# Efficiency of Pulsating Base Bleeding to Control Trailing Edge Flow Configurations
## 3 Results and Discussion
### Trailing Edge Pulsating Actuation
#### 3.2.2 Airfoil Lift Force  
In this Section, the effect of the pulsating base bleed on the frequency and amplitude of the oscillations of the lift force coefficient is discussed. The definition of the Strouhal number considered for the interpretation of the results shown herein follows the definition:  
\[\text{St}=\frac{fD}{U}, \tag{3}\]  
where \(U\) is the velocity of the incident flow, \(D\) is the thickness of the considered airfoil at the trailing edge, and \(f\) is the lift force main oscillation frequency. The reference value for the Strouhal number is associated with a non-blowing configuration, \(\text{St}=0.287\). According to the underlying physics, there are three main possible contributions to the lift force oscillations:  
1. Vortex shedding phenomenon
2. Oscillations of the jet angle
3. Injection frequency  
The characteristic frequency is determined through a Fast Fourier Transform (FFT) of the time series obtained from the URANS simulations, which have been ensured to have reached convergence by showing periodic flow tendencies. Figure 7 depicts the Strouhal number obtained of the most energetic frequency plotted against the non-dimensional base bleed rate. The injection has a strong impact on the frequency of the lift oscillations, and despite the fact that there is no clear relation between St and \(C_{b}\), certain conclusions can be extracted.  
The dependency of the associated frequencies with the base bleed rate follows the observed trend for steady base bleed [19], peaking as \(C_{b}\) increases. At certain ranges of base bleed intensities (\(C_{b}=0.1\)-\(0.3\) and \(C_{b}>0.8\)), the oscillations are so small that it can be assumed that vortex shedding has been suppressed. The use of base bleed generally reduces the amplitude of the oscillations when compared to the non-blowing configuration, but the effect of the pulsating injection appears to be less evident than a steady actuation. For each injection cycle, the flow patterns at the base region are modulated with the _duty cycle_. Although base bleed mostly affects the base region area, the downstream region flow topology is also severely altered. A probe located downstream of the injection channel is used to monitor flow variables over time (point \(F_{w}\) on Figure 8). In Figure 9, spectrograms based on pressure time series of four actuation cycles are gathered for a non-blowing configuration and two different base bleed intensities. As the profiling point is located in the symmetry plane of the model, the first shows a clear dominance of a frequency value that doubles the frequency corresponding to the natural vortex shedding. However, the other two frequencies appear modulated by the actuation cycle, with the  
Figure 7: Strouhal number (**a**) and relative lift coefficient amplitude (**b**), \(A_{C_{b},\,R}=A_{C_{b}}/A_{C_{b},\,NB}\), against non-dimensional base bleed rate. Results for constant (-\(\square\)-) [19] and pulsating base bleeds at 100 Hz (-\(\triangle\)-), 150 Hz (-\(\times\)-) and 200 Hz (-\(\bigtriangledown\)-).  
former showing a disappearance of the vortex shedding related oscillations as the strength of the base bleed jet generates a symmetric flow topology.