We numerically investigate natural convection in a bottom-heated top-cooled cavity, fully and partially filled with adiabatic spheres (with diameter-to-cavity-size ratio d/L=0.2) arranged in a Simple Cubic Packing (SCP) configuration. We study the influence of packing height and location of porous media. We carry out the simulations using water as the working fluid with Prandtl number, Pr=5.4 at Rayleigh number Ra=1.16×105, 1.16 × 106 and 2.31 × 107. The applicability and suitability of Darcy-Forchheimer assumption to predict the global heat transfer is analysed by comparing it with the pore-structure resolved simulations. We found that the heat transfer in pore-structure resolved simulations is comparable to that in fluid-only cavities at high Rayleigh numbers, irrespective of the number of layers of packing and its location. Discrepancies in heat transfer between the Darcy-Forchheimer and the fully resolved simulations are observed when the porous medium is close to the isothermal wall and at high Ra, while it vanishes when the porous medium is away from the isothermal bottom wall.@en

In the chain of steel production, the blast furnace converts iron ore into liquid iron. The hearth of the blast furnace, where the liquid metal is collected and tapped off, is filled with relatively large coke particles (D ~ 20 – 100 mm). The meandering flow of hot liquid metal in the coarse-grained porous medium in the hearth causes erosion of the refractory walls containing the hearth through the formation of hot spots. This has a severe impact on the lifetime of blast furnaces. Therefore, it is crucial to understand the liquid metal flow and heat transfer through the packed bed of relatively large coke particles. With the hot metal flowing in from the top and the refractory walls being cooled, the flow of the liquid metal in the hearth is a natural and mixed convection flow characterized by the dimensionless Rayleigh and Reynolds numbers, and their ratio, viz. the Richardson number. Since the pores between the large coke particles are not small compared to the flow and thermal length scales, there is a strong interaction between the flow and the pore geometry. Therefore, it is important to capture the details of fluid flow and temperature distribution at the pore level and to resolve the strong interaction between the flow and the solid grains.In order to gain a fundamental understanding of the above types of flow, this dissertation reports on experimental investigations of natural and mixed convection in cubical cavities filled with coarse-grained porous media consisting of packed beds of relatively large solid spheres. Bottom-heated natural convection, side-heat natural convection, and vented mixed convection configurations have been considered. Accurate global heat transfer measurements have been performed for various sphere packings, sphere sizes, and sphere conductivities in a wide range of Rayleigh numbers (and Reynolds numbers in the mixed convection case). Refractive index matching between water and hydrogel spheres enabled the use of optical measurement techniques, i.e. Particle Image Velocimetry and Liquid Crystal Thermography, to obtain highly-resolved pore-scale velocity and temperature fields.In bottom-heated natural convection, it was observed that at lower Rayleigh numbers, the Nusselt numbers for the porous medium-filled cavity are reduced compared to the pure-fluid cavity (Rayleigh-Bénard convection) and the Nusselt number reduction strongly depends on packing type, size, and conductivity of spheres. However, at high Rayleigh numbers, when the flow and thermal length scales become sufficiently smaller than the pore length scale, the flow penetrates into the pores with much higher velocities and is not obstructed by the presence of coarse-grained porous media. This leads to an asymptotic regime in which the convective heat transfer for all sphere conductivities, sizes and packing types converge into a single curve which is very close to the pure Rayleigh-Bénard convection curve. The results indicate that the ratio between the thermal length scale and the pore length scale is a determining factor in the effect of porous media on flow and heat transfer.In side-heated natural convection, the presence of the porous medium decreases the heat transfer compared to the corresponding pure-fluid cavity. This is due to the fact that the layers of the spheres touching the isothermal side walls hinder the boundary layers along these walls and divert a portion of the boundary layer fluid away from the walls. This subsequently alters the temperature distribution and reduces the mean temperature gradient at the walls. The heat transfer measurements demonstrate a transition from Darcy to non-Darcy regime by increasing the Rayleigh number and the size of spheres. A new Nusselt number correlation for coarse-grained porous is presented which takes into account the strong effect of the porous medium conductivity. In vented mixed convection, three flow and heat transfer regimes were observed depending on the Richardson number. For Ri < 10, the porous medium directs a portion of the strong forced inflow downward towards the hot wall, and therefore the flow structure and the Nusselt number scaling are similar to pure forced convection and are independent of Rayleigh number. For Ri > 40, the strong upward directed natural convection flow dominates and the Nusselt number becomes less sensitive to the Reynolds number. For 10 < Ri < 40, the upward directed natural convection flow competes with the downward directed forced flow at the hot wall, leading to a minimum effective Nusselt number. A Nusselt number correlation is presented which covers all three regimes. This dissertation concludes by discussing the contribution of this work in improving the knowledge on the physics of natural and mixed convection in coarse-grained porous media and its relevance for understanding and modelling of the fluid flow and heat transfer processes in the blast furnace hearth, as well as in other application fields such as in air ventilation and in the food industry.@en

We report numerical simulations of natural convection and conjugate heat transfer in a differentially heated cubical cavity packed with relatively large hydrogel beads (d/L=0.2) in a Simple Cubic Packing configuration. We study the influence of a spatially non-uniform, sinusoidally varying, wall temperature on the local flow and heat transfer, for a solid-to-fluid conductivity ratio of 1, a fluid Prandtl number of 5.4, and fluid Rayleigh numbers between 10⁵ and 10⁷. We present local and overall flow and heat transfer results for both sphere packed and water-only filled cavities, when subjected to variations of the wall temperature at various combinations of the amplitude and characteristic phase angle of the imposed wall temperature variations. It is found that imposing a sinusoidal spatial variation in the wall temperature may significantly alter the local flow and heat transfer, and consequently the overall heat transfer. At identical average temperature difference, applying a spatial variation in wall temperature at well-chosen phase angle can lead to significant heat transfer enhancement when compared to applying uniform wall temperatures. However, this is achieved at the cost of increased entropy generation.

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This paper reports on an experimental study of mixed convection flow and heat transfer in a vented, differentially side-heated cubical cavity filled with a porous medium consisting of relatively large solid low-conductivity spheres. Rayleigh numbers and Reynolds numbers are varied over the ranges 6 × 106 < Ra < 7 × 107 and 240 < Re < 4250, respectively, for a fixed Prandtl number of Pr = 6.75, thus covering more than three decades in Richardson numbers Ri = Ra/(Re2 Pr). Heat transfer measurements were combined with measurements of the velocity field (using particle image velocimetry) and the temperature field (using liquid crystal thermography) to better understand the dependence of the Nusselt number, Nu, on the Richardson number. We observed three different flow and heat transfer regimes depending on the Richardson number. For Ri < 10, the flow structure and the Nusselt number scaling are similar to those for the pure forced convection, i.e., the Nusselt number scales as Nu ~ Re0.61 independent of Rayleigh number. For Ri > 40, natural convection dominates the flow in the vicinity of the heating wall. The Nusselt number becomes less sensitive to the Reynolds number and is mainly determined by the Rayleigh number. In the intermediate regime for 10 < Ri < 40, the upward directed natural convection flow at the heating wall competes with the downward directed forced flow leading to a minimum effective Nusselt number. A Nusselt number correlation is derived that is valid in the range 0.1 < Ri < 100 covering all three regimes.@en

We report numerical simulations of assisting and opposing mixed convection in a side-heated, side-cooled cavity packed with relatively large solid spheres. The mixed convection is generated by imposing a movement on the isothermal vertical walls, either in or opposite to the direction of natural convection flow. For a fluid Prandtl number of 5.4 and fluid Rayleigh numbers of 106 and 107, we varied the modified Richardson number from 0.025 to 500. As in fluids-only mixed convection, we find that the mutual interaction between forced and natural convection, leading to a relative heat transfer enhancement in assisting - and a relative heat transfer suppression in opposing - mixed convection, is most prominent at a Richardson number of approximately one, when the Richardson number is modified with the Darcy number Da and the Forchheimer coefficient Cf = 0.1 as Rim = Ri × Da0.5/Cf. We focus on local flow and heat transfer variations in order to explain differences in local and average heat transfer between a coarse grained and fine grained (Darcy-type) porous medium, at equal porosity and permeability. We found that the ratio between the thermal boundary layer thickness at the isothermal walls and the average pore size plays an important role in the effect that the grain and pore size have on the heat transfer. When this ratio is relatively large, the thermal boundary layer is locally disturbed by the solid objects and these objects cause local velocities and flow recirculation perpendicular to the walls, resulting in significant differences in the wall-averaged heat transfer. The local nature of the interactions between flow and solid objects cannot be captured by a volume averaged approach, such as a Darcy model.@en

The present study concerns Lagrangian transport and (chaotic) advection in three-dimensional (3D) flows in cavities under steady and laminar conditions. The main goal is to investigate topological equivalences between flow classes driven by different forcing; streamline patterns and their response to nonlinear effects are examined. To this end, we consider two prototypical systems that are important in both natural and industrial applications: a buoyancy-driven flow (differentially heated configuration with two vertical isothermal walls) and a lid-driven flow governed by the Grashof (Gr) and the Reynolds (Re) numbers, respectively. Symmetries imply fundamental similarities between the streamline topologies of these flows. Moreover, nonlinearities induced by fluid inertia and buoyancy (increasing Gr) in the buoyancy-driven flow vs fluid inertia (increasing Re) and single- or double-wall motion in the lid-driven flow cause similar bifurcations of the Lagrangian flow topology. These analogies imply that Lagrangian transport is governed by universal mechanisms, and differences are restricted to the manner in which these phenomena are triggered. Experimental validation of key aspects of the Lagrangian dynamics is carried out by particle image velocimetry and 3D particle-tracking velocimetry.@en

We report numerical simulations of fluid natural convection with conjugate heat transfer in a bottom-heated, top-cooled cubical cavity packed with relatively large (d/L=0.2) solid spheres in a Body Centred Tetragonal (BCT) configuration. We study largely varying solid-to-fluid thermal conductivity ratios between 0.3 and 198, for a fluid Prandtl number of 5.4 and fluid Rayleigh numbers between 1.16 × 10 ⁶ and 1.16 × 10 ⁸ and compare global heat transfer results from our present simulations to our previously published experimental results. The interplay between convection suppression due to the solid packing, and conductive heat transfer in the packing leads to three different regimes, each with a distinct impact of the solid packing on the flow and heat transfer. At low Rayleigh numbers ≈ 10 ⁶ , all packings suppress convective flow. Compared to fluid only Rayleigh–Bénard convection, heat transfer is therefore reduced in low conductivity packings, whereas for high conductivity packings it is increased due to significant conductive heat transfer. At intermediate Rayleigh numbers ≈ 10 ⁷ , low conductivity packings no longer suppress convection, whereas flow is still suppressed in high conductivity packings due to the thermal stratification imposed on the fluid by the solid. Consequently, heat transfer is lower compared to fluid only Rayleigh–Bénard convection, even in high conductivity packings. With a further increase of Rayleigh number ≳ 10 ⁸ , convection starts to be the dominant heat transfer mechanism in all packings, and convective heat transfer is close to that for fluid only Rayleigh–Bénard convection. The contribution of solid conduction in high conductivity packings causes the overall heat transfer to be above that for Rayleigh–Bénard convectin.

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This paper reports on an experimental study of natural convection in an enclosure that is heated at the bottom and cooled at the top, filled with a packed bed of relatively large solid spheres. Nusselt numbers were measured for various sphere conductivities, spheres sizes and sphere packings for Rayleigh numbers varying between 10⁷ and 10⁹. The Nusselt number measurements showed that at lower Rayleigh numbers, the heat transfer is lower than that for pure Rayleigh-Bénard convection, with the difference depending on packing type, size, and conductivity of the spheres. However, at high Rayleigh numbers, there exists an asymptotic regime where the convective contribution of the total heat transfer for all sphere conductivities, sizes, and packing types collapse on a single curve which is very close to the curve for pure Rayleigh-Bénard convection. Refractive index-matching of the fluid and the solid spheres enabled the use of particle image velocimetry and liquid crystal thermography to obtain highly resolved velocity and temperature fields. The comparison of the velocity and temperature fields for the two heat transfer regimes showed that the velocity magnitudes inside the pores in the core region are much higher in the asymptotic regime than those in the low Rayleigh number regime, which lead to a deeper penetration of cold and hot fluid elements and higher heat transfer.

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Flow and heat transfer in a differentially side heated cubic cavity filled with relatively large solid spheres forming a coarse porous medium have been studied experimentally. Nusselt numbers were measured for Rayleigh numbers between 1.9 × 107 and 1.7 × 109, solid-to-fluid conductivity ratios between 0.32 and 618, and for different sphere sizes (d/H = 0.065, 0.14, 0.20), and packing geometries. The heat transfer results indicate that the presence of a porous medium in the cavity decreases the heat transfer compared to the pure-fluid cavity unless the solid spheres are highly conductive. We present a new Nusselt number correlation for coarse porous media based on porous medium dimensionless numbers. Particle image velocimetry and liquid crystal thermography measurements were performed in a refractive index-matched porous medium to obtain pore-scale velocity and temperature fields. The results show that the layers of spheres adjacent to the hot/cold walls play the most prominent role in the heat transfer reduction by hindering the formation of high-velocity boundary layers along the hot/cold walls, causing a portion of the boundary layer fluid to divert away from these walls, thus changing the stratified temperature distribution to a tilted one which leads to a lower overall heat transfer.@en