The knowledge of density current behaviours as a result of two or more fluids of different densities interacting is of particular importance in many practical applications. Within the field of hydraulic engineering, examples include buoyant effluent discharges from desalination plants, advancements of saline water under freshwater in estuaries, and flows occurring when a gate is removed at the outflow/inflow of a river. The main goal of this study is to improve the understanding of the mixing patterns of density currents as well as their related numerical simulation. In this study, first, an advanced numerical solver for 2D variable-density shallow water equations is developed and validated where both well balanced and positivity preserving properties are achieved over an unstructured grid. The improved numerical scheme is flexible, and accounts for flooding over irregular bed topographies by using a triangular grid. Second, a numerical study of two-layer stratified flows over an isolated submerged dune is conducted. This part focuses on modeling density currents created when a narrow channel connects two water bodies with different densities and a stratified two-layer flow is subsequently generated. A 3D Large Eddy Simulation (LES) model is developed in OpenFoam and validated with the experimental data to investigate the flow patterns and entrainment. In addition to the LES model, a RANS numerical model is also used, and the results are compared in order to prove the superiority of the LES method in modeling complex mixing behaviours. LES predictions showed good agreement with the experimental measurements, as the LES model was able to capture the KH instabilities. In the third part of this study, the interaction between inclined negatively buoyant jets and waves, such as in the case of brine discharges from desalination plants into the ocean, is experimentally investigated. In addition to discharges in a wave environment, experiments are also performed in a stagnant environment and a wave-current environment in order to compare the results. A combination of the Particle Image Velocimetry (PIV) technique and the full-field Laser Induced Fluorescence (LIF) technique is employed to reveal the mixing patterns. The results showed that the wave motion affects the inclined negatively buoyant jet geometry, resulting in the jet’s rotation and an increase in its width. This study led to derivation of empirical formulae calculating terminal rise height and minimum dilution at specific points. In the fourth part, the numerical simulations of 45° inclined dense jets in wavy ambient have been conducted using a finite volume model (OpenFOAM). The selected turbulence models include RNG k-ε, realizable k-ε; Nonlinear k-ε; and LRR. The results of this study are compared to the results from experimental investigations in the third part and comparative figures and tables are presented and discussed. It has been observed that the LRR turbulence model as well as the realizable k-ε model predict the flow more accurately among the various turbulence models studied herein.

Coastal regions are the most densely populated regions of the world. The populations of these regions continue to grow which has created a high demand for water that stresses existing water resources. Coastal aquifers provide a source of water for coastal populations and are generally part of a larger system where freshwater aquifers are hydraulically connected with a saline surface-water body. They are characterized by salinity variations in space and time, sharp freshwater/saltwater interfaces which can lead to dramatic density differences, and complex groundwater chemistry. Mismanagement of coastal aquifers can lead to saltwater intrusion, the displacement of fresh water by saline water in the freshwater regions of the aquifers, making them unusable as a freshwater source. Saltwater intrusion is of significant interest to water resource managers and efficient simulators are needed to assist them. Numerical simulation of saltwater intrusion requires solving a system of flow and transport equations coupled through a density equation of state. The scale of the problem domain, irregular geometry and heterogeneity can require significant computational resources. Also, modeling sharp transition zones and accurate flow velocities pose numerical challenges. Discontinuous Galerkin (DG) finite element methods (FEM) have been shown to be well suited for modeling flow and transport in porous media but a fully coupled DG formulation has not been applied to the variable density flow and transport model. DG methods have many desirable characteristics in the areas of numerical stability, mesh and polynomial approximation adaptivity and the use of non-conforming meshes. These properties are especially desirable when working with complex geometries over large scales and when coupling multi-physics models (e.g. surface water and groundwater flow models). In this dissertation, we investigate a new combined local discontinuous Galerkin (LDG) and non-symmetric, interior penalty Galerkin (NIPG) formulation for the non-linear coupled flow and solute transport equations that model saltwater intrusion. Our main goal is the formulation and numerical implementation of a robust, efficient, tightly-coupled combined LDG/NIPG formulation within the Department of Defense (DoD) Proteus Computational Mechanics Toolkit modeling framework. We conduct an extensive and systematic code and model verification (using established benchmark problems and proven convergence rates) and model validation (using experimental data) to verify accomplishment of this goal. Lastly, we analyze the accuracy and conservation properties of the numerical model. More specifically, we derive an a priori error estimate for the coupled system and conduct a flow/transport model compatibility analysis to prove conservation properties. / text

Variable-density thinning (VDT) is a management option designed to increase structural heterogeneity in second-growth conifer stands. This study examined subcanopy tree growth response to two variations of VDT. At the Forest Ecosystem Study in western Washington, thinning intensity was found to have a significant effect on height growth of Douglasir (Pseudotsuga menziesii (Mirb.) Franco) seedlings which established following the thinning. At the Olympic Habitat Development Study in western Washington, basal area growth response was examined for residual midcanopy western hemlock (Tsuga heterophylla (Raf.) Sarg.) and western redcedar (Thuja plicata ex. D. Don). Both species retained the ability to respond to thinning. The results of this study suggest that non-uniform thinning practices, like VDT, can lead to variation in growth response of residual subcanopy trees and new regeneration. This may accelerate the development of more structurally diverse forests than traditional management practices.

Aquifer Storage Recovery (ASR) is a recently developed (circa 1970) method (in the U.S.A.) to reduce groundwater-pumping stresses by injecting treated wastewater or surface water during periods of low demand into an aquifer followed by its recovery during periods of high demand. This method has been successfully implemented in numerous locations across the U.S.A. and worldwide, mainly due to the cost savings provided by the use of an unlimited reservoir (aquifer) in which to store water compared to the costs to construct surface impoundments and the inherent problems with storing such water for extended periods of time under evaporative atmospheric conditions. "This study describes the use of a highly discretized, three-dimensional, variable-density, numerical model (SEAWAT 2000) that incorporates the vertical variation of hydraulic conductivities, measured foot by foot, from a continuous core collected from the upper Floridan aquifer in southwest Florida, to evaluate the effects of small-scale heterogeneities on a hypothetical ASR system well. In order to compare these effects to the more general case in which average hydraulic parameters are used to characterize flow zones, a model is constructed with average parameters taken from the heterogeneous case. This study attempts to determine whether aquifer heterogeneities influence the performance of ASR systems, compared to assumed homogeneous conditions, by quantifying differences in recovery efficiency, horizontal and vertical flow due to advection and dispersion, plume dimensions, and storage periods. The results of this study indicate that 1) the geometry of the injectate plume under homogeneous and heterogeneous conditions differ significantly; 2) background formation total dissolved solids (TDS) concentrations significantly control the quantity of potable water available for recovery; 3) dispersion exhibits a strong control on vertical mixing; 4) multiple injection cycles are required to generate a plume of potable water for long term storage; and 5) the percent recoveries under homogeneous and heterogeneous conditions are generally similar only in low-salinity background concentrations, due to the absence of the effects of buoyancy. Although the percent recoveries of the systems modeled are similar, the success of an ASR well is strongly controlled by the existence of heterogeneities, which essentially determine the degree of horizontal and vertical mixing of the injectate with formation waters. Heterogeneities result in varying groundwater and mass transport paths during injection and recovery periods. Presumably these variations would need to be considered when evaluating potential variations in groundwater quality due to mixing between formation and injected water. Understanding potential variations in groundwater quality and treatment alternatives due to the presence of ASR-associated geochemical conditions, e.g., elevated arsenic concentrations, may also be improved with a detailed heterogeneous numerical model.

Storage of freshwater in saline aquifers has a strategic importance in water deficit countries. The freshwater stored in these aquifers may be the only source of water available during times of crisis. Coupled simulation and optimization type groundwater management models have been developed that will achieve the optimal control of the storage of freshwater in a stagnant manner for constant density and variable density flows in hypothetical single- and multi-layered saline aquifers. The study is carried out in two stages. In the first stage, a transient model of five years is simulated that allows sufficient time for the freshwater mound to be created. In the second stage, an optimization model is formulated which minimizes the pumping/injection rates of a set of hydraulic gradient control wells subject to a set of constraints consisting of systems response equations, demand requirements, hydraulic gradient controls, pumping and injection limitations. The optimization models select which wells to be pumped and which ones to be injected and decide on their pumping/injection schedules to maintain the freshwater mound from migration. The results of the optimization models showed that the mound is successfully contained in its original location by controlling the hydraulic gradient via pumping/injection wells.

Une étude expérimentale du développement de jets turbulents à masse volumique variable est menée. Les comportements axiaux et radiaux des propriétés statistiques moyennes et fluctuantes obtenues sur les champs de vitesse et de concentration sont analysés. Ces résultats apportent une meilleure compréhension des phénomènes de mélange et de l’effet de la variation de densité dans le but d’apporter des données complémentaires pour le développement des calculs numériques et accroître leurs précisions. Les cas étudiés dans cette thèse sont deux jets d’hélium marqués par de la vapeur d’acétone pour des nombres de Reynolds Re = 7000 et 11000 permettant d’explorer l’effet de fortes variations de masse volumique (S = 0,39 et 0,41, respectivement) par rapport à l’air ambiant. Le cas d’un jet d’air (Re = 16000) également porteur de vapeur d’acétone est utilisé comme cas de référence comparable au cas d’un contaminant passif avec S = 1,17. L’étude porte sur la région de proche sortie de jet, jusqu’à une distance de 40 fois le diamètre Dj de sortie du jet. La configuration adoptée est celle d’un jet de tube rond, libre, axisymétrique, vertical et ascendant dont le diamètre intérieur du tube est Dj = 3,5mm se développant dans l’air ambiant. La particularité de cette étude est la mise en œuvre d’un système de mesure par diagnostic optique qui permet un couplage spatial et temporel des mesures de vitesse et de concentration sur une région de l’écoulement de quelques cm2 et non sur un seul point. Pour ce faire, le couplage des mesures PIV, pour la mesure du champ de vitesse, et PLIF basée sur la fluorescence de la vapeur d’acétone, pour la mesure du champ de concentration, a été étudié, conçu et testé. Il nous a permis d’obtenir une base de données, encore trop rares aujourd’hui, sur l’évolution des flux turbulents croisés de vitesse et concentration. Ces données ont mis en évidence une évolution plus rapide du jet le plus léger. Cependant, les coefficients de corrélation semblent identiques lorsque l’on atteint la zone autosimilaire du jet. Une approche basée sur les probabilités de densité conjointes vitesse-concentration a permis de mettre en évidence des différences dans la région extérieure des jets, où l’intermittence de frontière donne son empreinte sur les propriétés du mélange. / An experimental study of the development of turbulent jets with variable density is presented. The axial and radial behaviours of the mean and fluctuating statistical properties obtained on the velocity and concentration fields are analysed. These results provide a better understanding of mixing phenomena and the effect of density variation in order to provide complementary data for the development of numerical calculations and to increase their precision. The cases studied in this thesis are two helium jets carrying acetone vapor for Reynolds numbers Re = 7000 and 11000 to explore the effect of large density variations (S = 0.39 and 0.41, respectively) relative to the ambient air. The case of an air jet (Re = 16000) also carrying acetone vapor is used as a reference case comparable to the case of a passive contaminant with S = 1.17. The study focuses on the region of near jet exit, up to a distance of 40 times the jet outlet diameter Dj. The adopted configuration is a round jet tube, free, axisymmetric, vertical and ascending whose internal diameter of the tube is Dj = 3.5 mm developing in the ambient air. The particularity of this study is the implementation of an optical diagnostic measurement system that allows a spatial and temporal coupling of speed and concentration measurements over a region of the flow of a few cm2. To do this, the coupling of the PIV measurements for the measurement of the velocity field and the PLIF based on the fluorescence of the acetone vapor for the measurement of the concentration field has been studied, designed and tested. It allowed us to obtain a database, still too rare today, on the evolution of the turbulent flow of speed and concentration. These data have shown a faster evolution of the lightest jet. However, the correlation coefficients appear to be identical when the self-similar zone of the jet is reached. An approach based on joint speed-concentration density probabilities has revealed differences in the outer region of the jets, where the intermittent boundary gives its imprint on the properties of the mixture.

Shallow water equations are widely used to model water flows in the field of hydrodynamics and civil engineering. They are complex, and except for some simplified cases, no analytical solution exists for them. Therefore, the partial differential equations of the shallow water system have been the subject of various numerical analyses and studies in past decades. In this study, we construct a stable and robust finite volume scheme for the shallow water equations over quadtree grids. Quadtree grids are two-dimensional semi-structured Cartesian grids that have different applications in several fields of engineering, such as computational fluid dynamics. Quadtree grids refine or coarsen where it is required in the computational domain, which gives the advantage of reducing the computational cost in some problems. Numerical schemes on quadtree grids have different properties. An accurate and robust numerical scheme is able to provide a balance between the flux and source terms, preserve the positivity of the water height and water surface, and is capable of regenerating the grid with respect to different conditions of the problem and computed solution. The proposed scheme uses a piecewise constant approximation and employs a high-order Runge-Kutta method to be able to make the solution high-order in space and time. Hence, in this thesis, we develop an adaptive well-balanced positivity preserving scheme for the shallow water system over quadtree grids utilizing different techniques. We demonstrate the formulations of the proposed scheme over one of the different configurations of quadtree cells. Six numerical benchmark tests confirm the ability of the scheme to accurately solve the problems and to capture small perturbations. Furthermore, we extend the proposed scheme to the coupled variable density shallow water flows and establish an extended method where we focus on eliminating nonphysical oscillations, as well as well-balanced, positivity preserving, and adaptivity properties of the scheme. Four different numerical benchmark tests show that the proposed extension of the scheme is accurate, stable, and robust.

With a growing desire to generate structural characteristics of late-successional conifer forests, managers are commonly seeking an approach to increase structural heterogeneity in otherwise simple second-growth stands. This study examined understory response to experimental thinning on the Olympic Peninsula of Western Washington. Variable-density thinning within the Olympic Habitat Development Study was found to have significant effects on both the density of seedling recruitment as well as early growth of western hemlock (Tsuga heterophylla (Raf.) Sarg.). In additional analysis, pre-commercial understory thinning, implemented by the Olympic National Forest, produced no observable acceleration in basal area growth. Results suggest that understory development is sensitive to previous management history as well as post-treatment stand structure. Better understanding the sources of variability in understory tree response to non-uniform thinning and understory density management will be principle in evaluating the efficacy of these treatments relative to traditional methods.

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Yes / The Caleva UK single-screw Variable Density Extruder (VDE) is a continuous powder processing equipment known for spheronization and extrusion. Its suitability for granulation remains uncertain, a common challenge in powder processing industries that deal with granules, pellets, and tablets. This study investigates the VDE's potential for granulation, using 65 µm CaCO3 powder and PEG 4000 as a liquid binder. In order to replicate several experimental setups with varying binder concentrations and liquid-to-solid ratios (L/S) of 0.1 and 0.15, eight DEM simulations were run. Our results indicate that higher binder concentrations yield more consistent products with fewer fines, while lower concentrations result in inconsistent products with increased fines. Low L/S ratios produce fragile, fine-sized products with a broad particle size distribution (PSD). DEM simulations reveal a direct relationship between liquid binder content and contact forces. Analysis of bonds formed, and particle counts in simulations corroborates experimental observations of fines production. Additionally, granule strength appears to be directly proportional to contact force. / Special gratitude is given to Ghana Scholarship Secretariat for providing the necessary funding for this research. / The full-text of this article will be released for public view at the end of the publisher embargo on 23 Jan 2025.