# On the Effect of Filling Rate on Positive Macrosegregation Patterns in Large Size Cast Steel [PERSON]
## 3 Results and Discussions
### Effect of Filling Rate on Fluid Flow and Solidification Time  
Considering the large size of the ingots, the solid percentage formed at the end of filling was not expected to induce changes in the melt density, temperature, and viscosity. Thus, the influence of filling velocity on the flows of the liquid steel during the filling stage (considered as isothermal flow of a single phase material) was analyzed using the dimensionless Reynolds number (Re) [22; 23]. The proposed approach is similar to the ones used by [PERSON] et al. [22] and [PERSON] et al. [24] for physical modelling of liquid melt flow in steel ingots:  
\[\mathrm{Re}=\frac{\rho vd}{\mu}\]  
In the above equation, \(\rho\) represents the density of the fluid (kg/m\({}^{3}\)), \(v\) the fluid flow velocity (m/s), \(d\) the characteristic length (m), and \(\mu\) the dynamic viscosity of the fluid (Pa\(\cdot\)s). The density and the dynamic viscosity of the investigated steel at the filling temperature, 1570 \({}^{\circ}\)C, were determined using Thermo-Calc(r) (Thermo-Calc Software, Pittsburgh, PA, USA) [16] and JMatPro(r) (Sente Software Ltd., Guildford, Surrey, UK) [25], respectively. The mean filling speed was taken as the characteristic velocity and the average diameter of the cylinder mold cavity as characteristic length. After calculation with all the determined parameters, Reynolds numbers of 3208 for LFR and 4375 for HFR during the pouring process were obtained. The higher value of Re\({}_{\mathrm{HFR}}\) indicates that more flow instabilities and movements were produced inside the mold under HFR condition. This flow instability is expected to result in some residual flow up to the initial stage of solidification under HFR condition. Macroetch analysis of the zones near the surface of the ingot (first solidified zones), as reported in Figure 6, revealed columnar grains in the casting body of LFR (Figure 6a) and equiaxed grains in the same position of HFR (Figure 6b). The examined region is encircled in red in the upper right corner of Figure 6. A schematic views of the grain morphologies are also provided for clarification (due to the large size of the blocks and the grains, it is difficult to capture high quality images with uniform light and shade in one single picture). [PERSON] [26] found that a dampened fluid flow promotes columnar growth, while an unsteady liquid movement promotes the development of equiaxed grain structure [27]. The presence of the equiaxed grain morphology in the first solidified zone in HFR is probably indicative of the presence of higher liquid instabilities at the start of solidification, as also predicted by the Reynolds number calculations. Figure 5: Segregation ratio profiles along the bottom of the cutting section of the two ingots: (**a**) carbon; (**b**) manganese; (**c**) chromium. Several researchers have examined the mutual influence of residual flow and solidification on the thermal and solutal behaviors of the ingot. [PERSON] et al. [28] and [PERSON] et al. [29] reported that the presence of residual flow can homogenize the temperature and solute field in the bulk liquid at the early stages of solidification, while [PERSON] et al. [30,31] and [PERSON] [32] related it to a decrease of temperature gradient in the pool of liquid. The lower temperature gradient can prolong the thermal convection time in the cavity, and delay the development of solutal convection [33], because of better mixing of solute ahead of the liquidus front and thus decreased density gradients [34]. Others reported that delayed solutal convection can significantly affect the distribution of solutes [35, 36, 37], and hence affect the evolution of macrosegregation patterns during the intermediate and final stages of solidification. Therefore, more intense movement of the liquid metal in the initial solidification stage, caused by higher filling velocity, is probably the source for the observed reduced solute segregation in the casting body in the HFR ingot as compared to LFR.