TY - JOUR

T1 - Optimal Taylor–Couette flow: direct numerical simulations

AU - Ostilla Monico, Rodolfo

AU - Stevens, Richard Johannes Antonius Maria

AU - Grossmann, S.

AU - Verzicco, Roberto

AU - Lohse, Detlef

PY - 2013

Y1 - 2013

N2 - 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=8×103 and Reo=±4×103 of the inner and outer cylinders, respectively, are reached, corresponding to Taylor numbers Ta up to 108. Effective scaling laws for the torque and other system responses are found. Recent experiments with the Twente Turbulent Taylor–Couette (T3C) 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=−ωo/ωi 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 aopt=0.15 for Ta=2.5×107. An explanation for this shift is elucidated, consistent with the experimental result that aopt 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

AB - 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=8×103 and Reo=±4×103 of the inner and outer cylinders, respectively, are reached, corresponding to Taylor numbers Ta up to 108. Effective scaling laws for the torque and other system responses are found. Recent experiments with the Twente Turbulent Taylor–Couette (T3C) 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=−ωo/ωi 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 aopt=0.15 for Ta=2.5×107. An explanation for this shift is elucidated, consistent with the experimental result that aopt 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

KW - METIS-294771

KW - IR-88395

U2 - 10.1017/jfm.2012.596

DO - 10.1017/jfm.2012.596

M3 - Article

VL - 719

SP - 14

EP - 46

JO - Journal of fluid mechanics

JF - Journal of fluid mechanics

SN - 0022-1120

ER -