Rayleigh-Benard Research Articles

Echo state networks for modeling turbulent convection

Turbulent Rayleigh-Bénard convection (RBC) is one of the very prominent examples of chaos in fluid dynamics with significant relevance in nature. Meanwhile, Echo State Networks (ESN) are among the most fundamental machine learning algorithms suited for modeling sequential data. The current study conducts reduced order modeling of experimental RBC. The ESN successfully models the flow qualitatively. Even for this highly turbulent flow, it is challenging to distinguish predictions from the ground truth. The statistical convergence of the ESN goes beyond the velocity values and is represented in secondary aspects of the flow dynamics, such as spatial and temporal derivatives and vortices. Finally, ESN’s main hyperparameters show values for best performance in strong relation to the flow dynamics. These findings from both the fluid dynamics and computer science perspective set the ground for future informed design of ESNs to tackle one of the most challenging problems in nature: turbulence.

Asymmetry of Two-Dimensional Thermal Convection at High Rayleigh Numbers

While thermal convection cells exhibit left–right and top–bottom symmetries at low Rayleigh numbers (Ra), the emergence of coherent flow structures, such as elliptical large-scale circulation in Rayleigh–Bénard convection (RBC), breaks these symmetries as the Rayleigh number increases. Recently, spatial double-reflection symmetry was proposed and verified for two-dimensional RBC at a Prandtl number of 6.5 and Ra values up to 1010. In this study, we examined this new symmetry at a lower Prandtl number of 0.7 and across a wider range of Rayleigh numbers, from 107 to 1013. Our findings reveal that the double-reflection symmetry is preserved for the mean profiles and flow fields of velocity and temperature for Ra<109, but it is broken at higher Rayleigh numbers. This asymmetry at high Ra values is inferred to be induced by a flow-pattern transition at Ra=109. Together with the previous study, our results demonstrate that the Prandtl number has an important influence on the symmetry preservation in RBC.

Side-heated Rayleigh–Bénard convection

Unlike in solids, heat transfer in fluids can be greatly enhanced due to the presence of convection. Under gravity, an unevenly distributed temperature field results in differences in buoyancy, driving fluid motion that is seen in Rayleigh–Bénard convection (RBC). In RBC, the overall heat flux is found to have a power-law dependence on the imposed temperature difference, with enhanced heat transfer much beyond thermal conduction. In a bounded domain of fluid such as a cube, how RBC responds to thermal perturbations from the vertical sidewall is not clear. Will sidewall heating or cooling modify flow circulation and heat transfer? We address these questions experimentally by adding heat to one side of the RBC. Through careful flow, temperature and heat flux measurements, the effects of adding side heating to RBC are examined and analysed, where a further enhancement of flow circulation and heat transfer is observed. Our results also point to a direct and simple control of the classical RBC system, allowing further manipulation and control of thermal convection through sidewall conditions.

The generalized quasilinear approximation of two-dimensional Rayleigh–Bénard convection

In the generalized quasilinear approximation (GQLA) (Marston et al., Phys. Rev. Lett., vol. 116, 2016, 214501), a threshold wavenumber ( $k_0$ ) in the direction of translational symmetry segregates the total into large- ( $l$ ) and small-scale ( $h$ ) fields. While the governing equation for the large-scale field is fully nonlinear, that for the small scales is linearized with respect to the large-scale field. In addition, some nonlinear triad interactions are omitted in the GQLA. Herein, the GQLA is applied to two-dimensional planar Rayleigh–Bénard convection (RBC). A scale separation between the large-scale convection rolls and small-scale turbulent fluctuations is typical in RBC. The present work explores the efficacy of GQLA in capturing the scale-by-scale energy transfer processes in RBC. The initial condition for the GQLA simulations was either the statistically stationary state obtained in direct numerical simulation (DNS) or random fluctuations superimposed on the linear conductive temperature profile and $\boldsymbol {u}=0$ . The GQLA simulations can capture the convection rolls for $k_0$ larger than or equal to the dominant wavenumber for thermal driving of the flow ( $k_0 \ge k_{\hat {Q}}$ ). Additionally, the GQLA emulates the fully nonlinear dynamics for $k_0$ larger than or equal to the first harmonic of the convection-roll wavenumber ( $k_0 \ge 2k_{roll}$ ). In the intermediate regime with $2k_{roll} > k_0 \ge k_{\hat {Q}}$ , the dynamics captured in GQLA simulations is different from the DNS. In DNS, two primary energy transfer processes dominate: (i) the energy transfer to/from the convection rolls and (ii) the scale-by-scale inverse kinetic energy and forward thermal energy cascades mediated by the convection rolls. The fully nonlinear dynamics is emulated by GQLA when these energy transfer processes are faithfully reproduced. Utilizing the framework of altering the triad interactions in GQLA, an additional intrusive calculation, including target triad interactions, is performed here to study their influence. This intrusive calculation shows that the convection rolls are not captured in GQLA for $k_0 < k_{\hat {Q}}$ because of the exclusion of the $h \to l \to l$ and $l \to h \to h$ triad interactions in GQLA. The inclusion of these triad interactions in the intrusive calculation yields the convection rolls, and the reproduced dynamics is similar to that of the intermediate GQLA regime with $2k_{roll} > k_0 \ge k_{\hat {Q}}$ .

Heat transport enhancement by rotating bottom endwall in a cylindrical Rayleigh–Bénard convection

Rotating thermal convection, commonly encountered in natural and industrial environments, is typically influenced by both buoyancy forces and boundary rotation. In this study, we conduct direct numerical simulations to explore the effect of rotating bottom on the flow structure and heat transport of Rayleigh–Bénard convection (RBC) in a cylindrical cavity. This cavity has a radius-to-height ratio of 1 and is filled with an incompressible fluid with a Prandtl number of 0.7. Our results show that the axisymmetric convection pattern, observed in RBC for Ra∈[4000,8000] without rotation, transitions into a double roll structure at low rotating speeds (ω), while for Ra≤4000, the pattern remains axisymmetric, independent of ω. We then focus on the impact of bottom rotation on heat transport in the axisymmetric regime. Based on the variation in the Nusselt number (Nu) with ω, two distinct regimes are identified: a convection-dominated regime at low ω, where Nu closely resembles that of standard RBC, and a rotation-dominated regime at high ω, where strong shear induced by the rotating bottom intensifies the meridional circulation, significantly boosting global heat flux. The critical rotating speed, ω*, marking the transition between these regimes, follows different power-law relations below and above the buoyant convection onset (Rac): ω*∼Ra−0.64 for Ra<Rac and ω*∼Ra0.33 for Ra>Rac. As ω increases, the exponents for Nu∼Raλ and Re∼Raγ evolve before converging to λ≈0.3 and γ=0.5, respectively. Scaling laws for Nu and Re as functions of ω and Ra in the rotation-dominated regime are finally derived: Nu∼Ra0.3ω0.64 and Re∼Ra0.5ω.

Transport of particles in a model of 2D Rayleigh-Benard convection that conserves energy and vorticity

In contrast with the Lorenz model for 2-dimensional Rayleigh - Bénard system, the model proposed by Howard - Krishnamurti (HK) allows the possibility of a large scale horizontally shear flow making feasible the study of particles transport. However, this model lacks conservation of energy and vorticity in the absence of forcing and dissipation. A model that incorporates conservation of energy and vorticity was proposed by A. Gluhovsky et al (GTA). We perform the linear stability analysis of this later model and study the transport process on this velocity field background and make a comparison with the features of the former model. We found that the basic bifurcation structure is retained by the GTA model and discuss the differences that they indeed have. In regard to the transport processes, the basic features found using the HK velocity field background are also kept by the GTA model. We determine the size of the rather small gap in the Rayleigh number where the transport process shift from being shear flow dominated to a Brownian diffusion process.

Design of a Contactless Inductive Flow Tomography system for a large Rayleigh–Bénard convection cell with aspect ratio [formula omitted]

Contactless Inductive Flow Tomography (CIFT) is a flow measurement technique that is able to reconstruct the time-dependent three-dimensional velocity field in electrically conducting fluids, e.g., liquid metals, from magnetic field measurements. The paper describes the design of a specific CIFT measurement set-up for flow studies in liquid metal Rayleigh–Bénard convection (RBC) in a large cylinder of aspect ratio (diameter/height) of Γ=0.5 filled with the ternary alloy GaInSn as model fluid. An optimized configuration for the CIFT excitation system and magnetic field sensor layout under consideration of the specific requirements for the application in turbulent RBC is determined by numerical simulations. The new experimental CIFT-RBC system resulting from the design process is constructed and a preliminary experiment at a Rayleigh number of Ra=2.13×107 and a Prandtl number of Pr=0.03 is performed and evaluated.

Modeling Water Clusters: Spectral Analyses, Gaussian Distribution, and Linear Function during Time

Our experimental and theoretical studies have consistently revealed the presence of water clusters in various environments, particularly under hydrophobic conditions, where slower hydrogen ion interactions prevail. Crucial methods like Nuclear Magnetic Resonance (NMR) and Fourier Transform Infrared (FTIR) method have played a pivotal role in our understanding of these clusters, unveiling their potential medical applications. The stability and behavior of these clusters can be influenced by factors such as metal ions’ presence, leading to stable clusters’ formation. This potential for medical applications should inspire hope and further research. Moreover, our research has revealed that water clusters exhibit characteristics of dissipative structures, demonstrating the self-organization under physical, chemical, or thermal changes akin to Rayleigh–Benard convection cells. This dynamic and significant behavior supports the notion that water’s role transcends simple chemistry, potentially influencing biological processes at a fundamental level. The interaction of water clusters with their environment and the ability to maintain non-equilibrium states through the energy exchanges further underscores their complexity and significance in both natural and technological contexts. Water filtration is a process for improving water quality. The effect is re-structuring hydrogen bonds and structuring water clusters, most of which are hexagonal. In our research, we applied filtered water using patented EVOdrop Swiss technology.

Scaling Law of Flow and Heat Transfer Characteristics in Turbulent Radiative Rayleigh-Bénard Convection of Optically Thick Media

Radiative natural convection is of vital importance in the process of energy storage, power generation, and thermal storage technology. As the attenuation coefficients of many heat transfer media in these fields are high enough to be considered as optically thick media, like nanofluids or molten salts in concentrated solar power or phase change thermal storage, Rosseland approximation is commonly used. In this paper, we delve into the impact of thermal radiation on the Rayleigh-Bénard (RB) convection. Theoretical analysis has been conducted by modifying the Grossmann-Lohse (GL) model. Based on turbulent dissipation theory, the corresponding scaling laws in four main regimes are proposed. Direct numerical simulation (DNS) was also performed, revealing that radiation exerts a notable influence on both flow and heat transfer, particularly on the formation of large-scale circulation. By comparing with DNS results, it is found that due to the presence of radiation, the modified Nu scaling law in small Pr range of the GL model is more suitable for predicting the transport characteristics of optical thick media with large Pr. The maximum deviation between the results of DNS and prediction model is about 10%, suggesting the summarized scaling law can effectively predict the Nu of radiative RB convection.

Experimental evidence of the correlation between the flow rolling structures and momentum transfer in Rayleigh–Bénard convection

The formation of large-scale circulating structures (LSC) is one of the critical characteristics of turbulent Rayleigh–Bénard convection (RBC). Although the effect of LSC in turbulent RBC was disputed due to conflicting results, recently, the results of three-dimensional direct numerical simulation [Zwirner et al., “Elliptical instability and multiple-roll flow modes of the large-scale circulation in confined turbulent Rayleigh-Bénard convection,” Phys. Rev. Lett. 125, 54502 (2020)] confirmed that in RBC flows with a low Prandtl number, Pr=0.1 within Oberbeck–Boussinesq assumption, the formation of higher number of LSC leads to a decrease in heat and momentum transfer. However, it was shown that for higher Prandtl numbers, heat/momentum transfer is not correlated with the number of LSC. Experimental evidence is investigated of an inverse correlation between the momentum transfer and small-scale rolling structures for high Prandtl non-Oberbeck–Boussinesq condition. Experiments were undertaken at a Prandtl number of Pr=7 and Rayleigh number of Ra=5.3×107 in a cubical convection cell with an unit aspect ratio. Particle image velocimetry along with a robust combinatorial vortex detection algorithm was used to capture the flow field, detect the rolling structures, and estimate their size. It was found that although the flow structures were dominated by the LSC, the number of smaller rolling structures was significant. The results also showed that after the initiation of convection while the flow was still undeveloped, the majority of rolling structures were small scale. For this state, an inverse correlation between the number of rolling structures and momentum transfer was observed highlighting the influence of flow rolling structures regardless of the formation of the LSC.

Computational study on cilia transport of Prandtl nanofluid (blood-Fe3O4) enhancing convective heat transfer along microorganisms under electroosmotic effects in wavy capillaries

Purpose This study aims to focuse on the flow behavior of a specific nanofluid composed of blood-based iron oxide nanoparticles, combined with motile gyrotactic microorganisms, in a ciliated channel with electroosmosis. Design/methodology/approach This study applies a powerful mathematical model to examine the combined impacts of bio convection and electrokinetic forces on nanofluid flow. The presence of cilia, which are described as wave-like motions on the channel walls, promotes fluid propulsion, which improves mixing and mass transport. The velocity and dispersion of nanoparticles and microbes are modified by the inclusion of electroosmosis, which is stimulated by an applied electric field. This adds a significant level of complexity. Findings To ascertain their impact on flow characteristics, important factors such as bio convection Rayleigh number, Grashoff number, Peclet number and Lewis number are varied. The results demonstrate that while the gyrotactic activity of microorganisms contributes to the stability and homogeneity of the nanofluid distribution, electroosmotic forces significantly enhance fluid mixing and nanoparticle dispersion. This thorough study clarifies how to take advantage of electroosmosis and bio convection in ciliated micro channels to optimize nanofluid-based biomedical applications, such as targeted drug administration and improved diagnostic processes. Originality/value First paper discussed “Numerical Computation of Cilia Transport of Prandtl Nanofluid (Blood-Fe3O4) Enhancing Convective Heat Transfer along Micro Organisms under Electroosmotic effects in Wavy Capillaries”.

Magnetothermal Rayleigh-Benard Convection of Paramagnetic Oxygen Gas in a Rotating Shallow Vertical Cylindrical Container

We carried out complete transient three-dimensional numerical computations to clarify the heat transfer rate characteristics of magnetothermal Rayleigh-Benard convection of paramagnetic oxygen gas in a rotating shallow vertical cylindrical container. When the container without rotation was fixed at the location where (gradB2)Z became minimum on the center line, the average Nusselt number of magnetothermal Rayleigh-Benard convection increased in comparison with that of Rayleigh-Benard convection. When the container with rotation was fixed at the same location, the average Nusselt number of rotating magnetothermal Rayleigh-Benard convection increased in comparison with that of magnetothermal Rayleigh-Benard convection for the specific rotational Reynolds number. Key Words: Rayleigh-Benard convection, Magnetothermal convection, Oxygen gas, Paramagnetic fluid, Rotating cylindrical container

Temperature Condition Impact on the Onset of Rayleigh-Benard Convection in a Binary Fluid Saturated Anisotropic Porous Layer

Rayleigh-Benard convection in a saturated anisotropic porous media is investigated numerically. The temperature-dependent viscosity effect was applied to the double-diffusive binary fluid, and the Galerkin method was used to determine the critical Rayleigh numbers for the free-free, rigid-free, and rigid-rigid representing the lower-upper boundaries. The lower and upper boundary was set to be either conducting or insulating to temperature. The purpose of this study is to study the stability of Rayleigh-Benard convection with different temperature conditions in a binary fluid saturated by an anisotropic porous layer. The obtained eigenvalue is numerically solved with respect to various temperatures and velocities using the single-term Galerkin technique. The results, presented graphically, indicate that the rigid-rigid boundaries are more stabilize compared to rigid-free and free-free boundaries. It is also shown that an increase of temperature-dependent viscosity tends to destabilize the onset of double-diffusive convection.

𝒫𝒯 and anti-𝒫𝒯 symmetries for astrophysical waves

Context. Discrete symmetries have found numerous applications in photonics and quantum mechanics, but remain little studied in fluid mechanics, particularly in astrophysics. Aims. We aim to show how 𝒫𝒯 and anti-𝒫𝒯 symmetries determine the behaviour of linear perturbations in a wide class of astrophysical problems. They set the location of ‘exceptional points’ in the parameter space and the associated transitions to instability, and are associated with the conservation of quadratic quantities that can be determined explicitly. Methods. We study several classical local problems: the gravitational instability of isothermal spheres and thin discs, the Schwarzschild instability, the Rayleigh-Bénard instability and acoustic waves in dust–gas mixtures. We calculate the locations and the order of the exceptional points using the resultant of two univariate polynomials, as well as the conserved quantities in the different regions of the parameter space using Krein theory. Results. All problems studied here exhibit discrete symmetries, even though Hermiticity is broken by different physical processes (self-gravity, buoyancy, diffusion, and drag). This analysis provides genuine explanations for certain instabilities, and for the existence of regions in the parameter space where waves do not propagate. Those two aspects correspond to regions where 𝒫𝒯 and anti-𝒫𝒯 symmetries are broken respectively. Not all instabilities are associated to symmetry breaking (e.g. the Rayleigh-Benard instability).

The Effect of First-Order Chemical Reaction on Rotating Rayleigh-Benard Convection in a Sparsely Packed Porous Layer

The Effect of First-Order Chemical Reaction on Rotating Rayleigh-Benard Convection in a Sparsely Packed Porous Layer

Rayleigh-Benard convection and sensitivity analysis of magnetized couple stress water conveying bionanofluid flow with thermal diffusivities effect

Bionanofluids containing biological nanoparticles suspended in base fluids exhibit altered dynamics due to coupled effects between the nanoparticles and fluid properties. More efficient cooling can enhance medical technology performance, reduce energy usage, and provide safer, more sustainable healthcare solutions. This work overcomes previous research limitations by elucidating the combined impacts of microorganisms and couple stress properties on the behavior of water-based bionanofluids containing copper nanoparticles, under inclined magnetic fields. Governing equations for momentum, energy, concentration, and microorganisms are transformed into ordinary differential equations (ODEs) via similarity methods. The resulting ODE system is then solved semi-analytically using the Homotopy Analysis Method, revealing distinct profile behaviors. Additionally, quantitative indicators including skin friction for different values of M, λ,β, and Nr increased by 7.19%, 62.81%, 31.27%, and 21.32% respectively. Similarly Nusselt number for different values Qe , Ec, and Df decrease by 3.502 %, 2.5705%, and 2.447% respectively. Furthermore, Sherwood Numbers for different values of Sc, Kc, increased by 16.41%, and 4.133% respectively. Finally, Microorganisms for different values of Lb, Pe, and σ1 increase by 2.934%, 2.61%, and 1.172% respectively.

Thermal convection of a liquid metal under an alternating magnetic field

The objective of this work is to measure the heat transfer of a liquid metal in a cylindrical cell under the conjugate effects of a temperature difference and a Lorentz force generated by an alternating current in a coil. The experimental results are compared to recent direct numerical simulations (DNS) (Guillou et al., 2022). 25 experiments are performed for a large range of frequency f, ac intensity amplitude I0 and temperature difference between the top and bottom walls ΔT0: 15≤f≤1000Hz, 2≤I0≤67 A and 6≤ΔT0≤11 K. In these experiments, the Hartmann number Ha, the shielding parameter Sω and Rayleigh number Ra vary in the following range: 6≤Ha≤200, 1≤Sω≤70, 2.3×106≤Ra≤4.1×106. The experiments with an ac magnetic field are compared with the Rayleigh–Bénard convection (RBC) experiments under the same thermal conditions. Three rings of thermocouples allow characterizing the fluid temperature distribution during the convection. The heat flux at the bottom and top walls are also measured. We observe a very good agreement between the experimental results and the DNS results. As previously shown by numerical simulations, a master curve of Nu/Peω vs. QJ/Qc allows predicting the evolution of the heat transfer under different conditions of temperature difference and Lorentz force. Here Nu and Peω are the Nusselt number and a Péclet number based on the Lorentz force, and QJ and Qc are the total power deposited by the Joule effect and the total conduction heat flux without motion, respectively. The experiments show that Nu/Peω∼(QJ/Qc)−2/5.

Statistics of kinetic and thermal energy dissipation rates in vibrational turbulent Rayleigh–Bénard convection with rough surface

In this paper, the statistical properties of the kinetic εu and thermal εθ dissipation rates in two-dimensional (2D) turbulent Rayleigh–Bénard convection (RBC) are studied by using the thermal lattice Boltzmann method (LBM). A series of direct numerical simulations (DNS) are implemented in a square cell with the unit aspect ratio for the Rayleigh number Ra = 108 and Prandtl number Pr = 4.38. The roughness height h* and vary the vibration frequency ω* from 0 to 1000 are fixed in the vibrational RBC with rough plates to explore their effect on the kinetic and thermal dissipation rates. The global features indicate that the εu and εθ are more intense in the regions with high gradients of velocity and temperature, which is in good agreement with the previous work. The scalings of Nu∼ω *0.55±0.1 and Re∼0.59±0.2 are proposed between the ensemble averaged Nusselt number Nu and Reynolds number Re. The probability density functions (PDFs) of both logarithmic kinetic dissipation rate lg εu and thermal dissipation rate lg εθ are not conformed to the log-normal distributions. Through the analysis of the time-averaged εu and εθ vertical profiles, it is further demonstrated that the local dissipation rates from the boundary layer region are still the major contribution in the vibrational RBC with rough plates.

Turbulent Thermal Convection At A Rough Surface

We present measurements of the near-wall velocity field in highly turbulent Rayleigh-Bénard(RB) convection with rough horizontal surfaces. The measurements have been undertaken in a large-scale RB experiment which is called "Barrel of Ilmenau". We used the technique of stereoscopic Particle Image Velocimetry to measure the three components of the velocity field in horizontal planes parallel to the heated bottom plate. The measurements reported here comprise two Rayleigh numbers Ra=8.6×10^{10} and Ra=6.3×10^{11}. The Prandtl number of the working fluid was Pr=0.7. We used a chess board-like pattern of cuboids with a base area of 30 mm by 30 mm and a height of h=12 mm. Our measurements confirm the observation from previous experiments that the relation Nu=f(Ra) remains unchanged with respect to RB convection with smooth surfaces as long as the thickness of the thermal boundary layer \delta_{th}=H/(2Nu) exceeds the height of the roughness elements h. If \delta_{th} falls below h, Nu becomes larger and grows faster with increasing Ra then it does in RB convection with smooth plates. We also could identify the valleys in between the cuboids as the main contribution for the increase of Nu

Exploration of the effects of anisotropy and rotation on Rayleigh–Bénard convection of nanoliquid-saturated porous medium using general boundary conditions

This paper presents an analysis of Rayleigh–Bénard convection (RBC) of a Newtonian-nanoliquid-saturated anisotropic porous medium in the presence of rotation (Rayleigh–Bénard–Taylor convection). The investigation is performed using non-classical boundary conditions. The effect of various parameters on the onset of convection is presented graphically. The system sees stabilisation due to an increase in the rotation rate and thermal anisotropy parameter whereas the system destabilises due to an increase in the mechanical anisotropy parameter. The results of 82 limiting cases can be extracted from the current work. The results of free-free, rigid-free and rigid-rigid isothermal/adiabatic boundaries are obtained from the present study by considering appropriate limits. The results of the limiting cases of the present study are in excellent agreement with those observed in earlier investigations.