Permeability calculations in three-dimensional isotropic and oriented fiber networks

Area of Science:

• Fluid Dynamics
• Materials Science
• Computational Mechanics

Background:

• Hydraulic permeability of fiber networks is vital for numerous applications.
• Limited research exists on permeability calculations in three-dimensional random networks.
• Direct simulation of flow through artificial networks is computationally intensive for large scales.

Purpose of the Study:

• To develop a correlation for permeability based on fiber properties (volume fraction, radius, orientation).
• To compare direct finite element calculations with volume-averaging theories for various fiber network configurations.
• To assess the impact of fiber volume fraction and orientation on network permeability.

Main Methods:

• Direct permeability calculations using the finite element method on artificial fiber networks.
• Volume-averaging theory applied to flows parallel and perpendicular to fibers.
• Comparison of results using drag coefficients for isolated fibers versus spatially periodic arrays.

Main Results:

• The finite element model validated well against analytical solutions for structured fiber arrays.
• Volume-averaging methods showed good agreement with direct calculations when using drag coefficients for periodic arrays.
• Using drag coefficients for isolated fibers overpredicted permeability in the studied range.

Conclusions:

• A weighted combination of drag coefficients for spatially periodic fiber arrays provides a good approximation for network permeability.
• Fiber volume fraction and orientation are more dominant factors influencing permeability than local network structure.
• This work offers a more computationally feasible approach to estimating fiber network permeability.