Suppression of Swirl Motion of a Bottom Blown Bath using a Circular Disk

Abstract

A swirl motion of a bubbling jet is induced in a cylindrical reactor under a certain gas injection condition. Mixing in the bath is highly enhanced in the presence of the swirl motion, whereas the swirl motion itself sometimes causes severe oscillation of the reactor and slopping of the molten metal contained in the reactor. A simple method of suppressing the swirl motion was proposed in this water model study. A circular disk in contact with the bath surface was found to successfully suppress the swirl motion for the disk diameter greater than a certain critical value. Empirical equations were derived for the critical disk diameter.

1. Introduction

Bubbles generated successively at a single-hole bottom nozzle of a steelmaking reactor rise upwards due to buoyant forces acting on them.^1,2,3) The molten metal behind each bubble also rises together with the bubble through the gas-lift effect. As a result, a jet of a mixture of bubbles and molten metal is formed above the nozzle. This jet is commonly called a bubbling jet.

Such a bubbling jet does not always rise straight upwards. It swirls around the vessel axis under a certain gas injection condition due to a hydrodynamic instability (see Fig. 1).^4,5,6,7,8) The liquid outside the bubbling jet rotates in the opposite direction in order to satisfy the conservation of angular momentum. Mixing time is known to be significantly shortened in the presence of the swirl motion.^6,7) Meanwhile, vessel oscillation and slopping of the molten metal contained in the reactor are sometimes induced by the swirl motion. Occurrence of these phenomena is undesirable in the steelmaking industry. Considering these circumstances, a circular disk was chosen in this water model study for suppressing the swirl motion.^7,9) The following two cases were considered:

Fig. 1.

Swirl motion of a bubbling jet in a cylindrical bath.

(1) A circular disk was placed on the bath surface before gas injection.

(2) A circular disk was placed on the bath surface after occurrence of a swirl motion.

2. Occurrence and Suppression Mechanisms of Swirl Motion

Molten metal contained in the wake of a bubble just leaving a reactor is slightly lifted above the bath surface of the reactor. If many bubbles successively leave, a molten metal dome is formed on the bath surface (Fig. 2). The dome is usually called the plume eye or the spout eye of a bubbling jet. It grows with an increase in the gas flow rate, Q_g. That is, both the diameter and height of the plume eye increase with an increase in Q_g. The plume eye oscillates in the vertical and lateral directions. When the lateral oscillation amplitude exceeds a certain critical value, two types of swirl motions of the bubbling jet are induced depending on the aspect ratio of the bath, H_L/D: shallow-water and deep-water wave types.^6,7) The boundary between the two types is located around H_L/D=0.3. Here, H_L is the initial bath depth and D is the vessel diameter. The shallow-water wave type is mainly affected by the bottom wall of the vessel, while the deep-water wave type is mainly done by the side wall. The period of each swirl motion is known to be very close to that of the corresponding type of rotary sloshing caused by an external oscillation of the reactor.⁵⁾

Fig. 2.

Plume eye caused through the gas-lift effect.

Unless a plume eye is formed, the swirl motion of a bubbling jet would not occur. A circular disk therefore was placed on the bath surface to prevent the formation of a plume eye and, hence, to suppress the swirl motion.

3. Experimental Apparatus and Procedure

The inner diameter of a cylindrical vessel made of transparent acrylic resin was D=150, 200, or 300[mm] (see Fig. 2). Air was injected into a water bath from a single-hole bottom nozzle of an inner diameter of d_ni=1.0[mm]. The gas flow rate ranged from Q_g=3[L/min] (50×10⁻⁶ m³/s) to Q_g=20[L/min] (333×10⁻⁶ m³/s). The diameter of the disk was D_s=16, 24, 32, 48, 64, or 80[mm]. Occurrence of a swirl motion was judged by eye inspection and with a high-speed camera having temporal resolution of 600 fps.

4. Experimental Results and Discussion

4.1. Effect of a Circular Disk Placed on the Bath Surface Before Gas Injection

A circular disk was placed on the bath surface before gas injection, as can be seen in Fig. 3. The center of the disk was located above the bottom nozzle. If the diameter of the disk, D_s, is much greater than the plume eye diameter, D_B, any swirl motion of a bubbling jet would not occur. The plume eye diameter, D_B, is approximated by⁷⁾   

$$D_{\mathrm{B}}=2b_{\mathrm{u}}=2\times 0.14H_{\mathrm{L}}=0.28H_{\mathrm{L}}$$(1)

where b_u is the half-value radius of the liquid flow in the bubbling jet. It should be noted that the half-value radius, b_u, is dependent only on the bath depth, H_L, as long as the flow in the jet is turbulent. That is, b_u is not a function of the other parameters such as the gas flow rate, Q_g, bath diameter, D, and inner nozzle diameter, d_ni.

Fig. 3.

Plume eye diameter, D_B, and disk diameter, D_s.

Figure 4 shows the occurrence map of swirl motions in the absence of a disk as a function of the aspect ratio, H_L/D, and the gas flow rate, Q_g, for D=200[mm]. Symbols, ○ and ●, denote the deep-water wave type and shallow-water wave type of swirl motions, respectively, and × does the case that no swirl motion takes place. One of the authors previously proposed empirical equations describing the boundary of the occurrence region of the deep-water wave type of swirl motion¹⁰⁾ (see Fig. 5). The boundary was divided into four sub-boundaries as follows:

Fig. 4.

Occurrence map of swirl motion in the absence of a disk (D=200[mm], d_ni=1.0[mm], —–: Eq. (2), – – -: Eq. (4)).

Fig. 5.

Occurrence region of the deep-water wave type of swirl motion.

(i) Sub-boundary (1)   

$$\frac{H_{\mathrm{L}}}{D}={0.19F{r}_{\mathrm{m}\mathrm{D}}}^{-1/20}$$(2)

  

$$F{r}_{\mathrm{m}\mathrm{D}}=\frac{{Q_{\text{g}}}^2}{g{D}^{\text{5}}}$$(3)

This sub-boundary was derived by assuming that the swirl motion occurs when the height of the plume eye exceeds a certain critical value.

(ii) Sub-boundary (2)   

$$\frac{H_{\mathrm{L}}}{D}=(1+0.3logWe){}^{1/2}$$(4)

  

$$\text{We}=\frac{{\rho }_L{Q_{\text{g}}}^2}{\sigma D^{\text{3}}}$$(5)

Equation (4) was obtained by correlating existing measured data on this sub-boundary as a function of the modified Weber number, We.

(iii) Sub-boundary (3)   

$$\frac{H_{\mathrm{L}}}{D}=1.06$$(6)

This sub-boundary was given by assuming that the swirl motion ceases when the diameter of the plume eye exceeds a certain critical value.

(iv) Sub-boundary (4)   

$$\frac{H_{\mathrm{L}}}{D}=\frac{3.4}{{D{d}_{\mathrm{n}\mathrm{i}}}^{0.5}}{\left[\frac{{\rho }_{\mathrm{g}}{Q_{\mathrm{g}}}^2}{{\rho }_{\mathrm{L}}g}\right]}^{0.30}$$(7)

where Fr_mD is the modified Froude number, g (= 9.8 m/s²) is the acceleration due to gravity, We is the Weber number, ρ_L is the density of liquid, σ is the surface tension, d_ni is the inner diameter of nozzle, and ρ_g is the density of gas. Equation (7) was proposed by assuming that the swirl motion ceases when the blowout of the bubbling jet takes place on the bath surface. In calculating the sub-boundaries the SI unit should be used.

The observed sub-boundaries (1) and (2) were satisfactorily approximated by Eqs. (2) and (4) (see solid and broken lines in Fig. 4). The same agreement was seen for D=150[mm] and 300[mm], as shown later.

As can be seen in Figs. 6, 7, 8, a swirl motion occurred for D_s=16 and 32[mm], whereas disappeared for D_s=48[mm]. The swirl motion is therefore assumed to be suppressed by a circular disk having a diameter between D_s=32[mm] and 48[mm]. Here, a mean value of 32[mm] and 48[mm] is chosen as the critical disk diameter, D_scr. The bath depth giving the largest plume eye diameter, D_Bmax, in the presence of the swirl motion is H_Lmax=225[mm]. Consequently, any swirl motion does not occur for D=200[mm] under the following condition.   

$$\begin{array}{l}{D}_{\mathrm{B}}/D_{\mathrm{s}}<0.28H_{\mathrm{L}\mathrm{m}\mathrm{a}\mathrm{x}}/D_{\mathrm{s}\mathrm{c}\mathrm{r}}=0.28\times 225/40\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.17em}\hspace{1em}\hspace{1em}=1.58(D=200[\mathrm{m}\mathrm{m}])\end{array}$$(8)

Fig. 6.

Occurrence map of swirl motion (D_s=16[mm], D=200[mm], and d_ni=1.0[mm]).

Fig. 7.

Occurrence map of swirl motion (D_s=32[mm], D=200[mm], and d_ni=1.0[mm]).

Fig. 8.

Occurrence map of swirl motion (D_s=48[mm], D= 200[mm], and d_ni=1.0[mm]).

Figures 9, 10, 11 show the occurrence map of swirl motion for D=150[mm]. The symbol, □, denotes an oscillation motion in the lateral direction. The critical disk diameter was found to be D_scr=40[mm] and the bath depth giving D_Bmax was H_Lmax=187.5[mm]. The following result was obtained.   

$$\begin{array}{l}{D}_{\mathrm{B}}/D_{\mathrm{s}}<0.28H_{\mathrm{L}\mathrm{m}\mathrm{a}\mathrm{x}}/D_{\mathrm{s}\mathrm{c}\mathrm{r}}=0.28\times 187.5/40\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.17em}\hspace{1em}\hspace{1em}=1.31(D=150[\mathrm{m}\mathrm{m}])\end{array}$$(9)

Fig. 9.

Occurrence map of swirl motion in the absence of a disk (D=150[mm], d_ni=1.0[mm], —–: Eq. (2), – – - : Eq. (4)).

Fig. 10.

Occurrence map of swirl motion (D_s=32[mm], D=150[mm], and d_ni=1.0[mm]).

Fig. 11.

Occurrence map of swirl motion (D_s=48[mm], D=150[mm], and d_ni=1.0[mm]).

The lateral oscillation motion also was suppressed under this condition.

The occurrence maps of swirl motion shown in Figs. 12, 13, 14 for D=300[mm] give:   

$$\begin{array}{l}{D}_{\mathrm{B}}/D_{\mathrm{s}}<0.28H_{\mathrm{L}\mathrm{m}\mathrm{a}\mathrm{x}}/D_{\mathrm{s}\mathrm{c}\mathrm{r}}=0.28\times 337.5/56\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.17em}\hspace{1em}\hspace{1em}=1.69(D=300[\mathrm{m}\mathrm{m}])\end{array}$$(10)

Fig. 12.

Occurrence map of swirl motion in the absence of a disk (D=300[mm], d_ni=1.0[mm], —–: Eq. (2), – – -: Eq. (4)).

Fig. 13.

Occurrence map of swirl motion (D_s=48[mm], D=300[mm], and d_ni=1.0[mm]).

Fig. 14.

Occurrence map of swirl motion (D_s=64[mm], D=300[mm], and d_ni=1.0[mm]).

As suggested from Eq. (6) and Fig. 5, the bath depth giving the largest plume eye diameter is not dependent on the gas flow rate, Q_g, Eqs. (8), (9), (10) are approximately valid for a gas flow rate greater than 20 [L/min]. Consequently, a mean value of 0.28 H_Lmax/D_scr=1.5 was chosen here to describe the suppression condition as follows:   

$$D_{\mathrm{B}}/D_{\mathrm{s}}<1.5\hspace{0.17em}(\mathrm{N}\mathrm{o}\mathrm{\hspace{0.17em} }\mathrm{s}\mathrm{w}\mathrm{i}\mathrm{r}\mathrm{l}\mathrm{\hspace{0.17em} }\mathrm{m}\mathrm{o}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n})$$(11a)

or   

$$D_{\mathrm{s}}>0.67\hspace{0.17em}{D}_{\mathrm{B}}\hspace{0.17em}(\mathrm{N}\mathrm{o}\mathrm{\hspace{0.17em} }\mathrm{s}\mathrm{w}\mathrm{i}\mathrm{r}\mathrm{l}\mathrm{\hspace{0.17em} }\mathrm{m}\mathrm{o}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n})$$(11b)

In a strict sense, Eqs. (8), (9), (10) collectively suggest that the critical value of D_B/D_s increases slightly with D. As the number of circular disks chosen in this study is limited, discussion on the precise critical disk diameter must be left for a future study.

4.2. Effect of a Circular Disk Placed on the Bath Surface After Occurrence of a Swirl Motion

As mentioned in the preceding section, the swirl motion of a bubbling jet can be suppressed by placing a circular disk on the bath surface before gas injection. The diameter of the disk, D_s, must be greater than 0.67D_B, where D_B is the plume eye diameter of the bubbling jet. This is because the formation of the plume eye is prevented by the disk. On the other hand, if the swirl motion is present already in the bath, the plume eye rotates around the vessel axis with a certain rotation radius. Therefore, the bath surface area in which the plume eye exists is much greater than that in the absence of the swirl motion. In order to suppress the plume eye rotating around the vessel axis, a circular disk larger than that used in the absence of the swirl motion is necessary, as explained below.

A circular disk was placed on the bath surface after a swirl motion occurred for D=200[mm] (Fig. 15). If the disk diameter, D_s, is greater than that of the locus of a bubbling jet on the bath surface, D_c, any swirl motion would not occur because plume eye formation is considered to be suppressed. Here, D_c is expressed as:⁷⁾   

$$D_{\mathrm{c}}=2\times 0.37R=0.37D$$(12)

where R is the vessel radius. It should also be noted that D_c is not dependent on Q_g, H_L, and d_ni.

Fig. 15.

Diameter of the locus of a bubbling jet, D_c, and disk diameter, D_s.

In Figs. 16, 17, 18 the swirl motion disappeared between D_s=64[mm] and 80[mm]. Accordingly, the critical disk diameter is assumed to be D_scr=(64+80)/2=72[mm]. Any swirl motion therefore does not occur under the following condition.   

$$\begin{array}{l}{D}_{\mathrm{c}}/D_{\mathrm{s}}<0.37D/D_{\mathrm{s}\mathrm{c}\mathrm{r}}=0.37\times 200/72\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.17em}\mathrm{\hspace{0.17em} }=1.03\hspace{0.17em}(D=200[\mathrm{m}\mathrm{m}])\end{array}$$(13)

Fig. 16.

Occurrence map of swirl motion (D_s=48[mm], D=200[mm], and d_ni=1.0[mm]).

Fig. 17.

Occurrence map of swirl motion (D_s=64[mm], D=200[mm], and d_ni=1.0[mm]).

Fig. 18.

Occurrence map of swirl motion (D_s=80[mm], D=200[mm], and d_ni=1.0[mm]).

The following result was obtained from Figs. 19, 20, 21 for D=150[mm].   

$$\begin{array}{l}{D}_{\mathrm{c}}/D_{\mathrm{s}}<0.37D/D_{\mathrm{s}\mathrm{c}\mathrm{r}}=0.37\times 150/56\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.17em}\mathrm{\hspace{0.17em} }=0.99\hspace{0.17em}(D=150[\mathrm{m}\mathrm{m}])\end{array}$$(14)

This 0.99 is very close to the value of 0.37D/D_scr for D=200[mm].

Fig. 19.

Occurrence map of swirl motion (D_s=32[mm], D=150[mm], and d_ni=1.0[mm]).

Fig. 20.

Occurrence map of swirl motion (D_s=48[mm], D=150[mm], and d_ni=1.0[mm]).

Fig. 21.

Occurrence map of swirl motion (D_s=64[mm], D=150[mm], and d_ni=1.0[mm]).

Even the largest disk of D_s=80[mm] was not able to suppress a swirl motion for D=300[mm], as can be seen in Fig. 22. The critical disk diameter, D_scr, therefore is greater than 80[mm]. Accordingly,   

$$\begin{array}{l}{D}_{\mathrm{c}}/D_{\mathrm{s}}<0.37D/D_{\mathrm{s}\mathrm{c}\mathrm{r}}<0.37\times 300/80\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.17em}\mathrm{\hspace{0.17em} }=1.39\hspace{0.17em}(D=300[\mathrm{m}\mathrm{m}])\end{array}$$(15)

Fig. 22.

Occurrence map of swirl motion (D_s=80[mm], D=300[mm], and d_ni=1.0[mm]).

The results shown above collectively suggest that any swirl motion does not occur under the condition shown below.   

$$D_{\mathrm{c}}/D_{\mathrm{s}}<1.0\hspace{0.17em}(\mathrm{N}\mathrm{o}\mathrm{\hspace{0.17em} }\mathrm{s}\mathrm{w}\mathrm{i}\mathrm{r}\mathrm{l}\mathrm{\hspace{0.17em} }\mathrm{m}\mathrm{o}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n})$$(16a)

or   

$$D_{\mathrm{s}}>D_{\mathrm{c}}\hspace{0.17em}(\mathrm{N}\mathrm{o}\mathrm{\hspace{0.17em} }\mathrm{s}\mathrm{w}\mathrm{i}\mathrm{r}\mathrm{l}\mathrm{\hspace{0.17em} }\mathrm{m}\mathrm{o}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n})$$(16b)

As D_c is not dependent on the gas flow rate, Q_g, Eqs.(16a) and (16b) are applicable in a higher gas flow rate range than 20[L/min].

4.3. Applicability of the Present Suppression Method to Real Steelmaking Processes

According to previous studies on the bubbling jet and occurrence of the swirl motion,^{4,5,6,7,8,9,10,11,12,13)} the swirl motion would occur also in a molten iron or molten steel bath in the real processes subjected to bottom gas injection. The presently proposed method for suppressing swirl motions is applicable to the real bottom blown baths as long as a circular disk keeps its initial size and shape during processing operations. As the erosion of the disk would be serious under gas injection condition in the real processes, development of refractory having high performance against erosion is desirable.

A circular disk in contact with the bath surface can strengthen the radial molten metal flow near the bath surface.⁹⁾ Such a strong radial flow induces a large scale circulating flow in the bath and, as a result, significantly shortens mixing time, as demonstrated in the previous papers.^7,9) The mixing time in the presence of the swirl motion becomes shorter than that measured when the swirl motion is suppressed by a circular disk.⁹⁾ In addition, splash and spitting are expected to be suppressed because a plume eye is not formed on the bath surface. Consequently, if new refractory satisfying the above-mentioned requirement for erosion is developed, an efficient refining process would be realized.

5. Conclusions

A simple method using a circular disk was proposed for suppressing the swirl motion of a bubbling jet. The disk was placed on the bath surface to prevent plume eye formation. Two cases were considered: a circular disk was placed on the bath surface before gas injection, while it was placed after the swirl motion appeared. The critical disk diameters enabling the swirl motion to suppress were derived in the following two cases.

(1) Contact of a circular disk with the bath surface before gas injection   

$$D_{\mathrm{s}}>0.67\hspace{0.17em}{D}_{\mathrm{B}}\hspace{0.17em}(\mathrm{N}\mathrm{o}\mathrm{\hspace{0.17em} }\mathrm{s}\mathrm{w}\mathrm{i}\mathrm{r}\mathrm{l}\mathrm{\hspace{0.17em} }\mathrm{m}\mathrm{o}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n})$$(11b)

(2) Contact of a circular disk with the bath surface after the occurrence of swirl motion   

$$D_{\mathrm{s}}>D_{\mathrm{c}}\hspace{0.17em}(\mathrm{N}\mathrm{o}\mathrm{\hspace{0.17em} }\mathrm{s}\mathrm{w}\mathrm{i}\mathrm{r}\mathrm{l}\mathrm{\hspace{0.17em} }\mathrm{m}\mathrm{o}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n})$$(16b)

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