Spatial numerical simulation of boundary layer transition: effects of a spherical particle

Abstract

In the present study, the effects of an isolated stationary spherical particle on the transition process in a flat-plate boundary layer are examined by a spatial direct numerical simulation. The full three-dimensional time-dependent incompressible Navier–Stokes equations are integrated by a time-splitting method and discretized spatially by a high-order finite difference/spectral method. A virtual boundary technique defining the no-slip boundary of a sphere is implemented within the Cartesian geometry of the computational grid.Two numerical simulations which consider the effects of the sphere on the boundary layer are presented. The subcritical Reynolds number case reveals the appearance of hairpin vortices shed into the sphere wake which decay as they are convected downstream. The initial interaction of the sphere and the boundary layer produces a three-dimensional isolated disturbance comprising a wave part and a transient part. The decaying transient part is convected downstream at the local mean velocity, while the wave part induces a decaying Tollmien–Schlichting wave in the flow field.In the second case, an increase in the Reynolds number results in a wedge of incipient turbulent flow downstream of the sphere. The development of the wake of the sphere is dominated by the appearance of an isolated disturbance which rapidly breaks down forming a structure resembling a turbulent spot. It is demonstrated that the transition induced by a sphere in the boundary layer is due to a mechanism related to bypass transition.