*3.3. Multiple Dendrites Rotation*

At the initial time, 5 crystal nuclei with preferential growth angles of 0 and a solid phase rate of 0.2 were placed in the middle of the simulation region. When the number of solidification grids is 3000, the dendrites stop growing. At this time, a uniform rotating flow is applied in the simulation region. It can be seen from the Figure 5 that the dendrite can maintain its original shape even after being rotated for multiple turns.

**Figure 5.** Dendritic morphology before and after rotation (**a**) Before rotation; (**b**) After rotation.

This article gives the formula for calculating the solid phase rate error, as follows:

$$
\Delta = (f\_{\text{Sin}} - f\_{\text{S0}}) / f\_{\text{S0}} \times 100 \tag{41}
$$

where *fS*<sup>0</sup> is the initial solid phase rate of the dendrite, *fSin* is the solid phase rate after dendrite rotation. According to Equation (41), it is calculated that the change of the solid phase rate of the equiaxed crystal is maintained within 0.2% after 10 revolutions. In the calculations of this paper, the amplitude of dendrite rotation is small (rad <1, rad represents the radian of dendrite rotation), so it can be considered that the numerical model for calculating dendrite rotation established in this paper has no great influence on the dendrite morphology.
