## 3 Results
### Plasma Actuator Case
Figure 15: Skin friction coefficient comparison between the baseline and plasma case. Figure 16 represents the change in pressure coefficient, \(C_{p}\), due to plasma actuator effects, and it compares the plasma result to the baseline result. The pressure dropped by a significant margin at the position where the separation started, i.e., \(x/c=0.66\). The sudden decrease in \(C_{p}\) indicated that the induced plasma body force increased the overall flow velocity compared to the baseline case. This flow remained separated and then reattached downstream of the trailing edge. The plasma force accelerated the fluid near the plasma affected area, which caused a local pressure drop. A significant increase in \(-Cp\) was observed at the same location, where a decrease in \(-Cp\) was seen for the baseline case. This was due to the pressure increasing suddenly at the separation point and caused the fluid flow near the wall to retard. The idea behind the plasma actuator was to add momentum to this retarded flow through a plasma induced body force. This was achieved and displayed in Figure 16, where the pressure decreased rapidly to verify the plasma actuator's effectiveness. The coefficient of pressure and the coefficient of skin friction plot shown above sufficiently shows the change in flow distribution, the reduction in flow separation, and the existence of added momentum. As the total mass was conserved, the increase in velocity along the y-axis would provide detailed information of the plasma actuator effect on the velocity field. Figure 17 shows the u-velocity profile along the y-axis at selected axial  
Figure 17 helps us to understand the effects of the plasma actuator on the flowfield. For the baseline case, at the locations inside the flow separation, i.e., \(x/c=0.80\), \(x/c=0.90\), and \(x/c=1.1\), the flow pattern in the boundary followed in the reverse direction for the separation and recirculation, which is also described in Figure 12. As the plasma actuator was located at the location where the separation began, the actuator assisted the flow to remain attached. Location \(x/c=0.80\) was still under the separation region, whereas location \(x/c=0.90\) was free from separation. Figure 17 also holds up the same conclusion with the skin friction coefficient results in Figure 15 regarding the flow reattachment at \(x/c=0.90\). The further the location was from the flow reattachment, due to sudden flow acceleration, the velocity increased rapidly at the boundary, but slowed down due to relative low momentum flow at the top. This caused the velocity to rise to reach the freestream condition. Figures 18 and 19 show the effect of the plasma induced force by comparing the Q-criterion and the vorticity magnitude, respectively. The positive value of the Q-criterion was the proof of the dominance of rotational components over the strain or stretching components. A push in the flow downstream is visible in Figure 18, and it visually demonstrates the effects of the plasma enabled body force. The blue contours in Figure 19 indicate the reversed flow. It is seen that, for the plasma case, flow reversal, and hence the separation, was significantly smaller than the separation in the baseline case. Figure 20 illustrates the plasma force effects on the instantaneous u-velocity over a certain period of time. After 300 time steps or 0.6 non-dimensional times, the initial accelerated momentum increased the velocity and reduced the flow instability near the wall, shown in the top left of Figure 20. The rest of the snapshots in the figure show the effects at later time steps. Flow separation and instabilities at the wall were pushed downstream with increasing time.