## 5 Results
### Functions of Plasma Actuator at Cruise Condition  
Thus far, we have only discussed the flow control authority of the DBD plasma actuator to avoid large-scale flow separation over an airfoil. This may be useful for avoiding aircraft stall. However, such a flow condition rarely occurs and therefore applications may be limited from the viewpoint of aeronautical engineering. We may need to show that a higher \(L/D\) would be obtained at cruise conditions. In this section, we show how the DBD plasma actuator works at the cruise condition and show another benefit of the DBD plasma actuator at a Reynolds number of the order \(10^{4}\) to \(10^{5}\) with the CFD analysis. The numerical approach is the same as above except for the angles of attack. The aerodynamic performance of an NACA0015 airfoil with a DBD plasma actuator is compared to that for the Ishii airfoil which is a high-performance airfoil at this Reynolds number range and is commonly used for model airplanes. Details of the analysis have been previously published [50] and only the key issues are described in this section. The Reynolds number is set to be 63,000. The lift to drag ratios for both the NACA0015 (without a DBD plasma actuator) and the Ishii airfoil are computed in advance and the angle of attack that achieves a maximum \(L/D\) is selected to be the flow condition for each airfoil. The angles of attack was \(6^{\circ}\) for the NACA0015 and \(4^{\circ}\) for the Ishii airfoil, respectively. Under these conditions, the flow is almost attached except in the region of the laminar separation bubble over the upper surface of the airfoils. The computed aerodynamic coefficients are presented in Figure 13a-c. Figure 13a shows that the NACA0015 airfoil, when it has the DBD plasma actuator, successfully achieves a higher \(L/D\) than that for the Ishii airfoil. Although the difference is only a few percent, there are several additional benefits. Firstly, the thickness of the Ishii airfoil is 7.1% of the chord length and that of the NACA0015 airfoil is 15.0%. We could use much thicker airfoil, which would greatly alleviate structural restrictions. Secondly, we might be able to have a high \(L/D\) for a wide angle-of-attack range with optimized choice  
Figure 12: Chordwise \(C_{p}\) distributions (Experiment): NACA0015, \(\alpha=22.0^{\circ}\), \(Re=7.6\times 10^{5}\), \(BR=10\%\). DBD plasma actuator is located at 5% of the chord, \(Vpp=9\) kV. for the parameters of the plasma actuator. In addition, we might obtain a still higher \(L/D\) by finding a suitable angle of attack where the \(L/D\) attain the maxim value with the DBD plasma actuator. Thus far, we have only tried the angle of attack when the \(L/D\) attains the maximum value without the DBD plasma actuator. Figure 13b,c shows the lift and drag coefficients. From these graphs, a high \(L/D\) was achieved mainly by the drag reduction rather than by lift increase. Reduction of pressure drag is the main reason. To find out why this occurred, the skin friction coefficients over the upper surface are plotted in Figure 14. The chordwise pressure coefficient (\(C_{p}\)) distributions over the airfoil surfaces are also plotted in Figure 15. A recirculating region due to a laminar separation bubble is located further forward for the Ishii airfoil compared to that for the NACA0015 airfoil without the DBD plasma actuator. The NACA0015 airfoil without a DBD plasma actuator has a separation bubble up to almost 50% of the chord, which increases the pressure drag. With a DBD plasma actuator \"ON\", this region becomes very small and moves forward. The reattachment point become almost the same as that for the Ishii airfoil. By moving the low-pressure region inside the separation bubble forward, the pressure drag is remarkably reduced. Figure 14: Chordwise skin friction coefficient distributions over the upper surface of the airfoils: NACA0015 (\(\alpha=6^{\circ}\)), Ishii airfoil (\(\alpha=4^{\circ}\)), \(Re=6.3\times 10^{4}\), \(F^{+}=6.0\), \(Dc=0.05\), \(BR=10\%\).