**5.1. Numerical simulation**

568 Numerical Simulation – From Theory to Industry

caused the change in slab broadening.

steel at various moments. (FU JianXun et al. 2011(b))

casting speed.

The slab width changed smoothly except from 45 to 55 min, during which time a sharp trough appears on the RUB curve. In the initial 6 minutes of this period, the RUB decreased to 1.4% from 2.25%, and in the following 4 minutes, the RUB increased to 2.1% from 1.4%. This trough was caused by the changing of the tundish, during which the casting speed decreased sharply, and then quickly recovered to normal; i.e., the change in casting speed

**Figure 7.** (a) Width of slab and RUB for SPHC steel at various moments; (b) Width and RUB for Q235

(a) (b)

Figure 7(b) shows the slab width and the RUB for Q235 steel at various times. The RUB for Q235 steel ranges from 0.77% to 2.91%, with an average of 2.04%. There are five sharp corners on the RUB curve for Q235 steel. By comparing the curve with the production process of Q235, it was found that each sharp corner corresponds to an unsteady production stage. The biggest one corresponds to the changing of the tundish, the last one corresponds

Figure 8 shows the relationship between the RUB and the casting speed for Q235 steel. The shapes of the RUB curve and the casting speed curve are very similar. When the tundish was changed, the casting speed decreased to 0.5 m/min over a 10-minute period and then recovered to normal in 5 minutes; this change formed a sharp trough in the casting speed curve. At nearly the same time, the RUB decreased to 1.91% from 0.77% in 10 minutes and then increased to 2.1% in 5 minutes, producing a sharp trough in the curve. When the ladle was changed, a similar change happened. When the casting speed was maintained at 1.0 m/min, the RUB remained stable at about 2.0%. The RUB is thus closely correlated with

There is a small lag between the RUB curve and the casting speed curve in Figure 12. The change in casting speed curve occurred earlier than that in the RUB curve. For example, the casting speed curve exhibits a sharp trough at about 100 minutes; a sharp trough appears in the RUB curve at about 110 minutes. Comparing Figure 7 and Figure 8, it can be seen that

the simulation results generally agree with the industrial measurement results.

to the end of casting, and the remaining three correspond to the changing of ladles.

One node of the slab was traced and the width was recorded at various positions of the secondary cooling zone. The RUB was derived from the calculated width of the slab.

The calculated RUB of Q235 steel slab with a cross section 2000 mm × 230 mm at speed of 1.0m/min is shown in Figure 9(a). The RUB changes from one segment to another; its value is over 0 throughout the secondary cooling zone, indicating slab broadening. The RUB increases in the first five segments, and then drops down gradually after reaching its maximum in the sixth segment. In the sixth segment, the width of the slab reaches its maximum with a large fluctuation due to the bulging of the slab in the direction of thickness. Figure 9(b) shows the simulated deformation of the slab in this direction. The shell of the slab has low yield strength and high plasticity; thus, the slab at the points contacting the rollers is depressed and bulges at the slit between the two rollers. Similar to the periodicity of bulging, the width of the slab fluctuates periodically.

The simulated broadening and bulging of the slab in the sixth segment are shown in Figure 10. There is an obvious correlation between broadening in the width direction and bulging in the thickness direction. The position in the slab where the smallest bulging is observed has the greatest broadening. This is due to the depression of slab in the thickness direction contributing to slab broadening in the width direction.

## **5.2. Effects of slab width on broadening (FU JianXun et al. 2010(b))**

230-mm-thick slabs of Q235 with various widths were simulated at a casting speed of 1.0 m/min. The RUB values for various segments are shown in Figure 11. It shows that the

simulated RUB of slab slightly increases with the increase of width. The maximum values are 1.27 %, 1.36 %, and 1.44 %, respectively. The RUBs at the exit of caster are 0.63 %, 0.70 %, and 0.76 %, respectively. There is no obvious increase of RUB for slabs with increasing the width, but the increase of broadened size is noticeable. In conclusion, slabs with great width have great broadening.

Numerical Simulation of Slab Broadening in Continuous Casting of Steel 571

 **2050mm 1800mm 1600mm**

> 250mm 300mm

**0 5 10 15 20 25 30 35 40 45**

**Distance from meniscus , m**

To study the effect of slab thickness on broadening, 2050-mm-thick Q235 slabs with thicknesses of 230 and 250 mm, respectively, were simulated at a casting speed of 1.0 m/min;

The calculated broadening values for the two slabs are slightly different. The maximum RUB values are 1.4% and 1.38% for 250- and 230-mm-thick slabs, respectively. The RUB values are 0.74% and 0.71% at the exit of the continuous caster, respectively. The difference of broadening is just 0.6 mm between the two slabs. This is because the bulging changes

0 10 20 30 40

**Figure 12.** Calculated RUB with different thicknesses. (FU JianXun et al. 2010(b))

**Distance from meniscus , m**

**Figure 11.** Calculated RUB values for slabs of various widths . (FU JianXun et al. 2010(b))

**0.0**

**5.3. Effects of slab thickness on broadening** 

0.0

0.2

0.4

0.6

0.8

**Ratio of ultimate broadending of slab, %**

1.0

1.2

1.4

1.6

the results are shown in Figure 12.

little with increasing thickness.

**0.3**

**0.6**

**0.9**

*RUB* **of slab , %**

**1.2**

**1.5**

**Figure 9.** (a) Calculated RUB of Q235 steel in the secondary cooling zone; (b)Calculated deformation of slab between rollers. (FU JianXun et al. 2010(b))

**Figure 10.** Broadening and bulging of slab in the sixth segment. (FU JianXun et al. 2010(b))

Under the same conditions, the wide slab has greater broadening than narrow slab because of compound effects of temperature and stress. Compared with wide slab, narrow slab has a larger range for heat flow distribution and hence the greater equivalent von Mises stress. But the wider slab has more enthalpy to be removed. So in the same position of caster, the narrow slab has higher yield strength and lower plasticity, and the solidified shell is able to resist great stress.

Numerical Simulation of Slab Broadening in Continuous Casting of Steel 571

**Figure 11.** Calculated RUB values for slabs of various widths . (FU JianXun et al. 2010(b))

#### **5.3. Effects of slab thickness on broadening**

570 Numerical Simulation – From Theory to Industry

slab between rollers. (FU JianXun et al. 2010(b))

**0.000**

**0.002**

**0.004**

**Bulging slab & broadending slab, m**

resist great stress.

**0.006**

**0.008**

have great broadening.

simulated RUB of slab slightly increases with the increase of width. The maximum values are 1.27 %, 1.36 %, and 1.44 %, respectively. The RUBs at the exit of caster are 0.63 %, 0.70 %, and 0.76 %, respectively. There is no obvious increase of RUB for slabs with increasing the width, but the increase of broadened size is noticeable. In conclusion, slabs with great width

**Figure 9.** (a) Calculated RUB of Q235 steel in the secondary cooling zone; (b)Calculated deformation of

(a) (b)

**0 50 100 150 200 250**

**broadening of slab bulging of slab**

**Time, s**

Under the same conditions, the wide slab has greater broadening than narrow slab because of compound effects of temperature and stress. Compared with wide slab, narrow slab has a larger range for heat flow distribution and hence the greater equivalent von Mises stress. But the wider slab has more enthalpy to be removed. So in the same position of caster, the narrow slab has higher yield strength and lower plasticity, and the solidified shell is able to

**Figure 10.** Broadening and bulging of slab in the sixth segment. (FU JianXun et al. 2010(b))

To study the effect of slab thickness on broadening, 2050-mm-thick Q235 slabs with thicknesses of 230 and 250 mm, respectively, were simulated at a casting speed of 1.0 m/min; the results are shown in Figure 12.

The calculated broadening values for the two slabs are slightly different. The maximum RUB values are 1.4% and 1.38% for 250- and 230-mm-thick slabs, respectively. The RUB values are 0.74% and 0.71% at the exit of the continuous caster, respectively. The difference of broadening is just 0.6 mm between the two slabs. This is because the bulging changes little with increasing thickness.

**Figure 12.** Calculated RUB with different thicknesses. (FU JianXun et al. 2010(b))
