## 3 Results
### Baseline Case  
In order to investigate the effects of a plasma actuator on a subsonic, incompressible flowfield numerically, it was necessary to understand the baseline flowfield prior to computing results with \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Freesstream Values** \\ \hline Velocity & 34.6 m/s \\ Mach Number & 0.1 \\ Reynolds Number & 936,000 \\ Prandtl Number & 0.72 \\ Strouhal Number & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Prescribed numerical parameters. Figure 4: Two-dimensional geometry. Figure 5: Computational grid. the plasma actuator turned on. The computational results were compared to the experimental results obtained by [PERSON] et al. [48; 49]. As the three-dimensional domain was used for the computation, the upper wall of the domain was modified to compensate for the effects of the side plates. The baseline model of the hump was also studied by several researchers [39; 42; 43; 44; 45; 46]. The time step of the computations was 0.002. Time-averaged variables were calculated after 7500 time steps, and sample data were collected after 7500 time steps. The time steps were chosen based on the Strouhal number of 0.2. Figure 6 shown above highlights the turbulent boundary layer flow separation in terms of velocity streamlines and vectors. Figure 6a,b represents the velocity streamlines and vectors, respectively. The streamline figure helps to observe visually the location of the unsteady flow separation on the leeside of the hump due to the adverse pressure gradient. It was observed from the result that the flow separation region was roughly between the non-dimensional length of 0.65 and 1.2. The velocity vectors in Figure 6b magnified the presence of the flow reversal. The instantaneous u-velocity contour shown in Figure 7 also captured the flow separation. Figure 7 shows the unsteady velocity flow field due to the turbulence. The blue region in the contour plot indicates the negative u-velocity, hence indicating the reversing flow region. The Q-criterion was the second variant of the velocity gradient tensor demonstrating the relative dominance of the rotational component of the velocity gradient over the stretching component in the deformation of a fluid element. The iso-surface of Q-criterion on the hump surface depicted the flow separation in the three-dimensional configuration shown in Figure 8. An instantaneous iso-surface of Q = 150 colored by the streamwise velocity magnitude exhibited the complex nature of flow separation at the aft portion of the hump. The vorticity magnitude of the flow over the hump is presented in Figure 9. It is noticeable from both figures that the turbulent length scales were larger downstream of the separation region. For external flow over an object, the resistive drag force consisted of the pressure drag and the drag due to surface roughness, known as the skin friction. The skin friction coefficient and the pressure coefficient are both non-dimensional parameters that represent the pressure and skin friction drag normalized by dynamic pressure and are defined as,  
\[C_{f}=\frac{\tau_{wall}}{\frac{1}{2}\rho_{ref}U_{ref}^{2}};C_{p}=\frac{p-p_{ref }}{\frac{1}{2}\rho_{ref}U_{ref}^{2}}\]  
Figures 10 and 11 represent the skin friction coefficient and the pressure coefficient, respectively. In both cases, the numerical result was compared with the available experimental result, recorded by [PERSON] [49]. It was observed that the baseline numerical results using CALC-LES predicted the experimental results with reasonable accuracy, thus proving the solver's ability to compute the flowfield using a hybrid turbulence model. The separation and reattachment of the flow near the wall could be estimated from the skin friction where the \(C_{f}\) value was zero. From Figure 10,  
Figure 6: Velocity streamlines and vectors showing the unsteady flow separation.