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Particle-based Numerical Analysis of Spray Water Flow in Secondary Cooling of Continuous Casting Machines

Norimasa YAMASAKI,1)* Shozo SHIMA,1) Keiji TSUNENARI,2) Satoru HAYASHI3) and Masahiro DOKI4)

1) Plant Engineering and Facility Management Center, Nippon Steel & Sumitomo Metal Corporation, 20-1 Shintomi, Futtsu,Chiba 293-8511 Japan.2) Nippon Steel & Sumitomo Metal Corporation, 6-1, Marunouchi 2-chome, Chiyoda-ku, Tokyo 100-8071 Japan.3) Process Research Laboratories, Nippon Steel & Sumitomo Metal Corporation, 20-1 Shintomi, Futtsu, Chiba 293-8511 Japan.4) Kimitsu Works, Nippon Steel & Sumitomo Metal Corporation, 1 Kimitsu, Kimitsu, Chiba 299-1141 Japan.

(Received on August 19, 2014; accepted on February 4, 2015; originally published in Tetsu-to-Hagané,Vol. 99, 2013, No. 10, pp. 593–600)

In continuous casting process, solidification should evenly proceed to have as good steel quality as pos-sible. Molten steel starts to solidify in a water-cooled mold to create solidified shell followed by shellgrowth and termination in a secondary water cooling zone. Visualization of the flow pattern of spray watergreatly helps to analyze how to have even shell. Computational fluid dynamics is useful represented bythe grid based methods of FVM, FDM, and FEM. However, they are not appropriate for simulation ofspray water flow because of complex free surfaces. So, the particle based method of MPS has beenapplied. A typical roll arrangement was modeled where spray water flow was particularly focused on. Asa result, standing water on rolls overflows according to the water flow rate of spray accounted for in thisstudy. Accuracy of the numerical model has been verified by water model experiments equipped byacrylic plates, rolls and spray nozzles. The computational results with a practical condition agreed wellwith the experimental results. Heat transfer coefficients between water and slab surface were estimatedby the calculated results to simulate how solidification proceeded in practice. It was found that unevenwater flow significantly affected unevenness in temperature distribution of a slab.

KEY WORDS: continuous casting; particle-based method; computational fluid dynamics; MPS; solidifica-tion; secondary cooling; spray water.

1. Introduction

To ensure evenness of solidification in continuous castingprocess is one of the important technologies for the produc-tion of high-quality slabs. In a secondary cooling zone, mul-tiple sprays spaced in width between rolls cool down thesurfaces of slabs to solidify molten steels. However,research of cooling by multiple spray units has never beendone so far. It is only by using simple spray units1) that havebeen studied. Therefore, problems of unevenness as forcooling in width by sprays are so difficult to be solved com-pletely because no quantitative analyses have been conduct-ed on the behavior of spray water. In particular, they includedripping water passing through roller bearing portions ofsplit rolls with intricately arranged pattern, and standingwater on rolls. In order to support a slab with thinner shellduring casting at higher speeds, roll pitches have to be nar-rower because of weaker shell than at conventional speeds.This may induce an issue to use rollers in smaller diameterresulting in lower rigidity leading to larger deformation forrolls.

Therefore, rolls divided into plural pieces in width havebeen recently used to have rolls less deflective. However, itis necessary for a couple of roller bearings to be arrangedas a result of division. Because of these roller bearings,spray water for slab cooling may unevenly flow downstreamthrough the space caused by roller bearings and a slab.

In order to analyze how this flow pattern affects unevensolidification, it is important to visualize the flow pattern ofspray water quantitatively. Computational fluid analysis iseffective, however, since the conventional method ofemploying grids (meshes) is judged to be inadequate fortreating complex free surfaces, a particle-based, meshlessmethod2) has been tried in this study.

In fact, this is the first trial to simulate the spray waterbehavior in a secondary cooling zone in a continuous cast-ing machine by means of the particle-based method. There-fore, the followings were unknown; how large the diameterof particles should be, how to treat the contact angle ofwater with the slab/rolls and how spray jet shapes influencethe fluid flow. That was why these factors were specificallyexamined in the process of modeling.

Heat transfer coefficients between cooling water and aslab under various conditions were measured using the flowof the spray water obtained from the analyses. Solidification

* Corresponding author: E-mail: yamasaki.x3s.norimasa@jp.nssmc.comDOI: http://dx.doi.org/10.2355/isijinternational.55.976

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progress of a slab was analyzed with the measured heattransfer coefficients employed as the boundary conditions.

Solidification analyses3,4) have been carried out by onedimensional calculation at the center of a slab and twodimensional analysis by a cross section perpendicular tocasting direction. But, quantitative analyses were usuallyconsidered to be difficult to clarify unevenness in slabwidth.

Therefore, a model has been developed considering sep-arate sprays and rolls, position of roller bearings and effectof standing water and dripping water. Finally, the origin ofunevenness caused by cooling in slab width could be deter-mined.

2. Modeling of Spray Water Behavior in SecondaryCooling

2.1. Actual Conditions of Uneven Temperature in aSlab

Figure 1 shows the surface temperatures of a slab insidethe strand of a continuous casting machine of a commonvertical bending type.

This was measured by a radiation thermometer with scan-ning along the width direction, which was installed at 18 mbelow the meniscus. The slab size was 300 mm × 2 200 mm,and the casting speed was 1.0 m/min. Secondary coolingzones of a continuous casting machine typically consist ofplural segments with multiple rolls arranged. Thereby, sur-face of a slab cannot be generally observed except for thespaces between the segments.

Measurement was conducted on the upstream side of anunbent segment with a comparatively large gap due to theextraction of a segment at the time of maintenance. A scan-ning radiation thermometer of mono-color (measurementwave length: 1.0 μm) was used to measure the surface tem-peratures. As realized in Fig. 1, the temperatures at thewidth center of the slab are 100°C lower than those at thevicinity of both edges. Similar tendency can be also seenunder the different conditions of casting speeds, steel gradeand secondary cooling patterns.

The origins to bring uneven solidification has been so farconsidered by “effects of fluid flow of molten steel” and“operations saving water at the edge portions to preventover-cooling in secondary cooling”.5) However, the extremetemperature drop in the width center as seen in Fig. 1 can’tbe clarified by the conventional concept.

Accordingly, a study has been performed to understandhow uneven cooling takes place. Especially, we focused onthe influence of the arrangement of the split roller bearingsshown in Fig. 2 along with the behavior of spray water flow-ing in secondary cooling zones.

2.2. Modeling of Spray Water FlowThe particle-based method (Moving Particle Simulation;

MPS)6,7) was applied to calculate the spray water flow pattern.Further, necessary functions were added to the commercialcomputational fluid dynamics software of Particleworks.8)

The key point of the particle-based method is meshlessresulting in easily calculating free surfaces. The particle-based method can be classified into two types; one is DEMmethod used to solve the target particles in analysis as par-ticles, and the other is MPS method applied in this study,that is good at solving a continuum as the calculation pointsof particles as shown in Fig. 3.

As for the two formulas of continuation formula andNavier-Stokes formula (Eq. (1)) which are also solved withthe finite volume method, the gradient term is discretizedusing an inter-particle interaction model as shown in Fig. 3.

.............. (1)

Where, u, p, ρ, ν and f denote the flow velocity, the pres-sure, the density, the dynamic viscosity coefficient and theexternal force (gravity), respectively. Figure 3 displays thediscretization of gradient vectors in the physical quantity φat the i-th position of particles. r, d, n0 and w denotes theposition of particles, the dimensional number of space, thedensity of particles and the weight function defined for theinfluences to be smaller with increasing the distancesbetween particles, respectively. <> denotes the symbolexpressing an inter-particle interactional model.

The following three matters were examined in detailbefore modeling the spray water flow with the particle-based method.

(1) Study of effects of the particle diameter on the spraywater flow

Diameter of particles must be defined to calculate the flu-id flow by the particle-based method. A smaller diameter ofparticles induces an enormous number of particles and lon-ger time is needed for calculation. A larger diameter of par-ticles causes the problem that they can not flow into smallgaps.

Accordingly, the effects of the various diameters on theflow pattern were analyzed using the model shown in Fig. 4.

The flow rate was measured at the positions indicated inFig. 4 with the respective diameters of particles; 2 mm, 3 mmand 4 mm.

Fig. 1. Measured surface temperature at 18 m below the meniscus. Fig. 2. Schematic view of the flow pattern of spray water.

D

Dt

Du

Dtp v f

ρρ

μ= = − ∇ + ∇ +01 2,

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The time average of flow rates (that for 3 seconds between2 and 5 seconds) and the standard deviation of flow rates atwhich the cooling water flows in Region A (the edges of theslab) and Region B (the intermediate portion of the rollerbearings) are shown in Figs. 5(a) and 5(b), respectively.

The results in Region C presented the same behavior asin Region A due to the symmetry of the model.

The minimum gap that allows water to flow is 10 mmbetween the top plate on the roller bearings and the slab. Theaverage flow rate is not so greatly affected by the diameterof particles, however, the larger the particles becomes, thegreater the variation of the flow rate does resulting in unsta-ble flows into gaps. This is also attributed to higher standarddeviation of flow rates ranges. The number of particles andcalculation time employed for calculation are shown in Fig.6. The particle diameter was determined as 3 mm after con-sidering the practicability of the calculation time and stabil-ity to flow into the narrow gap. The gap of 10 mm betweenthe roller bearing and the slab can accommodate three par-ticles with this condition.

(2) The effects of the contact angle between water andthe roll/slab on fluid flow

A study was made to see how the contact angle betweencooling water and the roll/slab affects fluid flow focusing onwhether the spray water through roller bearings portion flowalong the rolls or not.

Analysis was done on the water flow that freely fallsdown in a space of 10 mm between the roller bearings andthe slab using the model shown in Fig. 7(a). There are noremarkable differences between the contact angles of 30°and 60°. (Figs. 7(b) and 7(c)) It is assumed that the flow isdominated by inertia due to the higher flow speed of thewater with free fall. Therefore, 30° was applied for everycalculation.

(3) Shape expressions of spray jetsIn a secondary cooling, it is preferable to minimize the

number of sprays in order to reduce maintenance costs.Therefore, sprays should be only in sufficient number to

achieve even cooling within the reachable positions.For this reason, the nozzles are set to be the spray nozzles

expanded in width relative to the casting direction jettingovally with a large angle. The commercial software used inthis analysis did not assume oval jets but common circularjets. Therefore, the program was properly modified to per-

Fig. 3. MPS Method and formulation of gradient φ .

Fig. 4. Simulation model to set particle diameters (unit: mm).

Fig. 5. Relationship between particle diameters and time-averagedwater flow rates or standard deviation of water flow rate at(a) region A and (b) region B defined by Fig. 4.

Fig. 6. Relationships between particle diameters and number ofparticles or computational time.

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mit independent setting of different angular spreads in twoorthogonal directions.

Usually, the density of water droplets in a unit volume hasa distribution to some extent within the reachable positionsof an oval jet. It is therefore assumed that particles areallowed to be jetted at random angles by providing anglesagainst the casting and width directions. The differencebetween circular (Fig. 8(a)) and oval jets (Fig. 8(b)) isshown in Fig. 8.

It should be noted that particles do not express actualwater droplets but calculation points. The purpose of thepresent analysis is to simulate the macroscopic behavior offluid flow after the spray water has impinged with a slab.Therefore the density distribution of water droplets in a unitvolume within an oval was not taken into consideration. Theabove three considerations can suggest the conditions of aparticle diameter of φ 3 mm, a contact angle of 30° betweenwater and rolls/slab and oval spray jets. The properties ofwater and the boundary conditions are shown in Table 1.

Analysis was performed through modeling with a charac-teristic pattern extracted from roller bearings arranged in thestrand; three steps of rolls and two steps of sprays as shownin Fig. 9.

The sprays with upper steps of eight pieces and the lowerones of seven pieces were reciprocally arranged along the

casting direction. The rolls are divided into three pieceswhile the intermediates roller bearings are provided in thetwo places at the central part of the width. The distancebetween the sprays and the slab, jetting angles of sprayswere set as 155 mm, 100° in width and 30° in the castingdirection, respectively.

3. Fluid Analysis of Spray Water by the Particle-basedMethod and Verification Through Actual Measure-ment

An analysis result arranged as in Fig. 9 is shown in Fig.10. This is the view from the side of the slab at 5 secondsafter the injection of the spray.

This output with the flow rate of 20 L/min a spray hasrevealed that the cooling water jetted onto the slab unevenlyflows down as the dripping water. Obviously, it passesthrough the roller bearings portions with a lot of waterstanding still on the upper part of the rolls of the down-stream side. In addition, some droplets spill over toward theback side. Accuracy of the model was verified by using awater model, in which water was jetted from the spraysplaced between acryl pipes attached to an acryl sheet thatsimulates a slab. Figure 11 shows a typical example of the

(a) (b) (c)

Fig. 7. Effect of contact angles on water flow. (a) Simulation model. (b) Calculated flow pattern (Contact angle is30 degree). (c) Calculated flow pattern (Contact angle is 60 degree).

Fig. 8. Spray patterns. (a) Circle-shaped pattern. (b) Oval-shapedpattern.

Table 1. Calculation conditions of the spray water flow model.

Density (kg/m3) 1 000

Dynamic coefficient of viscosity (m2/s) 1.0×10–6

Coefficient of surface tension (N/m) 0.072

Boundary condition of wall Non-slip

Turbulence model None

Fig. 9. Simulation model for spray water flow between rolls (unit:mm).

Fig. 10. Calculated spray water flow (View from slab side).

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experimental result. The flow rate for each spray unit was20 L/min the same as the calculation of Fig. 10. The behav-ior of the spray water was successfully simulated; waterflowed downward passing through the roller bearings alongwith some water standing still on the rolls. For more quan-titative evaluation, comparison was made on the flow rateof water flowing out from the roller bearings portion and theedges of the slab obtained by the calculation with the exper-iments as shown in Fig. 12.

At Regions 1-8 defined in Fig. 9, the flow rates obtainedby the calculation agreed well with the measurements. Threefigures of (a), (b) and (c) display the results with the flowrates per spray piece of 5, 10 and 20 L/min, respectively.

The difference can be seen in the flow rates between theactual measurements and the calculations at Regions 6 and7 when the water flow rates are higher. This might be attrib-uted to the variation of water amount that overflowed fromthe system, since the amount of standing water on the rollsvaried owing to the slight difference in diameter of the acrylpipes and the rolls of the calculation.

The subsequent analyses were performed only by calcu-lation, because it was proved that fluid flow of spray watercould be more accurately analyzed by the particle-basedmethod.

Further analysis was carried out to see the effects of thedripping water stood on the downstream side with increas-ing the step number of the rolls and spays. The behavior ofspray water was analyzed at a flow rate of 20 L/min perspray piece in the model which consists of the five-step rollsand the four-step sprays between the rolls. The results fromthe slab and roll sides are shown in Figs. 13 and 14 at 5 sec-onds after the injection of the spray jets, respectively.

The standing water on the intermediate rolls overflows tothe rear side. The water amount becomes larger as itapproaches to the downstream side. On the other hand, theoutflow becomes larger at the edges of the slab with no sig-nificant effects on the flow rate at the roller bearing posi-tions in the vicinity of the central part in width. This meansthat modeling the characteristic sprays of around two-stepallows us to analyze the flow of spray water sufficiently.

This analysis allows us to understand the generation of alarge quantity of water kept standing on the intermediaterolls of the split rolls that flows downward from the posi-tions of the roller bearings. A question arises if this behaviorof the cooling water affects over-cooling in the vicinity ofthe central part of slab width. Therefore, solidification anal-ysis was performed taking the spray water flow into consid-eration.

4. Estimation of Uneven Temperature in Width byMeans of Solidification Calculation in the Strand

Solidification calculation was made to understand thesolidification conditions of the strand considering above-mentioned dripping water etc.

Before calculation, heat transfer coefficients were mea-sured by the following method. Temperature variation of aheated steel plate cooled by a spray was measured with mul-

Fig. 11. Measured spray water flow from the water model (Viewfrom slab side).

Fig. 12. Comparison between the calculated and the measured waterflow rates. (a) Water flow rate of each nozzle is 5 L/min.(b) Water flow rate of each nozzle is 10 L/min. (c) Waterflow rate of each nozzle is 20 L/min.

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tiple thermocouples simulating the dripping water and thestanding water.9) The procedure was that the plate was heat-ed to 900°C in a furnace under a controlled atmosphere fol-lowed by cooled with sprays immediately after beingextracted from the furnace. An image during the measure-ment with a single spray is shown in Fig. 15. Heat transfercoefficients were determined by reverse analysis10) of themeasured temperatures of the steel plate. Figure 16 showsthe temperature variation of the steel plate as time at thepositions of the center and 210 mm away from the center.Figure 17 shows the heat transfer coefficient distributionwith a water flow rate of 10.45 L/min when the surface tem-perature reached 800°C. Reverse analysis of a result makesit possible to calculate heat transfer coefficients as functionsof time implying that coefficients can be determined at var-ious surface temperatures. However, at the lower tempera-tures, in general, obtained heat transfer coefficients are notaccurate enough due to the effect of the three-dimensionalheat conduction in the steel plate. Accordingly, heat transfer

coefficients were measured at a temperature 100°C belowthe initial temperature of the plate. For instance, when theheat transfer coefficients at 700°C are required, the platewas initially heated to 800°C.

Heat transfer coefficients were thus obtained as functionsof the density of sprayed water in a local unit volume, sur-face temperature of the steel plate and the impingementpressure of the sprays by the experiments under variouswater flow rates from the sprays in conjunction with varioustemperatures of the steel plate.

The effect of the dripping water on heat transfer coeffi-cients was determined by providing a water flow fromabove the sprays simulating the dripping water on the rollerbearings.

The amount of dripping water was set referring to theflow rates provided in Fig. 12. In consideration of the effectof water standing on the rolls, cooling experiments wereperformed with a steel sheet assembled with the steel platesimulating an actual situation.

Fig. 13. Calculated spray water flow (View from slab side).

Fig. 14. Calculated spray water flow (View from roll side).

Fig. 15. Experimental image (Water is sprayed on the heated steelplate). (Online version in color.)

Fig. 16. Measured temperatures at the center and 210 mm from thecenter of the steel plate.

Fig. 17. Heat transfer coefficients (W/m2K) calculated from themeasured temperatures at the cooling test. (Online versionin color.)

Fig. 18. Boundary conditions for the simulation model of solidifi-cation.

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It was found that the water calmly standing on the rollsdid not show significant cooling effects. On the other hand,an important finding was that cooling was facilitated whenthe standing water was interfered with the spray water, thatleads to vigorous agitation. These experiments couldsuccessfully determine the heat transfer coefficients in theportions of sprays with and without interference of waterstanding on the rolls, dripping water, and so forth. There-fore, these values were substituted as the boundary condi-tions of the solidification calculation in the strand.

The boundary conditions of heat transfer were given tothe four separated regions between the rolls. (Fig. 18) I, II,III, and IV denote the roll cooling region, the air coolingregion or roller bearing dripping water region, the spraycooling region, and the region of water standing on the rollsor spray dripping water region, respectively. As for the vari-ation of the heat transfer coefficient in width, in the portion(II) of the dripping water interfered with the spray water,heat transfer coefficient was given as 1.1 times higher thanthat in the portion only with the dripping water. Similarly,heat transfer coefficient in the portion (IV) of the standingwater interfered with the spray water was given as 1.5 timeshigher than that in the portion only with the standing water.These coefficients of 1.1 and 1.5 were determined by theexperiments described above. Various phenomena duringsolidification were calculated by inputting the heat transfercoefficients as the boundary conditions for every regionshown in Fig. 18. Here, the two-dimensional sections verti-cal to the casting direction were considered under a fixedcasting speed. The enthalpy method was used for the solid-ification calculation. Table 2 shows the values of materialproperties and the boundary conditions. Calculation wassucceeded accounting for the effects of the split rolls, thedripping water and standing water created due to the rollerbearings and the rolls. As explained above, these effectswere identified by the particle-based method providing heattransfer coefficient distributions.

As a result, it was found that there was an over-cooledpart at the central portion in the width center of the slab. Itcould clearly reveal the uneven solidification as shown inFigs. 20(a), 20(b) and 20(c), indicating surface temperature,heat transfer coefficient and solid fraction at the center ofthe slab in thickness, respectively.

Heat transfer coefficients in Fig. 20(b) are larger in the

central portion of the width in the vicinity of a point at 5 mbelow the meniscus due to the previously mentioned inter-ference between the standing water on the rolls and the

Fig. 19. Simulation model of solidification.

Table 2. Calculation conditions of the simulation model of solidi-fication.

Density (kg/m3) 7 800

Reference specific thermal conductivity (W/mK) 59

Reference specific heat (kJ/kgK) 0.47

Latent heat (kJ/kg) 260

Reference temperature (°C) 30

Heat transfer coefficient (W/m2K)

Roll-Slab 1 700

Spray water-Slab Measured data

Fig. 20. Calculated results of solidification. (a) Surface tempera-tures. (b) Heat transfer coefficients. (c) Solid fraction atthe center of the slab in thickness.

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spray water. Surface temperatures at 5 m below the menis-cus are relatively lower due to this effect. Further, distribu-tion of the center solid fractions in Fig. 20(c) shows thatsolidification at the center portions complete prior to thevicinity of the slab edges.

Figure 21 shows comparison of the surface temperaturebetween the measurement results obtained by the thermom-eter and the calculation results. This indicates that the tem-peratures of the central portions tend to be 100°C lower orless than those of the vicinity of the edge portions. The over-cooled phenomena at the center are considered to be causedby the higher heat transfer coefficients due to the vigorouslyagitated water originated from the dripping water passingthrough the roller bearings in the central portion of the splitrolls.

5. Conclusions

A study was undertaken to understand how uneven solid-ification phenomena occur along the width direction of aslab during secondary cooling in continuous casting process.Numerical analyses was performed by the particle-basedmethod to see the behavior of spray water inside the strand.In addition, solidification analysis was conducted takingheat transfer coefficients into consideration, which is affect-ed by the fluid flow of spray water.

The following words conclude this study.(1) The optimal diameter of particles used for calcula-

tion was found to be φ3 mm. It was further found that theeffects of the contact angle between the water and the roll/slab on the behavior of spray water were negligibly small.

(2) The present simulation by the particle-based methodwas verified by the experiments using a water model

because of good agreement with each other.(3) The present model successfully simulated the

behaviors of dripping water flowing to the downstream sidein the roller bearing portion and water standing still on therolls.

(4) Determinations of heat transfer coefficients wereperformed accounting for the interference of dripping waterwith water standing on the rolls leading to vigorous agita-tion.

(5) Solidification calculation using the measured heattransfer coefficients revealed that the dripping waterbetween the roller bearings and standing water on the rollscontributed to the unevenness along the width direction.

(6) Temperature distribution along the width directionobtained by the analyses well agreed with the measured val-ues by a radiation thermometer.

(7) It was understood that interference of water standingstill on the intermediate roll portion among the split rollswith the spray water caused temperature drop in the centralportion of the slab width.

AcknowledgementsThe present study was assisted by Professor Seiichi

Koshizuka, who majored in the Department of SystemsInnovation, Graduate School of Engineering, the Universityof Tokyo and the staff of Prometech Software Company Ltd.for the particle-based method analysis; Mr. ToshihiroKawano of Meitec Company Ltd. for construction/process-ing and visualization of the calculation models; and the staffof Kyoritsu Gokin Company Ltd., for the measurement ofheat transfer coefficients. I am sincerely grateful for theircontributions.

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Fig. 21. Comparison between the measured and the calculated sur-face temperatures at 18 m below the meniscus.