Performing geometry-resolved simulations of flows over rough and porous walls is highly expensive due to their multiscale characteristics. Effective models that circumvent this difficulty are often used to investigate the interaction between the free-fluid and such complex walls. These models, by construction, employ an intrinsic averaging process and capture only macroscopic physical processes. However, physical experiments or direct simulations yield micro- and macroscale information, and isolating the macroscopic effect from them is crucial for rigorously validating the accuracy of effective models. Despite the increasing use of effective models, this aspect received the least attention in the literature. This paper presents an efficient averaging technique to extract macroscopic interface data from the flowfield obtained via direct simulations or physical experiments. The proposed methodology employs a combination of signal processing and polynomial interpolation techniques to capture the macroscopic information. Results from the ensemble averaging are used as the reference to quantify the accuracy of the proposed method. Compared to the ensemble averaging, the proposed method, while retaining accuracy, is cost-effective for rough and porous walls. To the best of our knowledge, this is the only averaging method that works for poroelastic walls, for which the ensemble averaging fails. Moreover, it applies equally to viscous- and inertia-dominated flows over irregular surfaces.
New insight into the contribution of the microscale vortex evolution towards convection heat transfer in porous media is presented in this paper. The objective is to determine how the microscale vortices influence convection heat transfer in turbulent flow inside porous media. The microscale temperature distribution is analyzed using flow visualization in 2D using streamlines and in 3D using Q structures. The pertinent observations are supplemented with the comparison of surface skin friction and heat transfer using: (1) surface skin friction lines and (2) joint PDF of pressure and skin fricti…
The focus of this paper is to systematically study the influence of solid obstacle surface roughness in porous media on the microscale flow physics and report its effect on macroscale drag and Nusselt number. The Reynolds averaged flow field is numerically simulated for a flow through a periodic porous medium consisting of an in-line arrangement of square cylinders with square roughness particles on the cylinder surface. Two flow regimes are identified with respect to the surface roughness particle height: fine and coarse roughness regimes. The effect of the roughness particles in the fine rou…
We extend the two-scale expansion approach of periodic homogenization to include time scales and thus can tackle the full instationary Navier-Stokes-Cahn-Hilliard model at the pore scale as microscale. Time scale separation allows us to keep microscale dynamics, responsible e.g. for hysteresis, and arrive at a numerically tractable micro-macro model including coupled generalized Darcy's laws.
Single fluid porous medium systems are typically modeled at an averaged length scale termed the macroscale using Darcy's law. Standard approaches for modeling macroscale single fluid phase flow of non-Newtonian fluids extend Darcy's law, using an effective viscosity and assuming that the permeability is invariant. This approach results in a need to determine the effective viscosity for every fluid and flow rate. We use the thermodynamically constrained averaging theory (TCAT) to examine the formulation and closure of a macroscale model for non-Newtonian flow that is consistent with microscale …
Droplet mobility under shear flows is important in a wide range of engineering applications, e.g., fog collection, and self-cleaning surfaces. For structured surfaces to achieve superhydrophobicity, the removal of stains adhered within the microscale surface features strongly determines the functional performance and durability. In this study, we numerically investigate the shear-induced mobility of the droplet trapped within porous surfaces. Through simulations covering a wide range of flow conditions and porous geometries, three droplet mobility modes are identified, i.e., the stick-slip, cr…
We present a description and validation of a finite volume solver aimed at solving the problems of microscale urban flows where vegetation is present. The solver is based on the five equation system of Reynolds-averaged Navier-Stokes equations for atmospheric boundary layer flows, which are complemented by the k-epsilon turbulence model. The vegetation is modelled as a porous zone, and the effects of the vegetation are included in the momentum and turbulence equations. A detailed dry deposition model is incorporated in the pollutant transport equation, allowing the investigation of the filteri…
We report forced radial imbibition of water in a porous medium in a Hele-Shaw cell. Washburn's law is confirmed in our experiment. Radial imbibition follows scaling dynamics and shows anomalous roughening dynamics when the front invades the porous medium. The roughening dynamics depend on the flow rate of the injected fluid. The growth exponents increase linearly with an increase in the flow rate while the roughness exponents decrease with an increase in the flow rate. Roughening dynamics of radial imbibition is markedly different from one dimensional imbibition with a planar interface window.…
Owing to the multiscale nature and the consequent high computational cost associated with simulations of flows over rough surfaces, effective models are being developed as a practical means of dealing with such flows. Existing effective models focus primarily on accurately predicting interface velocities using slip length. Moreover, they are concerned mainly with flat interfaces and do not directly address the drag computation. In this work, we formulate the Transpiration-Resistance model in polar coordinates and address the challenge of computing drag components on rough surfaces. Like slip l…
We performed an experimental observation on the spontaneous imbibition of water in a porous media in a radial Hele-Shaw cell and confirmed Washburn's law, where r is distance and t is time. Spontaneous imbibition with a radial interface window followed scaling dynamics when the front invaded into the porous media. We found a growth exponent (\b{eta}=0.6) that was independent of the pressure applied at the liquid inlet. The roughness exponent decreased with an increase in pressure. The roughening dynamics of two dimensional spontaneous radial imbibition obey Family-Vicsek scaling, which is diff…
The wetting behaviour of surfaces is important for various applications like super-hydrophobic surfaces, enhanced oil recovery, mining of metal ores and anti-icing surfaces etc. For rough surfaces, which are the rule rather than the exception, designing textured surfaces that have wetting properties tailored to suit these applications generally involves either bio-mimicry or trial and error. Existing wetting theories such as the well-known Wenzel (1936) and Cassie & Baxter (1944) models do not predict wetting regimes and importantly, only give a single equilibrium angle rather than a range of …
The surface texture of materials plays a critical role in wettability, turbulence and transport phenomena. In order to design surfaces for these applications, it is desirable to characterise non-smooth and porous materials by their ability to exchange mass and momentum with flowing fluids. While the underlying physics of the tangential (slip) velocity at a fluid-solid interface is well understood, the importance and treatment of normal (transpiration) velocity and normal stress is unclear. We show that, when slip velocity varies at an interface above the texture, a non-zero transpiration veloc…
Interfacial boundary conditions determined from empirical or ad-hoc models remain the standard approach to model fluid flows over porous media, even in situations where the topology of the porous medium is known. We propose a non-empirical and accurate method to compute the effective boundary conditions at the interface between a porous surface and an overlying flow. Using multiscale expansion (homogenization) approach, we derive a tensorial generalized version of the empirical condition suggested by Beavers & Joseph (1967). The components of the tensors determining the effective slip velocity…
We derive a homogenized macroscopic model for fluid flows over ordered homogeneous porous surfaces. The unconfined free-flow is described by the Navier-Stokes equation, and the Darcy equation governs the seepage flow within the porous domain. Boundary conditions that accurately capture mass and momentum transport at the contact surface between these two domains are derived using the multiscale homogenization technique. In addition to obtaining the generalized version of the widely used Beavers-Joseph slip condition for tangential velocities, the present work provides an accurate formulation fo…
In this paper we consider a multiscale phase-field model for capillarity-driven flows in porous media. The presented model constitutes a reduction of the conventional Navier-Stokes-Cahn-Hilliard phase-field model, valid in situations where interest is restricted to dynamical and equilibrium behavior in an aggregated sense, rather than a precise description of microscale flow phenomena. The model is based on averaging of the equation of motion, thereby yielding a significant reduction in the complexity of the underlying Navier-Stokes-Cahn-Hilliard equations, while retaining its macroscopic dyna…
Microscale turbulence in porous media is a new physical phenomenon that exhibits unique properties unlike those in classical turbulence flows. At low values of porosity, the surface forces on the solid obstacles compete with the inertial force of the fluid flow to result in the formation of flow instabilities. In this paper, we report the origin and mechanism of a symmetry-breaking phenomenon in periodic porous media that causes a deviation in the direction of the mean flow from that of the applied pressure gradient. Large Eddy Simulation (LES) is used to simulate turbulent flow in a homogeneo…
Methane adsorption and its effect on fluid flow in shale matrix are investigated through multi-scale simulation scheme by using molecular dynamics (MD) and lattice Boltzmann (LB) methods. Equilibrium MD simulations are conducted to study methane adsorption on the organic and inorganic walls of nanopores in shale matrix with different pore sizes and pressures. Density and pressure distributions within the adsorbed layer and the free gas region are discussed. The illumination of the MD results on larger scale LB simulations is presented. Pressure-dependent thickness of adsorbed layer should be a…
In this contribution we review recent efforts on investigations of the effect of (apparent) boundary slip by utilizing lattice Boltzmann simulations. We demonstrate the applicability of the method to treat fundamental questions in microfluidics by investigating fluid flow in hydrophobic and rough microchannels as well as over surfaces covered by nano- or microscale gas bubbles.
The Brinkman equation has found great popularity in modelling the interfacial flow between free fluid and a porous medium. However, it is still unclear how to determine an appropriate effective Brinkman viscosity without resolving the flow at the pore scale. Here, we propose to determine the Brinkman viscosity for rough porous media from the interface slip length and the interior permeability. Both slip and permeability can be determined from unit-cell analysis, thus enabling an a priori estimate of the effective viscosity. By comparing the velocity distribution in the porous material predicte…
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 ori…
Gas slippage occurs when the mean free path of the gas molecules is in the order of the characteristic pore size of a porous medium. This phenomenon leads to the Klinkenberg's effect where the measured permeability of a gas (apparent permeability) is higher than that of the liquid (intrinsic permeability). A generalized lattice Boltzmann model is proposed for flow through porous media that includes Klinkenberg's effect, which is based on the model of Guo et al. (Z.L. Guo et al., Phys.Rev.E 65, 046308 (2002)). The second-order Beskok and Karniadakis-Civan's correlation (A. Beskok and G. Karniad…
Simulation approaches for fluid-structure-contact interaction, especially if requested to be consistent even down to the real contact scenarios, belong to the most challenging and still unsolved problems in computational mechanics. The main challenges are twofold - one is to have a correct physical model for this scenario, and the other one is to have a numerical method that is capable of working and being consistent down to a zero gap. And when analyzing such challenging setups of fluid-structure interaction that include contact of submersed solid components it gets obvious that the influence…
Dynamics of fluid-fluid displacements in a model rough fracture beyond the quasistatic limit: A spectral approach
Institute of Environmental Assessment and Water Research (IDAEA), Spanish National Research Council (CSIC)（环境评估与水资源研究所，西班牙国家研究委员会）；Universitat de Barcelona（巴塞罗那大学）；University of Barcelona Institute of Complex Systems (UBICS)（巴塞罗那大学复杂系统研究所）
A stochastic modeling framework to generate 2-D rough-wall high-Reynolds-number turbulent boundary layers
Saint Anthony Falls Laboratory, University of Minnesota（明尼苏达大学圣安东尼瀑布实验室）；Department of Civil, Environmental, and Geo-Engineering, University of Minnesota（明尼苏达大学土木、环境与地球工程系）
Derivation of macroscopic models for advection-diffusion processes in the presence of dominant heterogeneous (e.g., surface) reactions using homogenisation theory or volume averaging is often deemed unfeasible due to the strong coupling between scales that characterise such systems. In this work, we show how the upscaling can be carried out by applying and extending the methods presented in literature. The approach relies on the decomposition of the microscale concentration into a reactive component, given by the eigenfunction of the advection-diffusion operator, the associated eigenvalue whic…
A sensitive porosity adjoint method (SPAM) for optimizing the topology of fluid machines has been proposed. A sensitivity function with respect to the porosity has been developed. In the first step of the optimization process, porous media are introduced into the flow regime according to the sensitivity function. Then the optimized porous media are transformed to solid walls. The turbulent flow in porous media is accounted for by a modified eddy-viscosity based turbulence model. Its influence on the adjoint equations is nevertheless neglected, which refers to the so called frozen turbulence as…
Pore-resolved direct numerical simulations of turbulent open channel flow are performed comparing the structure and dynamics of turbulence over impermeable rough and smooth walls to a porous sediment bed at permeability Reynolds number ($Re_K$) of 2.6, representative of aquatic beds. Four configurations are investigated; namely, (i) permeable bed with randomly packed sediment grains, (ii) an impermeable-wall with full layer of roughness elements matching the top layer of the sediment bed, (iii) an impermeable-wall with half layer of roughness elements , and (iv) a smooth wall. A double-averagi…
We perform more than 6000 steady-state simulations with a dynamic pore network model, corresponding to a large span in viscosity ratios and capillary numbers. From these simulations, dimensionless quantities such as relative permeabilities, residual saturations, mobility ratios and fractional flows are computed. Relative permeabilities and residual saturations show many of the same qualitative features observed in other experimental and modeling studies. However, while other studies find that relative permeabilities converge to straight lines at high capillary numbers we find that this is not …
Permeability is the key parameter for quantifying fluid flow in porous rocks. Knowledge of the spatial distribution of the connected pore space allows, in principle, to predict the permeability of a rock sample. However, limitations in feature resolution and approximations at microscopic scales have so far precluded systematic upscaling of permeability predictions. Here, we report fluid flow simulations in capillary network representations designed to overcome such limitations. Performed with an unprecedented level of accuracy in geometric approximation at microscale, the pore scale flow simul…
