Large-eddy simulation of flow over a grooved cylinder up to transcritical Reynolds numbers

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 is an element of, invariant in the spanwise direction. Based on the two parameters, is an element of/ D and the Reynolds number Re-D = U-infinity D / v where U-infinity is the free-stream velocity, D the diameter of the cylinder and v the kinematic viscosity, two main sets of simulations are described. The first set varies is an element of/ D from 0 to 1 / 32 while fixing Re-D = 3.9 x 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-f0 and the non-dimensional pressure gradient parameter beta. It is found that, with increasing is an element of = 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 LB and nearly constant minimum pressure coefficient. In contrast, while the non-dimensional pressure gradient parameter beta remains nearly constant for the front part of the smooth cylinder flow, beta shows an oscillatory variation for the grooved-cylinder case. The second main set of LES varies Re-D from 3.9 x 10(3) to 6 x 10(4) with fixed is an element of/ D = 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.