Screening effects in flow through rough channels

TL;DR

This paper investigates how rough channel geometries affect flow and stress distribution at various Reynolds numbers, revealing surprising similarities and complex behaviors related to recirculation zones and permeability.

Contribution

It demonstrates a novel similarity between hydrodynamic stress and Laplacian flux distributions in rough channels and uncovers unique permeability behaviors linked to wall geometry.

Findings

Hydrodynamic stress distribution resembles Laplacian flux in irregular channels.

Permeability decreases with Reynolds number in random channels.

Deterministic rough channels show increased permeability with roughness.

Abstract

A surprising similarity is found between the distribution of hydrodynamic stress on the wall of an irregular channel and the distribution of flux from a purely Laplacian field on the same geometry. This finding is a direct outcome from numerical simulations of the Navier-Stokes equations for flow at low Reynolds numbers in two-dimensional channels with rough walls presenting either deterministic or random self-similar geometries. For high Reynolds numbers, when inertial effects become relevant, the distribution of wall stresses on deterministic and random fractal rough channels becomes substantially dependent on the microscopic details of the walls geometry. In addition, we find that, while the permeability of the random channel follows the usual decrease with Reynolds, our results indicate an unexpected permeability increase for the deterministic case, i.e., ``the rougher the better''. We show that this complex behavior is closely related with the presence and relative intensity of recirculation zones in the reentrant regions of the rough channel.