A computational study of three-dimensional vortex–cylinder interaction is reported
for the case where the nominal orientation of the cylinder axis is normal to the vortex
axis. The computations are performed using a new tetrahedral vorticity element
method for incompressible viscous fluids, in which vorticity is interpolated using a
tetrahedral mesh that is refit to the Lagrangian computational points at each timestep.
Fast computation of the Biot-Savart integral for velocity is performed using a box-point multipole acceleration method for distant tetrahedra and Gaussian quadratures
for nearby tetrahedra. A moving least-square method is used for differentiation,
and a flux-based vorticity boundary condition algorithm is employed for satisfaction
of the no-slip condition. The velocity induced by the primary vortex is obtained
using a filament model and the Navier–Stokes computations focus on development
of boundary-layer separation from the cylinder and the form and dynamics of the
ejected secondary vorticity structure. As the secondary vorticity is drawn outward
by the vortex-induced flow and wraps around the vortex, it has a substantial effect
both on the essentially inviscid flow field external to the boundary layer and on
the cylinder surface pressure field. Cases are examined with background free-stream
velocity oriented in the positive and negative directions along the cylinder axis, with
free-stream velocity normal to the cylinder axis, and with no free-stream velocity.
Computations with no free-stream velocity and those with free-stream velocity tangent
to the cylinder axis exhibit similar secondary vorticity structures, consisting of a vortex
loop (or hairpin) that wraps around the primary vortex and is attached to the cylinder
boundary layer at two points. Computations with free-stream velocity oriented normal
to the cylinder axis exhibit secondary vorticity structure of a markedly different
character, in which the secondary eddy remains close to the cylinder boundary and
has a quasi-two-dimensional form for an extended time period.