Influence of slip on the three-dimensional instability of flow past an elongated superhydrophobic bluff body

Abstract

The effects of superhydrophobic surfaces (SHSs), which consist of microgrates oriented transverse to the flow direction, on the onset of three-dimensional instability of flow past a bluff body were studied using Floquet analysis. The SHS was modelled on an air–water interface with a shear-free condition. The results showed that SHSs increased the vortex shedding frequency. Floquet analysis revealed that modes B$^{\prime }$ and S$^{\prime }$ were suppressed dramatically by the partial-slip condition compared with a regular no-slip body; however, mode A was less affected. Correspondingly, the critical spanwise wavelengths were not significantly affected by SHSs. A similar phenomenon was observed in flow past a circular cylinder coated by SHSs. The results also revealed that modes B$^{\prime }$ and S$^{\prime }$ were collapsed into mode A due to the increased width of the air–water region for flow past an elongated body. Furthermore, the critical Reynold numbers of different modes were diversely affected by gas fraction (GF) variations. The unstable modes with short wavelengths, such as modes B$^{\prime }$ and S$^{\prime }$, stabilized with increasing GF. Conversely, the opposite was seen for the unstable mode A with a longer wavelength. The exact critical Reynolds number depended on the geometric configuration, which should be between the critical values of the two extreme cases. The application of SHSs could modify the transition route from two- to three-dimensionality by alternating different unstable modes. As the wavelength of the unstable mode decreases, the inhibition of three-dimensional instability becomes more efficient by SHSs.