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l46’l2 Vol.46No.22010 2 l129—134jACTAMETALLURGICASINICAFeb.2010pp.129–134 ;qGasarv2:i % no $ w3-k t+∗AGEDAC(RWYaJ()0 8O:! #DnP_, 100084)IBF=?H=(uD(WYar(Y ,u650093)61 =& 2 p a7 ?e9 |1 =,QEfAyITn$ rnOM Gasar)v?e)v*p P 6 k / +6 6p%sf 6b ?eEfwM, {E?vb 6 k /e ?eEf , ; 5?9 Qd ; R , ; v,Ef , ; Qd ;H C. , ;2W, +6 rgE6p%L{E?vbveK }i,℄ 6b V D, n1pS Rr[5* :r1.72g·v=AEL1.72·v=B( ?,AEBz[)( \KpH2EpArsf7 |Te3p).y j 6 k, k– , ,OM,E?vb9’psÆ{TG249.6,TG146),d# A)7{0412−1961(2010)02−0129−06THEORETICALANALYSISONEFFECTOFTRANSFER-ENCEVELOCITYONSTRUCTUREOFPOROUSMETALSFABRICATEDBYCONTINUOUSCASTINGGASARPROCESSLIUYuan,LIYanxiang,LIURunfaKeyLaboratoryforAdvancedMaterialsProcessingTechnology,MinistryofEducation,DepartmentofMechanicalEngineering,TsinghuaUniversity,Beijing100084ZHOURong,JIANGYehua,LIZhenhuaFacultyofMechanicalandElectricalEngineering,KunmingUniversityofScienceandTechnology,Kunming650093Correspondent:LIUYuan,associateprofessor,Tel:(010)62789328,E-mail:yuanliu@tsinghua.edu.cnSupportedbyNationalNaturalScienceFoundationofChinaandYunnanProvincialGovernment(No.u0837603),NaturalScienceFoundationofBeijing(No.2092017),ScientificRe-searchFoundationfortheReturnedOverseasChineseScholars,StateEducationMin-istry(No.20091020471)andKeyTalentsFoundationofTsinghuaUniversityManuscriptreceived2009–07–31,inrevisedform2009–10–19ABSTRACTTransferencevelocityisanimportantprocessingparametertoinfluencethefinallotus–typeporousstructurefabricatedbycontinuouscastingGasarprocess.Viasolvingthesolutediffusionequation,atheoreticalmodelwasdevelopedtopredicttheeffectofthetransferencevelocityontheporosity,theporediameterandtheinter–porespacing.ThepredictedvaluesatdifferenttransferencevelocitieshaveagoodagreementwiththecorrespondingexperimentalresultsobtainedbyJapaneseresearcher.Theaverageporediameterandtheinter–porespacingLbothhaveaprominentdecreasewiththeincreaseoftransferencevelocityv,buttheporosityonlyhasaslightdecrease.Thetheoreticalrelationshipsbetweentheporeradiusrg,theinter–porespacingandthetransferencevelocitycanbedescribedbythetwosimpleequationsasr1.72g·v=AandL1.72·v=B,whereAandBareallconstants*9lV.1Z_ [– }M1t. MH_ EoA{u0837603, ^V.1Z_ A{2092017f Æ$YZZ91 1^ x_ A{20091020471E#SXZ1 1’/?jUA{TKb‘G!4 :2009–07–31,b‘U !4 :2009–10–19℄’rÆ:[ ,~,1974 I, g, YDOI:10.3724/SP.J.1037.2009.00527 130 i X l46’dependingontheusedgaspressuresandthemelttemperature.KEYWORDSporousmetal,metal–gaseutectic,continuouscasting,transferencevelocity 7 l&V = (H t+ ?0 #0h qfT [I,-Hx: oC4 f*&V a A fFa, ;Æimo3\Fgf_3 . ;Æ*wB,z/ G; zh N l7d C 86 l h,^)G*w% 7f 0+qF ! S Ff8;Fs,,% \8#N 7 0[1].Gasar*w\oCH l– - + ℄o ^ SwC 3,: ’JO,|3:o wCH J5,R \ Q8# 7 lfL*w[2].GasarN 7 0( 7fQkF !)\| 2G n* ~ af, 7, 7 {|y2s. 0K$ N 7 lfT p,;6= } C^ S( L (}hT ,X$ WF hfL[F0[T Z.Gasar*w\1 Shapovalov[2,3] J _,2O5 [4−6] m:?-tgSandia:mRe‘[7−9]tg: $TY[[10−15].$U: _*^.)G _Ig) ; 1a~XfrBÆk O*0NNA\wC 3,z/O9s\ +,^ 3w% s8 0( 3w l Æk qY0+qtg l Ff_0+q)w, |S 3f S, 3 q qw ~j), 3w l ^ o%Fgf*w+qA SwSW_, Ige ℄L 8 }h+qf q.* s\N f,p,Parkh[16]\ . U; 1b~XfPN Gasar*w. f p!\, q qw + FwA)w, ,% 3 3w{2t Mw ,,% 32t t$ / S.X , *wX2J0YBV ,$ * L.^pAf\,a| 6,Fw( q qw) 7BV 7q&f 7 !6[16] Q 7CufRe7. B,-Xl o%I℄fFgxNA SSW -,t X3– R:H J5;, ) :6Fgf F5_J0{$ Fgyz.‘ P, !RFg ’d, & soN l– l- J5f qJackson–HuntxN[17], ’ 3 q b8 fH2 } !,H qJackson–HuntxNf\EB} #,zJo% so 3w(Fw) 7BV 7q&tg 7 fFgxN, 5 [(fRe [16] S , OWfPN ;Æ, Q 7 l*w +Fg5_,nG Gasar 3f3S.1 . 1.1 x /!8 mufl PNFw ,\f 7BVF4q !{ , ,)y S l– - wC 3T S$ 3 ~.|P,2t ; 2~XfXy Aso l– - wC 3gF= Q 7 0, zJ l– - 3f:==? . 3 qB,zJ| 3 q C f J‘ +Orθz.rg 7 ,L 7q&,rs -℄ Qhqd , L≈0.95·(2rs)(1) 72 X ε=r2g/r2s(2) UsW }2’ ,V^;/ow:(1)F=f Q 8# 7 0h 7BVF !{, ,rgFrsMw.(2) 3 q bf8 , S q CB% \.(3) 3wvMw , ,hvr=vθ=0,vz=v.(4) 3 q bm:, S q CBf } !, o8.(1Gasar)v?( e2BvB 2 E Fig.1TwokindsofdirectionalsolidificationtechniquesusedinGasarprocess(a)simplemouldcasting(b)continuouscastingl2 Z g:NL Gasar(uDua 5 j . dDe &131 (2 k– , vB 2Wx f& |1e9 _ *Fig.2Schematicdiagramsformetal–gaseutecticunidirectionalsolidification(a)andtheideallotus–typeporousstructure(b),andthecorrespondingcoordinatesystem(c)forsolvingthesolutefield(5) 3 qB’Jf , }h lf8p }Tm. Boowf‘LB,J‘ /8 f3DN= 2sW $ =? ∂2cl∂r2+1r∂cl∂r+∂2cl∂z2+vDl∂cl∂z=0(3)V,cl 8 fH2 },mol/m3;Dl ! U 8 f=?+q.V(3)\o% 4 , w ∂cl∂z z=0=vDlpbRgTm(0≤r≤rg)∂cl∂z z=0=−vDl(¯c∗l−¯c∗s)=−vDl(1−k0)¯c∗l(rgr≤rs)(4)V,¯c∗lF¯c∗s H2 3 qB lm:F3:f , },mol/m3;k0 := L +q;Rg y 4q;pb ℄ . V(3)’ f-u!6[17,18],2t’J cl=c0+∞Xn=0Bnexp(−ωnz)J0(λnr/rs)(5)V,J0(x)\W Besselq;λn\o BesselqJ1(x)=0f&;c0 8 HU! },2 Sievertw‘’c0=ξ(T)√pH2(6)+qωn ωn=(v/2Dl)+p(v/2D1)2+(λn/rs)2(7)+qBn2&# w’JB0=(1−k0)(1−ε)¯c∗l−pbRgTm·ε(n=0)Bn=−2√εJ1(√ελn)λnωnJ20(λn)vDlh(1−k0)¯c∗l+pbRgTmi(n≥1)(8)V(5)h 3 q bf:= } ! , d 2’J 3 qB(z=0)m: ,H2 }¯c∗l,h¯c∗l=Zrsrg2πrcl z=0drπ(r2s−r2g)=c0+B0+vDlh(1−k0)¯c∗1+pbRgTmi∞Xn=14εJ2l(√ελn)(1−ε)λ2nωnJ20(λn)(9)ZB0Oa¯c