Convective heat transfer in coarse-grained porous media: A numerical investigation of natural and mixed convection

Heat transfer by the motion of fluids, referred to as convective heat transfer, is ubiquitous. Convective heat transfer in enclosures packed with solid obstacles, is of great importance in various engineering and real-life applications, such as in blast furnaces, refrigeration devices, distribution transformers, nuclear waste disposal, energy storage, etc. Both natural convection, where the heat transfer occurs due to the flow induced by density differences, and mixed convection, where the combined influence of natural convection and forced convection is of importance, play an important role in these applications.ChemE/Transport Phenomen

Numerical analysis of effects of fins and conductive walls on heat transfer in side heated cavities — Onset of three-Dimensional phenomena in natural convection

In the present study, we analyse individual and combined effects of conductive horizontal walls and conductive fins on the natural convection of air in side heated cavities (SHC). The flow and heat transfer are studied for Rayleigh numbers in the range of 104−−109: Direct Numerical Simulation (DNS) is conducted for the lower and Large Eddy Simulation (LES) for the higher Rayleigh numbers (>108). Thermally conductive walls destabilize the flow yielding an earlier transition to turbulence and expedite the decay in boundary layer thickness with increase in Rayleigh number. The preheating/precooling along the conductive walls reduces the actual heat transfer at the vertical walls. Above the fin, instabilities are only marginally enhanced for adiabatic horizontal walls, whereas for conductive horizontal walls, plumes erupt from the fin. This localized Rayleigh-Bénard-like effect triggers 3D instabilities in the entire flow field and yields a steeper slope in Nusselt-Rayleigh diagram. The presence of a fin increases the integral heat transfer by 18% for adiabatic and 21% for conductive horizontal walls. We show that 2D and 3D simulations are similar for the smooth cases (i.e., without fin), but differ by 4% and 13% for the adiabatic and conductive fin cases respectively. The local heat transfer characteristics even deviates up to 50%, therefore a 2D simplification should be avoided.ChemE/Transport PhenomenaJ.M. Burgers Center for Fluid Mechanic

Effect of double-diffusive convection with cross gradients on heat and mass transfer in a cubical enclosure with adiabatic cylindrical obstacles

We investigate natural convection driven by a horizontal temperature gradient and a vertical concentration gradient in fluid-filled enclosures with obstructions inside it. Within the domain, nine adiabatic and impermeable cylinders are placed, occupying 30% of the domain volume. The Boussinesq approximation is used to account for density variations within the fluid and the flow is fully resolved. The solutal Rayleigh number has been fixed at RaC=106 and the Prandtl number at Pr=5.4. The Lewis number has been varied in the range of 1 ≤ Le ≤ 100 and the buoyancy ratio in the range of 0.1 ≤ |N| ≤ 10. The rate of heat and mass transfer are compared to those found in single-scalar natural convection, i.e solely thermal or concentration driven convection. Besides, the obtained heat and mass transfer rate in the cylinder-packed enclosure have been compared to those found in a fluid-only domain. We observe that the addition of a destabilizing concentration gradient to a side-heated enclosure results in heat transfer enhancement, which decreases with Lewis number and thermal Rayleigh number. Similarly, the temperature gradient increases the mass transfer, especially at high Lewis numbers and lower concentration buoyancy force over its thermal counterpart. Although the presence of the cylindrical obstacles reduced the flow velocity, the mass transfer was enhanced at lower buoyancy ratio.ChemE/Transport Phenomen

Numerical analysis of natural convection with conjugate heat transfer in coarse-grained porous media

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. Accepted Author ManuscriptChemE/Transport PhenomenaChemE/Chemical EngineeringFluid Mechanic

Numerical analysis of natural convection in a differentially heated packed bed with non-uniform wall temperature

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.ChemE/Transport PhenomenaFluid Mechanic

Experiments on mixed convection in a vented differentially side-heated cavity filled with a coarse porous medium

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.ChemE/Transport PhenomenaFluid Mechanic

Flow and heat transfer measurements in natural convection in coarse-grained porous media

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.Accepted Author ManuscriptChemE/Transport PhenomenaFluid Mechanic

Assisting and opposing mixed convection with conjugate heat transfer in a differentially heated cavity filled with coarse-grained porous media

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.ChemE/Transport PhenomenaFluid Mechanic

Effect of packing height and location of porous media on heat transfer in a cubical cavity: Are extended Darcy simulations sufficient?

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.ChemE/Transport PhenomenaFluid Mechanic

An experimental study of flow and heat transfer in a differentially side heated cavity filled with coarse porous media

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.ChemE/Transport PhenomenaFluid Mechanic