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.