Turbulent boundary layers perturbed by an array of cylinders

Abstract

Turbulent boundary layers (Reτ = 2500) were perturbed by a spanwise array of cylinders, and the effects on the large-scale flow organization within the logarithmic layer were investigated. Boundary layer and vortex packet recovery trends were quantified downstream of several arrays. Two array spacings, each with two cylinder heights were considered. For S = 0.2δ arrays, cylinder heights of H = 0.2δ (H+ = 500, aspect ratio, AR = 4) and H = δ (H+ = 2500, AR = 20) were investigated. For the S = 0.6δ arrays, cylinder heights were H = 0.2δ and H = 0.05δ (H+ = 125, AR = 1). Stereoscopic and planar PIV measurements were acquired in both fixed and flying configurations at three measurement heights across the logarithmic layer, z+ = 125, 300 and 500. Furthermore, 3-D PTV volumes were acquired downstream of the S= 0.2δ arrays over a depth of 155 < z+ < 465. Results of time-averaged velocity statistics, instantaneous velocity fields and structural analyses of low and high uniform streamwise momentum zones were discussed. In addition, a vortex packet identification algorithm (VPIA) was developed to quantify relaxation trends of individual packet signatures in the flow downstream of the arrays. All of the arrays affected mean and RMS streamwise velocities averaged across the span downstream, due to the blockage posed to the oncoming flow. Undulating wakes due to Karman shedding occurred behind the cylinders, while the average wake structure at the cylinder tips suggested formation of streamwise aligned tip vortices. For the S = 0.2δ array, relaxation trends differed for the two cylinder heights, H = 0.2δ and H = δ. Downstream of the H = δ array, instantaneous PIV and VPIA results showed a bottom-up mechanism for the recovery of the large-scale flow organization. Flow features recovered first closer to the wall (z+ = 125), then later at z+ = 300, while hardly any recovery was seen at z+ = 500 up to 7δ downstream of the array, the furthest measurement location. In contrast, some indications of top-down recovery were observed for the flow perturbed by the shorter H = 0.2δ array. In this case, however, flow features and packets closer to the wall at z+ = 125 remained altered up to 7δ downstream, even though streamwise velocity statistics relaxed substantially to the unperturbed values. The difference in recovery trends between the two cylinder heights was related to weaker and stronger outer-inner interactions respectively, relative to the unperturbed flow. For the S = 0.6δ arrays, perturbations to mean and RMS velocity statistics were weaker than for the S = 0.2δ arrays as blockage was reduced substantially. Nevertheless, the flow downstream of the S = 0.6δ, H = 0.2δ array was profoundly affected, such that the energy contained in the 0.6δ spanwise wavelength was increased throughout the logarithmic layer over a distance of 7δ. The energy increase was related to the array preferentially re-aligning incoming high and low uniform momentum zones to spanwise locations corresponding to cylinder locations and the regions between them respectively. The re-alignment effects were stronger for low and high momentum zones that were longer than 0.5δ. The H = 0.05δ case also showed similar but much weaker trends.