Bulletin of the American Physical Society
76th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2023; Washington, DC
Session J33: Porous Media Flows: Theory |
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Chair: Mostafa Aghaei Jouybari, Johns Hopkins University Room: 159AB |
Sunday, November 19, 2023 4:35PM - 4:48PM |
J33.00001: Generalized Darcy-Forchheimer law for capturing flow refraction effects in anisotropic porous media Mostafa Aghaei Jouybari, Jung-Hee Seo, Sasindu N Pinto, Louis N Cattafesta, Charles Meneveau, Rajat Mittal Flow refraction, characterized by a misalignment between the bulk flow direction and the bulk pressure drop direction, has been observed in anisotropic porous media at intermediate and high pore-scale Reynolds number flows. Within these porous media, certain principal geometrical axes exhibit significant flow sheltering, resulting in reduced drag on the flow and causing it to deviate in those directions. Motivated by the use of high porosity porous media for flow control, we studied this phenomenon both numerically, using 2D direct numerical simulations, and experimentally. The results confirm the existence of flow refraction as seen in both simulations and experiments. The standard Darcy-Forchheimer (DF) law, which assumes that the nonlinear permeability tensor is orientation-independent, fails to capture these flow refraction effects. To address this limitation, a generalized DF law is proposed to incorporate these effects by allowing the Forchheimer permeability tensor to vary based on the flow orientation relative to the principal geometric directions of the porous structure. Good agreement of flow refraction angles in simulations, experiments and the proposed model is obtained. |
Sunday, November 19, 2023 4:48PM - 5:01PM |
J33.00002: Optimizing Mixing in Porous Media with Automatic Differentiation Kaylie Hausknecht, mohammed alhashim, Michael P Brenner Dispersion in porous media is a fundamental process in many industrial settings. Prediction of mixing behavior in a porous medium for a given flow geometry is well-understood. However, the inverse problem of systematically designing the flow (i.e. porous medium geometry, fluid properties, etc.) to target specific mixing behavior is computationally extremely expensive. The advent of efficient automatic differentiation algorithms has made such optimization possible. In this work, we combine a fully differentiable CFD solver that accounts for the presence of solid obstacles with a differentiable Brownian dynamics solver to enable Lagrangian studies of fluid flows that include the effects of molecular diffusion. We use this technique to simulate and quantify mixing in periodic structured porous media. By differentiating through the entire simulation, we identify optimum array arrangements that maximize mixing in porous media across a range of Péclet numbers, Reynolds numbers, and solid packing fractions. More broadly, our results demonstrate the versatility of using automatic differentiation for the design and optimization of fluid systems to target specific flow properties. |
Sunday, November 19, 2023 5:01PM - 5:14PM |
J33.00003: Effects of the geothermal gradient on the convective dissolution in CO2 sequestration Chenglong Hu, Ke Xu, Yantao Yang Convective dissolution is regarded as a stable mechanism for the long-term storage of sequestered CO2 in deep saline aquifers. The primary focus of this study is to investigate the influence of unstable geothermal gradient on the transport and dynamics of convective dissolution. |
Sunday, November 19, 2023 5:14PM - 5:27PM |
J33.00004: Data-Driven Derivation of Governing Equations for Fluid Flow in Porous Media Hamid Abderrahmane, Moussa Tembely Accurate estimation of fluid flow in porous media has significant impact on a wide range of applications, including water management, the oil & gas industry, CO2 sequestration, and environmental cleanup technology. For subsurface flow modeling, current approaches rely heavily on the Darcy equation. However, it is believed that the simplified nature of the Darcy equation, in conjunction with the need for accurate geological representation, may be a potential source of discrepancies between numerical and experimental results. This highlights the need for a refined fluid flow model in porous media. The present study reexamines fluid flow in heterogeneous porous media based on data-driven modeling. Starting with the canonical problem of flow over a cylinder in a channel, we gradually increased the complexity of the problem by adding more cylinders in varying configurations, approximating heterogeneous porous media. Numerical simulations, based on the finite volume method to solve the continuity and Navier-Stokes equations, were used to collect data. Subsequently, the governing equations were inferred from the spatiotemporal snapshots of the vorticity field using a sparse regression algorithm. The results indicate that the convective terms of the vorticity transport equation vanish while quadratic terms emerge. Moreover, as the flow configuration approaches a more heterogeneous medium representation, the coefficients of the discovered PDEs become time-dependent, exhibiting increasing regularity and periodic dependency. Therefore, the study paves the way for improvements to the Darcy equation as the asymptotic limit for fluid flow in complex porous media, and questions its ability to accurately capture the underlying physics responsible for the growth of small perturbation within the context of hydrodynamic instabilities. |
Sunday, November 19, 2023 5:27PM - 5:40PM |
J33.00005: Poroviscoelasticity: Governing model and fundamental solutions Jennifer Castelino, Samuel S Pegler, Susanna K Ebmeier Poroviscoelastic flows can be observed in many natural phenomena. Recent evidence suggest that large volumes of volcanic melt are disseminated in large crystal mush regions that may span the length of the crust. Furthermore, current studies also suggest that ground surface deformation in these mushy magmatic systems may be caused by both poroelastic and viscoelastic deformation. Some other important examples of coexisting poroelastic and viscoelastic behaviour include boreholes, soil consolidation and hydrocephalic brain tissue. |
Sunday, November 19, 2023 5:40PM - 5:53PM |
J33.00006: Multiscale modeling of electromagnetohydrodynamic flow through porous media PROMASREE MAJUMDAR, Debabrata Dasgupta The investigation of electromagnetohydrodynamic (EMHD) flow in porous media entails examining the combined influence of electric and magnetic fields on the flow dynamics within the porous structure. This study employs a two-scale computational homogenization technique to model a single-phase fluid flow through an idealized 3D periodic porous domain. The pore-scale analysis enables the examination of microscopic porosity features that are often inaccessible during physical testing, such as the formation of the Electrical Double Layer (EDL) at the fluid-solid interface. This study introduces an important novel property, “electromagneto (EM)-permeability”, associated with EMHD flows. To achieve broader applicability of the research, we perform non-dimensionalization of the governing equations. We investigate the impact of different wall zeta potential values, as well as the intensity of external magnetic and transverse electric fields, denoted by Hartmann number and non-dimensional parameter S, respectively, on EM-permeability. It is observed that the flow behaviour and EM-permeability are significantly affected by the existence of the flow-assisting and flow-opposing components of the Lorentz force term in the momentum equation. |
Sunday, November 19, 2023 5:53PM - 6:06PM |
J33.00007: On mathematical modeling of filtration and drying in filter membranes Pejman Sanaei, Hangjie Ji In this work, we formulate a coupled mathematical model for the filtration and drying dynamics in a porous medium occurring consecutively. Our model accounts for the porous medium internal morphology (internal structure, porosity, etc.), the contaminant deposition, and the evolution of dry-fluid interfaces due to evaporation. An asymptotic model is derived based on the small aspect ratio of the thin filter membrane. The reduced model provides insights to the overall porous medium evolution over cycles of filtration and drying processes and predicts the timeline to discard the filter based on its optimum performance. Given the complexity of fluid boundary movements due to the filtration and drying processes, the reduced model still acts as an efficient prediction tool offering a tremendous reduction in computational costs. |
Sunday, November 19, 2023 6:06PM - 6:19PM |
J33.00008: Lie Symmetry Analysis of a cross-flow induced porous media flow in a weakly permeable channel Sukhendu Ghosh, Sougata Mandal This investigation focuses on the symmetry analysis and solution of a viscous and incompressible flow in a channel filled with isotropic porous material. There is a uniform cross-flow through the upper and lower walls of the channels that generates a flow inside the porous media. The flow dynamics inside the channel is governed by the full Darcy-Brinkman equations. The tangential velocity slip along the walls is modeled by Navier slip boundary condition. The Lie symmetry analysis based on invariance principle are adopted to reduce the number of independent variables of the system of governing equations. Consequently, a single fourth order non-linear ordinary differential equation is obtained, which is solved analytically by the perturbation method in the small parameter range. However, it is solved for arbitrary parameter range analytically with variation of Iteration method (VIM) as well as numerically using a fourth order Runge–Kutta solver. A stronger cross-velocity enhances the flow rate and advances the mean flow inside the channel. Consequently, the maximum velocity and total shear rate become higher. A relatively larger Darcy number allows a faster flow through the porous medium and the axial velocity profile becomes fuller. The obtained results and outcomes are usefull for biomedical applications. |
Sunday, November 19, 2023 6:19PM - 6:32PM |
J33.00009: Mathematical modeling of deposition and erosion dynamics in a complex branching pore morphology Emeka P Mazi, Pejman Sanaei Deposition and erosion are fundamental processes in fluid dynamics, and they play a crucial role in various natural phenomena and engineered systems. These processes involve the transport of particles by the fluid flow, resulting in erosion of materials from one location and their subsequent deposition at another. In this study, we propose a mathematical model to simulate the deposition and erosion processes occurring in a porous medium represented by an idealized structure composed of bifurcating cylindrical channels, featuring two types of branching: symmetric and asymmetric. The fluid flow within the channels is governed by the Stokes equations, while the transport, deposition and erosion of solid particles are described by an advection-diffusion equation. Furthermore, we investigated the effects of deposition and erosion processes on the evolution of the porous medium internal morphology. |
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