# Experimental Study of the Performance of a Novel Vertical-Axis Wind Turbine
## 5 Wall Effects of the Wind Tunnel  
Wind tunnel wall effects have an impact on the drag coefficient \(\mathrm{C_{D}}\), and hence the drag on the model being tested in the wind tunnel. [PERSON] et al. [22] discovered that for blockage ratios ranging from 0.5% to 0.6% and angles of attack within \(\pm 10^{\circ}\), wind tunnel wall effects are negligible within measurement uncertainties. Other researchers performed numerical simulations on models with blockage ratios of 1.875% and 15% and arrived at the conclusion that the drag coefficient increased with the blockage ratio [23]. Per these researchers, it is reasonable to use the method of images in studying wall effects of a wind tunnel on the drag experienced by a model being tested in it. In this study, the method of images is used to study wind tunnel wall effects on the drag on the AVAWT rotor. Working with a spherical model, [PERSON] et al. [24] discovered that the drag coefficient did not vary with the Reynolds number Re for Re ranging from \(6.5\times 10^{4}\) to \(2.2\times 10^{5}\), but it increased with the blockage ratio. This increase in the drag coefficient is lower for critical values of Re than it is for values less than the critical Re. The increase in the drag coefficient is lower for the critical Re because the wake is narrower, resulting in a lower wake blockage effect. The method of gathering images for blockage correction splits wind tunnel wall effects into the solid blockage \(\delta_{s}\) due to physical dimensions of the model and the wake blockage \(\delta_{\omega}\) due to the wake. Summing the two blockage factors yields the overall blockage factor \(\delta\):  
\[\delta=\delta_{s}+\delta_{\omega} \tag{37}\]  
The net effect of a wind tunnel wall is the sum of the induced speed and the wind tunnel free-stream speed [23]:  
\[U=U_{0}(1+\delta) \tag{38}\]  
For the AVAWT rotor, the effect of blockage is to reduce the wind tunnel air speed, since the rotor rotates with energy extracted from the air that flows past it. Thus, Equation (38) becomes  
\[U=U_{0}(1-\delta) \tag{39}\]  
After some algebraic manipulations on the Thom formula [24], the drag coefficient is given in terms of \(\delta_{\omega}\) and the blockage ratio \(r_{b}\):  
\[C_{D}=\frac{4\delta_{\omega}}{r_{b}} \tag{40}\]  
Based on average conditions determined in the foregoing sections, using the results from this experiment yields  
\[1-\delta=1-(1.34\pm 0.1122)\delta_{s} \tag{41}\]  
which leads to  
\[\delta=(1.34\pm 0.1122)\delta_{s} \tag{42}\]  
The blockage ratio \(r_{b}\) for the AVAWT rotor is 0.22. By Equation (37), \(\delta_{\omega}=\delta-\delta_{s}\), and substituting Equation (42) into this expression yields \(\delta_{\omega}=(0.34\pm 0.1122)\delta_{s}\). Substituting the expression for \(\delta_{\omega}\) into Equation (40) yields  
\[C_{D}=6.182\delta_{s} \tag{43}\]where by Equation (39),  
\[\delta_{\rm s}=1-\left(\frac{U_{1}}{U_{0}}\right) \tag{44}\]  
Use of Equations (43) and (44) and the expression for Re yields the drag coefficient shown in Figure 13, which is a cubic polynomial with a 99.91% coefficient of determination and a correlation coefficient of 99.95%:  
\[C_{D}=9.591\times 10^{-15}\rm{Re}^{3}-4.32\times 10^{-9}\rm{Re}^{2}+6.164 \times 10^{-4}\rm{Re}-23.12 \tag{45}\]  
It is discernible from Figure 13 that the drag coefficient increases from a value of about 3.55 at \(\rm{Re}\cong 8.1\)\(\times\)\(10^{4}\) to a peak of about 5.23 at \(\rm{Re}\cong 1.16\times 10^{5}\), after which it drops to a trough of about 5.1 at \(\rm{Re}\cong 1.81\)\(\times\)\(10^{5}\). It then increases to a value of about 5.5 at \(\rm{Re}\cong 1.96\times 10^{5}\).