High Rayleigh Number Research Articles

Robust wall states in rapidly rotating Rayleigh–Bénard convection

We show, using direct numerical simulations with experimentally realizable boundary conditions, that wall modes in Rayleigh–Benard convection in a rapidly rotating cylinder persist even very far from their linear onset. These nonlinear wall states survive in the presence of turbulence in the bulk and are robust with respect to changes in the shape of the boundary of the container. In this sense, these states behave much like the topologically protected states present in two-dimensional chiral systems even though rotating convection is a three-dimensional nonlinear driven dissipative system. We suggest that the robustness of this nonlinear state may provide an explanation for the strong zonal flows observed recently in experiments and simulations of rapidly rotating convection at high Rayleigh number.

Analysis of Rayleigh–Taylor instability at high Atwood numbers using fully implicit, non-dissipative, energy-conserving large eddy simulation algorithm

Large eddy simulation of three-dimensional, multi-mode Rayleigh–Taylor instability at high Atwood numbers is performed using a recently developed, kinetic energy-conserving, non-dissipative, fully implicit, finite volume algorithm. The algorithm was especially designed for simulating low-Mach number, variable density/viscosity, transitional, and turbulent flows. No interface capturing mechanism is required. Buoyancy and heat transfer effects can be handled without relying on the Boussinesq assumption. Because of this feature, unlike the pure incompressible ones, it does not suffer from the loss of physical accuracy at high Atwood and Rayleigh numbers. In this study, the mixing phenomenon in Rayleigh–Taylor instability and the effects of high Atwood numbers on the development of the flow are investigated using various diagnostics such as local mole fractions, bubble and spike penetration lengths and growth rates, mixing efficiencies, Taylor micro-scales, and corresponding Reynolds numbers and energy ratios. Additionally, some important terms of the Reynolds stress transport equation are also introduced, such as Reynolds stresses (and their anisotropies) and turbulent production. Results show that Rayleigh–Taylor instability at high Atwood numbers is characterized by rapid development of instability due to the increasing growth rates and higher velocities of spike fronts, larger asymmetry in the mixing region, denser interactions in the non-linear phase, and changes in bubble and spike morphologies. It is also found that interactions of spike-fronts with their surroundings are the primary mechanisms of turbulent production and transition to turbulence. However, late time mean flow measures such as energy ratio and mixedness are not significantly affected. A scaling relation between the spike to bubble penetration ratio and the heavy to light density ratio is also provided.

A 3D numerical study on natural convection flow of nanofluid inside a cubical cavity equipped with porous fins using two-phase mixture model

This paper is concerned with 3D-numerical studies on free convection flow of CuO–water nanofluid in a cubical cavity with porous fins embedded. The two-phase mixture model is employed and the numerical simulations are performed for natural flow of the nanofluid with volume concentrations from 0% to 3% at different Rayleigh (Ra) numbers inside the cavity equipped with 1, 2 and 3 porous fins. Increasing the nanoparticle fraction shows an improvement in heat transfer and Nusselt number. By increment of Ra and domination of convection, the nanofluid flow becomes truly irregular and consequently, the average Nusselt number enhances. For low Ra, isotherms are rather uniform due to weak buoyancy force. While, at higher Rayleigh numbers, augmentation of buoyancy force strongly reduces the isotherms uniformity. In the presence of porous fins, the flow velocity decreases with no significant change in the flow pattern. Also, at low Rayleigh numbers, embedding porous fins results in agitating parallel arrangement of isotherms. The influence of three mentioned variables (i.e., volume fraction, Rayleigh number and number of porous fins) on average Nusselt number is comparatively determined using Taguchi technique and signal to noise ratio according to which nanoparticle loading shows the most principal effect of all.

Lattice Boltzmann Computations of Natural Convection Heat Transfer of Nanofluid in a Square Cavity Heated by Protruding Heat Source

Abstract This paper reported the mathematical modeling and numerical simulation of natural convection flow of Cu/water nanofluid in a square enclosure using the lattice Boltzmann method (LBM). The cavity is heated from below by heat source and cooled by the top wall. The vertical walls are adiabatic. After validating the numerical code against the numerical and experimental data, simulations were performed for different Rayleigh numbers (104–0.5 × 107), nanoparticles volume fractions (0–8%), and cavity inclination angle (0 deg–90 deg). The effects of the studied parameters on the streamlines, on isotherms distributions within the enclosure, and on the local and average Nusselt numbers are investigated. It was found that heat transfer and fluid flow structure depend closely on the nanoparticle concentration. Results show differences in stream separation between a base fluid and the nanofluid. Also, adding small nanoparticles fractions, less than 6%, to the base fluid enhances the heat transfer for higher Rayleigh numbers and cavity inclination angle less than 30 deg. It is concluded that the optimal dilute suspension of copper nanoparticles can be applied as a passive way to enhance heat transfer in natural convection engineering applications.

Gravity, Topography, and Melt Generation Rates From Simple 3‐D Models of Mantle Convection

AbstractConvection in fluid layers at high Rayleigh number (Ra ∼106) have a spoke pattern planform. Instabilities in the bottom thermal boundary layer develop into hot rising sheets of fluid, with a component of radial flow toward a central upwelling plume. The sheets form the “spokes” of the pattern, and the plumes the “hubs.” Such a pattern of flow is expected to occur beneath plate interiors on Earth, but it remains a challenge to use observations to place constraints on the convective planform of the mantle. Here we present predictions of key surface observables (gravity, topography, and rates of melt generation) from simple 3‐D numerical models of convection in a fluid layer. These models demonstrate that gravity and topography have only limited sensitivity to the spokes and mostly reflect the hubs (the rising and sinking plumes). By contrast, patterns of melt generation are more sensitive to short‐wavelength features in the flow. There is the potential to have melt generation along the spokes but at a rate which is relatively small compared with that at the hubs. Such melting of spokes can only occur when the lithosphere is sufficiently thin ( km) and mantle water contents are sufficiently high ( ppm). The distribution of volcanism across the Middle East, Arabia, and Africa north of the equator suggests that it results from such spoke pattern convection.

Numerical investigation of the internally heated melt pool natural convection behavior with the consideration of different high internal Rayleigh numbers

The melt pool could form in the nuclear reactor lower plenum under a hypothetic severe accident. In such condition, remaining the integrity of reactor pressure vessel (RPV) is treated as one of the severe accident management strategies. The investigation of melt pool natural convection behavior is one of the most important aspects in the in-vessel retention (IVR) investigation. Various experimental and numerical research regarding the internally heated melt pool natural convection behavior has been conducted before. However, there is a lack of comprehensive investigation of internally heated melt pool natural convection behavior. The numerical investigation of the internally heated melt pool natural convection behavior with the consideration of different high internal Rayleigh numbers is conducted in this work. This work could bring the reference for the further investigation of internally heated molten pool natural convection behavior.

Parameter analysis of natural convection thermal characteristics in internally heated pool

The natural convection thermal behavior with high Rayleigh number was important in many industrial situations accompanied by internal heating, strong turbulence and solidification process. Experiments were carried out to investigate natural convection thermal characteristics in internally heated pool. Both water and nitrate were selected as simulant materials. The pool temperature along height, heat flux and crust thickness along polar angle were obtained from experiments. The effects of heating power density, pool height, crust solidification, cooling boundary were investigated. Moreover, the geometry effect of 2D and 3D were investigated based on the CFD simulation. The crust formation resulted in higher heat transfer on top with the largest heat flux ratio of 2.4 in nitrate cases and only 1.9 in water cases, indicating that the relationship without solidification applied in system codes may lead to lower peak heat flux at pool top. The Nudn increased exponentially and the Nudn from nitrate tests were higher than those from water tests with larger temperature gap Tmax-Tint. The cooling effectiveness of 3D hemispherical pool was 1.5 times that of 2D slice pool. However, the Nudn from hemispherical simulation was 24.06% higher than the COPRA relation prediction. The application of two-dimensional results needs consideration of geometry extrapolation for further application.

Nanofluid buoyancy-driven heat transfer in three-dimensional horizontal annuli

The effect of Rayleigh number and nanoparticle concentration on the flow dynamics and natural convection in three-dimensional large- and moderate-gap annuli is analyzed in detail in this work. A nanofluid is applied as the working fluid, with typical nanoparticle concentration ranging from zero to nine percent. The results indicate that the flow strength and deformation of isotherms becomes less intensive with an increase in the nanoparticle concentration for both large- and moderate-gap annuli. There exists a core region in the large-gap annulus, where the flow is two-dimensional and the value of the local Nusselt number is almost uniform in the axial direction. The core region exists between two secondary rolls, which are adjacent to the primary end rolls. The secondary flow decreases in size and finally disappears with an increase in the nanoparticle concentration. For the moderate-gap annulus, the space between the two end walls near the top portion is filled by multiple rolls, and an increase in the nanoparticle concentration gradually reduces the number of the rolls. The locations of the descending and ascending rolls relate to the maximum peaks of the Nusselt number on the inner and outer cylinders, respectively. The heat transfer enhancement only occurs at low nanoparticle concentrations (φ < 3%) and higher Rayleigh numbers (Ra > 105) for a large-gap annulus. Otherwise, in general, a deterioration in heat transfer is observed when the nanoparticle concentration increases from 1 to 9% for both large- and moderate-gap annuli.

Three-dimensional electroconvective vortices in cross flow.

This study focuses on the three-dimensional (3D) electrohydrodynamic flow instability between two parallel electrodes driven by unipolar charge injection with and without cross flow. Lattice Boltzmann method with a two-relaxation time model is used to compute flow patterns. In the absence of cross flow, the base-state solution is hydrostatic, and the electric field is one-dimensional. With strong charge injection and high electrical Rayleigh number, the system exhibits electroconvective vortices. Disturbed by perturbation patterns, such as rolling pattern, square pattern, and hexagon pattern, the flow develops corresponding to the most unstable mode. The growth rate and pattern transitions are studied using dynamic mode decomposition of the transient numerical solutions. The interactions between cross flow and electroconvective vortices lead to suppression and disappearance of structures with velocity components in the direction of cross flow, while the other components are not affected. Surprisingly, the transition from a 3D to a 2D flow pattern enhances the convective charge transport, marked by an increase in the electric Nusselt number. Hysteresis in the 3D to 2D transition is characterized by the nondimensional parameter Y, a ratio of the electrical force term to the viscous term in the momentum equation.

Numerical analysis of entropy generation in a square cavity filled with boron-water nanofluid

The entropy generation and natural convection in a square cavity filled with boron-water nanofluid is numerically investigated under the influence of different nanoparticle volume fractions and buoyancy forces when heated from left vertical wall and cooled from right vertical wall while horizontal walls are insulated. The results are compared with copper (Cu) and aluminum oxide (Al2O3) nanoparticles generally used in the applications. Differential equations are discretized over the SIMPLE algorithm and solved iteratively using the finite control volume method. Entropy generation contours due to heat transfer and fluid friction are presented. Local and average Bejan numbers are also investigated. The results of the study show that the entropy generation increases with the increase in Rayleigh number for all nanoparticles, and fluid friction irreversibility is more dominant in entropy generation with increasing Rayleigh number, and almost all entropy generation is caused by fluid friction in high Rayleigh numbers.

Natural convection from cross blade inside a nanofluid-filled cavity using ISPH method

Purpose The purpose of this study is to apply the incompressible smoothed particle hydrodynamics method for simulating the natural convection flow inside a cavity including cross blades or circular cylinder cylinder. Design/methodology/approach The base fluid is water and copper-water nanofluid is treated as a working fluid. The left and rights walls are maintained at a cool temperature, the horizontal cavity walls are isolated and the inner shape was heated. The physical parameters are the length of the blades L_Blade, the number of cross blades, circular cylinder radius L_R, Rayleigh number Ra and the nanoparticles volume fraction. Findings The results reveal that the lengths of the cross blade, number of the blades and radius of the circular cylinder is working as an enhancement factor for heat transfer and fluid flows inside a cavity. Adding nanoparticles augments heat transfer and reduces the fluid flow intensity inside a cavity. The best case for buoyancy-driven flow was obtained when the inner shape is the circular cylinder at a higher Rayleigh number. Originality/value This work uses a distinctive numerical method to study the natural convection heat from cross blades inside a cavity filled with nanofluid. It provides a new analysis of this issue and presented good results.

Free convection of a hybrid nanofluid past a vertical plate embedded in a porous medium with anisotropic permeability

PurposeThis study aims to carry out an analysis for flow and heat transfer of a new hybrid nanofluid over a vertical flat surface embedded in a saturated porous medium with anisotropic permeability at high Rayleigh number. Here the hybrid nanofluid is considered as the working fluid, with different kinds of small particles in nanoscale being suspended.Design/methodology/approachThe generalized homogenous model is introduced to describe the behaviors of hybrid nanofluid. Within the framework of the boundary layer approximations, the governing equations embodying the conservation equations of total mass, momentum and thermal energy are reduced to a set of fully coupled ordinary differential equations via relevant scaling transformations. A flow stability analysis is performed to examine the behavior of convective heat energy. Accurate solutions are obtained by means of a very efficient homotopy-based package BVPh 2.0.FindingsResults show that the linear correlations of physical quantities among the base fluid and its suspended nanoparticles are adequate to give accurate results for simulation of behaviors of hybrid nanofluids. Heat enhancement can be also fulfilled by hybrid nanofluids. A flow stability analysis suggests the heat-related power index m > −1/3 for satisfying the increasing behavior of convective heat energy.Originality/valueFree convection of a hybrid nanofluid near a vertical flat surface embedded in a saturated porous medium with anisotropic permeability is investigated for the first time. The simplified hybrid nanofluid model is proposed for describing nanofluid behaviors. The results of this proposed approach agree well with those given by the traditional hybrid nanofluid model and experiment. It is expected that, by using different combinations of various kinds of nanoparticles, the new generation of heat transfer fluids can be fabricated, which possess similar thermal-physical properties as regular nanofluids but with lower cost.

Magneto hydrodynamic convection in a nanofluid saturated enclosure with porous fins

PurposeThis paper aims to numerically investigate the magnetohydrodynamic (MHD) convection heat transfer of nanofluid inside a differentially heated enclosure with various fin morphologies.Design/methodology/approachThe fluid flow within the cavity was governed by N-S equations while it within porous medium was solved by the non-Darcy model, called the Darcy–Forchheimer model based on representative element-averaging method. Empirical correlations from experimental data are used to evaluate the effective thermal conductivity and dynamic viscosity. Relevant governing parameters, including thermal Rayleigh number (105-107), Hartmann number (0-50), Darcy number (10−6-10−1), thermal conductivity ratio of porous matrix (1-103), nanoparticles volume fraction (0-0.04) and topology designs of porous fins, are sensitively varied to identify their effects and roles on the fluid flow and heat transfer. Particularly, heatlines are used to investigate the mechanism of heat transport.FindingsNumerical results demonstrate that the predictions of average Nusselt number are augmented by using more porous fins with high permeability, and this effect becomes opposite in tiny Darcy numbers. Particularly, for high Darcy and Rayleigh numbers, the shortest fins could achieve the best performance of heat transfer. In addition, the prediction of average Nusselt number reduces with an increase in Hartmann numbers. An optimal nanoparticles concentration also exists to maximize heat transfer enhancement. Finally, numerical correlations for the average Nusselt number were proposed as functions of these governing parameters.Practical implicationsPresent work could benefit the thermal design of electronic cooling and thermal carriers in nanofluid engineering.Social implicationsPresent work could benefit the thermal design of electronic cooling and thermal carriers in nanofluid engineering. In addition, optimum thermal removals could enhance the lifetime of electronics, therefore reducing the cost of energy and materials.Originality/valueTo the best knowledge of authors, there are not any studies considering the synergetic effects of porous fins on MHD convection of nanofluids. Present work could benefit the thermal design of electronic cooling and thermal carriers in nanofluid engineering.

An experimental investigation on natural convection of non-covalently functionalized MWCNTs nanofluids: Effects of aspect ratio and inclination angle

Abstract An experimental analysis was conducted to study natural convection heat transfer of water-based nanofluids. Two enclosures with the length × width × height(cm) dimensions of 10 × 10 × 10 and 20 × 10 × 10 and the inclination slopes of 0, 45 and 90° were considered. One of the walls was cooled and the opposite wall was heated. Multi-walled carbon nanotube (MWCNT)/water nanofluids were used as the heat transfer fluid while the MWCNTs were non-covalently functionalized by gum Arabic (GA). The MWCNT-GA/water nanofluids were prepared using 0.005, 0.05 and 0.1 wt% nanoparticles. According to the results, adding MWCNTs to water reduced free convection heat transfer in both enclosures. The effect of increasing MWCNT concentration on Nusselt number was found to be greater than the impact of changing Rayleigh number. Furthermore, free convection heat transfer increased with reducing inclination angle from 90° to 0° at high Rayleigh numbers. It was noticed that changing inclination angle has no considerable influence on Nusselt number at lower Rayleigh numbers. Moreover, free convection heat transfer increased about 8.77% with increasing the aspect ratio from 1 to 2. The highest reduction of Nusselt number was attributed to a system with the aspect ratio, concentration and inclination angle of 1, 0.1 wt% and 90°, respectively.

Thermal and hydraulic analysis of selective artificial ground freezing using air insulation: Experiment and modeling

Abstract In some artificial ground freezing (AGF) applications of civil or mining projects, only particular parts of the ground need to be frozen. Selective artificial ground freezing (S-AGF) is an AGF technique where a specific portion of the freeze pipe is insulated, usually by an air gap, to prevent any undesirable ground freezing. In this study, a laboratory scale experimental setup that mimics actual S-AGF systems has been established. The experimental rig is built in a fully controlled environment and equipped with advanced instrumentation. Additionally, a mathematical model coupling the flow of the coolant, air, and porous ground is developed by solving the conservation equations of mass, momentum, and energy. The mathematical model is then validated against the experimental measurements of the ground and outlet coolant temperatures. Moreover, the natural convection inside the air gap is further validated at higher Rayleigh numbers with an experimental study from the literature. The results indicate that the energy consumption of AGF plants can be significantly reduced by applying the S-AGF concept, as compared to convectional AGF systems. Also, it is found that the optimum air gap thickness, L opt , relates to the cavity height, H, and Rayleigh number, Ra H , as L opt ~ 2 HRa H - 1 / 4 .

Mixed baroclinic convection in a cavity

We study the convective patterns that arise in a nearly semicylindrical cavity fed in with hot fluid at the upper boundary, bounded by a cold, porous semicircular boundary at the bottom, and infinitely extended in the third direction. While this configuration is relevant to continuous casting processes that are significantly more complex, we focus on the flow patterns associated with the particular form of mixed convection that arises in it. Linear stability analysis (LSA) and direct numerical simulations (DNS) are conducted, using the spectral-element method to identify observable states. The nature of the bifurcations is determined through Stuart–Landau analysis for completeness. The base flow consists of two counter-rotating rolls driven by the baroclinic imbalance due to the curved isothermal boundary. These are, however, suppressed by the through-flow, which is found to have a stabilising influence as soon as the Reynolds number based on the through-flow exceeds 25. For a sufficiently high Rayleigh number, this base flow is linearly unstable to three different modes, depending on . For , the rolls destabilise through a supercritical bifurcation into a travelling wave. For , a subcritical bifurcation leads to a standing oscillatory mode, whereas for , the unstable mode is non-oscillatory and grows out of a supercritical bifurcation. The DNS confirm that in all cases the dominant mode returned by the LSA precisely matches the topology and evolution of the flow patterns that arise out of the fully nonlinear dynamics.

Nanoliquid thermal convection in I-shaped multiple-pipe heat exchanger under magnetic field influence

The present work is investigated the heat management of thermogravitational convection inside a shell and tube heat exchanger filled with Fe3O4/water nanoliquid by lattice Boltzmann method (LBM). The seven internal pipes with hot or cold temperature insert in the I-shaped heat exchanger. The impacts of Rayleigh number (104-106), nanoparticles concentration (0–0.06), Hartmann number (0–60), magnetic field inclination angle (0-π/2) and the thermal arrangement of active pipes (Case 1–4) on the flow structure and energy transport characteristics are examined. The computational data are shown by streamlines, isothermal lines and the variations of the mean Nusselt number. It has been ascertained that the thermal arrangement of active pipes affects the velocity patterns and thermal transmission performance significantly. However, an increasing in the volume fraction of nano-size particles and Rayleigh number, the average Nusselt number raises regardless of the thermal arrangement. The rate of energy transport showed an opposite dependence with Hartmann number, but a direct relationship with the magnetic field inclination angle. The most suitable thermal arrangements for heat transfer rate of heated and cooled pipes are same at low magnitudes of the Rayleigh number, but different at high Rayleigh number.

Simplified and highly stable thermal Lattice Boltzmann method simulation of hybrid nanofluid thermal convection at high Rayleigh numbers

A new method called simplified and highly stable thermal lattice Boltzmann method, which is based on the lattice Boltzmann framework, was used to simulate the hybrid nanofluid natural convection and heat transfer in a square enclosure with a heating obstacle at high Rayleigh numbers. Four fins protrude from the heating obstacle to affect the flow pattern and heat transfer performance. The effects of the Rayleigh number (106 ≤ Ra ≤ 109), nanoparticle volume fraction (0 ≤ ϕ ≤ 0.05), and length of the fin (0.1 ≤ h ≤ 0.3) on the flow pattern, temperature distribution, and heat transfer characteristics were illustrated and analyzed. To validate the present method, the benchmark simulation results were performed. Three kinds of flow patterns (steady symmetry, unsteady symmetry, and unsteady asymmetry) can be identified at various Rayleigh numbers. At different lengths of fins, the critical Rayleigh number of flow pattern transition (from steady symmetry to steady asymmetry and from steady asymmetry to unsteady asymmetry) is different. ϕ and h also significantly affect the flow pattern. At higher ϕ, the flow inside the enclosure is steadier and the effect of h on the flow pattern varies at different Ra.

Computational study of natural convection and entropy generation in 3-D cavity with active lateral walls

Numerical simulation of the natural convection and entropy generation in an air-filled cubical cavity with active lateral walls is performed in this work. Both the lateral front and right sidewalls are maintained at an isothermal cold temperature. While an isothermal hot temperature is applied for both the lateral back and left sidewalls. The upper and lower walls are kept adiabatic. Entropy generation rates due to the fluid friction and the heat transfer are simulated by using the Second law of thermodynamics. Results are illustrated for Rayleigh numbers varied from (103 ? Ra ? 106). It was shown that the increase in the Rayleigh number leads to increase the average Nusselt number and to decrease the Bejan number. Also, it was found that both, Sth, and Stot, increase slightly with the increase in Rayleigh number until they reach (Ra = 105) and then begin to jump after this value. After (Ra = 105), the increase in both, Stot, and Sfr, is greater than Sth. Moreover, it was observed that iso-surfaces of Stot are similar to Sth at (103 ? Ra ? 105), while they are similar to Sfr at high Rayleigh number.

Numerical study of the coupled natural convection with surface radiation in a cylindrical annular enclosure

The interaction of natural convection with thermal radiation of black surfaces in a cylindrical enclosure filled with air has been numerically investigated. The steady-state continuity, Navier-Stokes and energy equations were discretized using the control volume method and solved numerically via the SIMPLER algorithm. Effects of Rayleigh number (Ra), wall emissivity (εp) and height ratio parameter (X) are studied. The result shows that surface radiation significantly altered the temperature distribution and the flow patterns, especially at higher Rayleigh numbers. The total average Nusselt number has also been discussed for valuating heat transfer through the enclosure.