ISIJ International, Vol. 55 (2015), No. 4, pp. 791–798
Transport Phenomena in a Beam-Blank Continuous Casting Mold with Two Types of Submerged Entry Nozzle
Mianguang XU and Miaoyong ZHU*
School of Materials and Metallurgy, Northeastern University, No. 3 Wenhua Road, Heping District, Shenyang, 110819 P.R. China.
(Received on September 18, 2014; accepted on December 22, 2014)
A three-dimensional full-coupled mathematical model is established to study the fluid flow, heat transferand solidification in a 450 mm × 350 mm × 90 mm beam-blank mold with two different types of submergedentry nozzle (SEN), namely single-port straight SEN and three-port radial flow SEN. Water modeling exper-iments, industrial trials and public results available in literature are performed to validate the numericalresults. The results show that, with the straight SEN which has been widely applied in beam-blank contin-uous casting, there is a very inactive top free surface in the mold which level fluctuation magnitude is lessthan 1 mm and velocity magnitude is far from a reasonable interval, and the shell thickness distribution atthe mold exit is very uneven, thick at the web but thin at the fillet. Moreover, there exists a “wavy con-tour” at the flange due to the washing effect of the off-center molten steel jet. While with the newdesigned radial flow SEN, a suitable meniscus status and a more uniform shell thickness at the mold exitcan be obtained, which is helpful to avoid the breakouts caused by the rupture of thin fillet and the flangedepression. The “self-braking” effect caused by two radial flow SENs provides good flow stability at theweb center.
Recently, as a near-net-shape continuous casting tech-nique, the need of beam-blank steel has been experiencinga dramatic rapid increase and more than ten beam-blankcontinuous casting machines have been put into productionin China due to its special usage, economic advantages andoutstanding mechanical properties. However, there is a com-mon problem that the producers have to face, that is thequality of continuously cast beam-blank, especially thecrack of the strand. As it is known, most of defects affectingsteel quality in the continuous casting process are associatedwith fluid flow in the mold which is largely determined bythe SEN structure.1) SEN structure can strongly affect thetransport phenomena in mold, including meniscus status,superheat dissipation, solidified shell growth and inclusionremoval. However, the complicated mold geometry shapecreates great difficulties for the design of a suitable SEN.Although the beam-blank caster was installed at MaanshanSteel in China in 1998, the simple straight SEN is still wide-ly used. With this nozzle, molten steel is directly openpoured into two ceramic funnels, which are located in thecentral flange regions, as shown in Fig. 1. Such pouringmethod can give rise to serious problems on the quality offinal products, especially in the production of some newsteel grade, so new types of SEN are necessary to be pro-
posed to meet the demand for higher quality.Mathematical modeling is very convenient for investigating
the suitable structure of SEN and has had a wide applicationas a powerful tool in the analysis of the transport phenomenain the mold. Unfortunately, most of mathematical modelsabout beam-blank continuous casting are based on the moldthermal-mechanical analysis,2–4) mold water channel design5,6)
and secondary cooling strategy,7,8) a few literatures foundare mainly on the straight SEN.4,9) With such SEN, twomajor problems engineers encountering in steelworks arethe inactive meniscus status and the non-uniform shellthickness distribution at the mold exit, which can seriouslyaffect the function of the mold flux and the uniform distri-
Fig. 1. Molten steel open poured into ceramic funnels: (a) indus-trial trial, two nozzles per mold are used for uniform steelfeeding; (b) schematic of upper nozzle and SEN.
bution of the stress and ultimately lead to a bad quality.In the current study, a mathematical model based on the
enthalpy-porosity approach in a single-framework has beendeveloped for the prediction of three-dimensional transportphenomena including fluid flow, heat transfer and solidifi-cation in a beam-blank slab casting process. With the under-standing of shortcomings of the straight SEN and previousstudies, a new designed three-port radial flow SEN geome-try and proper relevant casting parameters are presented forthe purpose of overcoming two major problems, and theeffects of port angle, casting speed and “self-braking”induced by two radial flow SENs are discussed.
2. Mathematical Models
2.1. Mathematical FormulationsThe general assumptions applied in the present solidifica-
tion of beam-blank continuous casting can be foundelsewhere.11) There are seven partial equations in the three-dimensional mathematical model which are solved by thealgorithm of SIMPLE, including one mass equation, threemomentum equations, two standard k-ε turbulenceequations12) and one energy equation.13) When the residualfor energy is smaller than 10–6 and others are smaller than10–4, the converged solution is obtained. The general formof all the partial equations can be written as the form of Eq.(1).
................. (1)
where ρ is the steel density, ui is the speed in i direction, ϕis the variables including velocities at three directions, tem-perature, enthalpy, turbulence energy and its dissipationrate, xi is the direction, Γϕ is the coefficient of diffusion andSϕ is the source term.
To accountant for the macro-solidification process, addi-tional source terms SDarcy
10) are added to momentum equa-tions and turbulence equations, as shown in Eqs. (2) and (3),respectively.
........ (2)
.............. (3)
where A is the mushy zone constant and its value is set tobe 5×10–6, fs is the solid fraction which is assumed to varylinearly between the liquidus temperature and solidus tem-perature, us,i is the moving speed of the solidified shell, andϕtur represents the turbulence quantity.
The top free surface profile in the beam-blank mold isexpressed in Eq. (4) by the liquid displacement estimatedfrom a simple potential energy balance.14)
.......................... (4)
where Δz is the top free surface height, p is the staticpressure of the top free surface, pmean is the area-weightedaverage value of the static pressure over the entire top freesurface, and ρflux is the flux density.
2.2. Geometrical Model, Boundary and Initial Condi-tions
The research object of present work is a five-strandbloom/beam-blank continuous casting machine with thelength about 37 m and the mold is not instrumented withthermo-couples. The single-port straight SEN used in steel-works is shown in Fig. 2(a) and the new designed three-portradial flow SEN is shown in Fig. 2(b).
The aspect ratio of thickness to height for the port of radi-al flow SEN is selected to be 0.83 in order to improve theeffectiveness of the SEN having a better direction of moltensteel flow to ensure its “self-braking” in the mold. Thegeometry for the port of radial flow SEN is shown in Fig.2(b), and the total area of these three ports is 32 pct largerthan that of the original straight SEN to enhance the inclu-sion removal ratio.15) The present simulations are performedfor port angles varying from –15 to +15 degree (downwardand upward port angles are denoted with + and – sign,respectively).
At all the refractory walls of SEN, the zero-slip boundarycondition is applied16) and the thermal insulation is assumed.The inlet velocity is computed by using the mass conserva-tion between the inlet and outlet according to castingspeed.17) The values of turbulent kinetic energy k and itsdissipation rate ε at the inlet of SEN are based on the semi-empirical expressions.18) The meniscus is specified as azero-shear condition.14)
In the mold region, the heat flux from the surface ofstrand to the mold is assumed to be a function of the castingspeed and the distance below the meniscus, as suggested byLee et al.4) and Luo et al.7) With the straight SEN, the mea-
∂∂
( ) = ∂∂
∂∂
⎛⎝⎜
⎞⎠⎟ +x
ux x
Si
ii i
ρ φφ
Γ φ φ
S Af
fu ui iDarcy_mom
s
ss= −
−( ) +−( )
2
31 0 001.
,
S Af
fDarcy_tur
s
stur= −
−( ) +
2
31 0 001.
ϕ
Δ = −−−( )
zp p
gmean
fluxρ ρ
Fig. 2. Schematic drawing of beam-blank mold and SEN verticalsection: (a) beam-blank mold with an original single-portstraight SEN; (b) beam-blank mold with a new design ofradial flow SEN.
surement of the mold water volume and water temperaturedifferences between the inflow and the outflow of coolingwater is employed, and the value of constant b obtained inthe Savage and Prichard’s relation q=a–b⋅t1/2 is 0.336.19)
The typical kinds of computation domains are presentedin Fig. 3, and the hexahedral mesh system is adopted toimprove calculation precision. The full-coupled simulationstarts from a previously converged flow-field solution andthe temperature of the pool region at the initial time is setto be 1 828 K. The geometry, casting conditions, materialproperties and computational conditions are summarized inTable 1, and SEN submergence depth is defined as the dis-
tance of SEN bottom from meniscus. In order to minimizethe end effect of fluid flow at the outlet boundary, thecomputational domain has a distance longer than the effec-tive length of the mold along the casting direction, thecalculation domain is cut off 700 mm below the mold exit,so the secondary cooling zone I (0.66 m, water flow rate 260L/min) is completely included and secondary cooling zoneII (1.6 m, water flow rate 70 L/min) is partly included. Inthe regions of secondary cooling spray, the heat transfer isdefined as the Robin boundary condition as shown in Eq. (5)and the spray cooling heat-transfer coefficient hspray is cal-culated by using Eq. (6).20) By calculating Eq. (6), hspary inEq. (5) is 1 004.5 W/m2/K in the secondary cooling zone Iand 768.2 W/m2/K in the secondary cooling zone II , respec-tively.
........................ (5)
....... (6)
where q is the heat flux, W is the water flow rate, Tslab is thetemperature of the slab surface, Tspray is the temperature ofthe spray cooling water, and α is a machine-dependentcalibration factor.
3. Results and Discussion
3.1. Top Free Surface CharacteristicsA number of studies have shed light on the important
aspects of top free surface characteristics in slab, billet andbloom continuous casting molds,1) but few studies are relat-ed to the beam-blank continuous casting.
Figure 4 shows the predicted level fluctuation, maximumvelocity magnitude and temperature distribution on the topfree surface. Using the straight SEN, the level fluctuation isless than 1 mm and the velocity magnitude is far from a rea-sonable interval. One of the reasons for the weak and calmtop free surface characteristics is that the use of two nozzlesper mold for uniform steel feeding which can reduce theimpact caused by molten steel injection, and meanwhile afew publications9,21) have suggested that the flow near themeniscus is characterized by a low turbulence.
Using the radial flow SEN, the “self-braking” effectcaused by two radial flow SENs provides good flow stabil-ity at the web region, as shown in Fig. 4(a). When the radialflow SEN is adopted, the level fluctuation, velocities andtemperature at the top free surface of the mold increaseeffectively when the SEN port angle changes upward. Withthe radial flow SEN, the maximum velocity and temperaturedistribution at the top free surface is obviously larger thanthat of using the straight SEN. Considering that low temper-ature and inactive meniscus status induced by the straightSEN are bad for the function of mold flux, which could giverise to bad strand quality and it implies the radial flow SENhas a better performance than that of using the straight SEN.Also, due to that the flow structures inside the mold have asignificant influence on the meniscus,22) though there is ahigh horizontal velocity magnitude near the fillet using theradial flow SEN as Fig. 4(b) shows, the fluctuation is notobvious.
However, the wave crest near the flange tip as shown in
Fig. 3. Geometrical model and mesh systems: (a) mold with thesingle-port straight SEN; (b) mold with the new designedthree-port radial flow SEN.
Table 1. Properties and conditions of the simulations.
Items Values
Geometry
Mold Length, m 0.8
Effective mold length, m 0.7
Casting parameter
Casting speed, m/min 0.6, 1.0
Superheat, K 20
Straight SEN submergence depth, mm 60–100
Radial flow SEN submergence depth, mm 115
Thermo-physical properties of steel
Liquids temperature, K 1 791
Solidus temperature, K 1 753
Specific heat of steel, J/kg/K 700
Latent heat of solidification of steel, J/kg 272 000
Thermal conductivity of steel, W/m/K 32
Density of steel, kg/m3 7 020
Density of flux, kg/m3 3 000
Viscosity of steel, kg/m/s 0.0062
Steel composition (Provided by some plant for specific conditions)
Steel chemistry in mass %: C=0.17, Si=0.19, Mn=0.51, P=0.017, S=0.016.
Fig. 4(a) which generates the thinnest liquid flux layer mayprevent the mold powder from penetrating into the gapbetween the mold and the solidifying shell, which is notfavorable for the mold lubrication, and the maximum tem-perature of the top free surface appears at the web center asshown in Fig. 4(c), and the mold flux at high temperaturelocations may be burned, thus, more reoxidation will occurdue to the reaction with air, and therefore reduce the steelcleanliness. For a suitable meniscus status, the radial flowSEN with a positive angle should use a submergence depthdeeper than 115 mm and the radial flow SEN with a nega-tive angle could be used at a faster casting speed.
3.2. Fluid Flow in the MoldTo verify acceptable accuracy of the present mathematical
model, the predictions are compared with experiments con-ducted using a transparent plastic water model of the sys-tem, as shown in Fig. 5. In order to observe the flow patternin the mold, a small quantity of visible tracer ink is injectedinto the water after steady-state conditions are achieved. Thecomputed results for the velocity fields are found to be in a
reasonably good agreement with the results of water modelboth for the single-port straight SEN and the radial flowSEN.
Figure 6 shows the flow patterns in a water model of thebeam-blank continuous casting mold with different SENs atthe same casting speed 1.0 m/min. It can be seen that usingthe radial flow SEN, with the port angles varying from –15
Fig. 4. Top free surface characteristics: (a) level fluctuation, calculate by using Eq. (4); (b) velocity magnitude, which isdefined as , where ux and uy are the velocities in x direction and in y direction, respectively; (c) tempera-ture distribution.
u ux y2 2+
Fig. 5. Schematic depiction of the full-scale geometry water modelexperiment.
to +15 degree, the active region obviously moves upward tothe meniscus. Zhang and his coworkers first proposed the“self-braking” for a single SEN with four ports,23) and in thepresent study, a clear “self-braking” effect as Fig. 6 shows hasbeen achieved in the web region by two radial flow SENs.
In the beam-blank mold, the SEN is closer to the flangeas Fig. 7(a) indicates, so the “reverse flow” will not appearnear the flange and there is a “washing zone”. In Fig. 7(b),on the wide face center-plane of the mold, two swirl centersat the same height can be found, which is a typical single-rollflow pattern and not favorable for the mold metallurgicalbehavior.24,25) Fig. 7(c) shows the three-dimensional pattern offluid flow in the vertical sections of the strand at castingspeed 1.0 m/min with submergence depth 80 mm. Fig. 7(d)shows the “self-braking” effect we obtained by two radialflow SENs and after the fluid leaves the SEN and enters themold, the flow out from two SENs’ ports will occur in theweb center. After collision of the two streams, a stream willflow upward, another downward. The upward stream willhelp to obtain an active meniscus, and both of the upwardand downward stream will augment the temperature of themeniscus and inside the mold.
3.3. Temperature Distribution and SolidificationFigure 8 shows the temperature distribution along the
mold surface with two different type SENs. It can be clearlyseen that both SEN structure and casting speed stronglyaffect the temperature distribution on the surface of thestrand. Using the radial flow SEN, molten steel jet first
Fig. 6. Flow patterns obtained with different nozzles in the mold at casting speed 1.0 m/min: (a) straight SEN: (b) radialflow SEN, port angle –15 degree; (c) radial flow SEN, port angle 0 degree; (d) radial flow SEN, port angle +15degree.
Fig. 7. Flow pattern in the beam-blank mold: (a) characteristics of straight SEN, locating in an off-center position; (b)flow field obtained with straight SEN, wide face center-plane, the velocity higher than 0.2 m/s is blanked for amore clearly visual effect; (c) flow field obtained with straight SEN, three-dimensional arrangement; (d) flow fieldobtained with radial flow SEN with port angle –15 degree at casting speed 1.0 m/min.
Fig. 8. Predicted shell surface temperature distribution in thebeam-blank mold.
impinges on the flange tip. The “self-braking” also createsimpingement near the “self-braking” zone. These impinge-ments produce a local maximum in superheat extraction atthis location, so a disproportionately large amount of thesuperheat is delivered to the flange tip and the web center,which increases the risk of breakouts and defects.
Details of the calculated surface temperature of the shellsurface in the two parts of the beam-blank are shown in Fig.9. At the initial stage of the solidification, the temperatureat the outer strand surface is largely determined by the SENstructure. Lower the SEN port angle or casting speed couldsignificantly decrease the local highest temperature. Consid-ering that the maximum heat flux from superheat dissipationis always centered about the point where the jet impingesupon the inside of the solidified shell,26) the local tempera-ture should be lower than that of the simulation results. Atthe flange center, the SEN port angle could not obviouslychange the temperature. Also, at the same casting speed,SEN structure cannot change obviously the temperature atthese positions. The radial flow SEN can increase the webtemperature at the lower part of the mold, as shown in Fig.9(b).
The corresponding distribution of shell thickness in theflange center and web center of the beam-blank are shownin Fig. 10 and it can be seen that, using the radial flow SEN,at the initial stage of the solidification, too much superheatis delivered to these regions because of the directly impinge-ment or “self-braking” effect which confines superheat to a
narrow region as Fig. 11 shows. Shell growth significantlyslows down or even reverses locally in these regions and itis likely to increase the incidence of breakouts and couldhave an important effect on other quality problems as well.
At the mold exit, the cross secion temperature distributionis presented in Fig. 12. Using the straight SEN, it can beseen that there is a high temperature gradient. Using theradial flow SEN, the temperature distribution at the moldexit is more uniform and may be helpful to avoid seriouscenter looseness caused by using the straight SEN or unsuit-able secondary cooling strategy, as shown in Fig. 13.
Figure 14 shows the solidified shell profile at the moldexit, from which it can be clearly seen that there are manydifferences. With the straight SEN, the shell thickness is
Fig. 9. Temperature distribution along the strand surface in the beam-blank mold and the legend could be found in Fig.10: (a) flange tip center; (b) web center.
Fig. 10. Shell thickness distribution along Z direction, the liquid fraction was set to be 0.2, which stands for a full solidi-fied shell: (a) flange tip center; (b) web center.
Fig. 11. Solidified shell profile and isothermal-surfaces using thethree-port radial flow SEN at casting speed 1.0 m/min.
thinner at the fillet but thicker at the web. The thin solidifiedshell thickness of the fillet could be validated by Fig. 15.According to the experience in a few steelworks, the break-
outs usually occur at the fillet, which further confirms thepresent calculation results. The radial flow SEN coulddecrease the risk of breakouts caused by rupture of skin at
Fig. 12. Contours of temperature field and velocity vectors at thebeam-blank mold exit at casting speed 1.0 m/min, straightSEN with submergence depth 60 mm and radial flow SENwith port angle 0 degree. Fig. 13. Macroetch of a transverse section of beam-blank.
Fig. 14. Comparison of solidified shell thickness at the mold exit: (a) single-port straight SEN with submergence depth 80mm at casting speed 1.0 m/min; (b) radial flow SEN with port angle –15 degree.
Fig. 15. Photographs of solidified shell: (a) obtained by adding radioactive tracer to the liquid pool;27) (b) obtained by abreakout.2)
Fig. 16. Solidified shell profile: (a) flange depression, from some steelworks in China; (b) calculated shell profile, an
average value of solid fraction 0.5 is chosen in order to have a better view; (c) calculated shell thickness distribu-tion of the flange at the mold exit at casting speed 1.0 m/min.
the fillet. With the radial flow SEN, the shell thickness isthinner at the web center, as shown in Fig. 14(b), and itshould be mentioned that the molten steel jet angle largelydetermined by the port angle could influence the heat fluxat the interface of mold cooper and solidified shell,26) so theshell thickness at the web center as Fig. 14(b) shows shouldbe treated critically.
Using the single-port straight SEN, the depression some-times occurs at the flange, as shown in Fig. 16(a). Thisdefect should be caused by the structure of straight SEN.The characteristics of this nozzle locating in an off-centerposition have been introduced in Fig. 7(a), and the washingeffect results in shell erosion in local thin spots and cause a“wavy contour” as shown in Figs. 14(a) and 15(b). Theflange depression indicates that the “wavy contour” shellcould be unable to withstand the stress of solidified shellshrinkage process and could be pushed back by the moldinner surface or the retaining rolls in the secondary coolingzone.
The simulated shell profile in the beam-blank mold isshown in Fig. 16(b), and how the impinging molten steel jetpouring from the straight SEN affects the shell distributionof the flange can be found. Fig. 16(c) clearly shows that theshell thickness of the flange at the mold exit is very non-uniform. Using the radial flow SEN, the shell thickness atthe flange is more uniform and thicker, and may avoid theflange depression. In addition, shell thickness is the mini-mum in the position which is about 0.03 m away from theflange center in Fig. 16(c), this may be induced by thereverse flow from the web region, as shown in Figs. 7(b)and 12, because the reverse flow can push the molten steeljet and change its shape slightly.
4. Conclusions
Since there are a number of quality problems in beam-blank casting using the straight SEN, such as the weak andcalm meniscus status, non-uniform shell thickness distribu-tion at the mold exit, flange depression and breakoutsinduced by the rupture of the fillet, mathematical modelinghas been used to investigate the suitable structure of SEN bythe analysis of the transport phenomena in the mold. Inorder to facilitate the comparison and analysis, in all thesimulations, the same thermal boundary is assumed. Thoughthe Savage and Prichard’s relation could provide a reason-able tendency to describe the heat flux profile along theheight of the mold, there are unavoidable partial differencein solidification, especially when the radial flow SEN isused and the results of solidification should be treated crit-ically.
(1) Using the single-port straight SEN, the major short-comings are inactive top free surface and non-uniform shellthickness distribution at the mold exit. It’s hard to obtain asuitable meniscus status by simply changing the SEN sub-mergence depth. Center looseness of a transverse section ofthe beam-blank is related with large temperature gradientcaused by molten steel jet from this nozzle. Characteristics
of the single-port straight SEN in a beam-blank mold locat-ing in an off-center position are illustrated and the flangedepression is possibly caused by the off-center molten steeljet washing effect.
(2) The new designed three-port radial flow SEN hasthe advantage to obtain an active meniscus status and a uni-form shell thickness distribution except the web center. Thistype nozzle could decrease the risk of breakouts caused bythe rupture of skin at the fillet and reduce the probability offlange depression, center looseness and the crack of strand.
(3) The “self-braking” effect caused by two radial flowSENs provides a good stability of flow at the meniscus, butthis braking effect could confine a large amount of superheatto a small region and a further improvement is necessary infuture.
AcknowledgementsThe authors would like to thank the financial support
from the Fundamental Research Funds for the CentralUniversities No. N130602005.
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