Numerical investigation of the natural transition in boundary layers on underwater axisymmetric bodies with superhydrophobic surfaces

The natural transition in boundary layers on axisymmetric bodies with superhydrophobic surfaces is studied using numerical methods. By boundary layer, we mean the boundary layer around the forebody and around the parallel body of an underwater vehicle. A method of calculating basic laminar flows on axisymmetric bodies with superhydrophobic curved surfaces is proposed, and a method of linear stability analysis for the boundary layers that considers the slip-velocity boundary condition for small disturbances is established. The eN method is used to predict the transition locations of the boundary layers. On a superhydrophobic surface, the slip velocity on the wall increases and then decreases along the streamwise direction, resulting in a maximum value at the forebody. The boundary layer thickness on a superhydrophobic surface becomes smaller than that on an ordinary surface. The superhydrophobic surface stabilizes the boundary layer and thus delays the natural transition. As the slip length on the superhydrophobic surface increases, the unstable zone shrinks, and the transition location moves further downstream, indicating that the delay effect of the superhydrophobic surfaces becomes stronger. As the oncoming flow velocity increases, the transition location on the superhydrophobic surface moves upstream and then downstream, leading to a “dangerous” velocity, at which the transition location is closest to the leading edge. The underlying mechanism of the dangerous velocity phenomenon is discussed: An increasing velocity has both stabilizing effect and destabilizing effect on the boundary layer.