Richard J.A.M. Stevens

Professor at the University of Twente

Wind energy · Turbulence · Environmental flows

Thermal convection

We study how buoyancy-driven turbulence transports heat and organizes itself across scales. Our direct numerical simulations examine numerical resolution, large-scale superstructures and finite-aspect-ratio effects, alongside comparisons with heat-transfer theory.

The model system is Rayleigh-Bénard flow: a fluid-filled cell heated from below and cooled from above. Besides the width-to-height aspect ratio Γ, the central control parameters are the Rayleigh number Ra, which measures the strength of buoyant forcing relative to viscous and thermal diffusion, and the Prandtl number Pr, the ratio of kinematic viscosity to thermal diffusivity.

Thermal-convection topics

Flow visualizations
Visualization of high Rayleigh number thermal convection.
High Rayleigh number convection: Extreme driving and the transition toward the ultimate transport regime. Full-resolution visualization
Visualization of rotating Rayleigh–Bénard convection.
Rotating Rayleigh–Bénard convection: Rotation-dependent heat transport and coherent flow organization. Full-resolution visualization
Temperature field showing turbulent thermal superstructures.
Turbulent superstructures: Large-scale patterns in laterally extended thermal turbulence. Full-resolution visualization
Direct numerical simulation of sheared thermal convection.
Sheared convection: Competition between imposed shear and buoyancy-driven transport. Full-resolution visualization
Visualization of two-dimensional thermal convection.
Two-dimensional convection: A reduced testbed for transport scaling and flow-state transitions. Full-resolution visualization

Heat-transfer scaling

Grossmann–Lohse (GL) theory describes heat transfer in Rayleigh-Bénard flow by combining exact global balances for kinetic and thermal dissipation with scaling estimates for boundary-layer and bulk contributions. The resulting regimes depend on which contributions dominate and predict the Rayleigh- and Prandtl-number dependence of the Nusselt number. Prandtl–Blasius boundary-layer scaling enters the classical formulation but is not the whole theory. Figure 1 shows the corresponding regimes in Ra–Pr parameter space.

Phase diagram in the Rayleigh number-Prandtl number plane showing turbulent convection regimes
Figure 1: Phase diagram in the Ra–Pr plane indicating the different turbulent regimes. The data points indicate where Nu has been measured or numerically calculated. Figure from Stevens et al. (2013), where details about the data points can be found. · Full-resolution figure

Resolution and large-scale organization

References

  1. X. Zhu, E. Phillips, V. Spandan, J. Donners, G. Ruetsch, J. Romero, R. Ostilla-Mónico, Y. Yang, D. Lohse, R. Verzicco, M. Fatica, R.J.A.M. Stevens,
    AFiD-GPU: A versatile Navier–Stokes solver for wall-bounded turbulent flows on GPU clusters,
    Comput. Phys. Commun. 229, 199-210 (2018).
  2. G.L. Kooij, M. A. Botchev, E.M.A. Frederix, B.J. Geurts, S. Horn, D. Lohse, E.P. van der Poel, O. Shishkina, R.J.A.M. Stevens, R. Verzicco,
    Comparison of computational codes for direct numerical simulations of turbulent Rayleigh-Bénard convection,
    Computers & Fluids 166, 1-8 (2018) Read the finding
  3. X. Zhu, R.J.A.M. Stevens, R. Verzicco, D. Lohse,
    Roughness-facilitated local 1/2 scaling does not imply the onset of the ultimate regime of thermal convection,
    Phys. Rev. Lett. 119, 154501 (2017). Read the finding
  4. J. Lülff, M. Wilczek, R.J.A.M. Stevens, R. Friedrich, D. Lohse,
    Turbulent Rayleigh-Bénard convection described by projected dynamics in phase space,
    J. Fluid Mech. 781, 276- 297 (2015).
    Read the finding
  5. R.J.A.M. Stevens, E.P. van der Poel, S. Grossmann, D. Lohse,
    The unifying theory of scaling in thermal convection: The updated prefactors,
    J. Fluid Mech. 730, 295-308 (2013).
    Read the finding
  6. R.J.A.M. Stevens, Q. Zhou, S. Grossmann, R. Verzicco, K.-Q Xia, D. Lohse,
    Thermal boundary layer profiles in turbulent Rayleigh-Bénard convection in a cylindrical sample,
    Phys. Rev. E 85, 027301 (2012).
    Read the finding