Rayleigh-Benard Convection Cell Research Articles

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.

Effect of aspect ratio on PCM melting behavior in a square cavity

For latent heat thermal energy storage applications with phase change material (PCM) in restricted space, the factors such as container shape and heating surface must be considered. In this paper, a 2D square cavity PCM is taken as the research object, and the melting process of PCM with different square cavity aspect ratio (AR) was simulated under the condition of constant heat flux (60 W) at the left wall/bottom wall. An innovative and effective indicator, i.e., differential liquid fraction curve along with solid-liquid interface evolution is proposed to reveal the melting rate and typical phase change characteristics. The results show that the complete melting time increases with the increase of AR for both left wall and bottom wall heating conditions. For general applications, the bottom wall heating has a higher melting rate compared with left wall, especially for the cavity with AR >1. During the phase change process, the melting rate can reach its maximum value at the peak of differential liquid fraction curve with an observation of the longest solid-liquid interface. In addition, the melting pattern of high AR cavity during the latter part of the left wall heating process would become similar to the low AR case under the “scouring effect” of natural convection on the solid-liquid interface. For bottom wall cases, the natural convection waveform presents Rayleigh-Benard convection cells, and with the increase of AR, the irregularity of the vortex structure becomes more obvious. The results can provide useful guidance for accurately evaluating phase change characteristics and designing thermal energy storage system.

Rayleigh-Bénard convection in air: out-of-plane vorticity from stereoscopic PIV measurements

We present results from stereoscopic PIV measurements in a Rayleigh-Benard convection (RBC) cell filled with (compressed) air at Rayleigh numbers: Ra = 1.5×104, 2×104, 1×105, 2×105, 5×105, and Prandtl number Pr ' 0.7. The three largest Rayleigh numbers are obtained pressurising the whole set-up including cameras and objective lenses, up to 4.5 bars. The main goal of this study is to reproduce DNS data that are acquired at the same Rayleigh numbers to study far-tail events of the out-of-plane vorticity component (ωz). The measurements are performed in a RBC cell with aspect ratio Γ = W/H = 10, where W is the width and H = 3 cm is the height of the domain. The cell is equipped with a transparent bottom plate heated by a thin oxide layer (for details see Kastner et al. (2018)), which allows us to measure 3C2D velocity fields on ¨a horizontal plane at mid height of the cell. The RBC cell set-up is inserted in the SCALEX facility of TU Ilmenau, a pressure vessel with several optical accesses that can be pressurised up to 10 bars The experiments aim firstly at improving the quality of previous measurements performed in the sameset-up [Kastner et al. (2018), Cierpka et al. (2019)], regarding the accuracy of the out-of-plane velocity ¨component. This has been realised by positioning the cameras at a larger stereo angle (about 25◦), which is possible by placing them inside the pressure vessel. Major challenges of the current measurements are caused by optical distortions due to the temperature gradients that are typical for thermal convection (see Valori (2018), Valori et al. (2019)). Probability Density Functions (PDFs) of ωz from stereo PIV experiments and from DNS data are shown respectively in figure 1(a) and 1(b) for all Rayleigh numbers studied. We can observe that for both kind of data the tails of the PDF becomes wider while increasing the Rayleigh number, which may be connected to intermittency. This crossover from Gaussian to intermittent statistic was recently studied in Valori and Schumacher (2021) from DNS. Figure2(a) shows the temporal evolution of ωz at the position of its largest (extreme) value at Ra = 2.5 × 105, while figure2(b) shows the spatial distribution of ωz at the time of its extreme event in the experiments. The experimental results are able to reproduce well the statistics of DNS data of the same flow, and allow the study of extreme events of ωz.

Experimental and numerical shadowgraph in turbulent Rayleigh–Bénard convection with a rough boundary: investigation of plumes

We show that, in the case of turbulent Rayleigh-Benard convection, shadowgraph can be used to have quantitative results on the plumes statistics and their velocity. For this purpose, we compare the experimental shadowgraph of a Rayleigh-Benard cell with the synthetic shadowgraph obtained by calculating the integrated 2D Laplacian of the temperature field from a numerical simulation very similar to the experiment. We use image processing tools to enhance the quality of the shadowgraph image, and obtain quantitative statistics for the thermal plumes, such as plume density, and plume velocity distribution. To highlight the efficiency of this new process of plume counting, we use, both in the experiment and in the numerical simulation, a turbulent Rayleigh-Benard convection cell with a rough bottom surface, and a smooth top surface, where the statistics of the plumes can be influenced (or not) by the roughness. In addition, the distribution of velocity obtained from processing the synthetic shadowgraph images of the DNS or the experimental shadowgraph images, are compared to the velocity fluid at mid plane of the DNS or PIV measurement in the experiment, respectively. It will be shown that the mean velocity profile measured using the advection of the plumes is different from the average eulerian velocity profile.

Natural convection in cylindrical containers with isothermal ring-shaped obstacles

By means of three-dimensional direct numerical simulations, we investigate the influence of the regular roughness of heated and cooled plates on the mean heat transport in a cylindrical Rayleigh–Benard convection cell of aspect ratio one. The roughness is introduced by a set of isothermal obstacles, which are attached to the plates and have a form of concentric rings of the same width. The considered Prandtl number $Pr$ equals 1, the Rayleigh number $Ra$ varies from $10^{6}$ to $10^{8}$ , the number of rings on each plate is 1, 2, 4, 8 or 10, the height of the rings is varied from 1.5 % to 49 % of the cylinder height and the gap between the rings is varied from 1.5 % to 18.8 % of the cell diameter. Totally, 135 different cases are analysed. Direct numerical simulations show that with small $Ra$ and wide roughness rings, a small reduction of the mean heat transport (the Nusselt number $Nu$ ) is possible, but, in most cases, the presence of the heated and cooled obstacles generally leads to an increase of $Nu$ , compared to the case of classical Rayleigh–Benard convection with smooth plates. When the rings are very tall and the gaps between them are sufficiently wide, the effective mean heat flux can be several times larger than in the smooth case. For a fixed geometry of the obstacles, the scaling exponent in the $Nu$ versus $Ra$ scaling first increases with growing $Ra$ up to approximately 0.5, but then smoothly decreases back towards the exponent in the no-obstacle case.

Pair dispersion in inhomogeneous turbulent thermal convection

Due to large scale flow inhomogeneities and the effects of temperature, turbulence small-scale structure in thermal convection is still an active field of investigation, especially considering sophis- ticated Lagrangian statistics. Here we experimentally study Lagrangian pair dispersion (one of the canonical problems of Lagrangian turbulence) in a Rayleigh-B enard convection cell. A sufficiently high temperature difference is imposed on a horizontal layer of fluid to observe a turbulent flow. We perform Lagrangian tracking of sub-millimetric particles on a large measurement volume in- cluding part of the Large Scale Circulation (LSC) revealing some large inhomogeneities. Our study brings to light several new insights regarding our understanding of turbulent thermal convection: (i) by decomposing particle Lagrangian dynamics into the LSC contribution and the turbulent fluc- tuations, we highlight the relative impact of both contributions on pair dispersion; (ii) using the same decomposition, we estimate the Eulerian second-order velocity structure functions from pair statistics and show that after removing the LSC contribution, the remaining statistics recover usual homogeneous and isotropic behaviours which are governed by a local energy dissipation rate to be distinguished from the global dissipation rate classically used to characterise turbulence in thermal convection; and (iii) we revisit the super-diffusive Richardson-Obukhov regime of particle dispersion and propose a refined estimate of the Richardson constant.

Effect of Periodic Bottom Plate Heating on Large Scale Flow in Turbulent Rayleigh-Bénard Convection

We report analysis of temperature fluctuations measured inside a Rayleigh-Benard convection cell of aspect ratio unity with steady and time-varying heating of the bottom boundary. The working fluid is cryogenic helium gas at Rayleigh number Ra = 10 13 , for which a large scale coherent flow (mean wind) exists. We observe the wind to occasionally vanish under both steady and time-varying heating conditions. However, with applied periodic modulation of the lower boundary temperature at the frequency of the wind, we can observe destruction of the periodic temperature variation at the cell mid-plane, due to relative changes in phase between the mean wind and the propagating temperature wave. The wind speed is not observed to change with modulation, demonstrating that it is set by mean properties of the system. Finally we propose that the frequency of the mean wind – and hence the large scale Reynolds number – could be better resolved by finding resonance with applied forcing.

Genetic sources and tectonophysical regularities of divisibility of the lithosphere into blocks of various ranks at different stages of its formation: tectonophysical analysis

The paper presents the first tectonophysical reconstruction of initial divisibility of the protolithosphere as a result of convection in the cooling primitive mantle. Initial division of the protolithosphere into separate masses, i.e. prototypes of the blocks, and their size are predetermined by the emerging Rayleigh-Benard convection cells. In studies of geology and geodynamics, the Rayleigh-Benard convection cells were first referred to as a factor to explain the formation of initial continental cores. Considering the Rayleigh-Benard cells and their structural relics can help clarify initial divisibility of the protolithosphere and the origin of the major lithospheric plates, i.e. prototypes of continents. In our opinion, the initial mega-scale block structure of the protolithosphere and the emerging lithosphere were predetermined by the Rayleigh-Benard cells as they were preserved in the emerging lithosphere and their lower boundaries corresponded to the core-mantle boundary, i.e. one of the major discontinuities of the planet. Our theoretical estimations are in good agreement with the number and sizes of the Earth's theorized first supercontinents, Vaalbara and Ur. In our tectonophysical discussion of the formation of the lithospheric block structure, we analyze in detail the map of modern lithospheric plates [ Bird , 2003 ] in combination with the materials from [ Sherman et al., 2000 ]. In the hierarchy of the blocks comprising the contemporary lithosphere, which sizes are widely variable, two groups of blocks are clearly distinguished. The first group includes megablocks with the average geometric size above 6500 km. Their formation is related to convection in the Earth mantle at the present stage of the geodynamic evolution of the Earth, as well as at all the previous stages, including the earliest one, when the protolithosphere emerged. The second group includes medium-sized blocks with the average geometric size of less than 4500 km and those with minimum sizes, such as rock lumps. They reflect primarily the degradation of megablocks as a result of their destruction due to high stresses in excess of the tensile strength of the medium. This group may also include blocks which formation is related to convection in the upper mantle layer, asthenosphere. There are grounds to assume that through the vast intermediate interval of geologic time, including supercycles of Kenorlend, Rodin, and and partically Pangea, the formation of the large lithospheric blocks was controlled by convection, and later on, they were 'fragmented' under the physical laws of destruction of solid bodies. However, it is difficult to clearly distinguish between the processes that predetermine the hierarchy of formation of the block structures of various origins – sizes of ancient lithospheric blocks cannot be estimated unambiguously. Thus, mantle convection is a genetic endogenous source of initial divisibility of the cooling upper cover of the Earth and megablock divisibility of the lithosphere in the subsequent and recent geodynamic development stages. At the present stage, regular patterns of the lithospheric block divisibility of various scales are observed at all the hierarchic levels. The areas of the lithospheric megaplates result from regular changes of convective processes in the mantle, which influenced the formation of plates and plate kinematics. Fragmentation of the megaplates into smaller ones is a result of destruction of the solid lithosphere under the physical laws of destruction of solid bodies under the impact of high stresses.

Time-dependent Rayleigh–Benard convection: Cell formation and Nusselt number

Rayleigh–Benard convection was investigated using experiments and numerical simulations for Rayleigh numbers in the range of 1.06×107–1.83×1010 and a Prandtl number of 2014. The plate separation and plate area were varied. High Rayleigh numbers were achieved using mass transfer experiments based on the heat and mass transfer analogy. The measured and calculated Nusselt numbers were in good agreement, and followed existing heat transfer correlations. The numerical analyses visualized the time evolution of the Rayleigh–Benard convection cell formation, as well as the time dependence of the Nusselt number.

Local Dissipation Scales and Integral-Scale Reynolds Number Scalings in Thermally-Driven Turbulence

We present direct multi-point velocity measurements of the two-dimensional velocity fields in a cylindrical Rayleigh-Benard convection cell using the particle image velocimetry (PIV) technique over the Rayleigh number range 5.9 × 109 ≲ Ra ≲ 1.1 × 1011. The longitudinal integral length scale of the horizontal and vertical velocity fields are obtained at the cell center, near the cell sidewall, and near the bottom plate of the cell, respectively. In addition, the Reynolds number based on these scales, ReLx and ReLz, are obtained. It is found that all measured ReL scales as ReL ∼ Raβ, with the exponent β ≃ 0.5, except ReLx for the horizontal velocity at the cell center, which has a β ≃ 0.75. The local dissipation scale field η at the three different places are also studied. Our results reveal two types of universality of η. The first one is that, for the same flow, the probability density functions (PDF) of η are insensitive to turbulent intensity and large-scale inhomogeneity and anisotropy of the system. The second is that the small-scale dissipation dynamics in buoyancy-driven turbulence can be described by the same models developed for homogeneous and isotropic turbulence. However, the exact functional form of the PDF of the local dissipation scale is not universal with respect to different types of flows, but depends on the integral-scale velocity boundary condition, which is found to have an exponential, not Gaussian, distribution in turbulent Rayleigh-Bénard convection.

Large Rayleigh number thermal convection: Heat flux predictions and strongly nonlinear solutions

We investigate the structure of strongly nonlinear Rayleigh–Bénard convection cells in the asymptotic limit of large Rayleigh number and fixed, moderate Prandtl number. Unlike the flows analyzed in prior theoretical studies of infinite Prandtl number convection, our cellular solutions exhibit dynamically inviscid constant-vorticity cores. By solving an integral equation for the cell-edge temperature distribution, we are able to predict, as a function of cell aspect ratio, the value of the core vorticity, details of the flow within the thin boundary layers and rising/falling plumes adjacent to the edges of the convection cell, and, in particular, the bulk heat flux through the layer. The results of our asymptotic analysis are corroborated using full pseudospectral numerical simulations and confirm that the heat flux is maximized for convection cells that are roughly square in cross section.

THE PROBLEM OF PALEODICTYON

History of study, ecology, taphonomy and variability of trace fossils classified as Paleodictyon Menengini are considered. The present study allows drawing a conclusion that Paleodictyon is not a trace fossil or a remain of some other organism. However it is absolutely identical with the so-called natural Rayleigh-Benard convection cells.

Coupled flow and reaction during natural convection PCR

Polymerase chain reaction (PCR) in a microfluidic Rayleigh–Benard convection cell represents a promising route towards portable PCR for point-of-care uses. In the present contribution, the coupled fluid mechanics and heat transport processes are solved numerically for a 2-D flow cell. The resultant velocity and temperature fields serve as the inputs to a convection-diffusion-reaction model for the DNA amplification, wherein the reaction kinetics are modeled by Gaussian distributions around the conventional bulk PCR reaction temperatures. These evolution equations are integrated to determine the exponential growth rate of the double-stranded DNA concentration. The predicted doubling time is approximately 10–25 s, increasing with the Peclet number. This effect is attributed to low velocity, slow kinetics “dead zones” located at the center of the reactor. The latter observation provides an alternative rationalization for the use of loop-based natural convection PCR systems.

Lyapunov exponents for small aspect ratio Rayleigh-Bénard convection

Leading order Lyapunov exponents and their corresponding eigenvectors have been computed numerically for small aspect ratio, three-dimensional Rayleigh-Benard convection cells with no-slip boundary conditions. The parameters are the same as those used by Ahlers and Behringer [Phys. Rev. Lett. 40, 712 (1978)] and Gollub and Benson [J. Fluid Mech. 100, 449 (1980)] in their work on a periodic time dependence in Rayleigh-Benard convection cells. Our work confirms that the dynamics in these cells truly are chaotic as defined by a positive Lyapunov exponent. The time evolution of the leading order Lyapunov eigenvector in the chaotic regime will also be discussed. In addition we study the contributions to the leading order Lyapunov exponent for both time periodic and aperiodic states and find that while repeated dynamical events such as dislocation creation/annihilation and roll compression do contribute to the short time Lyapunov exponent dynamics, they do not contribute to the long time Lyapunov exponent. We find instead that nonrepeated events provide the most significant contribution to the long time leading order Lyapunov exponent.

PCR in a Rayleigh-Bénard convection cell.

PCR in a Rayleigh-Bénard convection cell.

Lattice Boltzmann representation of neutral turbulence in the cold gas blanket divertor regime

In the divertor plasma detachment regime one expects to encounter turbulent collisional neutral gas dynamics. These conditions are ideally simulated by lattice Boltzmann methods — methods ideal for application on multi-parallel processors. As illustrative of this method, we specifically show the effect of conductivity in the Rayleigh-Benard convection cells, using an octagonal velocity lattice.

Diffusion in laminar Rayleigh–Bénard convection: Boundary layers versus boundary tubes

New results on the advection–diffusion of a passive tracer in a periodic system of hexagonal Rayleigh–Bénard convection cells at high Péclet number P=Lv/D0≫1 are presented, where L is the characteristic length scale of the flow, v is the velocity amplitude, and D0 is the molecular diffusivity. It is shown that the transport properties of this three-dimensional (3-D) laminar flow are drastically different from those of the well-studied two-dimensional convection rolls. The 3-D topology of the streamlines in the hexagonal convection leads to the formation of boundary tubes near the axes and the edges of the hexagons, in addition to the standard boundary layers found near the faces and the bases. A scaling theory is given and confirmed by test-particle simulations that show that the transport enhancement due to the hexagonal cells is controlled by the boundary tubes and scales only logarithmically with P. On the other hand, it is found that the subdiffusive regimes of transport in hexagons are similar to those found in other flows with constrained streamlines. The described effects can be used for the experimental investigation of structures in thermal convection.

On the aspect ratio of Rayleigh‐Benard convection cells

We report numerical model calculations of isoviscous bottom‐heated convection in a two‐dimensional box with aspect ratio twelve. The aim was to determine the preferred aspect ratio of convection cells. Time‐dependent runs were started from two widely different initial conditions. At Rayleigh numbers in the range 105‐106 about eight cells with a mean aspect ratio of 1.5 formed eventually in each case. Thus neither the preference for approximately square cells, nor the stability of very elongated cells could be confirmed. The existence of large‐scale convective structures in the earth's mantle must be due to deviations from the simple Rayleigh‐Bénard model of convection.

Time-dependent thermal convection in dilute solutions of 3He in superfluid 4He

Time-dependent thermal convection can occur in a unity-aspect-ratio Rayleigh-Benard convection cell containing a dilute solution of 3He in superfluid 4He when the fluid is heated from above. Results are presented primarily for a 0.24 mole % He solution at 0.925 K. Means is provided for introducing heat at the top and separately for a central plug and an outer ring such that both are at a constant temperature gDT above the bottom. A critical temperature difference δT cfor convection can be defined above which both steady and time-dependent convection occur. The time-dependent effects include a region of δT. near δT cand characterized only by excessive noise, a region of somewhat higher δT where there are intermittent major changes in the plug heating rate with a time distribution like that for random events, and a region at still higher δT where periodic but nonsinusoidal variation of the heat flow is observed. When a long enough time, several months, has elapsed after cooling down the apparatus, time-dependent states no longer occur, and the heat flow above δT cis limited to steady convection. Briefly raising the temperature of the apparatus to 77 K is sufficient to restore the possibility of time-dependent states.