Convection de Rayleigh-Bénard pour des fluides rhéofluidifiants : approche théorique et expérimentale (original) (raw)
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We present an experimental and theoretical study of Rayleigh-Bénard convection in shearthinning fluids with temperature dependent properties. Experiments were performed using a cylindrical cell of radiusR = 60 mm and height adjustable atd = 15 mm and 20 mm giving a radius-toheight ratio L = 4 and 3 respectively. The fluids used are glycerol (Newtonian fluid) and aqueous xanthan gum solutions (shear-thinning fluids) at 1000 ppm and 1200 ppm. Convection patterns are visualized by the shadowgraph method. In the theoretical part of this study, the weakly nonlinear
Effects of modulation on Rayleigh-Benard convection. Part I
International Journal of Mathematics and Mathematical Sciences, 2004
The linear stability of a horizontal layer of fluid heated from below and above is considered. In addition to a steady temperature difference between the walls of the fluid layer, a time-dependent periodic perturbation is applied to the wall temperatures. Only infinitesimal disturbances are considered. Numerical results for the critical Rayleigh number are obtained at various Prandtl numbers and for various values of the frequency. Some comparisons have been made with the known results.
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L'objectif du présent travail est d'analyser, par le biais d'une méthode numérique basée sur les volumes finis, l'effet du nombre de Rayleigh ainsi que la présence d'un obstacle isotherme sur les caractéristiques hydrodynamiques et thermiques de l'écoulement d'un fluide newtonien. Ce dernier se trouve emprisonné dans une cavité carrée, de parois verticales isothermes et froides, d'une paroi inférieure isotherme, maintenue à une température chaude et d'une paroi supérieure adiabatique. Le code de calcul basé sur l'algorithme SIMPLER a été validé par comparaison des résultats avec ceux de la littérature. Les résultats
Rayleigh-Bénard Convection: Thirty Years of Experimental, Theoretical, and Modeling Work
Springer Tracts in Modern Physics, 2006
A brief review of Rayleigh-Bénard studies performed all along the twentieth century is presented, with an emphasis on the transition to turbulence and the appropriate theoretical framework, relying on the strength of confinement effects and the distance to threshold, either dynamical systems for temporal chaos in the strongly confined case, or models of space-time chaos when confinement effects are weak.
Physics of Fluids, 2023
The effect of viscoelasticity on the flow and heat transport in the Rayleigh-Bénard convection (RBC) in a rectangular with horizontal periodic boundary is investigated via direct numerical simulation. The working fluid is described by the finitely extensible nonlinear elastic-Peterlin (FENE-P) constitutive model that is able to capture some of the most important polymeric flow behaviors. Numerical simulations are conducted at a low concentration β = 0.9, where β = μs/μ0, μs is the solvent viscosity, μ0 = μs + μp is sum of μs and the polymer viscosity μp. A parametric analysis is performed to understand the influence of the Weissenberg number Wi, the viscosity ratio β and the extension length L on the oscillating mode of the viscoelastic RBC. It is found that both Wi and β weakly inhibit the convection onset and the transition from steady to oscillatory convection. The amplitude and frequency of the oscillations in the oscillatory flow regime are both suppressed. However, the elastic nonlinearity may make the flow transition irregular and even may bring about the relaminarization or lead to the convection cells traveling in the horizontal direction. The extension length L may induce multiple pairs of roll flow patterns at a specific setting of (Ra, Wi). Heat transport is reduced by elasticity but still obeys the power law with Ra if the flow pattern has one pair of rolls. However, heat transfer enhancement occurs if multiple pairs of rolls are induced.
Journal of Fluid Mechanics, 2015
The convective and absolute nature of instabilities in Rayleigh-Bénard-Poiseuille (RBP) mixed convection for viscoelastic fluids is examined numerically with a shooting method as well as analytically with a one-mode Galerkin expansion. The viscoelastic fluid is modelled by means of a general constitutive equation that encompasses the Maxwell model and the Oldroyd-B model. In comparison to Newtonian fluids, two more dimensionless parameters are introduced, namely the elasticity number λ 1 and the ratio Γ between retardation and relaxation times. Temporal stability analysis of the basic state showed that the three-dimensional thermoconvective problem can be Squire-transformed. Therefore, one must distinguish mainly between two principal roll orientations: transverse rolls TRs (rolls with axes perpendicular to the Poiseuille flow direction) and longitudinal rolls LRs (rolls with axes parallel to the Poiseuille flow direction). The critical Rayleigh number for the appearance of LRs is found to be independent of the Reynolds number (Re). Depending on λ 1 and Γ , two different regimes can be distinguished. In the weakly elastic regime, the emerging LRs are stationary, while they are oscillatory in the strongly elastic regime. For TRs, it is found that in the weakly elastic regime, the stabilization effect of Re is more important than in Newtonian fluids. Moreover, for sufficiently elastic fluids a jump is observed in the oscillation frequencies and wavenumbers for moderate Re. In the strongly elastic regime, the effect of the imposed throughflow is to promote the appearance of the upstream moving TRs for low values of Re, which are replaced by downstream moving TRs for higher values of Re. Moreover, the results proved that, contrary to the case where Re = 0, the elasticity number λ 1 (the ratio Γ ) has a strongly stabilizing (destabilizing) effect when the throughflow is added. The influence of the rheological parameters on the transition curves from convective to absolute instability in the Reynolds-Rayleigh number plane is also determined. We show that the viscoelastic character of the fluid hastens the transition to absolute instability and even may suppress the convective/absolute transition. Throughout this paper, similarities and differences with the corresponding problem for Newtonian fluids are highlighted.
Effect of Coriolis force on Rayleigh-Bénard convection with internal heat generation
International Journal of Advanced Technology and Engineering Exploration
The objective of this paper is to analyze the influence of the Coriolis force and internal heat source on Rayleigh-Bénard convection in a Boussinesquian fluid of depth d. A linear theory which is oriented towards the normal mode analysis technique is used for this mono-diffusive convection in order to find the criteria for the onset of Rayleigh-Bénard convection. The eigenvalue of the said problem was obtained by the use of the Galerkin method in the cases of rigid-rigid, rigid-free, and free-free velocity boundary combinations considering the isothermal and adiabatic temperature boundaries that determine the stability of the system. The effects of various parameters, Taylor number and the internal Rayleigh number are put under consideration only for stationary convection. Treating Taylor number as a critical parameter, shown that it plays a major role in stabilization of the system in case of any particular infinitesimal disturbance. The destabilization of the system has been possible with rotation by treating internal Rayleigh numbers as a critical parameter since the increase in values of the internal Rayleigh number advances the onset of convection. Oscillatory convection seems highly improbable as the scaled frequency of oscillation remains less than 0 for all combinations of Prandtl number, internal Rayleigh number, and Taylor number.
Rayleigh-Bénard convection in shear-thinning fluids : Theoretical and experimental approaches
2016
Theoretical and experimental study of Rayleigh-Benard convection in a non-Newtonian shear-thinning fluid was performed. The theoretical approach consists in a linear and a weakly nonlinear of thermo-convective instability in a horizontal layer of a non-Newtonian fluid, assumed infinite in extent, heated from below and cooled from above. The rheological behavior of the fluid is described by the Carreau model. For this rheological model, the critical threshold is the same as for a Newtonian fluid. The objective of the weakly non linear analysis is to determine on one hand the critical value of the shear-thinning degree above which the bifurcation becomes subcritical and on the other hand, the influence of shear-thinning effects on the pattern selection near the onset, taking into account the possibility of wall slip, a finite thermal conductivity of the walls as well as the thermo-dependency of the viscosity. The impact on the viscosity field and on the evolution of the Nusselt number...
Pattern Selection in Rayleigh Bénard Convection with Non-Linear Viscoelastic Fluids
Physical Review Fluids, 2022
Rayleigh-Bénard convection in a rectangular enclosure of aspect ratio 2:1 filled by a class of non-linear viscoelastic fluids represented by the Phan Thien-Tanner (PTT) constitutive equation is investigated numerically. Governing equations are discretized by finite difference methods in space and time. The momentum and PTT constitutive equations are written in a quasi-linear formulation. Quasi-linear terms are treated with the High-Order Upwind Central (HOUC) method and velocity-pressure coupling is handled through the projection method. The developed model is validated for Oldroyd-B type of working fluids. The onset of time-dependent convection is observed and the critical Rayleigh number is determined for PTT type of fluids. Time-dependent flow pattern transition is investigated and explained. Transition from time-dependent flow to steady-state flow is observed at a higher Rayleigh number and the corresponding critical Rayleigh number is computed, for the first time in the literature. This is a new original finding. The effect of the rheological parameters on heat transfer is investigated.