## 4 Wind Tunnel Test
### Uncertainty Analyses  
Experimental results always contain errors, so uncertainty should also be analyzed. The wind velocity \(U\) of the incoming flow was measured using an anemometer (Testo 425, Testo SE & Co., Titisee-Neustadt, Germany). The range of velocity measurement was from 0 to 20 m/s. The resolution of the anemometer was 0.01 m/s. The accuracy of the anemometer was \(\pm\)(0.03 m/s + 5% of measured values). The bluff body was produced with a 3D printer (Form 3 L, Formlabs Corp, Somerville, MA, USA), with a resolution of 0.025 mm. The accuracy of the bluff body's width and length were \(\pm\)1.2 mm and \(\pm\)0.2 mm, respectively, because the bluff bodies were thin-walled structures, prone to temperature strain. The force was measured using a six-dimensional force balance (Gamma, ATI industrial automation, Apex, NC, USA). The resolution of the force balance was 0.00625 N. The accuracy of the force balance was \(\pm\)1%. The resolution of the wind direction was 0.017\({}^{\circ}\). The accuracy of the wind direction was \(\pm\)0.036\({}^{\circ}\). The resolution of the electric resistance was 1000 \(\Omega\), and the accuracy is 1%. The voltage across the load resistance was measured with a DAQ module (NI-9229, National Instruments, Austin, TX, USA). The resolution of the voltage DAQ module was 3.6 \(\times\) 10\({}^{-6}\) V. The accuracy of the voltage DAQ module was \(\pm\)0.03% of the measured value. The accuracy and resolution of the measuring instruments and equipment are shown in Table 1.  
The average output power of the wind energy harvester was computed using the associated voltage as \(P=V_{rms}^{2}/R\), where \(V_{rms}\) is the root mean square of the voltage. The uncertainty was assessed using the Taylor series method (TSM) [58]. The correlated random  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable** & **Resolution** & **Accuracy** \\ \hline Velocity & 0.01 m/s & \(\pm\)(0.03 m/s + 5\% of the measured value) \\ Width of bluff body & 0.025 mm & \(\pm\)2.4\% \\ Length of bluff body & 0.025 mm & \(\pm\)0.4\% \\ Force & 0.00625 N & \(\pm\)1\% \\ Wind direction & 0.017\({}^{\circ}\) & \(\pm\)0.5\% \\ Resistance & 1000 \(\Omega\) & \(\pm\)1\% \\ Voltage & 3.6 \(\times\) 10\({}^{-6}\) V & \(\pm\)0.03\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: The accuracy and resolution of measuring instruments and equipment.  
Figure 5: Configuration of force measurement tests.  
error terms were assumed to be zero. The standard uncertainty of average output power \(P\) is expressed as  
\[s_{P}=\sqrt{4s_{V}^{2}+s_{R}^{2}} \tag{16}\]  
where \(S_{V}\) and \(S_{R}\) are standard uncertainties of voltage and resistance, respectively. The random uncertainty values for output power \(P\) is \(\pm 1.0\%\).  
The transverse force coefficient \(C_{Fy}\) is expressed as  
\[C_{Fy}=\frac{F_{y}}{\frac{1}{2}\rho_{a}U^{2}BL} \tag{17}\]  
where \(\rho_{a}\) is the air density, \(B\) and \(L\) are the width and length of the bluff body, and \(U\) is wind velocity.  
The errors in the values of the variables on the right-hand side of Equation (17) will cause errors in the experimental result \(C_{Fy}\). The uncertainty was calculated using the Taylor series method (TSM) [58]. It was assumed that only \(U\), \(B\), \(L\), and \(F_{y}\) contributed to the random uncertainty. These correlated random error terms were assumed to be zero. The standard uncertainty of force coefficient is expressed as  
\[s_{C_{Fy}}=\sqrt{4s_{u}^{2}+s_{Fy}^{2}+s_{B}^{2}+s_{L}^{2}} \tag{18}\]  
where \(S_{u}\), \(S_{Fy}\), \(S_{B}\), and \(S_{L}\) are standard uncertainties of the wind velocity, force, width, and length of the bluff body. The random uncertainty values for \(C_{Fy}\) using the TSM are shown in Table 2. The standard uncertainty of force coefficient was caused by the error of the anemometer. The accuracy of the anemometer was \(\pm(0.03\) m/s + 5% of measured value), and the force was proportional to the square of the wind velocity.