A numerical study on the natural transition locations in the flat-plate boundary layers on superhydrophobic surfaces

Abstract

In this paper, the natural transition locations in the flat-plate boundary layers on the superhydrophobic surfaces are studied by numerical methods. The laminar flow field in the whole stream-wise computational domain is obtained by solving the Blasius equation with the slip-velocity boundary condition on the wall. The boundary layer on the superhydrophobic surface becomes thinner than that on the ordinary surface. The linear instability analysis is performed on the laminar boundary layer, and the eN method is employed to predict the transition location. The two-dimensional (2D) Tollmien–Schlichting (T–S) waves are still more unstable than the three-dimensional (3D) ones on the superhydrophobic surfaces, so only the 2D waves are taken into consideration to predict transition. As the slip length becomes longer, the critical location of flow instability moves further downstream, and the unstable zone becomes smaller. Therefore, the superhydrophobic surfaces have the effect of delaying the natural transition and that the delay effect becomes stronger as the slip length becomes longer. The higher oncoming flow velocity leads to higher frequencies of the unstable T–S waves and the larger unstable zone. As the oncoming flow velocity rises, the transition location on the superhydrophobic surface moves once upstream and then downstream. Consequently, there is a “dangerous” oncoming flow velocity corresponding to the transition location, which is the closest to the lead edge. Furthermore, the transition delay effect of the superhydrophobic surface becomes stronger with the increase in the oncoming flow velocity.