A discussion on the interpretation of the Darcy equation in case of open-cell metal foam based on numerical simulations

It is long known that for high-velocity fluid flow in porous media, the relation between the pressure drop and the superficial velocity is not linear. Indeed, the classical Darcy law for shear stress dominated flow needs to be extended with a quadratic term, resulting in the empirical Darcy–Forchheimer model. Another approach is to simulate the foam numerically through the volume averaging technique. This leads to a natural separation of the total drag force into the contribution of the shear forces and the contribution of the pressure forces. Both representations of the total drag lead to the same result. The physical correspondence between both approaches is investigated in this work. The contribution of the viscous and pressure forces on the total drag is investigated using direct numerical simulations. Special attention is paid to the dependency on the velocity of these forces. The separation of the drag into its constituent terms on experimental grounds and for the volume average approach is unified. It is shown that the common approach to identify the linear term with the viscous forces and the quadratic term with the pressure forces is not correct

Applying the volume averaging theory to open-cell metal foam in natural convection/radiation

Papers presented to the 11th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, South Africa, 20-23 July 2015.Heat sinks made out of open-cell aluminium foam are investigated numerically in natural convection. Results derived from a 2D numerical model are compared to results for in-house experiments. Different foam heights are studied. The numerical model is based on the volume averaging theory. The aluminium foam that is used has 10 pores per linear inch and a porosity of 93%. The temperature of the substrate was varied between 55°C and 95°C. The geometry used in the numerical model replicates the experimental test rig as well as possible. A discussion of the determination of the closure terms is given. If only convective heat transfer is taken into account in the numerical model, the relative differences between the numerical and experimental results are smaller than 29% for all foam heights studied. However, when the influence of radiation is included in the numerical model, it is shown that the numerical results differ less than 9% with the experimental ones. This validates the choice of closure terms used in the model and this shows that it is necessary to properly model radiative heat transfer in numerical models of open-cell aluminium foam in natural convection.am201

A Discussion on the Interpretation of the Darcy Equation in Case of Open-Cell Metal Foam Based on Numerical Simulations

It is long known that for high-velocity fluid flow in porous media, the relation between the pressure drop and the superficial velocity is not linear. Indeed, the classical Darcy law for shear stress dominated flow needs to be extended with a quadratic term, resulting in the empirical Darcy–Forchheimer model. Another approach is to simulate the foam numerically through the volume averaging technique. This leads to a natural separation of the total drag force into the contribution of the shear forces and the contribution of the pressure forces. Both representations of the total drag lead to the same result. The physical correspondence between both approaches is investigated in this work. The contribution of the viscous and pressure forces on the total drag is investigated using direct numerical simulations. Special attention is paid to the dependency on the velocity of these forces. The separation of the drag into its constituent terms on experimental grounds and for the volume average approach is unified. It is shown that the common approach to identify the linear term with the viscous forces and the quadratic term with the pressure forces is not correct

How to Study Thermal Applications of Open-Cell Metal Foam: Experiments and Computational Fluid Dynamics

This paper reviews the available methods to study thermal applications with open-cell metal foam. Both experimental and numerical work are discussed. For experimental research, the focus of this review is on the repeatability of the results. This is a major concern, as most studies only report the dependence of thermal properties on porosity and a number of pores per linear inch (PPI-value). A different approach, which is studied in this paper, is to characterize the foam using micro tomography scans with small voxel sizes. The results of these scans are compared to correlations from the open literature. Large differences are observed. For the numerical work, the focus is on studies using computational fluid dynamics. A novel way of determining the closure terms is proposed in this work. This is done through a numerical foam model based on micro tomography scan data. With this foam model, the closure terms are determined numerically

Effect of a sharp return bend on two-phase refrigerant flow void fraction

In this work, the void fraction is measured for two-phase refrigerant flow at several locations up-and downstream of a sharp return bend. The tube diameter D ranges between 4.83 mm and 8 mm and the curvature radius of the bend (2R/D) ranges between 2.5 and 4.5. The void fraction measurement is based on the electrical capacitance of the flow. The refrigerant used is R134a, the mass flux was varied between 200 and 600 kg/m²s and the vapour quality varied between 0 and 1. The tubes up-and downstream of the return bend are horizontal and the plane of the bend is placed vertical. Downward as well as upward oriented flow through the bend was tested. Three flow regimes were observed: slug flow, intermittent flow and annular flow. A significant effect is observed downstream of the return bend, upstream the result was limited. Furthermore, the influence of the bend decreases with decreasing channel diameter

Experimental study of the effects of foam height, orientation and radiative heat transfer on buoyancy-driven convection

Air-saturated buoyancy-driven convection in open-cell aluminium foam is studied. The effects of foam height, radiative heat transfer and orientation are experimentally investigated. Two aluminium foam heat sinks with the same baseplate dimensions (6″ by 4″) are tested. Their respective foam height is 22.2 mm and 40 mm. The aluminium foam has a porosity of 0.946 and a pore density of 10 pores per linear inch. The heat sinks are tested in a vertical and a horizontal orientation. The effect of radiation is studied by comparing untreated heat sinks with painted versions. During the experiments the power dissipated by the heat sinks is measured as function of the temperature difference between the baseplate of the heat sink and the ambient. This temperature difference is varied from 10 to 70°C