scholarly journals An experimental investigation of convection in a fluid that exhibits phase change

1981 ◽  
Vol 102 ◽  
pp. 85-100 ◽  
Author(s):  
D. E. Fitzjarrald
Keyword(s):  
Thin Layer ◽  
Phase Change ◽  
Latent Heat ◽  
Thermal Gradient ◽  
Lower Boundary ◽  
Working Fluid ◽  
Heavy Fluid ◽  
Convective Motions ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Convection flows have been systematically observed in a layer of fluid between two isothermal horizontal boundaries. The working fluid was a nematic liquid crystal, which exhibits a liquid–liquid phase change at which latent heat is released and the density changed. In addition to ordinary Rayleigh–Bénard convection when either phase is present alone, there exist two distinct types of convective motions initiated by the unstable density difference. When a thin layer of heavy fluid is present near the top boundary, hexagons with downgoing centres exist with no imposed thermal gradient. When a thin layer of light fluid is brought on near the lower boundary, the hexagons have upshooting centres. In both cases, the motions are kept going once they are initiated by the instability due to release of latent heat. Relation of the results to applicable theories is discussed.

The large-scale flow structure in turbulent rotating Rayleigh–Bénard convection

2011 ◽  
Vol 688 ◽  
pp. 461-492 ◽  
Author(s):  
Stephan Weiss ◽  
Guenter Ahlers
Keyword(s):  
Large Scale ◽  
Working Fluid ◽  
Flow Mode ◽  
Unexpected Result ◽  
Vertical Sidewall ◽  
Number Range ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

AbstractWe report on the influence of rotation about a vertical axis on the large-scale circulation (LSC) of turbulent Rayleigh–Bénard convection in a cylindrical vessel with aspect ratio $\Gamma \equiv D/ L= 0. 50$ (where $D$ is the diameter and $L$ the height of the sample). The working fluid is water at an average temperature ${T}_{av} = 40{~}^{\ensuremath{\circ} } \mathrm{C} $ with a Prandtl number $\mathit{Pr}= 4. 38$. For rotation rates $\Omega \lesssim 1~\mathrm{rad} ~{\mathrm{s} }^{\ensuremath{-} 1} $, corresponding to inverse Rossby numbers $1/ \mathit{Ro}$ between 0 and 20, we investigated the temperature distribution at the sidewall and from it deduced properties of the LSC. The work covered the Rayleigh-number range $2. 3\ensuremath{\times} 1{0}^{9} \lesssim \mathit{Ra}\lesssim 7. 2\ensuremath{\times} 1{0}^{10} $. We measured the vertical sidewall temperature gradient, the dynamics of the LSC and flow-mode transitions from single-roll states (SRSs) to double-roll states (DRSs). We found that modest rotation stabilizes the SRSs. For modest $1/ \mathit{Ro}\lesssim 1$ we found the unexpected result that the vertical LSC plane rotated in the prograde direction (i.e. faster than the sample chamber), with the rotation at the horizontal midplane faster than near the top and bottom. This differential rotation led to disruptive events called half-turns, where the plane of the top or bottom section of the LSC underwent a rotation through an angle of $2\lrm{\pi} $ relative to the main portion of the LSC. The signature of the LSC persisted even for large $1/ \mathit{Ro}$ where Ekman vortices are expected. We consider the possibility that this signature actually is generated by a two-vortex state rather than by a LSC. Whenever possible, we compare our results with those for a $\Gamma = 1$ sample by Zhong & Ahlers (J. Fluid Mech., vol. 665, 2010, pp. 300–333).

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.

Flow reversals in Rayleigh–Bénard convection with non-Oberbeck–Boussinesq effects

2016 ◽  
Vol 798 ◽  
pp. 628-642 ◽  
Author(s):  
Shu-Ning Xia ◽  
Zhen-Hua Wan ◽  
Shuang Liu ◽  
Qi Wang ◽  
De-Jun Sun
Keyword(s):  
Large Scale ◽  
Mass Conservation ◽  
Working Fluid ◽  
Large Temperature ◽  
Cold Wall ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Flow Reversals ◽  
Rayleigh Benard

Flow reversals in two-dimensional Rayleigh–Bénard convection led by non-Oberbeck–Boussinesq (NOB) effects due to large temperature differences are studied by direct numerical simulation. Perfect gas is chosen as the working fluid and the Prandtl number is 0.71 for the reference state. If NOB effects are included, the flow pattern $P_{11}$ with only one dominant roll often becomes unstable by the growth of the cold corner roll, which sometimes results in cession-led flow reversals. By exploiting the vorticity transport equation, it is found that the asymmetries of buoyancy and viscous forces are responsible for the growth of the cold corner roll because both such asymmetries cause an imbalance between the corner rolls and the large-scale circulation (LSC). The buoyancy force near the cold wall increases and decreases near the hot wall originating from the temperature-dependent isobaric thermal expansion coefficient ${\it\alpha}=1/T$ if NOB effects are included. Moreover, the decreased dissipation due to lower viscosity is favourable for the growth of the cold corner roll, while the increased viscosity further suppresses the growth of the hot corner roll. Finally, it is found that the boundary layer near the cold wall plays an important role in the mass transport from LSC to corner rolls subject to mass conservation.

scholarly journals ROBUST HETEROCLINIC CYCLES IN TWO-DIMENSIONAL RAYLEIGH–BÉNARD CONVECTION WITHOUT BOUSSINESQ SYMMETRY

2002 ◽  
Vol 12 (11) ◽  
pp. 2501-2522 ◽  
Author(s):  
ISABEL MERCADER ◽  
JOANA PRAT ◽  
EDGAR KNOBLOCH
Keyword(s):  
Rayleigh Number ◽  
Lower Boundary ◽  
Two Dimensions ◽  
External Parameter ◽  
Onset Of Convection ◽  
Current Dissipation ◽  
Parameter Values ◽  
Rayleigh Benard Convection ◽  
Spatial Resonance ◽  
Rayleigh Benard

The onset of convection in systems that are heated via current dissipation in the lower boundary or that lose heat from the top boundary via Newton's law of cooling is formulated as a bifurcation problem. The Rayleigh number as usually defined is shown to be inappropriate as a bifurcation parameter since the temperature difference across the layer depends on the amplitude of convection and hence changes as convection evolves at fixed external parameter values. A modified Rayleigh number is introduced that does remain constant even when the system is evolving, and solutions obtained with the standard formulation are compared with those obtained via the new one. Near the 1 : 2 spatial resonance in low Prandtl number fluids these effects open up intervals of Rayleigh number with no stable solutions in the form of steady convection or steadily traveling waves. Direct numerical simulations in two dimensions show that in such intervals the dynamics typically take the form of a nearly heteroclinic modulated traveling wave. This wave may be quasiperiodic or chaotic.

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.

Numerical and Experimental Investigation of Phase Change Heat Transfer in the Presence of Rayleigh–Benard Convection

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Mohammad Parsazadeh ◽  
Xili Duan
Keyword(s):  
Nusselt Number ◽  
Phase Change ◽  
Local Heat ◽  
Liquid Interface ◽  
Interface Location ◽  
Local Heat Flux ◽  
Solid Liquid Interface ◽  
Solid Liquid ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Abstract This research investigates the melting rate of a phase change material (PCM) in the presence of Rayleigh–Benard convection. A scaling analysis is conducted for the first time for such a problem, which is useful to identify the parameters affecting the phase change rate and to develop correlations for the solid–liquid interface location and the Nusselt number. The solid–liquid interface and flow patterns in the liquid region are analyzed for PCM in a rectangular enclosure heated from bottom. Numerical and experimental results both reveal that the number of Benard cells is proportional to the ratio of the length of the rectangular enclosure over the solid–liquid interface location (i.e.,, the liquified region aspect ratio). Their effect on the local heat flux is also analyzed as the local heat flux profile changes with the solid–liquid interface moving upward. The variations of average Nusselt number are obtained in terms of the Stefan number, Fourier number, and Rayleigh number. Eventually, the experimental and numerical data are used to develop correlations for the solid–liquid interface location and average Nusselt number for this type of melting problems.

scholarly journals Turbulent transition in Rayleigh-Bénard convection with fluorocarbon (a)

2021 ◽  
Vol 136 (1) ◽  
pp. 10003
Author(s):  
Lucas Méthivier ◽  
Romane Braun ◽  
Francesca Chillà ◽  
Julien Salort
Keyword(s):  
Heat Transfer ◽  
Velocity Field ◽  
Rayleigh Number ◽  
Working Fluid ◽  
Turbulent Transition ◽  
Bénard Convection ◽  
Benard Convection ◽  
Image Velocimetry ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Abstract We present measurements of the global heat transfer and the velocity field in two Rayleigh-Bénard cells (aspect ratios 1 and 2). We use Fluorinert FC770 as the working fluid, up to a Rayleigh number . The velocity field is inferred from sequences of shadowgraph pattern using a Correlation Image Velocimetry (CIV) algorithm. Indeed the large number of plumes, and their small characteristic scale, make it possible to use the shadowgraph pattern produced by the thermal plumes in the same manner as particles in Particle Image Velocimetry (PIV). The method is validated in water against PIV, and yields identical wind velocity estimates. The joint heat transfer and velocity measurements allow to compute the scaling of the kinetic dissipation rate which features a transition from a laminar scaling to a turbulent Re 3 scaling. We propose that the turbulent transition in Rayleigh-Bénard convection is controlled by a threshold Péclet number rather than a threshold Rayleigh number, which may explain the apparent discrepancy in the literature regarding the “ultimate” regime of convection.

Rayleigh–Bénard convection in the presence of spatial temperature modulations

2011 ◽  
Vol 673 ◽  
pp. 318-348 ◽  
Author(s):  
G. FREUND ◽  
W. PESCH ◽  
W. ZIMMERMANN
Keyword(s):  
Rayleigh Number ◽  
Numerical Solutions ◽  
Critical Rayleigh Number ◽  
Lower Boundary ◽  
Spatial Modulation ◽  
Bénard Convection ◽  
Benard Convection ◽  
Wide Range ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Motivated by recent experiments, we study a rich variation of the familiar Rayleigh–Bénard convection (RBC), where the temperature at the lower boundary varies sinusoidally about a mean value. As usual the Rayleigh number R measures the average temperature gradient, while the additional spatial modulation is characterized by a (small) amplitude δm and a wavevector qm. Our analysis relies on precise numerical solutions of suitably adapted Oberbeck–Boussinesq equations (OBE). In the absence of forcing (δm = 0), convection rolls with wavenumber qc bifurcate only for R above the critical Rayleigh number Rc. In contrast, for δm≠0, convection is unavoidable for any finite R; in the most simple case in the form of ‘forced rolls’ with wavevector qm. According to our first comprehensive stability diagram of these forced rolls in the qm – R plane, they develop instabilities against resonant oblique modes at R ≲ Rc in a wide range of qm/qc. Only for qm in the vicinity of qc, the forced rolls remain stable up to fairly large R > Rc. Direct numerical simulations of the OBE support and extend the findings of the stability analysis. Moreover, we are in line with the experimental results and also with some earlier theoretical results on this problem, based on asymptotic expansions in the limit δm → 0 and R → Rc. It is satisfying that in many cases the numerical results can be directly interpreted in terms of suitably constructed amplitude and generalized Swift–Hohenberg equations.

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