Permeability of open-pore microcellular materials

Numerical Simulation of Heat Transfer in Porous Metals for Cooling Applications

“…If the Reynolds number, Re, increases to a critical value, the fluid will become turbulent and this relationship will change to nonlinear and the Forchheimer equation needs to be used. [15] This new relationship between pressure drop and permeability is shown in Eq. [8].…”

The permeability of virtual macroporous structures generated by sphere packing models: Comparison with analytical models

“…It also highlights the importance of accurate representation of the coordination number, which is a complex function of several parameters and not easy to measure by microscopy or from CT images, if the analytical models are to be accurate. This approach, with some minor modification to either the DEM step or to the particle data processing in MATLAB, could be extended to model more complex geometries that deviate from monosized, spheres to those that have increased particle contact areas (windows) produced by a compaction step (such as in [5]). …”

“…The coordination number and window radius are defined in separate equations, the coordination number as a function of the packing fraction (also shown in Eq 1), and the window radius in terms of the infiltration pressure and particle (pore) size. The model in [5] reduces to the same expression for permeability for the case of dense random particle packing if Nc = 6 (which is not atypical of this packing condition [7,8] Reasonable correlation between experimental measurements of permeability and the models was observed in both cases, with deviations attributed, in part, to the non-spherical nature of some of the salt particles used. Thus a strong dependence upon the size of the windows connecting the pores and the permeability is apparent and controlling the window size, through varying the infiltration pressure [6] has the capacity (for a given pore size) to vary the permeability by more than a factor of 10 and would be more convenient way to vary the permeability rather than by altering the packing (porosity) through additional and potentially costly processing steps.…”

“…Simple permeability models for laminar flow have been developed [5,6] which could assist with the design of these porous metal structures to meet the requirements for specific applications. Both approaches use the same premise, considering the window between the pores to be a "bottleneck" to the flow through the structure.…”

“…Both approaches use the same premise, considering the window between the pores to be a "bottleneck" to the flow through the structure. The models consider different particle contact cases (loose packing [6] and packing enhanced through compaction [5]) with different approaches to including contributions from the window size and coordination number. The model to predict the permeability according to [6] is presented in Eq 1 where  is the porosity, Nc the coordination number, rw the window radius and rp the radius of the pore.…”