scholarly journals Heat transport in Rayleigh–Bénard convection and angular momentum transport in Taylor–Couette flow: a comparative study

2017 ◽  
Vol 375 (2089) ◽  
pp. 20160079 ◽  
Author(s):  
Hannes J. Brauckmann ◽  
Bruno Eckhardt ◽  
Jörg Schumacher
Keyword(s):  
Angular Momentum ◽  
Couette Flow ◽  
Nusselt Numbers ◽  
Bénard Convection ◽  
Benard Convection ◽  
Taylor Couette ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Good Agreement ◽  
Taylor Couette Flow

Rayleigh–Bénard convection and Taylor–Couette flow are two canonical flows that have many properties in common. We here compare the two flows in detail for parameter values where the Nusselt numbers, i.e. the thermal transport and the angular momentum transport normalized by the corresponding laminar values, coincide. We study turbulent Rayleigh–Bénard convection in air at Rayleigh number Ra =10 7 and Taylor–Couette flow at shear Reynolds number Re S =2×10 4 for two different mean rotation rates but the same Nusselt numbers. For individual pairwise related fields and convective currents, we compare the probability density functions normalized by the corresponding root mean square values and taken at different distances from the wall. We find one rotation number for which there is very good agreement between the mean profiles of the two corresponding quantities temperature and angular momentum. Similarly, there is good agreement between the fluctuations in temperature and velocity components. For the heat and angular momentum currents, there are differences in the fluctuations outside the boundary layers that increase with overall rotation and can be related to differences in the flow structures in the boundary layer and in the bulk. The study extends the similarities between the two flows from global quantities to local quantities and reveals the effects of rotation on the transport. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

Effect of Sidewall Conductance on Nusselt Number for Rayleigh-Bénard Convection: A Semi-Analytical and Experimental Correction

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
U. Madanan ◽  
R. J. Goldstein
Keyword(s):  
Thermal Conductivity ◽  
Nusselt Number ◽  
Analytical Model ◽  
Thermal Conductance ◽  
Bénard Convection ◽  
Benard Convection ◽  
Extended Surfaces ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Good Agreement

Abstract The effect of sidewall conductance on Nusselt number for the Rayleigh-Bénard convection is examined by performing nearly identical sets of experiments with sidewalls made of three different materials. These experimental results are utilized to extrapolate and estimate the Nusselt number for an ideal zero-thermal-conductivity sidewall case, which is the case when the sidewalls are perfectly insulating. A semi-analytical model is proposed, based on the concept of extended surfaces, to compute the discrepancy in Nusselt number caused by the presence of finite thermal conductance of the sidewalls. The predictions obtained using this model are found to be in good agreement with the corresponding experimentally determined values.

scholarly journals Convectively driven shear and decreased heat flux

2014 ◽  
Vol 759 ◽  
pp. 360-385 ◽  
Author(s):  
David Goluskin ◽  
Hans Johnston ◽  
Glenn R. Flierl ◽  
Edward A. Spiegel
Keyword(s):  
Heat Flux ◽  
Heat Transport ◽  
Large Scale ◽  
Mean Flow ◽  
Nusselt Numbers ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Scale Shear

AbstractWe report on direct numerical simulations of two-dimensional, horizontally periodic Rayleigh–Bénard convection between free-slip boundaries. We focus on the ability of the convection to drive large-scale horizontal flow that is vertically sheared. For the Prandtl numbers ($\mathit{Pr}$) between 1 and 10 simulated here, this large-scale shear can be induced by raising the Rayleigh number ($\mathit{Ra}$) sufficiently, and we explore the resulting convection for $\mathit{Ra}$ up to $10^{10}$. When present in our simulations, the sheared mean flow accounts for a large fraction of the total kinetic energy, and this fraction tends towards unity as $\mathit{Ra}\rightarrow \infty$. The shear helps disperse convective structures, and it reduces vertical heat flux; in parameter regimes where one state with large-scale shear and one without are both stable, the Nusselt number of the state with shear is smaller and grows more slowly with $\mathit{Ra}$. When the large-scale shear is present with $\mathit{Pr}\lesssim 2$, the convection undergoes strong global oscillations on long timescales, and heat transport occurs in bursts. Nusselt numbers, time-averaged over these bursts, vary non-monotonically with $\mathit{Ra}$ for $\mathit{Pr}=1$. When the shear is present with $\mathit{Pr}\gtrsim 3$, the flow does not burst, and convective heat transport is sustained at all times. Nusselt numbers then grow roughly as powers of $\mathit{Ra}$, but the growth rates are slower than any previously reported for Rayleigh–Bénard convection without large-scale shear. We find that the Nusselt numbers grow proportionally to $\mathit{Ra}^{0.077}$ when $\mathit{Pr}=3$ and to $\mathit{Ra}^{0.19}$ when $\mathit{Pr}=10$. Analogies with tokamak plasmas are described.

Effects of Coriolis force and nonuniform temperature gradient on the Rayleigh–Benard convection

1986 ◽  
Vol 64 (1) ◽  
pp. 90-99 ◽  
Author(s):  
N. Rudraiah ◽  
O. P. Chandna
Keyword(s):  
Temperature Gradient ◽  
Coriolis Force ◽  
Fluid Layer ◽  
Nonuniform Temperature ◽  
Bénard Convection ◽  
Benard Convection ◽  
Bounding Surfaces ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Good Agreement

The effects of the Coriolis force and a nonuniform temperature gradient on the onset of the Rayleigh–Benard convection in a thin, horizontal, rotating fluid layer is studied using linear-stability analysis. It is shown analytically that the method and rate of heating, the Coriolis force, and the nature of the bounding surfaces of the fluid layer significantly influence the value of the Rayleigh number at the onset of marginal convection. The mechanism for suppressing or augmenting convection is discussed in detail. The Galerkin technique employed here is much easier to use than that the method of Chandrasekhar (5). The analytical results obtained from using this procedure are compared with the published experimental data and the results obtained from numerical procedures; good agreement is found.

Rayleigh-Bénard Convection in Open and Closed Rotating Cavities

2005 ◽  
Vol 129 (2) ◽  
pp. 305-311 ◽  
Author(s):  
Martin P. King ◽  
Michael Wilson ◽  
J. Michael Owen
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Nusselt Numbers ◽  
Bénard Convection ◽  
Published Evidence ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Numbers ◽  
Rayleigh Benard

Buoyancy effects can be significant in the rotating annular cavities found between compressor discs in gas-turbine engines, where Rayleigh numbers above 1012 are common. In some engines, the cavity is “closed” so that the air is confined between four rotating surfaces: two discs and inner and outer cylinders. In most engines, however, the cavity is “open” and there is an axial throughflow of cooling air at the center. For open rotating cavities, a review of the published evidence suggests a Rayleigh–Bénard type of flow structure, in which, at the larger radii, there are pairs of cyclonic and anti-cyclonic vortices. The toroidal circulation created by the axial throughflow is usually restricted to the smaller radii in the cavity. For a closed rotating annulus, solution of the unsteady Navier–Stokes equations, for Rayleigh numbers up to 109, show Rayleigh–Bénard convection similar to that found in stationary enclosures. The computed streamlines in the r-θ plane show pairs of cyclonic and anti-cyclonic vortices; but, at the larger Rayleigh numbers, the computed isotherms suggest that the flow in the annulus is thermally mixed. At the higher Rayleigh numbers, the computed instantaneous Nusselt numbers are unsteady and tend to oscillate with time. The computed time-averaged Nusselt numbers are in good agreement with the correlations for Rayleigh–Bénard convection in a stationary enclosure, but they are significantly higher than the published empirical correlations for a closed rotating annulus.

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