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Numerical study of particle filtration in an induction crucible furnace
International Journal of Heat and Fluid Flow 62 (2016) 299–312
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Numerical study of particle filtration in an induction crucible furnace Amjad Asad a,∗, Christoph Kratzsch a, Steffen Dudczig b, Christos G. Aneziris b, Rüdiger Schwarze a a b
Institute of Mechanic and Fluid Dynamics, Technische Universität Bergakademie Freiberg, Germany Institute of Ceramic, Glass and Construction Materials, Technische Universität Bergakademie Freiberg, Germany
a r t i c l e
i n f o
Article history: Available online 10 November 2016 Keywords: Numerical simulation Euler–Lagrange Non-metallic particles Induction furnace Melt filtration OpenFOAM
a b s t r a c t The present paper deals with a numerical investigation of the turbulent melt flow driven by the electromagnetic force in an induction furnace. The main scope of the paper is to present a new principle to remove non-metallic particles from steel melt in an induction furnace by immersing a porous filter in the melt. The magnetic field acting on the melt is calculated by using the open source software MaxFEM® , while the turbulent flow is simulated by means of the open source computational fluid dynamics library OpenFOAM® . The validation of the numerical model is accomplished by using experimental results for the flow without the immersed filter. Here it is shown that the time-averaged flow, obtained numerically is in a good quantitive agreement with the experimental data. Then, the validated numerical model is employed to simulate the melt flow with the immersed filter in the induction furnace of a new type of real steel casting simulator investigated at Technische Universität Bergakademie Freiberg. The considerable effect of the filter on the flow pattern is indicated in the present work. Moreover, it is shown that the filter permeability and its position have a significant influence on the melt flow in the induction furnace. Additionally, particles are injected in the flow domain and tracked by using Lagrangian framework. In this case, the efficiency of the used filter is determined in the present investigation depending on its permeability, its position and the particles diameter. © 2016 Elsevier Inc. All rights reserved.
1. Introduction Induction crucible furnaces (ICF) are widely applied nowadays in the steelmaking industry. The ICF offers contactless electromagnetic stirring of the melt that enhances the chemical homogeneity and the mixing of the melt. In such kinds of furnaces, the time harmonic current I inside a coil generates an oscillating magnetic field that heats up the metal in the ICF. The magnetic field is controlled due to its harmonic nature by the so-called skin effect. This effect implies that the magnetic field is concentrated mainly in a skin layer near to the surfaces of the melt. The induced eddy currents in the melt j interact with the field B yielding in the Lorentz force F lor = j × B driving the melt inside the ICF to generate one or several toroidal vortices (Campbell, 2013; Jones et al., 2003). The basic working principle of the ICF is presented in Fig. 1. During the steelmaking process, non-metallic particles such as deoxidation products (e.g., alumina) may arise in the steel melt (Zhang and Thomas, 2003). Moreover, impurities can be generated by other chemical reactions in steel melt. The presence of such
∗
Corresponding author. E-mail address: [email protected] (A. Asad).
http://dx.doi.org/10.1016/j.ijheatfluidflow.2016.10.002 0142-727X/© 2016 Elsevier Inc. All rights reserved.
particles in the melt controls its cleanliness and may lead to different quality problems. Therefore, particle removal plays a significant role in order to gain “high-steel quality”. Melt flow can either enhance the steel quality by bringing particles to the free surface, or lower the steel quality by sending them to be entrapped in the solidification front (Yuan and Thomas, 2005; Zhang, 2013; Zhang et al., 2012). Particle-related phenomena in steelmaking are summarised, e.g. in a paper conducted by Zhang (2013). The melt flow in ICF has often been investigated numerically and experimentally (Baake et al., 1995, 20 03a,b, 20 05, 20 09; Bojarevics et al., 2010; Schwarze and Obermeier, 2004; Umbrashko et al., 2005, 2006, 2008). In a numerical and an experimental investigation conducted by Baake et al. (1995), it was indicated that the standard k-ε turbulence model provided good agreement of the averaged flow velocities measured in the experiment. However, this model was not able to predict the low-frequency pulsations of velocity taking place in the zone between main eddies. The occurrence of low-frequency pulsations are known to be responsible for mass and heat transport in this process. In order to enhance the description of the mass and heat transport, the Large Eddy Simulation (LES) was found to be a good choice to describe this process (Baake et al., 2005; Umbrashko et al., 2006, 2008) and to ob-
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2. Numerical modelling 2.1. Magnetic field The skin effect controls the harmonic magnetic field in the ICF, as described previously. The skin-layer thickness δ can be determined in terms of the angular frequency ω of the magnetic field, the electrical conductivity of the melt σ and the magnetic permeability μ0 as follows:
δ=
Fig. 1. Schematic sketch of an induction crucible furnace presents toroidal vortices generated by the Lorentz force Flor resulting from the interaction between the time harmonic magnetic field (B) and the induced eddy current (j) in the melt.
tain a more precise temperature distribution in the melt (Baake et al., 2003a). Schwarze and Obermeier (2004) conducted an unsteady Reynolds averaged Navier–Stokes equation (URANS) with a Reynolds stress turbulence model to compute the flow in an ICF. Here, the authors claimed that the URANS showed that the flow has large flow structures with low frequency fluctuations. The presence of conductive and non-conductive particles in the melt flow are investigated in many works by means of a Euler– Lagrange model (Kirpo, 2008; Kirpo et al., 2009; Šˇcepanskis et al., 2012, 2015, 2011). In this model, the phases are treated separately. The particles in the flow field are tracked as individual mass points by their equation of motion including the forces acting on them, while the melt is described in an Eulerian framework. Kirpo et al. (2009) conducted a numerical investigation to study the behaviour of a particle cloud in a melt. In this work, particle accumulation near to crucible boundaries was observed depending on the density ratio of the melt and the injected particles. The effect of the forces acting on the particle transport was studied statistically by Šˇcepanskis et al. (2012). Here, it was recommended to apply drag, lift, buoyancy and electromagnetic force on the particles moving inside a melt. The main intention of the present paper is to introduce an innovative way of removing non-metallic particles from the steel melt by using a ceramic filter. The application of this principle is expected to enhance non-metallic particle removal by capturing the particles using a ceramic filter. A numerical model is implemented and formulated in the open source computational fluid dynamics library OpenFOAM® to describe the melt flow inside the ICF. In the case of a filter not being present, validating the flow field resulting from the numerical model is done by using an experiment on an ICF first conducted by Baake et al. (1995). The validated numerical model is then used to describe the melt flow in the induction crucible furnace of a new type of real steel casting simulator, taking into account the presence of a porous filter immersed in the melt. This real steel casting simulator is investigated at Technische Universität Bergakademie Freiberg with the aim of developing new melt filters in the frame of the Collaborative Research Centre (CRC 920) (Aneziris et al., 2013; Dudczig et al., 2013, 2014). In this case, particles are injected and their trajectories are computed. Moreover, the efficiency of the ceramic filter and its effect on the flow is studied.
2
σ μ0 ω
.
(1)
The Lorentz force Flor can be decomposed into the mean and oscillating part. When the frequency of the applied magnetic field exceeds 5–10 Hz, the melt flow can not follow the oscillating part due to inertia (Felten et al., 2004; Galpin and Fautrelle, 1992). This part is therefore neglected in the present work, while the effect of the mean part of F lor = j × B is considered. The mean Lorentz force is calculated by means of the induction equations of the magnetic field and the Maxwell’s equations (Moreau, 1990). The magnetic Reynolds number Rem is estimated as follows:
Rem = uch r0 σ
μ0 ,
(2)
where r0 is the radius of the crucible. The characteristic velocity uch is equal to the maximal velocity arising in the crucible uch = 0.05 m s−1 . This leads to the fact that Rem is much smaller than 1 (Moreau, 1990). Therefore, the effect of the conducting fluid on the magnetic fluid is neglected in the present study. This assumption leads to a simplification of Ohm’s law. Then, j is calculated as a function of the electrical field E as follows:
j=σE
(3)
In the present paper, the axisymmetrical eddy current model implemented in the MaxFEM software is adopted in order to obtain the mean Lorentz force field in the melt. For this purpose, an axisymmetrical model of the ICF is utilised. Here, the presence of the non-conductive crucible walls can be neglected due to the fact that a non-conductive material does not have an effect on B . The Dirichlet boundary condition with a magnetic vector potential A = 0 is set on the whole outer boundary of the computational domain. In the induction furnace, the potential drop is set to V = 0. Then, the Lorentz force field is interpolated on the computationaschefflerl grid in OpenFOAM to simulate the flow field. For more details about the determination of the Lorentz force and case-setup, the reader is referred to Bermúdez et al. (2014). Melt heating due to the Joule dissipation is not accounted for in the present study. 2.2. Fluid phase In the current paper, the melt flow is described in an Eulerian framework and is considered to be incompressible, isothermal and turbulent. Therefore, the motion of the Newtonian liquid is described by the unsteady Reynolds-averaged Navier–Stokes (URANS) equations for mass and momentum conservation:
∇ · u=0
(4)
1 ∂u + (u · ∇ )u = − ∇ p + ∇ · (ν ∇ u ) + ∇ · τ RS + F lor + Sfilter ∂t ρ (5) where ρ and ν stand for the density and the kinematic viscosity of the melt, respectively. u is the Reynolds-averaged velocity, p denotes the Reynolds-averaged pressure. F lor denotes the Lorentz force driving the melt flow. Sfilter is the Darcy term to account for the pressure drop in the filter (see, Section 2.5). Reynolds stress
A. Asad et al. / International Journal of Heat and Fluid Flow 62 (2016) 299–312
tensor τ RS is modelled by using the k-ω SST turbulence model (Menter, 1994) .The formulation of this model switches between the standard k-ε model (Launder and Spalding, 1974) and the kω model (Wilcox, 1988). The switch to the k-ω behaviour occurs in the wall vicinity to exploit the advantages of this model in describing the flow at the crucible walls. The transport equations for the kinetic energy k and turbulent specific dissipation rate ω are expressed as follows:
∂k + ∇ · (k u ) = Pk − β ∗ k ω + ∇ · [(ν + σk νt )∇ k] ∂t
(6)
+
2
ω
(1 − F1 ) σw2 ∇ k ∇ ω.
(7)
Here, the model coefficients are σk = σw = 0.5, σw2 = 0.85, α1 = 0.31, αw = 0.44, β = 0.075 and β ∗ = 0.09. The magnitude of the strain rate is represented by S. The blending functions F1 and F2 are responsible to switch between the two models depending on the flow region (in the wall vicinity or far from the wall). The impact of F lor on the turbulence is neglected in the present paper. 2.3. Disperse phase In the present numerical model, each particle is tracked as a Lagrangian mass point in the flow field. The calculation of particle trajectories is performed, taking into account the assumption that the particles do not influence the flow structure and velocities (one-way coupling). This assumption is valid because the volume of the particles does not exceed 0.1% of the fluid volume (Šˇcepanskis et al., 2014). Moreover, the particle-particle interaction can be neglected, since the relation described by Loth (20 0 0) is valid. This relation is based on eddy life time and the time for a particle to traverse such an eddy. The used relation is expressed as follows:
=
Nt π
V
d2p
(γ 2 + 1 )
1,
(8)
where Nt is the total number of the particles in the fluid volume, dp is the particle diameter, γ is ratio of the particle terminal velocity up,term to root mean square velocity urms of the turbulent fluctuations. V denotes the volume of the utilised crucible. is the eddy integral length scale. For the simulation parameters, lies in the 0.0 05–0.0 08 range, which implies that the particle-particle interaction can be neglected in the simulations. Furthermore, it is assumed that the particles possess a spherical shape with a constant diameter. The following equation describes the particle motion in the flow field:
mp
du p dt
= F B + F G + F D + F EM + F V M + F L .
(9)
Here, mp and up denote the mass and velocity of a particle, respectively. FB , FG , FD , FEM , FVM and FL stand for buoyancy, gravitational, drag, electromagnetic, virtual mass force and lift force. The modelling of the forces is described in the following paragraphs. Buoyancy and gravitational force The buoyancy force FB and gravitational force FG are calculated in OpenFOAM using the following equation:
FB + FG =
(ρ p − ρ ) π d3p 6
Drag force The drag force FD is calculated in the present work by using the following equation:
d p u p − u 3 μ FD = C Re u − u , Re = . p p D p 4 ρ p d2p ν
(11)
u is the Reynolds-averaged fluid velocity obtained from Eq. (5). The drag coefficient CD is estimated by means of an empirical relation implemented in OpenFOAM 2.3.x for a spherical solid particle. It is expressed as follows:
CD =
∂ω + ∇ · (ω u ) = αw S2 − β ω2 + [(ν + σw νt )∇ ω] ∂t
301
24
1+ 0.424 Re p
1 6
Re0p.687
; Re p ≤ 10 0 0 ; Re p > 10 0 0.
(12)
Electromagnetic force The particles are affected by the electromagnetic field, since their electrical conductivity differs from that of the melt. This introduces inhomogeneity in a locally homogeneous magnetic field which leads to an electromagnetic force FEM moving the particles in the direction of the wall within the skin depth δ . The relation of this force can be derived by solving the Laplace equations for current density Leenov and Kolin (1954). In the case of steady-state magnetic field and non-magnetic particles, this relation can be reduced as shown in Šˇcepanskis et al. (2012, 2011) to:
F EM = −
3 σ − σp Vp F lor . 2 2σ + σ p
(13)
Here, σ , σ p and Vp represent the electrical conductivity of the steel melt, the electrical conductivity of a particle and the volume of a particle. In this study, it is assumed that the particles in the flow field are non-conductive. Thus, σ p can be set to 0; hence the calculation of FEM can be simplified to:
3 F EM = − Vp F lor . 4
(14)
The equation of FEM is adopted as well in a study conducted by Šˇcepanskis et al. (2012, 2011) in order to investigate particle-laden turbulent flow in an induction furnace. Lift force The lift force FL acting on the particle in the shear flow can be estimated as follows:
F L = CL ρ
π d3p 6
u − u p × (∇ × u ).
(15)
CL is the lift coefficient calculated in OpenFOAM according to the Saffman–Mei model. This model was derived by Saffman (1965) and extended later by Mei (1992). Virtual mass force The virtual mass force FVM is computed as:
F VM = CVM ρ
π d3p Du 6
Dt
−
Du p Dt
.
(16)
In the present study, the particles are assumed to be spherical. Also, the particle diameter is much smaller than the Kolmogorow length. This leads to the fact that the flow around the particle is laminar. Thus, the virtual mass coefficient CVM for spherical particles can be equal to 0.5 resulting from the potential theory (Crowe et al., 1998). 2.4. Particle dispersion
g.
(10)
Here, ρ p , ρ and g represent the density of a particle, the density of the liquid and the gravitational acceleration, respectively.
In order to consider the particle dispersion, the Discrete Random Walk (DRW) model, or “eddy lifetime” model is adopted. Here, the fluctuating velocity components u is kept constant over
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the eddy lifetime. The value of u obeys a Gaussian probability distribution. It then follows on the assumption of isotropic turbulence:
u =
ξd
2k , 3
(17)
where ξ is a scalar formed by normally distributed random numbers. d is a random vector added in OpenFOAM to realise the spatial randomness of turbulence. 2.5. Porous medium To simplify the numerical model, the filter is considered as being a homogeneous isotropic porous medium. Therefore, the source term Sfilter included in Eq. (5) is computed by applying Darcy’s law:
S f ilter = −
1
ρ
∇p =
μ u. κ
(18)
Ceramic filters are expected to be produced with a pore density in the range of 8–100 ppi (Scheffler and Colombo, 2006). This implies that the filter permeability κ is expected to be approximately in the range of 10−6 -10−11 m2 according to the results summarised in Scheffler and Colombo (2006). To cover a larger range of κ , it is varied in the range of 10−5 -10−12 m2 in the present investigation in order to study its effect on the filter efficiency η. To our knowledge, there is no validated empirical model to detect the separation probability of particles from a melt moving through a porous filter used in metallurgical processes. Therefore, the authors defined a random number χ for each particle traversing the porous filter. If χ > 50%, the particle should be stuck in the filter; otherwise it passes the filter.
Fig. 2. Axisymmetrical section of the induction crucible furnace (ICF1 and ICF2) with the important dimensions.The height of the melt and the coil in the case of ICF1 is equal (H1 = H2 = 0). Table 2 lists the dimensions of the ICF1 and ICF2.
2.6. Flow simulation setup As mentioned previously, an experiment conducted by Baake et al. (1995) is used as a reference configuration in order to validate the performance of the developed numerical model to describe the flow field in an ICF without a filter. This configuration is described in the following ICF1. The numerical model is then employed to describe the melt flow inside the induction crucible furnace of a new type of real steel casting simulator, described in the following ICF2. In this case, a filter is immersed in the melt. A schematic sketch of the ICF1 and the ICF2 is presented in Fig. 2. The ICF1 and the ICF2 have different dimensions and shape (see, Table 2). Here, it should be noted that the ICF2 has a curvature with a radius of R3 at the lower corner, while the ICF1 has an angled lower corner (R3 = 0). Moreover, it should be noted that the height of the melt and the coil are equal in the case of ICF1. In the present investigation, the effect of the filter position is studied. The filter positions studied here are presented in Fig. 3. Here, the position (2) denotes the place of the filter at the central axis of the ICF2, while positions (1) and (3) show off-centre positions of the filter. In the present study, the filter has a squared shape and its dimension is listed in Table 2. The Wood’s alloy is used as an operating fluid in the ICF1, while the operating fluid in the ICF2 of the casting simulator is a steel melt. The material properties of both fluids can be found in Table 1 and are assumed to be constant. The operation parameters of the ICF1 and ICF2 are listed in Table 1. Convection in the Navier-Stokes Eq. (5) is discretised by using the second order central differencing scheme, while convection in the turbulence model is (see, Eqs. (6) and (7)). For the temporal discretisation scheme, the second order backward differencing scheme is adopted in Eqs. (5–7).
Fig. 3. Schematic sketch of the ICF2 to show filter positions studied in the present paper. Table 1 Physical parameters of the simulations performed in the present paper. Process parameters of the induction furnaces Quantity
ICF1
ICF2
Coil current (rms) I [A] Frequency f [Hz] Number of coil windings n [-] Coil length l[m] Magnetic field strength B[T]
20 0 0 400 12 0.57 0.069
180 3400 10 0.4 0.01
Wood melt
Steel melt
9400 4.2e − 3 1.257e − 6 6e6
70 0 0 6e − 3 1.257e − 6 7e5
Liquid properties Quantity
−3
Density ρ kg m Dynamic viscosity μ m2 s−1 Magnetic permeability μ0 [H m−1 ] Electrical conductivity σ [S m−1 ] Particles properties Quantity
−3
Density ρ p kg m Diameter dp [μm] Electrical conductivity σ [S m−1 ]
30 0 0 20, 40, 60 0
A. Asad et al. / International Journal of Heat and Fluid Flow 62 (2016) 299–312 Table 2 Important dimensions of the simulated configuration ICF1 and ICF2 in the present paper. Dimensions[mm]
ICF1
ICF2
H1 Hc Rc1 Rc2 R1 R2 R3 Hf df
0 570 197 207 158 R2 = R1 – – –
165 400 222.5 240 110 105 20 60 10
The computational grid of the ICF1 consists of 20 0,0 0 0 cells, while the computational grid of the ICF2 has 50 0,0 0 0 cells. In both cases, the mesh is generated by SnappyHexMesh, which is a meshing tool in OpenFOAM. The hybrid mesh is structured and equidistant in the core region of the melt, while near-wall layers are unstructured. The crucible walls are treated as no-slip walls. The free surface deformation is neglected and considered as a slip wall. To our knowledge, there is no suitable wall function to describe the magnetically driven turbulent flow in the near wall region. Therefore, the standard wall functions are employed in this study (Spalding, 1961). Particle separation at the crucible walls is not taken into account in the present paper. Moreover, the effect of the material of the crucible walls on the filtration rate is not considered. 3. Results and discussion 3.1. ICF1 The ICF1 is employed in order to validate the numerical model. As mentioned previously, the Lorentz force distribution is computed by means of MaxFEM. Here, an axisymmetical model of the ICF1 is utilised. Then, it is interpolated using the “KDTree algorithm for nearest neighbour lookup” (Maneewongvatana and Mount, 2002) on the 3D OpenFOAM-mesh to simulate the melt
303
flow in the ICF1. The flow field in the ICF1 is averaged over 270 s. The averaged flow pattern indicated in Fig. 4 consists of a twovortices structure, which is created by the interaction of the flow coming from the top and bottom along the crucible wall. It can be noticed that higher velocities are found in the region close to the wall. Furthermore, regions of low velocity are found in the area between the lower and upper vortices. A little asymmetry is found in the time-averaged flow pattern due to the long-term oscillations of the large vortex structure that typically dominate the flow in an ICF. In Fig. 5, a comparison between the numerical prediction and the experimental data is presented over Line 1 located at y = −158 mm between x = 0 and x = 158 mm (see, Fig. 4). The experimental data is obtained from an experiment conducted by Baake et al. (1995) by using magnetic sensors (see, Fig. 4). It is apparent that the numerical predication of the timeaveraged liquid velocity matches well with the experiment. 3.2. ICF2 In this section, the numerical model validated previously in Section 3.1 is employed to describe the steel melt flow in the ICF2 of the real steel casting simulator investigated experimentally in our laboratory. Here, it must be stated that flow measurements in liquid steel are still not possible. Therefore, the numerical results of the ICF2 are not compared with experimental data. Additionally, 1100 solid particles are injected from the upper wall of the flow field at a time step t = 30 s, as the flow is fully developed in order to determine the filtration efficiency of the different flow configurations. The filter is then immersed in the melt at t = 60 s. The flow field is averaged over 240 s. Here, the time averaging of the flow field starts at t = 60 s. 3.2.1. Magnetic field Fig. 6 presents the radial and vertical Lorentz force distribution in the steel melt. The core region of the melt with low Lorentz force is omitted in Fig. 6. Due to the skin effect in the melt, it is clearly seen that the Lorentz force is concentrated in the region
Fig. 4. Mean flow velocity and streamlines in the central plane of the ICF1. Line 1 is used as a sampling line to compare the numerical and experimental results. Line 1 is located at y = −158 mm between x = 0 and x = 158 mm.
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Fig. 5. A comparison between the numerical results of the time-averaged vertical velocity in the ICF1 uy with the experimental data (Baake et al., 1995) over Line 1 (see, Fig. 4).
close to the wall. From Fig. 6a, one can observe that the radial Lorentz force component Flor,r has an asymmetrical profile with the respect to the axial direction, where a higher value of Flor,r is observed at the upper corner of the melt. The vertical Lorentz force component Flor,y is indicated in Fig. 6b. Here, it is observed that Flor,y is not mirror symmetric with the respect to the axial direction by comparing the upper and lower corners of the melt. This asymmetry of Flor,r and Flor,y can be attributed mainly to the asymmetrical position of the melt relative to the coil. Although the Lorentz force distribution is not mirror symmetric, the Lorentz force exhibits an rotational symmetrical distribution. 3.2.2. Flow field without filter In Fig. 7, the time-averaged velocity field and streamlines in the horizontal and vertical planes of the ICF2 are indicated. Although the flow setup and the Lorentz force distribution are axisymmetric, slight deviations from axisymmetry are found in the time-averaged numerical results. This implies that long-term flow fluctuations have a significant impact on the results. An exemplary snapshot of the velocity field shown in Fig. 8 indicates the influence of the these fluctuations. Here, the right-hand and the left-hand side toroidal vortex is connected by streamlines, which pass through the symmetry line (central axis) of the crucible. Secondary eddy structures are present in the low-velocity core region of the instantaneous flow (see, Fig. 8b). Here, a nearly symmetric flow structure is only observed in the long-term averaged flow in Fig. 7b.
Fig. 6. Lorentz force distribution in an axisymmetrical section of the ICF2: radial Lorentz force (a); vertical Lorentz force (b). The core region of the melt with low Lorentz force is omitted.
3.2.3. Flow field with filter Firstly, the influence of filter position and of filter permeability on the melt flow pattern in the ICF2 are studied. The averaged flow pattern in case of one ceramic filter located at the central axis of the ICF2 is shown in Fig. 9. For filter permeability in the range of (κ = 10−6 , 10−12 m2 ), it is clear that the filter leads to a lower flow velocity in the central region of the melt due to the higher flow resistance in this region, compared to the case without the filter presented previously. Comparing the averaged flow pattern in the vertical plane of the ICF2, higher flow velocity in the lower part of the used filter and in the region beneath the filter can be observed in the case of κ = 10−6 m2 , which is expected to be corresponded to a ceramic filter with a pore density of about 8–10 ppi. Exemplary snapshots of the instantaneous velocity field are presented in Fig. 10. The flow field in the vertical middle plane for all considered permeability is dominated by the large eddies as noticed in the case of the time-averaged velocity field as well. The difference between the instantaneous and the time-averaged velocity field can be noticed
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305
Fig. 7. Mean flow velocity and streamlines in the ICF2: a) vertical middle plane; b) horizontal plane at y = 17 mm.
considerably in the horizontal plane, where the secondary eddy structure is observed in this plane. In case the of κ = 10−6 m2 , it is seen that the eddy enters the filter due to the low flow resistance in this case. For κ = 10−12 m2 , the eddies do not enter the filter. Moreover, streamlines are deflected at the filter. Fig. 11 depicts the time-averaged velocity field in the case of one immersed filter located at position (3) (see, Fig. 3). The secondary eddies are still observed in the time-averaged flow for all filter permeability considered here. For κ = 10−6 m2 , the streamlines are not influenced by the filter significantly, as indicated in Fig. 11a. However, it can be seen in the vertical plane of the ICF2 that the toroidal vortex is shifted to the region between the melt surface and the immersed filter. On the contrary, the filter impacts the streamlines considerably in the case of κ = 10−12 m2 . In the horizontal plane, it is found that the streamline are deflected at the filter and they do not enter the filter because of the high flow resistance. The considerable impact of the filter with κ = 10−12 m2 is found in the instantaneous snapshots of the flow field as well, as shown in Fig. 12b. The effect of using two ceramic filters on the melt flow is investigated as well in the present paper. The two filters are situated at
positions (1) and (3) shown in Fig. 3. The time-averaged flow field indicated in Fig. 13b has a little asymmetry, which implies that the long-term fluctuations affects the numerical results in this case as well. As seen previously, the filter with κ = 10−12 m2 has a higher effect on the flow than the filter with κ = 10−6 m2 . The secondary eddies in the horizontal plane are observed in the time-averaged as well as in the instantaneous flow field (see, Fig. 14). Video 1 shows the simulation of the velocity field in case of one filter at position (2) and two filters at positions (1) and (3) for κ = 10−12 .
3.3. Filter efficiency The effect of the filter permeability κ , particle diameter dp and filter position on the filter efficiency η is investigated in the following paragraphs. In order to focus on the capability of the filter to capture the particles moving in the melt, no additional implementation is included to keep the particles at the free surface because of the wetting effect, which can happen in the reality. The ratio of the particles captured by the filter Nc to the total num-
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Fig. 8. Instantaneous flow velocity and streamlines in the ICF2: a) vertical middle plane; b) horizontal plane at y = 17 mm.
ber of injected particles Nt = 1100 characterises the filter efficiency η = Nc/Nt. The filtration time is 240 s.
3.3.1. Filter permeability The impact of the filter permeability κ on η is presented in Fig. 15. Here, the filter is located at position (2) (see, Fig. 3). As it can be seen here, the permeability and efficiency of the used filter are directly correlated. Reducing the permeability results in capturing less particles by the filter. This finding is explained by the fact that the flow rate through the filter is lower in the case of the low permeability compared to those cases with high permeability. At the end, this leads to a reduction in the number of particles reaching the filter. The higher filter efficiency is achieved by using a filter with a permeability of κ = 10−5 m2 . For a filter permeability in the range of 10−7 –10−12 m2 , the efficiency does not depend on the permeability. This result might be attributed to the slightly changed flow pattern for this range as indicated previously.
3.3.2. Particle diameter The number of particles captured by the filter located at position (2) depends on the particle diameter as can be recognised from Fig. 15. For a particle diameter of d p = 60 μm, the filter exhibits a lower efficiency compared to the cases with a smaller particles diameter. The reason for these results is that, the particles with d p = 60 μm are frequently accumulated at the upper corners of the flow field, where the flow velocity is not enough to force the particles to follow the melt flow and the buoyancy is dominated for these particles. This implies that they are not able to follow the flow to reach the filter. This aspect does not occur often for the smaller particles with d p = 20 μm. Video 2 shows the simulation of the particles for d p = 20 μm and d p = 60 μm. 3.3.3. Filter position Fig. 16 compares the effect of filter position and filters number on η for two filters permeability (κ = 10−6 , 10−12 m2 ). As it can be seen, η is affected considerably by filter position and the number of the used filter. A strong increase of η is observed in the case of two filters for κ = 10−6 , 10−12 m2 . However, η is not doubled
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Fig. 9. Mean velocity flow in the case of one filter located at position (2) in the ICF2 (see, Fig. 3) to show the effect of the filter permeability κ on the velocity field of the liquid in the vertical middle plane (left) and horizontal plane at y = 17 mm (right) of the ICF2, the red box represents the position of the filter: a) κ = 10−6 m2 b) κ = 10−12 m2 . (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 10. Instantaneous snapshots of flow in the case of one filter located at position (2) in the ICF2 (see, Fig. 3) to show the effect of the filter permeability κ on the instantaneous velocity field of the liquid in the vertical middle plane (left) and horizontal plane at y = 17 mm (right) of the ICF2, the red box represents the position of the filter: a) κ = 10−6 m2 ; b) κ = 10−12 m2 . (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 11. Mean velocity flow in the case of one filter located at position (3) in the ICF2 (see, Fig. 3) to show the effect of the filter permeability κ on the velocity field of the liquid in the vertical middle plane (left) and horizontal plane at y = 17 mm (right) of the ICF2, the red box represents the position of the filter: a) κ = 10−6 m2 ; b) κ = 10−12 m2 . (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 12. Instantaneous snapshots of the melt flow in the case of one filter located at position (3) to show the effect of the filter permeability κ on the instantaneous velocity field of the liquid in the vertical middle plane (left) and horizontal plane at y = 17 mm (right) of the ICF2, the red box represents the position of the filter: a) κ = 10−6 m2 ; b) κ = 10−12 m2 . (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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309
Fig. 13. Mean velocity flow in the case of two filters located at position (1) and (3) to show the effect of the filter permeability κ on the velocity field of the liquid in the vertical middle plane (left) and horizontal plane at y = 17 mm (right) of the ICF2, the red box represents the position of the filter: a) κ = 10−6 m2 ; b) κ = 10−12 m2 . (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 14. Instantaneous snapshots of the melt flow in the case of two filters located at position (1) and (3) to show the effect of the filter permeability κ on the instantaneous velocity field of the liquid in the vertical middle plane (left) and horizontal plane at y = 17 mm (right) of the ICF2, the red box represents the position of the filter: a) κ = 10−6 m2 ; b) κ = 10−12 m2 . (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 15. Influence of the filter permeability κ and particles diameter dp on the filtration rate η.
in the case of two filters. The shift of filter from position (2) to position (3) shows only a small effect in case of κ = 10−6 m2 and no effect in the case of κ = 10−12 m2 . In case of one filter located at position (3), η does not show a strong increase by using a filter with κ = 10−12 m2 compared to the case with the filter located at position (2). 4. Conclusion The present paper proposes a new principle to enhance nonmetallic particles removal in an induction furnace by using a ceramic filter immersed in the melt. A numerical model is formulated in order to describe the electromagnetically driven turbulent melt flow and the behaviour of small dispersed particles in an induction furnace. Experimental data is used to validate the numerical model for the melt flow. Here, it is indicated that the numerical model is able to estimate the averaged flow velocity well. Then, the validated numerical model is adopted to simulate the melt flow in an induction furnace of a real steel casting simulator. In this case, the flow is studied, taking into account the effect of an immersed ceramic filter. In this case, the considerable effect of the filter and its permeability on the melt flow is presented. The filter leads to a decrease in the flow velocity in the region, where it is
located. Moreover, it is found that the flow streamlines in the filter region depends considerably on its permeability. Low filter permeability caused a high flow resistance. This leads to the fact that flow streamlines try to turn around the filter. Additionally, the significant impact of the filter position on the flow pattern is shown. The filter efficiency to capture these particles is investigated in the present work as well. The filter provides the ability to sufficiently capture the particles in case of high permeability. Furthermore, it is indicated that the number of particles captured by the filter decreases by increasing the particles’ diameter. In addition, the numerical result shows that the filter efficiency also depends on filter position and number of used filter. Based on the results from this study, experimental investigations of the filtration efficiency in an induction furnace are planned. In the experiment, the filters are placed at the locations, which show high filtration efficiency in the simulation. In future study, the enhancement of filter performance to capture the non-metallic particles will be investigated by optimising filter position and filter permeability. Moreover, the influence of crucible walls and their materials on particle separation will be considered and discussed. Furthermore, the effect of the choice of the turbulence models and the mesh resolution on the quality of the results will be studied and discussed and in further studies.
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Fig. 16. Influence of the filter position on the filtration rate η. The filter positions can be found in Fig. 3.
Acknowledgments The authors would like to thank the German Science Foundation (DFG) for supporting the scientific work in terms of the Collaborative Research Centre Multi-Functional Filters for Metal Melt Filtration-A Contribute towards Zero Defect Materials (CRC 920 B06). The authors are grateful to Pascal Beckstein and Thomas Wondrak for providing the interpolation tool used in the present work. Supplementary material Supplementary material associated with this article can be found, in the online version, at 10.1016/j.ijheatfluidflow.2016.10. 002. References Aneziris, C., Dudczig, S., Hubálková, J., Emmel, M., Schmidt, G., 2013. Alumina coatings on carbon bonded alumina nozzles for active filtration of steel melts. Ceram. Int. 39 (3), 2835–2843. doi:10.1016/j.ceramint.2012.09.055. Baake, E., Mühlbauer, A., Jakowitsch, A., Andree, W., 1995. Extension of the k-ε model for the numerical simulation of the melt flow in induction crucible furnaces. Metall. Mater. Trans. B 26 (3), 529–536. doi:10.1007/BF02653870. Baake, E., Nacke, B., Bernier, F., Vogt, M., Mühlbauer, A., Blum, M., 2003. Experimental and numerical investigations of the temperature field and melt flow in the induction furnace with cold crucible. COMPEL -Int. J. Comput. Math. Electr. Electron. Eng. 22 (1), 88–97. doi:10.1108/03321640310452196.
Baake, E., Nacke, B., Umbrashko, A., Jakovics, A., 2003. Turbulent flow dynamics, heat transfer and mass exchange in the melt of induction furnaces. COMPEL -Int. J. Comput. Math. Electr. Electron. Eng. 22 (1), 39–47. doi:10.1108/ 03321640310452006. Baake, E., Umbrashko, A., Jakovics, A., 2005. Numerical modelling of metallurgical processes using LES. Arch. Electr. Eng. 54 (214), 425–437. Baake, E., Umbrashko, A., Jakovics, A., 2009. Numerical simulation and analysis of heat and mass transfer processes in metallurgical induction applications, pp. 1578–1583. doi:10.1109/EURCON.2009.5167852. Bermúdez, A., Gómez, D., Salgado, P., 2014. Eddy Currents with Maxfem. In: Mathematical Models and Numerical Simulation in Electromagnetism, 74. Springer International Publishing, pp. 325–345. doi:10.1007/978- 3- 319- 02949- 8_15. Bojarevics, V., Roy, A., Pericleous, K., 2010. Magnetic levitation of large liquid volume. Magnetohydrodynamics (4) 339–351. Campbell, F., 2013. Metals Fabrication: Understanding the Basics. ASM International. Crowe, C., Sommerfeld, M., Yutaka, T., 1998. Multiphase Flows with Droplets and Particles. CRC press. Dudczig, S., Aneziris, C., Dopita, M., Rafaja, D., 2013. Application of oxide coatings for improved steel filtration with the aid of a metal casting simulator. Adv. Eng. Mater. 15 (12), 1177–1187. Dudczig, S., Aneziris, C., Emmel, M., Schmidt, G., Hubalkova, J., Berek, H., 2014. Characterization of carbon-bonded alumina filters with active or reactive coatings in a steel casting simulator. Ceram. Int. doi:10.1016/j.ceramint.2014.08.038. Felten, F., Fautrelle, Y., Terrail, Y.D., Metais, O., 2004. Numerical modelling of electromagnetically-driven turbulent flows using les methods. Appl. Math. Model 28 (1), 15–27. http://dx.doi.org/10.1016/S0307-904X(03)00116-1. Galpin, J., Fautrelle, Y., 1992. Liquid-metal flows induced by low-frequency alternating magnetic fields. J. Fluid Mech. 239, 383–408. Jones, P., Taylor, S., Nakai, S., Jennings, J., 2003. 9 - Electroheat and Materials Processing. In: Laughton, M., Warne, D. (Eds.), Electrical Engineer’s Reference Book (Sixteenth Edition). Newnes, Oxford, pp. 1–38. http://dx.doi.org/10.1016/ B978- 075064637- 6/50 0 09-5.
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Kirpo, M., 2008. Modeling of Turbulence Properties and Particle Transport in Recirculated Flows. University of Latvia. Kirpo, M., Jakovicˇ s, A., Baake, E., Nacke, B., 2009. LES study of particle transport in turbulent recirculated liquid metal flows. Magnetohydrodynamics (3) 439–450. Launder, B.E., Spalding, D.B., 1974. The numerical computation of turbulent flows. Comput. Methods Appl. Mech. Eng. 3 (2), 269–289. Leenov, D., Kolin, A., 1954. Theory of electromagnetophoresis. i. magnetohydrodynamic forces experienced by spherical and symmetrically oriented cylindrical particles. J. Chem. Phys. 22 (4), 683–688. Loth, E., 20 0 0. Numerical approaches for motion of dispersed particles, droplets and bubbles. Prog. Energy Combust. Sci. 26 (3), 161–223. http://dx.doi.org/10.1016/ S0360-1285(99)0 0 013-1. Maneewongvatana, S., Mount, D.M., 2002. Analysis of approximate nearest neighbor searching with clustered point sets. Data Structures, Near Neighbor Searches, and Methodology 59, 105–123. Mei, R., 1992. An approximate expression for the shear lift force on a spherical particle at finite reynolds number. Int. J. Multiphase Flow 18 (1), 145–147. doi:10.1016/0301-9322(92)90012-6. Menter, F., 1994. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 32 (8), 1598–1605. Moreau, R., 1990. Magnetohydrodynamics (Fluid Mechanics and Its Applications). Springer. Saffman, P.G., 1965. The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22, 385–400. doi:10.1017/S0022112065000824. Scheffler, M., Colombo, P., 2006. Cellular Ceramics: Structure, Manufacturing, Properties and Applications. John Wiley & Sons. Schwarze, R., Obermeier, F., 2004. Modelling of unsteady electromagnetically driven recirculating melt flows. Modell. Simul. Mater. Sci. Eng. 12 (5), 985–993. doi:10. 1088/0965-0393/12/5/015. Spalding, D.B., 1961. A single formula for the law of the wall. J. Appl. Mech. 28, 445–458. Umbrashko, A., Baake, E., Nacke, B., Jakovics, A., 2005. Experimental investigations and numerical modelling of the melting process in the cold crucible. COMPEL -Int. J. Comput. Math. Electr. Electron. Eng. 24 (1), 314–323. doi:10.1108/ 03321640510571336.
Umbrashko, A., Baake, E., Nacke, B., Jakovics, A., 2006. Modeling of the turbulent flow in induction furnaces. Metall. Mater. Trans. B 37 (5), 831–838. doi:10.1007/ s11663-006-0065-0. Umbrashko, A., Baake, E., Nacke, B., Jakovics, A., 2008. Thermal and hydrodynamic analysis of the melting process in the cold crucible using 3d modeling. Heat Transf. Res. 39 (5), 413–421. doi:10.1615/HeatTransRes.v39.i5.50. Šˇcepanskis, M., Jakovicˇ A.s, A., Baake, E., Nacke, B., 2012. Analysis of the oscillating behaviour of solid inclusions in induction crucible furnaces. Magnetohydrodynamics 48 (4), 677–686. Šˇcepanskis, M., Jakovicˇ s, A., Baake, E., Nacke, B., 2014. Solid inclusions in an electromagnetically induced recirculated turbulent flow: simulation and experiment. Int. J. Multiphase Flow 64, 19–27. http://dx.doi.org/10.1016/j.ijmultiphaseflow. 2014.04.004. Šˇcepanskis, M., Jakovicˇ s, A., Baake, E., Nacke, B., 2015. A model for homogenization of solid alloying admixtures in an induction crucible furnace. Steel Res. Int. 86 (2), 169–174. doi:10.10 02/srin.20140 0118. Šˇcepanskis, M., Jakovis, A., Baake, E., 2011. Statistical analysis of the influence of forces on particles in em driven recirculated turbulent flows. J. Phys. Conf. Ser. 333 (1). doi:10.1088/1742-6596/333/1/012015. Wilcox, D.C., 1988. Reassessment of the scale-determining equation for advanced turbulence models. AIAA J. 26 (11), 1299–1310. Yuan, Q., Thomas, B., 2005. Transport and entrapment of particles in continuous casting of steel, pp. 745–759. Zhang, L., 2013. Nucleation, growth, transport, and entrapment of inclusions during steel casting. JOM 65 (9), 1138–1144. doi:10.1007/s11837- 013- 0688- y. Zhang, L., Thomas, B., 2003. State of the art in evaluation and control of steel cleanliness. ISIJ Int. 43 (3), 271–291. Zhang, L., Wang, Y., Martinez, E., Peaslee, K., 2012. Fluid Flow, Solidification and Inclusion Entrapment During Steel Centrifugal Casting Process doi:10.1002/ 9781118364697.ch1.
Contents lists available at ScienceDirect
International Journal of Heat and Fluid Flow journal homepage: www.elsevier.com/locate/ijhff
Numerical study of particle filtration in an induction crucible furnace Amjad Asad a,∗, Christoph Kratzsch a, Steffen Dudczig b, Christos G. Aneziris b, Rüdiger Schwarze a a b
Institute of Mechanic and Fluid Dynamics, Technische Universität Bergakademie Freiberg, Germany Institute of Ceramic, Glass and Construction Materials, Technische Universität Bergakademie Freiberg, Germany
a r t i c l e
i n f o
Article history: Available online 10 November 2016 Keywords: Numerical simulation Euler–Lagrange Non-metallic particles Induction furnace Melt filtration OpenFOAM
a b s t r a c t The present paper deals with a numerical investigation of the turbulent melt flow driven by the electromagnetic force in an induction furnace. The main scope of the paper is to present a new principle to remove non-metallic particles from steel melt in an induction furnace by immersing a porous filter in the melt. The magnetic field acting on the melt is calculated by using the open source software MaxFEM® , while the turbulent flow is simulated by means of the open source computational fluid dynamics library OpenFOAM® . The validation of the numerical model is accomplished by using experimental results for the flow without the immersed filter. Here it is shown that the time-averaged flow, obtained numerically is in a good quantitive agreement with the experimental data. Then, the validated numerical model is employed to simulate the melt flow with the immersed filter in the induction furnace of a new type of real steel casting simulator investigated at Technische Universität Bergakademie Freiberg. The considerable effect of the filter on the flow pattern is indicated in the present work. Moreover, it is shown that the filter permeability and its position have a significant influence on the melt flow in the induction furnace. Additionally, particles are injected in the flow domain and tracked by using Lagrangian framework. In this case, the efficiency of the used filter is determined in the present investigation depending on its permeability, its position and the particles diameter. © 2016 Elsevier Inc. All rights reserved.
1. Introduction Induction crucible furnaces (ICF) are widely applied nowadays in the steelmaking industry. The ICF offers contactless electromagnetic stirring of the melt that enhances the chemical homogeneity and the mixing of the melt. In such kinds of furnaces, the time harmonic current I inside a coil generates an oscillating magnetic field that heats up the metal in the ICF. The magnetic field is controlled due to its harmonic nature by the so-called skin effect. This effect implies that the magnetic field is concentrated mainly in a skin layer near to the surfaces of the melt. The induced eddy currents in the melt j interact with the field B yielding in the Lorentz force F lor = j × B driving the melt inside the ICF to generate one or several toroidal vortices (Campbell, 2013; Jones et al., 2003). The basic working principle of the ICF is presented in Fig. 1. During the steelmaking process, non-metallic particles such as deoxidation products (e.g., alumina) may arise in the steel melt (Zhang and Thomas, 2003). Moreover, impurities can be generated by other chemical reactions in steel melt. The presence of such
∗
Corresponding author. E-mail address: [email protected] (A. Asad).
http://dx.doi.org/10.1016/j.ijheatfluidflow.2016.10.002 0142-727X/© 2016 Elsevier Inc. All rights reserved.
particles in the melt controls its cleanliness and may lead to different quality problems. Therefore, particle removal plays a significant role in order to gain “high-steel quality”. Melt flow can either enhance the steel quality by bringing particles to the free surface, or lower the steel quality by sending them to be entrapped in the solidification front (Yuan and Thomas, 2005; Zhang, 2013; Zhang et al., 2012). Particle-related phenomena in steelmaking are summarised, e.g. in a paper conducted by Zhang (2013). The melt flow in ICF has often been investigated numerically and experimentally (Baake et al., 1995, 20 03a,b, 20 05, 20 09; Bojarevics et al., 2010; Schwarze and Obermeier, 2004; Umbrashko et al., 2005, 2006, 2008). In a numerical and an experimental investigation conducted by Baake et al. (1995), it was indicated that the standard k-ε turbulence model provided good agreement of the averaged flow velocities measured in the experiment. However, this model was not able to predict the low-frequency pulsations of velocity taking place in the zone between main eddies. The occurrence of low-frequency pulsations are known to be responsible for mass and heat transport in this process. In order to enhance the description of the mass and heat transport, the Large Eddy Simulation (LES) was found to be a good choice to describe this process (Baake et al., 2005; Umbrashko et al., 2006, 2008) and to ob-
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2. Numerical modelling 2.1. Magnetic field The skin effect controls the harmonic magnetic field in the ICF, as described previously. The skin-layer thickness δ can be determined in terms of the angular frequency ω of the magnetic field, the electrical conductivity of the melt σ and the magnetic permeability μ0 as follows:
δ=
Fig. 1. Schematic sketch of an induction crucible furnace presents toroidal vortices generated by the Lorentz force Flor resulting from the interaction between the time harmonic magnetic field (B) and the induced eddy current (j) in the melt.
tain a more precise temperature distribution in the melt (Baake et al., 2003a). Schwarze and Obermeier (2004) conducted an unsteady Reynolds averaged Navier–Stokes equation (URANS) with a Reynolds stress turbulence model to compute the flow in an ICF. Here, the authors claimed that the URANS showed that the flow has large flow structures with low frequency fluctuations. The presence of conductive and non-conductive particles in the melt flow are investigated in many works by means of a Euler– Lagrange model (Kirpo, 2008; Kirpo et al., 2009; Šˇcepanskis et al., 2012, 2015, 2011). In this model, the phases are treated separately. The particles in the flow field are tracked as individual mass points by their equation of motion including the forces acting on them, while the melt is described in an Eulerian framework. Kirpo et al. (2009) conducted a numerical investigation to study the behaviour of a particle cloud in a melt. In this work, particle accumulation near to crucible boundaries was observed depending on the density ratio of the melt and the injected particles. The effect of the forces acting on the particle transport was studied statistically by Šˇcepanskis et al. (2012). Here, it was recommended to apply drag, lift, buoyancy and electromagnetic force on the particles moving inside a melt. The main intention of the present paper is to introduce an innovative way of removing non-metallic particles from the steel melt by using a ceramic filter. The application of this principle is expected to enhance non-metallic particle removal by capturing the particles using a ceramic filter. A numerical model is implemented and formulated in the open source computational fluid dynamics library OpenFOAM® to describe the melt flow inside the ICF. In the case of a filter not being present, validating the flow field resulting from the numerical model is done by using an experiment on an ICF first conducted by Baake et al. (1995). The validated numerical model is then used to describe the melt flow in the induction crucible furnace of a new type of real steel casting simulator, taking into account the presence of a porous filter immersed in the melt. This real steel casting simulator is investigated at Technische Universität Bergakademie Freiberg with the aim of developing new melt filters in the frame of the Collaborative Research Centre (CRC 920) (Aneziris et al., 2013; Dudczig et al., 2013, 2014). In this case, particles are injected and their trajectories are computed. Moreover, the efficiency of the ceramic filter and its effect on the flow is studied.
2
σ μ0 ω
.
(1)
The Lorentz force Flor can be decomposed into the mean and oscillating part. When the frequency of the applied magnetic field exceeds 5–10 Hz, the melt flow can not follow the oscillating part due to inertia (Felten et al., 2004; Galpin and Fautrelle, 1992). This part is therefore neglected in the present work, while the effect of the mean part of F lor = j × B is considered. The mean Lorentz force is calculated by means of the induction equations of the magnetic field and the Maxwell’s equations (Moreau, 1990). The magnetic Reynolds number Rem is estimated as follows:
Rem = uch r0 σ
μ0 ,
(2)
where r0 is the radius of the crucible. The characteristic velocity uch is equal to the maximal velocity arising in the crucible uch = 0.05 m s−1 . This leads to the fact that Rem is much smaller than 1 (Moreau, 1990). Therefore, the effect of the conducting fluid on the magnetic fluid is neglected in the present study. This assumption leads to a simplification of Ohm’s law. Then, j is calculated as a function of the electrical field E as follows:
j=σE
(3)
In the present paper, the axisymmetrical eddy current model implemented in the MaxFEM software is adopted in order to obtain the mean Lorentz force field in the melt. For this purpose, an axisymmetrical model of the ICF is utilised. Here, the presence of the non-conductive crucible walls can be neglected due to the fact that a non-conductive material does not have an effect on B . The Dirichlet boundary condition with a magnetic vector potential A = 0 is set on the whole outer boundary of the computational domain. In the induction furnace, the potential drop is set to V = 0. Then, the Lorentz force field is interpolated on the computationaschefflerl grid in OpenFOAM to simulate the flow field. For more details about the determination of the Lorentz force and case-setup, the reader is referred to Bermúdez et al. (2014). Melt heating due to the Joule dissipation is not accounted for in the present study. 2.2. Fluid phase In the current paper, the melt flow is described in an Eulerian framework and is considered to be incompressible, isothermal and turbulent. Therefore, the motion of the Newtonian liquid is described by the unsteady Reynolds-averaged Navier–Stokes (URANS) equations for mass and momentum conservation:
∇ · u=0
(4)
1 ∂u + (u · ∇ )u = − ∇ p + ∇ · (ν ∇ u ) + ∇ · τ RS + F lor + Sfilter ∂t ρ (5) where ρ and ν stand for the density and the kinematic viscosity of the melt, respectively. u is the Reynolds-averaged velocity, p denotes the Reynolds-averaged pressure. F lor denotes the Lorentz force driving the melt flow. Sfilter is the Darcy term to account for the pressure drop in the filter (see, Section 2.5). Reynolds stress
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tensor τ RS is modelled by using the k-ω SST turbulence model (Menter, 1994) .The formulation of this model switches between the standard k-ε model (Launder and Spalding, 1974) and the kω model (Wilcox, 1988). The switch to the k-ω behaviour occurs in the wall vicinity to exploit the advantages of this model in describing the flow at the crucible walls. The transport equations for the kinetic energy k and turbulent specific dissipation rate ω are expressed as follows:
∂k + ∇ · (k u ) = Pk − β ∗ k ω + ∇ · [(ν + σk νt )∇ k] ∂t
(6)
+
2
ω
(1 − F1 ) σw2 ∇ k ∇ ω.
(7)
Here, the model coefficients are σk = σw = 0.5, σw2 = 0.85, α1 = 0.31, αw = 0.44, β = 0.075 and β ∗ = 0.09. The magnitude of the strain rate is represented by S. The blending functions F1 and F2 are responsible to switch between the two models depending on the flow region (in the wall vicinity or far from the wall). The impact of F lor on the turbulence is neglected in the present paper. 2.3. Disperse phase In the present numerical model, each particle is tracked as a Lagrangian mass point in the flow field. The calculation of particle trajectories is performed, taking into account the assumption that the particles do not influence the flow structure and velocities (one-way coupling). This assumption is valid because the volume of the particles does not exceed 0.1% of the fluid volume (Šˇcepanskis et al., 2014). Moreover, the particle-particle interaction can be neglected, since the relation described by Loth (20 0 0) is valid. This relation is based on eddy life time and the time for a particle to traverse such an eddy. The used relation is expressed as follows:
=
Nt π
V
d2p
(γ 2 + 1 )
1,
(8)
where Nt is the total number of the particles in the fluid volume, dp is the particle diameter, γ is ratio of the particle terminal velocity up,term to root mean square velocity urms of the turbulent fluctuations. V denotes the volume of the utilised crucible. is the eddy integral length scale. For the simulation parameters, lies in the 0.0 05–0.0 08 range, which implies that the particle-particle interaction can be neglected in the simulations. Furthermore, it is assumed that the particles possess a spherical shape with a constant diameter. The following equation describes the particle motion in the flow field:
mp
du p dt
= F B + F G + F D + F EM + F V M + F L .
(9)
Here, mp and up denote the mass and velocity of a particle, respectively. FB , FG , FD , FEM , FVM and FL stand for buoyancy, gravitational, drag, electromagnetic, virtual mass force and lift force. The modelling of the forces is described in the following paragraphs. Buoyancy and gravitational force The buoyancy force FB and gravitational force FG are calculated in OpenFOAM using the following equation:
FB + FG =
(ρ p − ρ ) π d3p 6
Drag force The drag force FD is calculated in the present work by using the following equation:
d p u p − u 3 μ FD = C Re u − u , Re = . p p D p 4 ρ p d2p ν
(11)
u is the Reynolds-averaged fluid velocity obtained from Eq. (5). The drag coefficient CD is estimated by means of an empirical relation implemented in OpenFOAM 2.3.x for a spherical solid particle. It is expressed as follows:
CD =
∂ω + ∇ · (ω u ) = αw S2 − β ω2 + [(ν + σw νt )∇ ω] ∂t
301
24
1+ 0.424 Re p
1 6
Re0p.687
; Re p ≤ 10 0 0 ; Re p > 10 0 0.
(12)
Electromagnetic force The particles are affected by the electromagnetic field, since their electrical conductivity differs from that of the melt. This introduces inhomogeneity in a locally homogeneous magnetic field which leads to an electromagnetic force FEM moving the particles in the direction of the wall within the skin depth δ . The relation of this force can be derived by solving the Laplace equations for current density Leenov and Kolin (1954). In the case of steady-state magnetic field and non-magnetic particles, this relation can be reduced as shown in Šˇcepanskis et al. (2012, 2011) to:
F EM = −
3 σ − σp Vp F lor . 2 2σ + σ p
(13)
Here, σ , σ p and Vp represent the electrical conductivity of the steel melt, the electrical conductivity of a particle and the volume of a particle. In this study, it is assumed that the particles in the flow field are non-conductive. Thus, σ p can be set to 0; hence the calculation of FEM can be simplified to:
3 F EM = − Vp F lor . 4
(14)
The equation of FEM is adopted as well in a study conducted by Šˇcepanskis et al. (2012, 2011) in order to investigate particle-laden turbulent flow in an induction furnace. Lift force The lift force FL acting on the particle in the shear flow can be estimated as follows:
F L = CL ρ
π d3p 6
u − u p × (∇ × u ).
(15)
CL is the lift coefficient calculated in OpenFOAM according to the Saffman–Mei model. This model was derived by Saffman (1965) and extended later by Mei (1992). Virtual mass force The virtual mass force FVM is computed as:
F VM = CVM ρ
π d3p Du 6
Dt
−
Du p Dt
.
(16)
In the present study, the particles are assumed to be spherical. Also, the particle diameter is much smaller than the Kolmogorow length. This leads to the fact that the flow around the particle is laminar. Thus, the virtual mass coefficient CVM for spherical particles can be equal to 0.5 resulting from the potential theory (Crowe et al., 1998). 2.4. Particle dispersion
g.
(10)
Here, ρ p , ρ and g represent the density of a particle, the density of the liquid and the gravitational acceleration, respectively.
In order to consider the particle dispersion, the Discrete Random Walk (DRW) model, or “eddy lifetime” model is adopted. Here, the fluctuating velocity components u is kept constant over
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the eddy lifetime. The value of u obeys a Gaussian probability distribution. It then follows on the assumption of isotropic turbulence:
u =
ξd
2k , 3
(17)
where ξ is a scalar formed by normally distributed random numbers. d is a random vector added in OpenFOAM to realise the spatial randomness of turbulence. 2.5. Porous medium To simplify the numerical model, the filter is considered as being a homogeneous isotropic porous medium. Therefore, the source term Sfilter included in Eq. (5) is computed by applying Darcy’s law:
S f ilter = −
1
ρ
∇p =
μ u. κ
(18)
Ceramic filters are expected to be produced with a pore density in the range of 8–100 ppi (Scheffler and Colombo, 2006). This implies that the filter permeability κ is expected to be approximately in the range of 10−6 -10−11 m2 according to the results summarised in Scheffler and Colombo (2006). To cover a larger range of κ , it is varied in the range of 10−5 -10−12 m2 in the present investigation in order to study its effect on the filter efficiency η. To our knowledge, there is no validated empirical model to detect the separation probability of particles from a melt moving through a porous filter used in metallurgical processes. Therefore, the authors defined a random number χ for each particle traversing the porous filter. If χ > 50%, the particle should be stuck in the filter; otherwise it passes the filter.
Fig. 2. Axisymmetrical section of the induction crucible furnace (ICF1 and ICF2) with the important dimensions.The height of the melt and the coil in the case of ICF1 is equal (H1 = H2 = 0). Table 2 lists the dimensions of the ICF1 and ICF2.
2.6. Flow simulation setup As mentioned previously, an experiment conducted by Baake et al. (1995) is used as a reference configuration in order to validate the performance of the developed numerical model to describe the flow field in an ICF without a filter. This configuration is described in the following ICF1. The numerical model is then employed to describe the melt flow inside the induction crucible furnace of a new type of real steel casting simulator, described in the following ICF2. In this case, a filter is immersed in the melt. A schematic sketch of the ICF1 and the ICF2 is presented in Fig. 2. The ICF1 and the ICF2 have different dimensions and shape (see, Table 2). Here, it should be noted that the ICF2 has a curvature with a radius of R3 at the lower corner, while the ICF1 has an angled lower corner (R3 = 0). Moreover, it should be noted that the height of the melt and the coil are equal in the case of ICF1. In the present investigation, the effect of the filter position is studied. The filter positions studied here are presented in Fig. 3. Here, the position (2) denotes the place of the filter at the central axis of the ICF2, while positions (1) and (3) show off-centre positions of the filter. In the present study, the filter has a squared shape and its dimension is listed in Table 2. The Wood’s alloy is used as an operating fluid in the ICF1, while the operating fluid in the ICF2 of the casting simulator is a steel melt. The material properties of both fluids can be found in Table 1 and are assumed to be constant. The operation parameters of the ICF1 and ICF2 are listed in Table 1. Convection in the Navier-Stokes Eq. (5) is discretised by using the second order central differencing scheme, while convection in the turbulence model is (see, Eqs. (6) and (7)). For the temporal discretisation scheme, the second order backward differencing scheme is adopted in Eqs. (5–7).
Fig. 3. Schematic sketch of the ICF2 to show filter positions studied in the present paper. Table 1 Physical parameters of the simulations performed in the present paper. Process parameters of the induction furnaces Quantity
ICF1
ICF2
Coil current (rms) I [A] Frequency f [Hz] Number of coil windings n [-] Coil length l[m] Magnetic field strength B[T]
20 0 0 400 12 0.57 0.069
180 3400 10 0.4 0.01
Wood melt
Steel melt
9400 4.2e − 3 1.257e − 6 6e6
70 0 0 6e − 3 1.257e − 6 7e5
Liquid properties Quantity
−3
Density ρ kg m Dynamic viscosity μ m2 s−1 Magnetic permeability μ0 [H m−1 ] Electrical conductivity σ [S m−1 ] Particles properties Quantity
−3
Density ρ p kg m Diameter dp [μm] Electrical conductivity σ [S m−1 ]
30 0 0 20, 40, 60 0
A. Asad et al. / International Journal of Heat and Fluid Flow 62 (2016) 299–312 Table 2 Important dimensions of the simulated configuration ICF1 and ICF2 in the present paper. Dimensions[mm]
ICF1
ICF2
H1 Hc Rc1 Rc2 R1 R2 R3 Hf df
0 570 197 207 158 R2 = R1 – – –
165 400 222.5 240 110 105 20 60 10
The computational grid of the ICF1 consists of 20 0,0 0 0 cells, while the computational grid of the ICF2 has 50 0,0 0 0 cells. In both cases, the mesh is generated by SnappyHexMesh, which is a meshing tool in OpenFOAM. The hybrid mesh is structured and equidistant in the core region of the melt, while near-wall layers are unstructured. The crucible walls are treated as no-slip walls. The free surface deformation is neglected and considered as a slip wall. To our knowledge, there is no suitable wall function to describe the magnetically driven turbulent flow in the near wall region. Therefore, the standard wall functions are employed in this study (Spalding, 1961). Particle separation at the crucible walls is not taken into account in the present paper. Moreover, the effect of the material of the crucible walls on the filtration rate is not considered. 3. Results and discussion 3.1. ICF1 The ICF1 is employed in order to validate the numerical model. As mentioned previously, the Lorentz force distribution is computed by means of MaxFEM. Here, an axisymmetical model of the ICF1 is utilised. Then, it is interpolated using the “KDTree algorithm for nearest neighbour lookup” (Maneewongvatana and Mount, 2002) on the 3D OpenFOAM-mesh to simulate the melt
303
flow in the ICF1. The flow field in the ICF1 is averaged over 270 s. The averaged flow pattern indicated in Fig. 4 consists of a twovortices structure, which is created by the interaction of the flow coming from the top and bottom along the crucible wall. It can be noticed that higher velocities are found in the region close to the wall. Furthermore, regions of low velocity are found in the area between the lower and upper vortices. A little asymmetry is found in the time-averaged flow pattern due to the long-term oscillations of the large vortex structure that typically dominate the flow in an ICF. In Fig. 5, a comparison between the numerical prediction and the experimental data is presented over Line 1 located at y = −158 mm between x = 0 and x = 158 mm (see, Fig. 4). The experimental data is obtained from an experiment conducted by Baake et al. (1995) by using magnetic sensors (see, Fig. 4). It is apparent that the numerical predication of the timeaveraged liquid velocity matches well with the experiment. 3.2. ICF2 In this section, the numerical model validated previously in Section 3.1 is employed to describe the steel melt flow in the ICF2 of the real steel casting simulator investigated experimentally in our laboratory. Here, it must be stated that flow measurements in liquid steel are still not possible. Therefore, the numerical results of the ICF2 are not compared with experimental data. Additionally, 1100 solid particles are injected from the upper wall of the flow field at a time step t = 30 s, as the flow is fully developed in order to determine the filtration efficiency of the different flow configurations. The filter is then immersed in the melt at t = 60 s. The flow field is averaged over 240 s. Here, the time averaging of the flow field starts at t = 60 s. 3.2.1. Magnetic field Fig. 6 presents the radial and vertical Lorentz force distribution in the steel melt. The core region of the melt with low Lorentz force is omitted in Fig. 6. Due to the skin effect in the melt, it is clearly seen that the Lorentz force is concentrated in the region
Fig. 4. Mean flow velocity and streamlines in the central plane of the ICF1. Line 1 is used as a sampling line to compare the numerical and experimental results. Line 1 is located at y = −158 mm between x = 0 and x = 158 mm.
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Fig. 5. A comparison between the numerical results of the time-averaged vertical velocity in the ICF1 uy with the experimental data (Baake et al., 1995) over Line 1 (see, Fig. 4).
close to the wall. From Fig. 6a, one can observe that the radial Lorentz force component Flor,r has an asymmetrical profile with the respect to the axial direction, where a higher value of Flor,r is observed at the upper corner of the melt. The vertical Lorentz force component Flor,y is indicated in Fig. 6b. Here, it is observed that Flor,y is not mirror symmetric with the respect to the axial direction by comparing the upper and lower corners of the melt. This asymmetry of Flor,r and Flor,y can be attributed mainly to the asymmetrical position of the melt relative to the coil. Although the Lorentz force distribution is not mirror symmetric, the Lorentz force exhibits an rotational symmetrical distribution. 3.2.2. Flow field without filter In Fig. 7, the time-averaged velocity field and streamlines in the horizontal and vertical planes of the ICF2 are indicated. Although the flow setup and the Lorentz force distribution are axisymmetric, slight deviations from axisymmetry are found in the time-averaged numerical results. This implies that long-term flow fluctuations have a significant impact on the results. An exemplary snapshot of the velocity field shown in Fig. 8 indicates the influence of the these fluctuations. Here, the right-hand and the left-hand side toroidal vortex is connected by streamlines, which pass through the symmetry line (central axis) of the crucible. Secondary eddy structures are present in the low-velocity core region of the instantaneous flow (see, Fig. 8b). Here, a nearly symmetric flow structure is only observed in the long-term averaged flow in Fig. 7b.
Fig. 6. Lorentz force distribution in an axisymmetrical section of the ICF2: radial Lorentz force (a); vertical Lorentz force (b). The core region of the melt with low Lorentz force is omitted.
3.2.3. Flow field with filter Firstly, the influence of filter position and of filter permeability on the melt flow pattern in the ICF2 are studied. The averaged flow pattern in case of one ceramic filter located at the central axis of the ICF2 is shown in Fig. 9. For filter permeability in the range of (κ = 10−6 , 10−12 m2 ), it is clear that the filter leads to a lower flow velocity in the central region of the melt due to the higher flow resistance in this region, compared to the case without the filter presented previously. Comparing the averaged flow pattern in the vertical plane of the ICF2, higher flow velocity in the lower part of the used filter and in the region beneath the filter can be observed in the case of κ = 10−6 m2 , which is expected to be corresponded to a ceramic filter with a pore density of about 8–10 ppi. Exemplary snapshots of the instantaneous velocity field are presented in Fig. 10. The flow field in the vertical middle plane for all considered permeability is dominated by the large eddies as noticed in the case of the time-averaged velocity field as well. The difference between the instantaneous and the time-averaged velocity field can be noticed
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Fig. 7. Mean flow velocity and streamlines in the ICF2: a) vertical middle plane; b) horizontal plane at y = 17 mm.
considerably in the horizontal plane, where the secondary eddy structure is observed in this plane. In case the of κ = 10−6 m2 , it is seen that the eddy enters the filter due to the low flow resistance in this case. For κ = 10−12 m2 , the eddies do not enter the filter. Moreover, streamlines are deflected at the filter. Fig. 11 depicts the time-averaged velocity field in the case of one immersed filter located at position (3) (see, Fig. 3). The secondary eddies are still observed in the time-averaged flow for all filter permeability considered here. For κ = 10−6 m2 , the streamlines are not influenced by the filter significantly, as indicated in Fig. 11a. However, it can be seen in the vertical plane of the ICF2 that the toroidal vortex is shifted to the region between the melt surface and the immersed filter. On the contrary, the filter impacts the streamlines considerably in the case of κ = 10−12 m2 . In the horizontal plane, it is found that the streamline are deflected at the filter and they do not enter the filter because of the high flow resistance. The considerable impact of the filter with κ = 10−12 m2 is found in the instantaneous snapshots of the flow field as well, as shown in Fig. 12b. The effect of using two ceramic filters on the melt flow is investigated as well in the present paper. The two filters are situated at
positions (1) and (3) shown in Fig. 3. The time-averaged flow field indicated in Fig. 13b has a little asymmetry, which implies that the long-term fluctuations affects the numerical results in this case as well. As seen previously, the filter with κ = 10−12 m2 has a higher effect on the flow than the filter with κ = 10−6 m2 . The secondary eddies in the horizontal plane are observed in the time-averaged as well as in the instantaneous flow field (see, Fig. 14). Video 1 shows the simulation of the velocity field in case of one filter at position (2) and two filters at positions (1) and (3) for κ = 10−12 .
3.3. Filter efficiency The effect of the filter permeability κ , particle diameter dp and filter position on the filter efficiency η is investigated in the following paragraphs. In order to focus on the capability of the filter to capture the particles moving in the melt, no additional implementation is included to keep the particles at the free surface because of the wetting effect, which can happen in the reality. The ratio of the particles captured by the filter Nc to the total num-
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Fig. 8. Instantaneous flow velocity and streamlines in the ICF2: a) vertical middle plane; b) horizontal plane at y = 17 mm.
ber of injected particles Nt = 1100 characterises the filter efficiency η = Nc/Nt. The filtration time is 240 s.
3.3.1. Filter permeability The impact of the filter permeability κ on η is presented in Fig. 15. Here, the filter is located at position (2) (see, Fig. 3). As it can be seen here, the permeability and efficiency of the used filter are directly correlated. Reducing the permeability results in capturing less particles by the filter. This finding is explained by the fact that the flow rate through the filter is lower in the case of the low permeability compared to those cases with high permeability. At the end, this leads to a reduction in the number of particles reaching the filter. The higher filter efficiency is achieved by using a filter with a permeability of κ = 10−5 m2 . For a filter permeability in the range of 10−7 –10−12 m2 , the efficiency does not depend on the permeability. This result might be attributed to the slightly changed flow pattern for this range as indicated previously.
3.3.2. Particle diameter The number of particles captured by the filter located at position (2) depends on the particle diameter as can be recognised from Fig. 15. For a particle diameter of d p = 60 μm, the filter exhibits a lower efficiency compared to the cases with a smaller particles diameter. The reason for these results is that, the particles with d p = 60 μm are frequently accumulated at the upper corners of the flow field, where the flow velocity is not enough to force the particles to follow the melt flow and the buoyancy is dominated for these particles. This implies that they are not able to follow the flow to reach the filter. This aspect does not occur often for the smaller particles with d p = 20 μm. Video 2 shows the simulation of the particles for d p = 20 μm and d p = 60 μm. 3.3.3. Filter position Fig. 16 compares the effect of filter position and filters number on η for two filters permeability (κ = 10−6 , 10−12 m2 ). As it can be seen, η is affected considerably by filter position and the number of the used filter. A strong increase of η is observed in the case of two filters for κ = 10−6 , 10−12 m2 . However, η is not doubled
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Fig. 9. Mean velocity flow in the case of one filter located at position (2) in the ICF2 (see, Fig. 3) to show the effect of the filter permeability κ on the velocity field of the liquid in the vertical middle plane (left) and horizontal plane at y = 17 mm (right) of the ICF2, the red box represents the position of the filter: a) κ = 10−6 m2 b) κ = 10−12 m2 . (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 10. Instantaneous snapshots of flow in the case of one filter located at position (2) in the ICF2 (see, Fig. 3) to show the effect of the filter permeability κ on the instantaneous velocity field of the liquid in the vertical middle plane (left) and horizontal plane at y = 17 mm (right) of the ICF2, the red box represents the position of the filter: a) κ = 10−6 m2 ; b) κ = 10−12 m2 . (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 11. Mean velocity flow in the case of one filter located at position (3) in the ICF2 (see, Fig. 3) to show the effect of the filter permeability κ on the velocity field of the liquid in the vertical middle plane (left) and horizontal plane at y = 17 mm (right) of the ICF2, the red box represents the position of the filter: a) κ = 10−6 m2 ; b) κ = 10−12 m2 . (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 12. Instantaneous snapshots of the melt flow in the case of one filter located at position (3) to show the effect of the filter permeability κ on the instantaneous velocity field of the liquid in the vertical middle plane (left) and horizontal plane at y = 17 mm (right) of the ICF2, the red box represents the position of the filter: a) κ = 10−6 m2 ; b) κ = 10−12 m2 . (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 13. Mean velocity flow in the case of two filters located at position (1) and (3) to show the effect of the filter permeability κ on the velocity field of the liquid in the vertical middle plane (left) and horizontal plane at y = 17 mm (right) of the ICF2, the red box represents the position of the filter: a) κ = 10−6 m2 ; b) κ = 10−12 m2 . (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 14. Instantaneous snapshots of the melt flow in the case of two filters located at position (1) and (3) to show the effect of the filter permeability κ on the instantaneous velocity field of the liquid in the vertical middle plane (left) and horizontal plane at y = 17 mm (right) of the ICF2, the red box represents the position of the filter: a) κ = 10−6 m2 ; b) κ = 10−12 m2 . (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 15. Influence of the filter permeability κ and particles diameter dp on the filtration rate η.
in the case of two filters. The shift of filter from position (2) to position (3) shows only a small effect in case of κ = 10−6 m2 and no effect in the case of κ = 10−12 m2 . In case of one filter located at position (3), η does not show a strong increase by using a filter with κ = 10−12 m2 compared to the case with the filter located at position (2). 4. Conclusion The present paper proposes a new principle to enhance nonmetallic particles removal in an induction furnace by using a ceramic filter immersed in the melt. A numerical model is formulated in order to describe the electromagnetically driven turbulent melt flow and the behaviour of small dispersed particles in an induction furnace. Experimental data is used to validate the numerical model for the melt flow. Here, it is indicated that the numerical model is able to estimate the averaged flow velocity well. Then, the validated numerical model is adopted to simulate the melt flow in an induction furnace of a real steel casting simulator. In this case, the flow is studied, taking into account the effect of an immersed ceramic filter. In this case, the considerable effect of the filter and its permeability on the melt flow is presented. The filter leads to a decrease in the flow velocity in the region, where it is
located. Moreover, it is found that the flow streamlines in the filter region depends considerably on its permeability. Low filter permeability caused a high flow resistance. This leads to the fact that flow streamlines try to turn around the filter. Additionally, the significant impact of the filter position on the flow pattern is shown. The filter efficiency to capture these particles is investigated in the present work as well. The filter provides the ability to sufficiently capture the particles in case of high permeability. Furthermore, it is indicated that the number of particles captured by the filter decreases by increasing the particles’ diameter. In addition, the numerical result shows that the filter efficiency also depends on filter position and number of used filter. Based on the results from this study, experimental investigations of the filtration efficiency in an induction furnace are planned. In the experiment, the filters are placed at the locations, which show high filtration efficiency in the simulation. In future study, the enhancement of filter performance to capture the non-metallic particles will be investigated by optimising filter position and filter permeability. Moreover, the influence of crucible walls and their materials on particle separation will be considered and discussed. Furthermore, the effect of the choice of the turbulence models and the mesh resolution on the quality of the results will be studied and discussed and in further studies.
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Fig. 16. Influence of the filter position on the filtration rate η. The filter positions can be found in Fig. 3.
Acknowledgments The authors would like to thank the German Science Foundation (DFG) for supporting the scientific work in terms of the Collaborative Research Centre Multi-Functional Filters for Metal Melt Filtration-A Contribute towards Zero Defect Materials (CRC 920 B06). The authors are grateful to Pascal Beckstein and Thomas Wondrak for providing the interpolation tool used in the present work. Supplementary material Supplementary material associated with this article can be found, in the online version, at 10.1016/j.ijheatfluidflow.2016.10. 002. References Aneziris, C., Dudczig, S., Hubálková, J., Emmel, M., Schmidt, G., 2013. Alumina coatings on carbon bonded alumina nozzles for active filtration of steel melts. Ceram. Int. 39 (3), 2835–2843. doi:10.1016/j.ceramint.2012.09.055. Baake, E., Mühlbauer, A., Jakowitsch, A., Andree, W., 1995. Extension of the k-ε model for the numerical simulation of the melt flow in induction crucible furnaces. Metall. Mater. Trans. B 26 (3), 529–536. doi:10.1007/BF02653870. Baake, E., Nacke, B., Bernier, F., Vogt, M., Mühlbauer, A., Blum, M., 2003. Experimental and numerical investigations of the temperature field and melt flow in the induction furnace with cold crucible. COMPEL -Int. J. Comput. Math. Electr. Electron. Eng. 22 (1), 88–97. doi:10.1108/03321640310452196.
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