorsputforwardamathmodelforoptimizingairflowpa
6、rameteralongbladeheightbyuseofeulerequationsandcalculusofvariation.1 .MATHMODELWhiletheminutematterGflowsaroundthebladewhichisformedbytwoneighboringflowsurfaces,accordingtoEulerCqUatiOn,fanspowerisP=o；(v2ur2-vur)G(1)Whereistheangularvelocityofthefan,vluisthecircumferentialspeedatthefaninlet,v2uisthe
7、circumferentialspeedatfanoutlet.rlisthefaninletradius,r2isIhefanoutletradius.Forthecaseofnon-guideblade,Eq.(l)becomesP=V2w2G(2)Wcsetuptherelationsbetweenrlandr2byuseoftheflowfunctionbasedoncontinuityofflow.Theflowfunctionisconstantalongtheflowsurface,andthethoroughfaresurfaceofflowpassageregioniscon
8、sideredasflowsurface.Thus,wehavethedefinitionoftheflowsurfaceG=2(3)SubstituteEq.(3)intoEq.(2).andintegralEq.(2),thenrP=2乃&LV2u22-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 inl
9、et 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, aGVifv2uSF2v2rqn1 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+)w+2f/?-年-g严FromEq.(18)w
