## 2 Wind Tunnel Test  
Wind tunnel tests were conducted in an Eiffel-type turbulent boundary layer wind tunnel. Pitch-controlled wind turbine was considered, and hub height and blade length were assumed to be 90 m and 60 m in full scale, respectively. A length scale of 1/100 and a time scale of 1/10 were assumed. Table 1 shows details of the wind turbine. Figure 1 shows the shapes of polygonal towers and blade used in the wind tunnel tests. In this study, the seven polygonal towers were considered. A circular tower size, as a prototype, was determined, considering existing wind turbines with a bottom diameter of 6 m and a top diameter of 4 m. The heights and cross-sectional areas of the polygonal towers were designed to be the same as that of the circular tower. The numbers in parenthesis are the number of pressure taps on the towers. Blades were made on the basis of the LM-Glasfiber blade [13], and a box-shaped nacelle and a half prolate spheroid hub were used. For direction comparison, the same hub, blade, and nacelle (topside structure) were used for all polygonal-cross-section towers. \begin{table}
\begin{tabular}{c c} \hline \hline
**Items** & **Value** \\ \hline Rated power & 5 MW \\ Control type & Pitch control \\ Hub height & 90 m \\ Hub length and diameter (half prolate spheroid) & 4 m/4 m \\ Nacelle (box shape) & 4 m \(\times\) 4 m \(\times\) 10 m \\ Circular tower top and bottom diameter & 4 m/6 m \\ Blade shape (slightly modified near root) & LM-Glasfiber \\ Blade maximum width and length & 4 m/60 m \\ Rotor diameter & 124 m \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Details of wind turbine (in full scale). Figure 2 shows the pressure measurement setting. Pressure taps were distributed along the tower heights at 13 levels, and the number of pressure taps ranged from 156 to 208. All pressures on the towers were measured at the same time using a simultaneous multi-channel pressure-sensing system, and tubing effects were numerically compensated using a transfer function. The phase difference of the pressure measurement system had a cut-off frequency of 300 Hz. Figure 3 shows the conditions of the oncoming flows at model position. Turbulent-boundary-layer flow representing an open area was simulated using spires and various-sized roughness elements. The turbulence intensity at hub height was about \(I_{u,ref}\approx 11\%\). Reference mean wind speed at hub height \(U_{ref}\) was 5 m/s for the pressure measurement tests, and for the aeroelastic tests, reference mean wind speeds were increased by up to about 6.3 m/s for the tower-only case and 5.6 m/s for a wind turbine case, giving a reduced velocity of 23 for the tower-only case and 32 for the wind turbine case, where a reduced velocity was defined as \(U^{*}=U_{ref}/(D_{ref}\times f_{0})\). \(D_{ref}\) is a reference length, which  
Figure 1: Polygonal cross-sectional towers and blade (LM-Glasfiber) used in the present study (the numbers in parentheses are the number of pressure taps on the towers). Figure 2: Pressure tap arrangement and wind turbine model with square tower (\(H_{ref}\) = 0.9 m). is the diameter at mid-height of the circular tower, and \(f_{0}\) is the natural frequency of the aeroelastic system with test models (\(f_{lower}\) or \(f_{turbine}\)). Wind tunnel tests were conducted by assuming two cases: with and without topside structures. In this study, results without topside structure are indicated as tower-only case. During the aeroelastic tests, displacements at the bottoms of the towers were measured by laser displacement sensors and recalculated to displacements at hub height. Two wind directions \(\theta_{\text{zf}}\) of 0\({}^{\circ}\) and 90\({}^{\circ}\) were considered for the aeroelastic tests, and 10 wind directions from 0\({}^{\circ}\) to 90\({}^{\circ}\) at 10\({}^{\circ}\) intervals were considered for the pressure measurements.