Three-dimensional Convection Research Articles

Formation of a future supercontinent through plate motion–driven flow coupled with mantle downwelling flow

Abstract Series of high-resolution numerical simulations of three-dimensional mantle convection were performed to examine the interaction between the drifting continental lithospheres and the underlying mantle structure for 250 m.y. from the present, and to predict the configuration of the future supercontinent. The density anomaly of the mantle interior was determined by the seismic velocity anomaly from global seismic tomography data sets, which contain well-resolved subducting slabs. The present-day plate motion was imposed for the first stage of the simulation as a velocity boundary condition at the top surface boundary, instead of a shear stress–free condition. The switching time from the plate motion boundary to shear stress–free conditions was taken as a free parameter. The results revealed that Australia, Eurasia, North America, and Africa will merge together in the Northern Hemisphere to form a new supercontinent within ∼250 m.y. from the present. The continental drift was assumed to be realized by plate-scale mantle flow, rather than large-scale upwelling plumes. That is, continuously moving plates at the surface for the first stage of the simulation are mechanically coupled with the subducting slabs in the mantle; this enhances the underlying mantle downwelling flow. As a result, persistent continental drift can be reproduced for long future time periods even though top surface boundary conditions may switch in response to shear stress–free conditions. The configuration of the numerically reproduced future supercontinent in this study is broadly consistent with the hypothetical model of Amasia as indicated by previous findings from geological correlations and a paleogeographic reconstruction.

Numerical simulation of three-dimensional natural convection in a cubic enclosure induced by an isothermally-heated circular cylinder at different inclinations

This study numerically examines three-dimensional natural convection of air induced by temperature difference between a cold outer cubic enclosure and a hot inner cylinder. Simulations have been carried out for Rayleigh numbers ranging from 103 to 107 and a titled angle of the enclosure varying from 0° to 90°. The developed mathematical model is governed by the coupled equations of continuity, momentum and energy and is solved by finite volume method. The effects of cylinder inclination and Rayleigh number on fluid flow and heat transfer are presented. The distribution of isocontours of temperature, components of velocity and streamtraces eventually reaches a steady state for Rayleigh numbers ranging from 103 to 107 for titled inclination of 90°. However, for the remaining inclinations, Rayleigh numbers must be in the range 103–106 to avoid unsteady state which is manifested by the subdivision of the area, containing the maximum local heat transfer rate, into three parts for a Rayleigh number equal to 107 and an inclination of 90°. We mention that instability study is not included in the present paper which is solely devoted to three dimensional calculations. Results indicate also that optimal average heat transfer rate is obtained for Rayleigh number set to 106 and an inclination of 90° for both cases of the inner cylinder and lateral walls of cubical enclosure.

Numerical simulation of three-dimensional double diffusive convection in a lid-driven cavity

In this work, the heat and mass transfers in 3D lid driven cavity is analyzed. Double-diffusive convective flow in a cubic enclosure with moving left side in −y (Case I) or +y (Case II) directions is studied numerically. The cavity is heated from left side and cooled from right and constant different concentration is imposed, while remaining surfaces are adiabatic.The FVM based on the 3D vector-potential – vorticity formalism is used as numerical method. Prandtl number and Lewis number are fixed at 10, 0.7 and 2, respectively. The study covers a wide range for Richardson number 0.1 ≤ Ri ≤ 10 and Buoyancy ratio −10 ≤ Ri ≤ 10. Results are presented by particle trajectories, isotherms, Iso-concentration and local and mean Nusselt and Sherwood numbers.

Taguchi Optimization Approach for Three-Dimensional Nanofluid Natural Convection in a Transformable Enclosure

In the present study, the Taguchi method was performed in assessing the maximum heat transfer rate for natural convection of a nanofluid in an enclosure with an adjustable wall. The simulations were planned based on the Taguchi L25 orthogonal array. The experiments were performed under different positions of the top and bottom walls of the cavity and particle volume fraction of the nanofluid. The thermal lattice Boltzmann method based on D3Q19 methods was employed to simulate the flow and thermal fields. A signal-to-noise ratio analysis was carried out in order to determine the effects of the process parameters and the optimal factor settings. The present results demonstrated great reliability of the Taguchi method in optimization of the thermal system.

Three-dimensional natural convection around an inner circular cylinder located in a cubic enclosure with sinusoidal thermal boundary condition

Three-dimensional numerical simulations were conducted for the natural convection phenomena around an inner circular cylinder positioned in a cold cubic enclosure in the relatively high Rayleigh numbers of Ra=105 and Ra=106 at the Prandtl number of Pr=0.7. In this study, we observed the flow and heat transfer characteristics in the enclosure according to the variation of thermal boundary conditions on the bottom wall of the enclosure as well as the inner cylinder surface in the convection-dominant region. The Immersed Boundary Method (IBM) was used to capture the virtual wall boundary of the inner cylinder, based on the Finite Volume Method (FVM). Detailed three-dimensional flow and thermal structures in the enclosure were analyzed using the distribution of streamlines, iso-surfaces of three-dimensional isotherms and two dimensional views of isotherms. They depended on the number, size, strength and rotational directions of ascending plumes from the bottom wall as well as the hot inner cylinder as a function of the Rayleigh number and thermal boundary conditions. In addition, the distribution of Nusselt number on the walls of enclosure as well as the cylinder surface was presented as a function of the sinusoidal temperature variation on the bottom wall of the enclosure for different Rayleigh numbers of 105 and 106.

Mixed convection squeezing three-dimensional flow in a rotating channel filled with nanofluid

Purpose – The purpose of this paper is to numerically solve the problem of an unsteady squeezing three-dimensional flow and heat transfer of a nanofluid in rotating vertical channel of stretching left plane. The fluid is assumed to be Newtonian, incompressible and electrically conducting embedded with nanoparticles. Effect of internal heat generation/ absorption is also considered in energy equation. Four different types of nanoparticles are considered, namely, copper (Cu), alumina (Al2O3), silver (Ag) and titanium oxide (TiO2) with the base fluid as water. Maxwell-Garnetts and Brinkman models are, respectively, employed to calculate the effective thermal conductivity and viscosity of the nanofluid. Design/methodology/approach – Using suitable similarity transformations, the governing partial differential equations are transformed into set of ordinary differential equations. Resultant equations have been solved numerically using Runge-Kutta-Fehlberg fourth fifth order method for different values of the governing parameters. Effects of pertinent parameters on normal, axial and tangential components of velocity and temperature distributions are presented through graphs and discussed in detail. Further, effects of nanoparticle volume fraction, squeezing parameter, suction/injection parameter and heat source/sink parameter on skin friction and local Nusselt number profiles for different nanoparticles are presented in tables and analyzed. Findings – Squeezing effect enhances the temperature field and consequently reduces the heat transfer rate. Large values of mixed convection parameter showed a significant effect on velocity components. Also, in many heat transfer applications, nanofluids are potentially useful because of their novel properties. They exhibit high-thermal conductivity compared to the base fluids. Further, squeezing and rotation effects are desirable in control the heat transfer. Originality/value – Three-dimensional mixed convection flows over in rotating vertical channel filled with nanofluid are very rare in the literature. Mixed convection squeezing three-dimensional flow in a rotating channel filled with nanofluid is first time investigated.

Three-Dimensional Steady and Oscillatory Natural Convection in a Rectangular Enclosure With Heat Sources

In this paper, a numerical study of three-dimensional (3D) natural convection air-cooling of two identical heat sources, simulating electronic components, mounted in a rectangular enclosure was carried out. The governing equations were solved by using the finite-volume method based on the SIMPLER algorithm. The effects of Rayleigh number Ra, spacing between heat sources d, and aspect ratios Ax in x-direction (horizontal) and Az in z-direction (transversal) of the enclosure on heat transfer were investigated. In steady state, when d is increased, the heat transfer is more important than when the aspect ratios Ax and Az are reduced. In oscillatory state, the critical Rayleigh numbers Racr for different values of spacing between heat sources and their aspect ratios, at which the flow becomes time dependent, were obtained. Results show a strong relation between heat transfers, buoyant flow, and boundary layer. In addition, the heat transfer is more important at the edge of each face of heat sources than at the center region.

Numerical analysis of periodic 3D convective heat transfer in fenestration with between-the-glass louvered blinds

A three-dimensional unsteady laminar natural convection in fenestration with between-the-glass louvered blinds. The considered system is a 3D vertical cavity with differentially heated vertical walls and with rotatable louvered blinds located exactly midway between the walls. The temperature imposed to the hot wall is periodic to be closer to real conditions. The effects of, louvered blinds inclination, thermal conductivity ratio, period and Rayleigh number on the temperature field, flow structure and heat transfer were examined.

Power law non-Newtonian fluid unsteady conjugate three-dimensional natural convection inside a vessel driven by surrounding air thermal convection in a cavity

This paper presents the results of a numerical study on the unsteady three-dimensional natural convection of a power-law fluid in a thick walled vessel being driven by natural heat convection in the surrounding air inside a cubical cavity. Continuity, linear momentum and energy equations for the internal Otswald the Waele shear thinning fluid, with a power index n = 0.4, are used to describe fluid mechanics and natural heat transfer along the conjugate continuity, Navier–Stokes and energy equations for the external Newtonian air flow and the transient heat diffusion equation in the walls of the inner fluid container. Unsteady 3D thermal convection of the inner shear-thinning fluid, with n = 0.4, is analyzed in comparison with the fluid mechanics and heat transfer results for the Newtonian fluid, with n = 1, for two values of the Rayleigh number: Ra = 2.09 × 104 and 2.09 × 106. Thermo-physical properties of the inner fluid are allowed to change with temperature for the two values of the Rayleigh number and for both the Newtonian and the power law non-Newtonian inner fluids. Numerical simulations were carried out by an -in house- Fortran 90 Finite Volume Method parallelized code. Results of the evolution of the fluid mechanics are described in terms of the streamlines and those related to the unsteady convective heat transfer in terms of the isotherms.

Three-dimensional buoyancy-driven convection structures in thermohaline stratification

We report on three-dimensional convection structures in thermohaline stratification with the high Rayleigh number RaT = 7 ⋅ 107, the diffusion ratio δ = 0.01 and various initial density stability ratios R = 0.5, 0.8, and 1.1. According to the classification of buoyancy-driven instability in the parameter space (R, δ), the three cases are referred to follow the Rayleigh-Taylor (RT) mode, the mixed mode (MM) and the diffusive-layer convection (DCL) mode, respectively. Whether the shape of the peak is a finger under the RT mode or a spike under the MM/DLC mode, the 3D view of the interface is likely to be a rolling mountain with a doughnut-shaped vortex around the peak and a banded vortex above the ridge. The doughnut-shaped vortex is maintained around the peak if its growth continues under RT convection; otherwise, the vortex sheds off and moves upward from the peak under the DLC mode. Additionally, we have observed the previously unreported vortex stratification by the contact interface due to the differential diffusion effect.

Effect of Periodic Imposed Heat Flux on Three-Dimensional Natural Convection in a Partially Heated Cubical Enclosure

The three-dimensional numerical study of natural convection in a cubical enclosure, discretely heated, was carried out in this study. Two heating square sections, similar to the integrated electronic components, are placed on the vertical wall of the enclosure. The imposed heating fluxes vary sinusoidally with time, in phase and in opposition of phase. The temperature of the opposite vertical wall is maintained at a cold uniform temperature and the other walls are adiabatic. The governing equations are solved using Control volume method by SIMPLEC algorithm. The sections dimension ε = D / H and the Rayleigh number Ra were fixed respectively at 0,35 and 106. The average heat transfer and the maximum temperature on the active portions will be examined for a given set of the governing parameters, namely the amplitude of the variable temperatures a and their period τp. The obtained results show significant changes in terms of heat transfer, by proper choice of the heating mode and the governing parameters.

Three-dimensional oscillatory mixed convection in a Czochralski silicon melt under the axial magnetic field

A three-dimensional time dependent computational model is developed to simulate the oscillatory mixed convection of the melt during the crystal growth in Czochralski crucible. To study the magnetic damping effects on the growth process, an axial steady magnetic field is considered. The governing equations of continuity, momentum, energy, and electric potential subject to Boussinesq approximation applied to gravity term, have been solved numerically by a computer program developed in FORTRAN language based on finite volume method in conjunction with SIMPLER and TDMA Algorithms. The obtained results show a good agreement with experimental data available in the literature. Without magnetic field, the flow structure shows an irregularity, and the critical Reynolds number decreased in function of Richardson number owing to the destabilizing contribution of the convection. The applied of the magnetic field involves an important regulation of the flow structure and the instability delayed for higher values of the Reynolds number. The magnetic stability diagram which is established shows the dependence of the critical Reynolds number with the increase of the Hartmann number, for various values of the Richardson number. This work confirms the possibility of stabilization of a liquid metal flow in mixed convection by application of a magnetic field.

Three-dimensional unsteady natural convection and entropy generation in an inclined cubical trapezoidal cavity with an isothermal bottom wall

Numerical computation of unsteady laminar three-dimensional natural convection and entropy generation in an inclined cubical trapezoidal air-filled cavity is performed for the first time in this work. The vertical right and left sidewalls of the cavity are maintained at constant cold temperatures. The lower wall is subjected to a constant hot temperature, while the upper one is considered insulated. Computations are performed for Rayleigh numbers varied as 103⩽Ra⩽105, while the trapezoidal cavity inclination angle is varied as 0°⩽Φ⩽180°. Prandtl number is considered constant at Pr=0.71. Second law of thermodynamics is applied to obtain thermodynamic losses inside the cavity due to both heat transfer and fluid friction irreversibilities. The variation of local and average Nusselt numbers is presented and discussed, while, streamlines, isotherms and entropy contours are presented in both two and three-dimensional pattern. The results show that when the Rayleigh number increases, the flow patterns are changed especially in three-dimensional results and the flow circulation increases. Also, the inclination angle effect on the total entropy generation becomes insignificant when the Rayleigh number is low. Moreover, when the Rayleigh number increases the average Nusselt number increases.

THE SPECTRAL AMPLITUDE OF STELLAR CONVECTION AND ITS SCALING IN THE HIGH-RAYLEIGH-NUMBER REGIME

ABSTRACT Convection plays a central role in the dynamics of any stellar interior, and yet its operation remains largely hidden from direct observation. As a result, much of our understanding concerning stellar convection necessarily derives from theoretical and computational models. The Sun is, however, exceptional in that regard. The wealth of observational data afforded by its proximity provides a unique test bed for comparing convection models against observations. When such comparisons are carried out, surprising inconsistencies between those models and observations become apparent. Both photospheric and helioseismic measurements suggest that convection simulations may overestimate convective flow speeds on large spatial scales. Moreover, many solar convection simulations have difficulty reproducing the observed solar differential rotation owing to this apparent overestimation. We present a series of three-dimensional stellar convection simulations designed to examine how the amplitude and spectral distribution of convective flows are established within a star’s interior. While these simulations are nonmagnetic and nonrotating in nature, they demonstrate two robust phenomena. When run with sufficiently high Rayleigh number, the integrated kinetic energy of the convection becomes effectively independent of thermal diffusion, but the spectral distribution of that kinetic energy remains sensitive to both of these quantities. A simulation that has converged to a diffusion-independent value of kinetic energy will divide that energy between spatial scales such that low-wavenumber power is overestimated and high-wavenumber power is underestimated relative to a comparable system possessing higher Rayleigh number. We discuss the implications of these results in light of the current inconsistencies between models and observations.

Three-Dimensional Visualization of Natural Convection in Porous Media

Carbon dioxide (CO2) geological storage (CGS) is a preferred technique to mitigate anthropogenic climate change. In terms of CGS, density-driven natural convection dominated dissolution of CO2 into formation brine results in a stable trapping increasing the storage security.A full utilization of a nonlinear density property of fluid system has been applied to mimic the natural convection in saline aquifers. Three-dimensional natural convection in porous medium has been observed by employing X-ray computer tomography (CT) technology. Since the X-ray attenuation depends on the concentration of sodium iodide, the distribution of local concentration can be evaluated during the downward extension based on the CT images.We successively visualized the process of formation and the development of Rayleigh-Bénard fingers. This process modelled natural convection between heavier CO2 loaded brine and brine with little (or no) CO2. High density fingers extend downward at the characteristic buoyancy velocity and coalescent with the neighbouring finger before reaching the bottom of the porous medium. The coalescence of fingers leads to a decrease in finger number and an increase in finger diameter. As the Rayleigh number increases, the finger tends to be fine and extends faster. The mass transfer rate increases with the Rayleigh number also.

Characteristics of flow and thermal boundary layer in turbulent Rayleigh-Bénard convection

The parallel direct method of direct numerical simulation (PDM-DNS) for Rayleigh-Bénard (RB) convection is used in this paper. The differences and similarities in flow characteristic between two-dimensional (2D) and three-dimensional (3D) turbulent RB convection are studied using mean field for Ra=109, 1010, 5×1010, and Pr=4.3. Each of 2D and 3D cases has a large-scale circulation and corner rolls. The shape of large-scale circulation becomes round and the size of corner roll turns small as Ra increases. In 2D RB convection, there are four corner vortices at the corner of the square cavity and a stable large-scale circulation which is elliptical. For spanwise averaged 3D RB convection with two corner vortices, large-scale circulation reveals spindle shape. Due to the characteristic of the corner roll, the region plume dominating is wider in 2D RB convection than in the spanwise-averaged 3D case. Further, the Ra-dependence of thermal boundary layer properties is also studied. The thermal boundary layer thickness is scaled with Ra and the scaling exponents of λθ with Ra in the 2D and 3D cases are very similar.

低重力場三次元層流熱対流に及ぼすg-jitterの影響について

低重力場三次元層流熱対流に及ぼすg-jitterの影響について

Experimental investigation on effects of crystal and crucible rotation on thermal convection in a model Czochralski configuration

A series of experiments are presented to understand the effects of crystal and crucible rotations on the thermal convection in a model Czochralski (Cz) configuration which consists of a crucible filled with the transparent 0.65cSt silicone oil (Pr=6.7) and a model crystal. The thermal convection is induced by the temperature difference between the crucible sidewall and the crystal sidewall. The results show that the critical Rayleigh number for the onset of instability of thermal convection increases with the increase of the crystal rotation rate without the crucible rotation. When the crucible rotates, the critical Rayleigh number is higher than that with standing crucible at small crystal rotation rates. After the flow destabilizes, a three-dimensional oscillatory convection is characterized by traveling spoke patterns at small crystal rotation rates. With the increase of the crystal rotation rate, the azimuthal propagating velocity of the spoke pattern increases. Furthermore, the spoke pattern dims gradually and gives way to the wave pattern. The crystal rotation has a slight effect on the spoke number until the spoke pattern disappears. Compared with the shallow pool, the crystal rotation makes the flow more likely to be disturbed in the deeper pool. On the contrary, the crucible rotation is more conducive to suppressing the oscillatory flow in the deeper pool.

Improvement of molten core–concrete interaction model in debris spreading analysis module with consideration of concrete degradation by heat

ABSTRACTUnderstanding the situation inside of the reactors at TEPCO's Fukushima Daiichi Nuclear Power Plant and planning of the methods for debris removal are important for decommissioning the reactors. A debris spreading analysis (DSA) module in the severe accident analysis code SAMPSON has been improved and verified to analyze composite phenomena of molten core (debris) spreading on a reactor containment floor and concrete erosion to the inside of the floor by molten core–concrete interaction (MCCI). The primary models in the DSA module were three-dimensional natural convection with simultaneous spreading, melting and solidification in an open space. In addition to these, the analysis capability has been improved to treat phenomena in a closed space, such as debris eroding laterally under concrete floors at the bottom of the sump pit which is done by an advanced method for boundary processing. A buffer cell for flow analysis, which is defined by a different array variable, is arranged in the same coordinates of the concrete cell (structure cell). Mass, momentum, and the advection term of energy between the debris melt cells and the buffer cells are solved. At the same instant, the heat transfer is calculated between the debris melt cells and the structure cells coexisting side by side with the buffer cells. In this study, technical knowledge regarding changes in physical properties due to thermal degradation of concrete was considered for the prediction of erosion rate, and the DSA module with the models noted above was verified by comparison with erosion data of the core–concrete interaction tests in the OECD/MCCI program. The calculated erosion depth, width, and erosion rate under the concrete floor showed good agreement with the test data and the analysis capability of the module was confirmed.

Three-dimensional natural convection of molten Lithium in a differentially heated rotating cubic cavity about a vertical ridge

Laminar natural convection heat transfer in three-dimensional molten Lithium filled differentially heated enclosure, rotating about the vertical ridge is studied numerically. Computations are performed for a wide range of dimensionless parameters including the rotational Rayleigh number, and Taylor number while the values of Rayleigh number and Prandtl numbers are maintained constant at Ra=2×104 and Pr=0.0321, respectively. The results indicate that Coriolis forces seem to have a dominant role to suppress the thermal buoyancy driven effects. Transverse velocity isovaleurs show three-dimensional characteristics of the flow. By increasing, the Taylor number, the maxima of heat transfer gradually reduced about 55%. In the contrast, high rotational Rayleigh number values are found to significantly alter the flow patterns by increasing mixing which turn enhances the heat transfer.