materials Article
Comprehensive Numerical Simulation of Filling and Solidification of Steel Ingots Annalisa Pola *, Marcello Gelfi and Giovina Marina La Vecchia Department of Mechanical and Industrial Engineering, University of Brescia, via Branze 38, Brescia 25123, Italy;
[email protected] (M.G.);
[email protected] (G.M.L.V.) * Correspondence:
[email protected]; Tel.: +39-030-371-5576 Academic Editor: Richard Thackray Received: 4 July 2016; Accepted: 5 September 2016; Published: 9 September 2016
Abstract: In this paper, a complete three-dimensional numerical model of mold filling and solidification of steel ingots is presented. The risk of powder entrapment and defects formation during filling is analyzed in detail, demonstrating the importance of using a comprehensive geometry, with trumpet and runner, compared to conventional simplified models. By using a case study, it was shown that the simplified model significantly underestimates the defects sources, reducing the utility of simulations in supporting mold and process design. An experimental test was also performed on an instrumented mold and the measurements were compared to the calculation results. The good agreement between calculation and trial allowed validating the simulation. Keywords: steel ingot; filling simulation; solidification; defects formation
1. Introduction Notwithstanding the percentage of steel semi-products obtained via ingot casting is decreased during the last years, this method is still fundamental for specific low-alloy steel grades and for special forging applications, where components of large size are needed, such as mill rolls, turbine rotors, shafts for power plants, etc. [1–4]. Nowadays, the production of crude steel in the world reaches about 60 million tons [5]. Mold filling of heavy ingot can be performed in two ways: top pouring and bottom pouring, also called uphill teeming. In the top pouring, the molten stream is more exposed to air, suffering from reoxidation problems. As the pouring stream impinges on the melt surface inside the mold, it carries reoxidation products and mold powder, floating on it, back into the bulk, resulting in macro-inclusions. Moreover, during filling, metal splash adheres to the mold walls and produces surface defects on the ingot skin, which subsequently needs surface conditioning [6]. This makes the top pouring method not suitable for high-quality steels, which prefer bottom pouring [7,8]. In bottom pouring, the liquid steel flows from the ladle down to the trumpet and, passing through the horizontal refractory runner, it enters the nozzle or ingate upwards, reducing the exposure to air, the entrapment of mold powder and the occurrence of splashing. The bottom pouring needs a controlled velocity during filling in order to avoid turbulences and, consequently, powder entrapment or reoxidation defects [7]. The mold shape (round, square or multi-fluted cross section) also contributes to the casting quality. It is chosen according to the expected quality grade and, above all, to the product shape to be forged. Hence, in order to obtain sound ingots, mold shape, runners’ cross-section and length, as well as nozzle diameter and height have to be properly designed. Typically, the design is the result of the factory know-how but, in last decades, numerical simulation has been progressively applied as a useful tool for the optimization of mold shape and process parameters, to further improve the ingot quality.
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Different authors focused their investigations preferentially on the solidification phase of steel ingots production, mainly to predict defects formation [9]. Other authors, studying the solidification phase, also took into account the fluid field due to thermal buoyancy or melt superheat [10–13]. A more limited number of papers deal with the filling phase. Due to the more time consuming calculations, typically, the used geometrical models are simplified. In fact, neither the column nor the horizontal runner is normally considered, and a boundary condition of velocity at the whole cross section of the bottom inlet is conventionally fixed. Kermanpur et al. [14], for example, showed the effects of casting parameters, including the pouring rate, but focusing the attention on the solidification of the steel ingot. They found that pouring the melt under a constant rate in a mold with a low slenderness ratio and using a proper design for the hot top improve the casting quality. Tkadleˇcková et al. [15] investigated the effect of total filling time on porosity formation, showing that a decrease of the casting temperature together with longer filling time reduce the porosity level. Tkadleˇcková et al. [16] also showed a comparison between simulation and real casting. Zhang et al. [17], by using a simulation, determined two dimensionless factors able to evaluate the effect of casting parameters on the shrinkage porosity. Some authors evaluated the effect of the fluid flow characteristics as a function of the entrance nozzle, like Eriksson et al. [18] who determined, for their case study, that a reduced risk of slag entrapment can be obtained using a 25 degree angle of the inlet nozzle. Marx et al. [19] assessed the influence of the feeding system design and the filling rate on ingot quality, also implementing user defined functions for agglomeration and trapping of inclusions at the free surface. All these simplifications, even though valid, do not allow properly considering the real flow of the metal entering the mold. Aside by the teeming rate, in fact, the flow is strongly influenced also by the height of the column, the geometry of the horizontal runner and the entrance nozzle. To the authors’ knowledge, there is only one paper taking into account the whole geometry including trumpet, runner channel and mold. In that paper, Tan et al. [20] made a first attempt of comparing the results of a complete and reduced geometry simulation, but they focused their attention only on the very early stage of the filling and without considering the heat transfer and solidification. The aim of this paper is to show the importance of simulating the complete mold geometry to appropriately predict the risk of defects formation, especially those due to non-metallic inclusions. As stated by Zigalo [21], in fact, during mold filling by bottom pouring technique inclusions can be formed because of the entrapment of mold flux. In particular, the emphasis of this analysis is not only on the initial stage but also on the entire mold filling, taking into account the thermodynamic aspects. To validate the numerical model, the results of the simulations were compared with the data collected during an experimental test performed on the industrial mold properly instrumented. 2. Experimental Procedure The ingot casting test was carried out on a cylindrical four-mold system for the production of 19 ton round section ingots. The mold consists of four parts made in hematite cast iron: the upper and bottom plates, the column and the ingot mold. The height of the ingot mold with the hot top (riser) is 5 m and the diameter is 840 mm; the height of the column is 6 m. An insulating ring, 33 mm thick and 350 mm high, was placed at the top of each mold. Pouring basin (trumpet) and running system were built up by using refractory bricks connected together. The diameter of the trumpet is 90 mm and the diameter of runners is 60 mm. The diverging entrance nozzle has a length of 260 mm and a diameter increasing from 60 to 80 mm. Calcium carbonate was used to fill the gap between the refractory bricks and the column and the plates. Bags of mold powder were located about 80 mm from the base of the mold. When the molten steel reached the riser, additional isolating powder was distributed on the metal free surface. 42CrMo4 steel grade was poured at 1560 ◦ C with a time dependent flow rate, as explained below.
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42CrMo4 steel grade was poured at 1560 °C with a time dependent flow rate, as 3 of 13 explained below.steel grade was poured at 1560 °C with a time dependent flow rate, as 42CrMo4 Two K-type thermocouples, with a recording rate of 1 per 5 min, were placed on the surface of explained below. Two K-type thermocouples, with a recording rate of 1 per 5 min, were placed on the surface of the the cast iron mold: the first 1430 mm the toprate andofthe second 1400 mm fromon thethe bottom, Two K-type thermocouples, withfrom a recording 1 per 5 min, were placed surfaceasof cast shown iron mold: the first 1430 mm fromprofile the top andmold the second 1400 mm from the bottom, in in Figure 1. The temperature of the in these two points was recorded for 4as h. shown the cast iron mold: the first 1430 mm from top and the second 1400 mm from the bottom, as
Figure 1. The temperature profile of the mold in these two points was recorded for 4 h. shown in Figure 1. The temperature profile of the mold in these two points was recorded for 4 h.
Figure 1. Four-mold system equipped with thermocouple. Figure 1. Four-mold system equipped with thermocouple.
Figure Four-mold system equipped with was thermocouple. The entire test, from the 1.mold filling to the ingot stripping, also monitored by means of a thermo-graphic Trotec IC120filling (Trotec, Germany), whose images where analyzed The entire camera test, from the mold to Heinsberg, the ingot stripping, was also monitored by means of a The entire test, from the mold filling toTrotec). the ingot stripping, was alsoimages monitored means of a by IC-Report DuoVision Software (1.08.16S, thermo-graphic camera Trotec IC120 (Trotec, Heinsberg, Germany), whose whereby analyzed During the test, no other ingots were cast in the area around the four-mold system toanalyzed avoid thermo-graphic camera Trotec IC120 (Trotec, Heinsberg, Germany), whose images where by by IC-Report DuoVision Software (1.08.16S, Trotec). radiation effects, which can (1.08.16S, modify the temperature profile of the four-mold mold andsystem ingots tounder During the test, no other ingots were cast in the area around avoid IC-Report DuoVision Software Trotec). investigation. However, self-radiation between column and molds wellmold as between the molds radiationthe effects, which caningots modify the cast temperature profile ofasthe and ingots under During test, no other were in the area around the four-mold system to avoid themselves is present. investigation. However, self-radiation between column and molds as well as between the molds
radiation effects, which can modify the temperature profile of the mold and ingots under investigation. themselves is present. However, self-radiation 3. Simulation Model between column and molds as well as between the molds themselves is present. 3. Simulation Model
A three Model dimensional model of the complete four-mold system was created, as shown in Figure 2a. 3. Simulation Considering the double symmetry, to reduce the calculation time, only as one moldinwas finally A three dimensional model of the complete four-mold system was created, shown Figure 2a. A three dimensional model of condition the complete four-mold system wasascreated, asFigure shown2b. in Figure 2a. considered, applying a boundary of symmetry on two planes, shown in Considering the double symmetry, to reduce the calculation time, only one mold was finally considered, applying a boundary condition of symmetry on two planes, as shown in Figure 2b.
Figure 2. Geometry of the four-mold gating system (a); and used model (b).
Figure 2. Geometry of the four-mold gating system (a); and used model (b). Figure 2. Geometry of the four-mold gating system (a); and used model (b).
The simulation of mold filling and casting solidification was performed by mean of the Considering the double symmetry, to reduce the Paris, calculation time, onlyonone mold was finally commercial software Procast (2015.0, Group, France), based finite element The simulation of mold® filling andESI casting solidification was performed by mean of the considered, applying a boundary condition of symmetry on two planes, as shown in Figure 2b. ® (2015.0, method (FEM).software A mesh Procast of 2,812,180 and tetrahedral elements the comprehensive model was commercial ESI Group, Paris, for France), based on finite element The simulation of mesh mold filling andunstructured casting solidification wasa performed by mean of model theenables commercial created. The software uses a FEM mesh with full-layer option, which method (FEM). A of 2,812,180 and tetrahedral elements for the comprehensive was
® (2015.0, ESI Group, Paris, France), based on finite element method (FEM). A mesh software Procast created. The software uses a FEM unstructured mesh with a full-layer option, which enables of 2,812,180 and tetrahedral elements for the comprehensive model was created. The software uses a FEM unstructured mesh with a full-layer option, which enables densification of nodes and tetra elements even if the surface mesh at this location has no interior nodes connecting the boundary edges. In addition, to increase the detail of flow solution, boundary layer option was applied. This is a very
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thin region of stagnated or even zero velocity flow that develops due to frictional effects with the wall. According to this accuracy in mesh definition, the results of this paper are mesh independent, as boundary layer elements allows handling wall stick-slip phenomena without any simplification for velocity conditions. A simplified model, without the running system, was also created just eliminating the entire running system. To calculate the fluid-dynamic field, the transport equations used in the simulation are the following: -
Energy equation ∂H ∂H ρ + ρui −∇ ∂t ∂xi
-
-
µ k+ T σT
∇T − q = 0
(1)
where $ is the temperature dependent density, H is the temperature dependent enthalpy, t is the time, ui is the component of the velocity, k is the temperature dependent conductivity, µT is the eddy viscosity, q is the spatial varying volumetric heat source, σT Prandtl number, and T is the temperature. Continuity equation ∂ρ ∂ρi =0 (2) + ∂t xi Momentum equation ∂u ∂u ∂ ρ i + ρu j i + ∂t ∂x j ∂x j
-
" pδij
∂u µ + µT i ∂x j
!#
= ρgi −
µ u K i
(3)
where uj is the component of the velocity, p is the pressure, δij is the Kronecker delta, µ is the viscosity, gi is the gravity acceleration, and K is the permeability. Turbulent kinetic energy equation: ∂ ρk ∂t
∂ ρk
+ uj
∂x j
∂ − ∂x j
µT ∂k σT ∂x j
!
= µT G − ρ
(4)
where k = 1/2 u2 + v2 + w2 ; u, v and w are the velocity components; ε is the turbulence dissipation rate; and G = ∂ui /∂x j + ∂u j /∂xi ∂ui /∂x j is the turbulence generation rate. Concerning the mushy zone, it was modeled using the dimensionless Niyama approach reported by Carlson et al. [22]: s . −1/3 ∆Pcr ∗ NY = Cλ T NY (5) µl β∆T f ˙ 0.5 is the Niyama thermal where Cλ is the taken material constant, T˙ is the cooling rate, NY = G·(T) parameter, G is temperature gradient, ∆P is the pressure drop across the mushy zone, µl is the liquid dynamic viscosity, and β = ($s − $l )/$l is the total solidification shrinkage, function of the liquid and solid densities. Flow solution at free surface is solved by AMG solver (Algebraic Multi-Grid), especially modified with EBFEM solver (Edge-Based Finite Element Method) [23]. The thermal buoyancy effect is considered through the variation of steel density and solid fraction as a function of temperature, in the fluid-dynamics calculations. To solve the equations, material data, initial and boundary conditions had to be properly defined. In particular, five different materials are present in the model: hematite cast iron, 42CrMo4 steel, refractory bricks, calcium carbonate and insulator. The temperature dependent thermophysical properties of steel and cast iron (conductivity, density, specific heat or enthalpy) are shown in
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Database®
Figure 3. They were calculated by means of Computherm (Pan Iron 5.0) available in available in Procast, as a function of the measured chemical composition and using the Procast, as a function of the measured chemical composition and using the “Back Diffusion” model. “Back Diffusion” model. The properties of insulating material and refractory were determined by The of insulating and which refractory determined by the data supplied theproperties data supplied by thematerial producers, are were in good agreement with those foundbyinthe producers, which are in good agreement with those found in literature [12,13]. literature [12,13].
Figure 3. Thermophysical properties of mold and steel as a function of temperature. Figure 3. Thermophysical properties of mold and steel as a function of temperature.
The steel was poured at 1560 °C. All the other materials were assumed to be initially at room ◦ C. All the other materials were assumed to be initially at room The steel was poured at 1560 temperature. External ambient pressure was also considered. temperature. External pressure alsoheat considered. As known, the ambient definition of the was proper transfer coefficient at the interface between As known, the definition of the proper heat transfer coefficient at the interface between different domains is a crucial parameter to achieve reliable results in solidification calculation. The different is between a crucialmold parameter to achieve reliable resultswas in set solidification interfacedomains coefficient and refractory/insulating materials at 100 W·m−2calculation. ·K−1. The 2 · K−1 . −2·K −1− The interface between coefficient between and refractory/insulating materials wasatset at W·m 100 W ·m coefficient molten steelmold and refractory/insulating materials was fixed 200 . The The coefficient molten and refractory/insulating materials waswas fixed at 200 W·account m−2 · K−1 . effect of gapbetween formation at thesteel steel/mold interface due to steel shrinkage taken into −2 −1 using a temperature dependent between and 500 W·mwas ·K taken . All ofinto theaccount used The effect of gap formation at the coefficient steel/moldranging interface due to150 steel shrinkage coefficients were estimated in agreement literature [9,14,24]. using a temperature dependent coefficientwith ranging between 150 and 500 W·m−2 ·K−1 . All of the used A boundary conditioninofagreement convectionwith withliterature air was defined for the mold, considering the values coefficients were estimated [9,14,24]. proposed in [9]. condition Both the emissivity and the increase of defined air temperature aroundconsidering the mold with A boundary of convection with air was for the mold, thetime, values due to the solidifying steel, were taken account. of The heat transfer also assessed, proposed in [9]. Both the emissivity and into the increase airradiation temperature around was the mold with time, considering the shadowing effecttaken (or view in The orderradiation to calculate the interaction the due to the solidifying steel, were intofactors), account. heat transfer was between also assessed, components (molds and molds and column) as well as with the environment. Hence, to include the considering the shadowing effect (or view factors), in order to calculate the interaction between the environment into the model, an artificial “enclosure” was defined, which surrounds the mold and components (molds and molds and column) as well as with the environment. Hence, to include the reproduces the effect of the environment. environment into the model, an artificial “enclosure” was defined, which surrounds the mold and The insulating effect of the mold powder, applied on the free surface of the incoming steel, was reproduces the effect of the environment. considered by reducing the heat exchange coefficient between steel and air to 3 W/m2/K and by The insulating effect of the mold powder, applied on the free surface of the incoming steel, reducing also the emissivity. was considered by reducing the heat exchange coefficient between steel and air to 3 W/m2 /K and by As shown in Figure 4, a time dependent teeming flow rate was applied according to the reducing alsoused the emissivity. procedure in the steel plant for the experimental test. This boundary condition was applied at shown Figure 4, a time dependent teeming flowofrate according to the procedure theAs top of thein trumpet, considering the nozzle diameter the was ladle.applied The reported values of the flow used in the steel plant for the experimental test. This boundary condition was applied at the top ofofthe rate applied at the trumpet are a quarter of the total amount, because of the used simplification trumpet, double considering symmetry. the nozzle diameter of the ladle. The reported values of the flow rate applied at the trumpet are a quarter of the total amount, because of the used simplification of double symmetry.
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Figure 4. Teeming flow rate vs. time recorded during experiment and simulated.
Figure 4. Teeming flow rate vs. time recorded during experiment and simulated.
4. Results and Discussion
4. Results and Discussion Figure 4. Teeming flow rate vs. time recorded during experiment and simulated. As shown in Figure 5, during the first seconds the pouring phase is performed with a high flow
As shown in Figure during the first seconds the pouring performed with ainhigh rate to guarantee the5,complete opening of the nozzle and tophase avoidissteel solidification the flow 4. Results and Discussion rate to guarantee the complete opening of the nozzle and to avoid steel solidification in the refractory refractory channels. Subsequently, in about 70 s, the flow rate is reduced down to 1400 kg/min. As shown in Figure 5, during the first seconds the pouring phase is performed with a high flow channels. Subsequently, about 70 early s, thestage flowofrate is reduced down to 1400 kg/min. Because of Because of this teeminginrate, in the the process, the steel enters the mold at very high rate to guarantee the complete opening of the nozzle and to avoid steel solidification in the velocity, increasing theearly risk of air and powder entrapment [7].enters In thisthe condition, without the this teeming rate, in the stage of the process, the steel mold atand very high velocity, refractory channels. Subsequently, in about 70 s, the flow rate is reduced down to 1400 kg/min. presence of insulating or powder entrapment bags laid on the mold base,condition, the steel spout reaches a height of increasing the of air seal and [7]. In this the high presence Because of risk this teeming rate,powder in the early stage of the process, the steel entersand the without mold at very about 630 mm before falling back under the gravity (Figure 5a). It can be additionally seen that the of insulating seal or powder the mold base, the spout reaches a without height of velocity, increasing the riskbags of airlaid andon powder entrapment [7].steel In this condition, and theabout metal spout is not centered but shifted of about 225 mm from the center and oppositely to the 630 mm before falling back under the gravity (Figure 5a). It can be additionally seen that the presence of insulating seal or powder bags laid on the mold base, the steel spout reaches a height ofmetal column (Figure 5b), as a consequence of the entrance nozzle geometry and of the abrupt variation of 630centered mm before back gravity 5a).center It can be additionally seen spoutabout is not butfalling shifted ofunder aboutthe225 mm (Figure from the and oppositely to that the the column flow direction at the elbow, i.e., from the horizontal runner to the vertical nozzle, whose connection metal spout is not centeredof but shifted of about 225geometry mm from and the center and oppositely to the (Figure 5b), as a consequence the entrance nozzle of the abrupt variation of flow is not properly designed. column (Figure 5b),i.e., as a from consequence of the entrance nozzle geometry and of the abrupt variation ofis not direction at the elbow, the horizontal runner to the vertical nozzle, whose connection The knowledge of these data allows defining the height where powder bags can be suspended flow designed. direction at the elbow, i.e., from the horizontal runner to the vertical nozzle, whose connection properly to avoid premature release of the insulating powder and subsequent entrapment. In fact, if the is not properly designed. The knowledge of when these adata allows the height where bags can bethe suspended to powder is released small pool defining of liquid metal has not beenpowder already formed and metal The knowledge of these data allows defining the height where powder bags can be suspended does not occupy completely the inlet cross section (like in Figure 5a), the molten steel can easily avoid premature release of the insulating powder and subsequent entrapment. In fact, if the powder is to avoid premature release of the insulating powder and subsequent entrapment. In fact, if the engulf the afluxes, creating defectsmetal in the ingot. Afteralready less than 30 s, aand pool ofmetal liquiddoes is formed released when small pool ofaliquid not metal been occupy powder is released when small pool ofhas liquid has not formed been already the formed and thenot metal inducing a dumping effect on the incoming steel. The free surface is characterized by a light completely the inlet cross section (like in Figure 5a), the molten steel can easily engulf the fluxes, creating does not occupy completely the inlet cross section (like in Figure 5a), the molten steel can easily fluctuating effect, as detectable in Figure 5c, which stops when the pool reaches a level of about defects in the less defects than 30ins, the a pool of liquid is formed on the engulf theingot. fluxes,After creating ingot. After less than 30inducing s, a poolaofdumping liquid is effect formed 250 mm and an almost flat free surface is settled. inducing dumping effect on the incoming by steel. The fluctuating free surfaceeffect, is characterized by in a Figure light 5c, incoming steel.a The free surface is characterized a light as detectable For comparison, in Figure 5d the result of the conventional simplified simulation is shown, i.e., fluctuating effect, as detectable Figure 5c, which stopsand when poolflat reaches a level is ofsettled. about whichwhere stops the when the pool reaches ainlevel of about 250 mm an the almost free surface velocity is imposed at the bottom section of the entrance nozzle to minimize the 250 mm and an almost flat free surface is settled. For comparison, in Figurethe5drunning the result of the conventional simplified is shown, calculation time, neglecting system. It can be clearly observed thatsimulation the nozzle cross For comparison, in Figure 5d the result of the conventional simplified simulation is shown, i.e., i.e., where the velocity is imposed at the bottom section of the entrance nozzle to minimize section is completely filled by the liquid steel, which enters the mold with a mushroom shape and the where the velocity is imposed at the bottom section of the entrance nozzle to minimize the calculation neglecting running system. can be clearly observed that the nozzle section fills thetime, base of the cavitythe without big spout. In It this case, no risk of premature release of the cross powder calculation time, neglecting the running system. It can be clearly observed that the nozzle cross and subsequent slag entrapment can be predicted. is completely filled by the liquid steel, which enters the mold with a mushroom shape and fills the section is completely filled by the liquid steel, which enters the mold with a mushroom shape and base fills of the cavity without big spout. In this case, no risk of premature release of the powder and the base of the cavity without big spout. In this case, no risk of premature release of the powder subsequent slag entrapment can becan predicted. and subsequent slag entrapment be predicted.
Figure 5. Entrance of steel spout in the case of complete mold with entire running system (a–c); and of simplified model (d). Figure 5. Entrance of steel spout in the case of complete mold with entire running system (a–c); and
Figure 5. Entrance of steel spout in the case of complete mold with entire running system (a–c); and of of simplified model (d). simplified model (d).
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In Figure Figure 6, 6, the the bottom bottom view view of of the the liquid liquid steel steel entering entering the the mold mold from from the the nozzle nozzle is is shown shown for for In In Figure 6, the bottom view of the liquid steel entering the mold from the nozzle is shown for both the comprehensive and simplified model. For the complete mold, it can be seen that the jet both the comprehensive and simplified model. For the complete mold, it can be seen that the jet both the comprehensive and simplified model. For the complete mold, it can be seen that the jet occupies less less than than 55% 55% of of the the nozzle nozzle cross cross section, section, inducing inducing an an increase increase of of velocity velocity compared compared to to the the occupies occupies less than 55% of the nozzle cross section, inducing an increase of velocity compared to the simplified case. The corresponding Reynolds number, calculated at the nozzle just before the exit, simplified case. The corresponding Reynolds number, calculated at the nozzle just before the exit, simplified case. The corresponding Reynolds number, calculated at the nozzle just before the exit, resulted ininthe order of 15,000 and 250,000 for the simplified and comprehensive models, respectively, resulted the order of 15,000 and 250,000 for the simplified and comprehensive models, resulted in the order of 15,000 and 250,000 for the simplified and comprehensive models, demonstrating the presence of turbulentofflow, as statedflow, in [25]. respectively, demonstrating thea presence a turbulent as stated in [25]. respectively, demonstrating the presence of a turbulent flow, as stated in [25].
Figure 6. Bottom view of the steel entering the mold in case of: complete model (a,b); and simplified Figure Figure 6. 6. Bottom Bottom view view of of the the steel steel entering entering the the mold mold in in case case of: of: complete complete model model (a,b); (a,b); and and simplified simplified model (c,d). model model (c,d). (c,d).
Figure 7 reports the filling sequence in terms of velocity velocity on the the middle longitudinal longitudinal section for Figure Figure 77 reports reports the the filling filling sequence sequence in in terms terms of of velocity on on the middle middle longitudinal section section for for both the comprehensive and the simplified models. In the case of the complete thestream main both thethe simplified models. In the of theofcomplete mold, mold, the main both the thecomprehensive comprehensiveand and simplified models. In case the case the complete mold, the main stream remains shifted oppositely to theduring column entire filling, an asymmetric remains shifted oppositely to the column theduring entire the filling, creating ancreating asymmetric descending stream remains shifted oppositely to the column during the entire filling, creating an asymmetric descending can the pull down theeasily, slag more easily, to the the case of thesimulation, simplified stream that stream can pullthat down more contrary to contrary the case of descending stream that can pullslag down the slag more easily, contrary to the simplified case of the simplified simulation, where the main stream is almost centered. An eccentrically located flow can create a where the main stream is almost centered. An eccentrically flow can createflow a slag-free zone, simulation, where the main stream is almost centered. Anlocated eccentrically located can create a slag-free zone,eye, the so-called close to the which can affect the slag the particles the so-called to theeye, wall, which canwall, affect the detachment of detachment slag particlesof main slag-free zone, theclose so-called eye, close to the wall, which can affect the detachment offrom slag particles from the main phase,inasladle it happens ladle stirring [26]. slag as itslag happens stirringin [26]. fromphase, the main slag phase, as it happens in ladle stirring [26].
Figure 7. Filling sequence in terms of velocity distribution for both the: complete model (left); and Figure 7. Filling sequence in terms of velocity distribution for both the: complete model (left); and Figure 7. model Filling(right). sequence in terms of velocity distribution for both the: complete model (left); simplified simplified model (right). and simplified model (right).
Additionally, the complete model is characterized by a higher velocity of the jet, related to the Additionally,the thecomplete completemodel modelisischaracterized characterized a higher velocity of the jet, related to not the Additionally, byby a also higher velocity of the jet, to the not fully filled cross section of the runner, which induces a higher velocity of related the metal on the not fully filled cross section of the runner, which induces also a higher velocity of the metal on the fullysurface, filled cross sectionthe of the which induces also a higher of the metal on the free free increasing riskrunner, of powder entrapment. This can be velocity better seen in Figure 8, where a free surface, increasing the risk of powder entrapment. This can be better seen in Figure 8, where surface, increasing riskcentral of powder This can better seen in Figure 8, where a plotthe ofa plot of the velocity the at the pointentrapment. of the nozzle exit as be a function of time is shown for both plotvelocity of the velocity at thepoint central point of the nozzle exit as aof function of timefor is shown for both the the at the central of the nozzle as a function time is both the simplified simplified and complete simulation. For theexit comprehensive model, theshown velocity results higher and simplified and complete simulation. For the comprehensive model, the velocity results higher and and complete simulation. due For to thethe comprehensive model, the velocity results higher and with a larger with a larger fluctuation, stronger turbulence. with a larger fluctuation, due to the stronger turbulence. fluctuation, duethe to the turbulence. To reduce riskstronger of powder entrapment it is fundamental to decrease the deformation of the To reduce reduce the the risk risk of of powder powder entrapment entrapment it is fundamental fundamental to to decrease decrease the the deformation deformation of of the the To free surface, i.e., the jet velocity. This result can itbeisachieved by properly design the running system, free surface, i.e., the jet velocity. This result can be achieved by properly design the running system, freeparticular surface, i.e., jet velocity. This resultauthors can be achieved by properly design the running system, in the the nozzle angle. Different have already shown the advantages of using a in particular the nozzle angle. Different authors have already shown the advantages of using a in particular the nozzle angle. Different authors have already shown the advantages of using divergent nozzle, also with the addition of a swirl [18,20,27,28]. In this case, the filling should bea divergent nozzle, also with the addition of a swirl [18,20,27,28]. In this case, the filling should be divergentimproved nozzle, also with the addition of a swirl [18,20,27,28]. In this case,absorber the filling should strongly by increasing the inlet nozzle angle and by adding a shock at the end be of strongly improved improved by by increasing increasing the the inlet inlet nozzle nozzle angle angle and and by by adding adding aa shock shock absorber absorber at at the the end end of of strongly the horizontal channel. the horizontal horizontal channel. channel. the
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Figure 8. Comparison between the velocities recorded in the middle point of the nozzle exit for the Figure 8. Comparison between the velocities recorded in the middle point of the nozzle exit for the simplified and comprehensive models. simplified comprehensive models. Figure 8.and Comparison between the velocities recorded in the middle point of the nozzle exit for the simplified and comprehensive models. During mold filling, the powder covering the liquid steel inside the mold forms a slag layer that During mold filling, the powder the liquid steel inside thepowder–metal mold forms a interface slag layercan that floats on top of the rising molten steelcovering [7]. An excessive turbulence at the During mold filling, the powder covering the liquid steel inside the mold forms a slag layer that floats on top of the rising molten steel [7]. An excessive turbulence at the powder–metal interface cause reoxidation and exogenous inclusions. To evaluate the tendency for powder entrapment, the on top of the steel inclusions. [7]. to Anthe excessive turbulence the powder–metal interface canfloats cause reoxidation and molten exogenous To evaluate the at tendency forErikson powder entrapment, Weber number wasrising calculated according modified equation reported by et al. [18]:can cause reoxidation and exogenous inclusions. To evaluate the tendency for powder entrapment, the Weber number was calculated according to the modified equation reported by Erikson et al.the [18]: ∙ ρ equation reported by Erikson et al. [18]: Weber number was calculated according to the modified = (6) u2 ·ρsteel We = rγ steel (6) ρ ∙ ρ− ρ = (6) γg ρsteel − ρslag
γ ρ
−ρ
where usteel is the tangential steel velocity on the free surface of the molten steel; ρsteel and ρslag are the density and of the powder, respectively; is the gravity; and γ issteel; the slag-steel where usteelofisthe thesteel tangential steel velocity on the free gsurface of the molten $steel and interfacial $slag are the where usteel is the tangential steel velocity on the free surface of the molten steel; ρsteel and ρslag are the tension. According to the finding of Xiao et al. [29], no problems occur when Weber number is lower density of the steel and of the powder, respectively; g is the gravity; and γ is the slag-steel interfacial density of the steel and of the powder, respectively; g is the gravity; and γ is the slag-steel interfacial than 12.3. tension. According to the finding of Xiao et al. [29], no problems occur when Weber number is lower tension. the finding of liquid Xiao etsteel al. [29], problems when Weber lower TheAccording tangentialtovelocity of the freenosurface wasoccur determined at 70,number 930 andis1810 s, than 12.3. than 12.3. which correspond to the first variations of flow rate (Figure 3). Additionally, two intermediate times The tangential velocity ofofthe liquid steel free surface was wasdetermined determinedatat70,70, 930 and 1810 s, The velocity the steel high free surface 930 andthe 1810 s, werecorrespond alsotangential analyzed, i.e.,first 24 and 480liquid s, because velocity3).values were observed during first which to the variations of flow rate (Figure Additionally, two intermediate times which correspond to the firstexample, variations of flow9,rate (Figure 3). Additionally, two intermediate times stage of mold filling. As in Figure the tangential velocity on the free surface 24 and were also analyzed, i.e.,i.e., 24 an and 480480 s, because high velocity values were observed during theatthe first stage were also analyzed, 24 and s, because high velocity values were observed during first 930 s are reported, using different scales for the two models to better visualize the predicted values. of stage mold of filling. As an example, in Figure 9, the tangential velocity on the free surface at 24 and 930 s moldthat filling. Assimplified an example, in Figure 9, the tangential velocity free surface 24 and It is evident in the model the velocity of the steel on the on freethe surface resultsatstrongly are930 reported, using different scales for the two models to better visualize the predicted values. It is s are reported, using different scales for the two models to better visualize the predicted values. lower than in the case of the complete simulation. evident that inthat the simplified modelmodel the velocity of theofsteel on the results strongly lower It is evident in the simplified the velocity the steel onfree the surface free surface results strongly than in the case of the simulation. lower than in the casecomplete of the complete simulation.
Figure 9. Tangential velocity at 24 and 930 s for the: complete model (left); and simplified model (right). Figure 9. Tangential velocity at 24 and 930 s for the: complete model (left); and simplified Figure 9. Tangential velocity at 24 and 930 s for the: complete model (left); and simplified model (right). model (right).
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maximum detected velocity in the above mentioned times are reported.
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Table 1. Steel velocity on the in free surface a function of time. In Table 1, the maximum detected velocity the aboveasmentioned times are reported. Time (s) Time24(s) 2470 480 70 930 480 1810 930 1810
Table Steel velocityModel on the free surface as a for function of time. Model (m/s) vMAX for 1. the Complete (m/s) vMAX the Simplified
1.73 Model (m/s) vMAX for the Complete 1.18 1.73 0.76 1.18 0.55 0.76 0.27 0.55 0.27
0.35 vMAX for the Simplified Model (m/s) 0.320.35 0.250.32 0.200.25 0.140.20 0.14
For estimating the Weber number, the powder density was set at 2500 kg/m3 , according to the Fordata estimating the Weber number, the powder density was set at in 2500 kg/m3, according the literature [18]. Four interfacial tension values were considered, agreement with thetoranges literature data [18]. Four interfacial tension values were considered, in agreement with the ranges found in literature: 0.5 N/m [18], 1.0 N/m [30], 1.5 N/m [31] and 2 N/m [18]. found in literature: 0.5 N/m [18], 1.0 N/m [30], 1.5 N/m [31] and 2 N/m [18]. In Figure 10, the determined Weber number as a function of the velocity between the steel and the In Figure 10, the determined Weber number as a function of the velocity between the steel and slag for different interfacial tensions in shown. It can be seen that, in the case of the simplified model, the slag for different interfacial tensions in shown. It can be seen that, in the case of the simplified the Weber number never exceeds the limit, independently from the considered velocity and interfacial model, the Weber number never exceeds the limit, independently from the considered velocity and tension, showing that no risk of powder entrapment can be expected. interfacial tension, showing that no risk of powder entrapment can be expected. OnOn thethe contrary, theWeber Webernumber numberis is higher very close to 12.3 contrary,for forthe thecomplete complete model, model, the higher or or very close to 12.3 for afor a wide range of velocities. Hence, the possibility of entrapping powder can be easily predicted. wide range of velocities. Hence, the possibility of entrapping powder can be easily predicted. Considering the that since since 480 480ssthe therisk riskofofdefect defectformation formation Considering thevalues valuesininTable Table1,1,ititcan canbe be assessed assessed that is is extremely high. extremely high. AtAt higher teeming time, when the the mold is filled enough to reduce the velocity on theonfree higher teeming time, when mold is filled enough to reduce the velocity thesurface, free thesurface, risk is strongly it is and disappears over 930 s, corresponding to about one third of the the risk isreduced strongly and reduced it is disappears over 930 s, corresponding to about one third mold filling. of the mold filling.
Figure 10. Variation of the Weber number as a function of the steel-powder interfacial tension. Figure 10. Variation of the Weber number as a function of the steel-powder interfacial tension.
In the last steps, the flow rate is progressively reduced to 300 kg/min. Thus, considering the low In the last steps, the flow rate is progressively reduced to 300 kg/min. Thus, considering the velocity and the very high metallostatic head into the mold, the final phases of the filling are not low velocity and the veryentrapment. high metallostatic head into the mold, the final phases of the filling are not dangerous for powder dangerous for powder entrapment. Almost at the end of the filling, when the metal reaches the hot top, a covering powder is Almost at the end the filling, whensteel. the This metal reaches hot top, a covering powder 3 and, is additionally applied to of insulate the molten powder hasthe a density of about 250 kg/m 3 and, additionally applied to insulate the molten steel. This powder has a density of about 250 kg/m because of the low velocity of the free surface, no risk of entrapment seems to exist. becauseTo ofavoid the low velocity the free surface, no risk of entrapment exist. erosion andof subsequent macro inclusions in the metal seems stream,tothe runners have to be To avoid subsequent inclusions in the metalminimizing stream, theturbulences runners have designed in erosion order toand keep the shearmacro velocity lower than 1 m/s, [7]. to be Considering designed inthe order to keep the shear velocity lower than 1 m/s, minimizing turbulences whole running system, it can be observed that the shear velocity of the molten steel[7]. flowing through the refractory this limit, closed toofthe Considering the whole running channels system, is it higher can be than observed that particularly the shear velocity thecentral molten distributor brick (Figure 11). This can allow the prediction of defects source and to determine optimal process parameters, contrary to the simplified model.
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steel flowing through the refractory channels is higher than this limit, particularly closed to the central distributor brick (Figure 11). This can allow the prediction of defects source and to determine optimal process parameters, contrary to the simplified model. Materials 2016, 9, 769 10 of 13 Materials 2016, 9, 769
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Figure 11. Shear velocity in the horizontal runner. Figure 11. Shear velocity in the horizontal runner. Figure 11. Shear in the horizontal runner. Finally, to verify the reliability of thevelocity developed simulation model, with complete runner
Finally, to verify the reliability of the developed simulation model, with completeplaced runner system, system, they were compared the temperature profiles recorded by the thermocouples close to Finally, to verify the reliability of the developed simulation model, with complete runner they compared recorded byand the those thermocouples placed to theas top thewere top and close tothe thetemperature bottom of theprofiles mold (see Figure 1) resulting from the close simulation system, they were compared the temperature recorded by thefrom thermocouples placed andwell close thethe bottom of the mold (see Figure profiles 1) and those resulting the simulation asclose welltoas as to from thermo-graphic camera. top and close to thecamera. bottom of the mold (see Figure 1) and those resulting from the simulation as fromthe theAs thermo-graphic shown in Figure 12, a good agreement was obtained, demonstrating the reliability of the well as from the thermo-graphic camera. As shown in Figure a good was obtained, reliability ofofthe model. In particular, the12, increase in agreement the mold temperature whendemonstrating the liquid steel the reaches the level As shown in Figure 12, a good agreement was obtained, demonstrating the reliability of the the thermocouples, starting exchanging heattemperature can be observed. model. In particular, the increase in the mold when the liquid steel reaches the level of the model. In particular, the increase in the mold temperature when the liquid steel reaches the level of Slightly higher values of the measured thermocouples, starting exchanging heat cantemperatures be observed.than the calculated ones can be detected at the thermocouples, starting exchanging heat can be observed. during the ingot cooling (solidification is competed in around This scatter at high Slightly higher values of the measured temperatures than3.5 theh).calculated ones can temperature be detected at Slightly higher values of the measured temperatures than the calculated ones can be detected at can be related to the limits of the measuring camera, in particular to the small variation of the during the ingot cooling (solidification is competed in around 3.5 h). This scatter at high temperature during the ingot cooling (solidification is competed in around 3.5 h). This scatter at high temperature emissivity, which was not set accordingly. can be to thetolimits of the measuring camera,camera, in particular to the small variation of the emissivity, canrelated be related the limits of the measuring in particular to the small variation of the which was not set accordingly. emissivity, which was not set accordingly.
Figure 12. Comparison between simulation and experimental measurements for the bottom (a) and top (b) thermocouples. Figure 12. Comparison between simulation and experimental measurements for the bottom (a) and Figure 12. Comparison between simulation and experimental measurements for the bottom (a) and top after (b) thermocouples. the stripping, about six hours from the end of the filling, the measured temperature topJust (b) thermocouples.
distribution on the ingot surface was compared to the predicted one. The good agreement between Just after the stripping, about six hours from the end of the filling, the measured temperature simulation (Figure 13a,b) from allowed the used model. The Just afterand the measurement stripping, about six hours thethe endfurther of thevalidation filling, theofmeasured temperature distribution on the ingot surface was compared to the predicted one. The good agreement between superficial temperature of the mold (Figure 13c) and also of the ingot resulted a little bit higher distribution onand the measurement ingot surface (Figure was compared to the predicted The good agreement between simulation 13a,b) allowed the furtherone. validation of the used model. The oppositelyand to the column and the adjacent mold, due to the radiation effects. simulation measurement (Figure 13a,b) allowed the further validation of the used model. superficial temperature of the mold (Figure 13c) and also of the ingot resulted a little bit higher The temperature along middle(Figure longitudinal section of the theingot ingotresulted (Figure a13d) an The oppositely superficial of the the 13c) also of littleshows bit higher totemperature the column and themold adjacent mold, dueand to the radiation effects. almost symmetric profile, only very limited moved towards the column, counterbalancing the oppositely to temperature the column and thethe adjacent due to the radiation The along middlemold, longitudinal section of theeffects. ingot (Figure 13d) shows an effected induced by the shifted stream during the filling. almost symmetric profile, only very limited moved towards the column, counterbalancing the effected induced by the shifted stream during the filling.
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The temperature along the middle longitudinal section of the ingot (Figure 13d) shows an almost symmetric profile, only very limited moved towards the column, counterbalancing the effected induced by the shifted stream during the filling. Materials 2016, 9, 769 11 of 13
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Figure 13. Temperature Temperature of the the ingot ingot on on the the surface surface just just after after the the stripping stripping phase: phase: (a) (a) measured by the Figure Figure 13. Temperature of (a) measured measured by by the the thermo-camera; (b) simulated on the ingot; (c) simulated on the mold; and (d) temperature along the thermo-camera; thermo-camera; (b) (b) simulated simulated on on the the ingot; ingot; (c) (c) simulated simulated on on the the mold; mold; and and (d) (d) temperature temperature along along the the middle longitudinal section. middle middle longitudinal longitudinal section.
In Figure 14, the heat flux on the surface ofofingot ingot and mold just after thethe stripping is reported, reported, as In and mold just after the stripping is as In Figure Figure 14, 14,the theheat heatflux fluxon onthe thesurface surfaceof ingot and mold just after stripping is reported, well as as its its variation along anan axial and angular profile. ItItcan can be seen that the heat flux resulted not well as its variation along an axial and angular as well variation along axial and angularprofile. profile.It canbe beseen seenthat thatthe theheat heatflux flux resulted resulted not not axi-symmetrical mainly because of the radiation effect. axi-symmetrical axi-symmetrical mainly because of the radiation effect.
Figure 14. 14. Heat Heat flux flux along along two two profiles profiles of of the the ingot ingot (a) (a) and and mold mold (b); (b); (c) (c) Local Local heat heat flux flux as as aa function function Figure Figure 14. Heatjust fluxafter along two profilesofofthe theingot. ingot (a) and mold (b); (c) Local heat flux as a function of of the distance the stripping of the distance just after the stripping of the ingot. the distance just after the stripping of the ingot.
5. Conclusions Conclusions 5. 5. Conclusions In this this paper, the the advantages of of using complete complete instead of of simplified models models for the the simulation In In this paper, paper, the advantages advantages of using using complete instead instead of simplified simplified models for for the simulation simulation of bottom-poured bottom-poured ingot ingot casting casting was was investigated. investigated. Starting Starting from from an an industrial industrial case, case, the the not not negligible negligible of of bottom-poured ingot casting was investigated. Starting from an industrial case, the not negligible effect of the running system on the prediction of mold filling and ingot quality was assessed. effect of mold mold filling filling and and ingot ingot quality quality was was assessed. assessed. effect of of the the running running system system on on the the prediction prediction of In particular, particular, it it was was found found that: that: in in the the early early stage stage of of the the process, process, the the steel steel spout spout is is quite quite high and and In In particular, it was found that: in the early stage of the process, the steel spout is quite high high and shifted oppositely to the column, as a consequence of the design of the running system (elbow and shifted shifted oppositely oppositely to to the the column, column, as as aa consequence consequence of of the the design design of of the the running running system system (elbow (elbow and and entrance nozzle geometry). This result can help in defining the position of the suspended bags to entrance nozzle geometry). geometry).This Thisresult resultcan can help in defining position ofsuspended the suspended bags to entrance nozzle help in defining the the position of the bags to avoid avoid premature premature release of of the the powder powder and and subsequent subsequent entrapment. entrapment. No No similar similar prediction can can be be avoid premature release release of the powder and subsequent entrapment. No similar predictionprediction can be performed performed when the simplified model is used: the main stream remains shifted oppositely to the performed when the model simplified model used: the main stream remains shiftedtooppositely to also the when the simplified is used: the ismain stream remains shifted oppositely the column column also also during during the the entire entire filling, filling, creating creating aa not not symmetric symmetric descending descending stream stream able able to to drag drag the the column slag more more easily, easily, contrary contrary to to the the case case of of the the simplified simplified simulation. simulation. A A high high risk risk of of slag slag entrapment entrapment can can slag be observed since the liquid steel reaches about one third of the mold, oppositely to the simplified be observed since the liquid steel reaches about one third of the mold, oppositely to the simplified model where where the the Weber Weber number number never never exceeds exceeds the the limit, limit, hence hence establishing establishing no no risk risk of of powder powder model entrapment. Considering the whole running system, the shear velocity of the liquid steel along the entrapment. Considering the whole running system, the shear velocity of the liquid steel along the
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during the entire filling, creating a not symmetric descending stream able to drag the slag more easily, contrary to the case of the simplified simulation. A high risk of slag entrapment can be observed since the liquid steel reaches about one third of the mold, oppositely to the simplified model where the Weber number never exceeds the limit, hence establishing no risk of powder entrapment. Considering the whole running system, the shear velocity of the liquid steel along the refractory channel showed the risk of refractory erosion and, thus, of macro inclusions formation, particularly close to the central distributor brick. No remarkable differences in the temperature profiles during the ingot cooling were observed between the complete and the simplified models. These results determined the importance of simulating the complete mold when a deep analysis of defects sources is required. Finally, the good fitting between calculated and recorded temperatures, both during filling and solidification as well as after the ingot stripping, allowed validating the simulation, demonstrating its reliability as predictive tool. Acknowledgments: The authors wish to thank Bortolo Bondioni and Nunki Steel Company for the support in the experimental tests, Cristian Viscardi of Ecotre for the helpful support in the simulation, and Mahdi Soltani for fruitful discussions. Author Contributions: Annalisa Pola conceived and designed the experiments and performed the simulations; Marcello Gelfi performed the experiments; Annalisa Pola and Marcello Gelfi analyzed the data and wrote the paper; Giovina Marina La Vecchia contributed in analyzing the data and writing the paper. Conflicts of Interest: The authors declare no conflict of interest.
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