*5.4. Effects of External Flow on the Characteristics of the Fluidic Oscillator*

The effect of the bending angle on the characteristics of the fluidic oscillators was also evaluated for external flow over a NACA0015 airfoil with a simple hinge flap. With the installation conditions shown in Figure 3, four bending angles (i.e., pitch angles) of β = 0◦, 20◦, 35◦, and 40◦ were tested. The values of Cμ used for the mass flow rates are presented in Table 5.


**Table 5.** Cμ values according to mass flow rates.

Figure 13 shows the comparison between frequencies of the fluidic oscillator with and without the external flow in a range of mass flow rates, . *m* = 0.30–0.62 g/s. Generally, the external flow reduces the frequency except at β = 40◦. The average relative difference in the frequency increases with the bending angle β. For β < 40◦, the largest relative difference of 7.62% is found at <sup>β</sup> = 35◦ and . *m* = 0.30 g/s.

**Figure 12.** Velocity contours and vectors for different bending angles and flow rates (Left: Φ = 90◦, Center: Φ = 270◦, Right: x-z cross section).

**Figure 13.** Comparison of jet frequency variation with mass flow rate between the cases with and without external flow for various bending angles.

With the external flow, the jet from the fluidic oscillator becomes steady at β = 40◦ beyond . *m* = 0.30 g/s, as in the case without external flow (Figure 9). At this bending angle, the external flow increases the frequency for . *m* = 0.30 g/s, unlike the other cases, and the relative difference in the frequency increases up to 14.4%. In the case with the external flow, oscillation of the jet also disappears at β = 35◦ for the highest mass flow rate of . *m* = 0.62 g/s, unlike the case without external flow. Therefore, the external flow acts to suppress the oscillation earlier.

The effects of the external flow on the peak velocity ratio of the fluidic oscillator for different bending angles are shown in Figure 14. Except at β = 40◦, where oscillation of the jet disappears for high mass flow rates, the external flow increases the peak velocity ratio, regardless of the mass flow rate. However, at β = 40◦, the peak velocity ratio shows almost uniform variation with the mass flow rate, and the external flow largely reduces the peak velocity ratio, even for . *m* = 0.30 g/s (relative difference of 24.3%), where the jet still oscillates. At <sup>β</sup> = 35◦, the peak velocity ratio increases rapidly for . *m* = 0.62 g/s, where the jet oscillation disappears, showing the largest relative difference of 33.8%. Except for the cases where the jet oscillation disappears, the effect of bending angle on the relative difference in the peak velocity ratio is not remarkable, and the range of the relative difference is 2.33–8.50%.

**Figure 14.** Comparison of peak velocity ratio variation with mass flow rate between the cases with and without external flow for various bending angles.

Figure 15 shows the effects of the external flow on the pressure drop in the fluidic oscillator. The external flow increases the pressure drop by 3–14% at all the tested bending angles, regardless of mass flow rate. The external flow reduces the pressure at the outlet of the oscillator by increasing the velocity there, and this becomes the reason for the increase in the pressure drop through the oscillator with the external flow. The relative difference in *Ff* does not vary largely with the mass flow rate. β = 20◦ shows the minimum relative differences, and β = 35◦ and 40◦ show similar *Ff* variations. Thus, there are similar relative differences in the tested range of mass flow rate. The existence of the jet oscillation does not seem to affect the pressure drop.

**Figure 15.** Comparison of *Ff* variation with mass flow rate between the cases with and without external flow for various bending angles.

Figure 16 shows the variations of the lift coefficient (CL) with C<sup>μ</sup> for different bending angles. The lift coefficient generally increases with Cμ. The relationship between Cμ and the mass flow rate in the oscillator is shown in Table 5. Except for the steady jets at β = 40◦, the lift coefficient increases as the bending angle increases for all Cμ values. Therefore, β = 35◦ shows the highest lift coefficients among the tested bending angles, but there is no further increase with C<sup>μ</sup> for C<sup>μ</sup> = 4.38 (i.e., . *m* = 0.62 g/s), where the jet oscillation disappears. The steady jets at β = 40◦ show CL values similar to those at β = 20◦. This reflects the combined effects of the increase in the pitch angle and the disappearance of the jet oscillation on the lift coefficient. Variations of CL in the tested C<sup>μ</sup> range for non-zero bending angles are much larger than that of the reference model.

Figure 17 shows the effects of bending angle on the drag coefficient (CD). The variation of CD with C<sup>μ</sup> is generally not large except at β = 0◦. Similar to the case of the lift coefficient shown in Figure 16, except for the case of β = 40◦, the drag coefficient decreases as the bending angle increases for all Cμ values. However, for the lowest value of Cμ = 1.02, β = 0◦ and 20◦ show similar drag coefficients. β = 40◦ shows much larger drag coefficients than those at β = 35◦ except for C<sup>μ</sup> = 1.02, where the jet oscillation still exists. However, these values with the steady jets are still lower than those of β = 20◦, which was probably due to the larger pitch angle.

**Figure 16.** Variations of lift coefficient with momentum coefficient for various bending angles (x0/c = 0.7, α = 8◦, *δ<sup>f</sup>* = 40◦).

**Figure 17.** Variations of drag coefficient with momentum coefficient for various bending angles (x0/c = 0.7, α = 8◦, *δ<sup>f</sup>* = 40◦).
