Numerical simulations of thermal convection in a rotating spherical fluid shell at high Taylor and Rayleigh numbers

1995 ◽  
Vol 7 (11) ◽  
pp. 2686-2699 ◽  
Author(s):  
Z.‐P. Sun ◽  
G. Schubert
Keyword(s):  
Numerical Simulations ◽  
Thermal Convection ◽  
Spherical Fluid ◽  
Rayleigh Numbers

scholarly journals Rotating turbulent thermal convection at very large Rayleigh numbers

2021 ◽  
Vol 912 ◽  
Author(s):  
Marcel Wedi ◽  
Dennis P.M. van Gils ◽  
Eberhard Bodenschatz ◽  
Stephan Weiss
Keyword(s):  
Thermal Convection ◽  
Rayleigh Numbers

Abstract

Numerical simulations of Rayleigh–Bénard convection for Prandtl numbers between 10−1 and 104 and Rayleigh numbers between 105 and 109

2010 ◽  
Vol 662 ◽  
pp. 409-446 ◽  
Author(s):  
G. SILANO ◽  
K. R. SREENIVASAN ◽  
R. VERZICCO
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Numerical Simulations ◽  
Multiple Solutions ◽  
Large Scale ◽  
Prandtl Numbers ◽  
Rayleigh Benard Convection ◽  
Rayleigh Numbers ◽  
Rayleigh Benard

We summarize the results of an extensive campaign of direct numerical simulations of Rayleigh–Bénard convection at moderate and high Prandtl numbers (10−1 ≤ Pr ≤ 104) and moderate Rayleigh numbers (105 ≤ Ra ≤ 109). The computational domain is a cylindrical cell of aspect ratio Γ = 1/2, with the no-slip condition imposed on all boundaries. By scaling the numerical results, we find that the free-fall velocity should be multiplied by $1/\sqrt{{\it Pr}}$ in order to obtain a more appropriate representation of the large-scale velocity at high Pr. We investigate the Nusselt and the Reynolds number dependences on Ra and Pr, comparing the outcome with previous numerical and experimental results. Depending on Pr, we obtain different power laws of the Nusselt number with respect to Ra, ranging from Ra2/7 for Pr = 1 up to Ra0.31 for Pr = 103. The Nusselt number is independent of Pr. The Reynolds number scales as ${\it Re}\,{\sim}\,\sqrt{{\it Ra}}/{\it Pr}$, neglecting logarithmic corrections. We analyse the global and local features of viscous and thermal boundary layers and their scaling behaviours with respect to Ra and Pr, and with respect to the Reynolds and Péclet numbers. We find that the flow approaches a saturation state when Reynolds number decreases below the critical value, Res ≃ 40. The thermal-boundary-layer thickness increases slightly (instead of decreasing) when the Péclet number increases, because of the moderating influence of the viscous boundary layer. The simulated ranges of Ra and Pr contain steady, periodic and turbulent solutions. A rough estimate of the transition from the steady to the unsteady state is obtained by monitoring the time evolution of the system until it reaches stationary solutions. We find multiple solutions as long-term phenomena at Ra = 108 and Pr = 103, which, however, do not result in significantly different Nusselt numbers. One of these multiple solutions, even if stable over a long time interval, shows a break in the mid-plane symmetry of the temperature profile. We analyse the flow structures through the transitional phases by direct visualizations of the temperature and velocity fields. A wide variety of large-scale circulation and plume structures has been found. The single-roll circulation is characteristic only of the steady and periodic solutions. For other regimes at lower Pr, the mean flow generally consists of two opposite toroidal structures; at higher Pr, the flow is organized in the form of multi-jet structures, extending mostly in the vertical direction. At high Pr, plumes mainly detach from sheet-like structures. The signatures of different large-scale structures are generally well reflected in the data trends with respect to Ra, less in those with respect to Pr.

scholarly journals Numerical simulations of thermal convection on a hemisphere

2018 ◽  
Vol 3 (4) ◽  
Author(s):  
C.-H. Bruneau ◽  
P. Fischer ◽  
Y.-L. Xiong ◽  
H. Kellay ◽  
Keyword(s):  
Numerical Simulations ◽  
Thermal Convection

Influence of Transverse Fins Attached to the Heated Wall of a Rayleigh-Be´nard Cavity

2004 ◽  
Author(s):  
Darren L. Hitt ◽  
Antonio Campo
Keyword(s):  
Thermal Conductivity ◽  
Nusselt Number ◽  
Numerical Simulations ◽  
Heat Transport ◽  
Local Heat ◽  
Heated Wall ◽  
Lower Plate ◽  
Maximum Heat ◽  
Rayleigh Numbers ◽  
Fin Spacing

In this article we examine the augmentation of classic Rayleigh-Be´nard convection by the addition of periodically-spaced tranverse fins attached to the heated, lower plate. The respective impacts of the fin size, the fin spacing and the thermal conductivity of the fin material are examined through numerical simulations for different laminar Rayleigh numbers and reported it terms of the Nusselt number. With the exception of very closely spaced fins, the heat transport is observed to exceed that of the idealized Rayleigh-Be´nard case. It is found that local heat transport maxima and minima do exist for specific fin spacings and that the maxima become more pronounced at higher Rayleigh numbers. For ‘small fins’ the fin spacing corresponding to maximum heat transport is such that the fin spacing is approximately equal to the enclosure height.

Thermal Convection in Porous Media at High Rayleigh Numbers

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Daniel J. Keene ◽  
R. J. Goldstein
Keyword(s):  
Boundary Layer ◽  
Porous Media ◽  
Thermal Convection ◽  
Thermal Boundary Layer ◽  
Packed Bed ◽  
Horizontal Layer ◽  
Homogeneous Fluid ◽  
Fluid Systems ◽  
Dimensionless Groups ◽  
Rayleigh Numbers

An experimental study of thermal convection in a porous medium investigates the heat transfer across a horizontal layer heated from below at high Rayleigh number. Using a packed bed of polypropylene spheres in a cubic enclosure saturated with compressed argon, the pressure was varied between 5.6 bar and 77 bar to obtain fluid Rayleigh numbers between 1.68 × 109 and 3.86 × 1011, corresponding to Rayleigh–Darcy numbers between 7.47 × 103 and 2.03 × 106. From the present and earlier studies of Rayleigh–Benard convection in both porous media and homogeneous fluid systems, the existence and importance of a thin thermal boundary layer are clearly demonstrated. In addition to identifying the governing role of the thermal boundary layer at high Rayleigh numbers, the successful correlation of data using homogeneous fluid dimensionless groups when the thermal boundary layer thickness becomes smaller than the length scale associated with the pore features is shown.

scholarly journals Energy and Variance Budgets of a Diffusive Staircase with Implications for Heat Flux Scaling

2016 ◽  
Vol 46 (8) ◽  
pp. 2553-2569 ◽  
Author(s):  
Magnus Hieronymus ◽  
Jeffrey R. Carpenter
Keyword(s):  
Heat Flux ◽  
Numerical Simulations ◽  
Scaling Laws ◽  
State Energy ◽  
Diffusive Regime ◽  
Diffusive Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Numbers ◽  
Rayleigh Benard ◽  
Double Diffusive

AbstractThe steady-state energy and thermal variance budgets form the basis for most current methods for evaluating turbulent fluxes of buoyancy, heat, and salinity. This study derives these budgets for a double-diffusive staircase and quantifies them using direct numerical simulations; 10 runs with different Rayleigh numbers are considered. The energy budget is found to be well approximated by a simple three-term balance, while the thermal variance budget consists of only two terms. The two budgets are also combined to give an expression for the ratio of the heat and salt fluxes. The heat flux scaling is also studied and found to agree well with earlier estimates based on laboratory experiments and numerical simulations at high Rayleigh numbers. At low Rayleigh numbers, however, the authors find large deviations from earlier scaling laws. Last, the scaling theory of Grossman and Lohse, which was developed for Rayleigh–Bénard convection and is based on the partitioning of the kinetic energy and tracer variance dissipation, is adapted to the diffusive regime of double-diffusive convection. The predicted heat flux scalings are compared to the results from the numerical simulations and earlier estimates.

scholarly journals Plume generation in natural thermal convection at high Rayleigh and Prandtl numbers

2001 ◽  
Vol 434 ◽  
pp. 1-21 ◽  
Author(s):  
C. LITHGOW-BERTELLONI ◽  
M. A. RICHARDS ◽  
C. P. CONRAD ◽  
R. W. GRIFFITHS
Keyword(s):  
Boundary Layer ◽  
Thermal Convection ◽  
Large Scale ◽  
Lower Boundary ◽  
Secular Change ◽  
Scaling Analysis ◽  
Temperature Dependent Viscosity ◽  
Earth’S Mantle ◽  
Dependent Viscosity ◽  
Rayleigh Numbers

We study natural thermal convection of a fluid (corn syrup) with a large Prandtl number (103–107) and temperature-dependent viscosity. The experimental tank (1 × 1 × 0.3m) is heated from below with insulating top and side boundaries, so that the fluid experiences secular heating as experiments proceed. This setup allows a focused study of thermal plumes from the bottom boundary layer over a range of Rayleigh numbers relevant to convective plumes in the deep interior of the Earth's mantle. The effective value of Ra, based on the viscosity of the fluid at the interior temperature, varies from 105 at the beginning to almost 108 toward the end of the experiments. Thermals (plumes) from the lower boundary layer are trailed by continuous conduits with long residence times. Plumes dominate flow in the tank, although there is a weaker large-scale circulation induced by material cooling at the imperfectly insulating top and sidewalls. At large Ra convection is extremely time-dependent and exhibits episodic bursts of plumes, separated by periods of quiescence. This bursting behaviour probably results from the inability of the structure of the thermal boundary layer and its instabilities to keep pace with the rate of secular change in the value of Ra. The frequency of plumes increases and their size decreases with increasing Ra, and we characterize these changes via in situ thermocouple measurements, shadowgraph videos, and videos of liquid crystal films recorded during several experiments. A scaling analysis predicts observed changes in plume head and tail radii with increasing Ra. Since inertial effects are largely absent no transition to ‘hard’ thermal turbulence is observed, in contrast to a previous conclusion from numerical calculations at similar Rayleigh numbers. We suggest that bursting behaviour similar to that observed may occur in the Earth's mantle as it undergoes secular cooling on the billion-year time scale.

scholarly journals Nonlinear Thermal Convection in a Layer with Imposed Energy Flux

1974 ◽  
Vol 27 (4) ◽  
pp. 481 ◽  
Author(s):  
R Van der Borght
Keyword(s):  
Boundary Conditions ◽  
Energy Flux ◽  
Thermal Convection ◽  
Average Energy ◽  
Finite Amplitude ◽  
Solar Granulation ◽  
Convective Motions ◽  
Rayleigh Numbers

Results are reported of an investigation into the effect of the chosen boundary conditions on the steady finite-amplitude convective motions in a layer in which the average energy flux is imposed. The boundary conditions are chosen with a view to the application of the results to solar granulation and supergranulation. It is shown that, at high Rayleigh numbers, solutions do in fact exist for which there is no modulation in the energy flux and little fluctuation in the temperature across the boundaries.

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