The Model Analysis of Inclusion Moving in the Swirl Flow Zone Sourcing from the Inner-Swirl-Type Turbulence Controller in Tundish

The inner-swirl-type turbulence controller (ISTTC) in tundish

In the actual tundish there was installed a conventional turbulence inhibitor (TI) to increase the mean residence time, depress the turbulence in the impact zone and enhance the coalescence of inclusions, as shown in Figure 1.

Figure 1:

The tundish with a conventional turbulence inhibitor.

In order to form swirling flow in the impact zone of tundish to enhance the inclusions removing, the inner-swirl-type turbulence controller (ISTTC) was developed, Figure 2. In the ISTTC, there were six blades arranged with an eccentric angle (θ) counterclockwise and the blades forced the fluid circulating counterclockwise, so the centrifugal force of molten steel could trap the inclusion in the swirling flow, and could enhance the coalescence and removal of inclusions. In this paper, the eccentric angle of blades in ISTTC, θ=15, 30 and 45 for mathematical model and water model.

Figure 2:

The tundish with ISTTC.

The mathematical model

The mathematical model for flow field in tundish was created with the following assumptions:

1. the flow field was under steady and turbulent condition;

2. the tundish was filled with a single-phase incompressible fluid with homogenous density;

3. the top surface of the fluid was a flat surface without tangential stress.

4. the fluid in tundish was isothermal.

The flow field of tundish was simulated with the continuity eq. (1) and the Navier–Stokes eq. (2) under steady condition as follows:

The continuity equation:

The Navier–Stokes equation:

In the Navier–Stokes equation, the effective viscosity (μ_eff) was determined by eq. (3):

where, the turbulence viscosity (μ_t) could be calculated by k–ε two equation model.

Boundary conditions of the model were summarized as follows:

1. the fluid at the inlet was normal to the entry plane with the flat velocity profile;

2. the gauge pressure of the flow field at the outlet was constant to zero;

3. the tundish walls were under the no-slipping conditions;

4. the top surface of tundish was under the conditions of all variables with the zero normal gradients.

In the tundish equipped with ISTTC, a swirling flow zone was formed outside the shroud. The molten steel and inclusion were circulated in this area, and the motion of inclusion in the steel melt was influenced by resultant force of centrifugal force of the molten steel, centrifugal inclusion itself and Stokes force, as described in eq. (4):

The centrifugal force of the molten steel (F_C) drove the inclusions toward the center of swirling flow, which could be determined with eq. (5).

The centrifugal force of the inclusion itself (F_A) kept the inclusions away from the center of swirling flow, which could be described in eq. (6).

The Stokes force dragged inclusions against the motion of themselves, which could be determined with eq. (7).

Combining the eqs (4), (5), (6) and (7), the equation of the inclusion motion could be described as eq. (8):

The inclusions’ radial relative velocity U_r in the swirling flow was evaluated with eq. (8) from inclusions’ tangential velocity U_pt, which was assumed to be same with the tangential velocity of swirling flow.

A sophisticatedly computational fluid dynamics (CFD) software package of ICEM CFD and ANSYS-Fluent had been applied in this study. The geometric models or boundary conditions of the prototype tundish were built by ICEM CFD software of 12.1 version and about 480,000 mixed tetrahedral grids with different mesh spacing at different parts of the tundish were generated. The N-S equations were solved by the SIMPLE (semi-implicit method for pressure-linked equations) algorithm. A criterion for convergence was established whereby the sum of all residuals for all variables in the momentum was <10^–5. The velocity fields were calculated at steady state.

The physical model

With the aim to study the inclusion removal rate of the tundish with ISTTC, a water model was established, in which polyethylene particles were injected with syringe to simulate the inclusion in the real tundish. The schematic of the water model was shown in Figure 3.

Figure 3:

The schematic of water model.

To ensure the water model to simulate the prototype tundish, geometrical and dynamic similarity rules should be fulfilled. In this case, the water model and the prototype should have the same Froude number. And the similarity ratio (λ) of the model to prototype model was 1:3. So with eq. (9), the inlet flow rate of the water model could be determined. The parameters of water model were listed in Table 2.

In order to simulate the inclusion movement in tundish with polyethylene particle, the ratio of the polyethylene particle’s floating velocity to water’s flow velocity should be equal to the ratio of inclusion’s floating velocity to molten steel’s flow velocity. Based on the Stokes formula for the particle floating velocity in liquid, the size of polyethylene could be determined with eq. (10).

The polyethylene particles of 3 size groups (58–75 μm, 75–106 μm and 106–150 μm) were used in water model to simulate the inclusion with the size: 21–28 μm, 28–39 μm and 39–56 μm in actual tundish.

In the experiment, after attaining steady-state fiow condition in water model, 5 g (W_e) polyethylene particles were injected into the shroud, and the particles were collected with filter cloth at the outlets. During the experiment time which was lapsed of 2000s, the particles collected at the outlets of tundish were dehydrated and weighed as W_g. The particle removal ratio of the water model was estimated with the eq. (11).

During the experiment time, it was found that there were few particles stuck at the walls in the tundish with conventional TI or ISTTC. Because buoyant force (due to polyethylene lighter than water) was larger than viscous drag force of water flow, most large size polyethylene particles (106–150 μm) were not trapped in the water flow going toward outlets, instead, they floated up to the surface of water and stayed at surface as the surface disturbance of water was weak. But for small size polyethylene particles (58–75 μm), viscous drag force of water flow was much larger than buoyant force, so the number of small size particles trapped in water flow was more than that of particles floating to water surface in the tundish with conventional TI. With the effect of swirling flow at the impact zone of tundish, the more number of particles floated up to surface in the impact zone and stayed at there, and less number of particles went with water flow to outlets in the tundish with ISTTC.

Comparison of traditional TI and ISTTC on fluid flow in tundish

The stream line of fluid in impact zone of tundish with traditional TI was shown in Figure 4. It showed that the incoming flow from shroud flushed down into the traditional TI, and then the reflection flow rushed up from the TI. So the reflection flow collided with the incoming flow at the confluence area above the TI and depressed the velocity of the two streams of flow. In other words, the turbulence inhibiting was taken place in the intersection zone above the traditional TI, instead of inside it. The vector diagram of flow field in impact zone of tundish with traditional TI was shown in Figure 5. It was found in Figure 5 that there was the strong reflection flow running up to the liquid surface around the shroud, so the slag open eye would be formed around the shroud, which exposed steel melt to the air.

Figure 4:

The stream line diagram of flow field in impact zone of tundish with traditional TI.

Figure 5:

The vector diagram of flow field in impact zone of tundish with traditional TI.

In Figure 6, it was shown that the helical type swirling flow was formed inside the ISTTC, which was induced by the blades arranged with an eccentric angle counterclockwise. So the turbulence was inhibited inside the ISTTC through the helical type swirling flow crashed with incoming flow and the collision probability of inclusions in the liquid steel was increased remarkably. And from the vector diagram of impact zone of tundish with ISTTC, it was shown that the up flow around the shroud was weak and swirling Figure 7(a). So ISTTC could decrease fluctuation of surface around shroud. And the swirling flow zone sourced from ISTTC was just around shroud, Figure 7(b), so the inclusion could be trapped in this region by centripetal force of the swirling flow, while the homogeneity of residence time of the outflows at the both side of tundish was ensured. The maximum turbulent dissipation rate occurred at the center of shroud, where the down flow had got the velocity with the maximum magnitude. For TI, the down flow was collided with the up flow sourced from TI, and for ISTTC, the down flow was transferred to swirling flow, there was no confluence between up and down flows. So the velocity at the center of shroud is larger for ISTTC than TI, and maximum turbulent dissipation rate is higher for ISTTC than TI (Figure 8(a) and 8(b)). With the traditional TI, the turbulence dissipation rate could be reduced to less than 0.05 at the region just outside TI, Figure 8(a), as the collision between the up and down flows could depress the turbulence dissipation rate. With ISTTC the turbulence dissipation rate could be reduced to less than 0.005 at the region outside of the swirling zone sourcing from ISTTC, Figure 8(b), as the helical type swirling flow formed inside ISTTC could crash the center down flow from shroud more effectively. It was clear that ISTTC had better effect to turbulence inhibiting than traditional TI.

Figure 6:

The stream line diagram of flow field in impact zone of tundish with ISTTC.

Figure 7:

The vector diagram of flow field in impact zone of tundish with ISTTC. (a) Front view of impact zone (b) Top view of impact zone.

Figure 8:

The contour of turbulent dissipation rate in impact zone of tundish with ISTTC. (a) tundish with tradition TI (b) tundish with ISTTC.

From the above analysis, the characteristics of flow field of impact zone in tundish with ISTTC was swirling flow formed above the ISTTC (Figure 7) and helical type swirling flow inside it (Figure 6). So it was clear that ISTTC was more effective on inhibiting turbulence of impact zone in tundish than the traditional TI.

Velocity distribution of the fluid flow formed by ISTTC

ISTTC formed swirling flow in the zone above itself and the tangential velocity in swirling flow was function of vertical height. The eccentric angle (θ) of blades erected in ISTTC had great effect on the swirling flow. All these aspects would be analyzed in the following section.

The tangential velocity distribution of zone above ISTTC with blades eccentric angle (θ) of 15° was shown in Figure 9(a). It was found that at the plane with vertical distance of 0.01 m from the upper surface of ISTTC (h_pl=0.01 m) the swirling flow band was formed within the range of interior edge of ISTTC, the radius of the band was 0.17 m, and the maximum tangential velocity in the swirling flow band was 0.045 m/s. It was evident that the center area of ISTTC(including down flow area) was involved in swirling flow. So in the whole area within the ISTTC there was swirling flow band and the turbulence of income flow could be effectively depressed. At the plane with h_pl=0.1 m, the swirling flow band was grown up to highest swirl intensity, the radius of the band was increased to 0.2 m, and the maximum tangential velocity was increased to 0.06 m/s. From the vector diagram of the plane (Figure 9(b)), it was evident that the swirling flow was very strong and fluid of surround area was drawn into the swirling flow zone, so the swirling flow band could promote trap the inclusions from the income flow. At the planes with h_pl equivalent to 0.2 m and 0.3 m, the shape of swirling flow bands was changed to annulus, the inner radiuses of the swirling flow band of the above planes were both 0.065 m, and the outer radiuses were both 0.2 m. As the height of planes increased and the planes were closer to the end of shroud, the effect of down flow from the shroud to the swirling flow band became greater and in the center area there was the strong down flow, so the annular shape of swirling flow band was formed. The maximum tangential velocity in the swirling flow band was 0.033 m/s and 0.049 m/s at the planes with the vertical distance of 0.2 m and 0.3 m, respectively.

Figure 9:

The tangential velocity distribution of zone above ISTTC with θ of 15°. (a) The tangential velocity distribution (b) The vector diagram of plane (h_pl=0.1 m)

Figure 10(a) showed the tangential velocity distribution of the swirling flow zone above ISTTC (θ=30°). At the plane (h_pl=0.01 m), the shape of the swirling flow band was annulus (Figure 10(b)), the outer radius of the swirling flow band was 0.17 m, the inner radius of the swirling flow band was 0.025 m and the maximum tangential velocity in the swirling flow band was 0.1 m/s, which was more than double the maximum tangential velocity of ISTTC (θ=15°). The swirling flow within the ISTTC (θ=30°) was stronger than that ISTTC (θ=15°), but the down flow area in center was not involved into swirling flow. So the effect of turbulence inhibition in ISTTC (θ=30°) was less than that in ISTTC (θ=15°). At the plane (h_pl=0.1 m), the swirling flow band had got almost the same swirl intensity as that of the plane (h_pl=0.01 m), the outer radius of the swirling flow band was increased to 0.2 m, and the maximum tangential velocity was 0.09 m/s. At the planes with the vertical distance of 0.2 m and 0.3 m, the shapes of swirling flow bands were annulus, the inner radiuses of the swirling flow band of the above planes were both 0.065 m, and the outer radiuses were both increased to 0.25 m. The maximum tangential velocity in the swirling flow band was 0.082 m/s and 0.071 m/s at the planes with the h_pl of 0.2 m and 0.3 m, respectively.

Figure 10:

The tangential velocity distribution of zone above ISTTC with θ of 30°. (a) The tangential velocity distribution (b) The vector diagram of plane (h_pl=0.01 m).

Figure 11 (a) illustrated that the tangential velocity distribution of swirling flow zone above ISTTC (θ=45°). At the plane (h_pl=0.01 m), the shape of the swirling flow band was annulus (Figure 11(b)), the outer radius of the swirling flow band was 0.17 m, the inner radius of the swirling flow band was 0.025 m and the maximum tangential velocity in the swirling flow band was 0.14 m/s, which was more than three times as much as the maximum tangential velocity of ISTTC (θ=15°). The swirling flow within the ISTTC(θ=45°) was stronger than that ISTTC (θ=30°), but the down flow area in center was not involved into swirling flow for both of ISTTC(θ=45°) and ISTTC (θ=30°). So the effect of turbulence inhibition in ISTTC (θ=45°) was not as good as that in ISTTC (θ=15°). At the plane (h_pl=0.1 m), the outer radius of the swirling flow band was increased to 0.2 m, and the maximum tangential velocity was 0.14 m/s. At the planes (h_pl=0.2 m), the shape of swirling flow band was also annulus, the inner radius of the swirling flow band of the above plane was 0.065 m, and the outer radiuses were both increased to 0.25 m. The maximum tangential velocity in the swirling flow band was 0.15 m/s, so the swirling flow was reached strongest at the plane (h_pl=0.2 m) for ISTTC (θ=45°). So the tundish with ISTTC (θ=45°) had got the largest and strongest swirling flow zone, compared with the tundishes with ISTTC (θ=15°) and ISTTC (θ=30°).

Figure 11:

The tangential velocity distribution of zone above ISTTC with θ of 45°. (a) The tangential velocity distribution (b) The vector diagram of plane (h_pl=0.01 m).

2.3 The force analysis of inclusion in the fluid flow induced by ISTTC

The aim of creating the swirling flow devices was to improve the inclusion removal efficiency in tundish with centripetal force of swirling flow. So the following section discussed the effect of swirling flow to motion of inclusion through the force analysis.

According to eq. (8), the centripetal force (F_ct) applied to inclusion in swirling flow could be expressed in eq. (12).

As shown in Figure 12, the maximal centripetal force applied to the inclusions with diameter of 5 μm and density of 2700 kg/m³ in swirling flow driven by ISTTC (θ=45°) was 7.5×10^–13 N, and in annular zone (0.025 m<r<0.18 m) there was centripetal force driving the inclusions to the center of shroud. In order to measure the centripetal force in more intuitive way, the force ratio between centripetal force and gravity was evaluated as eq. (13).

Figure 12:

The centripetal force applied to inclusion in swirling flow formed from ISTTC (θ=45°).

As shown in Figure 13, the force ratio between centripetal force and gravity (R_F) in swirling flow from ISTTC (θ=45°) was larger than 0.01 in annular zone (0.025 m<r<0.18 m), i. e. swirling flow band, and the maximum value was 0.055. So the centripetal force from swirling flow could influence the trajectory of inclusions.

Figure 13:

The force ratio between centripetal force and gravity in swirling flow from ISTTC (θ=45°).

According to eq. (12), as increasing the rotate speed, the R_F would increase significantly, but the turbulence also increased. As shown in Figure 14, the maximum rotate speed in swirling flow band driven by ISTTC (θ=45°) was equal to 25 rmp, which was at the same magnitude level of the rotate speed (40 rmp) of swirling flow driven by electromagnetic force in the centrifugal fiow tundish (CFT) [12]. However, the swirling flow band driven from ISTTC was confined within the radius of 0.25 m, so the average turbulence in tundish could be confined in low level and the uniformity of the flows at four outlets of tundish was obtained.

Figure 14:

The maximum rotate speed in swirling flow driven by different swirling flow devices.

The comparison of inclusion removal ratio

With the aim to clarify the effect of ISTTC to the removal ratio of inclusions, water model experiment was carried out, in which polyethylene particles were used to simulate inclusions in liquid steel. The particle removal ratio (R) in water model represented the removal ratio of inclusions in actual tundish.

From the Figure 15, it was found that for large size particle (106–150 μm) all devices had perfect removal effect, i. e. R>95 %. For medium size particle (75–106 μm) the R value of ISTTC was obviously better than that of traditional TI, and the θ value of ISTTC had little influence to particle removal. For small size particle (58–75 μm) the R value of ISTTC (θ=15° and 30°) was almost 50 % better than that of traditional TI, the R value of ISTTC (θ=45°) was near that value of traditional TI. The reasons of these phenomena were that large size particles were easy to separate from fluid, so there were little differences between different devices; for medium size particles, although from eq. (12) the centripetal force (F_ct) applied to inclusion in swirling flow decreased with the reduction of size of particles, F_ct could still have enough influence to the trajectory of particles of that size, and the R values of three types of ISTTCs were better than that of traditional TI; for little size particles F_ct caused by swirling flow was very weak, the ISTTC (θ=15° and 30°) had got better effect for inhibiting turbulence of fluid, so the R value of tundishes with ISTTC (θ=15° and 30°) were obviously better than that value of tundishes with ISTTC (θ=45°) and traditional TI.

Figure 15:

The particle removal ratio (R) in water models with different swirling flow devices.