Effect of axially varying sandpaper roughness on bubbly drag reduction in Taylor–Couette turbulence

Abstract

We experimentally investigate the influence of alternating rough and smooth walls on bubbly drag reduction (DR). To this end, we apply rough sandpaper bands of width s between 48.4mm and 148.5mm, and roughness height k=695μm, around the smooth inner cylinder of the Twente Turbulent Taylor–Couette facility. Between two sandpaper bands, the inner cylinder is left uncovered over similar width s, resulting in alternating rough and smooth bands, forming a constant pattern in axial direction. We measure the DR in water that originates from introducing air bubbles to the fluid at (shear) Reynolds numbers Res ranging from 0.5 × 106 to 1.8 × 106. Results are compared to bubbly DR measurements with a completely smooth inner cylinder and an inner cylinder that is completely covered with sandpaper of the same roughness k. The outer cylinder is left smooth for all variations. The results are also compared to bubbly DR measurements where a smooth outer cylinder is rotating in opposite direction to the smooth inner cylinder. This counter rotation induces secondary flow structures that are very similar to those observed when the inner cylinder is composed of alternating rough and smooth bands. For the measurements with roughness, the bubbly DR is found to initially increase more strongly with Res, before levelling off to reach a value that no longer depends on Res. This is attributed to a more even axial distribution of the air bubbles, resulting from the increased turbulence intensity of the flow compared to flow over a completely smooth wall at the same Res. The air bubbles are seen to accumulate at the rough wall sections in the flow. Here, locally, the drag is largest and so the drag reducing effect of the bubbles is felt strongest. Therefore, a larger maximum value of bubbly DR is found for the alternating rough and smooth walls compared to the completely rough wall.