Large-eddy simulation of flow over a grooved cylinder up to transcritical Reynolds numbers. (27th November 2017) - Cheng, W.; Pullin, D. I.; Samtaney, R.
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 [STIX]x1D716, invariant in the spanwise direction. Based on the two parameters, [STIX]x1D716/D and the Reynolds number Re_D=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 Re_D=3.9× 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[STIX]x1D703 and the non-dimensional pressure gradient parameter [STIX]x1D6FD . It is found that, with increasing [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 [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 Re_D from 3.9× 10^3 to 6× 10^4 with fixed [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.