The karst research community has known that traditional numerical groundwater flow codes ignore the non-Darcian, dual-permeability components of flow that can occur in karst aquifers. In this study, the potential limitations of using such tools are quantified by evaluating the relative performances of 3 groundwater flow models at a test-site near Weeki Wachee, Florida, in the dual-permeability Upper Floridan aquifer. MODFLOW-2005 and MODFLOW-2005 Conduit Flow Process (CFP), a Darcian/non-Darcian, dual-permeability groundwater flow code recently developed by the U.S. Geological Survey, are used in this study. A monitoring program consisting of discharge measurements and high frequency data from 2 springs and monitoring wells penetrating the matrix and conduit networks of a karst aquifer was initiated to characterize the test-site and constrain new parameters introduced with MODFLOW-2005 CFP. The monitoring program spanned conditions prior to, during, and following convective and tropical storm activity, and a drought. Analytical estimates for Reynolds numbers, ranging from 105 to 106, suggest that turbulent flow occurs in portions of the underlying conduit network. The direction and magnitude of fluid exchange observed between the matrix and conduit network indicate the conduit network underlying the test-site drains the matrix. Head differences and observed responses in monitoring wells penetrating the matrix and conduit network indicate that the hydraulic conductivities between the 2 networks do not significantly differ from each other. A conceptual model for the spatial distribution of preferential flow pathways using multiple data types, including shallow recession limbs observed in discharge hydrographs indicate a slow responding aquifer with a high storage capacity, and a poorly integrated conduit drainage network with little to no point recharge. Model performances were evaluated by comparing observed hydrographs for discharge and monitoring wells penetrating the matrix and conduit network following convective and tropical storm events, and drought conditions, to simulated values from transient simulations. Model statistics for 32 target wells and sensitivity analysis were included in the evaluation. The dual-permeability model using the MODFLOW-2005 CFP Mode 1 displayed the highest performance with improved matches ranging from 12 to 40% between simulated and observed discharges relative to the laminar and laminar/turbulent equivalent-continuum models.

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.

Non-Darcian flow in a finite fractured aquifer is studied in this thesis. A stream bounds the aquifer at one side and an impervious stratum at the other. The aquifer consists of fractures capable of transmitting water rapidly and porous blocks which mainly store water. Unsteady flow in the aquifer due to a sudden or a gradual rise in the stream level is analysed by the double-porosity conceptual model. Governing equations for the flow in fractures and blocks are developed using the continuity equation. The fluid velocity in fractures is often too high for the linear Darcian flow so that the governing equation for fracture flow is modified by Forcheimer&rsquo / s equation which incorporates a nonlinear term. Governing equations are coupled by an interaction term that controls the quasi-steady state fracture-block interflow. Governing equations are solved numerically by the Crank-Nicolson implicit scheme. The numerical results are compared to the analytical results for the same problem which assumes Darcian flow both in fractures and blocks. Numerical and analytical solutions give same results when Reynold&rsquo / s number is less than 0.1. The effect of non-linearity on the flow appears when Reynold&rsquo / s number is greater than 0.1. The larger the piezometric head gradient, the higher the flow rate and, thus, higher the non-linearity is. The effect of aquifer parameters on the flow is also investigated. The proposed model and its numerical solution is a unique application of non-linear flow models to the fractured aquifers. It can be used in predicting water levels in fractured aquifers and evaluating time dependent flow rates in the analysis of recession hydrographs.

Les mousses à cellules ouvertes ont diverses applications industrielles, par exemple pour des échangeurs de chaleur, des réacteurs structurés, la filtration, la catalyse, récepteurs solaires volumétriques en raison de leurs propriétés uniques telles qu'une importante porosité et une surface spécifique élevée. Pour déterminer théoriquement la surface spécifique géométrique et les relations entre les paramètres géométriques de mousses, une corrélation mathématique généralisée a été développée. A cet effet, la géométrie de la tetrakaidecahedron a été utilisé et différentes formes de sections transversales de brins de structures en mousse ont été pris en compte de façon explicite. La corrélation dérivée pour prédire les propriétés géométriques peut facilement être étendue à des formes différentes. Des simulations numériques 3-D à l'échelle des pores ont été réalisées pour étudier la perte de charge et la conductivité effective thermique. L'écoulement du fluide à travers la mousse à cellule ouverte a été réalisé dans trois régimes différents: les régimes de Darcy, transitoire et inertiel. L'importance des propriétés géométriques sur les caractéristiques d'écoulement de fluide et leurs inclusions dans les corrélations proposées pour prédire la perte de charge est discutée. La question « Les paramètres d'Ergun peuvent-ils avoir des valeurs numériques constantes ou non ? » est discutée. Trois différentes corrélations étaient dérivées pour prédire la conductivité thermique effective à la fois isotrope et anisotrope des mousses. Les paramètres géométriques de la matrice de mousse étaient introduits dans les corrélations pour prédire la conductivité thermique effective. / Open cell foams have diverse industrial applications e.g. heat exchangers, structured reactors, filtration due to their unique properties such as high porosity and high specific surface area. In order to theoretically determine the geometric specific surface area and relationships between geometrical parameters of isotropic open cell foams, a generalized mathematical correlation was developed. For this purpose the tetrakaidecahedron geometry was used and different shapes of strut cross-sections of foam structures were taken explicitly into account. The derived correlation to predict geometrical properties can be easily extended to different strut shapes. 3-D numerical simulations at pore scale were performed to study the pressure drop characteristics and effective thermal conductivity. Fluid flow through open cell foam was performed in three different regimes: Darcy regime, transition regime and inertia regime. Importance of geometrical properties on fluid flow characteristics and their inclusion in the proposed correlations for predicting pressure drop is discussed. "Can Ergun parameters have constant numerical values or not" is also extensively discussed. Three different correlations were derived to predict the effective thermal conductivity for both, isotropic and anisotropic open cell foams. Geometrical parameters of foam matrix were introduced in the correlations to predict effective thermal conductivity.