Modelling-based Innovative Feeding Strategy for Beam Blanks Mould Casting Aimed at As-cast Surface Quality Improvement

Abstract

Within an investigation focused on effect of casting conditions on steel quality in an industrial beam blanks mould, different nozzle geometries were tested with Computational Fluid Dynamics modelling. The innovative nature of the work consisted in feeding with only one nozzle, whereas two nozzles in the flange-tip zone are commonly used. This configuration has the advantage of a simplified mono-slide gate casting layout, but single nozzle feeding can bring about risks of too high steel velocity in the mould, harmful for shell integrity and meniscus stability.

Having in mind the mentioned constraints, different geometry solutions were checked and, to assess the solutions found, suitable indices were defined, related to flow conditions able to prevent slag entrapment at the meniscus, and hot-spotting at walls, harmful for the solid shell integrity.

The modelling work gave general indications on undesired flow features and guidelines to improve reference conditions, involving number of holes and holes angle, size and shape. For the caster mould and the operating conditions under concern, a solution was found satisfying the indices, and expected to fulfil the quality requests. It consisted of a nozzle with a 50 mm diameter throat, a 50 mm× 60 mm elliptical lateral port inclined 25° downwards and a 20 mm-diameter bottom hole. A water model check with such a nozzle prototype validated the model supporting the solution identified to be used on plant.

1. Foreword

In continuous casting of beam blanks, the occurrence of longitudinal surface cracks plays a relevant role in affecting as-cast quality. Not so many studies on surface crack occurrence in beam blanks are shown in literature. Lee and others,¹⁾ within the as-cast beam blank shape (Fig. 1) identified the web and fillet region as mostly prone to crack formation, also noticing that shell formation is somewhat retarded at the flange-center region, due to the steel stream impingement from the feeding nozzle. The conclusions were gained based on a suitably defined crack susceptibility coefficient. Furthermore, Seok and Yoon²⁾ investigated the effect of steel composition on longitudinal crack formation. The most relevant results were the identification of: a) a mostly sensitive crack susceptibility range of carbon contents (0.12–0.13 wt.%); b) the effect of casting speed on crack formation (a linear relationship). Then, Hibbeler et al.,³⁾ performed a thorough 3D thermo-mechanical analysis of beam blank steel solidification without accounting for liquid metal flow. A coupled thermal-mechanical model of steel casting was applied to accurately simulate casting of steel beam blanks, validated with plant measurements. An efficient local-global numerical procedure is given to integrate a realistic elastic-visco-plastic phase-dependent constitutive model implemented into the commercial package ABAQUS, and insights are provided into the mechanisms of shell failure triggered first by a thinner shell under combined thermo-mechanical stress conditions, and then accelerated by a shoulder gap opening, leading to crack formation.

Fig. 1.

Schematic of a beam blank section and typical 2-nozzle position.

Based on the experience of conventional casting process, a regular shell growth is expected in the mould if the steel coming from the nozzle spreads over the mould volume without excessive local thermal and mechanical load, with risk of skin remelting and, in presence of too high velocity at meniscus, slag entrapment from the meniscus. The mentioned aspect becomes of outmost importance within the typical dog-bone shaped mould. In this case, it is of outmost importance an adequate nozzle design to achieve even flow and thermal field in the mould able to ensure thermal homogeneity at the solid shell interface and reliable conditions for even shell growth.

The investigation, whose results are presented within this paper, was aimed at finding the best solutions to support this feeding strategy. In particular, the mono-nozzle innovative feeding solution was considered to simplify the casting layout, even not easy to accept at a first sight. As a matter of fact, possible related drawbacks are harmful effects on quality induced by flow asymmetry, due to the asymmetric nozzle position with respect to the beam blank section, as shown next. The individuation of the more suitable nozzle geometry has been supported by numerical modelling and by the assessment of the fluid-dynamic performance through dedicated indices, related to quality features and whose design criteria are described in the next section.

2. Technical Approach and Modelling Description

Several literature examples of flow modelling in beam blanks can be found.^4,9) They deal with nozzle geometry and immersion depth effect on fluid flow in mould, but are all focused on two-nozzles feeding, broadly used in beam blank casting. Most of them are focused on the use of a straight nozzle. One of them also accounts for the use of a multi-port nozzle, up to three ports, one pointing towards the mould center and two at 120° from each other, pointing towards the mould narrow faces.⁸⁾

Nevertheless, also with this particular geometrical feature two symmetric nozzles are foreseen. Of course, the use of two nozzles, placed at centre section half-way between flange tips (‘triple point’), brings about a particular lay-out arrangement to couple tundish and mould feeding, different from casters of other as-cast shapes. In such a scenario, a step forward is represented by the use on only one nozzle, which simplifies casting lay-out with mono-slide gate in line with the current conventional flat and long product casters. The advantage of such a configuration is a simplified mono-slide gate casting layout, but feeding from a single nozzle, dragging all flow rate through only one throat, can bring about risks of too high steel velocity in the mould harmful for shell integrity and meniscus stability. This explains why it is of outmost importance on one hand to have suitable indices to highlight warnings concerning the achievement of undesired flow conditions in critical mould zones, as meniscus and narrow face, on the other hand to tune suitably the geometrical parameters (ports area, number, angle) also accounting for lay-out limitations (e.g., space ‘filled’ by the nozzle compatible with the mould section and the need to avoid short-circuited flow zones).

Since high steel velocity in the nozzle throat was found to be responsible for risks of slag emulsification onset at meniscus,¹⁰⁾ the aim of the investigation was to find a compromise between the need of exploiting pouring in a volume large enough to avoid flow-short circuiting around the nozzle and the need of avoiding steel streams with too high steel velocity.

Within the work presented hereinafter, the technical information achieved consisted mainly of the in-mould velocity field, from which it was possible to assess values of indices relating process quantities to the possible occurrence of defect/drawbacks with the scope of finding innovative feeding solutions using only one nozzle. As a matter of fact, there are critical flow conditions associated to defect occurrence:^{10,11,12,13,14,15,16)}

- harmful waves at meniscus, able to break the interface steel-slag, and therefore to bring risks for slag entrapment affecting steel cleanliness;

- too high steel impingement velocity at walls, harmful for solid shell integrity;

- marked local velocity unevenness (e.g., at meniscus, feature related in turn to thermal unevenness and, as a consequence, to risk of cracks).

As a result, adequate evaluation criteria were identified as follows.

2.1. Evaluation Criteria

Threshold values. The relevant threshold values for the velocity, related with defect occurrence, were the following:

- maximum velocity at meniscus: indicative threshold for slag entrapment occurrence: 0.3 m/s;¹⁰⁾

- maximum velocity at wall: indicative threshold for direct ’hot spot’: 0.35 m/s. This value can be derived from a literature logarithmic relationship between flow velocity U (cm/s), solidification rate f (cm/s) and dendrites arm deflection angle θ (degrees¹³⁾).   

$$ln\mathrm{\hspace{0.17em} }\text{U}=\frac{\theta +\text{9}\text{.73 ln f}+\text{33}\text{.7}}{\text{1}\text{.45 ln f}+\text{12}\text{.5}}$$

Also based on what shown in,¹⁵⁾ for f~0.36 one obtains θ = 15° with U= 35 cm/s.

Indices. First of all, from the velocity values at meniscus, relating velocity to temperature, an index of velocity unevenness at meniscus can be defined. This is made via the velocity variation coefficient, defined as the ratio between velocity standard deviation to average velocity. Due to the link between mass and heat transport in the mould steel pouring physics, such a index can be intended as the tendency of the meniscus to be fed uniformly.

Then, since for achieving an ‘optimum mould flow’ it is recommended:

- an average ‘high’ velocity at meniscus, of course below the threshold, as index of good meniscus feeding avoiding ‘freezing’ and favouring powder melting. Temperature is related to energy, so it is reasonable to consider for the index the square of velocity;

- a low variation coefficient (std deviation normalised to average), index of reduced risk of thermal unevenness and in turn of local cracks formation,

a reliable flow index can be defined as:   

$$\begin{array}{l}\text{Flow index}=\text{FI}={\left(\text{Average velocity}\right)}^2/\hfill \\ \left(\text{Variation coefficient}\right)*100\hfill \end{array}$$

This index should be zero for velocity at hot spot and/or meniscus exceeding the threshold, so:   

$$\begin{array}{c}\text{FI}={\alpha }_{\text{m}}\text{*}{\beta }_{\text{hs}}\text{*}{\left(\text{Average velocity}\right)}^{\text{2}}/\hfill \\ \left(\text{Variation coefficient}\right)\text{*100}\hfill \end{array}$$

where α_m=0 for max velocity at meniscus > 0.3 m/s, β_hs=0 for max velocity at hot spot > 0.35 m/s.

Working conditions

The plant scenario under investigation is the GHC ESI - Phase 2 steelshop, situated in Abu Dhabi, whose main features are the following:

- an over 1600000 ton-per-year (tpy) DRI plant;

- an over 1400000 tpy steel making and casting plant for blooms, beam blanks and billets production;

- an over 1000000 tpy medium and heavy section mill.

The caster (Fig. 2) is a 12m-curved, 5 strands Combi-Caster able to cast sections, from 150 mm × 150 mm billet to 1050 mm × 460 mm × 120 mm, with feasibility to roll profiles up to sheet piles in rolling mill (Table 1). ESI phase 2 is casting a wide range of Si–K steel grades in semi-open casting condition with %C ranging from 0.06 to 0.20 (for instance grade 355J2), and – in order to increase share of Al–K steels added-value products - a closed stream casting technique is needed.

Fig. 2.

Investigated beam blank caster: front view.

Table 1. Investigated Beam Blank Caster features.

Machine type	Curved
No. of strands	5
Machine radius	12/18/35 m
Billet section	150×150 mm
Bloom section	220×350 mm
Casting Beam Blank sections	BB1 430×350×90
	BB2 480×250×90
	BB3 500×435×100
	BB4 670×350×90
	BB5 1050×460×120
Ladle capacity	150 ton
Mould lubrication	Oil and powder
Oscillating unit	Hydraulically actuated
Dummy bar	Rigid

The operational conditions for our investigation were the following:

- beam blank format 430 mm × 350 mm × 90 mm (BB1 in the mentioned table);

- casting speed 1.16 m/min,

- mould length 780 mm.

The nozzle reference immersion depth considered was 100 mm. A straight mould was simulated.

Modelling description

The numerical modelling work was performed by means of the Ansys-Fluent code,¹⁷⁾ based on a 3D Computational Fluid Dynamics model implemented in software release 13. The governinq equations are listed in Table 2. One can found the Navier-Stokes’ formulation and the constants of the standard κ-ε turbulence model, used as proven to be reliable for similar modelling works. SIMPLE scheme with spatial discretization with momentum-2nd order upwind was used as solver.

Table 2. Governing equations (Navier Stokes’, turbulence, dissipation rate) of the physical system under investigation.

$\begin{array}{l}\rho \left(\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}+w\frac{\partial u}{\partial z}\right)=-\frac{\partial p}{\partial x}+\mu \left(\frac{{\partial }^{2}u}{\partial x^2}+\frac{{\partial }^{2}u}{\partial y^2}+\frac{{\partial }^{2}u}{\partial z^2}\right)+\rho g_x,\\ \rho \left(\frac{\partial v}{\partial t}+u\frac{\partial v}{\partial x}+v\frac{\partial v}{\partial y}+w\frac{\partial v}{\partial z}\right)=-\frac{\partial p}{\partial y}+\mu \left(\frac{{\partial }^{2}v}{\partial x^2}+\frac{{\partial }^{2}v}{\partial y^2}+\frac{{\partial }^{2}v}{\partial z^2}\right)+\rho g_y\\ \rho \left(\frac{\partial w}{\partial t}+u\frac{\partial w}{\partial x}+v\frac{\partial w}{\partial y}+w\frac{\partial w}{\partial z}\right)=-\frac{\partial p}{\partial z}+\mu \left(\frac{{\partial }^{2}w}{\partial x^2}+\frac{{\partial }^{2}w}{\partial y^2}+\frac{{\partial }^{2}w}{\partial z^2}\right)+\rho g_z.\\ \frac{\partial }{\partial t}\left(\rho k\right)+\frac{\partial }{\partial x_i}\left(\rho k{u}_i\right)=\frac{\partial }{\partial x_j}\left[\left(\mu +\frac{{\mu }_t}{{\mathrm{\sigma }}_k}\right)\frac{\partial k}{\partial x_j}\right]+P_k+P_b-\rho \mathit{\epsilon }-Y_M+S_k\\ \frac{\partial }{\partial t}\left(\rho \mathit{\epsilon }\right)+\frac{\partial }{\partial x_i}\left(\rho \mathit{\epsilon }{u}_i\right)=\frac{\partial }{\partial x_j}\left[\left(\mu +\frac{{\mu }_t}{{\mathrm{\sigma }}_{\mathit{\epsilon }}}\right)\frac{\partial \mathit{\epsilon }}{\partial x_j}\right]+C_{1\mathit{\epsilon }}\frac{\mathit{\epsilon }}{k}\left(P_k+C_{3\mathit{\epsilon }}{P}_b\right)-C_{2\mathit{\epsilon }}\rho \frac{{\mathit{\epsilon }}^2}{k}+S_{\mathit{\epsilon }}\\ C_{1\mathit{\epsilon }}=1.44,\hspace{1em}{C}_{2\mathit{\epsilon }}=1.92,\hspace{1em}{C}_{3\mathit{\epsilon }}=-0.33,\hspace{1em}{C}_{\mu }=0.09,\hspace{1em}{\mathrm{\sigma }}_k=1.0,\hspace{1em}{\mathrm{\sigma }}_{\mathit{\epsilon }}=1.3\end{array}$

The domain was meshed by means of the Gambit –preprocessor of Ansys-Fluent solver. Body-fitted coordinates with about 600000 hybrid cells (mix of tetrahedral and hexahedral, see Fig. 3) were used. After first checks, the cell number was chosen as the best compromise among the need of a detailed description with cells of the order of mm close to the walls and in the narrow gaps between nozzle and flange-tip zones, and the need of avoiding too time consuming calculations. Of course the number of cell was limited by the 1-phase isotherm description. As a matter of fact, no energy equation solution was needed since the main information resulting from the simulation is the velocity map, from which to derive the indices values. Moreover, the double symmetry of the domain allowed representing ¼ of the mould. The time needed for achieving convergence for a typical run on Processors Dual Intel Xeon 3.0 Ghz–32GB RAM was about 6 hours for about 20000 iterations.

Fig. 3.

Example of hybrid meshing.

Boundary conditions. At inlet, steel velocity was imposed (from flow rate and nozzle throat diameter), with 5% turbulence intensity (recommended value¹⁷⁾ for the Reynolds number of concern) on a 0.1 m turbulent length scale. At walls, log-law standard wall functions were imposed. At outlet, free outflow was imposed. As a matter of fact,¹⁷⁾ outflow boundary conditions are appropriate in case similar to those of concern, where the exit flow is close to a fully developed condition, with a domain length simulates of 1 m (longer than the mould height). The outflow boundary condition assumes a zero streamwise gradient for all flow variables except pressure.

‘Free surface’ was represented with a slip-wall no-shear description. This approximation can be considered at first sight inadequate to describe waves, assumed to be the main cause of steel-slag interface rupture and in turn to slag emulsification. As a matter of fact, the vertical (=upwards) velocity components are blocked and in turn the tangential components are somewhat overestimated. But, as shown in the Appendix, the criteria identified to indicate the possible onset of emulsification are related to the tangential velocity of the steel.¹⁰⁾ So, considering the slag pressure effect on the steel surface reasonably negligible, the approach can be considered reliable.

Finally, no time dependent flow effect was found, being the flow regime in the system investigated not strongly turbulent (Reynolds number = ρvl/μ = 50000, with ρ = density, v and l characteristic velocity and length, μ viscosity).

Design Of Experiment strategy

To achieve the most reliable configuration, a Design of Experiment strategy was set up to identify the geometrical features to be changed once a time within the nozzle design. The choice was based on the main features to manage steel flow acting on the nozzle geometry as follows.

a) Nozzle ports: from the ports, steel is driven within the mould along desired directions. Therefore, they are useful for ensuring proper feeding to a single nozzle in the triple point to the opposite sidewall, and flow rate partitioning to favour local feeding and reduce flow impact at walls. Here, the range examined was 1–3 ports, round/elliptical. The elliptical option was also considered to have a large exit section which breaks the stream and in turn reduces the risk of too intense hot spotting.

b) Nozzle angle: managing the port angle design allows to manage excessive kinetic energy at meniscus after hot-spotting. Based on literature experience^5,6) a reasonable range was identified in between 0° to –20° (downwards). Streams directed upwards were considered prone to induce thermal and velocity unevenness at meniscus; with a more marked stream inclination downwards, a frozen meniscus was expected due to the very weak eddies pointing upwards to the meniscus.

c) Bottom hole: its effect consists in reducing the kinetic energy of the stream poured from the nozzle into the mould and, after eddies, to the meniscus. The range examined for the hole diameter was 0–20 mm, based on a criterion, supported by CSM experience, that the bottom hole diameter should be smaller than half the throat diameter, otherwise flow short-circuiting downwards can occur preventing severely the steel stream to flow towards the lateral holes.

d) Throat diameter: in principle it is the most effective way to reduce steel velocity in the nozzle and some criteria foreseeing the onset of harmful waves at meniscus are related to steel velocity in the throat.¹⁰⁾ The possible variations were made within the lay-out (space in between nozzle and mould walls) and feasibility (minimum reasonable refractory thickness) constraints. Based on information concerning operational aspects and feasibility from refractory suppliers, a nozzle refractory thickness of 20 mm was assumed, allowing a minimum space between the nozzle and the closer wall of about 20 mm. Moreover, as refers to the throat section, together with the option of a round section with 50 mm diameter, an elliptical one (50 mm × 60 mm) was also considered.

Based on the mentioned criteria, and starting from the 2-straight nozzle with inner diameter 50 mm as reference conditions, the test matrix investigated was that shown in Table 3.

Table 3. Test matrix of the performed numerical simulations. Hole diameter in mm. Nozzle immersion depth 100 mm.

Test	Hole no	Holes diameter		Hole angle (deg)	Bottom hole diameter
		Throat	Side hole
a	1	50	–	–	50
b	2		0	–15	No
c	2		0	–15	15
d	2		50×70	–15	15
e	2	50×60 elliptical	50	0	20
f	2		50	–25	20

3. Results and Discussion

Relevant velocity maps (mid-plane, meniscus, lateral walls for hot-spot close-up) are shown for all the cases examined in the Figs. 4,5,6,7,8,9. The results (velocity values and normalised flow index values) are shown in Table 4.

Fig. 4.

Case a) configuration. Steel velocity (m/s) in relevant planes (midplane, meniscus, walls).

Fig. 5.

Case b) configuration. Steel velocity (m/s) in relevant planes (midplane, meniscus, walls).

Fig. 6.

Case c) configuration. Steel velocity (m/s) in relevant planes (midplane, meniscus, walls).

Fig. 7.

Case d) configuration. Steel velocity (m/s) in relevant planes (midplane, meniscus, walls).

Fig. 8.

Case e) configuration. Steel velocity (m/s) in relevant planes (midplane, meniscus, walls).

Fig. 9.

Case f) configuration. Steel velocity (m/s) in relevant planes (midplane, meniscus, walls).

Table 4. Velocity and flow index values for the cases investigated. VC= Variation Coefficient; FI= Flow Index. Values with asterisks (*) have flow index value 0 due to excessive velocity threshold at hot spot.

Test	Velocity (m/s)				VC	FI
	meniscus		Hot spot
	Ave	Max	nozzle side	opposite side
a	0.03	0.09	0.13	0.13	0.62	3
b	0.08	0.24	0.11	0.53 (*)	0.68	0 (*)
c	0.07	0.17	0.13	0.48 (*)	0.63	0 (*)
d	0.03	0.08	0.13	0.38 (*)	0.52	0 (*)
e	0.12	0.27	0.10	0.40 (*)	0.61	0 (*)
f	0.17	0.29	0.14	0.35	0.59	100

The most important feature arising from the flow maps is the strong hot-spotting in the flange region far from the nozzle. Apart for the a) case (the ‘reference’ one), where the used straight nozzles allows to avoid shell remelting, within almost all the other cases the velocity in the hot spot zone exceeds the threshold value. Only for the case f) the achieved values are within the threshold, as discussed later.

In the mould fed with the two-straight nozzles (Fig. 4), the highest velocity values are found in the region between the nozzles and the zones all along the mould height behind the flange center. The flow eddies towards the center appear to be weak, so the meniscus appears to be relatively stagnant, also close to the tips. On the other hand, the flow achieved in the other cases is strongly oriented from the nozzle to the opposite flange. The hot spot and the flow eddy towards the meniscus are both associated with relatively high steel velocity values.

When the nozzle geometry is designed with a lateral port driving the stream 15° downwards (case b) in Fig. 5), the velocity at hot spot increases harmfully up to 0.53 m/s. Also the maximum velocity at meniscus is high (0.24 m/s) even though within the threshold indicated for shell remelting.

Anyway, relevant velocity unevenness is found, when moving at meniscus from side to side. This is highlighted by the variation coefficient, the highest among all cases examined. It is relevant the velocity difference in between the opposite flange regions, with maximum intensity on the hot spot side, and with a broad stagnant zone in the region close to the nozzle.

As effect of making a bottom hole in such a nozzle layout (corresponding to case c), see Fig. 6), the velocity at hot spot is slightly lower (0.48 m/s), although still well above the threshold for shell remelting. On the contrary, the maximum velocity at meniscus is relatively much lower (0.17 m/s, –30% than in the previous case).

In order to further reduce the steel velocity at the nozzle ports, within the lay-out constraints, the lateral hole was enlarged up to a 50×70 mm elliptical shape, keeping the same bottom hole size. Consequently (Fig. 7), a further tendency to reduce velocity at hot spot was kept (0.38 m/s), again above the threshold value. But most of the braking effect on the flow coming from the lateral port was achieved at the meniscus, where the maximum velocity is approximately similar to that resulting from the use of two straight nozzles. This can be explained by the role of the elliptical port in favouring the steel spreading all throughout the mould. As a result, at the lateral wall opposite to that close to the nozzle, the stream has lost a significant part of the kinetic energy and the resulting eddy towards the meniscus is relatively weak.

The next steps were then aimed at further reducing the stream kinetic energy from the nozzle by acting on the throat geometry. A 50×60 mm elliptical section was then considered together with a 20 mm bottom hole. For what previously argued concerning flow behaviour at the elliptical port exit, at this stage it was chosen to design a round (50 mm diameter) lateral hole. In the first case (Fig. 8, case e) in Table 1), a better compromise between adequate meniscus feeding and hot spotting was achieved with respect to case d), although still accompanied with steel velocity at hot spot exceeding the critical threshold for slag emulsification (0.4 m/s).

Finally, within case f), a solution was achieved where all the defined indices were acceptable, although just below the threshold (0.29 m/s for the maximum velocity at the meniscus, 0.35 m/s for the velocity at the hot spot). The reliability of the configuration is also proved by the values of variation coefficient achieved. In fact, the value measured is the second in the cases ranking. But it should be remarked that the case where the best variation coefficient score is achieved (case d) in Table 1), on one hand should be skipped from the global ranking as refers to the Flow index value, on the other hand, has a lower value just because the meniscus is almost stagnant, so the evenness refers to a surface in practice expected to be ‘frozen’.

Concerning flow impingement on the solid shell, in general it was found for all configurations that the stream coming from the nozzle hits tangentially the walls (see Fig. 10), with a velocity of about 0.4 m/s. As this value can be currently reached in electromagnetic stirred moulds, it is expected no effect on shell remelting occurs.

Fig. 10.

Steel velocity (m/s) at walls. Top view for three cases (a, b, d in Table 1).

From the obtained results, it can be concluded that a feeding single-nozzle solution is expected not to affect as-cast beam blank quality. The defined indices request was satisfied by the multi-hole solution of the last simulated case, consisting in a two-holes (one lateral and one at nozzle bottom) geometry. Further change (e.g. in case of requested increased productivity) can be further managed acting on the hole size and shape according to the productivity needs. So, in general, the design strategy supported by the modelling technique used and the indices defined proved to be reliable in helping to find new layout solutions for beam blanks mould casting, together with the adequate Design of Experiment Strategy.

Model validation and solution check. The solution found was checked with a 1:1 scale water model of the beam blank format under investigation. According to the similarity theory, a full scale water model allows to reproduce in the model the same velocity field as in the real plant. Neglecting the solid shell presence in the mould and the effects on the liquid fluid flow of the convective motion due to the steel dependence on temperature (including fluid velocity generally one order of magnitude weaker with respect to the average liquid velocity in the mould), the main field forces are related to viscosity and gravity.

The relevant dimensionless numbers for this physical systems are the Froude number Fr = v²/gl and the Reynolds number Re = ρvl/μ, where g=acceleration of gravity. One can found that they are the same in both model and real plant provided water is used, being the ρ/μ ratio the same (approximately equal to 7) for steel and water.

The perspex water model is shown in Fig. 11. Feeding occurs by means of a pump to supply the proper water flow rate. Flow regulation occurs by means of a stopper rod in a reservoir, representing the tundish just above the mould. A perspex prototype of the ‘best nozzle’ was mounted for testing under the same operating conditions of the numerical model check.

Fig. 11.

Mould water model used for validation and solution check.

Velocity was measured 10 mm below meniscus in multiple directions with ultrasonic velocity system (Fig. 12). Focus was given on values at web and both flange sides. The data achieved were the average and the maximum velocity value. The average value is index of the overall flow intensity. The maximum is index of the peak intensity, that in case of waves formation can be harmful for the shell quality.

Fig. 12.

Flow Ultrasonic Velocity Profile sensors position.

Qualitatively, the flow features were in line with the pattern achieved with numerical modelling. Also the hot spot location at the flange opposite to the nozzle was in agreement with the calculation made (about 250 mm from meniscus).

On a quantitative point of view, the comparison among results is shown in Table 5. A reasonable agreement results among the two data sets. The maximum difference between values was on average 20% (lower values measured with the numerical model), probably due to the way of describing the free surface ‘blocking’ velocity upward components, and, as refers to the maximum velocity, to the formation of real waves in the water model with local flow reinforcement and resulting higher velocity peaks.

Table 5. Comparison of velocity values at meniscus (cm/s) in both modelling tests with nozzle best solution.

	water model -		CFD
	Ave	Max	Ave	Max
web	20	26	17	24
flange-nozzle side	4	8	3	7
flange-opposite side	13	16	11	13

This check with the nozzle prototype acted as a model validation, also supporting the solution identified to be used on plant.

4. Conclusions

Within the presented study, different nozzle geometries for beam blanks mould feeding were tested with numerical modelling based on a suitable Design Of Experiments strategy. The innovative step of the work consisted in finding new layout solutions able to allow simplified mono-slide gate casting.

The challenge was to face the risks related to such a feeding strategy of having excessive stream kinetic energy harmful for shell integrity and meniscus stability. To do this, multi-holes nozzle geometries were tested and the fluid-dynamics performance assessed based on suitable indices related to suitable flow conditions at meniscus, to avoid slag entrapment occurrence, and at walls, to avoid hot-spotting harmful for the solid shell integrity and in turn for the as-cast surface quality.

For the caster mould and the operating conditions under concern, a solution, based on a multi-hole geometry, was found satisfying the indices, and expected to fulfil the quality requests. It consisted of a nozzle with a 50 mm diameter throat, a 50 mm×60 mm elliptical lateral port inclined 25° downwards and a 20 mm-diameter bottom hole proved to be the most suitable satisfying all the indices defined. A water model check with such a nozzle prototype validated the model supporting the solution identified to be used on plant.

Appendix

Slag entrapment at meniscus was thoroughly investigated in literature due to its effect on steel quality. A comprehensive review was recently made by Hibbeler and Thomas (Fig. 13¹⁸⁾). At the steel slag interface Oeters¹³⁾ related the critical tangential slag velocity u_i,crit at the interface with density of slag ρ_s and metal ρ_m, the interface tension at the interfaces and the contact angle between phases α:   

$${\text{U}}_{1,\text{ crit}}={\left(\frac{8}{{\rho }_s}\right)}^{1/2}{[0.67\mathrm{\sigma }\text{g }({\rho }_m–{\rho }_s)\text{ cos}\alpha ]}^{1/4}$$(1)

Moreover, it was shown¹⁹⁾ a criterion relating tangential velocities of slag and steel V_1cr and V_2cr at the steel-slag interface, interface tension σ₁₂ and densities ρ_steel and ρ_slag (see also Fig. 14):   

$${\left({\text{V}}_{1\text{cr}}-{\text{V}}_{2\text{cr}}\right)}^2=({\rho }_2–{\rho }_1)\text{g }({\text{H}}_1/{\rho }_1+{\text{H}}_2/{\rho }_2)$$(2)

Combining (1) and (2), with slag density 2800 kg/m³, steel density 7200 kg/m³, interfacial tension = 1 N/m,¹³⁾ contact angle (limit value²⁰⁾)=80°, with a typical slag liquid pool of 1.5 cm depth²¹⁾ and a H₁/H₂ ratio equal to 5 for slag/steel interface,¹⁵⁾ bringing to a H₁ value reasonably comparable with a possible minimum immersion depth achievable in practice on plant operations, one obtains V_2cr=0.35 as the limit steel tangential velocity for onset of interface instability.

Fig. 13.

Schematic of relevant slag entrapment mechanisms.¹⁹⁾

Fig. 14.

Schematic of the physical system steel-slag.

References

• 1)   J. –E.  Lee,  T.-J.  Yeo,  H. H.  Oh,  J.-K.  Yoon and  U.-S.  Yoon: Metall. Meter. Trans. A, 11 (2000), 225.
• 2)   Y.-J.  Seok and  J.-K.  Yoon: Metall. Mater. Int., 8 (2002), 543.
• 3)   L. C.  Hibbeler,  S.  Koric,  K.  Xu,  B. G.  Thomas and  C.  Spangler: AISTech 2008, AIST, Warrendale, PA, (2008), 1.
• 4)   J.-K.  Yoon: ISIJ Int., 48 (2008), 879.
• 5)   Y. P.  Du,  J. W.  Wang,  R.  Shi and  X. C.  Cui: Acta Metall. Sin. (Engl. Lett.), 17 (2004), 705.
• 6)   J.–E.  Lee,  J.-K.  Yoon and  H.-N.  Han: ISIJ Int., 38 (1998), 132.
• 7)   W.  Chen,  Y.-Z.  Zhang,  L.-G.  Zhu,  C. J.  Zhang,  Y.  Chen,  B.-X.  Wang and  C.  Wang: Ironmaking Steelmaking, 39 (2012), 551.
• 8)   W.  Chen,  Y.-Z.  Zhang,  L.-G.  Zhu,  C. J.  Zhang,  Y.  Chen,  B.-X.  Wang and  C.  Wang: Ironmaking Steelmaking, 39 (2012), 560.
• 9)   F. M.  Najjar,  B. G.  Thomas and  D. E.  Hershey: Metall. Mater. Trans. B, 26 (1995), 735.
• 10)   A.  Panaras,  A.  Theodorakakos and  G.  Bergeles: Metall. Mater. Trans. B, 29 (1998), No. 5, 1117.
• 11)   K.  Saito,  H.  Nakato,  H.  Yamasaki,  N.  Bessho,  T.  Fujii,  T.  Nozaki and  Y.  Oguchi: Proc. of 9th PTD Conf., ISS-AIME, Warrendale, PA, (1990), 153.
• 12)   Y.  Natsume,  K.  Ohsasa and  T.  Narita: Mater. Trans., 43 (2002), 2228.
• 13)   H.  Kato and  T.  Umeda: Metall. Mater. Trans. A, 31 (2000), 225.
• 14)   L.  Zhang,  S.  Yang,  K.  Cai,  J.  Li,  X.  Wan and  B. G.  Thomas: Metall. Mater. Trans. B, 38 (2007), 63.
• 15)   F.  Oeters: Metallurgy of Steelmaking, Springer-Verlag, Berlin, (1995), 286.
• 16)   M.  Iguchi,  J.  Yoshida,  T.  Shimizu and  Y.  Mizuno: ISIJ Int., 40 (2000), 685.
• 17)  Ansys-Fluent User’s Guide, version 12.0, ed. by Fluent Inc., Canonsburg, PA, (2009), Chap. 7.
• 18)   N.  Kasai and  M.  Iguchi: ISIJ Int., 47 (2007), 982.
• 19)   L. C.  Hibbeler and  B. G.  Thomas: AISTech 2013, AIST, Warrendale, PA, (2013), 1215.
• 20)  Slag Atlas, 2nd ed., Stahl-Eisen Verlag, Düsseldorf, (1995).
• 21)   R.  Striedinger: Enhanced Steel Product Quality and Productivity, Through Improved Flux Performance in the Mould by Optimising the Multiphase Flow Conditions, European Commission, Directorate-General for Research and Innovation, Dictus Publishing, Luxembourg, (2012), 55.