Optimal Taylor–Couette flow: radius ratio dependence

Abstract

Taylor-Couette flow with independently rotating inner (i) & outer (o) cylinders is explored numerically and experimentally to determine the effects of the radius ratio η on the system response. Numerical simulations reach Reynolds numbers of up to Re i = 9.5 · 10 3 and Re o = 5 · 10 3 , corresponding to Taylor numbers of up to T a = 10 8 for four different radius ratios η = r i /r o between 0.5 and 0.909. The experiments, performed in the Twente Turbulent Taylor-Couette (T 3 C) setup, reach Reynolds numbers of up to Re i = 2 · 10 6 and Re o = 1.5 · 10 6 , corresponding to T a = 5 · 10 12 for η = 0.714−0.909. Effective scaling laws for the torque J ω (T a) are found, which for sufficiently large driving T a are independent of the radius ratio η. As previously reported for η = 0.714, optimum transport at a non-zero Rossby number Ro = r i |ω i − ω o |/[2(r o − r i )ω o ] is found in both experiments and numerics. Ro opt is found to depend on the radius ratio and the driving of the system. At a driving in the range between T a ∼ 3 · 10 8 and T a ∼ 10 10 , Ro opt saturates to an asymptotic η-dependent value. Theoretical predictions for the asymptotic value of Ro opt are compared to the experimental results, and found to differ notably. Furthermore, the local angular velocity profiles from experiments and numerics are compared, and a link between a flat bulk profile and optimum transport for all radius ratios is reported.

Exploring the phase diagram of fully turbulent Taylor–Couette flow

“…Figure 8 shows both the Nusselt number and the compensated Nusselt number plotted as a function of T a for the three values of η simulated. As seen in Ostilla-Monico et al (2014a) for η = 0.714 (and now also for η = 0.909), the flow undergoes a structural transition at around T a ≈ 3 · 10 6 , where the local exponent α of the effective scaling law N u ∼ T a α rapidly decreases. This is associated with the breakdown of coherence in the flow and the onset of time-dependence in the Nusselt number.…”

“…11 for η = 0.909) (Ostilla-Monico et al 2014a). A larger decrease of ω across the bulk can be seen for η = 0.5.…”

“…Ostilla et al (2013) for the full derivation). This results in a linear relationship between Ro −1 and ∂ r ω z (Ostilla-Monico et al 2014a). …”

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

“…For lower Reynolds numbers, numerical investigation of Ostilla et al 25 proposed a local power scaling as: Nu~Re 0.66 , with a change in the local scaling above Ta>3. 10 6 for η=0.909.…”

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

“…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]. Hence the Taylor-Couette geometry is a versatile geometry in physics, engineering, and beyond.…”