In the present study, we apply a distributed (i.e., spatially varying) forcing to flow over a circular cylinder for drag reduction. The distributed forcing is realized by a blowing and suction from the slots located at upper and lower surfaces of the cylinder. The forcing profile from each slot is sinusoidal in the spanwise direction but is steady in time. We consider two different phase differences between the upper and lower blowing/suction profiles: zero (in-phase forcing) and π (out-of-phase forcing). The Reynolds numbers considered are from 40 to 3900 covering various regimes of flow over a circular cylinder. For all the Reynolds numbers larger than 47, the present in-phase distributed forcing attenuates or annihilates the Karman vortex shedding and thus significantly reduces the mean drag and the drag and lift fluctuations. The optimal wavelength and amplitude of the in-phase forcing for maximum drag reduction are also obtained for the Reynolds number of 100. It is shown that the in-phase forcing produces the phase mismatch along the spanwise direction in the vortex shedding, weakens the strength of vortical structures in the wake, and thus reduces the drag. Unlike the in-phase forcing, the out-of-phase distributed forcing does not reduce the drag at low Reynolds numbers, but it reduces the mean drag and the drag and lift fluctuations at a high Reynolds number of 3900 by affecting the evolution of the separating shear layer, although the amount of drag reduction is smaller than that by the in-phase forcing.

Distributed forcing of flow over a circular cylinder

Three-dimensional nature of vortices in the near wake of a wavy cylinder

Numerical investigation of the compressible flow past a wavy cylinder was carried out using large-eddy simulation for a free-stream Mach number M ∞ =0.75 and a Reynolds number based on the mean diameter Re = 2 × 10 5 . The flow past a corresponding circular cylinder was also calculated for comparison and validation against experimental data. Various fundamental mechanisms dictating the intricate flow phenomena, including drag reduction and fluctuating force suppression, shock and shocklet elimination, and three-dimensional separation and separated shear-layer instability, have been studied systematically. Because of the passive control of the flow over a wavy cylinder, the mean drag coefficient of the wavy cylinder is less than that of the circular cylinder with a drag reduction up to 26 %, and the fluctuating force coefficients are significantly suppressed to be nearly zero. The vortical structures near the base region of the wavy cylinder are much less vigorous than those of the circular cylinder. The three-dimensional shear-layer shed from the wavy cylinder is more stable than that from the circular cylinder. The vortex roll up of the shear layer from the wavy cylinder is delayed to a further downstream location, leading to a higher-base-pressure distribution. The spanwise pressure gradient and the baroclinic effect play an important role in generating an oblique vortical perturbation at the separated shear layer, which may moderate the increase of the fluctuations at the shear layer and reduce the growth rate of the shear layer. The analysis of the convective Mach number indicates that the instability processes in the shear-layer evolution are derived from oblique modes and bi-dimensional instability modes and their competition. The two-layer structures of the shear layer are captured using the instantaneous Lamb vector divergence, and the underlying dynamical processes associated with the drag reduction are clarified. Moreover, some phenomena relevant to the compressible effect, such as shock waves, shocklets and shock/turbulence interaction, are analysed. It is found that the shocks and shocklets which exist in the circular cylinder flow are eliminated for the wavy cylinder flow and the wavy surface provides an effective way of shock control. As the shock/turbulence interaction is avoided, a significant drop of the turbulent fluctuations around the wavy cylinder occurs. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to the passive control of the compressible flow past a wavy surface.

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Large-eddy simulation of the compressible flow past a wavy cylinder

Experimental investigation of the mean and fluctuating forces of wavy (varicose) cylinders in a cross-flow

Large eddy simulation of flow around wavy cylinders at a subcritical Reynolds number

Transverse flow over a wavy cylinder was investigated experimentally; surface‐pressure distributions and flow visualizations were obtained for a set of wavy cylinders with different axial wavelengths. Significant spanwise pressure gradients were present, resulting in three‐dimensional separation lines and the formation of streamwise trailing vortex structures near the geometric nodes. Despite the symmetry of the geometries, the separated flow structures near the geometric nodes were distinctly asymmetric a large fraction of time. Integration of the pressure data revealed greater sectional drag coefficients at the geometric nodes than at the geometric saddles.

Byram Bays‐Muchmore

Papers

Transverse flow over a wavy cylinder