# Measurement and Model-Based Control of Solidification in Continuous Casting of Steel Billets
## 3 Results
### Dynamic Control of Crater End Position  
3.1 Parameter Studies Regarding Influence of Different Casting Parameters on Strand Temperature and Solidification Front  
The dynamic temperature and solidification model DynSolidCC developed by BFI was used within appropriate offline simulations for parameter studies regarding the influence of the following parameters on the resulting temperature profile and solidification front in the billet caster at ESF:  
* Spray water flows in secondary cooling zone;  
Figure 11: Evolution of casting speed and metallurgical length during the second vibrometer measurement campaign. * Casting speed;
* Initial superheat of steel. These casting parameters have been varied from a defined reference case. * Variation of spray water flows in secondary cooling zone  
In a first parameter study, the spray water flows for the four secondary cooling loops have been varied between values of 50% and 150% of the flow rates defined for the reference case. The other casting conditions were kept constant. Figure 12 shows the surface temperature and shell thickness for the middle of the strand top side resulting from the offline simulations with the DynSolidCC model for the different cases of applied spray water flows:  
* At the end of the last spray water cooling loop, the mid-surface temperatures decrease with the first 10% increase in spray water (from 50% to 60% of reference flow rates) by 19 K and with the last 10% increase (from 140% to 150% of reference flow rates) by 10 K.
* The maximum difference in surface temperatures between the cases of 50% and 150% of reference spray water flow at the end of the last cooling loop is about 135 K;
* It decreases to about 54 K at a length of 23 m, where the cutting torch is located. * The crater end position moves from 17.4 m for the case with the highest spray water cooling to 21.0 m for the case with the lowest cooling. * With the first 10% increase in spray water (from 50% to 60% of reference flow rates), the crater end position decreases by 0.58 m, and with the last 10% increase (from 140% to 150% of reference flow rates) by 0.26 m.  
Figure 12: Surface temperature and shell thickness for the middle of the strand top side simulated with DynSolidCC for billet casting at ESF with stationary reference casting conditions and variation of secondary spray water flows between 50% and 150% compared to defined reference case. 2. Variation of casting speed In a second model simulation campaign, the influence of variations in the casting speed between \(\mathrm{v_{c}}^{\mathrm{min}}\) and \(\mathrm{v_{c}}^{\mathrm{max}}\) on the temperature field and solidification front of the strand was studied. In order to take into account the increased heat transfer in the mould with increasing casting speeds, the related heat flow densities across the strand boundary were scaled appropriately with the casting speed \(\mathrm{v_{c}}\) by a factor \(\mathrm{v_{c}}/\mathrm{v_{c}}\)rf, where \(\mathrm{v_{c}}\)rf is the reference casting speed. The other defined reference casting conditions were kept constant. Figure 13 shows the simulated surface temperature and shell thickness for the middle of the strand top side for the different cases of applied casting speed: * At the end of the last spray water cooling loop, the mid-surface temperatures increase with the first increase in casting speed \(\mathrm{\Delta v_{c}}\) by 18 K and with the last increase by 9 K. * The maximum difference in surface temperatures between the casting speed cases of \(\mathrm{v_{c}}^{\mathrm{min}}\) and \(\mathrm{v_{c}}^{\mathrm{max}}\) at the end of the last cooling loop is about 66 K; * It increases to about 113 K at a length of 23 m, where the cutting torch is located. * The crater end position moves from 14.5 m for the case with the lowest casting speed to 23.2 m for the case with the highest casting speed.