Abstract:Green roofs are considered an attractive alternative to standard storm water management methods; however one of the primary issues hindering their proliferation is the lack of data regarding their ability to retain and reduce storm water under a variety of climatic conditions. This lack of data is partly due to the complexity of physical processes involved, namely the heterogeneous microscopic behavior that characterize flows in unsaturated porous media.
“…For further details regarding the methodology, the specific algorithm and a series of validation test cases the reader is referred to [25][26][27].…”
We report and discuss, by means of pore-scale numerical simulations, the possibility of achieving a directional-dependent two-phase flow behaviour during the process of invasion of a viscous fluid into anisotropic porous media with controlled design. By customising the pore-scale morphology and heterogeneities with the adoption of anisotropic triangular pillars distributed with quenched disorder, we observe a substantially different invasion dynamics according to the direction of fluid injection relative to the medium orientation, that is depending if the triangular pillars have their apex oriented (flow-aligned) or opposed (flow-opposing) to the main flow direction. Three flow regimes can be observed: (i) for low values of the ratio between the macroscopic pressure drop and the characteristic pore-scale capillary threshold, i.e. for ∆p0/pc ≤ 1, the fluid invasion dynamics is strongly impeded and the viscous fluid is unable to reach the outlet of the medium, irrespective of the direction of injection; (ii) for intermediate values, 1 < ∆p0/pc ≤ 2, the viscous fluid reaches the outlet only when the triangular pillars are flow-opposing oriented; (iii) for larger values, i.e for ∆p0/pc > 2, the outlet is again reached irrespective of the direction of injection. The porous medium anisotropy induces a lower effective resistance when the pillars are flow-opposing oriented, suppressing front roughening and capillary fingering. We thus argue that the invasion process occurs as long as the pressure drop is larger then the macroscopic capillary pressure determined by the front roughness, which in the case of flow-opposing pillars is halved. We present a simple approximated model, based on Darcy's assumptions, that links the macroscopic effective permeability with the directional-dependent front roughening , to predict the asymmetric invasion dynamics. This peculiar behaviour opens up the possibility of fabrication of porous capillary valves to control the flow along certain specific directions.
“…For further details regarding the methodology, the specific algorithm and a series of validation test cases the reader is referred to [25][26][27].…”
We report and discuss, by means of pore-scale numerical simulations, the possibility of achieving a directional-dependent two-phase flow behaviour during the process of invasion of a viscous fluid into anisotropic porous media with controlled design. By customising the pore-scale morphology and heterogeneities with the adoption of anisotropic triangular pillars distributed with quenched disorder, we observe a substantially different invasion dynamics according to the direction of fluid injection relative to the medium orientation, that is depending if the triangular pillars have their apex oriented (flow-aligned) or opposed (flow-opposing) to the main flow direction. Three flow regimes can be observed: (i) for low values of the ratio between the macroscopic pressure drop and the characteristic pore-scale capillary threshold, i.e. for ∆p0/pc ≤ 1, the fluid invasion dynamics is strongly impeded and the viscous fluid is unable to reach the outlet of the medium, irrespective of the direction of injection; (ii) for intermediate values, 1 < ∆p0/pc ≤ 2, the viscous fluid reaches the outlet only when the triangular pillars are flow-opposing oriented; (iii) for larger values, i.e for ∆p0/pc > 2, the outlet is again reached irrespective of the direction of injection. The porous medium anisotropy induces a lower effective resistance when the pillars are flow-opposing oriented, suppressing front roughening and capillary fingering. We thus argue that the invasion process occurs as long as the pressure drop is larger then the macroscopic capillary pressure determined by the front roughness, which in the case of flow-opposing pillars is halved. We present a simple approximated model, based on Darcy's assumptions, that links the macroscopic effective permeability with the directional-dependent front roughening , to predict the asymmetric invasion dynamics. This peculiar behaviour opens up the possibility of fabrication of porous capillary valves to control the flow along certain specific directions.
“…In the present study, the dynamic viscosity ratio is set as M = ∕ g = 35 (with and g the viscosities of liquid and gas, respectively), a value that we found as a good compromise between accuracy of the solution ( M = 100 for water-air systems) and numerical stability. The reader is referred to the work presented in Pettersson et al (2020) for the two-phase flow algorithm validation.…”
Section: Lattice Boltzmann Methods For Two-phase Flow Simulationsmentioning
We present pore-scale simulations of two-phase flows in a reconstructed fibrous porous layer. The three-dimensional microstructure of the material, a fuel cell gas diffusion layer, is acquired via X-ray computed tomography and used as input for lattice Boltzmann simulations. We perform a quantitative analysis of the multiphase pore-scale dynamics, and we identify the dominant fluid structures governing mass transport. The results show the existence of three different regimes of transport: a fast inertial dynamics at short times, characterised by a compact uniform front, a viscous-capillary regime at intermediate times, where liquid is transported along a gradually increasing number of preferential flow paths of the size of one–two pores, and a third regime at longer times, where liquid, after having reached the outlet, is exclusively flowing along such flow paths and the two-phase fluid structures are stabilised. We observe that the fibrous layer presents significant variations in its microscopic morphology, which have an important effect on the pore invasion dynamics, and counteract the stabilising viscous force. Liquid transport is indeed affected by the presence of microstructure-induced capillary pressures acting adversely to the flow, leading to capillary fingering transport mechanism and unstable front displacement, even in the absence of hydrophobic treatments of the porous material. We propose a macroscopic model based on an effective contact angle that mimics the effects of the such a dynamic capillary pressure. Finally, we underline the significance of the results for the optimal design of face masks in an effort to mitigate the current COVID-19 pandemic.
“…The reader is referred to the work presented in Pettersson et al (2020) for the two-phase flow algorithm validation. The fluid-wall interaction at the three-phase contact line (liquid-gas-solid), in terms of chemical properties of the surface (wetting), can be tuned by means of an averaging of the pseudopotential values in the neighboring nodes N : Finally, the macroscopic fluid density and momentum are determined through the statistical averaging of the molecular probability distribution functions as (Succi, 2001):…”
Section: Lattice Boltzmann Methods For Two-phase Flow Simulationsmentioning
We present pore-scale simulations of two-phase flows in a reconstructed fibrous porous layer. The three dimensional microstructure of the material, a fuel cell gas diffusion layer, is acquired via X-ray computed tomography and used as input for lattice Boltzmann simulations. We perform a quantitative analysis of the multiphase pore-scale dynamics and we identify the dominant fluid structures governing mass transport. The results show the existence of three different regimes of transport: a fast inertial dynamics at short times, characterised by a compact uniform front, a viscous-capillary regime at intermediate times, where liquid is transported along a gradually increasing number of preferential flow paths of the size of one-two pores, and a third regime at longer times, where liquid, after having reached the outlet, is exclusively flowing along such flow paths and the two-phase fluid structures are stabilised. We observe that the fibrous layer presents significant variations in its microscopic morphology, which have an important effect on the pore invasion dynamics. Liquid transport is affected by the presence of a microstructure-induced capillary pressure acting adversely to the flow, leading to capillary fingering transport mechanisms even in the absence of hydrophobic treatments of the porous material. We propose a macroscopic model based on an effective contact angle that mimics the effects of the such a dynamic capillary pressure. Finally, we underline the significance of the results for the optimal design of face masks in an effort to mitigate the current COVID-19 pandemic.
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