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 [STIX]x1D716 , invariant in the spanwise direction. Based on the two parameters, [STIX]x1D716/D and the Reynolds number ReD=U∞D/[STIX]x1D708 where U∞ is the free-stream velocity, D the diameter of the cylinder and [STIX]x1D708 the kinematic viscosity, two main sets of simulations are described. The first set varies [STIX]x1D716/D from $0$ to $1/32$ while fixing ReD=3.9× 10³ . 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 LB , the pressure coefficient Cₚ , the skin-friction coefficient C_f[STIX]x1D703 and the non-dimensional pressure gradient parameter [STIX]x1D6FD . It is found that, with increasing [STIX]x1D716/D at fixed ReD , some properties of the mean flow behave somewhat similarly to changes in the smooth-cylinder flow when ReD is increased. This includes shrinking LB and nearly constant minimum pressure coefficient. In contrast, while the non-dimensional pressure gradient parameter [STIX]x1D6FD remains nearly constant for the front part of the smooth cylinder flow, [STIX]x1D6FD shows an oscillatory variation for the grooved-cylinder case. The second main set of LES varies ReD from 3.9× 10³ to 6× 10⁴ with fixed [STIX]x1D716/D=1/32 . It is found that this ReD 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 Cₚ and the drag coefficient CD . 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 featu