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

摘要

Bubbly turbulent Taylor-Couette (TC) flow is globally and locally studied atReynolds numbers of Re = 5 x 10^5 to 2 x 10^6 with a stationary outer cylinderand 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 volumefraction 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 10^6and 2.0 x 10^6 with, remarkably, more than 40% of DR at Re = 2.0 x 10^6 anda_global = 4%. To shed light on the two apparently different regimes of moderate DR andstrong DR, we investigate the local liquid flow velocity and the local bubblestatistics, in particular the radial gas concentration profiles and the bubblesize distribution, for the two different cases; Re = 5.1 x 10^5 in the moderateDR 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 gapclose to the IC wall, we observe that the crossover from the moderate to thestrong DR regime occurs roughly at the crossover of We ~ 1. In the strong DRregime at Re = 1.0 x 10^6 we find We > 1, reaching a value of 9 (+7, -2) whenapproaching the inner wall, indicating that the bubbles increasingly deform asthey draw near the inner wall. In the moderate DR regime at Re = 5.1 x 10^5 wefind We ~ 1, indicating more rigid bubbles, even though the mean bubblediameter is larger, namely 1.2 (+0.7, -0.1) mm, as compared to the Re = 1.0 x10^6 case, where it is 0.9 (+0.6, -0.1) mm. We conclude that bubbledeformability is a relevant mechanism behind the observed strong DR. Theselocal results match and extend the conclusions from the global flow experimentsas found by van den Berg et al. (2005) and from the numerical simulations byLu, Fernandez & Tryggvason (2005).