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

Abstract

Bubbly turbulent Taylor-Couette (TC) flow is globally and locally studied at Reynolds numbers of Re = 5 × 10 5 to 2 × 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 α global over the range 0-4%. We observe a moderate DR of up to 7% for Re = 5.1 × 10 5 . Significantly stronger DR is achieved for Re = 1.0 × 10 6 and 2.0 × 10 6 with, remarkably, more than 40% of DR at Re = 2.0 × 10 6 and α 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 × 10 5 in the moderate DR regime and Re = 1.0 × 10 6 in the strong DR regime, both at α global = 3 ± 0.5% .In both cases the bubbles mostly accumulate close to the inner cylinder (IC). Surprisingly, the maximum local gas concentration near the IC for Re = 1.0 × 10 6 is ≈ 2.3 times lower than that for Re = 5.1 × 10 5 , in spite of the stronger DR. Evidently, a higher local gas concentration near the inner wall does not guarantee a larger DR.By defining and measuring a local bubble Weber number (W e) in the TC gap close to the IC wall, we observe that the cross-over from the moderate to the strong DR regime occurs roughly at the cross-over of W e ∼ 1. In the strong DR regime at Re = 1.0×10 6 we find W e > 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 × 10 5 we find W e ≈ 1, indicating more rigid bubbles, even though the mean bubble diameter is larger, namely 1.2 (+0.7, -0.1) mm, as compared with the Re = 1.0 × 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).

Effect of bubble’s arrangement on the viscous torque in bubbly Taylor-Couette flow

“…For bubbles larger than the Kolmogorov length scale, torque reduction is likely to be associated either with a de-structuration of the Taylor vortices by the bubble upward motion in the case of weak turbulent and turbulent Taylor vortex flow 7,8 or associated with the deformation of the bubbles in the case of the high Reynolds numbers (Re>8 10 5 ) [9][10][11][12] . According to Murai et al 7 , there is a Reynolds number range, for which the relative contribution of the Taylor vortices to the global flow and the contribution of the bubble deformation are too small to bring about torque reduction, thus leading on the contrary to a torque increase.…”

“…For the weak turbulent flow and turbulent Taylor vortex flow, it was highlighted that bubbles have preferential accumulation regions, depending on the bubble size to the gap width ratio (d b /d) and the Reynolds number: either in the Taylor vortices or in the outflow region near the inner cylinder 7,[14][15][16] . For the turbulent flow, there is a preferential accumulation near the inner cylinder with a homogeneous axial distribution 12 .…”

“…In the case of experimental study of bubble dispersion inside Taylor-Couette flow, as the void fraction was characterized by intrusive method (optical probes), very few profiles of void fraction has been so far studied in the literature 12,15,17,18 . Optical probes can measure the radial distribution of the void fraction at a given axial position but they do not enable to characterize the axial distribution when it is subjected to the Taylor vortices.…”

The boiling Twente Taylor-Couette (BTTC) facility: Temperature controlled turbulent flow between independently rotating, coaxial cylinders

“…Though well known in the context of rheology, the Taylor-Couette geometry-a geometry in which fluid is bound between two concentric rotating cylinders-has also been used in many fundamental concepts: the verification of the no-slip boundary condition, hydrodynamic stability [1], higher and lower order bifurcation phenomena and flow structures [2][3][4][5], but also in the field of combustion [6][7][8], drag reduction [9][10][11][12], magnetohydrodynamics in order to study e.g. the MRI [13][14][15][16][17], astrophysics to study Keplerian flow in accretion discs [18][19][20][21], rotating filtration in order to extract plasma from whole blood [22][23][24][25][26], cooling of rotating machinery [27], flows in bearings, the fundamentals of high Reynolds number flows [5,[28][29][30][31][32][33][34][35], and as a catalytic and plasmapheretic reactor [36][37][38].…”

About bubbles and vortex rings

“…Otherwise, at subcritical Weber numbers, We < We c , the bubble will remain unbroken or it might break at much longer times due to the resonance mechanism. Besides the interest in modelling the turbulent bubble breakup process, another important aspect of the bubble dynamics and deformation is its relevance in drag reduction applications due to their interaction with the turbulent structures of the flow (see van Gils et al 2013).…”