Keywords

Introduction

Blockage of submerged entry nozzle (SEN) is a long-term problem in steel continuous casting. It can result in operation disruptions and different casting defects [1,2,3]. Among several mechanisms suggested for clogging , deposition of non-metallic inclusions (NMIs) as de-oxidation and re-oxidation products, e.g. Al2O3, on the SEN wall is considered as the primary reason [4], because similar morphologies and chemical compositions of NMIs were observed in the melt, clog material, and as-cast product [5].

Clogging generally occurs through four steps, as depicted in Fig. 1: (1) transport of particles to the wall, (2) interactions of the fluid and the particles with the wall, (3) formation and growth of the clog, and (4) probable fragmentation or resuspension of the clog.

Fig. 1
figure 1

Schematic of clogging phenomenon (four steps)

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High temperature, opaque nature of steel melt, and difficulties of precise control of steel casting make experimental investigation of the process very hard. Therefore, numerical modeling provides a helpful tool to study the clogging process. Diverse modeling efforts have been made for the clogging of SEN by emphasizing one or more critical steps of Fig. 1. Bai and Thomas [6] studied the effect of the clog on the flow through a slide-gate nozzle and Zhang et al. [1] investigated influence of blocking half of one out-port of the SEN. They manually changed the geometry of SEN to mimic the as build clog. To model clogging the Eulerian-Lagrangian approach is a common method which provides detailed information about particle and its trajectory. It was used to find correlations between SEN designs and clogging tendency [7], to study the influence of the velocity gradient of the melt flow and the turbulent kinetic energy on the particle deposition [8], and to investigate effects of SEN diameter on clogging [9]. Eulerian-Eulerian is also used to simulate the inclusion deposition rate in a SEN [10, 11].

Most of the modeling efforts about SEN clogging focused only on the fluid flow and particle transport, i.e. step 1 of Fig. 1, and other steps were ignored. Moreover, in previous simulations clogging was assumed as a steady process and SEN wall stays clean during the process. To the knowledge of authors, none of them has calculated mutual interactions of the clog growth with the melt flow. In the current paper a transient model has been proposed to simulate nozzle clogging in pilot scale by considering the further clogging step (steps 1–3). The current version of the model neglects fragmentation of the clog (step 4).

Model in Brief

In the present paper an Eulerian-Lagrangian model as developed by the authors [12] is used. The flow of the melt as the primary continuous medium is described by the conservation equations of mass and momentum. To model the turbulence, shear-stress transport (SST) k-ω model is adopted. The solid non-metallic inclusions are assumed as spherical particles and a force balance of buoyancy, drag, lift, virtual mass, and pressure gradient controls motion of them. The equations for the turbulent flow and forces acting on particle are listed in Tables 1 and 2, respectively.

Table 1 Governing equations for the fluid flow
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Table 2 Equations for particle transport and forces acting on a particle in bulk flow
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Due to the different structure of flow in bulk and near the wall, a stochastic model [13], which is developed for particle motion in wall-bounded flow, is used for wall boundary cells.

When a NMI meets the SEN wall, made of refractory or ceramic, the capillary force, also termed adhesion force, is the dominant force. Several studies concluded that once the capillary force is imposed, the particle stays in contact with the wall [14,15,16]. The model has considered a tricking probability of particles as they approaching wall. This sticking probability must be determined experimentally or using other models. In this paper, it is assumed to be 100%. To couple particle deposition with the fluid flow pattern, two stages are considered for clogging . In early stage, particle deposition leads to change in wall roughness, as shown in Fig. 2a, b. This stage lasts until the roughness height is larger than half of boundary cell thickness. Thereafter, in later stage, the computational cell is converted to a porous medium, marked in gray in Fig. 2c. Further deposition results in fully occupation of the cell by particles, as indicated by line pattern in Fig. 2d. Neighbor cells then are exposed to particle deposition. Hence, the clog material grows as a porous medium. Regarding to the permeability of the clog, Darcy source terms are applied for the clog region to take into account the effects of clog growth on the fluid flow. More details about the model can be found in [12].

Fig. 2
figure 2

Schematic illustration of clogging evolution in the model: a initial wall roughness considered as uniform sand-grain roughness, b enhanced wall roughness due to the particle deposition , c formation of porous clog, and d clog growth

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Clogging in a pilot scale device which has been used to investigate the nozzle clogging [1, 17, 18] has been simulated. This device is made from a laboratory induction furnace and a circular nozzle with 5 mm diameter as situated at the bottom of the furnace. Molten steel flows through the nozzle until clogging in the nozzle stops the flow. Figure 3 shows mesh and boundary conditions. Regarding the physics controlling the process, multiphase fluid flow (melt and air) is modeled using volume of fluid (VOF) method. On the top surface, pressure-inlet boundary condition is set for air, and for the nozzle outlet, pressure-outlet is imposed. Due to the gravity, the furnace becomes empty gradually. However, due to the clogging, the nozzle could be blocked before run out of the whole melt. Non-slip boundary condition is applied on all walls. To save computation costs and avoid unimportant calculation of particle tracking in the furnace, particles are injected on the connection plane between bottom of the furnace and top of the nozzle. A full 3D domain is simulated and the equations are numerically solved using commercial CFD code ANSYS-FLUENT with extended user defined functions (UDFs) for considering the growth of clog.

Fig. 3
figure 3

Computational domain and boundary conditions. The initial interface between air and melt is plotted on the furnace wall

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Results and Discussion

Clogging process and the clog growth are plotted in Fig. 4 by snapshots of the clog from different views. It shows that after 50 s a smooth layer of deposited material covers the nozzle wall. Continuous deposition of particles leads to formation of some bulges in narrowest section of the nozzle and a part of the middle section. Growth of the clog bulges finally blocks the flow passage as shown at 250 s.

Fig. 4
figure 4

Evolution of the clogging in the nozzle. Horizontal cross sections in different heights and the vertical sections are shown at different times

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In Fig. 5a velocity magnitude during the process is plotted on a vertical symmetry plane. The clog front is marked by solid lines and here the velocity magnitude in the clog material decreases because of its porous character. At 250 s the melt still flows due the small hole left in the clog, as shown in Fig. 4, however the value of the melt velocity is negligible. Figure 5b depicts a zoomed view of the flow field and the clog at 150 s. It shows how the presence of the clog changes the flow pattern. Some eddies can be found below bulges which may result in trapping of particles and finally attaching them to the clog. Therefore, it reveals that two-way coupling between flow field and particle deposition is critical to understand the clogging process.

Fig. 5
figure 5

Changes in melt velocity magnitude during clogging process (a) and zoomed view of flow arrows at 150 s (b). The clog front is marked by solid lines

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To show the importance of clog growth in simulation of clogging , particle deposition results are compared with a case without effects of clog growth on the melt flow, i.e. particles are deleted from calculation once reach the nozzle wall and nozzle wall stays with constant roughness during the process. In Fig. 6 total deposition mass along height of the nozzle is shown for different times. The comparison of two graphs indicates that in both cases at first, deposition is almost uniform and then after 100 s becomes wavy. In the case (a) deposition mass decreases dramatically at y = 0.040 m when t = 200 s, while it happens at y = 0.054 m fore case (b). Moreover, the maximum deposition occurs at y = 0.03 m in case (a), whereas in case (b), maximum deposition happens at y = 0.03 and 0.05 m. The difference between deposition mass at maximum peak(s) and other positions in Fig. 6a is much larger than that in Fig. 6b. However without clog growth, case (a), initial deposition areas can be found, they may change after a while due to the change of the flow pattern, as found in case (b). The deposition mass values generally in Fig. 6b are larger than those in Fig. 6a. It is because of different melt flow rates in two cases, as shown in Fig. 7. In case (a), the melt flow rate decreases during the process because of narrowing of the flow passage in addition to hydrostatic pressure loss. While, in case (b), the only reason is the hydrostatic pressure loss. Therefore, simulation without considering clog growth leads to unrealistic results and would show incorrect time and region of nozzle blockage.

Fig. 6
figure 6

Comparison of deposition mass along nozzle height during time with (a) and without (b) considering the clog growth

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Fig. 7
figure 7

Mass flow rate of the melt during the process with and without considering the clog growth

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Conclusions

A two-way coupling model is used to simulate clogging in pilot scale. The model covers most of clogging steps, i.e. transport of particles by turbulent flow, deposition of particle on the wall, and growth of the clog due to the particle deposition . Interactions between particle deposition and fluid flow are taken into account in two stages: enhancement of wall roughness in early stage of particle deposition and development of clog as a porous medium in later stage. The simulation results declare that the model can reproduce clogging steps well particularly clog growth step. This step is critical to understand the clogging as a transient process. In the present pilot scale neglecting the clog growth leads to unrealistic high melt flow rate and hence incorrect particle deposition rate for whole process. Moreover, when the clog growth is ignored, distribution of deposition material on the nozzle is modeled much more uniform than that when the clog growth is considered in the simulation.