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In this paper, the controlled stability of insect hovering flight is analyzed in detail based on a simplified dynamic model of the flyer and flow. The simplified dynamic model incorporates PIDbased wing-kinematic controllers. The control stability of the hovering flight is evaluated based on the cycle-mean dynamic equations. The stability analyses and the simplified dynamic model allow us to derive and test the control coefficients for stable free hovering, firstly in the longitudinal mode of flight and then the lateral mode. In this manner, coefficients for wing-kinematic control for full CFD-FSI simulation could be obtained very efficiently. The coefficients thus determined are verified against full-fidelity CFD-FSI free flight simulations.

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A superhydrophobic (SH) surface has shown great potential in reducing flow resistance and saving energy in hydrodynamic applications. In this paper, we have tried to investigate the effects of liquid–gas interface curvature of a SH wall in turbulent flows with the wall-resolved large eddy simulation (LES). The LES is first validated against direct numerical simulation results before the curvature shape is parameterized and examined at various Reynolds numbers (Reτ = 180, 395, and 590). The parametric study shows that a positive curvature angle leads to a higher flow rate, while the effect of a negative curvature angle on the flow resistance is minimal. In addition, the effect of the interface curvature on the flow rate is weakly dependent on the Reynolds number. Analysis shows that larger flow rate can be obtained by reducing the spanwise momentum exchange. A positively curved interface bows into the liquid and shifts the transverse flow circulation (in the cross-sectional plane) away from the solid wall, which helps to reduce spanwise momentum exchange and thus the flow resistance significantly. In contrast, a negatively curved interface does not change the location of the transverse circulation but deforms its shape, which hardly affects the spanwise momentum exchange or the flow rate. The near-wall streak patterns above the SH wall distribute with roughly the same spacing of the surface texture. In addition, the absolute distance plays a more important role than the viscous distance in the variation of the streaks with the distance from the SH wall.