# Efficiency of Pulsating Base Bleeding to Control Trailing Edge Flow Configurations
## 3 Results and Discussion
### Trailing Edge Pulsating Actuation
#### 3.2.1 Airfoil Drag Force  
To track the evolution of the viscous drag forces with respect to the base bleed intensity, a relative non-dimensional coefficient for the aerodynamic drag forces, \(\overline{C_{d,R}}\), is defined as:  
\[\overline{C_{d,R}}=\frac{C_{d}}{C_{d_{NB}}}, \tag{2}\]  
where \(C_{d}\) is the drag force coefficient for a specific configuration and \(C_{d_{NB}}\) is the corresponding drag coefficient for a non-blowing configuration. Its dependency with the non-dimensional base bleed rate, \(C_{b}\), is depicted in Figure 5 for different pulsating base bleed frequencies. Increasing the values of \(C_{b}\), the drag force coefficient initially decreases until it reaches a minimum at \(\simeq\)\(C_{b}=0.13\), approximately 17% lower than the reference value. However, higher values of \(C_{b}\) imply a further increment of the drag force coefficient, this being more pronounced for a steady base bleed. This increment of the drag force coefficient is related to a decrease in the base pressure value, as the ejected mass flow evacuates flow from the base region, hence increasing the pressure drag. Nevertheless, this  
Figure 4: Evolution of the temporal averaging of the static base pressure ratio (\(P_{ratio}=P_{base}/P_{baseNB}\)) and the Strouhal number (\(S=fD/U_{\infty}\)) when the base bleed intensity is increased. Those mass flows related to non-symmetrical trailing edge flows are highlighted in blue, while those associated with the disappearance of vortex shedding are marked in green. Reproduced from [PERSON] et al. [19]. Copyright © 2021, published by Elsevier Masson SAS. All rights reserved.  
trend is more pronounced for a steady base bleed actuation, indicating that a pulsating injection may be more beneficial in terms of aerodynamic drag than its steady counterpart.  
In the evaluated injection frequency range of 100-200 Hz, the drag forces appear to be quite insensitive to the frequency of the bleeding. Lower frequency ejections (below 100 Hz) may show a smooth transition from the numbers observed on a steady actuation to those shown herein for a pulsating actuation, but that remains out of the scope of the present analysis.  
For illustration, snapshots of instantaneous pressure coefficient contours obtained from an URANS solution at \(C_{b}=0.13\) and \(C_{b}=0.90\) for a pulsating base bleed frequency of \(f=100\) Hz are depicted in Figure 6. The pulsation of base bleed modulates the pattern of trailing edge vortex shedding but does not neutralize it for high values of the non-dimensional base bleed rate, as observed in steady base bleed actuation [19].  
Figure 5: Mean drag coefficient relative to a non-blowing configuration against non-dimensional base bleed rate for constant (-\(\square\)-) [19] and pulsating base bleeds at 100 Hz (-\(\triangle\)-), 150 Hz (-\(\times\)-) and 200 Hz (-\(\bigtriangledown\)-).  
Figure 6: Snapshots of instantaneous pressure coefficient contours for a pulsating base bleed of \(f=100\) Hz and non-dimensional base bleed rates of \(C_{b}=0.13\) and \(C_{b}=0.90\). (**a**) \(t=0.1T\). (**b**) \(t=0.4T\). (**c**) \(t=0.7T\). (**d**) \(t=T\). (**e**) \(t=0.1T\). (**f**) \(t=0.4T\). (**g**) \(t=0.7T\). (**h**) \(t=T\).