High Rayleigh Number Research Articles

Numerical Simulation of Free Convection in a Partially Heated Three-Dimensional Enclosure Filled with Ionanofluid ([C4mim][NTf2]-Cu)

A numerical analysis was performed to study free convection in a stationary laminar regime in a partially heated cube filled with ionanofluid. To numerically solve the dimensionless equations, we applied the finite volume method using the SIMPLEC algorithm for pressure correction. All walls are adiabatic, except for the left and right side walls which are partially heated differently. At the end of this simulation, several results are given in the form of current lines, isotherms, and variations in the Nusselt number. These results are obtained by analyzing the effect of a set of factors such as Rayleigh number, particle volume fraction, cold and source position on the dynamic and thermal fields, and heat transfer. It has been shown that the percentage of nanoparticles and high Rayleigh numbers significantly increase heat transfer by ionanofluid. Two comparisons have been made, between ionic fluid and ionanofluid at isotherms and streamlines, and between nanofluid and ionanofluid at Nusselt number, which show the advantage of using ionanofluid in heat transfer.

Regime transitions in thermally driven high-Rayleigh number vertical convection

Abstract

Numerical Study of Natural Convection Heat Transfer in a Porous Annulus Filled with a Cu-Nanofluid.

Natural convection heat transfer in a porous annulus filled with a Cu nanofluid has been investigated numerically. The Darcy–Brinkman and the energy transport equations are employed to describe the nanofluid motion and the heat transfer in the porous medium. Numerical results including the isotherms, streamlines, and heat transfer rate are obtained under the following parameters: Brownian motion, Rayleigh number (103–105), Darcy number (10−4–10−2), nanoparticle volume fraction (0.01–0.09), nanoparticle diameter (10–90 nm), porosity (0.1–0.9), and radius ratio (1.1–10). Results show that Brownian motion should be considered. The nanoparticle volume fraction has a positive effect on the heat transfer rate, especially with high Rayleigh number and Darcy number, while the nanoparticle diameter has an inverse influence. The heat transfer rate is enhanced with the increase of porosity. The radius ratio has a significant influence on the isotherms, streamlines, and heat transfer rate, and the rate is greatly enhanced with the increase of radius ratio.

Effect of time-dependent wall temperature on natural convection of a non-Newtonian fluid in an enclosure

This paper presents the results of computational analysis of unsteady natural convection of a non-Newtonian fluid in an enclosure, taking into account the time sinusoidal dependence of the wall temperature. The analysis has been carried out to reveal the dependence of the emerging streamlines, isotherms, average Nusselt number and flow intensity on the controlling parameters such as Rayleigh number (Ra = 104–106), power-law index (n = 0.6–1.4), and side wall temperature oscillation frequency (f = 0.01π–0.05π). The problem has been worked out by the finite difference technique including the successive under-relaxation procedure, the locally one-dimensional Samarskii scheme, and the Thomas algorithm. The results show that a pseudoplastic fluid with high Rayleigh numbers and high oscillation frequencies is more suitable for intensifying the convective heat and mass transfer.

A dual-mesh hybrid RANS-LES simulation of the buoyant flow in a differentially heated square cavity with an improved resolution criterion

In this work, the dual-mesh hybrid RANS-LES approach was applied for the first time to a natural convection flow, namely a high Rayleigh number differentially heated square cavity flow. This approach involves running an unsteady Reynolds Averaged Navier-Stokes (RANS) simulation and a coarse Large Eddy Simulation (LES) simultaneously using two different grids that overlap each other (typically, a highly wall-refined grid is used for the RANS, whereas a more homogenous and isotropic mesh is used for the LES). The two simulations correct each other using a switching criterion that determines the driving and the driven simulations at every point in space. It is demonstrated that the flow unsteadiness and the coexistence of laminar and turbulent regions in the square cavity complicate the task of choosing a suitable switching criterion. Accordingly, a new criterion based on comparing the turbulence lengthscales to the grid size was developed to account for the presence of the aforementioned complex flow features. The behaviour of this criterion and comparisons of the dual-mesh predictions against pure RANS, pure coarse LES and Direct Numerical Simulation (DNS) results are also presented in the current paper.

Thermal and flow characteristics of buoyancy-driven non-Newtonian flows at a high Rayleigh number of 107 and predictions from an artificial neural network

The thermal and flow characteristics at Ra = 107 were evaluated in a square cavity containing a circular cylinder in different places along the diagonal and horizontal centerlines. The enclosure contained non-Newtonian fluids of pseudoplastic and dilatant natures. The power-law index was varied in the range of 0.6–1.6 with an interval of 0.2 and a fixed Prandtl number of 10. The effects on the laminar natural convection are reported. The flow regimes were categorized as steady symmetric, steady asymmetric, non-periodic unsteady symmetric, non-periodic unsteady asymmetric, periodic unsteady symmetric, and periodic unsteady asymmetric. Artificial neural network was used to predict the thermal performance in the enclosure. The thermal transport in cases of n 1. The ANN model was effective in estimating the heat transfer performance with appropriate training.

Direct measurements of the thermal dissipation rate in turbulent Rayleigh–Bénard convection

We report measurements of the thermal dissipation rate in turbulent Rayleigh-Bénard convection using a four-thermistor temperature gradient probe. The measurements have been undertaken in a Rayleigh-Bénard cell filled with air (Prandtl number Pr=0.7). The focus of this work is on large aspect ratios Γ (ratio between the horizontal and vertical extension of the cell), for which reason four datasets in the range of Rayleigh number Ra=3.9×106 to Ra=1.8×109 were taken at Γ≥8. In order to extend the range toward higher Rayleigh numbers, two smaller aspect ratios were also investigated (Γ=4 with Ra=1.7×1010 and Γ=2 with Ra=1.6×1011). We present highly resolved, vertical profiles of the thermal dissipation rate in the central vertical axis and discuss how these profiles change with the Rayleigh number. With its maximum near the wall and at the highest Rayleigh number, the thermal dissipation rate decreases monotonically with the distance from the plate. Moreover, the normalized, volume-averaged thermal dissipation rate, which effectively results in the Nusselt number Nu, scales with an exponent of about 0.29 with the Rayleigh number. In the Rayleigh number range investigated here, the dissipation is always higher in the boundary layer than in the bulk region. However, by means of an extrapolation of the considered Rayleigh number range to larger Rayleigh numbers, the intersection point between the dissipation in the boundary layer and the bulk region can be estimated as Ra≈3×1012.

Immersed boundary method for MHD unsteady natural convection around a hot elliptical cylinder in a cold rhombus enclosure filled with a nanofluid

In this study, the numerical investigation of the natural convection heat transfer around a hot elliptical cylinder inside a cold rhombus enclosure filled with a nanofluid in the presence of a uniform magnetic field is conducted. An immersed boundary method as a computational tool has been extended and applied to solve the problem. The influence of various parameters such as cylinder diameters (a, b), Hartmann number (Ha = 0, 50 and 100), nanofluid volume fraction (varphi = 0 , 2.5% and 5%), and Rayleigh number (Ra = 103, 104, 105, 106, and 107) has been studied. Streamlines and isotherms contours as well as average Nusselt number have been specified for different modes. An equation for the average Nusselt number as a function of mentioned parameters is presented in this paper. The results show that at lower Ra numbers of Ra = 103 and 104, the magnetic field effect is negligible. However, at higher Rayleigh numbers, the average Nusselt number (Nuave) decreases with the increasing Ha number. The maximum decrease in Nuave at Ra = 105, 106 and 107are calculated −8.15%, −23.4% and −27.3%, respectively. An asymmetry-unsteady flow is observed at {text{Ra}} = 10^{7} for Ha = 0. However, at higher Ha numbers a steady-symmetrical flow is formed.

A stable and accurate scheme for solving the Stefan problem coupled with natural convection using the Immersed Boundary Smooth Extension method

The dissolution of solids has created spectacular geomorphologies ranging from centimeter-scale cave scallops to the kilometer-scale “stone forests” of China and Madagascar. Mathematically, dissolution processes are modeled by a Stefan problem, which describes how the motion of a phase-separating interface depends on local concentration gradients, coupled to a fluid flow. Simulating these problems is challenging, requiring the evolution of a free interface whose motion depends on the normal derivatives of an external field in an ever-changing domain. Moreover, density differences created in the fluid domain induce self-generated convecting flows that further complicate the numerical study of dissolution processes. In this contribution, we present a numerical method for the simulation of the Stefan problem coupled to a fluid flow. The scheme uses the Immersed Boundary Smooth Extension method to solve the bulk advection-diffusion and fluid equations in the complex, evolving geometry, coupled to a θ-L scheme that provides stable evolution of the boundary. We demonstrate 3rd-order temporal and pointwise spatial convergence of the scheme for the classical Stefan problem, and 2nd-order temporal and pointwise spatial convergence when coupled to flow. Examples of dissolution of solids that result in high-Rayleigh number convection are numerically studied, and qualitatively reproduce the complex morphologies observed in recent experiments.

Free Convection Heat Transfer and Entropy Generation in an Odd-Shaped Cavity Filled with a Cu-Al2O3 Hybrid Nanofluid

The present paper aims to analyze the thermal convective heat transport and generated irreversibility of water-Cu-Al2O3 hybrid nanosuspension in an odd-shaped cavity. The side walls are adiabatic, and the internal and external borders of the enclosure are isothermally kept at high and low temperatures of Thand Tc, respectively. The control equations based on conservation laws are formulated in dimensionless form and worked out employing the Galerkin finite element technique. The outcomes are demonstrated using streamlines, isothermal lines, heatlines, isolines of Bejan number, as well as the rate of generated entropy and the Nusselt number. Impacts of the Rayleigh number, the hybrid nanoparticles concentration (ϕhnf), the volume fraction of the Cu nanoparticles to ϕhnf ratio (ϕr), width ratio (WR) have been surveyed and discussed. The results show that, for all magnitudes of Rayleigh numbers, increasing nanoparticles concentration intensifies the rate of entropy generation. Moreover, for high Rayleigh numbers, increasing WR enhances the rate of heat transport.

Mixed finite elements for convection-coupled phase-change in enthalpy form: Open software verified and applied to 2D benchmarks

Melting and solidification processes are often affected by natural convection of the liquid, posing a multi-physics problem involving fluid flow, convective and diffusive heat transfer, and phase-change reactions. Enthalpy methods formulate this convection-coupled phase-change problem on a single computational domain. The governing equations can be solved accurately with a monolithic approach using mixed finite elements and Newton’s method. Previously, the monolithic approach has relied on adaptive mesh refinement to regularize local nonlinearities at phase interfaces. This contribution instead separates mesh refinement from nonlinear problem regularization and provides a continuation procedure which robustly obtains accurate solutions on the tested 2D uniform meshes. A flexible and extensible open source implementation is provided. The code is formally verified to accurately solve the governing equations in time and in 2D space, and convergence rates are shown. Two benchmark simulations are presented in detail with comparison to experimental data sets and corresponding results from the literature, one for the melting of octadecane and another for the freezing of water. Sensitivities to key numerical parameters are presented. For the case of freezing water, effective reduction of numerical errors from these key parameters is successfully demonstrated. Two more simulations are briefly presented, one for melting at a higher Rayleigh number and one for melting gallium.

Effect of inclination on nonlinear evolution and bifurcation of thermal convection in a square cavity

Heat transfer of natural convection in inclined cavities is one of the hot research topics in nonlinear non-equilibrium systems. In this paper, direct numerical simulations of natural convection in an inclined square cavity are carried out by using a high-accuracy numerical method. The effects of the different trends of inclination angle in a range of 0°–180° on the nonlinear evolution of flow field, heat transfer efficiency, and bifurcation are investigated. The Rayleigh number varies in a range from 10<sup>3</sup> to 10<sup>6</sup>. The results show that the heat transfer efficiency characterized by Nusselt number is highly dependent on the Rayleigh number, Prandtl number, and the inclination angle. When the Rayleigh number is high, the Nusselt number will have a small jump near the inclination angle in a range of 80°–100°. The evolution of the flow field and temperature field are more complicated at high Rayleigh number. There are one to three vortices of different intensities in the cavity. At low Rayleigh number and inclination angle of the cavity being close to 90°, the flow state is composed mainly of heat conduction state. In addition, it is found that there exist two stable branches of solutions in a range of Rayleigh number (4949, 314721) when the inclination angle is in the interval of (70°, 110°).

NUMERICAL ANALYSIS OF NATURAL CONVECTION IN A HEATED ROOM AND ITS IMPLICATION ON THERMAL COMFORT

A heated room is numerically analyzed to study thermal comfort. Cold air flowing in from the inlet gets heated by a heat source (placed just below the inlet), before being distributed throughout the room. The presence of the heat source and a high Rayleigh number causes the flow of air to be buoyant and turbulent. Two RANS based turbulence models, RNG k-ε and k-ω SST turbulence models are used to model turbulence and the Discrete Ordinate (DO) radiation model is used to model radiation heat transfer between different surfaces in the room. In order to account for buoyant air movement, air is approximated as a Boussinesq fluid. Parameters that affect comfort such as comfort temperature, operative temperature, turbulence intensity, velocity and the temperature difference between the head and ankle level are investigated. It is found that the comfort temperature and operative temperature predicted in this study have similar profiles irrespective of the turbulence models. Predicted values of turbulence intensity and velocity were low, which shows a low risk of drought in the occupied zone. The two RANS models give results similar to earlier studies that were performed with different turbulence and radiation models, proving their robustness and viability for a variety of flow problems.

Natural convection and surface radiation in an insulated square cavity with inner hot and cold square bodies

A numerical investigation of laminar natural convective heat transfer and surface radiation around two square isothermal cylinders maintained at a temperature difference was carried out. These cylinders are placed inside a square cavity whose walls are perfectly adiabatic. The governing equations were iteratively solved using the control volume and the discreet ordinate approaches. The Rayleigh number (103≤Ra≤107), the walls emissivity (0≤ε≤1), the sides-ratio (1≤ζ≤5), the active area (0.02≤S≤0.2), the horizontal (0.25≤Dh≤0.75) and the vertical (0.2≤DV≤0.8) positions are the governing parameters. The effect of the mentioned governing parameters on the streamlines, isotherms and the convective and radiative Nusselt number are presented. The present results show that surface radiation considerably affects the flow structure in the annulus especially at high Rayleigh numbers. The effect of the locations of the inner square cylinders, the sides-ratio and their sizes are found to play a significant role in radiative and convective heat transfers.

ENTROPY GENERATION ANALYSIS OF NATURAL CONVECTION IN A NON-DARCY ANISOTROPIC POROUS CAVITY

The entropy generation associated with the natural convection in a non-Darcy anisotropic porous cavity is numerically analyzed using the finite element method (FEM). Furthermore, it is endeavored to investigate the effects of different anisotropic porous parameters on the flow, thermal field, and entropy generation. The main considered parameters in the study consist of the Rayleigh number (103 ≤ Ra ≤ 109), the Darcy number (10-2 ≤ Da ≤ 10-6), the permeability ratio (K* = 0.1,1,10), the thermal conductivity ratio (k* = 0.1,1,10), the ratio of Forchheimer constant (F* = 0.1, 1, 10), and the inclination angle of principal axis on the flow (θ = 0°, 45°, 90°). It is found that the anisotropic properties have a significant influence on the entropy generation. Change in the inclination of the principal axis θ alters the average Bejan number and the total entropy generation. The effects of ratio of the Forchheimer constant on the entropy generation and the average Bejan number appear clearly at high values of Rayleigh number. Entropy generation has the highest values in the case of high permeability ratio and low ratio of Forchheimer constant. Lower values of the average Bejan number and the total entropy gerneration are found at high values of thermal conductivity ratio. An increase of the Rayleigh number strongly enhances the total entropy generation. The entropy generation due to the fluid friction is dominant over the entropy generation due to heat transfer at high Rayleigh and Darcy numbers.

Lattice Boltzmann Simulation of MHD Rayleigh-Bénard Natural Convection in a Cavity Filled With a Ferrofluid

In this study, we examine the effect of a uniform external magnetic field on Rayleigh-Bénard convection in a square cavity filled with a ferrofluid. Numerical simulations are based on the Lattice Boltzmann method. The effects of physical parameters, which are the Rayleigh number, the Hartmann number, and the angle of inclination of the magnetic field are studied. The results obtained are graphically illustrated and discussed for a volume fraction of four percent. These results show that the rate of heat transfer decreases by increasing the Hartmann number. For high Rayleigh number values, the maximum heat transfer rate was obtained for a specific Hartmann number when the Lorentz and buoyancy forces are perpendicular

Simulating natural convection with high Rayleigh numbers using the Smoothed Particle Hydrodynamics method

This paper conducts the simulation of natural convection in a differentially heated square cavity at high Rayleigh numbers by using the smoothed particle hydrodynamics (SPH) method. Due to the decrease of the accuracy and stability, it is challenging for the SPH method to simulate natural convection at high Rayleigh numbers, and there are few reported SPH literatures of natural convection at Ra>106 for air (Pr = 0.71). In this study, four integrated SPH models are presented to simulate the natural convection and their accuracy and stability are assessed. These four SPH models are associated with Kernel Gradient Correction (KGC) to improve approximation accuracy and Particle Shifting Technology (PST) to regularize particle distribution while they are different in treating density diffusion and calculating the pressure term. The numerical results show that SPH model_4 (KGC, PST, δ-SPH and asymmetric pressure approximation) is the most suitable for simulating the closed natural convection problems, especially at high Rayleigh numbers. Good agreements with reference solutions are obtained by SPH model_4 for the natural convection at 104≤Ra≤108. Furthermore, the simulation of natural convection at Ra=109 is conducted by SPH model_4. The evolutions of thermal convection are described in detail. It is found that dynamics characteristic reveals that the dominant force is the pressure gradient, rather than the buoyancy force before the quasi-steady state. In addition, the chaotic motion at Ra=109 has significant influence to the heat transfer characteristic in the vertical boundary layers.

The structure of the lithosphere and upper mantle beneath the Eastern Mediterranean and Middle East

Surface velocity measurements show that the Middle East is one of the most actively deforming regions of the continents. The structure of the underlying lithosphere and convecting upper mantle can be explored by combining three types of measurement. The gravity field from satellite and surface measurements is supported by the elastic properties of the lithosphere and by the underlying mantle convection. Three dimensional shear wave velocities can be determined by tomographic inversion of surface wave velocities. The shear wave velocities of the mantle are principally controlled by temperature, rather than by composition. The mantle composition can be obtained from that of young magmas. Application of these three types of observation to the Eastern Mediterranean and Middle East shows that the lithosphere thickness in most parts is no more than 50-70 km, and that the elastic thickness is less than 5 km. Because the lithosphere is so thin and weak the pattern of the underlying convection is clearly visible in the topography and gravity, as well as controlling the volcanism. The convection pattern takes the form of spokes: lines of hot upwelling mantle, joining hubs where the upwelling is three dimensional. It is the same as that seen in high Rayleigh number laboratory and numerical experiments. The lithospheric thicknesses beneath the seafloor to the SW of the Hellenic Arc and beneath the NE part of the Arabian Shield are more than 150 km and the elastic thicknesses are 30–40 km.

Reconstruction of natural convection within an enclosure using deep neural network

The deep neural network (DNN) is an extensively used technique to fit the high dimensional data. Fluid flow and heat transfer in macroscale are one of the complex physical phenomena which are governed by the Navier-Stokes (N-S) equation. The conventional numerical method (e.g., finite difference method) can solve the equation with corresponding boundary conditions using kinds of spatial discretized methods. In the present paper, the deep neural network can also be used to train and compute the results even if the training data only comes from boundary conditions of velocities and temperature. For the natural convection with few computational fluid dynamics (CFD) based velocities and temperature, the loss function of deep neural network, which mixes the explicit constraint of N-S equation, can reconstruct the fluid and heat field accurately. Usually, the complex geometry or high Rayleigh (Ra) number are corresponding to the complicate distribution of velocities and temperature field, which need more training points to achieve impressive accuracy. The present paper comprehensively investigates reconstructing results with different training data when Ra=103, and finds that only 1.48% points of CFD based data can obtain the impressive conclusion. Besides, the attempt of predicting velocities and temperature of the whole domain from partial region training data has been conducted. Global relative errors of velocities and temperature of Ra=105converge to the value, which is a little larger thanRa=104, although the latter case possesses more training points. When increasing the Rayleigh number to 106, the reconstruction of unsteady natural convection still remains high accuracy even if only 10 snapshots are considered. For the reconstruction of natural convection with complex geometry, the results show that more training points should be fed into the deep neural network to train and learn accurate results.

Towards model order reduction for fluid-thermal analysis

The authors develop basic components of a parametric model-order reduction (pMOR) procedure targeting high Rayleigh-number buoyancy-driven flows. The pMOR is based on Galerkin formulation of the governing Boussinesq equations using eigenfunction bases derived from proper orthogonal decomposition. The advantages of pMOR over parametric interpolation are demonstrated for quantities of interest (QOIs) with linear and nonlinear dependencies on the solution in low Rayleigh-number cases. Constraint-base and Leray-type regularizations are shown to offer significant advantages over the standard reduced-order Galerkin formulation in a variety of examples including 3D Rayleigh–Bénard flow at Rayleigh number 107 and turbulent flow in a half-pipe at Reynolds number 5300.