Supergravitational turbulent thermal convection

Abstract

High-Rayleigh number convective turbulence is ubiquitous in many natural phenomena and in industries, such as atmospheric circulations, oceanic flows, flows in the fluid core of planets, and energy generations. In this work, we present a novel approach to boost the Rayleigh number in thermal convection by exploiting centrifugal acceleration and rapidly rotating a cylindrical annulus to reach an effective gravity of 60 times Earth's gravity. We show that in the regime where the Coriolis effect is strong, the scaling exponent of Nusselt number versus Rayleigh number exceeds one-third once the Rayleigh number is large enough. The convective rolls revolve in prograde direction, signifying the emergence of zonal flow. The present findings open a new avenue on the exploration of high-Rayleigh number turbulent thermal convection and will improve the understanding of the flow dynamics and heat transfer processes in geophysical and astrophysical flows and other strongly rotating systems.

Fig. 1. System configuration and parameter space.

(A) Three-dimensional render of the experimental setup. A fluid is confined in a rotating cylindrical annulus having its inner (blue) and outer (red) cylindrical surfaces made out of copper, which is known for its excellent thermal conductivity. The bottom plate is made of teflon for thermal insulation, and the top plate is made of plexiglass allowing flow visualization. The coolant pipes and electric cables go through the hollow stainless steel shaft and connect to a slip ring and a rotary union. The toothed pulley is driven by a servo motor. (B) Schematical diagram of the setup, which defines the geometric parameters. (C) Explored parameter space of Ra and Ro⁻¹ for our study of supergravitational thermal convection. The red discs, blue circles, and blue triangles correspond to the parameters used in the experiments (EXP), in the three-dimensional (3D) numerical simulations, and in the two-dimensional (2D) numerical simulations, respectively. The parameter space is divided into three regimes according to the influence of Coriolis force. In addition, for comparison, we have also performed the simulations for Ro⁻¹ = 10⁻⁵ (not shown here), for which the Coriolis force is negligible. For more details about the experimental apparatus, we refer to the Supplementary Materials and movie S1.

Fig. 2. Effects of the Coriolis force on the heat transfer and flow structures.

(A) Nusselt number (Nu) as a function of Ro⁻¹ for Ra = 10⁶, 2.2 × 10⁶, 4.7 × 10⁶, 10⁷, 2.2 × 10⁷, 4.7 × 10⁷, 10⁸, 2.2 × 10⁸, and 4.7 × 10⁸ for Pr = 4.3. (D) Root mean square axial velocity fluctuation 〈(u_z)_rms〉_{r, φ, z} versus Ro⁻¹ for Ra = 10⁷ and Ra = 10⁸. (B, C, E, and F) Instantaneous temperature fields from DNS at Ra = 10⁸ for Ro⁻¹ = 0.1, 0.5, 1, and 25 (Pr = 4.3). The inner and outer surfaces locate 0.02L away from the cold and hot cylinder correspondingly.

Fig. 3. Global heat transport.

(A) Nusselt number (Nu) as a function of Ra from experiments (the solid symbols), DNS (the open symbols) in ACRBC, and the prediction from Grossmann-Lohse (G-L) theory (39) in classical RBC (dashed line). (B) The same plots as (A), but the vertical axis is compensated. Inset: An enlarged portion of the compensated plot at the large Ra regime, which shows the transition of the effective scaling exponent (Nu ∝ Ta^γ) to γ > 1/3.

Fig. 4. Revolution of convective rolls.

(A and B) Experiments at Ra = 1.8 × 10⁹ and Ro⁻¹ = 13.8. (A) Snapshots of streak images revealing the flow patterns. Seeing from the top, the whole system rotates clockwise in experiments. The corresponding movie is available in movie S2. (B) Time series of local temperature fluctuations. The measured point locates 30 mm away from the cold inner cylinder and at mid-height. (C and D) Simulations at Ra = 10⁷ and Ro⁻¹ = 1. (C) Snapshots (top view) of instantaneous temperature fields. (D) Averaged azimuthal velocity profile along the radial direction. The reference of the frame is on the clockwise direction, and the corresponding movie is available in the Supplementary Movie.