scholarly journals Comparison between two- and three-dimensional Rayleigh–Bénard convection

2013 ◽  
Vol 736 ◽  
pp. 177-194 ◽  
Author(s):  
Erwin P. van der Poel ◽  
Richard J. A. M. Stevens ◽  
Detlef Lohse
Keyword(s):  
Three Dimensional ◽  
State Dependence ◽  
Constant Factor ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Bénard Convection ◽  
Benard Convection ◽  
The Difference ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

AbstractTwo-dimensional and three-dimensional Rayleigh–Bénard convection is compared using results from direct numerical simulations and previous experiments. The phase diagrams for both cases are reviewed. The differences and similarities between two- and three-dimensional convection are studied using $Nu(Ra)$ for $\mathit{Pr}= 4. 38$ and $\mathit{Pr}= 0. 7$ and $Nu(Pr)$ for $Ra$ up to $1{0}^{8} $. In the $Nu(Ra)$ scaling at higher $Pr$, two- and three-dimensional convection is very similar, differing only by a constant factor up to $\mathit{Ra}= 1{0}^{10} $. In contrast, the difference is large at lower $Pr$, due to the strong roll state dependence of $Nu$ in two dimensions. The behaviour of $Nu(Pr)$ is similar in two and three dimensions at large $Pr$. However, it differs significantly around $\mathit{Pr}= 1$. The Reynolds number values are consistently higher in two dimensions and additionally converge at large $Pr$. Finally, the thermal boundary layer profiles are compared in two and three dimensions.

Direct numerical simulations of Rayleigh–Bénard convection in water with non-Oberbeck–Boussinesq effects

2019 ◽  
Vol 881 ◽  
pp. 1073-1096 ◽  
Author(s):  
Andreas D. Demou ◽  
Dimokratis G. E. Grigoriadis
Keyword(s):  
Numerical Simulations ◽  
Two Dimensions ◽  
Direct Numerical Simulations ◽  
Wall Region ◽  
Number Range ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Near Wall

Rayleigh–Bénard convection in water is studied by means of direct numerical simulations, taking into account the variation of properties. The simulations considered a three-dimensional (3-D) cavity with a square cross-section and its two-dimensional (2-D) equivalent, covering a Rayleigh number range of $10^{6}\leqslant Ra\leqslant 10^{9}$ and using temperature differences up to 60 K. The main objectives of this study are (i) to investigate and report differences obtained by 2-D and 3-D simulations and (ii) to provide a first appreciation of the non-Oberbeck–Boussinesq (NOB) effects on the near-wall time-averaged and root-mean-squared (r.m.s.) temperature fields. The Nusselt number and the thermal boundary layer thickness exhibit the most pronounced differences when calculated in two dimensions and three dimensions, even though the $Ra$ scaling exponents are similar. These differences are closely related to the modification of the large-scale circulation pattern and become less pronounced when the NOB values are normalised with the respective Oberbeck–Boussinesq (OB) values. It is also demonstrated that NOB effects modify the near-wall temperature statistics, promoting the breaking of the top–bottom symmetry which characterises the OB approximation. The most prominent NOB effect in the near-wall region is the modification of the maximum r.m.s. values of temperature, which are found to increase at the top and decrease at the bottom of the cavity.

scholarly journals Buoyancy statistics in moist turbulent Rayleigh–Bénard convection

2010 ◽  
Vol 648 ◽  
pp. 509-519 ◽  
Author(s):  
JÖRG SCHUMACHER ◽  
OLIVIER PAULUIS
Keyword(s):  
Piecewise Linear ◽  
Three Dimensional ◽  
Boussinesq Approximation ◽  
Phase Changes ◽  
Bénard Convection ◽  
Benard Convection ◽  
Convection Layer ◽  
The Impact ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We study shallow moist Rayleigh–Bénard convection in the Boussinesq approximation in three-dimensional direct numerical simulations. The thermodynamics of phase changes is approximated by a piecewise linear equation of state close to the phase boundary. The impact of phase changes on the turbulent fluctuations and the transfer of buoyancy through the layer is discussed as a function of the Rayleigh number and the ability to form liquid water. The enhanced buoyancy flux due to phase changes is compared with dry convection reference cases and related to the cloud cover in the convection layer. This study indicates that the moist Rayleigh–Bénard problem offers a practical framework for the development and evaluation of parameterizations for atmospheric convection.

scholarly journals Rayleigh–Bénard convection with a melting boundary

2018 ◽  
Vol 858 ◽  
pp. 437-473 ◽  
Author(s):  
B. Favier ◽  
J. Purseed ◽  
L. Duchemin
Keyword(s):  
Heat Flux ◽  
Stokes Equations ◽  
Two Dimensions ◽  
Convection Cell ◽  
Solid Boundary ◽  
Melting Front ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We study the evolution of a melting front between the solid and liquid phases of a pure incompressible material where fluid motions are driven by unstable temperature gradients. In a plane-layer geometry, this can be seen as classical Rayleigh–Bénard convection where the upper solid boundary is allowed to melt due to the heat flux brought by the fluid underneath. This free-boundary problem is studied numerically in two dimensions using a phase-field approach, classically used to study the melting and solidification of alloys, which we dynamically couple with the Navier–Stokes equations in the Boussinesq approximation. The advantage of this approach is that it requires only moderate modifications of classical numerical methods. We focus on the case where the solid is initially nearly isothermal, so that the evolution of the topography is related to the inhomogeneous heat flux from thermal convection, and does not depend on the conduction problem in the solid. From a very thin stable layer of fluid, convection cells appear as the depth – and therefore the effective Rayleigh number – of the layer increases. The continuous melting of the solid leads to dynamical transitions between different convection cell sizes and topography amplitudes. The Nusselt number can be larger than its value for a planar upper boundary, due to the feedback of the topography on the flow, which can stabilize large-scale laminar convection cells.

scholarly journals Three-dimensional visualization of columnar vortices in rotating Rayleigh–Bénard convection

2020 ◽  
Vol 23 (4) ◽  
pp. 635-647
Author(s):  
Kodai Fujita ◽  
Yuji Tasaka ◽  
Takatoshi Yanagisawa ◽  
Daisuke Noto ◽  
Yuichi Murai
Keyword(s):  
Three Dimensional ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Turbulent Rayleigh–Bénard convection in a near-critical fluid by three-dimensional direct numerical simulation

2009 ◽  
Vol 619 ◽  
pp. 127-145 ◽  
Author(s):  
G. ACCARY ◽  
P. BONTOUX ◽  
B. ZAPPOLI
Keyword(s):  
Numerical Simulations ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Thermal Balance ◽  
Transition To Turbulence ◽  
Convective Structures ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

This paper presents state of the art three-dimensional numerical simulations of the Rayleigh–Bénard convection in a supercritical fluid. We consider a fluid slightly above its critical point in a cube-shaped cell heated from below with insulated sidewalls; the thermodynamic equilibrium of the fluid is described by the van der Waals equation of state. The acoustic filtering of the Navier–Stokes equations is revisited to account for the strong stratification of the fluid induced by its high compressibility under the effect of its own weight. The hydrodynamic stability of the fluid is briefly reviewed and we then focus on the convective regime and the transition to turbulence. Direct numerical simulations are carried out using a finite volume method for Rayleigh numbers varying from 106 up to 108. A spatiotemporal description of the flow is presented from the convection onset until the attainment of a statistically steady state of heat transfer. This description concerns mainly the identification of the vortical structures in the flow, the distribution of the Nusselt numbers on the horizontal isothermal walls, the structure of the temperature field and the global thermal balance of the cavity. We focus on the influence of the strong stratification of the fluid on the penetrability of the convective structures in the core of the cavity and on its global thermal balance. Finally, a comparison with the case of a perfect gas, at the same Rayleigh number, is presented.

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