Periodic excitation with different frequencies

Experimental investigations show that different excitation frequencies require different intensities to get the same kind of flow control in post-stall cases [1,15]. In order to find an optimum excitation mode, simulations with different frequencies are performed at an intensity of $C_{\mu}=50 \cdot 10^{-5}$.

Figure: Mean separation position for different excitation frequencies and $C_{\mu}=50 \cdot 10^{-5}$ intensity

Figure: Mean lift coefficient for different excitation frequencies and $C_{\mu}=50 \cdot 10^{-5}$ intensity

Figure: Mean drag coefficient for different excitation frequencies and $C_{\mu}=50 \cdot 10^{-5}$ intensity

The largest lift can be found at a frequency of $F^+ =0.62$ (Fig. ). In this case the lift coefficient can be enhanced by $14\%$ compared to the baseline simulation. The optimum frequency is slighly larger than the frequency of detaching vorticies without excitation ($F^+ =0.62$). At the same time the mean separation position moves from less than $5\%$ chord downstream to $15.5\%$ (Fig. ) and drag drops from $c_d = 0.2$ in the baseline case down to $c_d = 0.11$ for frequencies of $F^+ \approx \ 0.4 \ - \ 1.0$ (Fig. ). The differences in drag and separation position, however, are very small over a wide range of frequencies.

Figure: Unsteady lift coefficient over the non-dimensional time for three different excitation frequencies

Visualizations of the flowfield indicate the relevance of the detaching vorticies for the effectivity of periodic excitation. This structure is dominated by the excitation frequency and turns out to be more important than the instability frequency of the free shear layer in the baseline case.

The periodic exciation behaves like a periodic suction that always moves the free shear layer close to the flap surface. At very high frequencies more than one vortex can detach during one excitation period (Fig.  left). In the case of low frequency excitation, however, the time between two suction events is too short to form a complete vortex (Fig.  right). Consequently only a part of a complete vortex can detach during one period and each vortex is devided into subvorticies. Both cases are less effective than excitation with a frequency that allows one complete vortex after the other to detach (Fig.  center). The same effect appeares in the time evolution of the lift coefficient in Fig. : in the case of low frequency excitation higher harmonics occur whereas for high frequency excitation a low frequency signal is superimposed on the main frequency. Only at $F^+ =0.62$, where a clear sinusoidal signal can be seen, the lift coefficient reaches a maximum.

In the numerical study frequencies arround $F^+ \approx 0.62$ appear to form an optimum excitation. In the experiments the range of frequencies with most promising results is $0.25 < F^+ < 0.5$ .