# Design and Testing of a LUT Airfoil for Straight-Baded Vertical Axis Wind Turbines
## 4 Results and Discussion
### Static LUT Airfoil Performance at Low Reynolds Number
#### 4.1.1 Pressure Coefficient Distribution on the Surface for the LUT Airfoil  
In Figure 7, the distribution of the pressure coefficients on the LUT airfoil surface is shown for some specific angles of attack at \(R_{e}=3\)\(\times\)\(10^{5}\) and at \(R_{e}=5\)\(\times\)\(10^{5}\). In this figure, the lines in black, red, and blue denoting the pressure coefficient (C\({}_{\rm p}\)) correspond to angles of attack of C\({}_{\rm L}\)/C\({}_{\rm d}\)-max, C\({}_{\rm L}\)-max, and post-stall, respectively. In the case of \(R_{e}=3\)\(\times\)\(10^{5}\), the LUT airfoil has a maximum lift coefficient of C\({}_{\rm L\_max}=1.47\) at an angle of attack of \(\alpha=14^{\circ}\) and a maximum lift-drag ratio of C\({}_{\rm L}\)/C\({}_{\rm d\_max}=64.4\) at an angle of attack of \(\alpha=10^{\circ}\). After an angle of attack of \(\alpha=14^{\circ}\), the LUT airfoil starts to stall, and separation occurs on the suction surface at about 39% of the chord with an angle of attack of \(\alpha=16^{\circ}\). Therefore, the pressure coefficient on the suction surface of the LUT airfoil keeps a constant value from about 39% of the chord to the trailing edge. In the case of \(R_{e}=5\)\(\times\)\(10^{5}\), the LUT airfoil has a maximum lift coefficient of C\({}_{\rm L\_max}=1.5\) at an angle of attack of \(\alpha=14^{\circ}\) and a maximum lift-drag ratio of C\({}_{\rm L}\)/C\({}_{\rm d\_max}=79.8\) with an angle of attack of \(\alpha=10^{\circ}\). After an angle of attack \(\alpha=14^{\circ}\), the LUT airfoil starts to stall, and separation occurs on the suction surface at about 48% of the chord when the angle of attack is \(16^{\circ}\). Moreover, after 48% of the chord, the pressure coefficient on the suction surface of the LUT airfoil keeps a constant value; that is, the LUT airfoil is fully stalled. Comparing the cases of \(R_{e}=3\)\(\times\)\(10^{5}\) and \(R_{e}=5\)\(\times\)\(10^{5}\), the suction peak value increases and moves to the leading edge of the LUT airfoil with the increase in \(R_{e}\). This indicates that the region of adverse pressure gradient on the suction surface of the LUT airfoil is extended when \(R_{e}=5\)\(\times\)\(10^{5}\). However, due to the effect of the turbulence, the flow separation is delayed [32]. Additionally, the pressure was  
Figure 7: Pressure coefficient distribution of the LUT airfoil: **(a)** the case of \(R_{e}=3\)\(\times\)\(10^{5}\); and **(b)** the case of \(R_{e}=5\)\(\times\)\(10^{5}\). The data were measured when the surface of the LUT airfoil was clean. The lines in black, red, and blue show the pressure coefficients corresponding to angles of attack of C\({}_{\rm L}\)/C\({}_{\rm d}\)-max, C\({}_{\rm L}\)-max, and post-stall, respectively. not measured at large angles of attack due to the measuring range of the wake rake. In the future, the performance of the LUT needs to be studied at large angles of attack. Figure 8 shows the changes in the pressure coefficient distribution with increasing angles of attack at different values of \(R_{e}\) for the LUT airfoil. In the case of \(R_{e}\) = 3 \(\times\)\(10^{5}\), the free transition position is located at 53% and 35% of the chord when the angle of attack is 0\({}^{\circ}\) and 8\({}^{\circ}\), respectively. Until an angle of attack of \(\alpha\) = 21\({}^{\circ}\), the pressure of the upper surface from the leading edge to the trailing edge remains constant due to the complete separation of the flows on the upper surface; that is, leading-edge separation is occurring. Combined with Figure 7, the transition position on the upper surface slightly develops in the range 8\({}^{\circ}\) < \(\alpha\) < 14\({}^{\circ}\) and is located at about 30% of the chord, indicating that the LUT is characterized by low drag, because the desirable pressure gradient exists at about 30% of the chord on the upper surface of the LUT airfoil [33], while the pressure coefficient on the lower surface is not obviously developed in the range 8\({}^{\circ}\) < \(\alpha\) < 14\({}^{\circ}\).