Natural and Mixed Convection in Coarse-grained Porous Media

Iman Ataei Dadavi

Research output: ThesisDissertation (TU Delft)

12 Downloads (Pure)


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.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • Delft University of Technology
  • Kleijn, C.R., Supervisor
  • Tummers, M.J., Advisor
Thesis sponsors
Award date29 Apr 2020
Print ISBNs978-94-6375-893-2
Publication statusPublished - 29 May 2020


  • Natural Convection
  • Mixed convection
  • heat transfer
  • Porous Media
  • Particle Image Velocimetry
  • Liquid Crystal Thermography

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