Optimal Taylor–Couette flow: direct numerical simulations


We numerically simulate turbulent Taylor–Couette flow for independently rotating inner and outer cylinders, focusing on the analogy with turbulent Rayleigh–Bénard flow. Reynolds numbers of Rei= 8 x 10^3 and Reo=+/-4 x 10^3 of the inner and outer cylinders, respectively, are reached, corresponding to Taylor numbers Ta up to 10^8 . Effective scaling laws for the torque and other system responses are found. Recent experiments with the Twente Turbulent Taylor–Couette ( T^3C ) setup and with a similar facility in Maryland at very high Reynolds numbers have revealed an optimum transport at a certain non-zero rotation rate ratio a=-wo/wi of about aopt=0.33 . For large enough Ta in the numerically accessible range we also find such an optimum transport at non-zero counter-rotation. The position of this maximum is found to shift with the driving, reaching a maximum of a(opi)=0.15 for Ta=2.5 x 10^7. An explanation for this shift is elucidated, consistent with the experimental result that a(opt) becomes approximately independent of the driving strength for large enough Reynolds numbers. We furthermore numerically calculate the angular velocity profiles and visualize the different flow structures for the various regimes. By writing the equations in a frame co-rotating with the outer cylinder a link is found between the local angular velocity profiles and the global transport quantities.



Convections, Direct numerical simulation, Taylor-Couette flow


Copyright 2013 Journal of Fluid Mechanics. This is a pre-print version of a published paper that is available at: https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/optimal-taylorcouette-flow-direct-numerical-simulations/33F0790029F35A47F3B84597BD8015F9. Recommended citation:Ostilla, Rodolfo, Richard JAM Stevens, Siegfried Grossmann, Roberto Verzicco, and Detlef Lohse. "Optimal Taylor–Couette flow: direct numerical simulations." Journal of fluid mechanics 719 (2013): 14-46. doi:10.1017/jfm.2012.596. The item has been deposited in accordance with publisher copyright and licensing terms and with the author's permission.