# Numerical Simulations of Novel Conning Designs for Future Super-Large Wind Turbines
## 3 Results and Discussions
### Special Coned Configurations: C4S0, C4S1, C4S2, C4, C-4S0, C-4S1, C-4 S2 and C-4
#### 3.2.3 Flow Field Analysis  
To understand the force characteristics presented in Section 3.2.2, further flow field analyses were carried out. Firstly, the streamline and the axial velocity contour in the \(YZ\) plane of C \(\pm\) 4S2, C \(\pm\) 4S0, and C \(\pm\) 4S1 are shown in Figure 12. In the range of \(R/3<r<2R/3\), the downwind cone C4S2 shown in Figure 12a had obviously lower velocity in the near wake region than that of C-4S2 shown in Figure 12b. This revealed that more energy was extracted by C4S2, which is consistent with the higher thrust force in Figure 11. Additionally, the downwind C4S2 had slightly larger wake expansion, which means a larger radial velocity. If the three figures on the left hand side are compared, the wake deficit is weaker and weaker when the blade tip is successively moving upstream from Figure 12a to Figure 12c,e. This means that the energy extracted by the rotor was progressively smaller, which is in agreement with the successive decline in the \(Ft\) and \(Fz\) curves in the range \(R/3<r<2R/3\) in Figure 11. If the right hand side figures are compared, the wake deficit becomes stronger when the blade tip transforms downstream. This also confirms the successive increases in the \(Ft\) and \(Fz\) curves from C-4S2 to C-4S0 and then C-4S1. In the range \(r>2R/3\), the streamlines of C4S1 and C4S2 were the most and the least perpendicular streamlines _w.r.t._ to the blade, respectively, which led to the largest and smallest \(Ft\). But, as shown in Equation (6), the large cone angle \(\beta\) reduces the value of \(Fz\), which causes the \(Fz\) of C4S1 to barely surpass the baseline.  
Utilizing the AAT AOA-extraction method introduced in Section 3.1.2, the \(\alpha_{z}\) and \(\alpha_{n}\) at different radial positions are compared in Figure 13. In the range of \(r>2R/3\), the \(\alpha_{z}\) and \(\alpha_{n}\) of C4S0 and C-4S0 nearly coincided with the straight baseline, which was consistent with the close \(Ft\) and \(Fz\) curves, as shown in Figure 11. This was because the three configurations were all without coning. What is more, C4 and C-4S1 had the same cone angle, which led to close \(\alpha_{n}\) distributions. Similarly, C-4 and C4S1 also had close \(\alpha_{n}\) distributions. In the range of \(R/3<r<2R/3\), the four configurations, C4S2, C4, C4S0 and C4S1, had nearly parallel \(\alpha_{n}\) curves. The \(\alpha_{n}\) line of C4S2 was the highest, and C4, C4S0 and C4S1 had successively lower curves, which matched the successive decreases of the \(Ft\) and \(Fz\) curves in Figure 11. As discussed in Section 3.2.2, this was caused by the upstream movement of the tip positions, which made caused the blade sections to be further immersed into the wake, leading to decreases in \(\alpha_{z}\) and \(\alpha_{n}\). In contrast, focusing on the group C-4S2, C-4, C-4S0, and C-4S1, the \(\alpha_{n}\) curves successively ascended with the downstream movement of the blade tips. In the range of \(r<R/3\), C4S1 and C-4S1 had similar \(\alpha_{z}\) and \(\alpha_{n}\) distributions to the straight baseline. This was because the three configurations had the same blade tip position, although distinctly different cones appeared at \(r>R/3\). Generally speaking, the \(\alpha_{n}\) distributions matched the force distributions in Figure 11. It is clear that the \(\alpha_{n}\) distributions can reveal the mechanism of force distributions on coned sections, even if the blades are coned into three parts. Additionally, correctly commutating \(\alpha_{n}\) is of vital importance for improving the traditional BEM method, although further discussion of this is beyond the scope of this paper.  
Figure 12: Streamline in the YZ plane with axial velocity contours: (**a**) C4S2; (**b**) C-4S2; (**c**) C4S0; (**d**) C-4S0; (**e**) C4S1; (**f**) C-4S1.