This work details the development and implementation of a numerical model capable of solving strongly-coupled fluid-structure interaction problems involving long thin structures, which are common multi-physics problems encountered in many applications. In most fluid-structure interaction problems the deformation of the slender elastic bodies is significant and cannot be described by a purely linear analysis. We present a new formulation to model these larger displacements. By extending the standard modal decomposition technique for linear structural analysis, the governing equations and boundary conditions are updated to account for the leading-order non-linear terms and a new modal formulation with quadratic modes is derived. The quadratic modal approach is tested on standard benchmark problems of increasing complexity and compared with analytical and full non-linear numerical solutions. Two computational fluid-structure interaction approaches are then implemented in a partitioned manner: a finite volume method for discretisation of both the fluid and solid domains and the quadratic modal formulation for the structure coupled with a finite volume fluid solver. Strong-coupling is achieved by means of a fixed-point solver with dynamic relaxation. The fluid-structure interaction approaches are validated and compared on benchmark problems of increasing complexity and strength of coupling between the fluid and solid domains. Fluid-structure interaction systems may become unstable due to the interaction between the fluid-induced pressure and structural rigidity. A thorough stability analysis of finite elastic plates in uniform flow is conducted by varying the structural length and flow velocity showing that these are critical parameters. Validation of the results with those from analytical methods is done. An analysis of the dynamic interactions between multiple finite plates in various configurations is also conducted.

The processes studied by nuclear engineers generally include coupled physics phenomena (Thermal-Hydraulics, Neutronics, Material Mechanics, etc.) and modeling such multiphysics processes numerically can be computationally intensive. A way to reduce the computational burden is to use spatial meshes that are optimally suited for a specific solution; such meshes are obtained through a process known as Adaptive Mesh Refinement (AMR). AMR can be especially useful for modeling multiphysics phenomena by allowing each solution component to be computed on an independent mesh (Multimesh AMR). Using AMR on time dependent problems requires the spatial mesh to change in time as the solution changes in time. Current algorithms presented in the literature address this concern by adapting the spatial mesh at every time step, which can be inefficient. This Thesis proposes an algorithm for saving computational resources by using a spatially adapted mesh for multiple time steps, and only adapting the spatial mesh when the solution has changed significantly. This Thesis explores the mechanisms used to determine when and where to spatially adapt for time dependent, coupled physics problems. The algorithm is implemented using the Deal.ii fiinite element library [1, 2], in 2D and 3D, and is tested on a coupled neutronics and heat conduction problem in 2D. The algorithm is shown to perform better than a uniformly refined static mesh and, in some cases, a mesh that is spatially adapted at every time step.

Renal failure or kidney failure is a medical condition when the kidneys fail to filter toxins and waste products from the blood. Most of the time, problems encountered in kidney malfunction include abnormal fluid levels in the body, increased acid levels and abnormal levels of Urea, Glucose, Endothelin, β2-Microglobulin, Complement Factor D. In medicine, dialysis is a method that is used to remove waste products from blood when the kidneys are in a state of renal failure. Parameters characterizing the structure of dialyzers are very important because they decide overall clearance of toxin molecules and at the same time should allow retaining useful molecules in the blood. It is however not clear how the changes of dialyzer parameters will affect the clearance. This can be found out by doing simulation of a dialysis process. In this thesis, a numerical model was developed to simulate the process that goes on inside a dialyzer to determine which parameters are important for getting better clearance of toxin molecules and how the changes of those parameters can improve the performance of dialysis. In order to do that, a model of dialyzer membrane with details of the porosity is necessary. The dialyzer membrane that was considered in this research was Polyflux 210H. Here the cross sectional images of Polyflux 210H dialyzer membrane were taken by FESEM (Field Emission Scanning Electron Microscope) to obtain the porosity values of different layers. Using these porosity values, a multilayered membrane model was developed in Finite Element Software- COMSOL Multiphysics 4.3. Then a blood flow containing - Urea, Glucose, Endothelin, β2-Microglobulin, Complement Factor D and Albumin was introduced. For a certain blood flow rate the toxins diffuse through the membrane and on the other side of the membrane a dialysate flow was introduced to remove the toxins. Two different definitions of effective diffusivity were considered for the phenomenon of the diffusion of the molecules in the membrane. Between the two, the better definition was found out by comparing the results with experimental data of the manufacturer of Polyflux 210H. Then for the chosen definition, further analysis was done and the results were compared with another set of experimental data to validate the model. Then different parameters - magnitude and direction of both blood and dialysate flow, length and diameter of the fiber, pore sizes were changed to simulate how these changes affect toxin clearance and the removal of useful molecules. The results suggest some very interesting points to achieve better dialysis performance. First of all, the clearance rate of both Urea and Glucose increase rapidly with the increasing blood flow rate. When a maximum allowable blood flow rate is attained, increasing the dialysate flow rate can ensure better clearance rate for Urea and Glucose. In both the cases of increasing radius or length of the dialyzer fiber, the clearance rate of Glucose increases more rapidly than the clearance rate of Urea. For Endothelin and β2-Microglobulin the clearance rate increases twice compared to the initial condition. Meanwhile, the clearance rate of Albumin does not change that much. Also increasing the pore diameter up to 20 nm (but not more than that) can ensure higher clearance rate of Urea and Glucose, moderate clearance rate of middle molecules and minimum loss of Albumin.

In a world where money often is the main controlling factor, everything that can be tends to be more and more optimized. Regarding electrical machines, developers have always had the goal to make them better. The latest trend is to make machines as efficient as possible, which calls for accurate simulation models where different designs can be tested and evaluated. The finite element method is probably the most popular approach since it makes it possible to, in an easy and accurate way, get numerical solutions to a variety of physics problems with complex geometries and non-linear materials. This licentiate thesis includes two different projects in which finite element methods have had a central roll. In the first project, the goal was to develop a simulation model to be able to predict demagnetization of permanent magnets. It is of great importance to be able to predict if a permanent magnet will be demagnetized or not in a certain situation. In the worst case, the permanent magnets will be completely destroyed and the machine will be completely useless. However, it is more probable that the permanent magnets will not be completely destroyed and that the machine still will be functional but not as good as before. In a time where money is more important than ever, the utilization has to be as high as possible. In this study the demagnetization risk for different rotor geometries in a 12 kW direct driven permanent magnet synchronous generator was studied with a proprietary finite element method simulation model. The demagnetization study of the different rotor geometries and magnet grades showed that here is no risk for the permanent magnets in the rotor as it is designed today to be demagnetized. The project also included experimental verification of the simulation model. The simulation model was compared with experiments and the results showed good agreement. The second project treated the redesign of the rotor in the generator previously mentioned. The goal was to redesign the surface mounted NdFeB rotor to use a field concentrating design with ferrite permanent magnets instead. The motivation was that the price on NdFeB magnets has fluctuated a lot the last few years as well as to see if it was physically possible to fit a ferrite rotor in the same space as the NdFeB rotor. A new rotor design with ferrite permanent magnets was presented together with an electromagnetic and a mechanical design.

Fluorine gas is produced industrially by electrolysing hydrogen fluoride in a potassium acid fluoride electrolyte. Fluorine is produced at the carbon anode, while hydrogen is produced at the mild-steel cathode. The fluorine produced has a wide range of uses, most notably in the nuclear industry where it is used to separate 235U and 238U. The South African Nuclear Energy Corporation (Necsa) is a producer of fluorine and requested an investigation into the hydrodynamics of their electrolysis cells as part of a larger national initiative to beneficiate more of South Africa’s large fluorspar deposits. Due to the extremely corrosive and toxic environment inside a typical fluorine electrolysis reactor, the fluid dynamics in the reactor are not understood well enough. The harsh conditions make detailed experimental investigation of the reactors extremely dangerous. The objective of this project is to construct a model that can accurately predict the physical processes involved in the production of fluorine gas. The results of the simulation will be compared to experimental results from tests done on a lab-scale reactor. A good correlation between reality and the simulacrum would mean engineers and designers can interrogate the inner operation of said reactors safely, effortlessly and economically. This contribution reports a time-dependent simulation of a fluorine-producing electrolysis reactor. COMSOL Multiphysics was used as a tool to construct a two dimensional model where the charge-, heat-, mass- and momentum transfer were fully coupled in one transient simulation. COMSOL is a finite element analysis software package. It enables the user to specify the dimensions of his/her investigation and specify a set of partial differential equations, boundary conditions and starting values. These equations can be coupled to ensure that the complex interaction between the various physical phenomena can be taken into account - an absolute necessity in a model as complex as this one. Results produced include a set of time dependent graphics where the charge-, heat-, mass- and momentum transfer inside the reactor and their development can be visualized clearly. The average liquid velocity in the reactor was also simulated and it was found that this value stabilises after around 90 s. The results of each transfer module are also shown at 100 s, where it is assumed that the simulation has achieved a quasi-steady state. The reactor, on which the model is based, is currently under construction and will be operated under the same conditions as specified in the model. The reactor, constructed of stainless steel, has a transparent side window through which both electrodes can clearly be seen. Thus the bubble formation and flow in the reactor can be studied effectively. Temperature will be measured with a set of thermocouples imbedded in PTFE throughout the reactor. The electric field will similarly be measured using electric induction probes. / Dissertation (MEng)--University of Pretoria, 2012. / Chemical Engineering / unrestricted

One of the most novel technologies developed in the past few decades is to convert mine wastes into cemented construction materials, otherwise known as cemented tailings backfill (CTB). CTB is an engineered mixture of tailings (waste aggregates), water and hydraulic binders. It is extensively used worldwide to stabilize underground cavities created by mining operations and maximize the recovery of ore from pillars. Moreover, the application of CTB is also an environmentally friendly means of disposing potential acid generating tailings underground. During and after its placement into underground mine excavations or stopes, complex multiphysics processes (including thermal, T, hydraulic, H, mechanical, M, and chemical, C, processes) take place in the CTB mass and thus control its behavior and performance. With the interaction of the multiphysics processes, the field variables (temperature, pore water pressure, stress and strain) and geotechnical properties of CTB undergo substantial changes. Therefore, the prediction of the field performance of CTB structures during their life time, which has great practical importance, must incorporate these THMC processes. Moreover, the self-weight effect, water drainage through barricades, thermal expansion and chemical shrinkage can contribute to the volumetric deformation of CTB. Consequently, CTB exhibits unique consolidation behavior compared to conventional geomaterials (e.g., soil). Furthermore, the consolidation processes can result in relative displacement between the rock mass and CTB. The resultant rock mass/CTB interface resistance can reduce the effects of the overburden pressure or the vertical stress (i.e., arching effect). Hence, a full understanding, through multiphysics modeling and simulation of CTB behaviors, is crucial to reliably assess and predict the performance of CTB structures. Yet, there are currently no models or tools to predict the fully coupled multiphysics behavior of CTB. In this Ph.D. study, a series of mathematical models which include an evolutive elastoplastic model, a fully coupled THMC model, a multiphysics model of consolidation behavior and a multiphysics model of the interaction between the rock mass/CTB interface are developed and validated. There is excellent agreement between the modeled results and experimental and/or in-situ monitored data, which proves the accuracy and predictive ability of the developed models. Furthermore, the validated multiphysics models are applied to a series of engineering issues, which are relevant for the field design of CTB structures, to investigate the self-desiccation process, consolidation behavior of CTB structures as well as to assess the pressure on barricades and the strength development in CTB structures. The obtained results show that CTB has different behaviors and performances under different backfilling conditions and design strategies, and the developed multiphysics models can accurately model CTB field behavior. Therefore, the research conducted in this Ph.D. study provides useful tools and technical information for the optimal design of CTB structures.

The most common design among U.S. nuclear power plants is the pressurized water reactor (PWR). The three primary design disciplines of these plants are system analysis (which includes thermal hydraulics), neutronics, and fuel performance. The nuclear industry has developed a variety of codes over the course of forty years, each with an emphasis within a specific discipline. Perhaps the greatest difficulty in mathematically modeling a nuclear reactor, is choosing which specific phenomena need to be modeled, and to what detail. A multiphysics computational environment provides a means of advancing simulations of nuclear plants. Put simply, users are able to combine various physical models which have commonly been treated as separate in the past. The focus of this work is a specific multiphysics environment currently under development at Idaho National Labs known as the LOCA Toolkit for US light water reactors (LOTUS). The ability of LOTUS to use uncertainty quantification (UQ) and sensitivity analysis (SA) tools within a multihphysics environment allow for a number of unique analyses which to the best of our knowledge, have yet to be performed. These include the first known integration of the neutronics and thermal hydraulic code VERA-CS currently under development by CASL, with the well-established fuel performance code FRAPCON by PNWL. The integration was used to model a fuel depletion case. The outputs of interest for this integration were the minimum departure from nucleate boiling ratio (MDNBR) (a thermal hydraulic parameter indicating how close a heat flux is to causing a dangerous form of boiling in which an insulating layer of coolant vapour is formed), the maximum fuel centerline temperature (MFCT) of the uranium rod, and the gap conductance at peak power (GCPP). GCPP refers to the thermal conductance of the gas filled gap between fuel and cladding at the axial location with the highest local power generation. UQ and SA were performed on MDNBR, MFCT, and GCPP at a variety of times throughout the fuel depletion. Results showed the MDNBR to behave linearly and consistently throughout the depletion, with the most impactful input uncertainties being coolant outlet pressure and inlet temperature as well as core power. MFCT also behaves linearly, but with a shift in SA measures. Initially MFCT is sensitive to fuel thermal conductivity and gap dimensions. However, later in the fuel cycle, nearly all uncertainty stems from fuel thermal conductivity, with minor contributions coming from core power and initial fuel density. GCPP uncertainty exhibits nonlinear, time-dependent behaviour which requires higher order SA measures to properly analyze. GCPP begins with a dependence on gap dimensions, but in later states, shifts to a dependence on the biases of a variety of specific calculation such as fuel swelling and cladding creep and oxidation. LOTUS was also used to perform the first higher order SA of an integration of VERA-CS and the BISON fuel performance code currently under development at INL. The same problem and outputs were studied as the VERA-CS and FRAPCON integration. Results for MDNBR and MFCT were relatively consistent. GCPP results contained notable differences, specifically a large dependence on fuel and clad surface roughness in later states. However, this difference is due to the surface roughness not being perturbed in the first integration. SA of later states also showed an increased sensitivity to fission gas release coefficients. Lastly a Loss of Coolant Accident was investigated with an integration of FRAPCON with the INL neutronics code PHISICS and system analysis code RELAP5-3D. The outputs of interest were ratios of the peak cladding temperatures (highest temperature encountered by cladding during LOCA) and equivalent cladding reacted (the percentage of cladding oxidized) to their cladding hydrogen content-based limits. This work contains the first known UQ of these ratios within the aforementioned integration. Results showed the PCT ratio to be relatively well behaved. The ECR ratio behaves as a threshold variable, which is to say it abruptly shifts to radically higher values under specific conditions. This threshold behaviour establishes the importance of performing UQ so as to see the full spectrum of possible values for an output of interest. The SA capabilities of LOTUS provide a path forward for developers to increase code fidelity for specific outputs. Performing UQ within a multiphysics environment may provide improved estimates of safety metrics in nuclear reactors. These improved estimates may allow plants to operate at higher power, thereby increasing profits. Lastly, LOTUS will be of particular use in the development of newly proposed nuclear fuel designs.

There is a renewed interest to use material as wood to construct large multi-storey buildings in Sweden, but lightweight material tends to increase the indoor temperature fluctuations during days with large changes in outdoor temperature. The problem can be resolved by integrating phase change material (PCM) in the construction. This increases thermal inertia which mitigates the fluctuations.           The scope of the study is to develop a simulation model in COMSOL Multiphysics, to validate the model experimentally and to determine the optimal position and thickness of a PCM layer in a multi-layer wall. The model, representing a building with the shape of a box, consists of two versions. The first version, called the test box, is modeled with 5 sides of pure gypsum and 1 side of PCM-gypsum composite. The second version without PCM, called the reference box, is modeled with 6 sides of pure gypsum. Since the study is focused on reducing the cooling load, the PCM gypsum composite material should function effectively during summer conditions in northern Sweden. The experimental part includes two real-life boxes, the experimental test box and reference box, built of the same type of material that is chosen for the simulation model boxes. A climate chamber is utilized for the temperature control of the two boxes while performing measurements to validate the simulation model. The simulation model showed deviations from the experimental measurements. The temperatures inside the climate chamber, at all five points of measurement, were lower than the equivalent points in the simulation. It was possible to compensate by adjusting the overall ambient temperature down with 0.6 °C in the simulation, resulting in smaller errors. The PCM positioning resulted in recommendations to place the PCM closest to the interior space. The testing of different PCM thicknesses showed the best heat storage for the thickest PCM layers, but the PCM storage efficiency should have been considered as well.

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