Numerical study on determination of thermal dispersion conductivity of metal foams

Abstract

In order to analyze transport phenomenon in metal foams two approaches are applied. These two approaches are microscopic and volume-averaged analysis. Due to complex structure of porous materials, pore-scale analysis is difficult. Therefore, volume averaging method is widely used to study flow and heat transfer in metal foams. Volume averaging the microscopic energy equation gives rise to two extra terms named as thermal dispersion and thermal tortuosity. Thermal dispersion conductivity is an important factor affecting the heat transfer. Therefore, understanding the phenomenon of thermal dispersion plays an important role in the analysis of convective heat transfer in porous media In this study numerical simulation using the commercial CFD software "COMSOL" is conducted to determine thermal dispersion conductivity for steady water flow through circular pipes filled with aluminum alloy 6101-T6 foam subjected to constant heat flux q^''=15,518 (W/m^2) for low flow rates (below 15 g/s) and q^''=26,865 (W/m^2) for higher flow rates from outside surface. The analysis is done for 10 and 40 PPI aluminum foam having same porosity of 88.5%. Total ten simulations are conducted for each foam type with various inlet velocities covering both Darcy and Forchheimer regimes. Local thermal equilibrium is assumed for this work. The one energy equation coupled with the volume averaged momentum equation is solved in order to obtain temperature distribution in computational domain. The flow condition and thermophysical properties of numerical simulation is same with experimental conditions reported in the literature. Thermal dispersion conductivity is ascertained through an iterative trial and error approach. The overall thermal conductivity is adjusted for specific inlet velocities to achieve a reasonable agreement between numerical and experimental results obtained in the literature for both wall temperature and local Nusselt number. The iterative process is terminated when deviation between numerical and experimental data is below 3% in thermally developed region. It is observed that numerical and experimental results are in a good agreement verifying the numerical simulation method. The dispersion conductivity is calculated to be around 150 percent of the effective conductivity in Forchheimer regime while this number is around 90 percent for Darcy flow. Therefore, it can be concluded that effect of dispersion conductivity is more significant in higher velocities. It is found that the slope of changes of dispersion conductivity is higher in Darcy velocity range while in Forchheimer velocity range, dispersion conductivity value remains almost constant for the same outer heat flux. Linear trend between overall Nusselt number and 〖Re〗_K 〖Pr〗_o is observed. The slope of linear trend is different for Darcy and Forchheimer regimes. Additionally, overall Nusselt number is higher for 40 PPI metal foam indicating that 40 PPI produces higher heat transfer than 10 PPI.