Contacting Problems Associated with Aluminum and Ferro-AIIoy Additions Steelmaking-Hydrodynamic Aspects

in

R. I . L. GUTHRIE, R. CLIFT, AND H. HENEIN

It is common prac t ice to drop a luminum and f e r ro -a l loy addit ions into teeming ladles e i ther p r i o r to, or dur ing furnace tapping operat ions . Water model exper iments a re desc r ibed in which spheres of var ious d i ame t e r s and specific gravi t ies were dropped f rom typical i ndus t r i a l heights into water . Maximum penet ra t ion dis tances , t r a j ec to r i e s and re ten t ion t imes were measu red and compared with theore t ica l predic t ions based on t r an s i en t fluid flow. The re la t ive impor tance of steady drag, added mass and h is tory forces were demons t ra ted . Resul t s indicate that i m m e r s i o n t imes a re ex t remely shor t (~1 s) for a luminum addit ions and low densi ty f e r ro -a l l oys . High densi ty f e r r o - a l l o y s r e m a i n i m m e r s e d cons iderab ly longer and pene t ra te much deeper .

T HE addition of sol ids to liquid s tee l baths for ad- jus t ing s tee l chemi s t ry to r equ i r ed speci f ica t ions or for cooling purposes is common s tee lmaking p rac t i ce . Specific examples of solid addit ions to molten s tee l include the occas ional use of sc rap meta l in B.O.F. fu rnaces for cooling 'hot ' heats, as wel l as the r eg u l a r u se of ladle addit ions of f e r ro -a l l oys , ca rbon and a l u m - inum for al loying a n d / o r deoxidation purposes . In genera l , these al loying addit ions a re made to the ladle e i the r before or dur ing furnace tapping opera t ions .

Although much informat ion has been gathered in the pas t on the way in which specific d issolved a l loy- ing e lements i n t e rac t with oxygen and sulfur in the s t ee l to form oxide/sul f ide type inc lus ions (e.g., Ref. 1), the in i t ia l d i s so lu t ion p r o c e s s e s themse lves have been la rge ly neglected. However, in o rder that opt i - m u m inject ion methods be ident if ied and some of the p r e s e n t e m p i r i c i s m in plant p rocedures be r a t i o n a l i - zed, i t is n e c e s s a r y to unders tand the bas ic phenom- ena involved in these f i r s t s teps .

So far , it has been demons t ra t ed 2,s that a solid s tee l she l l wil l in i t ia l ly form around any object that is i m m e r s e d in a bath of molten s tee l . Also, provided the mel t ing 'point ' of the addition is lower than the f r eez ing 'point ' of the s teel , the object wil l no rmal ly proceed to melt ins ide this shel l . 4 Thus, one commonly ends up with the s i tua t ion of a mol ten core of f e r r o - a l loy or a luminum sur rounded by a solid jacket . The jacke t then takes an appreciable t ime to melt back and r e l e a s e i ts contents to the bath.

Much of this l a t te r work has concent ra ted on t he rma l aspec t s , and has supposed that the addit ions r e m a i n i m m e r s e d during the course of the i r mel t ing h i s tory . This wil l not nece s sa r i l y be the case in actual plant p rac t i ces , s ince many of the addit ions commonly made to teeming ladles , e t c . are l e s s dense than mol ten s t ee l and exper ience buoyancy forces . This is p a r t i c -

R. I. L. GUTHRIE is Associate Professor, Department of Mining and Metallurgical Engineering, McGiIl University, R. CLIFT is Associate Professor, Department of Chemical Engineering, McGifl University, and H. HENEIN is Research Metallurgist, Sidbec-Dosco, Contrecoeur, Quebec, and was formerly Graduate Student, Department of Mining and Metallurgical Engineering, McGill University.

Manuscript submitted May 16, 1974.

u l a r ly t rue of a luminum whose densi ty is 2.7 g m / c m 3 compared with s teel of 7 to 7.2 g m / c m s.

PRESENT WORK

The work presently described was undertaken to elucidate the hydrodynamic effects occur r ing when alloy addit ions a re in jec ted into baths of mol ten s teel , and sought to es tab l i sh max imum likely depths of pene t ra t ion and re ten t ion t imes . Such informat ion provides usefu l indicat ions on the extent or feas ibi l i ty of subsur face mel t ing for a p a r t i c u l a r al loy addit ive.

In no rma l s tee lmaking prac t ice , alloy addit ions to a teeming ladle a re made dur ing furnace tapping, and en te r the s tee l af ter passage through al loy chutes located on e i ther s ide of the teeming ladle . These chutes a re s teel tubes, about 0.3 m I.D., 3 m e t e r s long, making an angle of about 45 deg to the hor izonta l so as to d i rec t the addit ions towards the cen te r of the f i l l ing ladle. The alloy addit ions leaving the tube fall in f ree flight about 2 to 4 m e t e r s before en te r ing the s tee l .

In o rder to examine the hydrodynamics of such s i tuat ions , some s impl i f ica t ions had to be made in the labora tory scale s tudies repor ted here . In the f i r s t ins tance , it was decided to cons ider the case of spher ica l addit ions, r a t h e r than i r r e g u l a r l y shaped lumps or ingots, so as to s impl i fy the equations desc r ib ing subsurface motion and also to take advan- tage of the l i t e r a tu re and theory that is avai lable on the motion of spheres through l iquids. For s i m i l a r r e a sons i t was decided to t r ea t the case of addit ions pene t ra t ing a s tee l bath ver t i ca l ly , r a the r than the i r en te r ing a turbulent ly s t i r r e d bath at a sl ight angle as occurs in p rac t ice . F ina l ly , due to the opacity of l iquid metals , a low t e m p e r a t u r e model was in i t ia l ly chosen. Thus, wooden spheres of va r ious d i ame te r s and specific g rav i t ies were dropped through a i r into a s tagnant column of wa te r . The resu l t ing subsurface t r a j ec to r i e s were recorded by cinephotography using a 16mm Bolex Reflex C a m e r a . These r e su l t s then allowed an appropr ia te hydrodynamic model to be chosen for p r e d i c t i n g t r a j e c t o r i e s , max imum i m m e r s i o n depths and t imes for a wide range of condit ions in - cluding those re l a t ing to s tee lmaking .

METALLURGICAL TRANSACTIONS B VOLUME 6B, JUNE 1975-321

DEVELOPMENT O F A PREDICTIVE MODEL FOR SUBSURFACE MOTION

Equat ion of Motion

A number of w o r k e r s (often a s s o c i a t e d with b a l l i s t i c s tud ies ) have a l r e a d y inves t iga t ed the phenomena oc - c u r r i n g when high dens i ty so l id ob jec t s en te r ba ths of s t agnan t w a t e r . (See r e c e n t r e v i e w s by Birkhoff 6 and May6). Fol lowing the c l a s s i c a l pho tograph ic work of Wor th ing ton and Cole at the tu rn of the century , 7 much of the subsequent r e s e a r c h has concen t r a t ed on s t udy - ing a) cav i ty fo rma t ion when the so l id body f i r s t e n t e r s the l iquid (e.g., Refs . 8, 9) and b) the body ' s sudden d e c e l e r a t i o n during, and i m m e d i a t e l y following, e n t r y (e.g., Refs . 10, 11). Those w o r k e r s (e.g., Refs . 11, 12) who t r i e d e s t i ma t i ng the d r a g f o r c e s on the body dur ing i t s subsequen t downward mot ion through the l iquid e i the r i gno red added m a s s ef fec ts , o r chose to d i s r e g a r d s t a n d a r d d r a g coef f i c ien t s ava i l ab l e in the l i t e r a t u r e in favor of deve lop ing the i r own r a t h e r spec i f i c c o r r e l a t i o n s . As a r e s u l t , t he i r conc lus ions l ack g e n e r a l i t y and cannot be u s e f u l l y appl ied to p r e - d ic t ing the motion of a body which is l e s s dense than the l iquid into which i t is p r o j e c t e d .

A f r e s h a p p r o a c h was t h e r e f o r e taken in the p r e s e n t work to d e t e r m i n e whe ther s u b s u r f a c e motion could be p r e d i c t e d s a t i s f a c t o r i l y on the b a s i s of Newton ' s Second Law of motion, by taking into account the v a r i o u s f o r c e s shown s c h e m a t i c a l l y in F i g . 1, i .e. ,

d (M s U) = E F [1 ] dt

w h e r e Ms i s the m a s s of the s p h e r e , U i s i t s i n s t a n - taneous ve loc i ty , and F a r e the v a r i o u s f o r c e s ac t ing on the body. The d i r e c t i o n s of t h e s e f o r c e s a r e i nd i - ca ted in F ig . 1, and the v a r i o u s t e r m s a r e :

1) The weight of the sphe re , FG = Msg. 2} The buoyancy fo rce , FB = Mg, w h e r e M is the m a s s

of l iquid d i s p l a c e d by the s p h e r e . 3) The d r a g d u e to the r e l a t i v e ve loc i ty be tween

s p h e r e and l iquid, FD = (CD~d~pUI UI ) /8 where d is the d i a m e t e r of the sphe re , U i s i t s ve loc i ty through the l iquid, p i s the l iquid dens i ty , and CD is the d r a g coe f f i c i en t for s t eady motion tabula ted , for example , by Lapp le and Shephe rd? 3

4) The " a d d e d m a s s " t e r m , FA = CAM .(dU/dt) , which a l lows for the fac t that a c c e l e r a t i o n of the s p h e r e a l so a c c e l e r a t e s l iquid a round i t . This r e s u l t s in a momentum l o s s to the su r round ing fluid. Two a l - t e r n a t i v e e s t i m a t e s a r e ava i l ab l e for FA, depending on whe the r the added m a s s coef f ic ien t , CA, i s equated to i t s c l a s s i c a l va lue of 1/214'1s o r i s a s s u m e d to v a r y with p a r t i c l e ve loc i ty and a c c e l e r a t i o n in the manne r d e s c r i b e d by Odar and Hami l ton . 16

5) The " h i s t o r y " t e r m , FH = Ctt(d2/4)~d'-~fot(dU/dr) (d'r/td'-t-Z-r-T),which a t t emp t s to account for the depend - ence of the ins tan taneous d r a g on the s t a t e of d e v e l o p - ment of f luid motion around the s p h e r e . The h i s t o r y t e r m t h e r e f o r e depends upon the p a s t a c c e l e r a t i o n or d e c e l e r a t i o n of the body. Two e s t i m a t e s for FH a r e ava i l ab le , depending on whether the h i s t o r y c o e f f i c i - ent, CB, i s a s s i g n e d i t s c l a s s i c a l va lue of 6, 14,~s or a l lowed to va ry with ve loc i ty and a c c e l e r a t i o a f f

Rewr i t ing Eq. [1 ],

dU Msg - M g - F D - F A - F H [21 Ms-~ =

Fig. 1--Forces on a sphere accelerating through a liquid (schematic).

and in se r t i ng g e o m e t r i c f ac to r s , s t e ady drag , added m a s s , and h i s t o ry coef f ic ien ts ,

~__ CD~d2pUfUl ~ ~d 3 dU 7rd 3 dU - g (P - Ps) --~" P s "-~ = 8 - t. A -~-- p -~-

^ d2 r"='--_, rt/dU\ dr [3] -c"~Tv~P~ Jo ~,-d-7-) ~-~.

Also

U dz = d--t- [4]

w h e r e z i s the d i s t ance of the Lowest point of the s p h e r e below the s u r f a c e . The in i t i a l condi t ions for Eqs . [3] and [4] a r e

t--o, z = 0 , U=Uo is]

w h e r e Uo is the s p h e r e en t ry v e l o c i t y . Since Eq. [3] i s too complex for ana ly t i ca l solut ion, n u m e r i c a l p r o - c e d u r e s were adopted to p r e d i c t va lue s of s p h e r e ve loc i ty , U, and ins tan taneous depth of i m m e r s i o n , z, a s funct ions of i m m e r s i o n t ime , t. (See Appendix) . I t i s a p p r o p r i a t e to note he re that if the h i s to ry t e r m in Eq. [3] is d i s c a r d e d , the equat ion can be s i m p l i - f ied to r ead :

dU CDpUI Ul [6] (Ps + CAp) ~ = - ( P - Ps)g - 3 4d

or

322-VOLUME 6B, JUNE 1975 METALLURGICAL TRANSACTIONS B

dU_ ( 1 - y ) g 3CDUrUF dt - ( ~ - ~ - A - ~ - 4d(y + CA)

w h e r e ~, = Ps/P.

[7]

EXPERIMENTAL PROCEDURES

In o rde r to ~ s t the adequacy of the equations out- l ined above for de sc r i b ing p a r t i c l e motion through a l iquid, wooden sphe re s of va r ious d i a m e t e r s ranging between 0.95 and 5.08 cms . , (3/8 to 2 in.), and va r ious spec i f i c g r av i t i e s (0.35 to 0.8) w e r e dropped f r o m heights of 2.13 and 3.57 m e t e r s r e s p e c t i v e l y into a 1.37 m deep, 0 .46m d iam tank of P .V.C. f i l led with w a t e r . A Bolex Ref lex C a m e r a opera t ing at 54 f r a m e s / s r e c o r d e d the sequence of events as the sphere pene- t.rated the wate r , sank to its max imum depth and then s t a r t ed to r i s e back to the su r f ace . No spin was i m -

par ted to the spheres as a r e su l t of the dropping mechanism, which cons is ted of a sp r ing - loaded p la t - f o r m which quickly opened when the tension on the spr ing w a s r e l e a s e d . A P.V.C. Guide Tube was used for the s m a l l e r bal ls to a im the i r ent ry about 2 in. away from, and s l ight ly to one s ide of, a m e a s u r i n g ru le . Subsequent f r ame by f r ame ana lys i s of the f i lm then provided the n e c e s s a r y data on t r a j e c t o r i e s for the se lec t ion of an appropr ia te ma thema t i ca l model . The bot toms of the sphe re s w e r e used to define the loci of the t r a j e c t o r i e s .

E xpe r im en t a l Resu l t s and Selec t ion of Mathemat i ca l Model for T r a j e c t o r y P red i c t i ons

Fig . 2 shows a typical sequence for a 3.65 cm d iam wooden sphere having a densi ty of 0.711 g c m -3, d r o p - ped f r o m a height of 3.57 m into wa te r . The back -

Fig. 2--Typical series of hydrodynamic events for a 3.65 cm diam wooden sphere having a density of 0.711 g e m -z dropped from a height of 3.57 meters into a 0.46 m diam tank of water. Subscripts denote frame number (Camera speed = 54 f.p.s.)

METALLURGICAL TRANSACTIONS B VOLUME 6B,JUNE 1975-323

ground scale is marked in intervals of 0.I feet (Sur- veyor's rule). Frame 0, corresponding to time zero, shows the sphere just about to enter the water, its reflection just below the water line being clearly evident. Frames 2, 4 and 6 demonstrate the rapidity of initial entry, as well as the formation and collapse of a large entrained air cavity. Frame 16, 0.296 s after initial entry, marks the maximum depth of pene- tration, (32 cms), while Frame 57 shows the sphere about to resurface 1.05 s after initial entry. It is interesting to note the spectacular entry period prior to cavity collapse (which represents about 10 pct of the total immersion time) and the evanescence of the r e m a i n i n g s m a l l en t r a ined a i r c av i t y dur ing the r e s t of the de scen t pe r i od .

F ig . 3 shows s o m e typ ica l e x p e r i m e n t a l and t h e o r e t i - c a l t r a j e c t o r i e s for two s p h e r e s d ropped into w a t e r . The t e r m ' t r a j e c t o r y ' i s u sed h e r e in the s e n s e of the depth of the ob jec t below the s u r f a c e us t ime ( i . e . , no

Fig. 3--Experimental and theoretical t rajectories of spheres dropped into water. Figures on theoretical t rajectories indi- cate model number. (a) d = 4.77 cm. Ps = 0.351 gm/ce, U 0 = 6.29 vs. s -l. (b) d = 1.07 cm. Ps = 0.716 gm/cc, U 0 = 6.15 m . S - i .

lateral motion is implied). The experimental results shown in Fig. 3(a) refer to a 4.77 cm diam sphere with a solid/liquid density ratio, y, of 0.351, while those in Fig. 3(b) correspond to a sphere with a y = 0.716 and diameter of 1.07 cm. As seen, in both cases, penetration into the liquid is rapid, as evidenced by the steepness of the curves close to time zero. The rapid entries are followed by decelerating penetra- tions until buoyancy forces finally reverse the direc- tion of motion and the spheres accelerate towards their terminal rising velocities. The maximum immer- sion time is considered reached when the top of the sphere surfaces.

Five possible mathematical models were consid- ered. They involved the following treatment of the drag terms in Eq. [3]:

1) CA = 0.5, CA = 6.0, CD 2) CA = v a r i a b l e , CH = v a r i a b l e , CD 3) CA = 0.5, no h i s t o r y , CD 4) CA = v a r i a b l e , no h i s to ry , CD 5) No added m a s s , no h i s to ry , CD

The c o r r e s p o n d i n g f ive p r e d i c t e d t r a j e c t o r i e s for c o m p a r i s o n with the e x p e r i m e n t a l r e s u l t s have been l abe l l ed , 1, 2, 3, 4 and 5, r e s p e c t i v e l y , in F i g s . 3(a) and (b).

I t i s i m m e d i a t e l y evident that c u r v e s 2 and 4, b a s e d on O d a r and H a m i l t o n ' s v a r y i n g coef f i c ien t s for CA and C// , show s ign i f i can t d i s c r e p a n c i e s , in that p r e - d i c t ed max imum depths and i m m e r s i o n t i m e s a r e o v e r e s t i m a t e d . S i m i l a r l y , cu rve 5 b a s e d p u r e l y on s t e a d y s t a t e d r a g with no h i s t o ry o r added m a s s t e r m s s e r i o u s l y u n d e r e s t i m a t e s m a x i m u m depths and i m m e r s i o n t i m e s .

However , use of the cons tan t c l a s s i c a l added m a s s coef f i c ien t (models 1 and 3) g ives pene t r a t i on depths and i m m e r s i o n t i m e s within 10 pc t of those o b s e r v e d . The ef fec t of including h i s t o ry d r a g i s seen by c o m p a r - Jag c u r v e s 1 and 3 in F i g s . 3(a) and (b) r e s p e c t i v e l y . The r e a s o n s for the d i f f e ren t e f fec t of h i s to ry d r ag on s p h e r e s of low and high spec i f i c g r a v i t i e s a r e d i s - c u s s e d in the Appendix . However , i t i s c l e a r f r o m each c a s e that even though the inc lus ion of a h i s t o r y d r a g t e r m may b r ing the o v e r a l l shape of the t r a j e c t - o r y c l o s e r to that obse rved , the e f fec t on p r e d i c t e d m a x i m u m depth and i m m e r s i o n t ime i s min ima l . T h e s e runs , and the o t h e r s examined , t he re fo re , i n d i - ca t e tha t adequate p r e d i c t i o n s can be made on the b a s i s of mode l 3, which i g n o r e s h i s t o ry ef fec ts and t akes a cons t an t added m a s s coef f ic ien t of 0.5. I t thus c o r r e s - ponds to Eq. [7], with CA : 1 /2 .

F ig . 4 shows p r e d i c t e d and e x p e r i m e n t a l c u r v e s for b a l l s of 1.07, 2.69 and 4.88 c m d i a m r e s p e c t i v e l y , and

= 0.71 d ropped in f r e e fa l l f r o m a height of 3.57 m e t e r s . In ca l cu la t ing in i t i a l en t ry ve loc i t i e s , account was taken of a i r r e s i s t a n c e dur ing the s p h e r e ' s d e s c e n t to the l iquid s u r f a c e . Th is c o r r e c t i o n d e c r e a s e d en t ry v e l o c i t i e s below tha t for u a r e s i s t e d motion ( i .e . , Uo = ~ ) by 1 to 5 pc t depending on sphe re d i a m e t e r and dens i ty . As s een f r o m F ig . 4, l a r g e r ba l l s s ink d e e p e r and s tay in l onge r . The a g r e e m e n t with mode l 3 i s aga in qui te s a t i s f a c t o r y in view of v a r i a b i l i t y in the e x p e r i m e n t a l da t a .

F ig . 5 shows a p lo t of m a x i m u m depths of p e n e t r a - t ion v s s p h e r e d i a m e t e r for s o l i d / l i q u i d dens i ty r a t i o s

324-VOLUME 6B, JUNE 1975 METALLURGICAL TRANSACTIONS B

of 0.72 and 0.365. The solid and broken curves r e p r e - sent theoret ica l predict ions for spheres re leased 2.13 and 3.57 meters above the liquid surface, and again show good agreement with the experimental data. Sim- i la r ly , good agreement is achieved in Fig. 6 where maximum immers ion t imes a r e plotted vs sphere d iamete r and compared with theoret ical predict ions.

It may be noted that very t i t t le effect of height of drop on maximum depths or immers ion t imes is either observed or predic ted .

Discussion of Mathematical Model

As seen f rom the preceding section, his tory effects a r e only of minor importance in determining par t ic le t r a j ec to r i e s under presen t c i rcumstances . It is equally c lea r that added mass effects assume s imi la r

Fig. 4 - - T r a j e c t o r i e s of s p h e r e s dropped into water : e x p e r i - mental , and predic ted by model 3. (a) d = 1.07 cm, Ps = 0.716 gm,/cc, U 0 = 7.74 m s -1. ( b ) d =2 .69 cm, Ps =0.711 g m / c c , U 0 = 8.09 m s -1. ( c ) d = 4.88 cm, Ps =0 .727 g m / c c , U 0 = 8.21 m s -i.

importance to steady drag forces in determining the depth and t ime of immers ion , and cannot be ignored.

The fact that model 3 (CA = 0.5, CH =0, CD = CD) gives such re l iab le predic t ions is quite su rp r i s ing in view of the complex phenomena occurr ing during a sphe re ' s descent through a liquid. In al l c a se s , l a rge cavi t ies of a i r were entrained for about the f i r s t half of their descent ( i .e . , Fig. 2). Consequently the flow around their r e a r sect ions bore l i t t le r e semblance to experimental conditions for which steady drag data have been obtained. The agreement between curves 3 and the experimental t r a j e c t o r i e s in F igs . 3(a) and (b) may therefore be par t ly fortuitous and resu l t f rom compensating e r r o r s in the s teady drag and added mass terms, both of which a r e l a rge during the ini t ia l descent stage through the liquid. However, it is interest ing to note that the p resen t work more c lea r ly dist inguishes the p rac t i ca l mer i t s between assigning a constant added mass coefficient of 0.5 and that of incorporat ing a var iab le added mass t e r m as

d 16 proposed by Odar an Hamilton. Odar subsequently showed '7 that their var iable coefficients gave re l i ab le predic t ions for buoyant spheres acce lera t ing f r o m r e s t through a stagnant fluid. Clift et al. ~a repeated s i m i l a r exper iments and found that good t r a j ec to ry predict ions could also be made by taking the s tandard constant coefficients for CA and Ctt. Taken with the findings of the p resen t work, i t would seem that the c lass ica l values for CA and CH are more appropr ia te and can be applied to more complex motions than has previously been supposed.

Finally, i t is appropr ia te to d i scuss the r easons for the shor t immers ion depths and t imes predic ted by model 5 vs the longer, more c o r r e c t values when added mass is taken into account. In the la t te r case, the sphere entering with a veloci ty Uo essent ia l ly entrains an added mass of liquid whose volume is equal to half that of the sphere ( i .e . , MA = 1//2pVs, Ms = PsVs). By impart ing some of i ts momentum to this liquid, the sphere must slow down, i ts new veloc- i ty being

MsUo [8] U~ (gVls + M A )

Since the steady drag t e rm is sma l l e r at lower ve loc- i t ies , the sphere (and its assoc ia ted liquid) is then

Fig. 5 - -Maximum depth of pene t r a t ion (cm) v s addit ion (cm); expe r imen ta l va lues compared with predic ted c u r v e s based on model 3.

Fig. 6--Immersion times (s) vs addition size (cm); experi- mental values compared with predicted curves based on model 3.

METALLURGICAL TRANSACTIONS B VOLUME 6B, JUNE 1975-325

ab le to p e n e t r a t e d e e p e r and s tay in longer than a s p h e r e with no added m a s s . In the l a t t e r ease , the s p h e r e ' s ve loc i ty does not d e c r e a s e on impact ; s ince d r a g f o r c e s a r e a p p r o x i m a t e l y p r o p o r t i o n a l to U z in th is high Reynolds Number r ange (CD ~ constant) , i t l o s e s i t s downward momen tum too r ap id ly , r e su l t ing in too s h o r t i m m e r s i o n depths and t i m e s . S i m i l a r a r g u m e n t s exl~lain why pene t r a t ion depths a r e not much i n c r e a s e d by dropping the s p h e r e s f rom a he ight of 3.58 vs 2.12 m e t e r s .

EXTENSION OF WATER MODEL TO STEELMAKIN G CONDITIONS

Since the e x p e r i m e n t s us ing w a t e r ind ica te that r e l i a b l e t r a j e c t o r y p r e d i c t i o n s may be obtained on the b a s i s of model 3, and s ince a l l the govern ing d i m e n s i o n l e s s groups for p a r t i c l e s p r o j e c t e d into s t e e l co inc ide with the r ange cove red by the p r e s e n t e x p e r i m e n t s in wa te r , good p r e d i c t i o n s can be made on the depths and i m m e r s i o n t i m e s of a l loy addi t ions d r opped into s t e e l ba ths . Thus , r e f e r r i n g to Eq. [7] which d e s c r i b e s the s p h e r e ' s mot ion (CI-1 = O, CA = 0.5, CD) i t i s seen that the i m p o r t a n t d i m e n s i o n l e s s p a r a m e t e r s a r e a) the s o l i d / l i q u i d dens i ty ra t ion , Y, and b) the s t a n d a r d d r a g coeff ic ient , CD. Since CD is s o l e l y a function of Re, the Reynolds Number (see A p - pendix) , and s ince the k inema t i c v i s c o s i t y of s t ee l [v = (y /p ) ~ 0.064/7 = 0.00914] a l m o s t co inc ides with that of w a t e r (~0.01), Reynolds N u m b e r s and d r a g c o - e f f i c i en t s a r e a l m o s t the s a m e in both s y s t e m s (for a given d and Uo). Thus, by d e l i b e r a t e l y choos ing s p h e r e d i a m e t e r s and s o l i d A i q u i d dens i ty r a t i o s cove r ing the r ange of i n t e r e s t in s t e e l m a k i n g p r a c - t i ce , c lo se matching was a s s u r e d . S i m i l a r l y , F roude N u m b e r (UZ/gL) matching was ach ieved by dropping the s p h e r e s f r o m the heights u sed i n d u s t r i a l l y . Also , a l though the su r f ace t ens ions of s t e e l and w a t e r a r e m a r k e d l y d i f fe ren t , su r f ace en t ry ef fec ts should be rn in imal in both i n s t ances . Taking the p a r t i c u l a r e xam p le shown in F ig . 2 which c r e a t e s a cav i ty hav- ing a m a x i m u m s u r f a c e a r e a about 38 t i m e s the c r o s s - s e c t i o n a l a r e a of the sphe re , the r a t i o of the s u r f a c e ene rgy r e q u i r e m e n t s (38aTrd2/4) to the en t ry k ine t ic ene rgy (psU~ �9 7ra~/12) i s 114 r I n s e r t i n g a p p r o - p r i a t e va lues (114 • 71/0.711 • 3.65 • (815) 2) shows the r a t i o to be 0.0047, which i s obviously negl ig ib le . One can make s i m i l a r a r g u m e n t s for a l loys p r o j e c t e d into s t ee l ba ths even though i t s s u r f a c e tens ion is much g r e a t e r than w a t e r (~1000 d y n e s / c m ) s ince the i m p o r t a n t r a t i o of p h y s i c a l ~parameters is r and Ps would be 4.98 g p e r cm- in th is c a s e . One may note that the d i m e n s i o n l e s s grouping (PsLU2/a) is s i m - i l a r to the W e b e r N o . (p/LU2/cr) which ind ica tes the r a t i o of i n e r t i a l to su r f ace t ens ion f o r c e s in a l iquid s y s t e m .

I t should be noted that the p r e s e n t work does not take into account t h e r m a l e f fec ts , such as the f o r m a - t ion of a so l id s t ee l shee l a round the objec t . If these a r e included (through s imul t aneous solut ion of the a p p r o p r i a t e p a r t i a l d i f f e ren t i a l equat ions for hea t t r a n s f e r with the hydrodynamic equat ions p r e s e n t e d here ; see Ref . 4), i t tu rns out tha t the i n c r e a s e d s t eady d r a g fo rce r e su l t i ng f rom a s p h e r e ' s growth is more than compensa ted by an i n c r e a s e in the added m a s s t e r m . The net r e su l t , for a luminum, is s l igh t ly

326-VOLUME 6B, JUNE 1975

longe r i m m e r s i o n t i m e s and pene t r a t i on depths about 4 pc t l e s s than those p r e s e n t l y p r e d i c t e d . Recent high t e m p e r a t u r e e x p e r i m e n t a l work has c o n f i r m e d th is l a t t e r point . ~9 F o r ins tance , a 2.5 cm d i a m s p h e r e of a luminum dropped f rom 3 m e t e r s wi l l r e m a i n i m m e r s e d for 0.39 s vs 0.31 s for an equiva lent wooden s p h e r e .

DISCUSSION OF APPLICABILITY OF RESULTS TO STEELMAKING

I t i s r e a l i z e d that the p r e s e n t e x p e r i m e n t s i nvo lv - ing s p h e r e s d ropped f rom v a r i o u s heights into s t a g - nant l iquids r e p r e s e n t an a p p r o x i m a t i o n of many hydrodynamic events in s t e e l m a k i n g p r a c t i c e s ince ,

a) the d e o x i d i z e r s may f i r s t p a s s through a s l ag l a y e r in the f i l l ing lad le

b) a l a r g e number of ob jec t s may fa l l s i m u l t a n e - ous ly

c) en t r a inmen t in the pour ing s t r e a m is p o s s i b l e d) tu rbu len t l iquid motions in the f i l l ing l ad le mus t

modify t r a j e c t o r i e s to v a r y i n g extents depending on the o b j e c t ' s 7 r a t io .

I t i s equal ly c l e a r that a ful l s c a l e wa te r mode l of the s y s t e m could answer many of these a s p e c t s . How- e v e r , in the mean t ime , i t is w o r t h noting tha t r e c e n t work on the t r a j e c t o r i e s of a l u m i n u m s p h e r e s d ropped into s t e e l ba ths , 19 showed that a 1 cm thick l a y e r of s l ag had no effect in inhibi t ing s t e e l she l l f o rma t io n . A l so , although the p r e s e n t w o r k i s r e s t r i c t e d to s i n - g le s p h e r e s , i t i s known that for high Reynolds num- b e r s typ ica l of the p r e s e n t s i tua t ion , the ob jec t s have to be in e x t r e m e l y c lose p r o x i m i t y be fore t h e r e i s any a p p r e c i a b l e i n c r e a s e in d r a g . 2~ Moreove r , such e f fec t s would s e r v e only to r e d u c e i m m e r s i o n t i m e s s t i l l f u r the r . F ina l ly , al though an addi t ion en t r a ined in a tapping s t r e a m should p e n e t r a t e much m o r e deep ly than one en te r ing a s tagnan t bath, qua l i t a t ive work 19 ind ica tes that i t should have a s t rong tendency to move away f r o m this l oca l i zed high ve loc i ty r e g i o n in the ladle and r e s u r f a c e in the n o r m a l way sho r t l y a f t e r w a r d s .

To conclude, the au thors c o n s i d e r that the p r e s e n t mode l l ing work r e p r e s e n t s a good f i r s t app rox ima t ion to ac tua l events , and c l e a r l y d e m o n s t r a t e s the type of hydrodynamic contact ing p r o b l e m s involved when so l id addi t ions a r e made to s t e e l ba ths .

Thus, r e f e r r i n g to F igs . 4 and 5, i t is seen tha t a so l id en te r ing a l iquid having a 7 r a t i o of 0.365 wi l l s ink about 13 c m s (5 in) and r e s u r f a c e 0.2 s a f t e r entry , even when dropped through a i r f r om a height of 3.58 m e t e r s . Th is 7 c o r r e s p o n d s a p p r o x i m a t e l y to an a luminum addi t ion in s t e e l . Although s u b s u r f a c e mel t ing is d e s i r a b l e for good r e c o v e r y and p r o c e s s con t ro l , i t i s v e r y unl ike ly under such condi t ions , and one mus t an t ic ipa te s e v e r e ( s l a g / a i r ) - a l u m i n u m i n t e r a c - t ions for a l l n o r m a l p r o c e d u r e s , at any addi t ion s i z e s . S i m i l a r c o n s i d e r a t i o n s would apply to a l loy add i t ions such as 25 pc t F e - S i (7 = 0.39 to 0.58), Z r - S i (7 = 0.48 to 0.52) and 50 pc t F e - S i (7 = 0.58 to 0.67). Al loys such as f e r r o m a n g a n e s e a r e somewha t d i f f e r en t s ince they have 7 r a t i o s in the r ange 0.9 to 1.04 and would pene t r a t e c o n s i d e r a b l y d e e p e r and s t ay i m m e r s e d much longer .

In o r d e r to p rov ide a c o m p r e h e n s i v e se t of p r e d i c -

METALLURGICAL TRANSACTIONSB

tions for steelmaking and to extrapolate outside the ranges covered by the present water model experi- ments, computer predictions based on model 3 were run, taking the density of liquid steel as 7.0 g per cm -3 and its viscosity as 6.4 cP.

Fig. 7 demonstrates the effect of drop height (or entry velocity) on immersion depths and times for 5 cm diam spheres of ferromanganese (apparent density 6.72 g per cm -3) and aluminum (p = 2.7) entering steel. As seen, predictions have been made far beyond the heights normally feasible (or desirable!) in practice. The results indicate very clearly the difficulty of maintaining low density alloy additions immersed, even when they are subjected to very high entry velocities. For example, a 5 cm diam aluminum sphere, dropped from a height of 100 meters with an entry velocity of 44 meters/s (145 ft/s) would only penetrate 1 meter (3.3 ft) and would remain immersed for 1.4 s. In the case of a ferromanganese addition with a density of 6.72 g per cm -3 maximum depths of penetration and total immersion times would be con- siderably increased compared to aluminum, i .e. , 2.4 meters and 11.2 s.

Striking confirmation of these predictions is pro- vided by the recent work of Tanoue et al. at who have developed a new method for adding aluminum to their ladles at the Wakayama and Kashirna Works in Japan. Known as the "Aluminum bullet shooting method", their results showed that somewhat improved yields and markedly better process control could be achieved over previous standard practice by using a rotary chamber type "shooter" to fire a continuous stream of bullets into fillingladles. Taking a specific exam- ple from Fig. 20 of Ref. 21, they show that a 5 cm diam bullet projected to adepth of i meter in still water will remain immersed for 2.4 s. This time compares closely with the 1.4 s immersion time predicted for a 5 cm diam sphere. It also suggests that carefully designed adding pieces can remain immersed almost twice as long as spheres projected to equivalent depths.

Fig. 8 p r e sen t s m ax im um depths of pene t r a t ion for 15 and 25 cm diam alloy addit ions v s alloy addi t ion densi ty for more normal en t ry ve loc i t i e s of 7.67 m e t e r s / s .

Fig. 9 p re sen t s s i m i l a r plots , giving m a x i m u m i m m e r s i o n t imes v s alloy addit ion dens i ty . The ent ry ve loc i ty quoted co r r e sponds to u n r e s i s t e d f r e e fa l l of objects f r o m a height of 3 m e t e r s above the bath. As in the case of Fig. 7, F igs . 8 and 9 a r e plot ted on a s e m i - l o g a r i t h m i c bas i s to c o v e r the wide r ange of depths and i m m e r s i o n t imes p red ic t ed . As one might expect , depths and i m m e r s i o n t imes i n c r e a s e rapid ly for those addit ions having dens i t i e s c lose to mol ten s t ee l . Thus, for al loy addi t ions such as f e r r o m a n g a n - ese , with nominal or apparen t dens i t i e s in the reg ion of 6.95 for instance, i m m e r s i o n t imes of 80 s and depths of 90 cm a re ach ieved . This ind ica tes that such addit ions will , in p r ac t i ce , have l i t t le tendency to sur face and should gene ra l l y follow the l iquid s t ee l flow pat te rns during the c o u r s e of the i r mel t ing h i s - tory in a f i l l ing ladle .

Fig. 7--Effect of height of drop (or entry velocity) on immer- sion times and maximum depth for 5 cm spheres of ferroman- ganese and aluminum in steel.

Fig. 8--Effect of density ratio on maximum penetration for spheres entering steel at 7.67 m per s -1.

METALLURGICAL TRANSACTIONS B VOLUME 6B,JUNE [975-327

Fig. 9--Effect of density ratio on immersion time for spheres entering steel at 7.67 m per s "1.

By the s a m e token, i t is a p p a r e n t that a luminum add i t ions have l i t t l e chance of s u b s u r f a c e mel t ing u n d e r normal p r a c t i c e .

APPENDIX

A s ment ioned in the text, the ful l equat ion d e s c r i b - ing the s p h e r e ' s subsu r face mot ion (i.e., Eqs. [3] and [4 9 i s too complex for ana ly t i ca l solut ion, and n u m e r - i c a l p r o c e d u r e s mus t be adopted for the p r e d i c t i o n of s p h e r e ve loc i ty , U, and ins tan taneous depth, z, a s a funct ion of i m m e r s i o n t ime . In v iew of the c o m p l e x - i t i e s involved in the full equat ion a r a t h e r high p o t e n - t i a l for e r r o r s ex i s t ed . Consequent ly two independent n u m e r i c a l p r o c e d u r e s we re deve loped for c r o s s - c h e c k - ing pu rposes ; a g r e e m e n t to b e t t e r than 5 pc t was obta ined for p r e d i c t e d t r a j e c t o r i e s .

The f i r s t p r o c e d u r e involved a s i m p l e n u m e r i c a l so lu t ion of Eq. [7] (CA = 0.5, CH = 0, CD =CD), u s ing the s t a n d a r d va lues of CD r e p o r t e d by Lapple and Shepherd ~a and Achenbach . aa Thus, a t any p a r t i c u l a r t i m e ins tan t dur ing the s p h e r e ' s i m m e r s i o n , the ve loc i t y U was u s e d to ca l cu la t e the Reynolds N u m - b e r . L i n e a r in t e rpo la t ion us ing l i s t e d va lue s z3'22 of CD for the va lues on e i the r s ide of the Reyno lds N u m b e r in ques t ion then gave the r e q u i r e d va lue of CD. In n u m e r i c a l fo rm, Eq. [7] thus r e a d s :

U'= u-(l-y)gat 3CDUIUIAt [AI] (T + 1/2) - 4 d (7 + 1/2)

wi th

z" = z + 05(U + U')At [A2]

w h e r e U" and z" r e p r e s e n t the new va lues of U and Z, a f t e r At s . An i t e r a t i v e rou t ine tak ing a t = 10 "~ seconds then p roved s a t i s f a c t o r y in p r e d i c t i n g s p h e r e t r a j e c t - o r i e s . F ina l l y , initial en t ry was taken into accoun t v i a Eq. [8] and g r adua l en t ry e f fec t s i gnored .

In the second rout ine , the fol lowing p r o c e d u r e s w e r e adopted for the ca lcu la t ion of the d r a g coef f ic ien t , CD added m a s s coeff ic ient , CA, and h i s t o r y coef f ic ien t , CH.

cv

1) The c o r r e l a t i n g po lynomia l s g iven by D a v i e s z~ w e r e used for Re < 104. 2) F r o m Re = 104 to the c r i t i - c a l Reyno lds N u m b e r of a p p r o x i m a t e l y 3 • l 0 S (Ref. 22), the equat ion of Cl i f t and Gauvin a4 was used , whi le above the c r i t i c a l Reynolds Number , c u r v e s w e r e f i t ted to the da ta of Achenbach . aa

CONCLUSIONS

1) The in jec t ion of a l loy add i t ions into s tagnan t s t e e l ba ths can be s imu la t ed with good a c c u r a c y by dropping wooden s p h e r e s of a p p r o p r i a t e spec i f i c g r a v i t y f rom the s a m e height into w a t e r .

2) Good t h e o r e t i c a l p r e d i c t i o n s can be made on s p h e r e t r a j e c t o r i e s and i m m e r s i o n t i m e s by taking into account s t a n d a r d d r ag and added m a s s e f fec t s .

3) Drag f o r c e s r e l a t i n g to the p r e v i o u s h i s t o r y of the o b j e c t ' s motion a r e s m a l l u n d e r p r e s e n t c i r c u m - s t a n c e s and can be ignored .

4) Al loy add i t ions of low d e n s i t y (e.g., A1, F e - S i , etc.) should exhib i t v e r y s h o r t i m m e r s i o n t i m e s (1 s), even when in jec ted at high v e l o c i t i e s (50 m p e r s-~), on account of a r a p i d lo s s in m o m e n t u m and high buoyancy f o r c e s .

5) A typ ica l high dens i ty a l loy add i t ion (e.g., 5 c m d i a m F e - M n , p 6.96) should r e m a i n i m m e r s e d for about a minute in a bath of s tagnan t s t e e l .

CA

The c l a s s i c a l va lue of 0.514 w a s t r i ed , and a l s o the c o r r e l a t i o n s p r o p o s e d by Odar and Hami l ton . z6

c~

The c l a s s i c a l va lue of 6.0 '4'z5 was t r i ed , and a l s o the Odar and Hami l ton c o r r e l a t i o n s . .6 The so lu t ion of Eqs . [3] and [4] then used p r e v i o u s l y deve loped n u m e r - i c a l p r o c e d u r e s zs for ca lcu la t ion of U and z a s funct ions of t a l lowing for the h i s t o ry t e r m . F o r the e a r l y s t a g e s of mot ion co r r e spond ing to i ncomple t e s u b m e r - s ion ( i . e . , z -< d), the d r ag t e r m s w e r e r e d u c e d by mul t ip ly ing by the f rac t ion of the s p h e r e vo lume i m - m e r s e d :

z2(3d - 2) f- d3 [A3]

ADowance was a l so made for in i t i a l en t ry in the added m a s s t e r m . Eq. [3] in the tex t then b e c a m e (0 <-z<-d),

328-VOLUME 6B, JUNE 1975 METALLURGICAL TRANSACTIONS B

~d ~ d U ua ~ --~- Ps-~-/-= - g - ~ - (fP - Os) - f C o pUI U I

d . 7rd 3 - ~ t f C A - ~ pU)

d 2 ( t (dg~ dr - fcH--4~4-~-ffff ~o k - ~ / 4 7 =- T �9

Multiplying by 12/~d2p and rearranging then gives

dU - 2 g d ( f - 7) - 1.SfCD U[ UI 2d (7 + fCA)-d- [ =

- 1 2 C A ~ Z ( d - Z)

[A4]

.['~" r t / d V \ dr [A5] - 3 f C H ~ ~P jo ~-~-} ~ / t - r .

T o a c c o u n t f o r e n t r y in the h i s t o r y i n t e g r a l , the v e l o c - i ty w a s a s s u m e d to c h a n g e i m p u l s i v e l y f r o m z e r o to [7o a t t = 0; i . e . , d U / d t took the f o r m of a D i r a c d e l t a - f u n c t i o n a t t = 0. W h e n t he h i s t o r y t e r m w a s i g n o r e d , t h e r e s u l t i n g e q u a t i o n s w e r e s o l v e d by the s t a n d a r d R u n g e - K u t t a - M e r s o n p r o c e s s . 2~

E x p l a n a t i o n fo r P r e d i c t e d H i s t o r y E f f e c t s in F i g . 3

R e f e r r i n g to Eq . [3], i t m a y b e no ted t h a t d U / d r i s n e g a t i v e s o t h a t t he h i s t o r y d r a g i s n e g a t i v e w i t h r e - s p e c t to the d i r e c t i o n i n d i c a t e d in F ig . 1; i .e . , h i s t o r y ( l ike a d d e d m a s s ) g e n e r a l l y a c t e d s o a s to c a r r y the s p h e r e f u r t h e r i n to the l i q u i d .

F o r the low d e n s i t y r a t i o ( F i g . 3(a)) , dU/d t i s v e r y l a r g e f o l l o w i n g e n t r y and t he n e g a t i v e h i s t o r y d r a g i s s i g n i f i c a n t d u r i n g t he e a r l y s t a g e s of the t r a j e c t o r y . H o w e v e r , a t l o n g e r t i m e s the c o n t r i b u t i o n s of the d e - c e l e r a t i o n to t h e h i s t o r y i n t e g r a l d e c a y s s o t h a t the i n i t i a l i m p u l s i v e a c c e l e r a t i o n t e r m a t t = 0 ( c o r r e s - p o n d i n g to i n i t i a l c o n t a c t w i t h t he f lu id a n d e q u a l to Uo/, /T) t h e n t a k e s o v e r , m a k i n g the h i s t o r y d r a g p o s i t i v e . T h e r e f o r e the p r e d i c t e d m a x i m u m d e p t h s o c c u r s o o n e r t h a n in the a b s e n c e of h i s t o r y . F o r t he l a T g e r d e n s i t y r a t i o h o w e v e r (F ig . 3(b)), t he d e c e l e r a - t i on w a s m o r e g r a d u a l w i t h t i m e so t h a t the h i s t o r y d r a g r e m a i n e d n e g a t i v e e x c e p t fo r v e r y s h o r t t i m e s .

I t s h o u l d b e n o t e d t h a t a l t h o u g h the a d d e d m a s s t e r m h a s fu l l t h e o r e t i c a l j u s t i f i c a t i o n b o t h a t h i g h a n d low R e y n o l d s n u m b e r s ( i .e . , ~ - inv i sc id ( po t en t i a l ) and c r e e p i n g f lows , r e s p e c t i v e l y ) , t he f o r m of the h i s t o r y t e r m i s on ly s t r i c t l y a p p l i c a b l e f o r " c r e e p i n g f l o w " . N e v e r t h e l e s s , fo r a s p h e r e a c c e l e r a t i n g f r o m r e s t , i n c l u s i o n of b o t h FA and FH h a s b e e n s h o w n to g ive a c c u r a t e p r e d i c t i o n s of t he m o t i o n up to h i g h R e *7'la a n d the h i s t o r y d r a g i s t h e n g e n e r a l l y m o r e i m p o r t a n t t h a n added m a s s . H o w e v e r , t he p r e s e n t s i t u a t i o n , w h i c h i n v o l v e s the m o t i o n of a body p r o j e c t e d i n to a l iqu id , i s c h a r a c t e r i z e d by a l a r g e i n i t i a l R e y n o l d s n u m b e r . I t w a s t hen u n c e r t a i n w h e t h e r t he c r e e p i n g f low c o n c e p t of a h i s t o r y d r a g i s v a l i d o r e v e n a p p l i - c a b l e . T h e m o d e l e x p e r i m e n t s and p r e d i c t e d t r a j e c t - o r i e s s e r v e d to r e s o l v e t h i s q u e s t i o n f o r t he p r e s e n t c a s e .

A C K N O W L E D G M E N T S

T h e a u t h o r s a r e i n d e b t e d to t h e N a t i o n a l R e s e a r c h of C a n a d a f o r f i n a n c i a l s u p p o r t of t h i s w o r k .

LIST O F SYMBOLS

C A A d d e d m a s s c o e f f i c i e n t CD Steady s t a t e d r a g c o e f f i c i e n t CH H i s t o r y c o e f f i c i e n t

d S p h e r e d i a m e t e r F D r a g f o r c e ( s )

FA D r a g f o r c e f r o m ' a d d e d m a s s ' FB B u o y a n c y f o r c e a c t i n g o n s p h e r e F D D r a g f o r c e f r o m s t e a d y t r a n s l a t i o n FG F o r c e of g r a v i t y a c t i n g on s p h e r e ( i . e . , w e i g h t ) F H D r a g f o r c e r e s u l t i n g f r o m h i s t o r y t e r m

g G r a v i t a t i o n a l c o n s t a n t h H e i g h t of d r o p t h r o u g h a i r

M M a s s of w a t e r d i s p l a c e d by s p h e r e M s M a s s of s p h e r e

t T i m e U V e l o c i t y

Uo I m p a c t v e l o c i t y Uo" R e d u c e d i m p a c t v e l o c i t y t a k i n g a d d e d m a s s in to

a c c o u n t Y S o l i d / l i q u i d d e n s i t y r a t i o ~t V i s c o s i t y t, K i n e m a t i c v i s c o s i t y p D e n s i t y of l i q u i d

Ps D e n s i t y of s o l i d a S u r f a c e t e n s i o n r T i m e ( d u m m y v a r i a b l e i n h i s t o r y t e r m )

REFERENCES

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4. L. Gourtsoyannis, H. Henein, and R. t. L. Guthrie: Physical Chemistry of Production or Use of Alloy Additives, John Farrell, ed., pp. 45-67, T.M.S., A.I.M.E., 1974.

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22. E. Achenbach: J. FluidMeclt, 1972, voL 54, p. 565. 23. C. N. Davies: Proc. Roy. Soc., 1945, vol. 57, p. 259. 24. R. Clift and W. H. Gauvin: Can. J. o[Chen~ Eng., 197I, vol. 49, p. 439. 25. G. N. Lance: NumericalMethods for High Speed Computers, Iliffe and Sons,

London, 1960.

METALLURGICAL TRANSACTIONS B VOLUME 6B,JUNE 1975-329