Experimental and numerical investigation of turbulent convection in a rotating cylinder

Abstract

The effects of an axial rotation on the turbulent convective flow because of an adverse temperature gradient in a water-filled upright cylindrical vessel are investigated. Both direct numerical simulations and experiments applying stereoscopic particle image velocimetry are performed. The focus is on the gathering of turbulence statistics that describe the effects of rotation on turbulent Rayleigh–Bénard convection. Rotation is an important addition, which is relevant in many geophysical and astrophysical flow phenomena.A constant Rayleigh number (dimensionless strength of the destabilizing temperature gradient) Ra = 109 and Prandtl number (describing the diffusive fluid properties) σ = 6.4 are applied. The rotation rate, given by the convective Rossby number Ro (ratio of buoyancy and Coriolis force), takes values in the range 0.045 ≤ Ro ≤ ∞, i.e. between rotation-dominated flow and zero rotation. Generally, rotation attenuates the intensity of the turbulence and promotes the formation of slender vertical tube-like vortices rather than the global circulation cell observed without rotation. Above Ro ≈ 3 there is hardly any effect of the rotation on the flow. The root-mean-square (r.m.s.) values of vertical velocity and vertical vorticity show an increase when Ro is lowered below Ro ≈ 3, which may be an indication of the activation of the Ekman pumping mechanism in the boundary layers at the bottom and top plates. The r.m.s. fluctuations of horizontal and vertical velocity, in both experiment and simulation, decrease with decreasing Ro and show an approximate power-law behaviour of the shape Ro0.2 in the range 0.1 ≲ Ro ≲ 2. In the same Ro range the temperature r.m.s. fluctuations show an opposite trend, with an approximate negative power-law exponent Ro−0.32. In this Rossby number range the r.m.s. vorticity has hardly any dependence on Ro, apart from an increase close to the plates for Ro approaching 0.1. Below Ro ≈ 0.1 there is strong damping of turbulence by rotation, as the r.m.s. velocities and vorticities as well as the turbulent heat transfer are strongly diminished. The active Ekman boundary layers near the bottom and top plates cause a bias towards cyclonic vorticity in the flow, as is shown with probability density functions of vorticity. Rotation induces a correlation between vertical vorticity and vertical velocity close to the top and bottom plates: near the top plate downward velocity is correlated with positive/cyclonic vorticity and vice versa (close to the bottom plate upward velocity is correlated with positive vorticity), pointing to the vortical plumes. In contrast with the well-mixed mean isothermal bulk of non-rotating convection, rotation causes a mean bulk temperature gradient. The viscous boundary layers scale as the theoretical Ekman and Stewartson layers with rotation, while the thermal boundary layer is unaffected by rotation. Rotation enhances differences in local anisotropy, quantified using the invariants of the anisotropy tensor: under rotation there is strong turbulence anisotropy in the centre, while near the plates a near-isotropic state is found.

Intensified heat transfer in modulated rotating Rayleigh–Bénard convection

“…These are based on an extension of the method by Verzicco and Orlandi (1996) and Oresta et al (2007) to also include the Euler force. We consider as working fluid pure water with Prandtl number r ¼ 6:4 and investigate turbulent flow at Ra ¼ 10 9 , identical to the value used in the study of Kunnen et al ( , 2010, in order to facilitate comparison with the constant rotation case.…”

“…The inclusion of a time-dependent rotation rate expressed by the so-called Euler force may qualitatively alter the flow from a condition of a domain filling large-scale circulation (LSC; occuring at low constant rotation rates) or dispersed local thermal plumes (at high constant rotation rates) (Stevens et al, 2013;Kunnen et al, , 2006Kunnen et al, , 2010Stevens et al, 2009), to a more or less segregated situation in which a pronounced thermal column forms along the centreline of the domain and highly sheared structures appear in the boundary layer near the vertical sidewalls. The ability to manipulate these flow structures allows to influence small-scale mixing (Geurts, 2001) and heat transfer characteristics.…”

Optimal Prandtl number for heat transfer in rotating Rayleigh–Bénard convection

“…lower rotation rate, when Pr is lower. Furthermore, at low Ro there is experimental [15,18] and numerical [25] evidence that the vertical component of the vorticity at mid height becomes more symmetric. Near the plates it is positively skewed for Ro 0.5, which points to the input of positive vorticity by Ekman pumping.…”

“…For Ro 0.3, there is a discrepancy between experimental and numerical measurements of the skewness near the plates, i.e. experiments [18] show that the vorticity distribution becomes more symmetric, while numerical results [25] show a further increase of the positive skewness when Ro is decreased.…”

“…To further verify the above explanation, we determined the horizontally averaged temperature at the kinetic BL height, defined as two times the height where u := u · ∇ 2 u has its maximum, see [23]- [25] for details. This height is chosen as it indicates the position where the effects of Ekman pumping are dominant.…”