Although ships have been used for thousands of years, modeling the dynamics of marine craft has historically been restricted by the complex nature of the hydrodynamics. The principal challenge is that the vehicle motion is coupled to the ambient fluid motion, effectively requiring one to solve an infinite dimensional set of equations to predict the hydrodynamic forces and moments acting on a marine vehicle. Additional challenges arise in parametric modeling, where one approximates the fluid behavior using reduced-order ordinary differential equations. Parametric models are typically required for model-based state estimation and feedback control design, while also supporting other applications including vehicle design and submarine operator training. In this dissertation, Lagrangian mechanics is used to derive nonlinear, parametric motion models for marine craft operating in the presence of a free surface. In Lagrangian mechanics, one constructs the equations of motion for a dynamic system using a system Lagrangian, a scalar energy-like function canonically defined as the system kinetic energy minus the system potential energies. The Lagrangian functions are identified under ideal flow assumptions and are used to derive two sets of equations. The first set of equations neglects hydrodynamic forces due to exogenous fluid motions and may be interpreted as a nonlinear calm water maneuvering model. The second set of equations incorporates effects due to exogenous fluid motion, and may be interpreted as a nonlinear, unified maneuvering and seakeeping model. Having identified the state- and time-dependent model parameters, one may use these models to rapidly simulate surface-affected marine craft maneuvers, enabling model-based control design and state estimation algorithms. / Ph. D. / Although ships have been used for thousands of years, modeling the dynamics of marine craft has historically been restricted by the complex nature of the hydrodynamics. The principal challenge is that the vehicle motion is coupled to the ambient fluid motion, effectively requiring one to solve an infinite dimensional set of equations to predict the hydrodynamic forces and moments acting on a marine vehicle. Additional challenges arise in parametric modeling, where one approximates the fluid behavior using reduced-order ordinary differential equations. Parametric models are typically required for model-based state estimation and feedback control design, while also supporting other applications including vehicle design and submarine operator training. In this dissertation, Lagrangian mechanics is used to derive nonlinear, parametric motion models for marine craft operating in the presence of a free surface. In Lagrangian mechanics, one constructs the equations of motion for a dynamic system using a system Lagrangian, a scalar energy-like function canonically defined as the system kinetic energy minus the system potential energies. The Lagrangian functions are identified under ideal flow assumptions and are used to derive two sets of equations. The first set of equations neglects hydrodynamic forces due to exogenous fluid motions and may be interpreted as a nonlinear calm water maneuvering model. The second set of equations incorporates effects due to exogenous fluid motion, and may be interpreted as a nonlinear, unified maneuvering and seakeeping model. Having identified the state- and time-dependent model parameters, one may use these models to rapidly simulate surface-affected marine craft maneuvers, enabling model-based control design and state estimation algorithms.

Nanofiltration (NF) can be used in water and wastewater treatment as well as water recycling applications, removing micropollutants such as hormones. Due to their potential health risk it is vital to understand their removal mechanisms by NF membranes aiming at improving and developing more effective and efficient treatment processes. Although NF should be effective and efficient in removing small molecular sized compounds such as hormones, the occurrence of adsorption onto polymeric membranes results in performances difficult to predict and with reduced effectiveness and efficiency. This study aims firstly at defining, understanding and quantifying the relevant filtration operation parameters and, secondly, in identifying the physical mechanisms of momentum and mass transfer controlling the adsorption and transport of hormones onto polymeric NF membranes in cross-flow mode. The hormones estrone (E1) and 17-b-estradiol (E2) were chosen as they have very high endocrine disrupting potency. The NF membranes used and tested were the NF 270, NF 90, BW30, TFC-SR2 and TFC-SR3 since they have a wide span of pore sizes. The first step is to experimentally acquire the knowledge of how fluid flow hydrodynamics and mass transfer close to the membrane affect hormone adsorption. The focus will be particularly on the effect of operating pressure, circulating Reynolds numbers (based on channel height, Reh) and hormone feed concentration. These hydrodynamic parameters play an important role in concentration polarisation development at the membrane surface. A Reh increase from 400 to 1400 for the NF 270 membrane caused the total mass adsorbed of E1 and E2 to decrease from 1.5 to 1.3 ng.cm-2 and 0.7 to 0.5 ng.cm-2, respectively. In contrast, a pressure increase from 5 to 15 bar yielded an increase in the adsorbed mass of E1 and E2 from 1.0 to 1.8 ng.cm-2 and 0.5 to 0.7 ng.cm-2, respectively. Moreover, increasing hormone feed concentration caused an increase in the mass adsorbed for both hormones. These observations led to the conclusion that adsorption is governed by the initial concentration at the membrane surface which, in turn, depends on the hormone feed concentration, operating Reh and pressure. Membrane retention, however, depends on the initial polarisation modulus, defined as the ratio between the initial concentration at the membrane surface and the initial feed concentration. The same trends were obtained for the TFC-SR2 membrane. However, this membrane has a much lower permeability compared to the NF 270 one (7.2 vs 17 L.h-1.m-2.bar-1, respectively) and concentration polarisation is less severe. The experimental variations in mass adsorbed and retention as a function of the operating filtration parameters (Reh and pressure) were therefore lower. Based on these experimental results, a sorption model was developed. This model predicts well both feed and permeate transient concentrations for both hormones and membranes (NF 270 and TFC-SR2) in the common range of operating pressures and Reh of spiral-wound membrane modules. The model was further applied for E2 in the presence of background electrolyte, yielding good predictions. These findings are an important advancement in determining which membrane would be more suitable to effectively remove hormones with a substantial reduction of experimental work. The above-mentioned developed model does not give insight into the phenomena occurring inside the membrane since it focuses on the feed conditions. However, membrane characteristics, such as material and pore radius were found to have an impact in adsorption and retention of hormones. It was found experimentally that polyamide, from which the active layer of the NF membranes is made, adsorbs three times more mass of hormone than any other polymers constituting the membranes. Since this active layer is the membrane selective barrier of the membrane that is in contact with the largest hormone concentration (due to concentration polarization in the feed solution) it is concluded that the active layer adsorbs most of the hormones. Further experimental work carried out in this thesis showed that increasing the pore radius from 0.32 nm to 0.52 nm increased the E2 mass adsorbed from 0.17 ng.cm-2 to 1.1 ng.cm-2 and decreased the retention from 88% to 34%. These results show that the wider the pore, the larger the quantity of hormone that penetrates (i.e. partitions) inside the membrane and, therefore, the more the membrane adsorbs the hormone. For membranes of similar pore radius, the membrane with larger internal surface area was found to adsorb more. All the previous results led to the establishment of a new model for the hormone transport inside the membrane pore taking convection, diffusion and adsorption into account. Since the differential equation describing the transport with adsorption inside the pore has no analytical solution, a numerical model based on the finite-difference approach was applied. With such a model, its validation against experiments and parametric studies it was possible to understand the transport mechanisms of adsorbing hormones through NF membranes. The results show that for low pressures the hormone transport is diffusion dominated. In contrast, for higher pressures (above 11 bar) the transport is convection dominated, showing that a purely diffusion transport model does not describe well the actual transport phenomena of hormones in NF membranes. Furthermore, it was found that two similar molecules can behave very differently in terms of adsorption on the membrane. E1, which adsorbs 20% more than E2 in static mode, being slightly smaller than E2, partitions more inside the membrane pore and adsorbs double under filtration conditions. This study contributes to illuminating the adsorption mechanisms of hormones onto NF membranes by understanding what parameters control adsorption such as hydrodynamics, materials, structure, etc. This not only identifies a potential problem in large scale applications, but it also provides an understanding of the mechanisms involved in the removal of these hormones and a tool that can be used to design future membranes for the improvement of micropollutant removal.

The depth-averaged Saint-Venant equations, which are used for most computational flow models, are adequate in simulating open channel flows with insignificant curvatures of streamlines. However, these equations are insufficient when applied to flow problems where the effects of non-hydrostatic pressure distribution are predominant. This study provides a comprehensive examination of the feasibility of a simple one-dimensional Boussinesq-type model equation for such types of flow problems. This equation, which allows for curvature of the free surface and a non-hydrostatic pressure distribution, is derived using the momentum principle together with the assumption of a constant centrifugal term at a vertical section. Besides, two Boussinesq-type model equations that incorporate different degrees of corrections for the effects of the curvature of the streamline are investigated in this work. One model, the weakly curved flow equation model, is the simplified version of the flow model based on a constant centrifugal term for flow situations that involve weak streamline curvature and slope, and the other, the Boussinesq-type momentum equation linear model is developed based on the assumption of a linear variation of centrifugal term with depth.

The depth-averaged Saint-Venant equations, which are used for most computational flow models, are adequate in simulating open channel flows with insignificant curvatures of streamlines. However, these equations are insufficient when applied to flow problems where the effects of non-hydrostatic pressure distribution are predominant. This study provides a comprehensive examination of the feasibility of a simple one-dimensional Boussinesq-type model equation for such types of flow problems. This equation, which allows for curvature of the free surface and a non-hydrostatic pressure distribution, is derived using the momentum principle together with the assumption of a constant centrifugal term at a vertical section. Besides, two Boussinesq-type model equations that incorporate different degrees of corrections for the effects of the curvature of the streamline are investigated in this work. One model, the weakly curved flow equation model, is the simplified version of the flow model based on a constant centrifugal term for flow situations that involve weak streamline curvature and slope, and the other, the Boussinesq-type momentum equation linear model is developed based on the assumption of a linear variation of centrifugal term with depth.