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 Turbulent Rayleigh–Bénard convection described by projected dynamics in phase space

2015 ◽  
Vol 781 ◽  
pp. 276-297 ◽  
Author(s):  
Johannes Lülff ◽  
Michael Wilczek ◽  
Richard J. A. M. Stevens ◽  
Rudolf Friedrich ◽  
Detlef Lohse
Keyword(s):  
Phase Space ◽  
Two Dimensions ◽  
Heat Diffusion ◽  
Convection Cell ◽  
Parallel Plates ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Average Behaviour

Rayleigh–Bénard convection, i.e. the flow of a fluid between two parallel plates that is driven by a temperature gradient, is an idealised set-up to study thermal convection. Of special interest are the statistics of the turbulent temperature field, which we are investigating and comparing for three different geometries, namely convection with periodic horizontal boundary conditions in three and two dimensions as well as convection in a cylindrical vessel, in order to determine the similarities and differences. To this end, we derive an exact evolution equation for the temperature probability density function. Unclosed terms are expressed as conditional averages of velocities and heat diffusion, which are estimated from direct numerical simulations. This framework lets us identify the average behaviour of a fluid particle by revealing the mean evolution of a fluid with different temperatures in different parts of the convection cell. We connect the statistics to the dynamics of Rayleigh–Bénard convection, giving deeper insights into the temperature statistics and transport mechanisms. We find that the average behaviour is described by closed cycles in phase space that reconstruct the typical Rayleigh–Bénard cycle of fluid heating up at the bottom, rising up to the top plate, cooling down and falling again. The detailed behaviour shows subtle differences between the three cases.

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 Experimental investigation of longitudinal space–time correlations of the velocity field in turbulent Rayleigh–Bénard convection

2011 ◽  
Vol 683 ◽  
pp. 94-111 ◽  
Author(s):  
Quan Zhou ◽  
Chun-Mei Li ◽  
Zhi-Ming Lu ◽  
Yu-Lu Liu
Keyword(s):  
Experimental Investigation ◽  
Velocity Field ◽  
Space Time ◽  
Turbulent Shear ◽  
Convection Cell ◽  
Mean Velocity ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

AbstractWe report an experimental investigation of the longitudinal space–time cross-correlation function of the velocity field, $C(r, \tau )$, in a cylindrical turbulent Rayleigh–Bénard convection cell using the particle image velocimetry (PIV) technique. We show that while Taylor’s frozen-flow hypothesis does not hold in turbulent thermal convection, the recent elliptic model advanced for turbulent shear flows (He & Zhang, Phys. Rev. E, vol. 73, 055303) is valid for the present velocity field for all over the cell, i.e. the isocorrelation contours of the measured $C(r, \tau )$ have an elliptical curve shape and hence $C(r, \tau )$ can be related to $C({r}_{E} , 0)$ via ${ r}_{E}^{2} = (r\ensuremath{-} U\tau )^{2} + {V}^{2} {\tau }^{2} $ with $U$ and $V$ being two characteristic velocities. We further show that the fitted $U$ is proportional to the mean velocity of the flow, but the values of $V$ are larger than the theoretical predictions. Specifically, we focus on two representative regions in the cell: the region near the cell sidewall and the cell’s central region. It is found that $U$ and $V$ are approximately the same near the sidewall, while $U\simeq 0$ at the cell centre.

The effect of boundary properties on controlled Rayleigh–Bénard convection

2000 ◽  
Vol 411 ◽  
pp. 39-58 ◽  
Author(s):  
LAURENS E. HOWLE
Keyword(s):  
Heat Flux ◽  
Control Method ◽  
Lower Boundary ◽  
Bénard Convection ◽  
Benard Convection ◽  
Boundary Properties ◽  
Parameter Ranges ◽  
Differential Control ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We investigate the effect of the finite horizontal boundary properties on the critical Rayleigh and wave numbers for controlled Rayleigh–Bénard convection in an infinite horizontal domain. Specifically, we examine boundary thickness, thermal diffusivity and thermal conductivity. Our control method is through perturbation of the lower-boundary heat flux. A linear proportional-differential control method uses the local amplitude of a shadowgraph to actively redistribute the lower-boundary heat flux. Realistic boundary conditions for laboratory experiments are selected. Through linear stability analysis we examine, in turn, the important boundary properties and make predictions of the properties necessary for successful control experiments. A surprising finding of this work is that for certain realistic parameter ranges, one may find an isola to time-dependent convection as the primary bifurcation.

LBE SIMULATIONS OF RAYLEIGH-BÉNARD CONVECTION ON THE APE100 PARALLEL PROCESSOR

1993 ◽  
Vol 04 (05) ◽  
pp. 993-1006 ◽  
Author(s):  
A. BARTOLONI ◽  
C. BATTISTA ◽  
S. CABASINO ◽  
P. S. PAOLUCCI ◽  
J. PECH ◽  
...  
Keyword(s):  
Lattice Boltzmann ◽  
Parallel Computer ◽  
Convection Cell ◽  
Two Dimensional ◽  
Parallel Processor ◽  
Bénard Convection ◽  
Benard Convection ◽  
Dynamics Simulations ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

In this paper we describe an implementation of the Lattice Boltzmann Equation method for fluid-dynamics simulations on the APE100 parallel computer. We have performed a simulation of a two-dimensional Rayleigh-Bénard convection cell. We have tested the theory proposed by Shraiman and Siggia for the scaling of the Nusselt number vs. Rayleigh number.

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