Controlling secondary flow in Taylor–Couette turbulence through spanwise-varying roughness

Abstract

Highly turbulent Taylor-Couette flow with spanwise-varying roughness is investigated experimentally and numerically (direct numerical simulations (DNS) with an immersed boundary method (IBM)) to determine the effects of the spacing and axial width s of the spanwise varying roughness on the total drag and on the flow structures. We apply sandgrain roughness, in the form of alternating rough and smooth bands to the inner cylinder. Numerically, the Taylor number is O(10 9 ) and the roughness width is varied between 0.47 s = s/d 1.23, where d is the gap width. Experimentally, we explore Ta = O(10 12 ) and 0.61 s 3.74. For both approaches the radius ratio is fixed at η = r i /r o = 0.716, with r i and r o the radius of the inner and outer cylinder respectively. We present how the global transport properties and the local flow structures depend on the boundary conditions set by the roughness spacings. Both numerically and experimentally, we find a maximum in the angular momentum transport as function ofs. This can be atributed to the re-arrangement of the large-scale structures triggered by the presence of the rough stripes, leading to correspondingly large-scale turbulent vortices.

Wall-bounded turbulence with streamwise curvature

“…The roughness used was P36 grit sandpaper (VSM, ceramic industrial-grade), that was fixed to the entire surface of the inner cylinder using double-sided adhesive tape (tesa 51970). We define the characteristic length scale of the roughness as k ≡ 6k σ ≈ 1.07 mm (corresponding to the 99.8% interval of the height), where k σ is the standard deviation of the local roughness height h(x, y) (quantified using confocal microscopy [103] over a square part of the roughness sandpaper with width 25 mm), and k/d = 0.014.…”

“…During the torque measurements, PIV was used to obtain the velocity field in the gap. To quantify the reproducibility of our torque measurements, we compared the torque data that were captured during the is the standard deviation of the sandpaper roughness, see [103]. The final row presents the values correponding to the smooth wall measurement of [27] PIV experiments with three separate torque measurements thereafter.…”

Drag of wall-bounded flows

“…The roughness used was P36 grit sandpaper (VSM, ceramic industrialgrade), that was fixed to the entire surface of the inner cylinder using doublesided adhesive tape (tesa 51970). We define the characteristic length scale of the roughness as k ⌘ 6k ⇡ 1.07 mm (corresponding to the 99.8% interval of the height), where k is the standard deviation of the local roughness height h(x, y) (quantified using confocal microscopy (Bakhuis et al, 2020b)), and k/d = 0.014.…”

“…is the dimensionless angular velocity flux, C f the friction factor, L + c the curvature Obukhov length as defined in equation (2.7). Finally, k + is the standard deviation of the sandpaper roughness, see Bakhuis et al (2020b), and + is the BL thickness from equation (2.12). working liquid at mid-height, through the transparent outer cylinder.…”

“…In this study we build on the work of Bakhuis et al (2020a), who have used spanwise-varying roughness to control the secondary flow configurations that show up as turbulent Taylor vortices in high Reynolds number Taylor-Couette flow. In the current work we will use the di↵erent secondary flow configurations to study the influence on bubbly drag reduction and the position of bubbles in the flow.…”