scholarly journals High Rayleigh number variational multiscale large eddy simulations of Rayleigh-Bénard convection

2020 ◽  
pp. 103614
Author(s):  
David Sondak ◽  
Thomas M. Smith ◽  
Roger P. Pawlowski ◽  
Sidafa Conde ◽  
John N. Shadid
Keyword(s):  
Rayleigh Number ◽  
Large Eddy Simulations ◽  
Variational Multiscale ◽  
Bénard Convection ◽  
Benard Convection ◽  
Large Eddy ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Interpretation of shadowgraph patterns in Rayleigh-Bénard convection

1988 ◽  
Vol 190 ◽  
pp. 451-469 ◽  
Author(s):  
D. R. Jenkins
Keyword(s):  
Rayleigh Number ◽  
Linear Theory ◽  
Vertical Component ◽  
Fluid Flows ◽  
Bénard Convection ◽  
Benard Convection ◽  
Higher Order Terms ◽  
The Relationship ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

The relationship between observations of cellular Rayleigh-Bénard convection using shadowgraphs and theoretical expressions for convection planforms is considered. We determine the shadowgraphs that ought to be observed if the convection is as given by theoretical expressions for roll, square or hexagonal planforms and compare them with actual experiments. Expressions for the planforms derived from linear theory, valid for low supercritical Rayleigh number, produce unambiguous shadowgraphs consisting of cells bounded by bright lines, which correspond to surfaces through which no fluid flows and on which the vertical component of velocity is directed downwards. Dark spots at the centre of cells, indicating regions of hot, rising fluid, are not accounted for by linear theory, but can be produced by adding higher-order terms, predominantly due to the temperature dependence of a material property of the fluid, such as its viscosity.

scholarly journals Traveling-Wave Convection with Periodic Source Defects in Binary Fluid Mixtures with Strong Soret Effect

Entropy ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 283
Author(s):  
Laiyun Zheng ◽  
Bingxin Zhao ◽  
Jianqing Yang ◽  
Zhenfu Tian ◽  
Ming Ye
Keyword(s):  
Rayleigh Number ◽  
Traveling Wave ◽  
Soret Effect ◽  
Binary Fluid ◽  
Fluid Mixtures ◽  
Bénard Convection ◽  
Benard Convection ◽  
Binary Fluid Mixtures ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

This paper studied the Rayleigh–Bénard convection in binary fluid mixtures with a strong Soret effect (separation ratio ψ = − 0.6 ) in a rectangular container heated uniformly from below. We used a high-accuracy compact finite difference method to solve the hydrodynamic equations used to describe the Rayleigh–Bénard convection. A stable traveling-wave convective state with periodic source defects (PSD-TW) is obtained and its properties are discussed in detail. Our numerical results show that the novel PSD-TW state is maintained by the Eckhaus instability and the difference between the creation and annihilation frequencies of convective rolls at the left and right boundaries of the container. In the range of Rayleigh number in which the PSD-TW state is stable, the period of defect occurrence increases first and then decreases with increasing Rayleigh number. At the upper bound of this range, the system transitions from PSD-TW state to another type of traveling-wave state with aperiodic and more dislocated defects. Moreover, we consider the problem with the Prandtl number P r ranging from 0.1 to 20 and the Lewis number L e from 0.001 to 1, and discuss the stabilities of the PSD-TW states and present the results as phase diagrams.

scholarly journals Rayleigh–Bénard convection in a creeping solid with melting and freezing at either or both its horizontal boundaries

2018 ◽  
Vol 846 ◽  
pp. 5-36 ◽  
Author(s):  
Stéphane Labrosse ◽  
Adrien Morison ◽  
Renaud Deguen ◽  
Thierry Alboussière
Keyword(s):  
Boundary Condition ◽  
Rayleigh Number ◽  
Phase Change ◽  
Time Scale ◽  
Critical Rayleigh Number ◽  
Classical Case ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Solid-state convection can take place in the rocky or icy mantles of planetary objects, and these mantles can be surrounded above or below or both by molten layers of similar composition. A flow towards the interface can proceed through it by changing phase. This behaviour is modelled by a boundary condition taking into account the competition between viscous stress in the solid, which builds topography of the interface with a time scale $\unicode[STIX]{x1D70F}_{\unicode[STIX]{x1D702}}$, and convective transfer of the latent heat in the liquid from places of the boundary where freezing occurs to places of melting, which acts to erase topography, with a time scale $\unicode[STIX]{x1D70F}_{\unicode[STIX]{x1D719}}$. The ratio $\unicode[STIX]{x1D6F7}=\unicode[STIX]{x1D70F}_{\unicode[STIX]{x1D719}}/\unicode[STIX]{x1D70F}_{\unicode[STIX]{x1D702}}$ controls whether the boundary condition is the classical non-penetrative one ($\unicode[STIX]{x1D6F7}\rightarrow \infty$) or allows for a finite flow through the boundary (small $\unicode[STIX]{x1D6F7}$). We study Rayleigh–Bénard convection in a plane layer subject to this boundary condition at either or both its boundaries using linear and weakly nonlinear analyses. When both boundaries are phase-change interfaces with equal values of $\unicode[STIX]{x1D6F7}$, a non-deforming translation mode is possible with a critical Rayleigh number equal to $24\unicode[STIX]{x1D6F7}$. At small values of $\unicode[STIX]{x1D6F7}$, this mode competes with a weakly deforming mode having a slightly lower critical Rayleigh number and a very long wavelength, $\unicode[STIX]{x1D706}_{c}\sim 8\sqrt{2}\unicode[STIX]{x03C0}/3\sqrt{\unicode[STIX]{x1D6F7}}$. Both modes lead to very efficient heat transfer, as expressed by the relationship between the Nusselt and Rayleigh numbers. When only one boundary is subject to a phase-change condition, the critical Rayleigh number is $\mathit{Ra}_{c}=153$ and the critical wavelength is $\unicode[STIX]{x1D706}_{c}=5$. The Nusselt number increases approximately two times faster with the Rayleigh number than in the classical case with non-penetrative conditions, and the average temperature diverges from $1/2$ when the Rayleigh number is increased, towards larger values when the bottom boundary is a phase-change interface.

Exploring the severely confined regime in Rayleigh–Bénard convection

2016 ◽  
Vol 805 ◽  
Author(s):  
Kai Leong Chong ◽  
Ke-Qing Xia
Keyword(s):  
Rayleigh Number ◽  
Flow Topology ◽  
Thermal Plumes ◽  
Bénard Convection ◽  
Benard Convection ◽  
Wide Range ◽  
Classical Boundary ◽  
Global And Local ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We study the effect of severe geometrical confinement in Rayleigh–Bénard convection with a wide range of width-to-height aspect ratio $\unicode[STIX]{x1D6E4}$, $1/128\leqslant \unicode[STIX]{x1D6E4}\leqslant 1$, and Rayleigh number $Ra$, $3\times 10^{4}\leqslant Ra\leqslant 1\times 10^{11}$, at a fixed Prandtl number of $Pr=4.38$ by means of direct numerical simulations in Cartesian geometry with no-slip walls. For convection under geometrical confinement (decreasing $\unicode[STIX]{x1D6E4}$ from 1), three regimes can be recognized (Chong et al., Phys. Rev. Lett., vol. 115, 2015, 264503) based on the global and local properties in terms of heat transport, plume morphology and flow structures. These are Regime I: classical boundary-layer-controlled regime; Regime II: plume-controlled regime; and Regime III: severely confined regime. The study reveals that the transition into Regime III leads to totally different heat and momentum transport scalings and flow topology from the classical regime. The convective heat transfer scaling, in terms of the Nusselt number $Nu$, exhibits the scaling $Nu-1\sim Ra^{0.61}$ over three decades of $Ra$ at $\unicode[STIX]{x1D6E4}=1/128$, which contrasts sharply with the classical scaling $Nu-1\sim Ra^{0.31}$ found at $\unicode[STIX]{x1D6E4}=1$. The flow in Regime III is found to be dominated by finger-like, long-lived plume columns, again in sharp contrast with the mushroom-like, fragmented thermal plumes typically observed in the classical regime. Moreover, we identify a Rayleigh number for regime transition, $Ra^{\ast }=(29.37/\unicode[STIX]{x1D6E4})^{3.23}$, such that the scaling transition in $Nu$ and $Re$ can be clearly demonstrated when plotted against $Ra/Ra^{\ast }$.

The effect of distant side-walls on the evolution and stability of finite-amplitude Rayleigh-Bénard convection

1981 ◽  
Vol 378 (1775) ◽  
pp. 539-566 ◽  
Keyword(s):  
Rayleigh Number ◽  
Prandtl Number ◽  
Finite Amplitude ◽  
Two Dimensional ◽  
Bénard Convection ◽  
Benard Convection ◽  
Side Walls ◽  
Rayleigh Benard Convection ◽  
Rayleigh Numbers ◽  
Rayleigh Benard

A recent study by Cross et al . (1980) has described a class of finite-amplitude phase-winding solutions of the problem of two-dimensional Rayleigh-Bénard convection in a shallow fluid layer of aspect ratio 2 L (≫ 1) confined laterally by rigid side-walls. These solutions arise at Rayleigh numbers R = R 0 + O ( L -1 ) where R 0 is the critical Rayleigh number for the corresponding infinite layer. Nonlinear solutions of constant phase exist for Rayleigh numbers R = R 0 + O ( L -2 ) but of these only the two that bifurcate at the lowest value of R are stable to two-dimensional linearized disturbances in this range (Daniels 1978). In the present paper one set of the class of phase-winding solutions is found to be stable to two-dimensional disturbances. For certain values of the Prandtl number of the fluid and for stress-free horizontal boundaries the results predict that to preserve stability there must be a continual readjustment of the roll pattern as the Rayleigh number is raised, with a corresponding increase in wavelength proportional to R - R 0 . These solutions also exhibit hysteresis as the Rayleigh number is raised and lowered. For other values of the Prandtl number the number of rolls remains unchanged as the Rayleigh number is raised, and the wavelength remains close to its critical value. It is proposed that the complete evolution of the flow pattern from a static state must take place on a number of different time scales of which t = O(( R - R 0 ) -1 ) and t = O(( R - R 0 ) -2 ) are the most significant. When t = O(( R - R 0 ) -1 ) the amplitude of convection rises from zero to its steady-state value, but the final lateral positioning of the rolls is only completed on the much longer time scale t = O(( R - R 0 ) -2 ).

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