International Institute of Welding r

Institut International de la Soudure

Annual Assembly

~ssernblck Annuelle

COLLOQUIUM

COLLOQUE

ABSTRACT

A MATHEMATICAL HODEL OF HEAT AND FLUID FLOW PHENOnlnA

Ill ELECTROSLA6 WELDING

J. Szekel y and T.U. Eagar

Department o f Mater ia ls Science and Enqlneerfng

ftessachnsetts Ins t I t u t e o f Technology

Canibridqe, Hçss 02139 USA

Dr. Szekely IS a Professor and Dr. Eaqar i s an Assis tant Professor

Suhmi t t e d to the In ternat ional I n s t i t u t e o f Welding C o l l o q u i ~

on Applicat ions o f Numerical Techniques i n Welding

t o be held I n Dublin, Ireland, 4 July. 1978

Subdivision A, Physical and He ta l l u rq l ca l E f fec ts

Through the statement o f Maxwell's equiitlons. the turbulent Navier-Stokes equations ç- the convectfve h a t balance equation, a n à § t h e w t l c a mod01 has been proooied 01 thr E l r c 1 ' ~ - a l l f l Walding Proeçsa I n thà formuliclun, aliowanca has Bean mada fo r bcit3 the r l ~ c t r r r - ~ i - n e t l c and the buoyancy forces that d r i ve tha slag and the metal flow. The r r i u l t a - x st-^:- taneous p a r t i a l d i f f e r e n t i a l equations were solved numerical ly using a d i a i t a l co^aJter.

The p r i n c i p a l f ind ings o f the work may be summarized as fol lows: 1) There I s .lppreciabIc f l u i d motion i n both the molten metal pool and i n

the s l a g and t h l s motion may a f fec t the heat t ransfer processes wick in the system, p a r t i c u l a r l y i n the s lag phase.

2) I n general t h i s f l u i d no t ion i s dr iven by both electro-aqnetic f i rce5 and by buoyancy forces. The elcctranaqnetlc force f i e l d res - i t s frm !^e s p a t i a l l y nonuniform current density d i s t r i b u t i o n i n the syste-. -E i l e the buoyancy d r i ven flows dre caused by the nonuniformity o f the te->era- Cure f i e lds . I t has been found that the geometry o f the sys?e- has a profound e f f e c t I n dctermlninu whether the f low f i e l d i s d f y i n a t f i by electromagnetic o r by buoyancy forces.

3) When w i re e lect rodes are used the f low f i e l d i s dr iven by elcctr.-T.:-clic forces while, f o r p l a t e e lcct rodcs the buoyancy forces doriinate. ::.- t y p i c a l condi t ions, the electromfignetici i l ly dr iven flows may be a"* c r i e r o f magnitude h igher than the buoyancy dr lven flows.

4) This marked dependenceof t h e m e l t v e l o c l t i e s o n the systenae,?¥¥--tr i s a l so manifested by d r a s t i c a l l y d i f f e ren t temperature d i s t r i bu t i f . " a - d elect rode mel t ing ra tes i n systems us inq wire type and p l a t f t ~ z e e!ectrcJei. The c i r c u l a t i o n I n the metal pool I s much less intense than i n ;"¥ 5 I . n .

and tends t o be laminar. A select Ion o f the c m p u t r d resu l t s I s presented i n the saper which "i"rc ; . . f i , - : r? .:t,:

modi f icat ions i n system geometry necessary t o optimize the u t i l i z a t i o n o f i w a l yer:,.

Input .

Introduct ion

Although invented over f o r t y years an@, e lect ros laq welding (EW) has -.at d-va!:.-< , i n t o a commercial process u n t i l the l a t e 1150's by Patnn and others i n the I - ? S D . l t ' , acceptance ho.wv*;r, has been slow i n sp i te o f the fact that i t i s potc-t i-sl '1f I*" -Ã :̂-.

e f f i c i e n t process fo r j o i n i n g o f th i ck sections. The main reason why ESU has not been used extensively I s the long t h e r a l cyc le i-'"*r-

ent i n the pr.-icess, which leads to poor mechanical propert ies o f the 5 . 1 s ~ ola!?. i>:.da-;r~ have been slow s ince dcvelopn'ental work t o improve welding procedures i s cos i ly . f u t h c r -

mare. the h igh :en:peraturcs involved make experimental deterr i inat ion o f the t f - ? e r a t ~ r e and v e l o c i t y f i e l d s w i t h i n the molten stag and metal pools extrer-eiy d i f f i c u l t .

Recent advances I n the computer modell ing o f e lec t rmaanr t i c flows i n r e t a l a rcc r5?h= operations have proven t o be q u i t e e f fec t i ve i n p red ic t i ng ve loc i t y d i s t r i b u t i n r s , t * e r a l d i s t r i b u t i o n s and heat f luxes which otherwise could only be determined wi th puch ewer : - mental d i f f i c u l t y and expense. It I s thought that app l i ca t ion o f these technicdes t a tpe ESW process may prove extremely valuable I n understanding the fundam-itals o f the process and hence I n an eventualImprovement o f the operation.

Formulat1.on.of t h e Model

Let us consider the e lect ros lag welding of two plates, as sketched i n Fioure 1. I t I s seen that b consumable w i re electrode (or :n some cases, a p la te electrode) i s teina

fed continuously I n t o a molten slag pool, whlch I s r e s l s t l v e l y heated by the current that passes from the electrode, through the molten s lag and the metal pool, t o the base plates. I t i t a lso seen tha t two water cooled copper "shoes1' prov ide a mold through whlch a por t ion. Q * the thtri-rl energy I s r f o v e d from the system. I t w l l l be noted that the passage o f e l e c t r i c current frm the narrow electrode throuqh the molten s lag and ne ta l phases must be t i ve raen t and hence w i l l generate an electromagnetic force f l e ld . I n a d d i t i o n the non- (.-;for- te-perature d i s t r i b u t i o n w i l l g i ve r i s e t o bouyancy forces. Both the electronag- pe t i c force f l e l d and bouyancy force f i e l d w l l l generate f l u i d motion, although o f generai ly ocsosina ro ta t iona l sense, as sketched I n F lgure 2.

The heat f l ux from the molten phases t o the base p la tes I s determined by the thermal f t d i e n t s whlch e x i s t across the s o l i d - l i q u i d Interface. These gradients are i n t u r n a '~ec ted by the f l u i d motion and the ra te o f i n te rna l heat generation, hence a model of t h i s arocess nust involve the simultaneous s o l u t i o n o f equations f o r the electromagnetic 'orcr F ie ld buoyancy force f l e l d and temperature f i e l d .

'or -nodel i lng purposes the physical geometry has been Idea l i zed as shown In Flgurm 3. : b i l l be noted that the p r i n c i p a l d i f ference between the pool p r o f i l e s shown In Flgure 3 a-3 if's actual ~ o o l prof I l e s i s that the model postu lates a f l a t metal pool. It w i l l be

Â¥-.. v i t i e ~ ~ e n t l y f a t the ESW process i s dominated by behavior I n the slag phase and hence c t r r - i d e a l i z a t i o n o f the metal pool p r o f i l e should not a f f e c t the general nature o f the ' : i ^ a i " ~ i .

I'pon considering a melt (me ta l l i c o r Ion ic ) contained I n a three-dimenslonxl enclosure, the à § q u ~ t l o . f motion f o r turbulent f low i s w r i t t e n as:

a-2 t * ~ e q u a t i n u f con t inu i t y i s given as:

-"<Â¥r . I s the densl ty I s the v e l o c i t y vector

? i s the pressure t I s t h e t i n e : i s the e f f e c t i v e v iscos i ty , whlch I s the sum o f the laminar and the turbulent

c o n i r i t u t Ions I s the body force vector whlch Incorporates the electromagnetlc force and the buoyancy force. .

I t 1s noted that Ue I s not known a t t h i s stage; It I s genera l ly s t rongly p o s l t i o l -

<'r--È-Jrn and i s a function o f the v e l o c i t y f l e ld . As discussed by Spaldlng [I], and Launder J-3 'Sraldin9 1 2 1 , the ca lcu la t ion o f v requires the so lu t lon o f p a r t i a l d i f f e r e n t i a l equa-

t . the procei'u.-â fo r ut i lch I s we l l documented 131. TÃ -̂ qeneral expression fo r the electromagnetic body force f l e l d I n In te rac t ing e l e c t r i c

a-<! - a y e t i c f i e l d s I s available I n the l i t e r a t u r e ['1,5]. It nay be read i l y shown that fo r t¥- condi t ions o f In terest I n the present ~ t u d y , the electromagnetic force vector, E, nay bà < ~ \ v l ~ t e d fron:

f - J x ! (3) Mftfrw

J 1s the current denslty

I n order t o evaluate F, we have t o solve M * m e l l l s equations (more precisely, the MHD - ~.-.~iw~l'ça Ion o f M à § x u e i l ' equations) whlch mre w r l t t e n as [5, 111:

where E I s the e l e c t r i c f i e ld , and - H I s the magnetic f i e l d Intensity. -

Furthermore, we have that - UJ!

here, p I s the permeabi l i ty I n vacuum.

~ l n i l l y , thm current densi ty I s given by Ohm's Law:

and

where 0 I s the e l e c t r i c a l conductivi ty, and . @ i s the scalar e l e c t r i c potent ia l . I n order to evaluate the body force diie t o buoyancy, the convective heat balance

equation must be solved wl t h due allowance f o r eddy transfer, heat aenerat io f riue t o " J : - l c heating", and the transport o f thermal energy by movlnq droplets. Such an equatic- i- 2 three-dlmenslonal enclosure may be wr i t ten as:

DT ^ , , O f - 7 - kc" + E * - J + ST

where T I s the temperature Cn I s the spec i f i c heat

ke i s the e f fec t i ve thermal conductivi ty. and

I s the source term, which describes the thermal energy transport due t o r o v r - p - i o f metal droplets from the t i p o f the electrode t o the metal pool.

The f l u i d f low equations have t o be wr i t t en down separately fo r the v l t e n 513: .>-.'

molten metal pool; these two sets o f equatlons arc re la ted thiouqh boundar-, coradlti.:--'. - L t v

equations representing the e lect rwdqnet i c force f i e l d and the conservat Ion of i^-er--41 c - r r . have t o be w r i t t e n down separately fo r the electrode, molten slao, neta l pool and s i l i d i r ; - . ' weld Inc lud ing the welding plates. These equations are related throuah the I rc .~ idarv cc':'". I t fol lows that Eqs. (1-9) cons t i tu te the governinq equations, tocethcr wi;h the diV,.re-t; ¥

equatlons used for def in ing the ef fect ive viscosity, 1 1 . The counlcd nature o f t ' - d - + * * - r t . . -

slons 1s r c a d l l y apparent. I n tha t the temperautre f l e l d enters the f l u i d f l e w e c u ~ t i o n ^ through the buoyancy term and the know': lge o f the v e l o c i t y f ie lds and tur?ulenctf rara-i- trr? needed I n the so lu t lon o f the convective heat t ransfer equations. The r-aanetic G r \ i equations may, however, be uncoupled since the magnetic Reynolds nunber for the svste- Â ¥ d n e c study I s much smaller than u n i t y [5.61; thus, the d i f f u s i v e transport o f the l imnet ic ' i c ' l . f

dominates over the convectlve transport. The actual ESW system I s three dlmensiunal I n space and time dependent due to r'ovf-i'-.

o f the boundaries. I t I s possible however t o model the process as two d iwnsional a id

The displacement current I s neglected.

quasl-steady state. The camoutatIonaI economies o f such a mod i f i ca t ion are s lgn l f l can t . Nonetheless the so lu t ion o f the two-dlmenslonal problem requi res approx l i u te l y 300 seconds on the 18H 370/168 a t H.I.T.

L I n I t a t I o n o f the problem t o two dlmenslons  ¥ H o w the c o n ~ t r u c t l o n o f two basically d l f r e r a n t ççorwlr la The f l r s t , b i r d on a CartasIan coordlnata nÈonÑtr 1s equlvblçn t o -e ld lnq b vary th i ck p la le w i t h n p la te e lect rode (cf. F igure l i (a)). The second I l l u - s t r a t e d I n Fiqure 4(b). uses a c y l l n d r l c a l geometry and approximates the more common p r a c t i c e o f ESW w i t h a wl re electrode. I t I s In te res t ing t o note that the former qeomctry, as shokn i n Figure ^(a), gives r i s e t o an electromagnetic force f l e l d whlch does no t induce f l ~ p r o v i d i n q the s v t r y o f the system 1s maintained (7). Hence, the f l ow be- hav ior o f the rectangular geometry I s dmlna ted soley by the buoyancy force f le ld . I n the l a t t e r a c m e t r y (Figure b(b)) both the electromagnetlc and buoyancy force f i e l d s p lay an l-portant role.

Boundary Condl t Ions Thr aovernina eauations and boundary condl t lons f o r bath the rectannular and c v l l n d r l -

cat g--tr ies i r e w r i t t e n I n f i n i t e d l f ferenca form as described elmwhçr (6-8). c ha scl-.it im l i obtained n u n r r l c ~ l l y m l n g i r a l a x i t l o n tachnlque.

Cir-outed P e ~ u l t s I n the following, we shal l present a se lec t ion o f the computed resul ts , whlch were

develooed fo r both c y l l n d r l c a l and f o r rectangular geometry. The comparison o f these two sets o f computed resu l t s w l l l tnen d l o w a r a t i o n a l assessmmt o f the system behavior I n the preneice and I n the absence of an e l cc~~omagne t 1c force f l e ld .

Tables 1 and 11 contain the property values used i n the computation o f the rectanqutar and the c y l i n d r i c a l systems. I t i s seen that these two systems are o f comparable l i near dl-enslons. Moreover, the tot81 heat Input was Iden t i ca l I n these ;xi systems.

Fiqures 5. 6 an") show the conputed streamline pat tern, the map o f t h e v e l o c i t y vector. and the cwcu ted isother""? for the rectangular system. The corresponding p l o t s fo r the c y l i n d r i c a l svsten are given i n Fiqures q, 3 and 10.

I t has t c be stressed. I n conparinq these two sets o f resul ts , tha t i n the reclangular syste-'. the f i o r i n the slaq and the n c t a l phases I s d r i ven by buoyancy forces only; I n the c y l i r - j r i c a l ifstem, the electrn-aqnetic force f l e l d p lays a major r o l e I n determining the flow pa t te rn and the absolute naonitb~de o f the ve loc i ty .

I t i s seen that I n the rectangular system, the buoyancy d r i ven v e l o c i t i e s i n the slag a i d i n the r e t a l phases are r e l a t i v e l y low, o f the order o f 2 cm/s o r less. I n contrast, as seen i n Figure 9, the ve loc i t i es are some 20 times l a m e r i n the s lag region and three t i n e s la rge r i n the m t a l pool o f tbe c y l i n d r l c a l system, where the electrogmagnetic force f i e l d p lays a major ro le i n d r i v i n g the slaq flow.

JDOI co"parin7 the temperature p r o f i l e s I n the two systems, the much more quiescent nature o f the rectanoular system i s read i l y apparent.

The co-puted resul ts reported up t o the present are he lp fu l I n the character izat ion o f the systen. but have only an Ind i rec t bearing on the weld character ls t lcs . As was discussed i n the introductory a c t i o n , the manner I n whlch the thermal energy I s d iss ipated throughout the system has a m j o r r o l e I n determining the charac te r i s t i cs and i n t e g r i t y o f the x l d r c n t produced.

Table I I 1 provides a thermal energy balance f o r both the rectangular and the c y l l n d r l - cat system. This balance i s based on the computed quan t i t i es l i s t e d i n Table IV. The f i r s t two rows i n Table Ill represent the heat Input, whi le the subsequent e n t r i e s represent the heat d i ss ipa t ion i n the various por t ions o f the system.

I n contrast ing the behavior o f the rectangular and the c y l l n d r l c a l systems. I t I s r e a d i l y seen that f o r the rectangular system, on ly some Z } t o f the t o t a l heat Input I s passed on t o the weldingplates, whi le the correspondlnq va lue f o r the c y l l n d r l c a l system I s sone 40?. I t I s a lso seen that a subs tan t ia l l y h igher propor t ion o f the thermal energy input i s beingused f o r ne t t i ng the electrode I n the rectangular system than I s the case fo r c y l l n d r l c 8 1 geometry. I n other words, I n the rectangular system, a much be t te r use I s -de

o f the thermal energy. Thls behavior I s read i l y explained by considering ft fact that t ' -r more vlqorous s t i r r i n g appl ied I n the c y l l n d r l c a l i y s t e n provides for a rather -or* rani,' heat t rans fe r from the molten s l o t to the surroundlnqs.

Thls p o l n t I s fu r the r I l l u s t r a t e d I n Fiqure 11. whlch shows the d i s t r i t u t i c n <tf tÈÂ

l oca l heat f l u x to the welding In ter face as a function o f tha distanca frcr' tt-r five k1.1

surface fo r both the rectangular and the c y l l nd r l ca l syitcm. It i s seen tnat t ? r r . a * - - . i s markedly non-uniform I n the case o f the c y l i n d r i c a l system; the sharp tea- a?;-.-=*;- . , the top r i g h t hand corner o f the qraph corresponds t o the "undercuttino ^ f c - " - Ã ‘ i t-~e: has been found I n he ld ing p rac t i ce [9l. This marked non-unifomi t y i n heat f!o" I! c.,~:,~, by the rap id c ~ n v e c t l v e heat t ransfer by t h t electronagnetical ly dr iven st-?*: fir,--

I n contrast , the d i s t r l b u t l o n o f the local heat f l u x t o the welding ir:e-race <i * - . > - * .

t o be much more uniform I n the rectangu!ar system, where the c i r cu la t ion i n tme s l a . '1- . #

by buoyancy forces. I s much less Intense.

D t n c u c l o n

I n t h i s paper a model o f the heat and f l u i d flow behavior o f t<m-di-er^i'o-al f ^ i systems has been presented, The key f ind lnn o f the model I s that the f IoA :ebavirr i s

markedly d i f f e r e n t when cmpar inq p la te and wl re electroi let. F u r t h ~ r - w e . ¥ >.as 'i:,,>i; t ha t the temperature qradlents are reduced i n the rectangular syste'~' : lat<- clcccrc:<' which leads t o reduced heat f l u x t o the base plate. The net resul t i s that th- - * . * . u t i l i z a t i o n i s more e f f i c i e n t w i th p l a l e electrodes than w i t h h i r e e:si-tr-::-s. F., .:- ,-,. ,' t h i s q u a l l t l a t l v e d i f ference I n thermal e f f i c iency resu l t s f r m the abce-*c* if d- v ' . * - ! ! . - magnetically d r i ven flow f i e l d w i t h p l a t e electrodes. I t should be stressed '-r^<'it-. t L - ' an electromagnetlc force f i e l d does e x i s t i n t h i s case, h- i r . svnt-etry ccndi:ic?s crv:l .,. the force f l e l d from I n i t i a t i n g flow. If i n pract ice svmetry i s not vair:ai-.ed. r e e lec t romaanet l c force f i e l d may become unbalanced and resu l t i n increased "low. *.:x.~v. less. the f low behavior w i t h p la te electrodes. even i f unbalanced. i s expected tn t'e 1e.s than w l r e electrodes o f equal current capacity.

The model as presented, predic ts a qreater maximum heat f lux t o the baw place A S

voltage I s Increased. In a p rac t i ca l sense, t h i s implies that increased volta-a ..--!! lead t o greater undercutt lng ( d i l u t i o n ) o f the base plate. This 15 i n fact ~bserve:. !<' Other p r a c t i c a l observations, such as the necessity of qroundinq both p latss a-d s:a:i-r m u l t l p l e wlre electrodes a t least 1! cm apart (10) I s a natura l consezuence o f tb:e .:,-, t .

maintain symet ry and prevent overlap o f the electronaqnetic force f i e l d s i f s tab le <!,,., a re to be achieved.

Conc lud i ng Remarks

The two dimensional model as presented. I s capable o f accurately pre-i ict ing i n e 'Ir.. and thermal behavior o f ESW. These behaviors may i n tu rn be used to ;x?liiin [be c ' -c- .n ; - - J

charac te r i s t i cs o f ESW. however, fur ther work i s necessary to extend the - 'cAel beso-: e r r , 1lmi tat lons. The tes t inq of a three dimensional analoq i s an obvious addi t ion, >ut -0'-P

importantly, i t i s hoped that refinements w i l l be able t o account fo r t w rfi-cnsio-a1 asymnetrles, a p r i o r 1 calculations o f electrode immersion depth, jou le l 'ca:inv or thr e i c i - trode p r i o r t o en t ry t o the siaq pool, e of mu l t i o le elrctroi ies and copair-able cu i r rs , etc. Although numerous assumptions have been made i n the a ia lys is , i t i s r e i t :bat a- Important step forward has been made i n our understandinq o f ESW. ~t i s ho-ied that t & ; + w l l l I l l u s t r a t e the advantages o f the app l i ca t ion of numerical techoiquei t o w i r i i n o . i rocci ' . i

Acknowledgements -- The authors m u l d l i k e t o acknowledge Dr. A. Dl lawari for h i s assistance i n p rov id i r c

the computed resul ts .

2. 8.E. Launder and D.8. Spalding: Computer Methods In Applied Hechanlcs and Englnee'-Ing, 1974, vol. 3. pp. 269-289.

3. A.D. Gosnan. et al: Heat and Hass Transfer In Recircul~tlng Flows. Academic Press, London and New York, 1969.

4. L.D. Landau and E.B. Llfshltz: Electrodynamics o f Continuous Media, Addison-Wesley, Reading, Mass., 1960.

5. u.6. Hughes and F.J. Young: The E1ectromagnetodyn~ics of Fluids, John Wiley, New York, 1966.

5. A.% Dilawarl and J. Szekely: Met. Trans. 8. mi. 80, pp. 227-236. 1977.

7. A. Oilawarl, J. Szekeiy. and T.W. Eaqar, to be published In Met. Trans.

8. J. Szeqely and A.H. Dllawarl: Proc. of the Fifth Int. Conf. on Vacuum Met. and ESR Proce. e%. Munich, Germany, l97& [in press).

9. I.E. Paton: Electroslaq Welding, American Uelding Society, New York. 1962.

10. "Prxiical T I P S for Electroslag Welding," Arcos Corporçtlon

11. J.C. Jackson, Classical Electrodynamics, John UIiey, New York, 1962.

TABLE I

Physical Property Values Vsed

ka thermal conductivity of slag, 10.5 x 1 0 - kJ/n-s-'K

km thermal conductivity of ulten metal, 20.9 x 10" kJ!r.-s-'K

Dona density of slag at reference temperature, To, 2.75 x 1 0

3 vOvm density of molten metal at reference temperature. To, 7.2 x 10' '^Â¥I

CP,= specific heat uf electrode, 0.50 k.I/kl;-"K

CP,= specific heat of slag, 9.8; k.l/kl;-'K

CpVm specific heat of molten metal or of metal droplet, 0 . 3 ;.I".,:-*K

T, liquidus temperature of electrode or of welding plate matert31, 1.c:J'K

To reference temperature, 350%

AH latent heat of fusion of electrode, 272 k.I!<:

fta thermal coefficient of cubical expansion for molten slat, 1.0 x lo(':Â¥:)-

ftm thermal coefficient of cubical expansion fur wlten ctftal. 1.1) x IU'('K!-' 1

0 electrical conductivity of wlcen sliis. 2.0 x 10" mho/n

5 electrical conductivity of molten metal, 7.14 x 10 nholn

c emisalvlty of free slag surface, 0.6

us viscoiiity of molten slap, 1.0 x 10- kc!"-s

1,, viscosity of molten wtal, 6.0 x 1 0 kg/n-s

TABLE I1

Nuwr lca l Values of Parameters Used i n the Computation

e l ec t rode radix* (ha l f t h i c k n e w ) . 1.5 x 10%

veld pool r ad ius ( h a l t th ickness) . 1.5 x 10-rn

2 e l ec t rode imacrsion In s l a g pool, 1.0 x 10- m

depth of. s l a g pool, 1.5 x 1 0 ~

depth of metal pool, 3.0 x 1 0 m

m ~ ~ n e t i c p e n ~ c a b l l i t y , 1.26 x 1 0 henry/m

Stephan- to l t tmnn cons t an t , 5.73 x 10"' k ~ / n - ~ - * ~

e l e c t r i c p o t e n t i a l a t the Immersed s u r f a c e of the e l e c t r o d e

( r ec t angu la r syscrir.), 14.52 volf

breadth of the r e r t a n ~ t i l a r e l ec t rode , 0.12 m

e l e c t r i c po t en t i a l a t the l m c r e c d s u r f a c e of e l e c t r o d e

( cy l ind r i ca l system). 47.80 v o l t s

TABLE XI1

THERMAL r:icncy numt-r. ~ ' m no-ni THE i t ix~~~cuuw AXD THE CYLINDRICAL SYSTEM

J o u l e hea t i ng i n 1 1 1 1 metal phases i

Hrat flow from s l a g t o metal pool by

- .- 1 8.1 1 8.7 1 2.;: 12-3 convect ion

Heat [low from s l a g t o nietal poul due t o tlie movement of t h e d rop l e t s 9.6 10.3 0.16 2.2

Heat flow from s l a g

I Heat r ad i a t ed from f r e e s l a g su r f ace 1 2.4 1 -2

I s .

L

Hent used t o pre- hea t the e lec- t r ode

t o welding p l a t e s

I I 37'6 1 i 5-86 32-5 '

22.4 1 23.6 7.15 3 9 3

TABLE IT

Electrode aç:.tln velocity 1 (alhr) 70.67

QUA-TIITIES COMPUTED FROM THE MODEL FOR

BOTH THE R I C T ~ G ~ ~ J U ~ AND ~ I N D R I C A L SVSTOS

I t~xtaua linear velocity i n 1 0.01 retal pool (nlsrc)

v

QluntUies C q u t e d

Electrode melting race (kz'sec)

ELECTRODE

. PLATE 2

Rectangular System

5.087 x 10"

WATER A COOLED

COPPER MOLD

7

Cylindrical System

7.917 x

Figure 1 . Schematic o f t h e electroslaq wtldinq process.

SLAG

METAL

Figure 2. Schenatic of the rotational flows expected fron a) thermal buoyancy forces Figure 3. Idealized model of the electroslag welding process. and b) electromagnetic forces.

0 0.3 0.6 0.9 12 1.5

DISTANCE FROM CENTER LINE (cml

Figure 5. Computed stream1 ine pattern for the rectanqular system.

. .

à . o as LO 15

DISTANCE FROM CENTER LINE (cm)

Figure 6. Velocity vector W n g , as computed for the rectawulir SVstm-

DISTANCE FROM CENTER LINE (cml

Figure 7. Confuted Isotherm for the rectangular system.

RADIAL DISTANCE (cmt Flgurà 8. Coiputed stream1 ine p t t t e r n for the cyl lndr icml syÈtm

1

t  : fr-

& >- . I n .

s + I n . 5 . -* t

RADIAL DISTANCE (on) Figure 9. Veloci ty vector napping, as computed for the cyclindrlcal sy"rm-

o a3 a6 as 12

RADIAL DISTANCE (cm) Figure 10. Computed Isotherm for the cyl lndrlct i SyitBm.

J 0 25 050 O X 1.00 125 1.50

DISTANCE FROM FREE SLAG SURFACE (crn) flgurm I t . Computed local heat flux to thm b a u plate for a) Rrctçnault s v n r r .

hut Input 93.4 kJ/sec; b) Cyllndrlcal syttc*): id c) Kuttnqular systm 111.0 kJ/sec.