Abstract
We report wall-resolved large-eddy simulation (LES) of flow over a grooved cylinder up to the transcritical regime. The stretched-vortex subgrid-scale model is embedded in a general fourth-order finite-difference code discretization on a curvilinear mesh. In the present study
$32$
grooves are equally distributed around the circumference of the cylinder, each of sinusoidal shape with height
$\unicode[STIX]{x1D716}$
, invariant in the spanwise direction. Based on the two parameters,
$\unicode[STIX]{x1D716}/D$
and the Reynolds number
$Re_{D}=U_{\infty }D/\unicode[STIX]{x1D708}$
where
$U_{\infty }$
is the free-stream velocity,
$D$
the diameter of the cylinder and
$\unicode[STIX]{x1D708}$
the kinematic viscosity, two main sets of simulations are described. The first set varies
$\unicode[STIX]{x1D716}/D$
from
$0$
to
$1/32$
while fixing
$Re_{D}=3.9\times 10^{3}$
. We study the flow deviation from the smooth-cylinder case, with emphasis on several important statistics such as the length of the mean-flow recirculation bubble
$L_{B}$
, the pressure coefficient
$C_{p}$
, the skin-friction coefficient
$C_{f\unicode[STIX]{x1D703}}$
and the non-dimensional pressure gradient parameter
$\unicode[STIX]{x1D6FD}$
. It is found that, with increasing
$\unicode[STIX]{x1D716}/D$
at fixed
$Re_{D}$
, some properties of the mean flow behave somewhat similarly to changes in the smooth-cylinder flow when
$Re_{D}$
is increased. This includes shrinking
$L_{B}$
and nearly constant minimum pressure coefficient. In contrast, while the non-dimensional pressure gradient parameter
$\unicode[STIX]{x1D6FD}$
remains nearly constant for the front part of the smooth cylinder flow,
$\unicode[STIX]{x1D6FD}$
shows an oscillatory variation for the grooved-cylinder case. The second main set of LES varies
$Re_{D}$
from
$3.9\times 10^{3}$
to
$6\times 10^{4}$
with fixed
$\unicode[STIX]{x1D716}/D=1/32$
. It is found that this
$Re_{D}$
range spans the subcritical and supercritical regimes and reaches the beginning of the transcritical flow regime. Mean-flow properties are diagnosed and compared with available experimental data including
$C_{p}$
and the drag coefficient
$C_{D}$
. The timewise variation of the lift and drag coefficients are also studied to elucidate the transition among three regimes. Instantaneous images of the surface, skin-friction vector field and also of the three-dimensional Q-criterion field are utilized to further understand the dynamics of the near-surface flow structures and vortex shedding. Comparison of the grooved-cylinder flow with the equivalent flow over a smooth-wall cylinder shows structural similarities but significant differences. Both flows exhibit a clear common signature, which is the formation of mean-flow secondary separation bubbles that transform to other local flow features upstream of the main separation region (prior separation bubbles) as
$Re_{D}$
is increased through the respective drag crises. Based on these similarities it is hypothesized that the drag crises known to occur for flow past a cylinder with different surface topographies is the result of a change in the global flow state generated by an interaction of primary flow separation with secondary flow recirculating motions that manifest as a mean-flow secondary bubble. For the smooth-wall flow this is accompanied by local boundary-layer flow transition to turbulence and a strong drag crisis, while for the grooved-cylinder case the flow remains laminar but unsteady through its drag crisis and into the early transcritical flow range.