scholarly journals Supergravitational turbulent thermal convection

2020 ◽  
Vol 6 (40) ◽  
pp. eabb8676
Author(s):  
Hechuan Jiang ◽  
Xiaojue Zhu ◽  
Dongpu Wang ◽  
Sander G. Huisman ◽  
Chao Sun
Keyword(s):  
Rayleigh Number ◽  
Thermal Convection ◽  
Zonal Flow ◽  
Scaling Exponent ◽  
Transfer Processes ◽  
Rotating Systems ◽  
Cylindrical Annulus ◽  
Fluid Core ◽  
Novel Approach ◽  
Astrophysical Flows

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.

Incipient Buoyant Thermal Convection in a Vertical Cylindrical Annulus

1990 ◽  
Vol 112 (4) ◽  
pp. 959-964 ◽  
Author(s):  
D. L. Littlefield ◽  
P. V. Desai
Keyword(s):  
Rayleigh Number ◽  
Boundary Conditions ◽  
Thermal Convection ◽  
Fluid Motion ◽  
Radius Ratio ◽  
Cellular Behavior ◽  
Cylindrical Annulus ◽  
Rayleigh Numbers ◽  
Number Of Cells

The incipient buoyant thermal convection in a vertical cylindrical annulus when heated from below is examined. The ends are assumed to be free, and the sidewalls perfectly conducting. The temperature needed to initiate fluid motion is expressed nondimensionally in terms of the Rayleigh number. The analytical conflict that arises for annuli of infinite aspects ratios due to insufficient independent boundary conditions is resolved. Calculations for the critical Rayleigh numbers are presented for a variety of geometries, and the corresponding velocity and temperature perturbations are also shown. The number of cells increases as the aspect and radius ratio decrease with a strong bias towards the development of azimuthally varying cells. These changes in cellular behavior are expected based on physical justifications and comparisons with previous studies.

Linear stability of rotating convection in an imposed shear flow

1997 ◽  
Vol 350 ◽  
pp. 271-293 ◽  
Author(s):  
PAUL MATTHEWS ◽  
STEPHEN COX
Keyword(s):  
Rayleigh Number ◽  
Shear Flow ◽  
Eigenvalue Problem ◽  
Linear Stability ◽  
Thermal Convection ◽  
Critical Rayleigh Number ◽  
Rotation Vector ◽  
Linear Stability Theory ◽  
Fixed Temperature ◽  
Differential Motion

In many geophysical and astrophysical contexts, thermal convection is influenced by both rotation and an underlying shear flow. The linear theory for thermal convection is presented, with attention restricted to a layer of fluid rotating about a horizontal axis, and plane Couette flow driven by differential motion of the horizontal boundaries.The eigenvalue problem to determine the critical Rayleigh number is solved numerically assuming rigid, fixed-temperature boundaries. The preferred orientation of the convection rolls is found, for different orientations of the rotation vector with respect to the shear flow. For moderate rates of shear and rotation, the preferred roll orientation depends only on their ratio, the Rossby number.It is well known that rotation alone acts to favour rolls aligned with the rotation vector, and to suppress rolls of other orientations. Similarly, in a shear flow, rolls parallel to the shear flow are preferred. However, it is found that when the rotation vector and shear flow are parallel, the two effects lead counter-intuitively (as in other, analogous convection problems) to a preference for oblique rolls, and a critical Rayleigh number below that for Rayleigh–Bénard convection.When the boundaries are poorly conducting, the eigenvalue problem is solved analytically by means of an asymptotic expansion in the aspect ratio of the rolls. The behaviour of the stability problem is found to be qualitatively similar to that for fixed-temperature boundaries.Fully nonlinear numerical simulations of the convection are also carried out. These are generally consistent with the linear stability theory, showing convection in the form of rolls near the onset of motion, with the appropriate orientation. More complicated states are found further from critical.

Heat flux enhancement by regular surface roughness in turbulent thermal convection

2014 ◽  
Vol 763 ◽  
pp. 109-135 ◽  
Author(s):  
Sebastian Wagner ◽  
Olga Shishkina
Keyword(s):  
Heat Flux ◽  
Surface Roughness ◽  
Thermal Convection ◽  
Large Scale ◽  
Secondary Flows ◽  
Scaling Exponent ◽  
Wall Roughness ◽  
Regular Surface ◽  
Large Scale Circulation ◽  
Flux Enhancement

AbstractDirect numerical simulations (DNS) of turbulent thermal convection in a box-shaped domain with regular surface roughness at the heated bottom and cooled top surfaces are conducted for Prandtl number $\mathit{Pr}=0.786$ and Rayleigh numbers $\mathit{Ra}$ between $10^{6}$ and $10^{8}$. The surface roughness is introduced by four parallelepiped equidistantly distributed obstacles attached to the bottom plate, and four obstacles located symmetrically at the top plate. By varying $\mathit{Ra}$ and the height and width of the obstacles, we investigate the influence of the regular wall roughness on the turbulent heat transport, measured by the Nusselt number $\mathit{Nu}$. For fixed $\mathit{Ra}$, the change in the value of $\mathit{Nu}$ is determined not only by the covering area of the surface, i.e. the obstacle height, but also by the distance between the obstacles. The heat flux enhancement is found to be largest for wide cavities between the obstacles which can be ‘washed out’ by the flow. This is also manifested in an empirical relation, which is based on the DNS data. We further discuss theoretical limiting cases for very wide and very narrow obstacles and combine them into a simple model for the heat flux enhancement due to the wall roughness, without introducing any free parameters. This model predicts well the general trends and the order of magnitude of the heat flux enhancement obtained in the DNS. In the $\mathit{Nu}$ versus $\mathit{Ra}$ scaling, the obstacles work in two ways: for smaller $\mathit{Ra}$ an increase of the scaling exponent compared to the smooth case is found, which is connected to the heat flux entering the cavities from below. For larger $\mathit{Ra}$ the scaling exponent saturates to the one for smooth plates, which can be understood as a full washing-out of the cavities. The latter is also investigated by considering the strength of the mean secondary flow in the cavities and its relation to the wind (i.e. the large-scale circulation), that develops in the core part of the domain. Generally, an increase in the roughness height leads to stronger flows both in the cavities and in the bulk region, while an increase in the width of the obstacles strengthens only the large-scale circulation of the fluid and weakens the secondary flows. An increase of the Rayleigh number always leads to stronger flows, both in the cavities and in the bulk.

Experiments on the inhibition of thermal convection by a magnetic field

1957 ◽  
Vol 240 (1220) ◽  
pp. 108-113 ◽  
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Rayleigh Number ◽  
Magnetic Fields ◽  
Thermal Convection ◽  
Kinematic Viscosity ◽  
Critical Rayleigh Number ◽  
Theoretical Relation ◽  
Horizontal Layers

Experiments on the magnetic inhibition of thermal convection in horizontal layers of mercury heated from below are described. A large 36½ in. cyclotron magnet reconditioned for hydromagnetic studies was used in these experiments. By using layers of mercury of depth 3 to 6 cm and magnetic fields of strength 500 to 8000 gauss, it has been possible to determine the dependence of the critical Rayleigh number for the onset of instability on the parameter Q 1 ( = σH 2 d 2 / π 2 ρν , where H denotes the strength of the field, σ the electrical conductivity, ν the coefficient of kinematic viscosity, ρ the density and d the depth of the layer) for Q 1 varying between 40 and 1·6 × 10 6 . The experiments fully confirm the theoretical relation derived by Chandrasekhar.

Natural Convection in a Micro Size Horizontal Cylindrical Annulus With Periodic Volumetric Heat Flux

2009 ◽  
Author(s):  
Kamyar Mansour
Keyword(s):  
Heat Flux ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Viscous Fluid ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Similarity Parameter ◽  
Symbolic Calculation ◽  
Cylindrical Annulus ◽  
Gap Ratio

We consider the two-dimensional problem of steady natural convection in a narrow (Micro size) Horizontal Cylindrical annulus filled with viscous fluid and periodic volumetric heat flux. The solution is expanded in powers of a single combined similarity parameter, which is the product of the Gap ratio to the power of four, and Rayleigh number and the series extended by means of symbolic calculation up to 16 terms. Analysis of these expansions allows the exact computation for arbitrarily accuracy up to 50000 figures. Although the range of the radius of convergence is almost zero but Pade approximation lead our result to be good even for much higher value of the similarity parameter.

Convection in a rotating cylindrical annulus. Part 2. Transitions to asymmetric and vacillating flow

1987 ◽  
Vol 174 ◽  
pp. 313-326 ◽  
Author(s):  
A. C. Or ◽  
F. H. Busse
Keyword(s):  
Rayleigh Number ◽  
Rossby Waves ◽  
Period Doubling ◽  
Critical Value ◽  
Coriolis Parameter ◽  
Onset Of Convection ◽  
Cylindrical Annulus ◽  
Propagating Waves ◽  
Annular Layer ◽  
Doubling Sequence

The instabilities of convection columns (also called thermal Rossby waves) in a cylindrical annulus rotating about its axis and heated from the outside are investigated as a function of the Prandtl number P and the Coriolis parameter η*. When this latter parameter is sufficiently large, it is found that the primary solution observed at the onset of convection becomes unstable when the Rayleigh number exceeds its critical value by a relatively small amount. Transitions occur to columnar convection which is non-symmetric with respect to the mid-plane of the small-gap annular layer. Further transitions introduce convection flows that vacillate in time or tend to split the row of columns into an inner and an outer row of separately propagating waves. Of special interest is the regime of non-symmetric convection, which exhibits decreasing Nusselt number with increasing Rayleigh number, and the indication of a period doubling sequence associated with vacillating convection.

Derivation of Rayleigh Number for Nonpenetrative Thermal Convection

1997 ◽  
Vol 119 (1) ◽  
pp. 180-183 ◽  
Author(s):  
A. K. Prasad
Keyword(s):  
Rayleigh Number ◽  
Thermal Convection

Large eddy simulations of thermal convection at high Rayleigh number

2000 ◽  
Vol 140 (1) ◽  
pp. 163-174 ◽  
Author(s):  
Noä Cantin ◽  
Alain P. Vincent ◽  
David A. Yuen
Keyword(s):  
Rayleigh Number ◽  
Thermal Convection ◽  
Large Eddy Simulations ◽  
Large Eddy
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