Direct numerical simulation and stability analysis of the transitional boundary layer on a marine propeller blade

It is generally assumed that the cross-flow instability exists on propeller blade boundary layers due to their similarity with the rotating disk flow. However, to the best of our knowledge, there is no experimental or numerical evidence that directly shows the existence of the cross-flow instability on propellers. In this paper, we present a direct numerical simulation of the boundary layer flow around a marine propeller blade. For the investigated case, the cross-flow velocity inside the attached laminar boundary layer is smaller than the rotating disk case, but it is large enough to lead to the cross-flow instability. The wave-numbers and wave-direction of the cross-flow vortices observed agree well with the prediction of linear stability theory. Linearized Navier-Stokes simulations show that the boundary layer is absolutely unstable in the radial direction but convectively unstable in the streamwise direction. A significant flow direction deviation between laminar and turbulent regions is also observed on the blade surface. In the separation bubble, there is an unusually large radial velocity (around 50% of the inviscid streamwise velocity). Both the flow direction deviation and the large radial velocity in the separation bubble can be explained by the relationship between Coriolis forces and circumferential velocities.