Bubble Drag Reduction Requires Large Bubbles

Abstract

In the maritime industry, the injection of air bubbles into the turbulent boundary layer under the ship hull is seen as one of the most promising techniques to reduce the overall fuel consumption. However, the exact mechanism behind bubble drag reduction is unknown. Here we show that bubble drag reduction in turbulent flow dramatically depends on the bubble size. By adding minute concentrations (6 ppm) of the surfactant Triton X-100 into otherwise completely unchanged strongly turbulent Taylor-Couette flow containing bubbles, we dramatically reduce the drag reduction from more than 40% to about 4%, corresponding to the trivial effect of the bubbles on the density and viscosity of the liquid. The reason for this striking behavior is that the addition of surfactants prevents bubble coalescence, leading to much smaller bubbles. Our result demonstrates that bubble deformability is crucial for bubble drag reduction in turbulent flow and opens the door for an optimization of the process.Theoretical, numerical and experimental studies on drag reduction (DR) of a solid body moving in a turbulent flow have been performed for more than three decades [1][2][3][4][5][6]. A few volume percent (≤ 4%) of bubbles can reduce the overall drag up to 40% and beyond [7][8][9][10][11][12][13][14]. However, the exact physics behind this drag reduction mechanism is unknown, thus hindering further progress and optimization, and even the dependence of the effect on the bubble size is controversial [15][16][17], though it is believed to be independent of the bubble size [1].In this Letter, we experimentally investigated the mechanism behind bubble drag reduction in a TaylorCouette (TC) system, i.e. the flow between two independently rotating coaxial cylinders. The TC system can be seen as "drosophila" of physics of fluids, with many concepts in fluid dynamics being tested therewith, ranging from instabilities, to pattern formation, to turbulence, see the reviews [18,19]. Here we inject bubbles into the system, which due to the density difference to water experience a centripetal force towards the inner cylinder, mimicking the upwards gravitational force acting on bubbles under a ship hull.The experiments are performed in the Twente Turbulent Taylor-Couette facility (T 3 C) [20], with the inner one strongly rotating, corresponding to very large Reynolds number of Re ∼ 10 5 − 10 6 . The setup has an inner cylinder with a radius of r i = 200 mm and an outer cylinder with a radius of r o = 279 mm, resulting in a radius ratio of η = r i /r o = 0.716. The inner cylinder rotates with a frequency up to f i = 20 Hz, resulting in Reynolds numbers up to Re = 2πf i r i (r o − r i )/ν α = 2 × 10 6 , in which ν α is kinematic viscosity of water-bubble mixture. The outer cylinder is at rest. The cylinders have a height of L = 927 mm, resulting in an aspect ratio of Γ = L/(r o − r i ) = 11.7. The flow is cooled through both endplates to prevent viscous heating through the viscous dissipation. The torque τ is measured with a co-axial torque transducer (Ho...

Drag reduction in boiling Taylor–Couette turbulence

“…These distributions reveal that We > 1, independent of the volume fraction, i.e. the vapor bubbles in our experiments are deformable, which supports the idea that also for vapor bubbles deformability is key for achieving large drag reduction, just as shown for bubbly drag reduction with gas bubbles (van Gils et al 2013; Verschoof et al 2016). Moreover, we find that the maximum of all distributions lies at We ≈ 2.5, which corresponds to bubbles of size ≈ 0.27 mm.…”

“…We note that by introducing the correction for both the viscosity ν(α) and density ρ(α) due to the presence of the dispersed phase, the net value of DR changes slightly as compared to the case when the correction is not used. In this study-as it also done in other studies of air bubble induced DR (van Gils et al 2013;Verschoof et al 2016)-we set ν = ν (1 + 5α/2) and ρ = ρ (1 − α) + ρ v α in order to draw accurate comparisons between our experiments with vapor and the case of air bubble injection. Note that by introducing these corrections to the viscosity and density (via α), the trivial effect of drag reduction due to the density decrease of the liquidvapor mixture is already taken into account.…”

“…A large Weber number We > 1 implies that the bubble is deformable. Indeed, Verschoof et al (2016) showed that for fixed gas volume fraction α ≈ 4% and fixed large Reynolds number, the large drag reduction (≈ 40%) could basically be "turned off" by adding a surfactant, which hinders bubble coalescence and leads to much smaller bubbles with We < 1 in the strongly turbulent flow.…”

Bubble puzzles: From fundamentals to applications

“…We decided to apply the same trick in turbulent bubbly TC flow, and indeed found that also here the addition of a few drops of Triton X (to 111 liter of water in our TC setup [210]) dramatically changed the flow [211], see figure 27, in spite of the unchanged bubble volume fraction: Optically ( fig. 27a-f), because the flow became very opaque, just as in ref.…”

Physical mechanisms governing drag reduction in turbulent Taylor–Couette flow with finite-size deformable bubbles

“…Drag in turbulent flows is a major drain of energy. It is well known that the addition of a secondary phase such as polymers or bubbles into a turbulent carrier fluid can lead to significant reduction in the overall drag in the system (van den Berg et al 2005;van Gils et al 2013;Verschoof et al 2016;White & Mungal 2008;Ceccio 2010). Here, we define drag reduction (DR) as…”