EVALUATION OF TEMPERATURE DISTRIBUTION AND FLUID FLOW IN FUSION WELDING PROCESSES

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1 Nume olume mch Jounl o Engneeng EALAION OF EMPERARE DISRIBION AND FLID FLOW IN FSION WELDING PROCESSES Ass. Po. D. Ihsn Y. Hussn Mech. Eng. Dep. College o Eng. nvesy o Bghdd Bghdd Iq Slh Seeh Aed - AlKeem Al-hee Insue Mnsy o Lo nd Socl As Bghdd Iq ABSRAC A heoecl sudy o he nse nd lud low phenomen n weldng pocess hs een ced ou n he pesen wok. he sudy nvolved he numecl soluon o he nsen Nve- Sokes nd Enegy equons o he weld pool egon y usng Fne Deence Mehod. he elecomgnec oce eld nd uoyncy wee ncluded n he omulon he sem-vocy omulon ws used n he mhemcl model. he numecl soluon s cple o clculng he vocy, sem uncon, velocy, empeue, nd he nece movemen o he weld pool n Gs Mel Ac Weldng (GMAW). he model cn e used o solve he Gs ungesen Ac Weldng (GAW) polem. A numecl clculons lgohm ws developed o cy ou he numecl soluon. he numecl esuls showed h he nge peneon phenomen occus n he Gs Mel Ac weld s dequely explned hough he pplcon o he model. I s ound h he equency o spy nse s domnn co n ddon o shpe o he weld pool geomey. A vecon o numecl esuls ws mde hough compson wh pevous wok, he geemen ws good, conmng he cply nd elly o he poposed numecl lgohm n clculng lud low nd he nse n Gs Mel Ac weld pools. ( ) ( ) ١٣١٣

2 I.Y. Hussn Evluon o empeue Dsuon nd Flud S. S. Aed - AlKeem Flow n Fuson Weldng Pocesses KEY WORDS He nse, Flud Flow, Elecomgnec Foce, Weld Pool, Numecl Soluon INRODCION he he nd lud low n he weld pool cn sgncnly nluence he pool geomey nd he empeue gdens. A deled knowledge o he empeue led nd hemlly nduced low n weld pool s mpon n undesndng he phenomen nd n developmen o mpoved weldng echnques, nd numecl smulons oe he possly o vodng hs dculy nd povde ee qunve descpon o he coupled soluon ehvo. I we consde molen weld pool esulng om n ppled suce empeue o he lux, he heml gdens nduce uoyncy oces n he weld pool h end o cuse lud low. I s o consdele pccl nees o undesnd qunvely he he nd lud low phenomen n weld pool, ecuse oh he velocy nd empeue dsuons o molen mel ec he weld pool geomey, mcosucue, nd mechncl popees o he weld poduced. Inheen o he weldng pocess s he omon o pool o molen mel decly elow he he souce. he shpe o hs molen pool s nluenced y he low o oh he nd mel, wh melng occung hed o he he souce nd soldcon ehnd. Flud low n weld pool cn songly ec he quly o he esuln weld. ons n he weld chcescs, whch e lkely o occu om chnges n he weld pool lud low e weld peneon, undecung, suce smoohness segegon pen, gs poosy nd soldcon sucue, (Gukn nd Sundn. ٢٠٠١), see Fg. (١). he polem ws nvesged n leues wh deen ppoches, (Oepe nd Sekely. ) developed genel mhemcl semen o desce he nsen weld pool developmen. In he omulon, x-symmec sysems e consdeed nd llownce s mde o uoyncy, suce enson, nd elecomgnec oces. (so nd Wu. ) developed mhemcl model o evlue he eec o he elecomgnec oce eld, he velocy eld nd he empeue eld n Gs Mel Ac (GMA) weld pool. (s nd Kou. ) suded he convecon low nduced y he elecomgnec oce n he weld pool dung gs ungsen c weldng. In ode o ccuely desce he oundy condons, (Km nd N. ) developed compue smulon o hee dmensonl he nse nd lud low n Gs Mel Ac (GMA) weldng y consdeng he hee dvng oces o weld-pool convecon. (Gukn, e. l. ) developed sysemc sudy o wo dmensonl model o nlye he ole o convecon n he sony (GA) welds o nlye he ehvo o weld pool convecon nd s eec on he weld geomey. he pesen wok epesens he egnnng o new esech lne n Iq h ms o nvesge he heml nd lud low phenomen ssoced wh weldng pocess. A compuonl sudy o lud low nd he nse phenomen occued n he weld pool. he smulon coves he molen phse, he wo phse nd he sold phse egon. MAHEMAICAL MODEL Fgue ( ) shows dgm o Gs Mel Ac (GMA) lqud pool nd he cylndcl coodne sysem chosen o nlyss. eloces long he dl nd xl decons e expessed s nd, especvely. A splly dsued he lux, q(), nd cuen lux, (), ll on he ee suce (Z ), whch s he suce o he wokpece, he enegy exchnge eween he spy doples nd molen pool s H.As shown n g( ), le (,) nd (,) denoe he velocy componens n he dl nd xl decons, especvely. he unsedy-se connuy, momenum nd enegy equon o he ncompessle lud n he molen pool s (Slh. ) ; ١٣١٤

3 Jounl o Engneeng olume mch Nume ١٣١٥ sng he vocy nspo omulon (Slh ), cn e shown h ; he sem uncon equon s ; he empeue equon n he consevve om s ; he elecomgnec oce em n equon ( ) s (so nd Wu ) ; nd he enegy exchnge (H) s ; Inl nd Boundy Condons Repesenons he nl condons used o solve empeue, vocy nd sem uncon equons e ;, w, ψ,, ٠ ٠ he oundy condons used e gven n Fg.(٣). NMERICAL SOLION he govenng equons menoned ove wee solved numeclly y usng he FDM. A gd ngemen ws geneed wh he noon o g.(٤). he empeue o ech gd pon n weldmen s comped wh he melng empeue m. Once he lqud egon emeges, he lud ψ ψ ψ ( ) ( ) ( ) ( ) ( ) ) ( H p F p F α µ ρ ρ µ ρ ρ / ρc p α B g β υ ( ) ( - 7) ) ( ) ( C p H ρ α ( ) ) 6 ( exp L L l C B o o σ π µ ( ) ) ( ) / (.8 C P C H e ρ ( )

4 I.Y. Hussn Evluon o empeue Dsuon nd Flud S. S. Aed - AlKeem Flow n Fuson Weldng Pocesses low nd he nse n he weld pool nd he he conducon ou o he molen pool e clculed. he nodl equon ; ١ M, ( ),,, 5, B()...(C 5) he nodl equon ; ١, ( ),, ( 5 ), q() B()...(C ) K he nodl equon R/١ (.e R),,, ( 5 ), q() B()...(C 7) K, A ; ١ (, (- k d / (ow cp d ) us d / d vs d / d) (, ( k d /( ow cp d ( k d / (ow cp d ) us d / d) ( ;... ) vs d / d) (, ) ph q() d / (ow cp d ) dh d /( ow cp) ;... (C - 5) A ; M (, (- *k *d / (ow *cp *d ) * h * d /( ow* cp * d))* (, (* k * d / (ow *cp *d ))* (,... (* k *d / (ow *cp *d ))* (, ) (* h * d / (ow *cp *d))* ;... (C - 6) A ; JFL < < M (, (- * k *d / (ow *cp *d ))* (, (* k * d /( ow* cp * d ( k * d /( ow* cp * d ))* (, ) ( k * d /( ow* cp * d ))* (,... ))* (, ) ;... (C - 7) A < < N q ; (, (- *k *d / (ow *cp*d ) * us * d / d * vs * d / d)* (, ( k * d /( ow* cp * d us * d / d) * (,... (*k *d / (ow *cp *d ) * vs * d / d)* (, ) * d * q( ) * ph /( ow* cp * d ) us * d / d)* (, ( k * d /( ow* cp * d ) dh * d /( ow* cp) ;... (C - 8) ١٣١٦ )

5 Nume olume mch Jounl o Engneeng A N q ; (, ( * k * d /( ow * cp * d ( k * d /( ow * cp * d ) * h * d /( ow * cp * d) us * d / d) * (, )) * (, ( k * d /( ow * cp * d ) us * d / d)* (,... ( * k *d/(ow *cp *d )) * (, ) * h * d * /( ow * cp * d) dh * d /( ow * cp) ;... (C - 9) A N ; ((, (- *k *d /(ow *cp*d ) * h* d / (ow *cp*d))*(, (*k *d / (ow *cp*d ))* (, ) (* k * d / (ow *cp*d ))* (, (* h* d / (ow *cp*d))* ;... (C - ) A N q < < N ; (, ( * k * d /( ow * cp * d ( k * d /( ow * cp * d (* k * d /( ow * cp * d ) * h * d /( ow * cp * d)) * (, )) * (, ( k * d /( ow * cp * d )) * (,... )) * (, ) (* h * d /( ow * cp * d)) * ;... (C - ) A N ; M (, ( * k * d /( ow* cp* d (* k * d /( ow* cp* d ) * h* d /( ow* cp* d))* (, ))* (, (* k * d /( ow* cp* d ))* (, ) (* h* d /( ow* cp* d))* ;...(C - ) A < < N ; M (, ( * k * d /( ow * cp * d ( k * d /( ow * cp * d (* k * d /( ow * cp * d ) * h * d /( ow * cp * d))* (, )) * (, ( k * d /( ow * cp * d )) * (,... )) * (, ) (* h* d /( ow * cp * d)) * ;... (C - ) A N ; < < M (, ( * k * d /( ow* cp * d (* k * d /( ow * cp * d ( k * d /( ow * cp * d ) * h * d /( ow * cp * d))* (, )) * (, ( k * d /( ow * cp * d )) * (, ) (* h* d /( ow * cp * d)) * ))* (, )... ;... (C - ) A < < IFL ( ; < < IFL (, ( * k * d /( ow* cp * d ))* (, ( k * d /( ow* cp * d ))* (, ( k * d /( ow* cp * d ))* (,...( k * d /( ow* cp * d ))* (, ) ١٣١٧ ( k * d /( ow* cp * d ))* (, ) ;... (C - 5)

6 I.Y. Hussn Evluon o empeue Dsuon nd Flud S. S. Aed - AlKeem Flow n Fuson Weldng Pocesses ١٣١٨ he empeue equon n weld pool ; Whee ; he elecomgnec oce eld n he vocy equon ; σ π µ L ) ( exp ) L( I C B) (J o o C )/ C (.8e B.5.5 P ) ( 5 ρ α α α α α α B..., 5,,,,, C..., 5,,,,, υ υ υ υ υ υ

7 Nume olume mch Jounl o Engneeng he empeue equon he cenelne s ;, ( ) ( ) ( ) ( ) ( ) α, ( ),,,,,,,,,, H...(.) ρcp Whee ; α C C C C C 5 H ρc ( ) ( ) ( ) ( ) ( ) p α α α α...(.5) he vocy equon cenelne ;, D, D, D, D, D5...(.6) Whee ; D D D ٠, ( ) ( ) ( ) ( ) ( ) ν ١٣١٩ ν ν...(.6)

8 I.Y. Hussn Evluon o empeue Dsuon nd Flud S. S. Aed - AlKeem Flow n Fuson Weldng Pocesses he sem uncon o he nex eon (m ) ; ψ Ω, ψ ψ ( m ) ( m) ( m) ( m ), Ω ψ,, ( m) ( m ) ( ψ, ψ, ) ]... ( 5), Fom (Peovc nd Supe. ) ; π π cos cos (N ) (N ) γ Ω O P γ... γ ( 7) he dl nd vecl veloces ;, ( Ψ Ψ ),,... Clculon o he ecl elocy Cenelne om (Chow.١٩٧٩) ; ( 8) Ψ,,... ( Ψ Ψ ),,,...( 9) ( ) RESLS AND DISCSSIONS ١٣٢٠

9 Nume olume mch Jounl o Engneeng Fgue ( ) shows he compued sohems nd convecon pens n he pool o he weld o ccoun o convecon nd empeue dsuon n movng weld pools dven y uoyncy nd elecomgnec oces mes (.,.,. nd. seconds). As me psses, he molen pool nceses o MIG weldng pocess. he deep peneon s oseved n he gue. he lqudus empeue s C nd he soldus C. Fgue ( ) shows he compued sem uncon n he cse o comned uoyncy nd elecomgneclly dven low o he weld pool mes (.,.,. nd. seconds), especvely. As me psses, he molen pool nceses. Fgue ( ) shows song couneclockwse cculon pen, wh vey hgh veloces, whch s domned y he comned eec o he uoyncy nd elecomgneclly dven low componens. he weld pool shpe, nvolvng deep peneon, s conssen wh he cculon pen, (.,.,. nd. seconds), nd he lge he weld pool. I s hs nse o ddonl he om he mel doples (H) n he GMA pocess whch plys vey mpon ole n he omon o he nge peneon n he GMA welds. hs phenomenon s no pesen n he GAW pocess. Fgues ( ) nd ( ) show he nece eween he molen pool nd he sold egon deen mes (.,.,. nd seconds) especvely dung MIG nd IG weldng pocesses. A compson eween he clculed numecl esuls o he pesen wok nd he esuls o SAO nd Wu ( ) wll e mde o vecon. Some esuls wee seleced n ode o check he model. Fgues ( ) nd ( ) o he pesen wok my e comped wh gues nd o SAO nd Wu ( ) o GMA nd IG esuls. he compson show good qulve nd qunve geemen. CONCLSIONS A numecl sudy o he nse nd lud low phenomen n weldng pocess hs een ced ou n he pesen wok. he weld pool se n GMA weldng nceses se e smll mes (.. Sec.) nd he sem uncon mes. sec nd. sec ppe ncesng n he () nd () decons. wo cculon loops n he weld pool ppes one ne he ee suce nd he ohe n he ulk weld pool, he mxmum velocy whch occus he ee suce. And he low he ee suce s dlly ouwd om he () xs o he pool oundy. Fg. ( ): Schemc Repesenon o Gs ungsen c Weld ١٣٢١ Phenomen (Gukn nd Sundn ).

10 I.Y. Hussn Evluon o empeue Dsuon nd Flud S. S. Aed - AlKeem Flow n Fuson Weldng Pocesses Fg. (٢): Skech he weldmen o GMAW (, ) equ. equ. equ. equ. equ. equ. Fg.( ): Nodes Equons o he Numecl gd ngemen o weldmen usng empeue dsuon, pool empeue dsuon nd oundy condons used n clculons ١٣٢٢

11 Nume olume mch Jounl o Engneeng Fg. ( ) he Nodl Pons sed n Numecl Soluon ١٣٢٣

12 I.Y. Hussn Evluon o empeue Dsuon nd Flud S. S. Aed - AlKeem Flow n Fuson Weldng Pocesses ١٣٢٤

13 Nume olume mch Jounl o Engneeng ١٣٢٥

14 I.Y. Hussn Evluon o empeue Dsuon nd Flud S. S. Aed - AlKeem Flow n Fuson Weldng Pocesses Fg.( ): Clculed Lqud Sold Inece o GMA Weldng Wh Sme He Inpu Deen mes. ١٣٢٦

15 Nume olume mch Jounl o Engneeng Fg.: Lqud Sold Inece o GMA Weldng Re.(so nd Wu ) ١٣٢٧

16 I.Y. Hussn Evluon o empeue Dsuon nd Flud S. S. Aed - AlKeem Flow n Fuson Weldng Pocesses REFERENCES Chow, C. Y., An Inoducon o Flud Mechncs, Wley, New Yok, ١٩٧٩. Gukn, R., Guh, B. nd Sundn,., Fne Elemen Modelng o Flud Flow on Weld Penon o Sony Gs-ungsen-Ac Weld Pool, Depmen o Mechncl Engneeng II Mds. Chemm-٦٠٠ ٠٣٦, ٢٠٠١, p.p. ٢٧٩-٢٨٥. Km, J. W. nd N, S. J., A Sudy on he hee-dmensonl Anlyss o He nd Flud Flow n Gs Mel Ac Weldng sng Boundy-Fed Coodnes, Jounl o Engneeng o Indusy, ol. ١١٦, Feuy ١٩٩٤, p.p. ٧٨-٨٥. Oepe, G. M. nd Sekely, J., A Compehensve Repesenon o nsen Weld Pool Developmen n Spo Weldng Opeons, Mellugcl nscons A, ol. ١٨A, July ١٩٨٧, p.p. ١٣٢٥. Peovc, Z. nd Suppe, S., Compuonl Flud Dynmcs One, Mechncl Engneeng Flculy, Belgde, ١٩٩٦. Slh S. Aed-Alkeem, " Evluon o empeue Dsuon nd Flud Flow n Fuson Weldng Pocesses ", P.H.D hess, he College o Engneeng, Mechncl Engneeng Dep.,nvesy o Bghdd, Mch ٢٠٠٥. once, K. E., Numecl Mehod n He nse, Hndook o He nse Fundmenls, McGw-Hll, second edon, ١٩٨٥. s, M. C. nd Kou, S., Elecomgnec Foce Induced Convecon n Weld Pools Wh A Fee Suce, Weldng Jounl, ol. ٦٩, No. ٦, June ١٩٩٠, p.p. ٢٤١S-٢٤٦S. so, K. C. nd Wu, C. S., Flud Flow nd He nse n GMA Weld Pools, Weldng Jounl, Mch ١٩٨٨, p.p. ٧٠S-٧٥S. ١٣٢٨

17 Nume olume mch Jounl o Engneeng NOMENCLARE Ln Symols Symol Denon n Co Lengh scle co scle uses n mm g Acceleon o gvy mm/sec h Convecon he nse coecen J/mm. sec. C H Lengh o ple mm Fne deence ndex n he -decon I Weldng cuen Ampee IFL Index o uson lm n -decon. Fne deence ndex n he -decon () Weldng cuen dsuon he plne ( ) Amp/mm JFL Index o uson lm n -decon. K L heml conducvy o lqud mel W/mm. C K s heml conducvy o sold mel W/mm. C L hckness o wok pece mm M Nume o gd n -decon N Nume o gd n -decon N Nume o gd n -decon o weld pool N Nume o gd n -decon o weld pool q() He lux on he plne J/mm Q He npu pe un me W Cylndcl coodnes. mm empeue n x-y coodnes, lso empeue o weldmen. C Amen empeue C Inl empeue C m Melng empeue C s Sold empeue C elocy n dl decon () mm/sec Avege ck velocy n -decon mm/sec Avege ck velocy cene lne mm/sec Avege on velocy n -decon mm/sec Avege on velocy cene lne mm/sec elocy n xl decon () mm/sec olge duy ols Avege ck velocy n -decon mm/sec Avege ck velocy cene lne mm/sec Avege on velocy n -decon mm/sec Avege on velocy cene lne mm/sec W Wdh o ple lso wdh o wokpece. mm Cylndcl coodne mm GREEK SYMBOLS Symol Denon n ١٣٢٩

18 I.Y. Hussn Evluon o empeue Dsuon nd Flud S. S. Aed - AlKeem Flow n Fuson Weldng Pocesses α L heml dusvy o molen mel mm /sec α S heml dusvy o sold mel mm /sec β Coecen o heml expnson (exposvy) /k H He nseed no weld pool y molen lle doples w/mm - Sep se n -decon mm Sep se n -decon mm η He npu ecency µ Dynmc vscosy kg/mm.sec µ Mgnec pemely o ee spce H/mm υ Knemc vscosy mm /sec ρ Densy o weldng we Kg/mm ρ Densy o lle dople Kg/mm σ Suce enson N/mm σ Cuen dsuon pmee Amp/mm σ q He lux dsuon pmee w/mm ψ Sem uncon M /sec Ω Successve ove elxon pmee Ω OP Opmum successve ove elxon pmee ocy /sec ƒ Spy nse equency HZ ١٣٣٠

Calculus 241, section 12.2 Limits/Continuity & 12.3 Derivatives/Integrals notes by Tim Pilachowski r r r =, with a domain of real ( )

Calculus 241, section 12.2 Limits/Continuity & 12.3 Derivatives/Integrals notes by Tim Pilachowski r r r =, with a domain of real ( ) Clculu 4, econ Lm/Connuy & Devve/Inel noe y Tm Plchow, wh domn o el Wh we hve o : veco-vlued uncon, ( ) ( ) ( ) j ( ) nume nd ne o veco The uncon, nd A w done wh eul uncon ( x) nd connuy e he componen