Rayleigh-Benard Research Articles

Modulation of Rayleigh–Bénard convection with a large temperature difference by inertial nonisothermal particles

This study investigates the modulation by inertial nonisothermal particles in two-dimensional Rayleigh–Bénard (RB) convection with non-Oberbeck–Boussinesq effects due to a large temperature difference. Direct numerical simulations combined with a Lagrangian point-particle method are performed for 1×106≤Ra≤1×108 and 6.1×10−3≤Stf≤1.2, where the Rayleigh number Ra and Stokes number Stf measure the vigor of convection and particle response time, respectively. The typical aspect ratio Γ = 1 is of primary concern. We find that a horizontally arranged double-roll flow pattern prevails at intermediate Stokes numbers with optimal heat transfer efficiency, which has never been reported before. Compared to the single-phase cases, the heat transfer efficiency is enhanced by a factor of two or three. For micro Stokes numbers, unlike cases in the Oberbeck–Boussinesq limit where the addition of particles causes a small amount of flow structure changes, in this study, it is observed that a tiny volume load of particles could actually induce significant flow oscillations or trigger fluid instability for Ra=106; conversely, for medium Rayleigh numbers (Ra=107), it is found that flow reversal is slightly suppressed by small particles. For intermediate Stokes numbers, where particle–fluid couplings are strongest and a wealth of new phenomena emerge, special attention is paid. Considering different aspect ratios, after the addition of particles, it is found that closed RB systems tend to contain an even number of convection rolls rather than odd ones. Quantitatively, heat transfer also improves significantly for various aspect ratios for intermediate Stokes numbers. Subsequent investigations reveal that the narrowing of the horizontal size of convection rolls cannot fully explain the significant enhancement; instead, it should also be attributed to strong couplings between particles and fluid dynamics. Moreover, it is found that both momentum and thermal couplings play crucial roles in enhancing heat transfer efficiency.

Stability of contact lines in 2D stationary Benard convection

Stability of contact lines in 2D stationary Benard convection

Mean velocity and temperature profiles in turbulent vertical convection

In this study, mean velocity and temperature profiles for turbulent vertical convection (VC) confined in an infinite channel are investigated theoretically. The analysis starts from the governing equations of the thermal flow, with Reynolds shear stress and turbulent heat flux closed by the mixing length theory. Employing a three-sublayer description of the mean fields, the mean velocity and temperature profiles are found to be linear laws near the channel wall (viscosity-dominated sublayer), and they follow power laws close to the channel centre (turbulence-dominated sublayer). The characteristic scales of velocity, temperature and length in the present profiles arise naturally from the system normalisation, rather than from scaling analyses, thus ensuring a sound mathematical description. The derived profiles are verified fully via various literature data available in the classical regime; further, they are compared with the reported profiles, and the results indicate that the present profiles are the only ones with the ability to interpret data accurately from different sources, demonstrating much better versatility. Meanwhile, we provide analytical arguments showing that in the ultimate regime, the mean profiles in VC may remain in power laws, rather than the log laws inferred by analogy with Rayleigh–Bénard convection (RBC) systems. The power profiles recognised in this study are induced by the effect of buoyancy, which is in parallel with the mean flow in VC and contributes to the streamwise momentum transport, whereas in RBC systems, buoyancy is perpendicular to the mean flow, and does not influence the streamwise momentum transport, resulting in log profiles, being similar to the case of wall shear flows.

Rayleigh-Benard Convection Inside Square Cavities Filled with Thermodependent Non-Newtonian Fluids and Subjected to External Magnetic Field

The aim of this study is to numerically evaluate the Rayleigh-Benard natural convection magnetohydrodynamic (MHD) of a non-Newtonian fluid along a square cavity whose viscosity depends on the temperature. The rheological behavior of the fluids under consideration is represented using the Ostwald-De-Weale power law. Subsequently, the dominant equations are transformed into a non-dimensional form and computed using the finite volume method (FVM). The literature was used to validate the model, and excellent agreement was achieved by varying the fluid characteristics with Prandtl numbers , Hartmann numbers, , Rayleigh numbers, , the behavior index, n, and inclination angle, . The numerical results are discussed in terms of velocity, mean Nusselt number , maximum current function , streamlines, and isotherms. The study finds that the onset of convection is delayed with increasing values of n and Ha. Additionally, it revealed that the flow intensity and heat transfer decrease as the Hartmann number rises for both Newtonian and non-Newtonian fluids. At very high Ha values, the heat transfer is mainly assured by the conduction regime. Moreover, the temperature-dependent viscosity in MHD results in the disappearance of the Centro symmetry of the central cell and the migration of the center towards the active wall.

A non-Newtonian thermal lattice Boltzmann method for simulation of Rayleigh–Bénard convection of power-law fluids

Despite the widespread popularity of the Bhatnagar–Gross–Krook lattice Boltzmann (BGK-LB) model due to its simplicity and efficiency, its application in heat transfer involving non-Newtonian fluids (NNFs) has been limited by inherent constraints. This paper proposes a numerically stable BGK-LB model for the thermal flow of NNFs. The modified model incorporates the local shear rate into the equilibrium distribution function of the velocity field and addresses the numerical instability problems encountered in the traditional BGK-LB model under low viscosity conditions by introducing an additional parameter. In addition, a temperature evolution equation that can accurately recover the convective diffusion equation is adopted. The accuracy of the current method is validated by performing simulations of Rayleigh–Bénard convection (RBC) in a square cavity filled with Newtonian fluids and NNFs. Subsequently, simulations are conducted to investigate the behavior of RBC in power-law fluids. The analysis focuses on examining the impact of the Rayleigh number (Ra = 5 × 103 − 105) and the power-law index (n = 0.8–1.3) on the convective structure and heat transfer characteristics while maintaining a fixed Prandtl number (Pr = 7) and aspect ratio (L/H = 2). It is discovered that, for a given n value, the convection intensity and heat transfer rate increase with increasing Ra, which is supported by the increasing trend of the mean Nusselt number (Nū) with Ra. Furthermore, compared to NFs, pseudo-plastic fluids display a higher Nū value due to an augmented heat transfer rate, while dilatant fluids exhibit a lower Nū value owing to a diminished heat transfer rate.

Benard cells – a possible mechanism of the formation of subaquatic and subfluidic stalactites

The mechanism of formation of stalactites in gravity feld of the Earth during their formation in air and subaquatic and subfuidic (magmatic) systems is considered. If the systems represent the cavities in solid bodies with ambient capillary-porous space flled with liquids, then it locally yields the convective subsystems: the Benard cells fxed by the formation of stalactites. The phenomenon is illustrated on examples of malachite, goethite, chalcedony, quartz-feldspar and magnetite stalactites.

Representative velocity scale of Rayleigh‐Bénard convection with shear‐thinning fluids

AbstractAlthough natural convection is frequently encountered in various chemical processes, Rayleigh number (Ra) cannot be defined fully in shear‐thinning fluid systems. In particular, the velocity scale, which is necessary to estimate the effective viscosity of the system, should be discussed carefully. Thus, in this study, the representative velocity scale of Rayleigh‐Bénard (RB) convection, which is a typical example of natural convection, with shear‐thinning fluids was investigated based on the velocity fields obtained using computational fluid dynamics. Numerical simulations revealed that the critical temperature difference at which RB convection starts to fully develop decreases with an increase in the shear‐thinning property. The shear‐thinning property also induced subcritical bifurcation. In addition, the velocity scale of convection increases with an increase in the shear‐thinning property. Thus, the shear‐thinning property is considered to accelerate convection. Compared with several types of velocity scales used by other researchers, significant deviations from the actual scale were observed. Therefore, a new type of velocity scale, including the buoyant to viscous force ratio, arbitrary parameter, and thermal diffusivity, was proposed. The proposed velocity scale allowed an approximate estimation of the actual velocity scale. Although further investigation of the validity is necessary with varying geometries and rheological parameters, this velocity scale will be useful for controlling RB convection with Newtonian/shear‐thinning fluids.

Physical Aspects of 2014 Nobel Prize in Physiology or Medicine: 2. The First Principle and Universality Class for Grid Cells in the Brain

The main purpose of this review article is to use the fluctuation theory of phase transitions for studying the process of the emergence of hexagonal grid cells in the brain (2014 Nobel Prize in Physiology or Medicine). Particular attention is paid to the application of the Feynman’s classification of three stages of the study of natural phenomena for: 1) a brief description of the experimental stage of the discovery of the hexagonal structures of grid cells in human and animal brains; 2) the theoretical stage of research on the hexagon formation in the physical system of Benard cells, as well as the neurophysiological system of grid cells, discovered by Edward Mozer and May-Britt Mozer; 3) the most important stage, which allows one to formulate the first principle of the emergence of grid cells in the brain and, generally speaking, the first principle for the hexagon formation in different objects of inanimate and living nature. Our original theoretical findings are the following: (a) Polyakov’s conformal invariance hypothesis is violated for a system of grid cells in the brain; (b) the system of grid cells in the brain belongs to the universality class including the 3D Ising model in a magnetic field, as well as a real classical liquid-vapor system;(c) to formulate the first principle for a reliable theoretical justification of the emergence of hexagonal grid cells in the brain, it is necessary to use the fluctuating part of Gibbs thermodynamic potential (the Ginzburg–Landau Hamiltonian) for a system with chemical (biochemical) reactions.

Asymmetric PCM melting and thermal convection in a rectangular enclosure with straight and wavy heat transfer passages

Experimental and numerical investigations of thermal convection in the vicinity of a straight and wavy horizontal heat transfer fluid passage (HTF)s placed in a rectangular enclosure filled with phase change material (PCM) are presented. The enthalpy-porosity-based finite volume solver is used to simulate the spatiotemporal evolution of the thermal convection, which is well-complemented by experimental visualization and thermocouple measurements. Heat transfer from the horizontal HTF exhibits asymmetrical melting. Heat diffusion is the dominating energy transfer mechanism on the bottom part of the HTF passage and is compared with the Stefan problem. The temporal evolution of thermal convection on the top part of HTF passage involves three distinct phases of melting, viz. initial conduction phase, Rayleigh–Bénard (R-B) convection with linear convection, and vortex coalescence effects. The final stage of the melting process is influenced by the topography of a peninsula of unmelt PCM, which is influenced by specific top-boundary conditions. Thermal convection in PCM above the wavy HTF passage exhibits restricted plume development leading to an improved melting rate and a higher average melt height. Augmentation of internal convection characteristics of HTF with the evolution of melting is also explored. A systematic investigation of the convection plume development and heat transfer characteristics in PCM by varying the HTF Reynolds (1700<Re<2750) and Stefan numbers (0.4<Ste<0.6) has been carried out, and analyzed the nature of thermal plumes, melt fraction, and average penetration length with the Fourier number. Additionally, novel correlations are proposed between Nusselt and Rayleigh numbers for straight and wavy tubes in the intermediate melting stage (1.3×104<Ra<4.7×107).

Laminar Rayleigh–Benard convection in a closed square field with meshless radial basis function method

Abstract Research on natural convection is exciting in some experimental and numerical cases, especially in rectangular cavities with relatively low heat dissipation and thermal control systems with low cost, reliability, and ease of use. The present study will use the meshless radial basis function method to solve the velocity formulation of the Navier–Stokes equations by varying some nominal Rayleigh numbers of 104, 105, and 106. The numerical accuracy is compared with the previous research. The advantages of the meshless method are that it does not require a structured mesh and does not require inter-nodal connectivity. The results show that the temperature pattern is identical to the previous research. The calculations have been done for three different Rayleigh numbers of 104, 105, and 106 for 151 × 151 nodes. The variations of the Ra number will affect the isothermal, velocity contours, and Nusselt number.

Synchronous optical intensity and phase measurements to characterize Rayleigh-Bénard convection.

Propagation of a laser beam through the Rayleigh-Bénard (RB) convection is experimentally investigated using synchronous optical wavefront and intensity measurements. Experimental results characterize the turbulence strength and length scales, which are used to inform numerical wave optic simulations employing phase screens. Experimentally found parameters are the refractive index structure constant, mean flow rate, kinetic and thermal dissipation rates, Kolmogorov microscale, outer scale, and shape of the refractive index power spectrum using known models. Synchronization of the wavefront and intensity measurements provide statistics of each metric at the same instance in time, allowing for two methods of comparison with numerical simulations. Numerical simulations prove to be within agreement of experimental and published results. Synchronized measurements provided more insight to develop reliable propagation models. It is determined that the RB test bed is applicable for simulating realistic undersea environments.

Rayleigh–Bénard convection of viscoelastic fluids in three-dimension finite cavity

The Rayleigh–Bénard convection (RBC) with viscoelastic fluids has captured wide attention in the past decades, caused by its ubiquitous uses in the heat transfer process. However, the numerical technique for simulating the viscoelastic fluid flows developed slowly until recent years because of the numerical instability raised by the hyperbolic characteristics of the viscoelastic constitutive equation. In the present work, a novel numerical scheme was developed to simulate the three-dimension (3D) RBC with viscoelastic fluids, where the quasi-linear treatment was applied to the hyperbolic terms of the momentum equation and the viscoelastic constitutive equation. The in-house solver was also optimized in the aspect of time cost. The results show that the critical value of convection onset in 3D is near to that in the two-dimension (2D); however, the flow pattern displays the wave characteristics in the horizontal direction. The viscoelastic kinetic energy budget of oscillating convection in 3D still conforms to the energy transport law of that in 2D [Zheng et al., Phys. Rev. Fluids 8, 023303 (2023)].

Simulation of Rayleigh convection during dichloromethane absorption by water using lattice Boltzmann method

Developing dichloromethane (DCM) waste gas purification and absorption technology is consistent with the demand of the circular economy and contributes to the goals of achieving carbon peaking and carbon neutrality. In addition, Rayleigh convection generated during the absorption of DCM by water is of great significance for understanding the interfacial mass transfer mechanism and enhancing the mass transfer efficiency. Thus, the absorption process of DCM discrete diffusion sources was simulated using the two-dimensional lattice Boltzmann method (LBM) with external forces to visualize the effect of Rayleigh convection evolution law on the mass transfer of the absorption process in this study. The concentration and velocity distribution with single or multiple diffusion sources were respectively simulated at 298.15 K and 1.00 atm. The results show that the convection structure of the simulated plume is similar to that of comparable studies, and the convective structure on both sides suppresses the development of the intermediate convective structure when convection occurs. At a constant gas-phase concentration (CB,g), the more the number of diffusion sources, the faster the convective structures integration, and the rapid integration of convective structures is associated with the sharp increasing instantaneous mass transfer flux. Meanwhile, increasing the gas phase concentration can effectively shorten the convection onset time (tc), increase the instantaneous mass transfer flux (Nins,t), and enhance the mass transfer efficiency by calculating the simulated transfer mass data. Furthermore, the critical onset time of Rayleigh convection first lengthens and then shortens with the number of diffusion sources (n) increasing. And the more the number of diffusion sources, the more significant the final cumulative (Nt) absorption amounts are. The simulation results can provide theoretical guidance for enhancing the mass transfer efficiency in the DCM absorption process.

Heat transfer in porous media Rayleigh–Bénard convection at various Prandtl numbers

We perform two-dimensional direct numerical simulations to study the effect of porous media on global transport properties and flow structures in Rayleigh–Bénard (RB) convection at different Prandtl numbers. The simulations are carried out in a square RB cell with uniformly placed circular obstacles, where the porosity spans between ϕ=1 and ϕ=0.75 with the Rayleigh number Ra fixed at 108, at two high Prandtl numbers (10,4.3) and two low Prandtl numbers (0.03,0.1). It is found that the Nusselt number Nu varies non-monotonically with decreasing porosity, first increased and then suppressed at both high-Pr and low-Pr cases, while the transition points are greatly advanced at low Pr. Though the trends are similar at low and high Pr, we point out that the physical mechanisms behind them are different. At high Pr, the porous media enhance the heat transfer by increasing the flow coherence at high porosity and inhibit the heat transfer by impeding the passage of the plume in the bulk region at low porosity. However, at low Pr, the viscous effect is weakened and the heat transfer is mainly through the large-scale circulation (LSC). As the porosity decreases, the LSC is enhanced and the flow is laminarized, inhibiting the shedding of the plume from the boundary layer. Moreover, we further explore the flow structure under the random distribution of obstacles and find some similarities in the evolution of the flow structure. The discovery of the new mechanism for porous media at low Pr advances the understanding of the effect of porous media on natural convection and may provide implications for industrial designs.

Experimental study of heat transfer in a rectangular cell with built-in lattice channels

We experimentally study the heat transfer and flow characteristics of thermal convection in a rectangular cell with built-in lattice channels. The working fluid used is water with a Prandtl number of 5.5, and the Rayleigh number ranges from 2.5×108 to 6.9×109. Three proposed models with different channel sizes and positions and the classical Rayleigh–Bénard convection (RBC) are studied, and the heat transfer and flow structure characteristics are analyzed using measured temperature signals. The first model included two short channels placed near the top and bottom plates, which disrupt the mixing zone and enhance heat transport. The second model involves relatively long channels positioned at the center of the cell, but far from the thermal boundary layer, resulting in a more coherent bulk flow that also enhances heat transport. For these two configurations, the heat transfer enhancement rate is approximately 20% compared to standard RBC. The third model uses long lattice channels that almost touches the top and bottom plates. This configuration results in a maximum heat transfer enhancement of about 138% due to the organized boundary layer and bulk flow induced by lattice channels. The presence of channels also results in a two-order smaller standard deviation of temperature, indicating a significant reduction in fluctuations. However, the average temperatures in the center of some channels were significantly different from the mean system temperature, suggesting the existence of cold or hot fluid flow through the channel. Our experimental results show that the inclusion of channels with appropriate lengths and positions can effectively regulate the flow near the boundary layer and in the bulk, leading to significant enhancements in heat transfer.

Heat transfer mechanism in vibrational turbulent Rayleigh–Bénard convection with rough plates

The joint effect of rectangular-type roughness and horizontal vibration on two-dimensional (2D) turbulent Rayleigh–Bénard convection (RBC) is investigated by using the thermal lattice Boltzmann method (LBM) in this article. The present work focuses on the Nusselt number and plume dynamics of the convection in the range of dimensionless vibration frequency 0 ≤ ω* ≤ 1000 and the range of dimensionless roughness height 0 ≤ h* ≤ 0.05. The Rayleigh number is 108 and Prandtl number is 4.38. Our numerical results indicate that the relationship between the Nusselt number and roughness height is mostly proportional, and the relationship between the Nusselt number and the vibration frequency is exponential. It is further found that heat transfer enhances by 3.06 times under the joint effect of horizontal vibration and rectangular roughness on turbulent RBC. It provides significant physical insight into the mechanism of cooperative heat transfer enhancement.

Nonlinear Analysis of Cross Rolls of Electrically Conducting Fluid under an Applied Magnetic Field with Rotation

The proposed planer layer dynamo physical model has real-world applications, especially in the Earth’s liquid core. Thus, in this paper, an attempt is made to understand the finite amplitude convection when there exists a coupling between the Lorentz force and the Coriolis force. In particular, the effect of a horizontally applied magnetic field is studied on the Rayleigh–Bénard convection (RBC) that contains the electrically conducting fluid and rotates about its vertical axis. Free–free boundary conditions are assumed on the geometry. Attention is focused on the nonlinear convective flow behavior during the occurrence of cross rolls which are perpendicular to the applied magnetic field and parallel to the rotation axis. The visualization of cross rolls is achieved using the Fourier analysis of perturbations up to the O(ε8). The relationship of the Nusselt number (Nu) with respect to the Rayleigh number (R), the Ekman number (E), and the Elsasser number (Λ) is investigated. It is observed that E generates a strong damping effect on the flow velocity and on the heat transfer at high rotation rates. Using the heatline concept, it is observed that the temperature within the central regime is enhanced as the Λ increases. The results show that either E decreases or Λ increases, then the heat transfer rate increases.

Darcy–Benard convection through a uniformly permeable porous slab

In this article, we study the onset of convection in porous media with through flow based on Darcy formulation. Unlike the impermeable porous medium problems between horizontal two parallel plates frequently accessed in the literature, the thermal instability of convective cells under the influence of a uniform vertical flow is of the prime concern here in an aim to control the thermal instability onset. Three devised thermal boundary constraints representing external heat transfer with isothermal or isoflux lines across the walls are investigated fully taking into account the linear stability equations with small flow/heat wave disturbances with respect to the normal modes. In each case, the neutral stability response of the saturated porous layer separating the stable and unstable perturbation regimes are identified affected by a Peclet number manifesting itself as the through flow strength. The pre-analysis of the analytical solutions of thermal fields proves that the thermal layer thickness is lowered by the opposing through flow, otherwise an assisting through flow enhances the thickness. The critical Darcy–Rayleigh numbers and Benard cell wavenumbers of lateral fluctuating perturbations initiating the convective Darcy–Benard thermal rolls within the porous media for a prescribed Peclet number are ultimately worked out numerically, except an analytical expression is elaborated where the heating is supplied from the walls via varying heat fluxes. The well-documented thresholds of Rayleigh numbers 39.47, 27.09 and 12 with vanishing Peclet number (Barletta, 2019) corresponding to the three studied thermal cases are reproduced successfully. Further results clarified that both opposing and assisting through flows are sources of stabilization when the walls are thermally isothermal. On the other hand, the other thermally conducting porous walls lead to a more unstable convection with the assisting through flow having a thermal layer growth, otherwise stable convection occurs with the opposing through flow.

Effects of isothermal-adiabatic boundary conditions on the transition characteristics in two-dimensional turbulent Rayleigh–Bénard convection

In this article, two-dimensional (2-D) Rayleigh–Bénard (RB) convection with isothermal-adiabatic boundary conditions is simulated by using the double distribution function approach of lattice Boltzmann method. The effects of isothermal-adiabatic boundary on the flow and the heat transfer characteristics in the RB system under instability, transition and turbulence are discussed in detail. The effect of the isothermal-adiabatic boundary on the scaling of Nusselt (Nu) number as a function of Rayleigh (Ra) number is analyzed. The 0.3 scaling is observed in the mixed boundary system when the Ra number is in the range of 107–108. The scaling is well consistent with that in the RB system with uniform boundaries. A comparison of the influence on the root mean square of Nu number between uniform isothermal boundary and isothermal-adiabatic boundary demonstrates that in both “transition” region and “turbulence” region, the intensity of the fluctuation of average Nu number at uniform isothermal boundary is higher than that at the isothermal-adiabatic boundary. The comparison of the fluctuation of the average Nu number between “transition” region and “turbulence” region shows that the isothermal-adiabatic boundary has a better suppression effect on the fluctuation of heat transfer in the “transition” region. The supression is related to ratio of the scale of plume and the “heat source core.” When the scales are comparable, the fluctuation of average Nu number will be significantly suppressed. Flow field and temperature field further show the plumes are generated at these “heat source cores,” which effectively supports the “heat source core” assumption.

Propagating beams carrying orbital angular momentum through simulated optical turbulence generated by Rayleigh–Bénard natural convection

Numerical simulations of Rayleigh–Bénard (RB) convective flow are performed to determine the optical and mechanical turbulence properties and resulting index of refraction field in order to study the propagation characteristics of a laser beam carrying orbital angular momentum. The simulations are carried out in air using a computational fluid dynamics package which solves the Navier-Stokes equations. The computational domain is 0.1 m × 0.5 m × 0.5 m with a temperature difference of 1°K maintained between the top and bottom plate. The simulated temperature field is then converted into refractive index values. To study light propagation through the turbulent volume the split-step screen method is employed with screens at 0.025 m distance from each other along the propagation path which ranges from 0.5 m to 2.5 m. The structure of the phase screens, their spatio-temporal correlation with respect to up/down drafts, and phase changes across regions of interest are discussed. It was observed as the propagation distance increased, the orbital angular momentum carrying Laguerre–Gaussian beams wandered and the beam phase singularity distorted thus impacting the light intensity distribution. In addition, it was found that higher topological charge and order of Laguerre polynomial result in increased distortion of the beam vortex.