Prediction of Raceway Size in Blast Furnace from Two Dimensional Experimental Correlations

Transcription

1 , pp Pediction of Raceway Size in Blast Funace fom wo imensional Expeimental Coelations S. RAJNEESH, S. SARKAR and G. S. GUPA epatment of Metallugy, Indian Institute of Science, Bangaloe , India. (Received on Febuay 2, 2004; accepted in final fom on May 11, 2004) It has been epoted in the liteatue that aceway measuement made duing the deceasing gas velocity is elevant to opeating blast funaces. Howeve, no aceway coelation is available fo deceasing gas velocity and none of the available coelations eithe in inceasing o deceasing gas velocity take cae of fictional popeties of the mateial. heefoe, a systematic expeimental study has been caied out on aceway hysteesis. Based on expeimental data and using dimensional analysis, two aceway coelations, one each fo inceasing and deceasing gas velocity, have been developed. Results of these coelations have been compaed with the data obtained fom liteatue on the cold models and plant data along with some expeimental data. A good ageement exists between the coelations and othe data. KEY WORS: aceway; blast funace; coelations; deceasing velocity; inceasing velocity; hysteesis; penetation facto and fictional foces. 1. Intoduction In the blast funace, gas is intoduced lateally at a high velocity though a pot, called tuyee, into the packed bed of coke. his ceates a cavity in font of the tuyee called a aceway. Coke is bunt in this zone to supply heat to the pocess. heefoe, coke paticles get consumed in this egion and they ae eplenished by fesh coke paticles fom the suounding of the aceway. So the whole buden descends in the downwad diection. he size and shape of the aceway affects the aeodynamics of the funace and thus affects the oveall heat and mass tansfe. ue to this eason, the aceway has been studied extensively both theoetically and expeimentally. A good eview on the pevious aceway wok is pesented in Ref. 1). In case of the blast funace, many authos have pesented aceway coelations to pedict the aceway size which ae listed in able 1. Most of these coelations ae based on cold model study and some of them ae based on hot model and plant data study. Unfotunately, none of these coelations pedicts the aceway size in industial conditions easonably and they also diffe to each othe. 2 3) It is obseved that all the expeimental coelations have been based on vaious foms of Foude numbe. he aceway size has been intuitively coelated with this numbe along with some othe paametes such as height of the bed, width of the model and tuyee opening. Howeve, these coelations 4 8) ae not evolved based on a systematic study i.e. by applying dimensional analysis and finding the elevant goups. In fact, some of the ealie coelations ae not dimensionally consistent as mentioned in Ref. 9). On the othe hand, theoetical coelations have been obtained by simplifying the actual theoetical equations logically. 1,10) hese coelations ae moe systematic. Most of the empiical coelations 1,6,10) fo the two and thee-dimensional models, have been obtained fo the velocity inceasing case. In few coelations it was not mentioned. Howeve, we believe these coelations ae also belong to inceasing velocity as deceasing velocity obsevation wee not made until 1985 except aylo et al. 5) who mentioned about the hysteesis. It must be mentioned hee that one can get two aceways size at the same gas velocity depending on whethe the measuement is made in the inceasing o deceasing gas velocity. his phenomena is called aceway hysteesis which has been descibed in detail by vaious authos 2,3,11) and it has been epoted 3) that the deceasing velocity coelation is moe elevant to blast funace. Since the aceway size in the inceasing and deceasing velocity case vay by appoximately a facto of 4, the aceway size can affect consideably the pedictions of heat, mass and momentum tansfe in the blast funace. At this junctue something about the aceway hysteesis should be mentioned because the backgound of the coelations developed in this study is based upon this phenomena. Recently Saka et al. 3) have explained aceway hysteesis phenomenon in details and have poposed that aceway hysteesis can be epesented by the following simplified equation (in absence of chemical eaction), based on thei expeimental esults. Pessue foce Bed weight Fictional foces (Stesses) 0...(1) he physical intepetation of this equation is that when the aceway is expanding, the paticles nea and above the aceway ae being moved by the foce due to fluid dag in the upwad diection. So the fictional stesses will tend to oppose this motion of the paticles and hence act in the down ISIJ 1298

2 able 1. List of vaious aceway coelations with emaks. wad diection and is fully mobilized. When we stat to decease the blast velocity fom a maximum value, the paticles above the aceway ae tying to fall down. So the fictional foces act against this movement and stat inceasing in magnitude in the upwad diection pogessively. Once the fictional stesses acting in the upwad diection become fully mobilized, futhe eduction in blast velocity esults in decease in the aceway penetation. hee is a tansition peiod in which fictional stesses change thei diections when the velocity is stated deceasing fom a maximum value. his coesponds to the constant egion of aceway size which is descibed in Fig. 3 late. Fom the above desciption of the hysteesis, it is obvious that fictional foces and thus the fictional popeties of the mateial play an impotant ole in detemining the aceway size. Howeve, none of the pevious coelations (able 1) conside the impotance of fictional foces which have been ecognized as impotant foces in the foce balance. Although, some of the ealie investigatos 9,11,12) did ecogonise the impotance of it and attibuted the discepancy ISIJ

3 able 2. List of geometical and expeimental vaiables. between the expeimental and pedicted esults to fictional foces. Maconald and Bidgewate 9) have studied the phenomenon of void fomation in stationay and moving beds of solids and unified the behaviou using dimensional analysis and the desciption of fluidisation. Expeimentally, they have found that the deceasing velocity condition is applicable to a moving bed. hey ecognised the impotance of fictional foces in coss flow; howeve, in the dimensional analysis they neglected it due to the complexity of the poblem. In this study, the authos had deived an expession fo the cavity size based on dimensional analysis. Howeve, the final fom of the expession has been adopted on a simila line as it was done fo the fluidized bed study by othes. 13) Apte et al. 11) have studied the stess distibution analysis aound a cavity fomed by an upwad gas blast fom the bottom of a two-dimensional packed bed. his setup clevely simplified the foce balance along the steamline coincident with the nozzle axis. hey wote the one dimensional elemental foce balance between the pessue, bed weight and fictional foce. hey did not pedict the size of cavity based on thei analysis. Mostly thei study was concentated on the stess distibution in a packed bed unde inceasing gas velocity. Raceway phenomena have been studied theoetically by expessing all the tems appeaing in the Eq. (1) in pope mathematical tems by othe authos in detail. 14) hey have clealy shown the impotance of fictional foces in packed bed egion. hei study was concentated fo inceasing gas velocity. Recently, a few authos 15,16) have tied to undestand stesses in the ganula bed using iscete Element Method (EM). In fact, some authos 17) have tied to explain the hysteesis phenomena using discete element analysis combined with continuum model fo fluid flow. In this model all the foces have been consideed as descibed by the Eq. (1). his appoach is still in its infancy but quite pomising. Howeve, this appoach also clealy shows the impotance of fictional foces in descibing the aceway phenomena. It has also been epoted that aceway sizes obtained in pseudo two-dimensional and two-dimensional appaatus could be diffeent. 18) wo-dimensional models ae those in which a tuyee, in the fom of a ectangula slot, is intoduced acoss the entie width of the model. hus, the phenomenon is confined stictly to two dimensions and thee is no expansion of jet occus in the thid dimension. In pseudo two-dimensional model, a jet of ai is intoduced though a tuyee placed in the longitudinal cental plane of the model. he jet can expand in font of the tuyee in all diections but it is assumed that thee is a negligible effect due to the jet expansion in the diection pependicula to the tuyee axis. In this aticle, only two-dimensional models have been used and two coelations one each fo inceasing and deceasing gas velocity have been developed based on dimensional analysis taking the fictional popeties of the mateial into account. Pedictions by coelations have been compaed with the published, expeimental, and plant data to veify thei validity. 2. Expeimental Plan As such the expeimental aceway size is a function of physical and fictional popeties of the mateial and geometical paametes of the expeimental setup. heefoe, many expeiments wee pefomed to obtain the aceway size as a function of these paametes in both inceasing and deceasing gas velocity. able 2 shows the ange of vaious vaiables (geometical) along with expeimental vaiables used duing the expeiments. All the paticles, which wee used duing the expeiments, wee having the atio of appaatus thickness (opening) to paticle diamete always geate than 12 o moe. All expeiments wee caied out in two-dimensional cold models which wee einfoced using ion bas to pevent the bulging. PVC slot tuyees wee used. A schematic diagam of the equipment is shown in Fig. 1. he bed was packed with a desied mateial to a desied bed height above the tuyee level. Room tempeatue ai was used as the blast gas to fom the aceway. he ai flow ate to the tuyee was inceased gadually until the point at which the aceway just began to fom, then it was shut off immediately. his pocedue was necessay to clea the tuyee of the beads which enteed the tuyee when the bed was filled. he ai flow ate was then inceased gadually fom zeo to the fluidisation limit of the bed in steps. At each step, two minutes wee allowed fo the aceway size to each equilibium, then the aceway penetation (size in the gas enty diection) and height wee measued diectly using a ule and tacing the aceway bounday on a tanspaent gaph pape. When the maximum gas flow ate fo the expeiment was eached, the flow ate was educed though the same steps. Raceway penetation and height wee measued in the same way. Each expeiment was epeated moe than thee times. Howeve, aveage value has been used in developing the coelations. Vaious physical popeties of the mateials used in the expeiment, ae listed in able 3. Hundeds of expeiments wee pefomed to obtain the aceway size by changing the dimensions of the appaatus, bed height, tuyee opening, 2004 ISIJ 1300

4 Fig. 1. Schematic of expeimental setup. able 3. Physical popeties of the mateials. gas flow ate and mateial popeties. 3. imensional Analysis 3.1. Velocity Inceasing Case he aceway is fomed due to a balance between the pessue foce exeted by the gas, bed weight and the fictional foces as descibed by the foce balance Eq. (1). he pessue foce exeted by the gas compises the inetial and viscous foce. he inetial foce exeted by the gas depends on the blast velocity (v b, m/s), density of the gas ( g, kg/m 3 ) and the tuyee opening (, m). he viscous foce exeted by the gas depends on the viscosity (m, Pa s) of the gas and the paticle diamete (d p, m). he bed weight exeted by the packing depends on the density of the solid ( s, kg/m 3 ), acceleation due to gavity (g, m/s 2 ), height of the bed (H, m) and void faction of the bed. he fictional foces (o stesses) depend on the intenal and wall angle of fiction and this causes the intoduction of the wall-paticle fictional coefficient m w and n, the inte-paticle fictional coefficient. Finally, the width of the bed W has also been consideed since it has been vaied duing the expeiments as it affects the aceway penetation. In othe wods, the aceway diamete (, m) in a packed bed is a function of the popety of mateial used fo packing, popety of the gas injected though the tuyee, the geometical paametes and the fictional paametes i.e. f ( eff, g, v b, g, d eff, m,, H, W, m w, n)...(2) he effective diamete of the paticle is given by d eff d p sh, 19) whee d p diamete of the paticle and sh shape facto of the paticle. Effective density of the bed is given by eff e g (1 e) s. Wall-paticle fictional coefficient is given by m w tan f w and inte-paticle fictional coefficient is given by n tan f. Whee, f and f w ae the intenal angle of fiction between the paticles and angle of fiction between the wall and paticle espectively. Since the total numbe of vaiables is 12 and the numbe of independent vaiables in tems of which the vaiables can be expessed is 3, the numbe of dimensionless goups that will be obtained fom the dimensional analysis is 9. Using p-theoem, the coelation fo the aceway diamete was obtained as ρg k ρ eff H a b c d vb 2 gd p e f g ( µ w ) ( ν) ρ v d µ g b p d p W h...(3) ISIJ

5 Last goup in the above equation can be neglected 9) as aceway fomation is dominated by continuum. It has been obseved theoetically 14) that in 2 cold model wall paticle fiction would be moe dominating than inte-paticle fiction. Moeove, the value of f changes with the gas flowate 20) which makes difficult to assign it single value. heefoe, Eq. (3) in simplified fom can be witten as ρg vb 2 ρgv d b p f k w ρ d eff p µ W H ( µ ) g...(4) he fist dimensionless goup on the ight side is the atio of fluid to solid density. Second goup is Foude numbe which gives the atio of inetial to gavitational foces. It is used to descibe the gas/solid systems. Many pevious authos have coelated aceway size with this numbe. he thid goup is well known Reynolds numbe. he left hand side goup of Eq. (4) is known as aceway penetation facto. Results and iscussion Fom the expeimental values, obtained in the velocity inceasing case, the values of dimensionless goups given in Eq. (4) ae evaluated. he esulting data is then subjected to egession analysis to detemine the constants a, b, c, d, e, f, and k. he values of the constant obtained ae a 0.79, b 0.81, c , d 0.88, e 0.89, f 0.24 and k Fom these values it is clea that Reynolds numbe is of least significance. All othe paametes ae impotant. heefoe, afte neglecting the Reynolds numbe tem and pefoming egession analysis again one gets the values of the coefficients as a 0.79, b 0.81, d 0.85, e 0.88, f 0.23 and k 247. It can be obseved that thee is not much change in the value of the coefficients afte neglecting the Reynolds numbe. he effect of the Reynolds numbe is negligible because of the inetial conditions pevailing duing the aceway expeiments pefomed. Since the value of coefficients a, b, d and e ae quite close, we can goup them into a single dimensionless goup and the simplify fom of the coelation can be witten as a b c d e ρgv 2 b 2 k ( µ w ) ρeff gdeff HW a b...(5) a b c d e ρg vb 2 ρgvbdeff f k ρ d µ W H ( µ w ) eff g eff...(4) A egession analysis was pefomed on the expeimental data, obtained in the gas velocity deceasing case, to detemine the constants a, b, c, d, e, f, and k. he values of constant obtained ae: a 0.60, b 0.62, c 0.024, d 0.51, e 0.095, f and k he R 2 value of the coelation was found to be As befoe, one can neglect the Reynolds numbe since its coefficient c is vey small. Since the values of othe coefficients a, b, and d ae quite close, one can combined these dimensionless goups into single goup. hus the simplify fom of the coelation can be expessed as ρgvb 2 c k µ w...(7) ρeff gd W H eff ( ) whee k, a, b and c have to be detemined by egession analysis again. Using the above equation and pefoming egession analysis, one obtains the following final fom of the coelation fo deceasing velocity ρgvb ( µ w )...(8) ρeff gd W H eff he R 2 value of the coelation was found to be Equations (6) and (8) ae the desied aceway size coelations fo the inceasing and deceasing velocity espectively. It is inteesting to note that the bed height and tuyee opening play an impotant ole in inceasing than deceasing velocity. Equation (6) shows that aceway diamete is popotional to almost squae of the velocity in inceasing velocity while the Eq. (8) shows it is almost linea to the velocity in deceasing case. In Fig. 2 the expeimental data points ae compaed with the deceasing coelation (8). Each point in the figue is an aveage of at least thee expeimental values. A good ageement between the two is appaent. A simila plot was ob- a b oing egession analysis again, we get the values of the coefficients as a 0.80, b 0.25 and k 164. he R 2 value of the coelation was found to be heefoe, the final fom of the coelation fo inceasing velocity is ρ v 164 ρeff gd HW g b 2 2 eff 080. ( µ ) w (6) 3.2. Velocity eceasing Case he coelation fo the aceway diamete as befoe is given by Fig. 2. eceasing coelation vs. expeimental data ISIJ 1302

6 Fig. 3. Expeimental aceway hysteesis fo plastic beads of 2.1 mm size. Fig. 4. Compaison of aceway diamete between expeimental and coelations in both inceasing and deceasing velocity. tained fo inceasing coelation. he esults obtained fom these coelations ae compaed with the expeiments and plant data below. Expeimental ata Figue 3 shows a typical expeimental hysteesis plot of aceway size. his plot is fo plastic beads of diamete 2.1 mm. Bed height was 600 mm fom tuyee level and tuyee opening was 5.5 mm. Appaatus numbe 3 (see able 2) was used duing the expeiments. One can clealy see that aceway size in deceasing gas velocity ae always highe than the inceasing case and can vay by a facto of 3. he detailed mechanism involved behind it is explained elsewhee. 3,14) Howeve, in bief it can be said that initially, thee is no aceway fomation with incease in velocity since the pessue foce exeted by the gas is unable to ovecome the fictional foces and bed weight. Late when the velocity (o pessue foce) is sufficiently high to ovecome these foces, void o aceway stats foming. As we stat inceasing the blast velocity futhe, the aceway size inceases in a paabolic manne. Afte a maximum gas velocity, as one stats deceasing the gas velocity, initially thee is almost no change in the aceway size. his is due to the fact that the fictional foces stat acting in the evese diection and incease in magnitude as we stat deceasing the gas velocity. Once the fictional stesses acting in the evese diection become fully mobilized, thee is a linea decease in the aceway penetation with futhe decease in the velocity. Othe expeimental esults ae not epoted hee as they have been discussed elsewhee. 3,14,21 24) It should be noted that in all figues (Figs. 4 to 7) compaison of coelation data has been done only with those expeimental data which have not been used in developing the coelation. If we use those data that have been used fo developing the coelations then thee has to be a good ageement between the two as shown in Fig. 2. heefoe, thee is no point in compaing those data with the developed coelations. A compaison between the expeimental and pedicted (using coelation equation, Eq. (8)) aceway size fo deceasing gas velocity is shown in Fig. 4. All the expeimental conditions ae same as given in Fig. 3. An excellent Fig. 5. Compaison of coelation aceway diamete with published 1) data of 3 mm polystyene. ageement between the two is appaent. ata in the velocity ange of 18 to 28 m/s (whee aceway size is constant) can not be compaed as the fiction is getting mobilized duing this peiod. It is changing its sign/diection and theefoe, thee is no change in the aceway size. Moe desciption of this behaviou is given elsewhee. 3,14) he coelations, which have been developed in this study, ae valid only when fiction is fully mobilized. heefoe, they ae valid fo Fig. 3 in inceasing case between 0 to 28 m/s velocity and in deceasing case between 0 to 18 m/s. he linea decease in the aceway penetation with blast velocity is pedicted well by the coelation. Similaly, one can see good ageement between the two values in inceasing gas velocity as shown in the same figue. Cold Model ata Figue 5 shows a compaison of aceway size obtained using the coelation and published expeimental values fo a 2 cold model. 1) he expeimental values of the aceway diamete have been obtained fo polystyene beads of diamete 3 mm, bed height fom the tuyee level 800 mm, and tuyee opening 5 mm. Angle between the wall and paticle was taken ) Othe values ae given in Ref. 1). Aveage aceway diamete was used in plotting the value as data wee available fo aceway penetation and aceway ISIJ

7 Fig. 6. Compaison of penetation factos obtained fom coelation and published 1) data of mm ballotini glass. Fig. 7. Compaison of expeimental blast funace 7) and cold model data fo both inceasing and deceasing velocity conditions. height. 1) hee is good ageement between the expeimental values of aveage aceway diamete and that obtained using the coelation with the maximum eo equal to the two paticles diamete except at the maximum blast velocity which is close to the fluidisation limit and one can not expect a good ageement fo those values. It should be noted that the coelation gives the diamete of the aceway which could be little diffeent, by definition, fom the aceway penetation o aveage aceway diamete as epoted by many investigatos. Anothe published expeimental esult 1) along with coelation data fo the glass bead of diamete mm, bed height fom the tuyee level 800 mm and tuyee opening 5 mm is given in Fig. 6. he esults ae fo 2 cold model in inceasing gas velocity condition. ata have been plotted in tems of penetation facto ( R / ) and non-dimensional numbe (((( g v 2 b 2 )/( eff gd eff HW ))0.8 (m w ) 0.25 ) as given by the Eq. (6). Wall-paticle angle was taken ) Again, thee is a good ageement between the expeimental values of penetation facto with that obtained using the coelation except the last expeimental point which is nea the fluidisation limit as explained in pevious figue. Fom Figs. 5 and 6 it is evident that tend of the pedicted values is same though they have been plotted in a diffeent way in each figue. his is an expected tend if only one paamete is vaied. All othe figues have been plotted in dimensionless numbes. Plant ata It was epoted by a few authos 2,3,21) that aceway size obtained in deceasing gas velocity is moe elevant to opeating blast funaces than inceasing gas velocity. It is because lage amount of coke is consumed nea the aceway duing combustion and in educing the oe. his coke is eplenished fom the suounding of the aceway. Also intemittently ion and slag is tapped fom the bottom due to which coke descends. It has also been found 9) that the deceasing gas velocity condition is applicable to the case of a moving bed as in the case of blast funace. It was obseved that the hoizontal injection into a moving bed gives effects simila to those encounteed with vetical injection into a moving bed. So the 2004 ISIJ 1304 deceasing coelation esults can be applied to the moving bed iespective of whethe thee is hoizontal o vetical injection of the gas. All the pevious coelations, which have been given fo the aceway penetation till now, ae mainly fo the inceasing velocity. hee is a doubt of thei applicability to the blast funaces. Now, it is the time to veify two points: 1. Whethe the deceasing gas velocity is elevant to blast funace o inceasing, and 2. Whethe the developed coelation, based on cold model esults, can epesent the commecial blast funace. Figue 7 shows the aceway facto values plotted as a function of penetation facto obtained using the coelation in both inceasing and deceasing velocity case along with the expeimental blast funace data. 7) In the expeimental blast funace, wate cooled pobe was used to measue the aceway size though the blow-pipe. In this figue data obtained fom the coelation ae based upon the cold model expeimental data fo the case of appaatus 1, tuyee diamete 6 mm, bed height 1m and polyethylene beads of equivalent diamete 4.1 mm. hee is an excellent ageement between the aceway facto values obtained in the velocity deceasing case with the expeimental blast funace data when plotted as a function of penetation facto. It confims both the points mentioned above that aceway size obtained in deceasing velocity is moe elevant to commecial blast funace and the coelations developed hee easonably pedict the aceway size. In Fig. 7, it was difficult to compae the penetation facto with the non-dimensional numbe, developed in this study, as many of the data wee not available. In fact, in most of the published wok on commecial blast funace, many data ae missing. Howeve, we have managed to extact most of the data fom these papes. Some of the values have been assumed in a easonable way which ae descibed duing the discussion of a paticula figue. Fom Figs. 8 to 11, aceway data ae compaed using the coelations and actual blast funace data. Befoe we stat to compae the data obtained using two-

8 dimensional (2) cold model coelations with thee-dimensional (3) blast funace one should econcile some paametes. W in 2 model is efeed to the width of appaatus. In blast funace this has been taken as adius of the heath that would be the appoximately maximum width one may get in the bosh egion in blast funace. Also, the value of this paamete is easily available in the liteatue. uyee opening in 2 is, howeve, in the case of blast funace (3) tuyee (cicula pipe) aea has been conveted into the equivalent 2 ectangula aea keeping one dimension is equivalent to the tuyee diamete (which is in 2 case would be the thickness of the bed, see Fig. 1). he othe dimension of the ectangula aea will give the tuyee opening,, fo the blast funace. Fo example, if tuyee diamete is 20 cm then tuyee opening,, in 2 would be 15.7 cm ((aea of the tuyee pipe, p 2 ) (aea of the ectangula slot, 2)). Wagstaff 4,6,25) epoted the data of commecial blast funaces almost half a centuy ago. hat time blast funace technology was not so advanced. We wee able to extact most of the data which ae equied by the coelation to pedict the aceway diamete except the height of the buden, coke size, appaent density of solid and heath adius (as W in the coelation). Afte going though a few text books, 19,26,27) coke size was assumed 40 mm and bulk density 900 kg/m 3. hese values wee kept constant in othe papes also (if applicable). Heath diamete, especially fo the old funaces of 1950, was assumed 19) 7 m. Buden height was calculated, fo all authos, as effective buden height using the fomula suggested by Sasty et al. 22) hey have shown, based on stesses at the bottom of a 2 appaatus and using modified Janssen equation fo a two-dimensional bed, that pessue becomes almost constant at the bottom of the appaatus afte a cetain buden height. Using thei fomula and assuming 15 m buden height, it was found that pessue at the bottom becomes constant afte 5 m of buden height. heefoe, this height (5 m) was taken as the effective buden height fo all the commecial funaces. It was also found that if buden height is taken to 20 m then thee is hadly any change in the effective bed height. Figue 8 shows a compaison of pedicted penetation facto with the actual blast funace data. 6) Raceway depth was measued using a wate cooled pobe. 4) All the data belong to one blast funace. An excellent ageement between the two is appaent. It shows the validity of the coelation to pedict the aceway diamete in opeating blast funaces afte econciling a few 3 paametes into 2. Anothe compaison between the plant 6) and coelation data is shown in Fig. 9 fo deceasing gas velocity. Eo bas ae also shown in the plant data as thee is a wide scatteing in the expeimental data. Each plant data point in this figue belongs to an aveage of one blast funace only. heefoe, five blast funaces data have been plotted along with pedicted values. It is pleasing to see a good ageement between the two again. Howeve, the eason fo wide fluctuations in the expeimental data should be addessed. In Fig. 9, each funace data point is an aveage of 20 o moe points except in one case. hee wee a few points of aceway penetation in each funace that wee eithe vey high o low and hence affecting the oveall aveage value significantly. We have included all the points in calculation. Fig. 8. Fig. 9. Compaison of penetation factos obtained fom deceasing coelation with published blast funace data 6) fo one funace. Compaison of penetation factos obtained fom coelation with published blast funace data 6) of vaious funaces. It was noted that at diffeent time vaying aceway penetation, at the same blast velocity, have been epoted. his is may be due to that duing the aceway measuement 4) pobing od tends to sag of its own weight when it is feely esting in the combustion zone, but when it is pushed back futhe and stikes the stationay solid mateial, the end deflects upwads. It has also been found that in some cases, one gets moe aceway penetation at less velocity than at high velocity. hese all factos can give a diffeent tend to blast funace cuve. Howeve, this is not the case in cold model data whee one has moe pecise and epoducible esults. Figue 10 shows anothe compaison between the coelation and Japanese blast funaces. 28) In this pape all the data wee available except bulk density of the coke which was taken 900 kg/m 3 as descibed befoe. In this figue aceway diamete has been plotted against gas velocity. In this figue seven blast funace data have been plotted. Each data belongs to one blast funace. Each funace has diffeent conditions such as coke size, heath diamete, blast velocity. Fo each funace only one data was available theefoe, thee is no eo ba in the expeimental values is ISIJ

9 Fig. 10. Fig. 11. Compaison of coelations with published blast funace data of Nishi et al. 28) Compaison of penetation factos obtained fom coelation with published blast funace data 29) of vaious funaces. Besides these, opeating data in this figue ae affected by fluctuations in blast pessue, auxiliay fuel supply ate and blast moistue which will futhe deteioate the compaison which is obvious fom this figue. We must mentioned that no manipulation in the data have been made in ode to get the penetation facto fom the coelations. Howeve, one should make the judicious choice of the opeating paametes, which ae not available based on available liteatue in this aea in ode to get the aceway diamete. One should be awae of that opeating aceway data could fluctuate to any extent depending on the opeating conditions of the blast funace and the fluctuations in the opeating paametes such as wind ate, blast tempeatue and pessue, etc. Also, aceway penetation depends with the casting conditions that whethe it has been measued befoe, afte o duing the cast. Futhe study on thee-dimensional cold and hot models would be desiable in this aea and to extend the coelations to eal blast funace taking into consideation the above mentioned blast funace conditions. In the blast funace coke is consumed in the aceway and theefoe the whole buden descends downwad towads the aceway. heefoe, fiction is expected to oppose this movement and will act in the upwad diection and be fully mobilized. his blast funace condition is satisfied expeimentally only when one does the expeiments in the deceasing gas velocity. Only unde these expeimental conditions fiction will act in the upwad diection as discussed in the begining. In inceasing gas velocity, paticles ae pushed upwads and theefoe, fiction will act in the downwad diection to oppose this motion of the paticles which is not the case in a blast funace. etailed analysis on this is available in Refs. 2), 3), 9), 14), 21) and 24). he above examples also confim that aceway data obtained on the opeating blast funaces ae elated to deceasing gas velocity in the two-dimensional cold model. shown. In this study aceway size was estimated fom tempeatue and gas composition. Hee the wall of aceway has been defined whee thee is an abupt change in tempeatue has occued in the aceway. he distance fom the aceway wall to the tip of the tuyee was expessed as aceway depth. he tempeatue within the funace has been estimated fom the gaphitization of the coke. Again a good ageement exists between the two. he diffeence between the two values is mostly within the limit of two to fou paticles diamete. Fo compaison pupose, inceasing velocity data has also been plotted in the same figue. It is obvious that deceasing velocity data ae elevant to blast funaces and ae well epesented by deceasing cold model coelation. Anothe compaison of coelation with opeating blast funace data 29) is shown in Fig. 11. In this figue also, almost all data wee given in the liteatue except the coke size and its bulk density which wee taken as 40 mm and 900 kg/m 3 espectively. Figue also shows the eo bas in the plant data. Each aveage data belongs to one funace. he technique to measue the aceway size is not descibed in the pape. A easonable ageement exists between the two. Again the same explanation can be given fo the wide fluctuations in opeating data as it was given in Fig Conclusions wo aceway size coelations have been developed one each fo inceasing and deceasing gas velocity unde the cold model conditions. Fictional popeties of the mateial have also been included in these coelations. wo-dimensional coelations have been applied to thee-dimensional geomety afte econciling a few paametes such as tuyee and heath diametes. Raceway size obtained fom the coelations and othe data such as published cold model, plant and expeimental data match easonably well. It has been shown that deceasing conditions pevails in the opeating blast funace and theefoe, deceasing coelation can be used to pedict the aceway size. Both the coelations ae able to pedict the aceway hysteesis in cold model. Acknowledgements he financial suppot povided by Council of Scientific and Industial Reseach (CSIR), India, by gant no: 22(0285)/99/EMR-2 is gatefully acknowledged. REFERENCES 1) P. J. Flint and J. M. Bugess: Metall. ans. B, 23B (1992), ) J.. Liste, G. S. Gupta, V. R. Rudolph and E.. White: CHEMECA 2004 ISIJ 1306

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