## 3 Results
### Plasma Actuator Case  
The hump model is a modified design of the Glauert airfoil and is used as a benchmark model for the CFD validation in flow separation at the NASA Langley workshop for synthetic jets and turbulence separation control. The baseline results suggested that the separation began at position \(x/c=0.66\), and so, the DBD plasma actuator was placed at that location. A total of five test cases were investigated for the plasma actuator simulations, based on the applied voltage frequency and the plasma actuator location. Table 2 below displays the test cases. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Case No.** & **Actuator Location** & **Applied Voltage Frequency** \\ \hline
1 & \(x/c=0.66\) & 3 kHz \\
2 & \(x/c=0.63\) & 3 kHz \\
3 & \(x/c=0.70\) & 3 kHz \\
4 & \(x/c=0.66\) & 1.5 kHz \\
5 & \(x/c=0.66\) & 5 kHz \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Plasma actuator test cases. Figure 13: Normalized mean Reynolds stress along y/c at different streamwise locations. Section 3.2 only describes the results of Test Case 1, whereas, the remaining test cases are discussed in the subsequent subsections. The length and the height of the plasma actuator were denoted by \(b\) and \(a\) respectively, where the normalized height \(a/c=0.018\) and normalized length \(b/c=0.024\). The plasma actuator location was modeled as a body force term in the momentum equation stated in Equation (14). The parametric values of the body force terms described in Table 3 were based on the original Shyy model. The non-dimensional plasma body force term, \(D_{c}\), was calculated using the formulation stated in Equation (15). The value of \(D_{c}\) was calculated based on model geometry and flow conditions. The plasma induced force pushed the existing fluid through the separation zone to reduce or eliminate the flow separation. The magnitude of this force was directly dependent on the plasma size, applied voltage frequency, and electric field strength. Thus, changing these parameters would cause changes in the magnitude of the force. The parameter values needed for the plasma model are illustrated in Table 3.  
Figure 14 shows the comparison between the baseline and plasma cases using velocity streamlines. The plasma induced streamlines are at the left side of Figure 14, whereas the right side of the figure represents the baseline result also shown in Figure 6a. The side-by-side representation of the streamline results indicated the changes in the flow field due to the plasma actuator. There was a substantial reduction in flow separation over the hump surface due to plasma induced force. Nevertheless, the quantitative description of flow separation and flow reattachment was understood from the coefficient of skin friction and the coefficient of pressure displayed in Figures 15 and 16, respectively. The skin friction coefficient gave a precise location of the flow separation and flow reattachment. At the time of flow separation, the \(C_{f}\) value decreased to zero, and it rose to zero when the flow reattached. Figure 15 shows the skin friction coefficient in the plasma actuator case and compares the result to the baseline case. The blue line represents the plasma actuator case, and the red line represents the baseline case. A change in the skin friction coefficient is shown in the figure. There was a small delay in separation at the leeside of the hump. The separation started at location \(x/c=0.69\). The biggest difference was found where the flow reattached. Flow reattachment occurred at location \(x/c=0.9\). The overall separation region for the plasma enabled flow was from \(x/c=0.68\) to \(x/c=0.90\), and the separation region was between location \(x/c=0.66\) and \(x/c=1.13\) for the baseline case. Thus, the overall flow separation was reduced by a reasonable margin. The horizontal dotted line is placed at \(C_{f}\) equal to zero to determine the streamwise locations of separation and reattachment. Figure 16: Coefficient of pressure comparison between the baseline and plasma case.