Richard J.A.M. Stevens

Professor at the University of Twente

Wind energy · Turbulence · Environmental flows

Taylor-Couette turbulence

We use direct numerical simulations to study angular-momentum transport in Taylor-Couette flow. Our work examines how cylinder rotation, wall roughness and curvature affect torque and flow structure, alongside studies of spiral turbulence and particle alignment.

Wall roughness and torque

Resolved sand-grain roughness on the inner cylinder strengthens plume ejection, angular-momentum transport, and torque in the tested Taylor-Couette simulations. See the six-panel smooth-versus-rough comparison and evidence boundaries.

Spiral turbulence

Near the simulated laminar–turbulent transition, spiral turbulence behaves as a finite-wavelength pattern whose selected wavelength changes the turbulent fraction and transport. See the amplitude–wavenumber evidence and scope boundaries.

Curvature and mean velocity profiles

Across the tested radius ratios, a curvature length organized the transition from a near-wall shear-dominated logarithmic layer to a curvature-affected layer and an approximately constant-angular-momentum bulk.

See the curvature-scaled profiles and evidence boundaries.

Particle alignment

In the tested Taylor-vortex flows, larger prolate ellipsoids clustered near vortex cores and developed a sharp tangential alignment. The strongest alignment coincided with low local axial vorticity and reduced particle rotation, but causality was not independently isolated.

See the alignment-width evidence and scope boundaries.

System and foundational results (2013)

Taylor-Couette flow, i.e. the flow in the gap between two independently rotating coaxial cylinders, see figure 1, is among the most investigated problems in fluid mechanics, due to its conceptual simplicity and to applications in process technology. Just as for Rayleigh-Bénard convection the system is:
(i) mathematically well-defined by the Navier-Stokes equations and the appropriate boundary conditions,
(ii) there exist exact global balance relations between the driving and the dissipation rate, and
(iii) the system is experimentally and numerically accessible with high precision due to the simple geometry

Sketch of the Taylor-Couette flow setup with inner and outer rotating cylinders
Figure 1: The Taylor-Couette system consists of two coaxial cylinders of length L. The inner cylinder has the radius ri and the angular velocity ωi, while the outer cylinder has the radius ro and the angular velocity ωo. Figure from Ostilla-Mónico et al. (2013). Full-resolution figure

We [1] numerically simulated turbulent Taylor-Couette flow for independently rotating inner and outer cylinders, focusing on the analogy with turbulent Rayleigh-Bénard flow. Reynolds numbers up to Rei = 8 x 103 and Reo = ±4 x 103 are reached for the inner and outer cylinders, respectively, corresponding to Taylor numbers Ta up to 108. Effective scaling laws for the torque and other system responses are found, see figure 2.

Experiments with the Twente Turbulent Taylor-Couette (T3C) setup and with a similar facility in Maryland at very high Reynolds numbers have revealed optimum transport at a 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 optimum transport at non-zero counter-rotation. The position of this maximum shifts with the driving, reaching aopt = 0.15 for Ta = 2.5 x 107. This is consistent with the experimental result that aopt becomes approximately independent of the driving strength at sufficiently large Reynolds numbers. In addition, we investigated the angular-velocity profiles and visualized the flow structures in the different regimes.

Graph of absolute Nusselt number versus Taylor number in Taylor-Couette flow, comparing experiments and simulations Graph of compensated Nusselt number versus Taylor number in Taylor-Couette flow
Figure 2: The first image shows the absolute (Nuω) number and the second image the compensated (Nuω / Ta0.21) Nusselt number versus Ta for η=ri/ro=5/7. Experiments (dots) and the numerics agree in shape, but there is a slight shift between the data, which we attribute to the different boundary conditions in the lateral direction. Figure from Ostilla-Mónico et al. (2013). Full-resolution image 1 · Full-resolution image 2

Computing project report

The Gauss Centre report Roughness in Highly Turbulent Taylor–Couette and Rayleigh–Bénard Flows (December 2019) describes AFiD simulations and lists Richard Stevens in the project team, with Detlef Lohse as principal investigator.

References

  1. R. Ostilla-Mónico, R.J.A.M. Stevens, S. Grossmann, R. Verzicco, D. Lohse,
    Optimal Taylor-Couette flow: direct numerical simulations,
    J. Fluid Mech. 719, 14-46 (2013). Read the finding
  2. P. Berghout, X. Zhu, D. Chung, R. Verzicco, R.J.A.M. Stevens, D. Lohse,
    Direct numerical simulations of Taylor-Couette turbulence: the effects of sand grain roughness,
    J. Fluid Mech. 873, 260-286 (2019). Read the finding
  3. P. Berghout, R.J. Dingemans, X. Zhu, R. Verzicco, R.J.A.M. Stevens, W. van Saarloos, D. Lohse,
    Direct numerical simulations of spiral Taylor-Couette turbulence,
    J. Fluid Mech. 887, A18 (2020). Read the finding