physical simulation on molten steel flow characteristics

Research ArticlePhysical Simulation on Molten Steel Flow Characteristics of RHVacuum Chamber with Arched Snorkels

Zhi-Feng Ren 123 Zhi-Guo Luo 1 Fan-Xia Meng 4 Zong-Shu Zou1 Yi-Hong Li23

Ai-Chun Zhao 23 and Hai-Lian Gui23

1School of Metallurgy Northeastern University Shenyang 110819 China2School of Materials Science and Engineering Taiyuan University of Science and Technology Taiyuan 030024 China3Engineering Research Center Heavy Machinery Ministry of Education Taiyuan University of Science and TechnologyTaiyuan 030024 China4State Key Laboratory of Rolling and Automation Northeastern University Shenyang 110819 China

Correspondence should be addressed to Zhi-Guo Luo luozgmailneueducn and Fan-Xia Meng 1610196stuneueducn

Received 11 May 2020 Revised 30 July 2020 Accepted 10 August 2020 Published 30 August 2020

Academic Editor Jan Koci

Copyright copy 2020 Zhi-Feng Ren et al-is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

-e RH vacuum refining technology is a vitally powerful method of producing clean steel -e inner diameter of traditionalcircular snorkel is very difficult to be increased owing to the metallurgical refractory thickness around the snorkels and thelimitation of the area under the vacuum chamber limiting the increase in refining efficiency In order to improve the refiningefficiency of the RH reactor a new designed RH degasser with an optimized arched snorkel is established -is design replaces thetraditional two circular snorkels structure with the two arched snorkels and greatly enhances the cross-sectional area of snorkel Inthis study the flow characteristics of this new type RH were studied and analyzed by establishing a 1 55 physical model of RHwith arched snorkels Results show that the circulation flow rate of RH with arched snorkels can increase by 100sim 180 and themixing time approximately decreases by 35 compared with RH with circular snorkels under actual production conditions -ecirculation flow rate of RH with arched snorkels continues to increase obviously when gas flow rate exceeds the saturated value ofRH with circular snorkels -e RH with arched snorkels can increase the refining efficiency significantly and has importantapplication prospect

1 Introduction

As a tool for molten steel secondary refining the Ruhr-stahlndashHeraeus (RH) processing has wide applications owingto its multiple metallurgical functions such vacuumdegassing decarburization inclusion removal denitroge-nation and inclusion removal It is widely used for theproduction of ultralow carbon steels bearing steels pipelinesteels spring steels silicon steels etc -e RH vacuum steeldegassing process depends on sucking the liquid steel fromthe ladle to the vacuum chamber equipped with two snorkels(up-leg and down-leg) [1] When the inert gas is blown to theliquid steel then the circulation flow of steel between vac-uum chamber and ladle is forced -e degassing processmainly occurs in liquid internal [1] at splashed metals invacuum chamber and bubble surfaces [2 3] which involves

complex chemical reactions and transport phenomena [4]-us to improve the degassing and decarburization rate andpromote the inclusion removal rate in the RH systems it isimportant to illustrate liquid steel flow characteristicsNevertheless the RH system can hardly be observed directlybecause of its complex physical and pyrometallurgicalprocess which involves thermodynamics kinetics andmultiphase flow and mass transfer [4] -e problem wassuddenly thrown into sharp focus In order to reduce costsmany researchers are very concerned about improving therefining efficiency of RH equipment It is generally con-sidered that the circulation flow rate [5ndash10] and the mixingtime [11ndash16] are two significant parameters during the RHprocess -us many researchers have developed physical[10 11 17ndash21] or mathematical models [5 13 22ndash27] tosimulate the multiphase flow [13 22 26ndash29] mixing

HindawiAdvances in Materials Science and EngineeringVolume 2020 Article ID 6525096 10 pageshttpsdoiorg10115520206525096

phenomena [10ndash16 28ndash31] behavior of bubble and inclu-sion removal [22 30 32] and decarburization process[1 2 8 20 23 25 33 34] during the RH treatment Based onthe physical simulation experiment work of predecessors oncirculation flow rate of RH some empirical formulas arelisted in Table 1 which includes the formulas put forward atthe first time and excludes similar equations reported later Itis generally accepted that the circulation flow rate of RH isrelated to the injected gas flow rate and the section size ofsnorkel From process parameter improvement view manyresearches have proved that a higher gas flow rate[5 7 29 30 34] a lower vacuum pressure [18 19 28] adeeper insertion depth of snorkel [3 14] would favor tooptimize the fluid flow of RH However the circulation ratewill reach a saturated value with the gas flow rate increasing[14 36] From equipment improvement view many in-vestigations have proved that a larger snorkel sectional area[24 26 29 38]blowing from the bottom of the vacuumchamber [15] or ladle [39] would favor to optimize the fluidflow of RH Recently many researchers have tried to in-crease the refining efficiency by using single-leg[12 28 31 40] multilegs [38 41] and magnetic field [42]imposed around the up-leg However the single-leg washardly used in the actual industrial manufacture consideringtechnical immaturity meanwhile multilegs and imposingmagnetic field around snorkel were also hardly used in theactual industrial manufacture considering the cost issue Allof the equations in Table 1 imply that the arched snorkelswith greater sectional area would bring a larger circulationflow rate Additionally the stimulus-response was thegeneral method used to measure the mixing time [7 10]another important parameter for the RH treatment In thephysical simulation experiments of this paper this methodwill continue to observe the mixing of molten steel

However little results [38 42] were reported to study theshape of RH snorkels which has always been circular until theoval snorkel was proposed by Kuwabara [15] -e oval snorkelswere favored to enhance fluid flow of RH but we want therefining efficiency to keep getting bigger including a greatincrease in circulation flow rate and saturated value of gas flowrate In the current study a new vacuumdegasser equippedwithtwo snorkels of larger sectional area was designed -e twotraditional circular snorkels were replaced with two archedsnorkels which was not reported in previous investigations Forthe arched snorkel the internal arc height is equal to the radiusof traditional circular snorkel and the internal diameter is 3 to 4times of the circular snorkel Hence the sectional area of archedsnorkel is much larger than that of circular snorkel Watermodeling was performed according to similarity criterion -eflow velocity of the RH water model down-on leg-outlet planewas captured by electronic tachometer and the stimulus-re-sponse method was used to measure the mixing time -eresults provided the experimental basis for promoting andimproving this new RH vacuum refining equipment

2 Experiment

21 Model Design -e prototype is one RH vacuumchamber with two circular snorkels from a steel plant in

China According to the empirical formulas listed in Table 1we have determined the kernel idea of this design is toincrease the cross-sectional area of snorkel as much aspossible -e scale of water model and prototype is 1 55Figure 1(a) shows the model size of circular snorkel -ecircular snorkel diameter is very difficult to be increasedowing to the metallurgical refractory thickness around thesnorkels and the limitation of the area under the vacuumchamber In order to increase the cross-sectional area of thesnorkel as much as possible two snorkels are changed toarched structures in this research So as to make full use ofthe space under the vacuum chamber the inner diameter ofthe vacuum chamber is determined as the diameter of archedsnorkel and the arc height is same as the inner diameter ofcircular snorkel utilizing the bottom space of the vacuumchamber optimized Figure 1(b) exhibits the top view of thearched snorkel water model Compared with circularsnorkel this arched structure increases the equivalent innerdiameter by approximately 70 and the cross-sectional areaby 193 in this design

22 Similarityeory A 1 55 scale water model of 170 t RHwas built according to the similarity principle Table 2 showsthe main parameters of the prototype and physical model-e lifting gas flow rate of model Qm is calculated from theactual gas flow rate on-site Qp with the modified Froudecriterion according to the following equation

Qm 001448Qp (1)

23 Experimental Device and Parameters -e water modelexperimental devices consist of vacuum chamber and ladlemade of plexiglass Two snorkels are equipped at the bottomof the vacuum chamber To the RH with two circularsnorkels compressed air is used as the lifting gas through sixevenly distributed gas injection nozzles in one horizontalplane of circular up-leg To the RHwith two arched snorkelsfour nozzles are distributed evenly in the arc of the archedup-leg two others are distributed evenly in the chord andthese six nozzles are in one horizontal plane of arched up-leg -is model also includes the gas source system gasdistributor and transmission pipeline vacuuming systemmetering system and detection system Figure 2 shows theschematic of the main apparatus of the water model

-e gas flow rate is 60sim130 Nm3middothminus1 the pressure in thevacuum chamber is 67 Pa and insertion depth of snorkel is627mm in the production site Table 3 shows the corre-sponding parameters of the prototype and water model

24 Experimental Index

241 Circulation Flow Rate -e circulation flow rate Gmwas obtained by measuring the fluid velocity which was20mm above the outlet of the down-leg Five measuringpoints were horizontally and longitudinally set at the cross-sectional center of down-leg -e fluid velocity at themeasuring point was obtained with an electronic tachometer

2 Advances in Materials Science and Engineering

(XC-LSB-1 XINGLIANCHEN Technology Co LtdChina) Each measurement was repeated three times andthe cross-sectional velocity was obtained by the averagevalue of all measuring points -e circulation flow rate wasthe product of the measured velocity and cross-sectionalarea of the down-leg

242 Mixing Time -e mixing time Tmix was measured byan electrical conductivity meter [18 36] -e saturated NaClaqueous solution was used as the tracer When the fluid flowin the model was stable the saturated NaCl aqueous solutionwas injected into the water through the spare nozzle on topof up-leg Meanwhile the conductivity instrument (DDS-307A INESA Scientific Instrument Co Ltd China) was

employed to measure the conductivity until a stable value(Cinfin) was reached -e time for reaching the stable value iscalled mixing time -e conductivity probe was placed60mm below the ladle liquid level in the center between theup-leg and down-leg

25 RHWork Principle and Bubble Behavior -e lifting gasis injected into the molten steel through the nozzles anddiscrete spherical bubbles are formed at the nozzle exit -ebubbles with initial horizontal velocity enter into up-legfrom the nozzles and then the bubbles float upward anddrive the molten steel up Figure 3 shows the schematic ofthe bubble formation and motion path

Table 1 Equations for circulation flow rate

Author Equations Variables ReferenceWatanabeet al Q 0020D15G033 Q circulation flow rate tmiddotminminus1

G gas flow rate NLmiddotminminus1 D diameter of snorkel m [35]

Tokio et al Q K middot D15G033 K constant [11]Seshadri andCosta Q ρ middot S middot (074G ln(P2P1))

13 ρ liquid density gmiddotcmminus3 S section area of snorkel m2

P1 pressure at top level Pa P2 pressure at injection point Pa [36]

Kuwabaraet al Q K middot G13D43[lnP1P2]

43 P1 pressure at blowing point atmP2 pressure at vacuum vessel atm [15]

Kamata et al Q 114Q(13)g d(43)

p (ln1 + ρ1ghPv)(13)Qg gas flow rate NLmiddotminminus1 dp diameter of snorkel m ρl liquiddensity gmiddotcm3 g gravitational acceleration mmiddotsminus2 h gas inject

depth cm PV vacuum chamber pressure Pa[37]

Φ92mm

Circular snorkels

Inner diameter ofvacuum chamber

Φ330mm

Φ92mm

(a)


Φ330mm

Arched snorkels

92mm 92mm

(b)

Figure 1 Model schematic of the RH vacuum chamber with (a) circular and (b) arched snorkels (top view)

Table 2 Parameters of the prototype and water model

Item Prototype(mm)

Water model for circular snorkels(mm)

Water model for arched snorkels(mm)

Diameter of ladle top 3077 564 564Diameter of ladle bottom 2666 489 489Height of ladle 3806 692 692Inner diameter of vacuum chamber 1800 330 330Height of vacuum chamber 10350 1000 1000Internal diameter of circular snorkel 500 92 92Internal diameter of arched snorkel 1800 330 330Internal arc height of arched snorkel 500 92 92Length of snorkels 1500 275 275Inner diameter of gas injection nozzles 6 11 11Distance between nozzles and bottom of vacuumchamber 550 100 100

Advances in Materials Science and Engineering 3

-e molten steel circulation process between the vacuumchamber and the ladle in RH vacuum degasser is similar to theldquobubble pumprdquo mechanism A certain height difference be-tween the liquid levels in the vacuum chamber and ladle iscreated in the vacuum degree of the vacuum chamber -elifting gas first enters into molten steel in the form of bubblesfloats upward and then expands with the temperature increaseand pressure decrease Accordingly the density of gas-liquidtwo-phase in the up-leg reduces -e molten steel in the ladle isdriven to the up-leg and then flows out through the down-legdue to gravity after entering the vacuum chamber -ereafter acirculation flow is formed and the following equation isachieved [8 14 17]

Agas Asteel + Aloss (2)

where Agas is the gas expansion work J Asteel is the work forlifting molten steel J and Aloss is the lost work J

Considering Aloss is small equation (2) can be expressedas

Agas Asteel MHg MP0 minus P

ρgminus1

P0 minus P

ρ11113888 1113889 (3)

where M is the quality of lifting liquid steel kg H is thelifting height of liquid steel m P0 is the atmosphericpressure Pa g is the acceleration of gravity mmiddotsminus2 P isvacuum chamber pressure Pa ρg-l is the density of gas-liquidtwo-phase kgmiddotmminus3 and ρl is the density of liquid kgmiddotmminus3-e density of the gas-liquid two-phase is the weighted valueof the gas and liquid phases and obtained from equation (4)[17] as follows

ρgminus1 α middot ρg +(1 minus α) middot ρ1 (4)

where α is the gas holdup

3 Results and Discussion

31 Comparison of RH with Circular Snorkels and RH withArched Snorkels

311 Flow Field Under the condition of vacuum chamberpressure (P 97709 Pa) insertion depth of snorkel(Himm 100mm) gas flow rate (Qm 10 Nm3middothminus1) andflow field using the black ink as tracer is shown in Figure 4-e ink was injected into up-leg through the spare nozzle onthe top of up-leg A high-speed camera was used to recordthe flow field As shown in the flow fields from the watermodels the molten steel driven by lifting gas flowed into thevacuum chamber through the up-leg and violent mixingoccurred in the vacuum chamber -en the molten steelflowed downward the ladle through down-leg reached theladle bottom and rose upward again -e time of tracer inRH with arched snorkels to complete the mixing in thevacuum chamber reaching the ladle bottom and completeone cycle was respectively 3 s 12 s and 18 s and that of RHwith circular snorkels was 3 s 18 s and 44 s Compared withRHwith circular snorkels the quantity of the flowingmoltensteel through down-leg increases with the increase of thecross-sectional area and has a better diffusion capacity in theladle while flowing to the bottom of the ladle in RH witharched snorkels -e mixing capacity of RH with archedsnorkels was stronger than that of RH with circular snorkels

312 Saturated Gas Flow Rate In water model experimentthe circulation flow rate increases with the gas flow rateAfter reaching a certain value the circulation flow rate tendsto be saturated-e circulation flow rate at this time is calledsaturated circulation flow rateGmmax and the minimum gasflow rate corresponding to the Gmmax is called saturated gasflow rate Qmmax [14 36]

-e horizontal section and horizontal trajectory of thebubbles in gas-liquid plume observed schematically at the


Main parameters Vacuum degree (Pa) Gas flow rate (Nm3middothminus1) Insertion depth of snorkel (mm)Prototype 67 35 69 104 138 173 193 382 545 710 818Model 97709 05 1 15 2 25 28 70 100 130 150

Air compressor

Gas flowmeter

Gas distributor

Vacuum pump

U-type manometer

Electricalconductivity meter

Computer

Flowmeter

Tracer

Figure 2 Schematic of water modeling


outlet of the up-leg are shown schematically in Figure 5 Forthe two RH models the bubbles in the gas-liquid plumeformed at the exit of each nozzle are individually close to thewall of up-leg at small gas flow rate With the increase of thegas flow rate the diameter and horizontal penetrating depthof bubbles in gas-liquid plume increase When the gas flowrate tends to be Qmmax the bubbles in gas-liquid plume will

collide with each other for RH with circular snorkels asshown in Figure 5(a) and bubbles from nozzle 2 and 3 willcollide the opposite wall lastly for RH with arched snorkelsas shown in Figure 5(b) If the gas flow rate continues toincrease and the bubbles are in the state of ejection the gasdriving power will be greatly reduced and the circulationflow rate will tend to be saturated -erefore it can be

3s 18s 44s

(a)

3s 12s 18s

(b)

Figure 4 Flow field of (a) RH with circular snorkels and (a) RH with arched snorkels in one circulation

Nozzle

Bubble formationsite

Nozzle

Snorkel wall

Bubble path

Figure 3 Schematic of the formation and path of bubbles in up-leg


considered that the gas flow rate corresponding to thecontact of bubbles from different nozzles with each other orthe contact of bubbles and opposite wall is Qmmax -ebubble is simulated by a complete sphere and the geometricconditions of this contact state of RH with circular snorkelsand RH with arched snorkels are expressed by equations (5)and (6) [10] Equations (7)ndash(9) [37] show the calculationformulas of diameter and horizontal penetrating depth ofbubble by combining equations (5) and (6) the Qmmax ofthe two RH water models can be calculated

dB dp

2 minus LB

+dB

21113888 1113889lowast 2 sin

θN

21113888 1113889

(5)

dp2 minus Hs

cos θN2( 1113857+ LB

dp

2 (6)

where dB is the bubble diameterm dp is the diameter of up-legm LB is the horizontal penetrating depth of bubble m Hs isinternal arc height and θN is the angle between adjacent nozzlesfor circular snorkelθN 2πnc (nc is the nozzle number) forarched snorkel θN arccos[(05dp minus Hs)05dp]25

dB 6σd0

ρ1g1113888 1113889

2

+ 054Qg

4nd0501113890 1113891

0289⎧⎨

⎩

⎫⎬

⎭

6⎡⎢⎢⎣ ⎤⎥⎥⎦

16

(7)

LB

d0 37

ρg

ρ1 minus ρg

V2g

gd01113890 1113891

13

(8)

Vg Qgn

πd204

(9)

where d0 is the nozzle diameterm σ is the surface tension inthe liquid phase Nmiddotmminus1 ρ1 and ρgare the density of liquidand phase kgmiddotmminus3 n is the nozzle number Vg is the orificegas velocity mmiddotsminus1 gis the acceleration of gravity mmiddotsminus2 andQg is the gas flow rate Nm3middotsminus1

-e Qmmax of RH with circular snorkels calculated fromabove is 252 Nm3middothminus1 And this is 503 Nm3middothminus1 to RH witharched snorkels -e Qmmax of RH with arched snorkels isapproximately 996 higher than that of the RH with cir-cular snorkels from theoretical calculations

Figure 6(a) shows the variation of circulation flow rate Gmand gas flow rateQm under the conditions that insertion depthof snorkel Himm is 70 100 130 and 150mm respectively -eGm increased with the increase ofHimm and theGm of RHwithcircular snorkels showed saturation tendency at about 250Nm3middothminus1 of Qm even at different Himm which was very con-sistent with the calculated value (252 Nm3middothminus1) -e Qmmax isthe result of the horizontal movement of the bubbles and isindependent of the insertion depth of snorkel -ereforeFigure 6(b) only shows the variation of the Gm and Qm underthe condition ofHimm 70mm the Gm kept increasing with theincrease ofQm because theQmmax of RH with arched snorkelswas 503 Nm3middothminus1

According to equation (1) the Qpmax of RH with archedsnorkels is 347 Nm3middothminus1 on-site which is far beyond the gasflow rate (60sim130 Nm3middothminus1) in the production site Ex-cessive gas flow rate will result in mismatching of vacuumpump and other equipment -erefore it is not necessary toextend the gas flow rate to its Qmmax of RH with archedsnorkels in this physical simulation

313 Circulation Flow Rate and Mixing Time Under thecondition of vacuum chamber pressure (P 97709 Pa) andinsertion depth of snorkel (Himm 100mm) the relation-ship between the circulation flow rate Gm and gas flow rateQm in RH with arched snorkels and RH with circularsnorkels is compared in Figure 7 It can be seen that the Gmof RH with arched snorkels was much larger than that of RHwith circular snorkels in the whole Qm Under the sameexperimental conditions the Gm of RH with arched snorkelswas 20sim 28 times that of RH with circular snorkels -isresult indicated that the Gm increases with the cross-sec-tional area increase of the arched snorkel such result verifiedthe previous studies that the circulation flow rate increaseswith the increase of cross-sectional area of the snorkel[3 24 38]

Under the condition of P 97709Pa and Himm 100mmthe relationship between mixing time Tmix and Qm in RH witharched snorkels and RH with circular snorkels is compared inFigure 8 It can be seen that the Tmix decreased with the increasein Qm When the Qm was 20 Nm3middothminus1 the Tmix of RH witharched snorkels was 74 s whereas that of RH with circularsnorkels was 118 s Under the experimental condition the Tmixof RH with arched snorkels was 63sim 70 that of RH withcircular snorkels

32 Effect of Gas Flow Rate and Insertion Depth of Snorkel onRHwithArchedSnorkels -eGm increases with the increaseof Qm and Himm Equations (7)ndash(9) demonstrate that thebubble number diameter and horizontal penetrating depthincrease with the increase in Qm the work conducted bybubble floatage increase Accordingly the ldquodrove efficiencyrdquoto molten steel of the lifting gas and the Gm increase Whenother parameters are fixed the liquid level in vacuumchamber increases with the Himm -e rising distance of thebubble increases and the contact time with themolten steel islonger and the ldquodrove efficiencyrdquo to molten steel of liftinggas increases so the Gm increases

However Himm should be controlled otherwise the gaslifting efficiency will be inefficient -e experimental resultsshowed that the Gm rapidly increases with the Himm increasewhen theQmwas small-eHimm influence on theGm graduallydecreased with the Qm increase Figure 9(a) shows when theHimm exceeded 100mm especially when the Qm was greaterthan 23 Nm3middothminus1 the Himm increasing had little significance toGm With Himm increase the travel of bubbles increases Alossincreases when theQm is fixed andAsteel will decrease accordingto equation (2) -e Himm should be le100mm and le550mmon-site whichwill improve the production efficiency of RHwitharched snorkels


-e Tmix decreased with the increase of theQm andHimmas shown in Figure 9(b) -e mixing time was obviouslyshortened with the increase ofQm -eGm increases with theincrease of theQm and the downflow of molten steel into theladle from the vacuum chamber increases which increasesthe stirring of molten steel and reduces the Tmix -e Tmixdecreased with theHimm increase at a certain vacuum degreeas shown in Figure 9(b) When the Himm was greater than100mm the trend of Tmix decreasing was weakened -isfinding indicates that theHimm of the arched snorkels shouldbele 550mm on-site -e result of immersion depth control

in the mixing time experiment is consistent with that in thecirculation flow rate experiment

Compared with then RH with circular snorkels the RHwith arched snorkels greatly improves the circulation flowrate reduces the mixing time and improves the mixingcapacity However the refractory building is highlydemanded -e RH with arched snorkels is seldom appliedon-site because the complex structure of arched snorkels-e ability of the refractory building to resist molten steelerosion of RH with arched snorkels needs be studied in thefuture

60

80

100

120

140

160

P = 97709Pa

05 10 15 20 25 30Qm(Nm3middothndash1)

Gm

(Lmiddot

min

ndash1)

Himm (mm)

70100

130150

(a)

50

100

150

200

250

300

350

400

450

P = 97709Pa

Himm = 70mm


Gm

(Lmiddot

min

ndash1)

(b)

Figure 6 Variation of circulation flow rate Gm as a function of gas flow rateQm (a) RH with circular snorkels (b) RH with arched snorkels

Horizontal bubbletrajectory

Bubble

Snorkel wall

Qm ltlt Qmmax Qm asymp Qmmax

(a)

1

2 3

4

56

(b)

Figure 5 Illustration of bubble dispersion behavior in up-leg observed from the bath bottom RH with (a) circular snorkels and (b) archedsnorkels


Gm

(Lmiddot

min

ndash1)

100

150

200

250

300

350

400

450

Himm (mm)

P = 97709Pa

05 10 15 20 25 30Qm(m3middothndash1)

70100

130150

(a)

T mix

(s)

Himm (mm)


70100

130150

60

70

80

90

100

110

120

P = 97709Pa

(b)

Figure 9 Effect of Qm and Himm on the Gm and Tmix of RH with arched snorkels

50

100

150

200

250

300

350

400

450

P = 97709PaHimm = 100mm

Gm

(Lmiddot

min

ndash1)


RH with circular snorkelsRH with arched snorkels

Figure 7 Relationship between Gm and Qm in RH with arched snorkels and RH with circular snorkels

60

80

100

120

140

160

180

T mix

(s) P = 97709Pa

Himm = 100mm



Figure 8 Relationship between Qm and Tmix in RH with arched snorkels and RH with circular snorkel


4 Conclusions

(1) -e circulation flow rate increases 100sim 180 andthe mixing time decreases by approximately 35compared with RH with circular snorkels in thewhole range of the gas flow rate

(2) -e saturated gas flow rate of RH with archedsnorkels is 996 more than that of RH with circularsnorkels which can greatly increase the gas flow raterange on-site

(3) Compared with the RH with circular snorkels thequantity of the flowing molten steel through down-leg increases with the increase of the cross-sectionalarea and has better diffusion in the ladle whileflowing to the bottom of the ladle -e RH witharched snorkels has stronger mixing capacity

(4) -e circulation flow rate increases and the mixingtime decreases with the increase of the gas flow rateand insertion depth -e insertion depth of thearched snorkel should bele 550mm on-site to im-prove the production efficiency

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

-e authors declare no conflicts of interest

Acknowledgments

-e authors are grateful for support from the NationalNatural Science Foundation of China (Nos U50704012U1710257 and 51704203) Excellent Talents Science andTechnology Innovation Project of Shanxi Province (No201605D211018) Scientific and Technological InnovationPrograms of Higher Education Institutions in Shanxi (No2019L0656) Key Research and Development Project ofShanxi Province (No 201903D121093) Science and Tech-nology Innovation Project of Educational Commission ofShanxi Province (No 2019L0616) and Doctoral ResearchFoundation of Taiyuan University of Science and Tech-nology China (No 20142001)

References

[1] J Pieprzyca T Merder M Saternus et al ldquoPhysical Mod-elling Of -e Steel Flow In RH Apparatusrdquo Archives ofMetallurgy and Materials vol 60 no 3 pp 1859ndash1863 2015

[2] M Takahashi H Matsumoto and T Saito ldquoMechanism ofdecarburization in RH degasserrdquo ISIJ International vol 35no 12 pp 1452ndash1458 2007

[3] Y G Park K W Yi and S B Ahn ldquo-e effect of operatingparameters and dimensions of the RH system on melt cir-culation using numerical calculationsrdquo ISIJ Internationalvol 41 no 5 pp 403ndash409 2001

[4] Y Luo C Liu Y Ren and L Zhang ldquoModeling on the fluidflow and mixing phenomena in a RH steel degasser with oval

down-leg snorkelrdquo Steel Research International vol 89no 12 Article ID 1800048 2018

[5] D Q Geng H Lei and J C He ldquoNumerical simulation of themultiphase flow in the rheinsahl-heraeus (RH) systemrdquoMetallurgical and Materials Transactions B vol 41 no 1pp 234ndash247 2010

[6] L C Trindade J J M Peixoto C A da Silva et al ldquoInfluenceof obstruction at gas-injection nozzles (number and position)in RH degasser processrdquo Metallurgical and MaterialsTransactions B vol 50 no 1 pp 578ndash584 2019

[7] X G Ai Y P Bao W Jiang J H Liu P H Li and T Q LildquoPeriodic flow characteristics during RH vacuum circulationrefiningrdquo International Journal of Minerals Metallurgy andMaterials vol 17 no 1 pp 17ndash21 2010

[8] S K Ajmani S K Dash S Chandra et al ldquoMixing evaluationin the RH process using mathematical modellingrdquo Transac-tions of the Iron amp Steel Institute of Japan vol 44 no 1pp 82ndash89 2007

[9] Y Kato H Nakato T Fujii S Ohmiya and S Takatori ldquoFluidflow in ladle and its effect on decarburization rate in RHdegasserrdquo ISIJ International vol 33 no 10 pp 1088ndash10941993

[10] W Zheng Z P He G Q Li et al ldquoPhysical simulation ofeffect of injection parameters on circulation flow rate andmixing time in RH vacuum refining processrdquo Journal of Ironamp Steel Research vol 29 no 5 pp 373ndash381 2017

[11] G Tokio H Katoh M Tetsuo et al ldquoMixing of molten steel ina ladle with RH reactor by the water model experimentrdquoDenki Seiko vol 50 no 2 pp 128ndash137 1979

[12] H Ono-Nakazato H Tajiri T Usui et al ldquoRate enhancementof the degassing reaction by the enlargement of RH and DHreactorsrdquo Tetsu-to-Hagane vol 89 no 11 pp 1113ndash11192009

[13] R Tsujino M J Nakashima and I Sawada ldquoNumericalanalysis of molten steel flow in ladle of RH processrdquo ISIJInternational vol 29 no 7 pp 589ndash595 1989

[14] J HWei N W Yu and Y Y Fan ldquoStudy on flow and mixingcharacteristics of molten steel in RH and RH-KTB refiningprocessesrdquo Journal of Shanghai University (English Edition)vol 6 no 2 pp 167ndash175 2002

[15] T Kuwabara K Umezawa K Mori and H WatanabeldquoInvestigation of decarburization behavior in RH-reactor andits operation improvementrdquo Transactions of the Iron and SteelInstitute of Japan vol 28 no 4 pp 305ndash314 1988

[16] B Li and F Tsukihashi ldquoModeling of circulating flow in RHdegassing vessel water model designed for two- and multi-legsoperationsrdquo ISIJ International vol 40 no 12 pp 1203ndash12092000

[17] V Seshadri C A Silva and I A Da Silva ldquoPhysical modelingsimulations of refining processes in Brazilian Steel IndustryrdquoScandinavian Journal of Metallurgy vol 34 no 6 pp 340ndash352 2005

[18] L Lin F Bao L Q Zhang and H L Ou ldquoPhysical model offluid flow characteristics in RH-TOP vacuum refining pro-cessrdquo International Journal of Minerals Metallurgy andMaterials vol 19 no 6 pp 483ndash489 2012

[19] H Ling C Guo A N Conejo et al ldquoEffect of snorkel shapeand number of nozzles on mixing phenomena in the RHprocess by physical modelingrdquo Metallurgical Research ampTechnology vol 114 no 111 pp 1ndash13 2017

[20] V Seshadri C A da Silva I A da Silva G A Vargas andP S B Lascosqui ldquoDecarburisation rates in RH-KTB degasserof CST steel plant through physical modelling studyrdquo Iron-making amp Steelmaking vol 33 no 1 pp 34ndash38 2013


[21] B Zhu D Q Liu M S XuRen and B Hu ldquoEffect of nozzleblockage on circulation flow rate in up-snorkel during the RHdegasser processrdquo Steel Research International vol 87 no 2pp 136ndash145 2015

[22] K Yang and J Szekely ldquoA mathematical model of fluid flowand inclusion coalescence in the RH vacuum degassing sys-temrdquo Transactions of the Iron amp Steel Institute of Japanvol 23 no 6 pp 465ndash474 2006

[23] H Ling L Zhang and C Liu ldquoMathematical modeling on thefluid flow during RH degassing processrdquo Metallurgical Re-search amp Technology vol 114 no 4 pp 510ndash519 2017

[24] J H Wei and H T Hu ldquoMathematical modelling of moltensteel flow in a whole degasser during RH refining processrdquoIronmaking amp Steelmaking vol 32 no 5 pp 427ndash434 2005

[25] B Li and H Huo ldquoHomogenous flow model for gas drivencirculating flow in RH refining systemrdquo Acta MetallurgicaSinica vol 41 no 1 pp 60ndash66 2005

[26] H Ling L Zhang and C Liu ldquoEffect of snorkel shape on thefluid flow during RH degassing process mathematicalmodellingrdquo Ironmaking amp Steelmaking vol 45 no 4pp 1ndash12 2016

[27] H Ling F Li L Zhang and A N Conejo ldquoInvestigation onthe effect of nozzle number on the recirculation rate andmixing time in the RH process using VOF+DPM modelrdquoMetallurgical and Materials Transactions B vol 47 no 3pp 1950ndash1961 2016

[28] M K Mondal N Maruoka S Kitamura G S GuptaH Nogami and H Shibata ldquoStudy of fluid flow and mixingbehaviour of a vacuum degasserrdquo Transactions of the IndianInstitute of Metals vol 65 no 3 pp 321ndash331 2012

[29] L Zhang and F Li ldquoInvestigation on the fluid flow andmixingphenomena in a ruhrstahl-heraeus (RH) steel degasser usingphysical modelingrdquo JOM vol 66 no 7 pp 1227ndash1240 2014

[30] X G Ai S L Li N Wang and N Lv ldquoSimulation of in-clusions removal influenced by snorkel and blowing pa-rameters in RH refiningrdquo Advanced Materials Researchvol 291 no 294 pp 155ndash158 2011

[31] Z You G Cheng X Wang Z Qin J Tian and J ZhangldquoMathematical model for decarburization of ultra-low carbonsteel in single snorkel refining furnacerdquo Metallurgical andMaterials Transactions B vol 46 no 1 pp 459ndash472 2015

[32] G Chen S He Y Li and Q Wang ldquoModeling dynamics ofagglomeration transport and removal of Al2O3 clusters in therheinsahl-heraeus reactor based on the coupled computa-tional fluid dynamics-population balance method modelrdquoIndustrial amp Engineering Chemistry Research vol 55 no 25pp 7030ndash7042 2016

[33] J H Wei and N W Yu ldquoMathematical modelling ofdecarburisation and degassing during vacuum circulationrefining process of molten steel application of the model andresultsrdquo Steel Research vol 73 no 4 pp 143ndash148 2002

[34] P H Li Q J Wu W H Hu et al ldquoMathematical simulationof behavior of carbon and oxygen in RH decarburizationrdquoJournal of Iron and Steel Research International vol 22no S1 pp 63ndash67 2015

[35] H Watanabe K Asano and T Saeki ldquoSome chemical en-gineering aspects of R-H degassing processrdquo Tetsu-to-Haganevol 54 no 13 pp 1327ndash1342 1968

[36] V Seshadri and S L Costa ldquoCold model studies of RHdegassing processrdquo Transactions of the Iron and Steel Instituteof Japan vol 26 no 2 pp 133ndash138 1986

[37] C Kamata S Hayashi and K Ito ldquoEstimation of circulationflow rate in RH reactor using water modelrdquo Tetsu-to-Haganevol 84 no 7 pp 484ndash489 1998

[38] S Fan and B Li ldquoModeling of circulating flow in RHdegassing vessel water model designed for two-and multi-legoperationsrdquo Acta Metallrugica Sinica vol 37 no 10pp 1100ndash1106 2001

[39] D Q Geng J X Zheng K Wang et al ldquoSimulation ondecarburization and inclusion removal process in the ruhr-stahl-heraeus (RH) process with ladle bottom blowingrdquoMetallurgical and Materials Transactions B vol 46 no 3pp 1484ndash1493 2015

[40] D Q Geng X Zhang X A Liu et al ldquoSimulation on flowfield and mixing phenomenon in single snorkel vacuumdegasserrdquo Steel Research International vol 86 no 7pp 724ndash731 2015

[41] P A Kishan and S K Dash ldquoPrediction of circulation flowrate in the RH degasser using discrete phase particle mod-elingrdquo ISIJ International vol 49 no 4 pp 495ndash504 2009

[42] G Dian-Qiao L Hong and H Ji-Cheng ldquoApplication ofMHD phenomenon on secondary refining and continuouscasting processrdquo Journal of Iron and Steel Research(Interna-tional) vol 49 no S2 pp 941ndash944 2012


phenomena [10ndash16 28ndash31] behavior of bubble and inclu-sion removal [22 30 32] and decarburization process[1 2 8 20 23 25 33 34] during the RH treatment Based onthe physical simulation experiment work of predecessors oncirculation flow rate of RH some empirical formulas arelisted in Table 1 which includes the formulas put forward atthe first time and excludes similar equations reported later Itis generally accepted that the circulation flow rate of RH isrelated to the injected gas flow rate and the section size ofsnorkel From process parameter improvement view manyresearches have proved that a higher gas flow rate[5 7 29 30 34] a lower vacuum pressure [18 19 28] adeeper insertion depth of snorkel [3 14] would favor tooptimize the fluid flow of RH However the circulation ratewill reach a saturated value with the gas flow rate increasing[14 36] From equipment improvement view many in-vestigations have proved that a larger snorkel sectional area[24 26 29 38]blowing from the bottom of the vacuumchamber [15] or ladle [39] would favor to optimize the fluidflow of RH Recently many researchers have tried to in-crease the refining efficiency by using single-leg[12 28 31 40] multilegs [38 41] and magnetic field [42]imposed around the up-leg However the single-leg washardly used in the actual industrial manufacture consideringtechnical immaturity meanwhile multilegs and imposingmagnetic field around snorkel were also hardly used in theactual industrial manufacture considering the cost issue Allof the equations in Table 1 imply that the arched snorkelswith greater sectional area would bring a larger circulationflow rate Additionally the stimulus-response was thegeneral method used to measure the mixing time [7 10]another important parameter for the RH treatment In thephysical simulation experiments of this paper this methodwill continue to observe the mixing of molten steel

However little results [38 42] were reported to study theshape of RH snorkels which has always been circular until theoval snorkel was proposed by Kuwabara [15] -e oval snorkelswere favored to enhance fluid flow of RH but we want therefining efficiency to keep getting bigger including a greatincrease in circulation flow rate and saturated value of gas flowrate In the current study a new vacuumdegasser equippedwithtwo snorkels of larger sectional area was designed -e twotraditional circular snorkels were replaced with two archedsnorkels which was not reported in previous investigations Forthe arched snorkel the internal arc height is equal to the radiusof traditional circular snorkel and the internal diameter is 3 to 4times of the circular snorkel Hence the sectional area of archedsnorkel is much larger than that of circular snorkel Watermodeling was performed according to similarity criterion -eflow velocity of the RH water model down-on leg-outlet planewas captured by electronic tachometer and the stimulus-re-sponse method was used to measure the mixing time -eresults provided the experimental basis for promoting andimproving this new RH vacuum refining equipment

2 Experiment

21 Model Design -e prototype is one RH vacuumchamber with two circular snorkels from a steel plant in

China According to the empirical formulas listed in Table 1we have determined the kernel idea of this design is toincrease the cross-sectional area of snorkel as much aspossible -e scale of water model and prototype is 1 55Figure 1(a) shows the model size of circular snorkel -ecircular snorkel diameter is very difficult to be increasedowing to the metallurgical refractory thickness around thesnorkels and the limitation of the area under the vacuumchamber In order to increase the cross-sectional area of thesnorkel as much as possible two snorkels are changed toarched structures in this research So as to make full use ofthe space under the vacuum chamber the inner diameter ofthe vacuum chamber is determined as the diameter of archedsnorkel and the arc height is same as the inner diameter ofcircular snorkel utilizing the bottom space of the vacuumchamber optimized Figure 1(b) exhibits the top view of thearched snorkel water model Compared with circularsnorkel this arched structure increases the equivalent innerdiameter by approximately 70 and the cross-sectional areaby 193 in this design

22 Similarityeory A 1 55 scale water model of 170 t RHwas built according to the similarity principle Table 2 showsthe main parameters of the prototype and physical model-e lifting gas flow rate of model Qm is calculated from theactual gas flow rate on-site Qp with the modified Froudecriterion according to the following equation

Qm 001448Qp (1)

23 Experimental Device and Parameters -e water modelexperimental devices consist of vacuum chamber and ladlemade of plexiglass Two snorkels are equipped at the bottomof the vacuum chamber To the RH with two circularsnorkels compressed air is used as the lifting gas through sixevenly distributed gas injection nozzles in one horizontalplane of circular up-leg To the RHwith two arched snorkelsfour nozzles are distributed evenly in the arc of the archedup-leg two others are distributed evenly in the chord andthese six nozzles are in one horizontal plane of arched up-leg -is model also includes the gas source system gasdistributor and transmission pipeline vacuuming systemmetering system and detection system Figure 2 shows theschematic of the main apparatus of the water model

-e gas flow rate is 60sim130 Nm3middothminus1 the pressure in thevacuum chamber is 67 Pa and insertion depth of snorkel is627mm in the production site Table 3 shows the corre-sponding parameters of the prototype and water model

24 Experimental Index

241 Circulation Flow Rate -e circulation flow rate Gmwas obtained by measuring the fluid velocity which was20mm above the outlet of the down-leg Five measuringpoints were horizontally and longitudinally set at the cross-sectional center of down-leg -e fluid velocity at themeasuring point was obtained with an electronic tachometer

















Φ92mm

Circular snorkels


Φ330mm

Φ92mm

(a)


Φ330mm

Arched snorkels

92mm 92mm

(b)



Item Prototype(mm)










ρgminus1

P0 minus P

ρ11113888 1113889 (3)











Air compressor

Gas flowmeter

Gas distributor

Vacuum pump

U-type manometer


Computer

Flowmeter

Tracer





3s 18s 44s

(a)

3s 12s 18s

(b)


Nozzle


Nozzle

Snorkel wall

Bubble path




dB dp

2 minus LB

+dB

21113888 1113889lowast 2 sin

θN

21113888 1113889

(5)

dp2 minus Hs

cos θN2( 1113857+ LB

dp

2 (6)


dB 6σd0

ρ1g1113888 1113889

2

+ 054Qg

4nd0501113890 1113891

0289⎧⎨

⎩

⎫⎬

⎭

6⎡⎢⎢⎣ ⎤⎥⎥⎦

16

(7)

LB

d0 37

ρg

ρ1 minus ρg

V2g

gd01113890 1113891

13

(8)

Vg Qgn

πd204

(9)













60

80

100

120

140

160

P = 97709Pa


Gm

(Lmiddot

min

ndash1)

Himm (mm)

70100

130150

(a)

50

100

150

200

250

300

350

400

450

P = 97709Pa

Himm = 70mm


Gm

(Lmiddot

min

ndash1)

(b)



Bubble

Snorkel wall


(a)

1

2 3

4

56

(b)



Gm

(Lmiddot

min

ndash1)

100

150

200

250

300

350

400

450

Himm (mm)

P = 97709Pa


70100

130150

(a)

T mix

(s)

Himm (mm)


70100

130150

60

70

80

90

100

110

120

P = 97709Pa

(b)


50

100

150

200

250

300

350

400

450

P = 97709PaHimm = 100mm

Gm

(Lmiddot

min

ndash1)




60

80

100

120

140

160

180

T mix

(s) P = 97709Pa

Himm = 100mm





4 Conclusions





Data Availability




Acknowledgments


References





























































Φ92mm

Circular snorkels


Φ330mm

Φ92mm

(a)


Φ330mm

Arched snorkels

92mm 92mm

(b)



Item Prototype(mm)










ρgminus1

P0 minus P

ρ11113888 1113889 (3)











Air compressor

Gas flowmeter

Gas distributor

Vacuum pump

U-type manometer


Computer

Flowmeter

Tracer





3s 18s 44s

(a)

3s 12s 18s

(b)


Nozzle


Nozzle

Snorkel wall

Bubble path




dB dp

2 minus LB

+dB

21113888 1113889lowast 2 sin

θN

21113888 1113889

(5)

dp2 minus Hs

cos θN2( 1113857+ LB

dp

2 (6)


dB 6σd0

ρ1g1113888 1113889

2

+ 054Qg

4nd0501113890 1113891

0289⎧⎨

⎩

⎫⎬

⎭

6⎡⎢⎢⎣ ⎤⎥⎥⎦

16

(7)

LB

d0 37

ρg

ρ1 minus ρg

V2g

gd01113890 1113891

13

(8)

Vg Qgn

πd204

(9)













60

80

100

120

140

160

P = 97709Pa


Gm

(Lmiddot

min

ndash1)

Himm (mm)

70100

130150

(a)

50

100

150

200

250

300

350

400

450

P = 97709Pa

Himm = 70mm


Gm

(Lmiddot

min

ndash1)

(b)



Bubble

Snorkel wall


(a)

1

2 3

4

56

(b)



Gm

(Lmiddot

min

ndash1)

100

150

200

250

300

350

400

450

Himm (mm)

P = 97709Pa


70100

130150

(a)

T mix

(s)

Himm (mm)


70100

130150

60

70

80

90

100

110

120

P = 97709Pa

(b)


50

100

150

200

250

300

350

400

450

P = 97709PaHimm = 100mm

Gm

(Lmiddot

min

ndash1)




60

80

100

120

140

160

180

T mix

(s) P = 97709Pa

Himm = 100mm





4 Conclusions





Data Availability




Acknowledgments


References



















































ρgminus1

P0 minus P

ρ11113888 1113889 (3)











Air compressor

Gas flowmeter

Gas distributor

Vacuum pump

U-type manometer


Computer

Flowmeter

Tracer





3s 18s 44s

(a)

3s 12s 18s

(b)


Nozzle


Nozzle

Snorkel wall

Bubble path




dB dp

2 minus LB

+dB

21113888 1113889lowast 2 sin

θN

21113888 1113889

(5)

dp2 minus Hs

cos θN2( 1113857+ LB

dp

2 (6)


dB 6σd0

ρ1g1113888 1113889

2

+ 054Qg

4nd0501113890 1113891

0289⎧⎨

⎩

⎫⎬

⎭

6⎡⎢⎢⎣ ⎤⎥⎥⎦

16

(7)

LB

d0 37

ρg

ρ1 minus ρg

V2g

gd01113890 1113891

13

(8)

Vg Qgn

πd204

(9)













60

80

100

120

140

160

P = 97709Pa


Gm

(Lmiddot

min

ndash1)

Himm (mm)

70100

130150

(a)

50

100

150

200

250

300

350

400

450

P = 97709Pa

Himm = 70mm


Gm

(Lmiddot

min

ndash1)

(b)



Bubble

Snorkel wall


(a)

1

2 3

4

56

(b)



Gm

(Lmiddot

min

ndash1)

100

150

200

250

300

350

400

450

Himm (mm)

P = 97709Pa


70100

130150

(a)

T mix

(s)

Himm (mm)


70100

130150

60

70

80

90

100

110

120

P = 97709Pa

(b)


50

100

150

200

250

300

350

400

450

P = 97709PaHimm = 100mm

Gm

(Lmiddot

min

ndash1)




60

80

100

120

140

160

180

T mix

(s) P = 97709Pa

Himm = 100mm





4 Conclusions





Data Availability




Acknowledgments


References
















































3s 18s 44s

(a)

3s 12s 18s

(b)


Nozzle


Nozzle

Snorkel wall

Bubble path




dB dp

2 minus LB

+dB

21113888 1113889lowast 2 sin

θN

21113888 1113889

(5)

dp2 minus Hs

cos θN2( 1113857+ LB

dp

2 (6)


dB 6σd0

ρ1g1113888 1113889

2

+ 054Qg

4nd0501113890 1113891

0289⎧⎨

⎩

⎫⎬

⎭

6⎡⎢⎢⎣ ⎤⎥⎥⎦

16

(7)

LB

d0 37

ρg

ρ1 minus ρg

V2g

gd01113890 1113891

13

(8)

Vg Qgn

πd204

(9)













60

80

100

120

140

160

P = 97709Pa


Gm

(Lmiddot

min

ndash1)

Himm (mm)

70100

130150

(a)

50

100

150

200

250

300

350

400

450

P = 97709Pa

Himm = 70mm


Gm

(Lmiddot

min

ndash1)

(b)



Bubble

Snorkel wall


(a)

1

2 3

4

56

(b)



Gm

(Lmiddot

min

ndash1)

100

150

200

250

300

350

400

450

Himm (mm)

P = 97709Pa


70100

130150

(a)

T mix

(s)

Himm (mm)


70100

130150

60

70

80

90

100

110

120

P = 97709Pa

(b)


50

100

150

200

250

300

350

400

450

P = 97709PaHimm = 100mm

Gm

(Lmiddot

min

ndash1)




60

80

100

120

140

160

180

T mix

(s) P = 97709Pa

Himm = 100mm





4 Conclusions





Data Availability




Acknowledgments


References















































dB dp

2 minus LB

+dB

21113888 1113889lowast 2 sin

θN

21113888 1113889

(5)

dp2 minus Hs

cos θN2( 1113857+ LB

dp

2 (6)


dB 6σd0

ρ1g1113888 1113889

2

+ 054Qg

4nd0501113890 1113891

0289⎧⎨

⎩

⎫⎬

⎭

6⎡⎢⎢⎣ ⎤⎥⎥⎦

16

(7)

LB

d0 37

ρg

ρ1 minus ρg

V2g

gd01113890 1113891

13

(8)

Vg Qgn

πd204

(9)













60

80

100

120

140

160

P = 97709Pa


Gm

(Lmiddot

min

ndash1)

Himm (mm)

70100

130150

(a)

50

100

150

200

250

300

350

400

450

P = 97709Pa

Himm = 70mm


Gm

(Lmiddot

min

ndash1)

(b)



Bubble

Snorkel wall


(a)

1

2 3

4

56

(b)



Gm

(Lmiddot

min

ndash1)

100

150

200

250

300

350

400

450

Himm (mm)

P = 97709Pa


70100

130150

(a)

T mix

(s)

Himm (mm)


70100

130150

60

70

80

90

100

110

120

P = 97709Pa

(b)


50

100

150

200

250

300

350

400

450

P = 97709PaHimm = 100mm

Gm

(Lmiddot

min

ndash1)




60

80

100

120

140

160

180

T mix

(s) P = 97709Pa

Himm = 100mm





4 Conclusions





Data Availability




Acknowledgments


References

















































60

80

100

120

140

160

P = 97709Pa


Gm

(Lmiddot

min

ndash1)

Himm (mm)

70100

130150

(a)

50

100

150

200

250

300

350

400

450

P = 97709Pa

Himm = 70mm


Gm

(Lmiddot

min

ndash1)

(b)



Bubble

Snorkel wall


(a)

1

2 3

4

56

(b)



Gm

(Lmiddot

min

ndash1)

100

150

200

250

300

350

400

450

Himm (mm)

P = 97709Pa


70100

130150

(a)

T mix

(s)

Himm (mm)


70100

130150

60

70

80

90

100

110

120

P = 97709Pa

(b)


50

100

150

200

250

300

350

400

450

P = 97709PaHimm = 100mm

Gm

(Lmiddot

min

ndash1)




60

80

100

120

140

160

180

T mix

(s) P = 97709Pa

Himm = 100mm





4 Conclusions





Data Availability




Acknowledgments


References














































Gm

(Lmiddot

min

ndash1)

100

150

200

250

300

350

400

450

Himm (mm)

P = 97709Pa


70100

130150

(a)

T mix

(s)

Himm (mm)


70100

130150

60

70

80

90

100

110

120

P = 97709Pa

(b)


50

100

150

200

250

300

350

400

450

P = 97709PaHimm = 100mm

Gm

(Lmiddot

min

ndash1)




60

80

100

120

140

160

180

T mix

(s) P = 97709Pa

Himm = 100mm





4 Conclusions





Data Availability




Acknowledgments


References














































4 Conclusions





Data Availability




Acknowledgments


References














































physical simulation on molten steel flow characteristics

Documents