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In this study, a comprehensive approach including mathematical, numerical and experimental study has been taken in order to develop new models for describing free surface flow behavior in porous media. The study suggested that modeling free-surface flow in porous media is possible using a single equation capable of showing proper transition between inertial and classical Darcian flow, based on the similarity distribution functions of depth and velocity. The developed integral model inherits both the flow regimes as depicted in the analysis. For both laminar and turbulent flows through porous media, the integral models give satisfactory results. Also the proposed algorithm for numerical simulation is capable of solving various problems of free-surface flow through porous media. This study adds a new dimension to fluid flow in porous media by replacing Darcy's equation with new models that are capable of representing both Darcy and non-Darcy flow behaviors. These are new nonlinear ordinary differential equations inherited both the flow regimes investigated. Integral formulations for unsteady depth distribution, velocity and front speed under constant water level and constant flux discharge inlet conditions have been developed based on similarity law. The formulations presented provide additional analytical insight about the intrusion dynamics. It is pointed out that, based on the self-similarity analysis, the temporal intrusion processes can be categorized into the inertia-pressure (IP) and the pressure-drag (PD) regimes. The early inertia-pressure regime is followed by the pressure-drag regime. In addition, the integral models proposed can be successfully used for the solution of a host of other nonlinear problems that admit self-similarity. The analytical and numerical solutions for constant inlet water level condition are verified with experimental observations. The unsteady distributions of flow depth, inflow velocity and front speeds are compared for various porous media characterized by its corresponding porosity and permeability. Analyses indicate that the integral models clearly represent the nonlinear flow behavior in porous media both in laminar and turbulent flow conditions. The integral model results are in agreement with those obtained by similarity solution for the temporal change of velocity, depth at inlet and front positions. The thesis also presents a computational fluid dynamics (CFD) model developed for the analysis of unsteady free-surface flows through porous media. Vertical two-dimensional numerical simulations are carried out for the free-surface flow inside the porous media governed by a set of Navier-Stokes equations extended for porous media flow. This model includes the convective and local inertia terms along with viscous diffusion term and resistance term comprising Darcy's linear resistance and Forchheimer's inertial resistance terms. The Finite volume method is applied using constrained interpolated propagation (CIP) method and highly simplified marker and cell (HSMAC) type pressure solver for the numerical solution. The evolution of moving free surface is governed by volume of fluid (VOF) method, adapted for the flow through porous media. To prevent the spurious oscillation and generate diffusion-free sharp interface, a third order monotone upstream-centered schemes for conservation laws (MUSCL) type total variation diminishing (TVD) schemes is used to solve the VOF convection equation. The power law derivation and validation for the general flux inflow condition are made for a channel having a backward facing step. The result of theoretical analysis is compared with that of the numerical simulation and it shows a good agreement. The model can be a tool for the proposition of some empirical flow relationships using multivariate correlation. In the case of rapid vertical infiltration of water through a vertical column filled with porous media, a number of experiments and analytical investigations are carried out to see the effect of acceleration in the intrusion process. It is concluded that the conventional infiltration models like Green-Ampts infiltration model cannot account for the acceleration effect in the case of high velocity flow. It is revealed that it takes certain time for intruding water to be accelerated to its peak velocity before decreasing to almost constant velocity. The investigations are made for two different cases: constant water level and variable water level above the porous media. For porous media having low permeability, the effect of acceleration was not so significant. In the case of dam break flow over horizontal porous strata, the model is applied to a complicated domain regarding both geometry and flow boundary conditions. Single set of governing equation is implemented to simulate the complex phenomenon. The model shows its capability in simulating the flow where interface between pressurized and open channel flow moves forward. The vertical acceleration has a significant effect on the rapid vertical infiltration which the shallow water equations cannot account for. In particular, it is shown that vertical two dimensional numerical solution that couples the fluid and solid systems simultaneously at macroscopic scale are feasible and extremely beneficial, shedding a new light into the phenomena unavailable otherwise. It is also found that the proposed numerical model can be used for the determination of storm water storage in porous sub-base in a typical road section. The capability of the model is assessed by using the unsteady inflow condition so as to simulate the condition during high precipitation. The model could be a promising tool for planners and decision makers for effective drainage calculations to mitigate urban flood. The model successfully simulates the free surface flow in the bulk fluid as well as in the porous region. The velocities and stresses are assumed to be continuous at the interface of free and porous media so that a single set of governing equations could be solved. The robustness of the model is demonstrated by the capability of the numerical approach proposed in this thesis.

学位授与大学：京都大学 ; 取得学位: 博士(工学) ; 学位授与年月日: 2007-11-26 ; 学位の種類: 新制・論文博士 ; 学位記番号: 論工博第3972号 ; 請求記号: 新制/工/1423 ; 整理番号: 25648

Multiphase flows are governed by three-dimensional Navier Stokes equations for each involved phase. Therefore, solution of these equations for given boundary and initial conditions, in principle, would determine the flow field in time and space. Generally, boundaries between involved phases are not known a priory, but are part of the, solution; or in the case of flows in a porous medium, these boundaries have too complicated geometry to be resolved mathematically. This resulted into development of simplified models, where the level of simplifications determines the model applicability. However, in order to represent simulated flows accurately, the model should include as much as possible relevant mechanisms and fluid properties. In this study, a numerical model is developed based on finite volume method, in which the volume averaged governing equations are solved. In contrary to the simplified models. a full momentum equations for each involved phase is considered. Such model is utilized in the study to investigate commonly adopted simplifications, and their effects on the model applicability. Namely, for the flows in porous media, the effects of acceleration terms in momentum equations are investigated; first for the saturated groundwater flow, and then; for the air/water flow during air injection into initially saturated soil. It is revealed that in the case of saturated flow in homogeneous, incompressible, low permeable soils, the pressure adapts the new imposed boundary conditions instantaneously, while the velocities reach the quasi-steady conditions extremely fast. In the case of heterogeneous soil, pressure and velocity field have transient nature, but quickly reach the quasi-steady conditions. Only during this onset of flow, the inertia terms play a role. In the case of air/water flow during air sparging, it is revealed that acceleration becomes important for porous medium with average grain size larger than 2 rum. This implies that simulations of such flow in coarse sands and gravels should include acceleration. It is explicitly shown that phenomena of flow pulsation, manifesting as steady pulsation at the constant air-injection flow rate, can be modeled only by inclusion of acceleration terms in governing equations. Theoretical analysis; conducted by application of one-dimensional stability analysis, revealed that inertial effects promote the instability, while the capillary forces oppose it. Ratio of these forces determines the onset of instability. It is showed that for materials with average grain size smaller than 2 mm, instability can not be expected. In order to apply the model for simulation of contaminant removal during air sparging, the contaminant transport model is supplied. Mechanistic numerical models inherently assume that involved phases are completely mixed, and by now reported models commonly assume the local equilibrium of contaminant between the air and water phase. As reported by many investigators, this leads toward an overestimated contaminant removal. Therefore, in this model a channel air flow pattern is considered, where transfer of contaminant between the water and the air phase is modeled according to two film theory. Diffusive process of contaminant transport toward the air phase is modeled by a first order kinetic process between two water compartments: a immobile compartment in contact with the air phase and mobile compartment which has no contact with the air phase. Application of the developed model to reported two-dimensional experiment, showed a good agreement between simulated and measured transient change of dissolved contaminant in the water. This study also showed that single numerical model, through the minor refinements, can be applied to wide variety of hydraulic engineering problems. By inclusion of gas compressibility, and mass exchange between the gas and the water phase in continuity equations, with adapting the drag term in momentum equations, a bubble phone model is proposed which can be utilized for simulation of lake amelioration by gas (air or pure oxygen) injection. Model is qualitatively and quantitatively validated by comparison with reported experiments from the literature. Hypothetical simulation of pure oxygen injection into 50 in deep lake showed that, due to ambient water entrainment into the gas plume, a significant spreading of dissolved oxygen can not be expected. Therefore, a optional gas injection strategy should be considered. Developed model can be utilized in order to propose an optimal gas injection design. Finally.. the same numerical model is proposed for simulation of flow in complex flow domains, consisting of bulk water and flow in porous medium with free surface boundary. Model is formulated in generalized curvilinear coordinates, in order to provide adequate representation of irregular boundaries. In contrast to earlier proposed boundary conditions at the two domain interface, in this model a continuity of velocities and stresses is assumed; for both regions a single set of governing equations is solved. Model application is illustrated by simulation of embankment overflow and its effect on effective stresses in the porous medium. It is showed that coupled, bulk water and groundwater flow, significantly influence the slope failure potential, here quantified by the Coulomb failure coefficient for non cohesive soils., 学位授与大学：京都大学 ; 取得学位: 博士(工学) ; 学位授与年月日: 2007-09-25 ; 学位の種類: 新制・課程博士 ; 学位記番号: 工博第2845号 ; 請求記号: 新制/工/1419 ; 整理番号: 25530