Model for classical and ultimate regimes of radiatively driven turbulent convection.

In a standard Rayleigh-Bénard experiment, a layer of fluid is confined between two horizontal plates and the convection regime is controlled by the temperature difference between the hot lower plate and the cold upper plate. The effect of direct heat injection into the fluid layer itself, for example by light absorption, is studied here theoretically. In this case, the Nusselt number (N u) depends on two non-dimensional parameters: the Rayleigh number (Ra) and the ratio between the spatial extension of the heat source (l) and the height of the fluid layer (h). For both the well-known classical and ultimate convection regimes, the theory developed here gives an analytical formula for the variations of the Nusselt number as a function of Ra and the l/h ratio. For large Rayleigh numbers and in the classical convection regime, by increasing l/h from 0 to 1/2, the Ra-dependent Nusselt number gradually changes from the standard scaling N u ∼ Ra 1/3 to the asymptotic scaling N u ∼ Ra 2/3. For the ultimate convection regime, N u gradually changes from N u ∼ Ra 1/2 scaling to an asymptotic behaviour seen only at very high Ra for which N u ∼ Ra 2. This theory is validated by the recent experimental results given by Bouillaut et al. (2019), at least in the classical regime. The predictions for the ultimate regime cannot be confirmed at this time due to the absence of experimental or numerical works on Rayleigh-Bénard convection both driven by internal sources and for very large Ra

Convection in a vertical channel

International audienceThe flow generated by heat convection in a long, vertical channel is studied by means of particle imagery velocimetry techniques, with the help of the thermal measurements from a previous paper (Gibert et al 2009 Phys. Fluids 21 035109). We analyse the mean velocity profiles and the Reynolds stresses, and compare the present results with the previous ones obtained in a larger cell and at a larger Reynolds number.We calculate the horizontal temperature profile and the related horizontal heat flux. The pertinence of effective turbulent diffusivity and viscosity is confirmed by the low value of the associated mixing length. We study the one-point and two-point statistics of both velocity components. We show how the concept of turbulent viscosity explains the relations between the local probability density functions (pdf) of fluctuations for temperature, vertical and horizontal velocity components. Despite the low Reynolds number values explored, some conclusions can be drawn about the small scale velocity differences and the related energy cascade

Comparison between rough and smooth plates within the same Rayleigh-Bénard cell

International audienceIn a Rayleigh-Bénard cell at high Rayleigh number, the bulk temperature is nearly uniform. The mean temperature gradient differs from zero only in the thin boundary layers close to the plates. Measuring this bulk temperature allows to separately determine the thermal impedance of each plate. In this work, the bottom plate is rough and the top plate is smooth; both interact with the same bulk flow. We compare them and address in particular the question whether the influence of roughness goes through a modification of the bulk flow

Thermal boundary layer near roughnesses in turbulent Rayleigh-Bénard convection: flow structure and multistability

We present global heat-transfer and local temperature measurements, in an asymmetric parallelepiped Rayleigh-B ́enard cell, in which controlled square-studs roughnesses have been added. A global heat transfer enhancement arises when the thickness of the boundary layer matches the height of the roughnesses. The enhanced regime exhibits an increase of the heat transfer scaling. Local temperature measurements have been carried out in the range of parameters where the enhancement of the global heat transfer is observed. They show that the boundary layer at the top of the square-stub roughness is thinner than the boundary layer of a smooth plate, which accounts for most of the heat-transfer enhancement. We also report multistability at long time scales between two enhanced heat-transfer regimes. The flow structure of both regimes is imaged with background-oriented synthetic Schlieren and reveals intermittent bursts of coherent plumes

Etude du transfert thermique dans un réacteur-échangeur à écoulement laminaire.

Les réacteurs-échangeurs micro-fluidiques permettent d'effectuer des réactions chimiques complexes sur des échantillons de taille réduite et d'analyser rapidement les produits obtenus. Le contrôle de la réaction chimique nécessite la maîtrise de deux processus fondamentaux : le mélange optimal des réactifs et le contrôle de la température en tout point du réacteur. En micro-fluidique, le mélange peut être assuré par le phénomène physique d'advection chaotique. Notre équipe a développé un mélangeur chaotique statique appelé ""MLLM"" (Multi-Level Laminating Mixer) qui approche au plus près la transformation du boulanger permettant ainsi un mélange efficace (Carrière, Phys. Fluids, 2007 ; Liao et al., Lab Chip, 2012 ; Creyssels et al., Int. J. Heat Mass Transfer, 2015). La présente étude vise à montrer la pertinence de ce dispositif utilisé comme un échangeur thermique pour des fluides, des débits et des tailles de canaux correspondant à ceux présents dans les micro-réacteurs fluidiques. Des mesures expérimentales de l'efficacité thermique du MLLM ont été réalisées en employant de l'eau et des mélanges d'eau et de glycérol. Des simulations numériques de l'écoulement au sein du mélangeur-échangeur ont également été menées (code OpenFOAM) et les résultats obtenus sont directement comparés aux résultats expérimentaux. Enfin, une comparaison directe de l'efficacité thermique avec le cas théorique du tube droit de Graetz est présentée

Etude du phénomène d'entraînement dans des jets turbulents dits Non-Boussinesq

Nous présentons une étude numérique de la dynamique de jets turbulents de fluides léger ou lourd dans un environnement non stratifié. La densité du jet est choisie bien inférieure ou bien supérieure à la densité du fluide environnant afin d'explorer les effets dits ""non-Boussinesq"" sur la dynamique de l'écoulement. Une question centrale est de savoir comment l'entraînement du fluide ambiant par le jet est modifiée lorsque l'écart entre les densités du jet et de l'environnement est fortement augmenté. L'entraînement est mesurée traditionnellement par un coefficient ? qui représente le rapport entre la vitesse d'entraînement horizontale du fluide ambiant et la vitesse verticale du jet. L'étude expérimentale de Ricou et Spalding (1961) a été interprétée de la façon suivante: le coefficient ? évoluerait comme la racine carrée du rapport de densité entre les deux fluides. Ainsi, pour un jet très léger, ? serait plus petit que pour un jet traditionnel dit ""Boussinesq"" tandis que pour un jet très lourd ? augmenterait comme la racine carrée du rapport de densité. Cependant l'origine physique de cette dépendance du coefficient d'entraînement avec le rapport de densité est sujette à caution. Afin de déterminer la dépendance du coefficient d'entraînement avec la densité du jet, des simulations numériques de jets légers et lourds ont été menées et les résultats ont été interprétés en suivant l'analyse proposée par Craske et Van Reeuwijk (2015) et Ezzamel et al. (2015). Cet approche permet de sonder les effets du rapport de densité des deux fluides sur la production d'énergie cinétique turbulente ainsi que ses relations avec le coefficient d'entraînement

Model for classical and ultimate regimes of radiatively driven turbulent convection.

In a standard Rayleigh-Bénard experiment, a layer of fluid is confined between two horizontal plates and the convection regime is controlled by the temperature difference between the hot lower plate and the cold upper plate. The effect of direct heat injection into the fluid layer itself, for example by light absorption, is studied here theoretically. In this case, the Nusselt number (N u) depends on two non-dimensional parameters: the Rayleigh number (Ra) and the ratio between the spatial extension of the heat source (l) and the height of the fluid layer (h). For both the well-known classical and ultimate convection regimes, the theory developed here gives an analytical formula for the variations of the Nusselt number as a function of Ra and the l/h ratio. For large Rayleigh numbers and in the classical convection regime, by increasing l/h from 0 to 1/2, the Ra-dependent Nusselt number gradually changes from the standard scaling N u ∼ Ra 1/3 to the asymptotic scaling N u ∼ Ra 2/3. For the ultimate convection regime, N u gradually changes from N u ∼ Ra 1/2 scaling to an asymptotic behaviour seen only at very high Ra for which N u ∼ Ra 2. This theory is validated by the recent experimental results given by Bouillaut et al. (2019), at least in the classical regime. The predictions for the ultimate regime cannot be confirmed at this time due to the absence of experimental or numerical works on Rayleigh-Bénard convection both driven by internal sources and for very large Ra

Model for thermal convection with uniform volumetric energy sources

International audienceA theoretical model is derived to predict both the heat fluxes at the upper and lower horizontal surfaces of an internally heated (IH) convection cell by extending the well-known [5] theory. The approach of [1] is generalized for a fluid heated internally and uniformly, confined between top and bottom plates of equal temperature. For each plate, a Nusselt number is defined and an analytical formula is given to predict its variations with the Rayleigh and Prandtl numbers. The turbulent flow produced in the upper half of the IH convection cell is very similar to that observed in standard Rayleigh-Bénard (RB) convection. On the contrary, the lower plate is swept by the large scale flow that circulates through the entire cell. The corresponding boundary layer is therefore modelled by a laminar boundary layer of the Blasius type. These predictions are confirmed by previous experimental and numerical results

Model for classical and ultimate regimes of radiatively driven turbulent convection.

In a standard Rayleigh-Bénard experiment, a layer of fluid is confined between two horizontal plates and the convection regime is controlled by the temperature difference between the hot lower plate and the cold upper plate. The effect of direct heat injection into the fluid layer itself, for example by light absorption, is studied here theoretically. In this case, the Nusselt number (N u) depends on two non-dimensional parameters: the Rayleigh number (Ra) and the ratio between the spatial extension of the heat source (l) and the height of the fluid layer (h). For both the well-known classical and ultimate convection regimes, the theory developed here gives an analytical formula for the variations of the Nusselt number as a function of Ra and the l/h ratio. For large Rayleigh numbers and in the classical convection regime, by increasing l/h from 0 to 1/2, the Ra-dependent Nusselt number gradually changes from the standard scaling N u ∼ Ra 1/3 to the asymptotic scaling N u ∼ Ra 2/3. For the ultimate convection regime, N u gradually changes from N u ∼ Ra 1/2 scaling to an asymptotic behaviour seen only at very high Ra for which N u ∼ Ra 2. This theory is validated by the recent experimental results given by Bouillaut et al. (2019), at least in the classical regime. The predictions for the ultimate regime cannot be confirmed at this time due to the absence of experimental or numerical works on Rayleigh-Bénard convection both driven by internal sources and for very large Ra

Stability Analysis of Sheared Thermal Boundary Layers and its Implication for Modelling Turbulent Rayleigh-Bénard Convection

Predicting the heat flux through a horizontal layer of fluid confined between a hot bottom plate anda cold top plate has always been the ultimate goal of theoretical, numerical and experimental work onRayleigh–B ́enard convection. Until now, the Nusselt number (the heat flux in non-dimensional form)has been modelled by one or several power-laws of the three following parameters, the Rayleigh,Reynolds and Prandtl numbers. On the one hand, dimensional analysis can predict the exponent ofeach of these power laws, and on the other hand, experimental and numerical results give the valueof each prefactor. Here, the theoretical approach is different in the sense that a heat flux predictionwithout adjustable parameters is sought. Starting from the early and simple model of Malkus [1]and Howard [2], the value of the Nusselt number is directly deduced from the stability of the twosheared thermal boundary layers along the upper and lower plates and their interaction with thelarge-scale flow developing in the whole fluid. The present approach maintains the simplicity of theMalkus–Howard model, including the absence of adjustable parameters for all that the intensityof the large-scale flow is known, and is in excellent agreement with available experimental andnumerical results