Дисертації з теми "Forchheimer flows"

In this dissertation, we study models for coupled active--passive pedestrian dynamics from mathematical analysis and simulation perspectives. The general aim is to contribute to a better understanding of complex pedestrian flows. This work comes in three main parts, in which we adopt distinct perspectives and conceptually different tools from lattice gas models, partial differential equations, and stochastic differential equations, respectively. In part one, we introduce two lattice models for active--passive pedestrian dynamics. In a first model, using descriptions based on the simple exclusion process, we study the dynamics of pedestrian escape from an obscure room in a lattice domain with two species of particles (pedestrians). The main observable is the evacuation time as a function of the parameters caracterizing the motion of the active pedestrians. Our Monte Carlo simulation results show that the presence of the active pedestrians can favor the evacuation of the passive ones. We interpret this phenomenon as a discrete space counterpart of the so-called drafting effect. In a second model, we consider again a microscopic approach based on a modification of the simple exclusion process formulated for active--passive populations of interacting pedestrians. The model describes a scenario where pedestrians are walking in a built environment and enter a room from two opposite sides. For such counterflow situation, we have found out that the motion of active particles improves the outgoing current of the passive particles. In part two, we study a fluid-like driven system modeling active--passive pedestrian dynamics in a heterogenous domain. We prove the well-posedness of a nonlinear coupled parabolic system that models the evolution of the complex pedestrian flow by using special energy estimates, a Schauder's fixed point argument and the properties of the nonlinearity's structure. In the third part, we describe via a coupled nonlinear system of Skorohod-like stochastic differential equations the dynamics of active--passive pedestrians dynamics through a heterogenous domain in the presence of fire and smoke. We prove the existence and uniqueness of strong solutions to our model when reflecting boundary conditions are imposed on the boundaries. To achieve this we used compactness methods and the Skorohod's representation of solutions to SDEs posed in bounded domains. Furthermore, we study an homogenization setting for a toy model (a semi-linear elliptic equation) where later on our pedestrian models can be studied.

Of all the strategies to reduce carbon emissions, carbon dioxide (CO₂) geological sequestration is an immediately available option for removing large amounts of the gas from the atmosphere. However, our understanding of the transition behavior between Forchheimer and Darcy flow through porous media during CO₂ injection is currently very limited. In addition, the kinetic mass transfer of SO₂ and CO₂ from CO₂ stream to the saline and the fully coupling between the changes of porosity and permeability and multiphase flow are two significant dimensions to investigate the brine acidification and the induced porosity and permeability changes due to SO₂ co-injection with CO₂. Therefore, this dissertation develops a multiphase flow, contaminant transport and geochemical model which includes the kinetic mass transfer of SO₂ into deep saline aquifers and obtains the critical Forchheimer number for both water and CO₂ by using the experimental data in the literature. The critical Forchheimer numbers and the multiphase flow model are first applied to analyze the application problem involving the injection of CO₂ into deep saline aquifers. The results show that the Forchheimer effect would result in higher displacement efficiency with a magnitude of more than 50% in the Forchheimer regime than that for Darcy flow, which could increase the storage capacity for the same injection rate and volume of a site. Another merit for the incorporation of Forchheimer effect is that more CO₂ would be accumulated in the lower half of the domain and lower pressure would be imposed on the lower boundary of the cap-rock. However, as a price for the advantages mentioned above, the injection pressure required in Forchheimer flow would be higher than that for Darcy flow. The fluid flow and contaminant transport and geochemical model is then applied to analyze the brine acidification and induced porosity and permeability changes due to SO₂ co-injection. The results show that the co-injection of SO₂ with CO₂ would lead to a substantially acid zone near the injecting well and it is important to include the kinetic dissolution of SO₂ from the CO₂ stream to the water phase into the simulation models, otherwise considerable errors would be introduced for the equilibrium assumption. This study provides a useful tool for future analysis and comprehension of multiphase Darcy-Forchheimer flow and brine acidification of CO₂ injection into deep saline aquifers. Results from this dissertation have practical use for scientists and engineers concerned with the description of flow behavior, and transport and fate of SO₂ during SO₂ co-injection with CO₂ in deep saline aquifers.

Cette thèse est consacrée à l'étude des équations du Darcy Brinkman Forchheimer (DBF) avec des conditions aux limites non standards. Nous montrons d'abord l'existence de différents type de solutions (faible, forte) correspondant au problème DBF stationnaire dans un domaine simplement connexe avec des conditions portants sur la composante normale du champ de vitesse et la composante tangentielle du tourbillon. Ensuite, nous considérons le système Brinkman Forchheimer (BF) avec des conditions sur la pression dans un domaine non simplement connexe. Nous prouvons que ce problème est bien posé ainsi que l'existence de la solution forte. Nous établissons la régularité de la solution dans les espaces L^p pour p >= 2.L'étude et l'approximation du problème DBF non stationnaire est basée sur une approche pseudo-compressibilité. Une estimation d'erreur d'ordre deux est établie dans le cas o\`u les conditions aux limites sont de types Dirichlet ou Navier.Enfin, une méthode d'éléments finis Galerkin Discontinue est proposée et la convergence établie concernant le problème DBF linéarisé et le système DBF non linéaire avec des conditions aux limites non standard
This thesis is devoted to Darcy Brinkman Forchheimer (DBF) equations with a non standard boundary conditions. We prove first the existence of different type of solutions (weak, strong) of the stationary DBF problem in a simply connected domain with boundary conditions on the normal component of the velocity field and the tangential component of the vorticity. Next, we consider Brinkman Forchheimer (BF) system with boundary conditions on the pressure in a non simply connected domain. We prove the well-posedness and the existence of a strong solution of this problem. We establish the regularity of the solution in the L^p spaces, for p >= 2.The approximation of the non stationary DBF problem is based on the pseudo-compressibility approach. The second order's error estimate is established in the case where the boundary conditions are of type Dirichlet or Navier. Finally, the finite elements Galerkin Discontinuous method is proposed and the convergence is settled concerning the linearized DBF problem and the non linear DBF system with a non standard boundary conditions

An impermeable weir constructed across a stream prevents the longitudinal movement of aquatic life and transportation of physical and chemical substances in water, eventually having a negative impact on river environment. However, a rubble mound weir is considered environmentally friendly, since its permeability allows the streamwise migration of aquatic life. This thesis investigates the performance of this type of weir as a water use facility. The particular objective of the investigation is to study the flow mechanism in terms of water surface profile and discharge through the weir. In the study, flow through the rubble mound weir is considered non-Darcian, steady, and one-dimensional. In the analysis, gradually varied open channel flow algorithm is applied to porous medium flow through the rubble mound weir in which laminar and turbulent components of flow are taken into consideration. Unlike previous studies where Stephenson and Wilkins relations were used, in this thesis Forchheimer equation is used. To verify the validity of numerical solution of governing equation based on Forchheimer relation, an experimental investigation is conducted in the laboratory. The experimentally obtained water surface profiles are compared with the numerical results. It is observed that there is a satisfactory agreement between numerical and experimental results. The water surface profiles obtained by numerical solution are further compared with those based on Stephenson and Wilkins relations. It is concluded that the proposed numerical solution technique for the Forchheimer based governing equation may be used in the analysis of flow through, and design of rockfill weirs.

Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2008.
Kirkconnell, Carl S., Committee Member ; Ghiaasiaan, S. Mostafa, Committee Chair ; Desai, Prateen V., Committee Member ; Jeter, Sheldon M., Committee Member.

Les aquifères fissurés de type karst contiennent d'importantes ressources en eau. Ces aquifères sont complexes et hétérogènes sur une gamme d'échelles importantes. Leur gestion nécessite l'utilisation d'outils et de méthodologies adaptés. Dans le cadre de cette étude, différents outils et méthodologies numériques d'étude ont été développés pour la modélisation des aquifères karstiques, et plus généralement, des milieux poreux très fissurés 2D et 3D - en mettant l'accent sur la morphologie et sur le comportement hydrodynamique du milieu à travers la notion de changement d'échelle ("second changement d'échelle", reposant sur un modèle d'écoulement local de type Darcy et/ou Poiseuille avec quelques généralisations). Plusieurs axes sont explorés concernant la morphologie du milieu poreux fissuré (milieux aléatoires, milieux booléens avec réseaux statistiques de fissures, mais aussi, modèles morphogénétiques). L'étude du changement d'échelle hydrodynamique tourne autour du concept de macro perméabilité. Dans un premier temps, l'étude porte sur un modèle de perte de charge linéaire darcien. Les perméabilités effectives sont calculées numériquement en termes des fractions volumiques de fissures et du contraste de perméabilité matrice/fissures. Elles sont analysées et comparées à des modèles théoriques (analytiques). Une étude particulière des effets de quasi-percolation pour les grands contrastes aboutit à la définition de trois fractions critiques liées à des seuils de percolation. Pour tenir compte des effets inertiels dans les fissures, l'étude est étendue au cas d'une loi locale comprenant un terme quadratique en vitesse (Darcy/Ward-Forchheimer). Une perméabilité macroscopique équivalente non linéaire est définie et analysée à l'aide d'un modèle inertiel généralisé (linéaire/puissance). Enfin, l'anisotropie hydraulique à grande échelle du milieu fissuré est étudiée, en termes de perméabilités directionnelles, à l'aide d'une méthode numérique d'immersion
Karstic aquifers contain large subsurface water resources. These aquifers are complex and heterogeneous on a large range of scales. Their management requires appropriate numerical tools and approaches. Various tools and numerical methodologies have been developed to characterize andmodel the geometry and hydraulic properties of karstic aquifers, more generally, of highly fissured 2D and 3D porous media. In this study, we emphasize morphological characterization, and we analyze hydrodynamic behavior through the concept of upscaling ("second upscaling"). Concerning the morphology of fissured porous media, several axes are explored : random media, composite random Boolean media with statistical properties, and morphogenetic models. Hydrodynamic upscaling is developed using the macro-permeability concept. This upscaling method is based on either Darcy's linear law, or on a linear/quadratic combination of Darcy's and Ward-Forchheimer's quadratic law (inertial effects). First, the study focuses on Darcy's linear head loss law, and Darcian effective permeabilities are calculated numerically in terms of volume fractions of fissures and "fissure/matrix" permeability contrasts. The results are analysed and compared with analytical results and bounds. A special study of percolation and quasi-percolation effects, for high contrasts, leads to defined three critical fractions. These critical fractions are "connected" to percolation thresholds. Secondly, in order to consider inertial effect in fissures, the study is extended to a local law with a quadratic velocity term (Darcy/Ward-Forchheimer). Then, an equivalent nonlinear macroscopic permeability is defined and analysed using a generalized inertial model (linear/power). Finally, the large scale hydraulic anisotropy of fissured medium is studied, in terms of directional permeabilities, using an "immersion" numerical method

Thesis (MScEng (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2006.
When considering flow through porous media, different flow regimes may be identified. At very small Reynolds numbers the relation between the pressure gradient and the velocity of the fluid is linear. This flow regime ...

Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2008.
Committee Co-Chair: Dr. S. Mostafa Ghiaasiaan; Committee Co-Chair: Dr. S.I. Abdel-Khalik; Committee Member: Dr. Sheldon M. Jeter.

Pulse tube cryocoolers (PTC) are a class of rugged and high-endurance refrigeration systems that operate without moving parts at their low temperature ends, and are capable of reaching temperatures down to and below 123 K. PTCs are particularly suitable for applications in space, guiding systems, cryosurgery, medicine preservation, superconducting electronics, magnetic resonance imaging, weather observation, and liquefaction of gases. Applications of these cryocoolers span across many industries including defense, aerospace, biomedical, energy, and high tech. Among the challenges facing the PTC research community is the improvement of system efficiency, which is a direct function of the regenerator component performance. A PTC implements the theory of oscillatory compression and expansion of the gas within a closed volume to achieve desired refrigeration. An important deficiency with respect to the state of art models dealing with PTCs is the limited understanding of the hydrodynamic and thermal transport parameters associated with periodic flow of a cryogenic fluid in micro-porous structures. In view of the above, the goals of this investigation include: 1) experimentally measuring and correlating the steady and periodic flow Darcy permeability and Forchheimer’s inertial hydrodynamic parameters for available rare-Earth ErPr regenerator filler; 2) employing a CFD-assisted methodology for the unambiguous quantification of the Darcy permeability and Forchheimer’s inertial hydrodynamic parameters, based on experimentally measured steady and periodic flow pressure drops in porous structures representing recently developed regenerator fillers; and 3) performing a direct numerical pore-level investigation for steady and periodic flows in a generic porous medium in order to elucidate the flow and transport processes, and quantify the solid-fluid hydrodynamic and heat transfer parameters. These hydrodynamic resistances parameters were found to be significantly different for steady and oscillatory flows.

Nous considérons un scénario hypothétique d’accident initié par une insertion de réactivité nucléaire entrainant la rupture de la gaine d’un crayon combustible. La violence du contact avec le fluide caloporteur dépendrait fortement du débit de fragment combustible, initialement confiné avec un gaz pressurisé, sortant du crayon. Ce travail de thèse a consisté à étudier cette dynamique en la modélisant par la vidange d’un milieu granulaire hors d’un silo pressurisé. Nous nous sommes d’abord concentrés sur le rôle de la géométrie interne du silo grâce à un fond incliné. Pour un faible angle d’inclinaison, l’orientation de l’écoulement granulaire (donc le débit) est contrôlée par la friction pariétale, tandis qu’une grande inclinaison détermine cette orientation. Nous nous sommes ensuite intéressés au rôle du gaz pressurisé d’abord en imposant une surpression d’air constante puis en considérant un cas transitoire dans lequel une surpression initiale provoque la rupture de l’orifice. Dans les deux configurations, le débit granulaire est mis à l’échelle par une loi de Beverloo modifiée où le gradient de pression du gaz près de l’orifice agit comme une force motrice supplémentaire qui peut être décrite par la loi de Forchheimer. Nous proposons un modèle quasi-stationnaire pour le débit granulaire ainsi qu’une simulation continue basée sur un modèle multiphasique qui reproduisent bien les résultats expérimentaux. A forts débits, nous observons une instabilité du jet, initiée par des oscillations de pression à l’orifice. Enfin nous avons montré que le milieu environnant agit sur la condition de pression à la sortie du silo
We consider a hypothetical scenario of reactivity initiated accident in a nuclear power plant. The violence of the so-called fuel-coolant interaction phenomena depends strongly on the flow rate of particles out of the gas pressurized rod. The aim of this thesis was to study how this discharge rate is driven by the internal geometry and the pressurized gas. We focused firstly on the discharge of a rectangular silo with an inclined bottom. For a small inclination angle, the granular flow orientation is controlled by the wall friction, whereas a large inclination angle fully determines this orientation. Secondly, we focused on two configurations with pressurized gas : a case with constant gas overpressure at the top of the silo and a more transient case for which an initial larger overpressure initiates the rupture of an orifice. The granular flow rate increases significantly with the gas flow, especially for the finer particles and the large overpressures. In both cases, the flow rate scales with a modified Beverloo law where the gas pressure gradient near the outlet acts as an additional driving force. The pressure gradient is well described by a Forchheimer resistance law through the granular medium. We therefore propose a quasi-steady model for the transient description of the granular flow rate. The two configurations were successfully reproduced by numerical simulations based on a continuum multiphase model. For the larger flow rates, instabilities of the granular jet were found to be initiated by pressure oscillations in the outlet region. The presence of water surrounding the silo only acts through an additional hydrostatic pressure effect

Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2009.
Committee Chair: Ghiaasiaan, S. Mostafa; Committee Member: Desai, Prateen; Committee Member: Jeter, Sheldon; Committee Member: Kirkconnell, Carl.

Permeable friction course (PFC) is a porous asphalt pavement placed on top of a regular impermeable roadway. Under small rainfall intensities, drainage is contained within the PFC layer; but, under higher rainfall intensities drainage occurs both within and on top of the porous pavement. This dissertation develops a computer model—the permeable friction course drainage code (PERFCODE)—to study this two-dimensional unsteady drainage process. Given a hyetograph, geometric information, and hydraulic properties, the model predicts the variation of water depth within and on top of the PFC layer through time. The porous layer is treated as an unconfined aquifer of variable saturated thickness using Darcy’s law and the Dupuit-Forchheimer assumptions. Surface flow is modeled using the diffusion wave approximation to the Saint-Venant equations. A mass balance approach is used to couple the surface and subsurface phases. Straight and curved roadway geometries are accommodated via a curvilinear grid. The model is validated using steady state solutions that were obtained independently. PERFCODE was applied to a field monitoring site near Austin, Texas and hydrographs predicted by the model were consistent with field measurements. For a sample storm studied in detail, PFC reduced the duration of sheet flow conditions by 80%. The model may be used to improve the drainage design of PFC roadways.
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A pore-scale understanding of fluid flow underpins the constitutive laws of continuum-scale porous media flow. Porous media flow laws are founded on simplified pore structure such as the classical capillary tube model or the pore-network model, both of which do not include diverging-converging pore geometry in the direction of flow. Therefore, modifications in the fluid flow field due to different pore geometries are not well understood. Thus this may translate to uncertainties on how flow in porous media is predicted in practical applications such as geological sequestration of carbon dioxide, petroleum recovery, and contaminant’s fate in aquifers. To fill this gap, we have investigated the role of a spectrum of diverging-converging pore geometries likely formed due to different grain shapes which may be due to a variety of processes such as weathering, sediment transport, and diagenesis. Our findings describe the physical mechanisms for the failure of Darcy’s Law and the characteristics of Forchheimer Law at increasing Reynolds Number flows. Through fundamental fluid physics, we determined the forces which are most responsible for the continuum-scale porous media hydraulic conductivity (K) or permeability. We show that the pore geometry and the eddies associated therein significantly modify the flow field and the boundary stresses. This has important implications on mineral precipitation-dissolution and microbial growth. We present a new non-dimensional geometric factor β, a metric for diverging-converging pore geometry, which can be used to predict K. This model for K based on β generalizes the original and now widely-used Kozeny (1927) model which was based on straight capillary tubes. Further, in order to better quantify the feasibility of geological CO2 sequestration, we have conducted laboratory fluid flow experiments at reservoir conditions to investigate the controls of media wettability and grain shapes on pore-scale capillary trapping. We present experimental evidence for the snap-off or formation of trapped CO2 ganglion. The total trapping potential is found to be 15% of porosity for a water-wet media. We show that at the pore-scale media wettability and viscous-fingering play a critical role in transport and trapping of CO2. Our investigations clearly show that that in single-phase flow pore geometry significantly modifies pore-scale stresses and impacts continuum-scale flow laws. In two-phase flows, while the media wettability plays a vital role, the mobility ratio of CO2 - brine system significantly controls the CO2 capillary trapping potential- a result which should be taken into consideration while managing CO2 sequestration projects.
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Permeable Friction Course (PFC) is a layer of porous asphalt pavement with a thickness of up to 50 millimeters overlain on a conventional impervious hot mix asphalt or Portland cement concrete roadway surface. PFC is used for its driver safety and improved stormwater quality benefits associated with its ability to drain rainfall runoff from the roadway surface. PFC has recently been approved as a stormwater best management practice in the State of Texas. The drainage properties of PFC are typically considered to be governed primarily by two hydraulic properties: porosity and hydraulic conductivity. Both of these hydraulic properties are expected to change over the life of the PFC layer due to clogging of the pore space by trapped sediment. Therefore, proper measurement of the hydraulic properties can be problematic. Laboratory and field tests are necessary for accurately determining the hydraulic conductivity of the PFC layer in order to ensure whether the driver safety and water quality benefits will persist in the future. During testing, PFC experiences a nonlinear flow relationship which can be modeled using the Forchheimer equation. Due to the two-dimensional flow patterns created during testing, the hydraulic conductivity cannot be directly measured. Therefore, numerical modeling of the two-dimensional nonlinear flow relationship is required to convert the measureable flow characteristics into the theoretical flow characteristics in order to properly determine the isotropic hydraulic conductivity. This numerical model utilizes a new scalar quantity, defined as the hydraulic conductivity ratio, to allow for proper modeling of nonlinear flow in two-dimensional cylindrical coordinates. PFC core specimens have been extracted from three different roadway locations around Austin, Texas for the past four years (2007 to 2010). Porosity values of the core specimens range from 12% to 23%, and the porosity data suggest a statistical decrease over time due to trapped sediment in the pore space. A series of constant head tests used in the laboratory and a falling head test used in the field are recommended for measurement of PFC hydraulic characteristics using a modified Forchheimer equation. Through numerical modeling, regressions equations are presented to estimate the hydraulic conductivity and nonlinear Forchheimer coefficient from the measureable hydraulic characteristics determined during experimental testing. Hydraulic conductivity values determined for laboratory core specimens range from 0.02 centimeters per second (cm/s) to nearly 3 cm/s. Field measurements of in-situ hydraulic conductivity vary over a range from 0.6 cm/s to 3.6 cm/s. The results of this research provide well-defined laboratory and field methods for measurement of the isotropic hydraulic conductivity of PFC experiencing two-dimensional nonlinear flow and characterized by the Forchheimer equation. This methodology utilizes a numerical model which presents a proper solution for nonlinear flow in two-dimensions.
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