InterPore2021

Scaling and errors estimates of the effective Brinkman viscosity

3 Jun 2021, 15:10

15m

Oral Presentation (MS9) Pore-scale modelling MS9

Speaker

Shervin Bagheri (KTH)

Description

We investigate the Brinkman equation for modelling free flows over porous media. Using scaling estimates we show that the Brinkman viscosity ${\mu }_b$ satisfies
$${\mu }_b=C\mu \frac{{\ell }_s^2}{k},$$
where $\mu$ is molecular viscosity of the fluid, $C$ is a constant of order one, $k$ is a measure of the permeability tensor and ${\ell }_s$ is the Navier slip length at the interface plane between the porous medium and the free flow. Using pore-scale direct numerical simulations of shear and pressure driven flows over a range of both regular and irregular porous materials, we confirm the scaling relation above for porous surfaces that form a rough interface with the overlying flow. We also assess the errors of using the Brinkman equation to model the interaction between free flows and porous materials. We find that the errors peak to large values ($\sim 30\mathrm{\%}$ in the 2-norm) around solid volume fractions $\mathrm{\Phi }={10}^{-2}$. We explain physically these errors and discuss the appropriateness of using the Brinkman equation to model free flows over porous media.