Numerical simulations of flow through a variable permeability circular cylinder

Abstract

This paper investigates flow through variable permeability, two-dimensional circular cylinders using a pseudospectral numerical model. Two types of permeability (K) distributions are considered: constant with a lower permeability blockage, and constant with a higher permeability duct. Boundary conditions set by external flow with high Reynolds number lead to streamwise flow asymmetry and more short length scale variability within the cylinder when compared to conditions set by potential flow. High permeability belts are observed to guide flow around regions of lower permeability, while low permeability belts are observed to impede flow from reaching areas surrounded by the low permeability region. Inward surface flux is used to quantify changes in flow through variable permeability cylinders relative to the constant permeability cylinder. For blocking cases, the relationship between ΔK/K0 and the largest possible change in relative surface flux is nearly linear. In ducting simulations, where ΔK/K0∼1 to ∼10, this relationship is no longer linear. Simple polynomial fits are derived for both situations, allowing for the calculation of the change in permeability required to achieve a given increase or reduction in inward flux. Finally, the numerical results are contrasted with theoretical perturbation results for the case of azimuthal variations in permeability, which lead to a fundamentally different pressure distribution.