# Numerical Simulations of Novel Conning Designs for Future Super-Large Wind Turbines
## 2 Modeling and Methods  
### Modelling of Different Cone Configurations  
In order to analyze the aerodynamic performance of the load-aligned concepts, different conning configurations were designed, as shown in Figures 2 and 3. These configurations are transformed from the DTU-10-MW Reference Wind Turbine (RWT) [26; 27] rotor, which is referred to as the baseline rotor, according to Equations (1) and (2). To focus on the effects of coning, a DTU-10-MW RWT without cone, tilt, prebend, nacelle or hub was used. At radial position \(r\), coned configurations had their blade stacking lines translated out of the rotor plane with a displacement of \(Z_{con}\).  
\[Z_{cone}=\left\{\begin{array}{cc}0,&r\leq T_{trans}R\\ (r/R-T_{trans})R/C_{cone},&r>T_{trans}R\end{array}\right. \tag{1}\]  
where \(R\) is the rotor radius, \(T_{trans}\) is the relative radial position where cone starts, and \(C_{cone}\) controls the slope of the stacking line. As shown in Figure 2a, \(T_{trans}=5/R\) means cone starting at 5 m, and \(T_{trans}=1/3\) means cone starting at \(R/3\). The cone angles are controlled by \(C_{cone}\). When \(C_{cone}=\pm 4\), \(\pm 8\), the rotors have cone angles of \(\pm 14.0362^{\circ}\), \(\pm 7.1250^{\circ}\), respectively. A larger \(1_{Cume}1\) produces a smaller cone angle, and a positive \(Z_{cone}\) makes a downwind cone. As shown in Figure 2b, several special coning configurations are shown, which are further coned at \(2R/3\). These special cone designs have an out of plane displacement of \(Z_{cone}\), as defined by Equation (2).  
\[Z_{cone}=\left\{\begin{array}{cc}0,&r\leq T_{trans}R\\ (r/R-T_{trans})R/C_{cone},&T_{trans}R<r<2R/3\\ (2/3-T_{trans})R/C_{cone},&r\geq 2R/3,\text{ for S0}\\ (4/3-T_{trans}-r/R)R/C_{cone},&r\geq 2R/3,\text{ for S1}\\ (2r/R-T_{trans}-2/3)R/C_{cone},&r\geq 2R/3,\text{ for S2}\end{array}\right. \tag{2}\]  
Figure 3: Down/upwind coned configurations with \(C_{cone}=\pm 4\) and \(T_{trans}=1/3\): (a) C4 and C-4; (b) C4S0 and C-4S0; (c) C4S1 and C-4S1; (d) C4S2 and C-4S2; (e) straight baseline.  
In the rest part of the paper, a name abbreviation rule is applied for \(T_{trans}=1/3\) configurations. \(C_{cone}=\pm 4\) and \(T_{trans}=1/3\) are named as C4 and C-4, respectively. Symbols S0, S1 and S2 are used to discriminate among the configurations at \(r>2R/3\). For example, the case of \(C_{cone}=\pm 4\) and \(T_{trans}=1/3\) followed by S2 is abbreviated as C4S2 and C-4S2, which have their blade tips farthest from the rotor plane. The symbol of S1 represents a reverse blade tip cone, such that C4S1 has its blade tip pointing to the upwind direction of a downwind cone at \(r<2R/3\). Lastly, the symbol S0 represents a zero cone angle at \(r>2R/3\). In short, C4 stands for downwind and C-4 for upwind, and S0, S1 and S2 represent blade tip configurations. For the sake of aerodynamic comparisons, all the configurations have the same projected areas and the same distribution of airfoil thickness, chord and twist. The shapes of different configurations are depicted in Figure 3, with the wind flow from the negative \(Z\) to the positive \(Z\).