## 3 Results and Discussion
### Flow Control Effect by AC-DBD Plasma Actuation
#### 3.2.2 Time-Averaged Velocity Field  
The effects of using the linear AC-DBD plasma actuation to manipulate the flow characteristics along the wake region is considered in this section. Figure 8 shows the streamtraces and the normalised velocity magnitude contour (\(\left|\text{U}\right|\)/\(\left|\text{U}\right)\) downstream of the trailer rear end. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Case** & **C\({}_{\text{D}}\)** & \(\Delta\)**C\({}_{\text{D}}\)** \\ \hline Baseline case, no plasma actuation & 0.725 & - \\ Controlled case, plasma actuation at 7 kHz & 0.729 & +0.004 \\ Controlled case, plasma actuation at 8 kHz & 0.725 & +0.000 \\ Controlled case, plasma actuation at 9 kHz & 0.724 & \(-\)0.001 \\ Controlled case, plasma actuation at 10 kHz & 0.725 & +0.000 \\ Controlled case, plasma actuation at 11 kHz & 0.726 & +0.001 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Coefficient of drag of the model with and without Alternate Current Dielectric Barrier Discharge (AC-DBD) plasma actuation. Figure 8: Streamtraces and normalised velocity magnitude contour downstream of the trailer rear end at various plasma actuation frequencies. (**a**) Baseline, (**b**) 7 kHz, (**c**) 8 kHz, (**d**) 9 kHz, (**e**) 10 kHz, and (**f**) 11 kHz. In the baseline trailer (Figure 8a), a large recirculating bubble appears downstream of the trailer rear end due to the coil up of the lower shear layer which emanates from the trailer's underbody. The core of this vortex is located at the normalised location x/H = 0.3 and y/H = \(-\)0.25. The size of this recirculating bubble is about 0.8 H (length) and 1.4 H (height) which is comparable to that shown in Lo and Kontis in Lo and Kontis in Lo and Kontis (2018). When implementing the linear AC-DBD plasma actuation, regardless of the actuation frequency, no significant change in the flow pattern is observed downstream of the trailer rear end. However, when the plasma actuation frequency is increased to 8 (Figure 8c) and 9 kHz (Figure 8d), the upper shear layer is deflected more downward in the region between 0.5 \(<\) x/H \(<\) 1.75 compared to that of the baseline trailer. In fact, the upper shear layer is deflected marginally more downwards when the actuation frequency is 8 kHz (Figure 8c) than when it is 9 kHz (Figure 8b). Further increases in the plasma actuation frequency to 10 (Figure 8e) and 11 kHz (Figure 8f) shows no additional effect on the shear layer deflection as the shear layer angle in these two cases is similar to that of the baseline case. The extent of the upper shear layer deflection with and without plasma actuation was quantified by measuring the average shear layer angle relative to the freestream direction downstream of the trailer rear end, and are compared as shown in Figure 9. From Figure 9, it can be seen that when the plasma actuation frequency is 8 kHz, the shear layer was deflected the most downwards followed by the frequency at 9 Hz. The stronger shear layer deflection downwards in these two cases is likely to be caused by the strong plasma-induced jet generated at these two actuation frequencies. In contrast, when the actuation frequency is at 7, 10, and 11 kHz, the angle of the shear layer relative to the freestream direction becomes similar to that shown in the baseline trailer (i.e., no plasma actuation). Normalised velocity contour and profiles in the x-direction (u/U) along the wake region of the articulate lorry model are presented in Figures 10 and 11, respectively. From Figure 10a-f, it is clear that very similar normalised x-velocity contour appeared in all cases being studied. No observable differences could be noticed from these velocity contour graphs. In fact, similar conclusions could also be drawn if the normalised velocity profiles along the wake region in the x-direction are considered. From Figure 11, it can be seen that very similar normalised x-velocity profiles appeared between \(-\)0.8 \(<\) y/H \(<\) 0.5 in all cases being studied.