A review of correlations to model the packing structure and effective thermal conductivity in packed beds of mono-sized spherical particles

[1] We present a model of heat conduction for mono-sized spherical particulate media under stagnant gases based on the kinetic theory of gases, numerical modeling of Fourier's law of heat conduction, theoretical constraints on the gas thermal conductivity at various Knudsen regimes, and laboratory measurements. Incorporating the effect of the temperature allows for the derivation of the pore-filling gas conductivity and bulk thermal conductivity of samples using additional parameters (pressure, gas composition, grain size, and porosity). The radiative and solid-to-solid conductivities are also accounted for. Our thermal model reproduces the well-established bulk thermal conductivity dependency of a sample with the grain size and pressure and also confirms laboratory measurements finding that higher porosities generally lead to lower conductivities. It predicts the existence of the plateau conductivity at high pressure, where the bulk conductivity does not depend on the grain size. The good agreement between the model predictions and published laboratory measurements under a variety of pressures, temperatures, gas compositions, and grain sizes provides additional confidence in our results. On Venus, Earth, and Titan, the pressure and temperature combinations are too high to observe a soil thermal conductivity dependency on the grain size, but each planet has a unique thermal inertia due to their different surface temperatures. On Mars, the temperature and pressure combination is ideal to observe the soil thermal conductivity dependency on the average grain size. Thermal conductivity models that do not take the temperature and the pore-filling gas composition into account may yield significant errors.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2008JE003308

A model of thermal conductivity for planetary soils: 1. Theory for unconsolidated soils

A numerical model of heat conduction through particulate media made of spherical grains cemented by various bonding agents is presented. The pore-filling gas conductivity, volume fraction, and thermal conductivity of the cementing phase are tunable parameters. Cement fractions <0.001-0.01% in volume have small effects on the soil bulk thermal conductivity. A significant conductivity increase (factor 3-8) is observed for bond fractions of 0.01 to 1% in volume. In the 1 to 15% bond fraction domain, the conductivity increases continuously but less intensely (25-100% conductivity increase compared to a 1% bond system). Beyond 15% of cements, the conductivity increases vigorously and the bulk conductivity rapidly approaches that of bedrock. The composition of the cements (i.e. conductivity) has little influence on the bulk thermal inertia of the soil, especially if the volume of bond <10%. These results indicate that temperature measurements are sufficient to detect cemented soils and quantify the amount of cementing phase, but the mineralogical nature of the bonds and the typical grain size are unlikely to be determined from orbit. On Mars, a widespread surface unit characterized by a medium albedo (0.19-0.26) and medium/high thermal inertia (200-600 J s(0.5)/sq m/K) has long been hypothesized to be associated with a duricrust. The fraction of cement required to fit the thermal data is less than approx.1-5% by volume. This small amount of material is consistent with orbital observations, confirming that soil cementation is an important factor controlling the thermal inertia of the Martian surface

A Model of Thermal Conductivity for Planetary Soils

Radiation represents an important contribution to the heat transfer through a packed bed. The packing structure is important in the determination of the radiation heat transfer, but this aspect is not explicit in most of the mathematical models proposed in the literature. Here, a new numerical approach is proposed to calculate the radiation heat transfer in such a bed from its structure using the Voronoi network model. On this basis, the effective thermal conductivity (ETC) is evaluated by taking into account the effects of the radiation heat transfer and conduction through neighbor particles and stagnant fluid. The validity of this approach is verified by comparing the calculated and measured ETCs under different conditions. This approach is used to investigate the effects of variables such as particle thermal conductivity, emissivity and size, and bed temperature as well. The relative contributions of different heat transfer mechanisms are analyzed. It is shown that there is a similarity in the probabil...

Particle Scale Evaluation of the Effective Thermal Conductivity from the Structure of a Packed Bed: Radiation Heat Transfer

The development of Module In-vessel degraded severe accident Analysis Code MIDAC and the relevant research for CPR1000 during the station blackout scenario

The radiative heat transfer, in a bed of negligible interparticle axial heat conduction, was measured by means of an original developed apparatus. The measurements were taken over a temperature range of 350 K to 930 K, in a bed packed with spherical particles of negligible heat resistance. The experimental results support a previously published (and here improved) theory, which was developed for the calculation of radiative heat transfer in terms of the radiative properties and the geometry of the packing material. The results are valid for particles of high heat conductivity.

D. Vortmeyer

Papers

Wärmestrahlung in Schüttungen aus Kugeln mit vernachlässigbarem Wärmeleitwiderstand