Abstract
This study focuses on the effect of spatial non-uniformity in the ambient flow on the
forces acting on a spherical particle at moderate particle Reynolds numbers. A scaling
analysis is performed to obtain conditions under which such effects are important. A
direct numerical simulation, based on spectral methods, is used to compute the three-dimensional time-dependent flow past a stationary sphere subject to a uniform flow
plus a planar straining flow. The particle Reynolds number, Re, in the range 10 to 300
covering different flow regimes, from unseparated flow to unsteady vortex shedding,
is considered. A variety of strain magnitudes and orientations are investigated. A
systematic comparison with the potential flow results and axisymmetric strain results
is given. Under elongational strain, both the planar and axisymmetric cases are found
to stabilize the sphere wake and delay the onset of unsteadiness, while compressional
strain leads to instability. In terms of separation angles, length of the recirculation
eddy and topology of the surface streamlines, planar and axisymmetric strains yield
nearly the same results. The drag force appears to have a linear relation with strain
magnitude in both cases, as predicted by the potential flow. However, contrary to the
potential flow results, the drag in planar strain is higher than that in axisymmetric
strain. The generation of higher drag is explained using the surface pressure and
vorticity distributions. Planar strain oriented at an angle with the oncoming uniform
flow is observed to break the symmetry of the wake and results in a lift or side
force. The variation of the drag and lift forces may be quite complex, and unlike
the potential flow results they may not be monotonic with strain magnitude. The
direction of the lift force may be opposite to that predicted by the inviscid and
low Reynolds number (Re [Lt ] 1) theories. This behaviour is dictated by the presence
or absence of a recirculation eddy. In the absence of a recirculation region at
low Reynolds numbers (Re < 20), or at a very high strain magnitude when the
recirculation region is suppressed, the results follow somewhat the pattern observed
in potential flow. However, with the presence of a recirculation region, results opposite
to those predicted by the potential theory are observed.