The importance of bubble deformability for strong drag reduction in bubbly turbulent Taylor-Couette flow

TL;DR

This study demonstrates that bubble deformability significantly enhances drag reduction in turbulent Taylor-Couette flow, with strong effects observed when bubbles deform near the inner wall at high Reynolds numbers.

Contribution

It reveals the critical role of bubble deformability in achieving strong drag reduction, linking local bubble dynamics to global flow behavior in turbulent Taylor-Couette flow.

Findings

Drag reduction up to 7% at Re=5.1x10^5

Over 40% drag reduction at Re=2.0x10^6 with 4% gas volume

Bubble deformability correlates with Weber number crossing unity

Abstract

Bubbly turbulent Taylor-Couette (TC) flow is globally and locally studied at Reynolds numbers of Re = 5 x 10^5 to 2 x 10^6 with a stationary outer cylinder and a mean bubble diameter around 1 mm. We measure the drag reduction (DR) based on the global dimensional torque as a function of the global gas volume fraction a_global over the range 0% to 4%. We observe a moderate DR of up to 7% for Re = 5.1 x 10^5. Significantly stronger DR is achieved for Re = 1.0 x 10^6 and 2.0 x 10^6 with, remarkably, more than 40% of DR at Re = 2.0 x 10^6 and a_global = 4%. To shed light on the two apparently different regimes of moderate DR and strong DR, we investigate the local liquid flow velocity and the local bubble statistics, in particular the radial gas concentration profiles and the bubble size distribution, for the two different cases; Re = 5.1 x 10^5 in the moderate DR regime and Re = 1.0 x 10^6 in the strong DR regime, both at a_global = 3 +/- 0.5%. By defining and measuring a local bubble Weber number (We) in the TC gap close to the IC wall, we observe that the crossover from the moderate to the strong DR regime occurs roughly at the crossover of We ~ 1. In the strong DR regime at Re = 1.0 x 10^6 we find We > 1, reaching a value of 9 (+7, -2) when approaching the inner wall, indicating that the bubbles increasingly deform as they draw near the inner wall. In the moderate DR regime at Re = 5.1 x 10^5 we find We ~ 1, indicating more rigid bubbles, even though the mean bubble diameter is larger, namely 1.2 (+0.7, -0.1) mm, as compared to the Re = 1.0 x 10^6 case, where it is 0.9 (+0.6, -0.1) mm. We conclude that bubble deformability is a relevant mechanism behind the observed strong DR. These local results match and extend the conclusions from the global flow experiments as found by van den Berg et al. (2005) and from the numerical simulations by Lu, Fernandez & Tryggvason (2005).