Doctor of Philosophy / Department of Mechanical and Nuclear Engineering / Zhongquan Zheng / In this study, a vortex particle method is used to simulate incompressible vortical flows, specifically aircraft wake vortices. This is particularly suitable for a wake vortex system that is slowly varying in the axial direction and has a high Reynolds number and low Mach number. The flow field, in the form of vorticity, is employed as the source in the far-field acoustic calculation using a vortex sound formula that enables computation of acoustic signals radiated from an approximated incompressible flow field. In a two-dimensional vortex system, the stretching effect in the axial direction is neglected. The purpose of this study is to focus on vortex core behaviors. A numerical simulation is performed in a more realistic wake consisting of a counter-rotating vortex pair with inviscid ground effects and shear flows. A Kirchhoff spinning-core vortex model is thus used as a starting point. In a vortex system with multiple vortices, such as a complicated aircraft vortex wake vortices, the sound emission frequency of the unsteady vortex core is subjected to change because of interactions between multiple vortices. The behaviors of the influence, indicated by the ratio between the core size and the distance of the vortices, are investigated as well as the underlining vortex core dynamic mechanisms. Cases of co-rotating vortices and a multiple-vortex system composed of two counter-rotating vortex pairs are studied for applications to aircraft wake vortex sound. In three-dimensional vortices, sinusoidal instabilities, which occur in the axial direction at various length scales, result in significant flow structure changes in these vortices, and thus influence their radiated acoustic signals. Cases of vortex rings and a pair of counter-rotating vortices are studied when they are undergoing both long-wave and short-wave instabilities. Both inviscid and viscous interactions are considered and the effects of turbulence are simulated using sub-grid-scale models. A higher peak frequency than the Kirchhoff frequency appears due to the straining field caused by mutual perturbation, under both long-wave and short-wave instabilities. Vortices with the initial core vorticity of the Gaussian distribution and the elliptic distribution are also studied.

No description available.

Airbags are a passive safety technology, required to function with zero failure rate. Advances in Computer Aided Engineering have allowed vehicle manufacturers to predict material and system behavior in the event of a crash. The sudden and rapid nature of a vehicle frontal crash, together with strict requirements put on safety make this a sensitive task. This thesis focuses on the front passenger airbag deployment and the instrument panel’s response. Various airbag modelling techniques are studied and presented in this document. This work is part of a larger-scale attempt to model a generic-sled that is physically representative of a real vehicle. Various component tests are to be performed in the sled environment, as opposed to a real vehicle, to save costs. Various modules are added to the sled once their behavior is verified by testing and in simulations. Software are advanced enough to identify location and magnitude of stress concentrations that develop during crash. LS-DYNA is used for explicit finite element simulations of the instrument panel (IP) in question with different airbag models. Verification has been achieved by design of experiment (DOE); with tests conducted to capture both the movements of the airbag housing and IP movements in response. These movements are broken down in various phases, facilitating implementation in the sled environment. Simplifications are made both to the computer models as well as the physical testing environment. The effects of these simplifications are quantified and discussed. Theoretical background is provided where fit while assumptions are justified wherever made. DYNAmore recommendations regarding costeffective calculations as well as result verification are followed. The obtained results show that the FE models replicate the real event with acceptable precision. The findings in this work can, by minor tweaks, be implemented on other IP models in the Volvo Cars range, leading to cost-saving solutions. This thesis provides the necessary information for sled implementations as well as future improvement suggestions. / Krockkudde är en s.k. passiv säkerhetsteknik som krävs att fungera felfritt. Framsteg inom Computer Aided Engineering har tillåtit biltillverkare att förutsäga material och systembeteende i samband med krock. Den plötsliga karaktären av krock, tillsammans med höga säkerhetskrav, gör detta till en känslig uppgift. Denna avhandling fokuserar på passagerarsidans krockkudde och instrumentbrädans (IP) respons under uppblåsning. Olika metoder för modellering av krockkuddar har studerats och presenteras i detta dokument. Arbetet är en del av en större skala försök att modellera en generisk-släde som är fysiskt representativ av en riktig bil; där olika komponent-tester skall utföras för att minska kostnader. När olika modulers beteende verifieras läggs de till släden. Denna verifiering sker genom finita element (FE) simuleringar så väl som fysiska tester. FE mjukvara är idag tillräckligt avancerad för att identifiera samt visualisera spänningskoncentrationer som uppstår i en konstruktion vid krock. LS-DYNA används i detta arbete för explicita FE simuleringar av en Volvo XC90 IP, lastad med olika krockkudde-modeller. Modell verifiering har uppnåtts genom försöksplanering (DOE); med tester utförda för att fånga rörelser av IP så väl som krockkudde-behållaren. Dessa rörelser är sedan uppdelade i olika faser för enklare genomförande i släde miljön. Förenklingar och antaganden görs både till FE modeller och fysiska testmiljön. Effekter av dessa har kvantifierats och relevant teoretisk bakgrund har inkluderats. Dokumentet innehåller även diskussion kring val av mätutrustning samt förbättringsförslag för fortsatt arbete. DYNAmore rekommendationer gällande kostnadseffektiva beräkningar och verifiering av simulerings-resultat har följts. Under arbetet visade sig att FE modellerna kan återskapa händelsen med hög noggrannhet; dessa trotts svårigheter i modellering av plast material. Möjligtvis kan man, genom mindre modifieringar, relatera slutsatserna i detta arbete till olika IP modeller i företagets produktkatalog vilket förmodligen leder till ytterligare kostnadsbesparingar. Denna avhandling ger den information som behövs för genomföranden i den generiska miljön.

O método numérico para fluidos incompressíveis desenvolvido no presente estudo é o Moving Particle Semi-Implicit Method (MPS) que enxerga o domínio discretizado em partículas, é baseado em representação lagrangeana e não tem a necessidade de utilização de malhas. O método MPS tem como equações governantes uma forma particular da equação de Navier-Stokes e a equação da continuidade para fluidos incompressíveis e não viscosos. Os métodos de simulação de fluidos mais comumente utilizados são baseados em representação euleriana e utilizam malhas para descrever a geometria do domínio a ser simulado. Devido a essas diferenças, uma das grandes virtudes do método de partículas é a facilidade de investigação de fenômenos altamente não-lineares como o de superfície livre com quebra de ondas, de líquidos no interior de uma embarcação em movimento, de ondas batendo na parte externa do casco de um navio, etc. Em artigos já publicados, resultados de experimentos físicos mostraram boa aderência aos resultados numéricos de simulações realizadas com o método MPS. No presente trabalho, resultados das forças de excitação das simulações com ondas regulares foram comparados com os resultados do programa Wave Analysis MIT (WAMIT) que é um programa consagrado no meio científico. Houve uma boa concordância de resultados entre os dois programas. A otimização do cálculo de vizinhança forneceu uma grande economia de tempo computacional. A maior contribuição deste estudo foi a otimização da função que resolve o sistema linear implementando no código desenvolvido um código paralelizado de uso público existente chamado Portable, Extensible Toolkit for Scientific Computation (PETSc) que proporcionou um bom ganho de desempenho. / A numerical method called Moving Particle Semi-implicit (MPS) method was developed in this study to analyze incompressible fluids. It is a particle method using a lagrangean representation without any grid. The governing equations are the Navier-Stokes equation and continuity equation for incompressible and non-viscous flow. Most of the computational fluid dynamics (CFD) methods are based on eulerian representation and use grids to describe the geometry of the simulated domain. These differences make the MPS method easier to analyze highly nonlinear phenomena as free surface with wave breaking, sloshing, slamming, etc. In previously published articles, results of physical experiments had shown good agreement with the numerical results obtained with MPS method. In the present work, results of exciting forces were compared with the results obtained with a validated program called Wave Analysis MIT (WAMIT). It had a good agreement of results between these two programs. The optimization of the neighborhood calculation function got a good economy of computational time. The greatest contribution of this study was the optimization of the linear system solver. It was made implementing in the developed code a parallelized public code called Portable, Extensible Toolkit for Scientific Computation (PETSc) that provided a good performance profit.

Cette thèse est dédiée au développement d’un modèle mathématique multi-échelle pour la régulation du cycle cellulaire par l’horloge circadienne. Ceci est motivé par le fait que plusieurs études ont montré un lien direct entre certains cancers et un dysfonctionnement du mécanisme de l’horloge circadienne. Le but est de comprendre l’effet des rythmes circadiens et leur perturbation sur la prolifération d’une population de cellules / This thesis is dedicated to the development of a multiscale mathematical model that describes the regulation of the cell cycle by the circadian clock. What motivated this work is the fact that several tumorigenic diseases are linked to circadian rhythms disruption. We would like to understand the effect of circadian rhythms on the proliferation of a cell population and hence give plausible explanation for diseases that arise form circadian clock disruption. The mammalian cell cycle and the circadian clock are two molecular processes that operate in a rhythmic manner and exquisite precision. On one hand, the cell cycle is driven by the rhythmic activity of cyclin dependent kinases which dictate the time a cell must engage mitosis and the time it must divide giving birth to two daughter cells. On the other hand, the circadian clock is a system of transcriptional and translational feedback-loops that generates sustained oscillations of different mRNAs and proteins with a period of approximately 24 h. It turns out that several components of the circadian clock regulates various cyclin-dependent kinases at different stages of the cell cycle. This makes the circadian clock a key player of the temporal organization of the cell cycle and makes these two biological processes act as two tightly coupled oscillators. Our modeling approach consists of using a molecular-structured partial differential equation that describes the proliferation of a cell population. Proliferation depends on the coupled cell cycle-circadian clock molecular state of cells. Due to the large number of molecular components involved in the cell cycle-circadian clock system, the problem becomes of high-dimensionality and specific numerical techniques are needed to solve the equation

Cette thèse est consacrée à l'étude théorique et numérique de deux problèmes non linéaires au sens de McKean en finance. Nous abordons dans la première partie le problème de calibration d'un modèle à volatilité locale et stochastique pour tenir compte des prix d'options Européennes vanilles observés sur le marché. Ce problème se traduit par l'étude d'une équation différentielle stochastique (EDS) non linéaire au sens de McKean à cause de la présence dans le coefficient de diffusion d'une espérance conditionnelle du facteur de volatilité stochastique par rapport à la solution de l'EDS. Nous obtenons l'existence du processus dans le cas particulier où le facteur de volatilité stochastique est un processus de sauts ayant un nombre fini d'états. Nous obtenons de plus la convergence faible à l'ordre 1 de la discrétisation en temps de l'EDS non linéaire au sens de McKean pour des facteurs de volatilité stochastique généraux. Dans l'industrie, la calibration est effectuée efficacement à l'aide d'une régularisation de l'espérance conditionnelle par un estimateur à noyau de type Nadaraya-Watson, comme proposé par Guyon et Henry-Labordère dans [JGPHL]. Nous proposons également un schéma numérique demi-pas de temps et étudions le système de particules associé que nous comparons à l'algorithme proposé par [JGPHL]. Dans la deuxième partie de la thèse, nous nous intéressons à un problème de valorisation de contrat avec appels de marge, une problématique apparue avec l'application de nouvelles régulations depuis la crise financière de 2008. Ce problème peut être modélisé par une équation différentielle stochastique rétrograde (EDSR) anticipative avec dépendance en la loi de la solution dans le générateur. Nous montrons que cette équation est bien posée et proposons une approximation de sa solution à l'aide d'EDSR standards linéaires lorsque la durée de liquidation de l'option en cas de défaut est petite. Enfin, nous montrons que le calcul des solutions de ces EDSR standards peut être amélioré à l'aide de la méthode de Monte-Carlo multiniveaux introduite par Giles dans [G] / This thesis is dedicated to the theoretical and numerical study of two problems which are nonlinear in the sense of McKean in finance. In the first part, we study the calibration of a local and stochastic volatility model taking into account the prices of European vanilla options observed in the market. This problem can be rewritten as a stochastic differential equation (SDE) nonlinear in the sense of McKean, due to the presence in the diffusion coefficient of a conditional expectation of the stochastic volatility factor computed w.r.t. the solution to the SDE. We obtain existence in the particular case where the stochastic volatility factor is a jump process with a finite number of states. Moreover, we obtain weak convergence at order 1 for the Euler scheme discretizing in time the SDE nonlinear in the sense of McKean for general stochastic volatility factors. In the industry, Guyon and Henry Labordere proposed in [JGPHL] an efficient calibration procedure which consists in approximating the conditional expectation using a kernel estimator such as the Nadaraya-Watson one. We also introduce a numerical half-step scheme and study the the associated particle system that we compare with the algorithm presented in [JGPHL]. In the second part of the thesis, we tackle the pricing of derivatives with initial margin requirements, a recent problem that appeared along with new regulation since the 2008 financial crisis. This problem can be modelled by an anticipative backward stochastic differential equation (BSDE) with dependence in the law of the solution in the driver. We show that the equation is well posed and propose an approximation of its solution by standard linear BSDEs when the liquidation duration in case of default is small. Finally, we show that the computation of the solutions to the standard BSDEs can be improved thanks to the multilevel Monte Carlo technique introduced by Giles in [G]

When dealing with the separation of materials, the metal shearing process such as punching, is widely used in theindustry due to its time efficient manner. There is however, a need to better understand the process in order toimprove quality of the final product. Working with numerical simulations of themetal shearing process, there aretwo major difficulties. One being the extremely large deformation, the other being material failure. The combinationof these two makes numerical modeling challenging and is the reason for this study.The problem was divided in to two main parts, one where material modeling was studied, the other part focusedon numerical modeling and experiments of the punching process. A material model considering both plasticityandmaterial failure was created for a boron steel material. Plasticity behavior of thematerial was modeled with anelasto-plastic model and a calibratedModifiedMohr-Coulomb (MMC) failure criterion to model the material failure.The resultingMMC-model agreed well with the experiments.Punching experiments with varying clearances were performed on the boron steel. Punch forces and displacementswere continuously sampled throughout the process, and after the punching experiments were finished the punchededge profiles were studied. The multiphysics simulation software LS-DYNA was then utilized, and three dimensionalsimulations of the punching process using the Smoothed Particle Galerkin (SPG)method were performed.Results from the SPG-simulation corresponded very well with the results from punching experiments, and it can beconcluded that the model was able to capture the material behavior of the sheet in a highly detailed level. When thepunched edge profiles from the simulations were compared to the experiments, there was an almost exact match forall the cases studied. The force-displacement behavior of the punch from simulations was in great consistency withexperimental results as well.Itwas also concluded that the combination of a stress state dependent failure criterion together with the SPG-methodshows significant possibilities to cope with three dimensional problems where large deformations in combinationwith difficultmaterial failure occurs. This study focuses on the punching process, but the generality of this novelmodeling technique can be applied to many industrial cases and is a step towards a better and more reliablemodeling of failure in combination with extremely large deformation.

Vortex breakdown is an important phenomenon observed in swirling flows involving the development of a stagnation point on the axis of the vortex followed by a region of recirculation when the swirl increases beyond a particular level. It has been studied extensively over past 50 years and various theories have been proposed to explain its various aspects. However, a single model explaining all the aspects together is yet to emerge. Numerical simulations of breakdown have been performed using a variety of grid-based as well as vortex methods. Vortex methods are a Lagrangian alternative to grid-based methods wherein the motion of the vorticity is determined by the local fluid velocity convection, with models for viscous effects when considered. The fluid velocity is obtained from the vorticity field. Only the rotational regions of the flow need to be considered leading to significant economy of computational effort for simulations of vorticity dominated flows, such as vortex breakdown. The inviscid vortex filament method has been used to simulate several aspects of the vortex breakdown phenomenon. The vortex filament method however, cannot easily simulate viscous effects. To simulate the viscous effects the viscous vortex particle method needs to be used. This work was intended to be a first step towards this end by initially evaluating the effectiveness of the inviscid version of the vortex particle method in simulating the breakdown phenomenon. The inviscid vortex particle method was found to satisfactorily simulate most qualitative aspects involved in the formation of vortex breakdown such as the retardation of axial velocity along centerline, radial swelling of the vortex core, formation of stagnation points, creation of azimuthal vorticity gradient from axial vorticity gradient and the turning of vortex lines along with the formation of a bubble-like structure with recirculating flow within. The effect of a wall placed adjacent to the vortex core was simulated by using image vortices. The wall was not found to influence the location of breakdown. However, the initiation of the spiral mode was found to occur earlier when a wall was present. For a quantitative assessment, a simulation of the experimental results of Faler and Leibovich (1978) was attempted. The simulation managed to predict the location of the breakdown and the extent of the bubble. The shape and height of the bubble obtained however were not in accord with the experimental observations. A single vortical cell was obtained in the interior of the bubble.

This thesis analyses the impact of granular aggregates with structures using experiments and numerical simulations. Original contributions include an insight into multiple factors affecting the loading and damage to the structures, along with study of numerical parameters important for realistic prediction of the interaction between the granular media and structures. It extends the current understanding related to such interactions, with an underlying motivation to guide strategies in order to reduce the structural damage. The response of structures impacted by granular media (sand or soil) is of significant research interest for many applications. One of the applications is for landmine explosions which causes ejection of soil from ground and damage to structures impacted by this ejected soil. Experimentation is done in a laboratory setting where the cylindrical sand slugs are generated at high speed using an impulse provided by a piston. This induces a velocity gradient along the slug, because of which the slug expands during the flight before impacting the target. Deformable as well as rigid flat targets are considered in two orientations relative to the incoming slug: perpendicular (i.e. normal orientation) and inclined at an angle of 45°. The targets are supported by force transducers to capture the loading from the slug. Simulations are performed using a combination of discrete particle and finite element schemes, which enables the analysis of the fully coupled interaction between the flowing granular media and the structure. A contact model involving multiple parameters is used for inter-particle and particle-target contact. Firstly, a numerical analysis is performed to characterise the temporal evolution of slugs and their impact on monolithic beams constrained at the ends. Out of all the parameters used for inter-particle contact definition in discrete particle method, only the contact stiffness is found to effect the velocity gradient in the slug before it impacts the target. Other factor influencing the gradient is the acceleration provided by the piston. A strong dependence of beam deflection on the stand-off distance is observed due to the velocity gradient in the slugs. As the second step, the effect of target surface properties on the transmitted momentum is analysed. Experiments are done by applying coatings of different hardness and roughness on the target surface impacted by sand slugs. For normally oriented targets, the transmitted momentum is observed to be insensitive to the change in surface coating. In contrast, for inclined targets, a significant influence of coatings is observed. Additionally, the momentum transmitted to the inclined targets is always less than that for normal targets. Numerical analysis of this surface effect reveals that assuming the slug particles to be spherical shape in simulations does not capture the particle/target interactions accurately and under-predicts the frictional loading on the target. Following this, a detailed numerical study is done to understand the effect of the shape of particles in the slug. Simple shaped non-spherical particles are constructed by combining spherical sub-particles. With increasing angularity of particles in the slug, the frictional loading on the target is shown to increase. This results in an increase of momentum transmitted to inclined targets. For normally oriented targets however, the particle shape does not affect the overall transmitted momentum, which is a behaviour similar to that observed when studying the effect of target surface properties. In addition, effect of fracture of particles in the slug is analysed by using beam connections between sub-particles that break during the impact with the target. If the fracture results in increasing particle angularity, the transmitted momentum increases, whereas the situation reverses if fracture results on more spherical shaped particles. Lastly, a strategy to reduce the loading on the targets is analysed by using sacrificial coating on the target surface. In experiments, this coating is placed on the rigid target surface using a lubricant at their interface. When impacted by the slug, this coating slides on the target surface, resulting in a reduction of frictional loading on the target. If the friction at the coating/target interface vanishes, the transmitted momentum approaches the theoretical minimum value. Simulations are used to first validate the experimental observations and then to extend the concept of sliding coatings using deformable targets. Both the transmitted momentum and deflections depended on the thickness of the target and coating. When a coating is used, the deflections increase due to reduction in target thickness. It is found that the best strategy to reduce the damage to the target is to use least possible thickness of the coating and minimise the friction at the interface between the coating and the target. The presented work examines many of the factors that affect the loading on the target impacted by granular slugs, in addition to characterising the expansion of slugs before the target impact. The analysed factors include those already known such as target stand-off distance, inclination and unveils others such as target surface properties and granular properties. The numerical analysis discloses important parameters and shows the effect of particle shape, highlighting the shortcomings of widely used spherical particle assumption in the numerical studies. A strategy using a sacrificial coating to reduce damage to the target is also analysed.

O presente trabalho tem como objetivo realizar um estudo comparativo entre os três métodos para obtenção das características aerodinâmicas de tabuleiros de pontes: analítico, experimental e numérico. O tema é motivado pelo crescimento das necessidades de conhecimento científico e tecnológico na área de desempenho aerodinâmico de seções típicas de pontes nas etapas mais iniciais de projeto. A precisão de uma ferramenta de previsão certamente acelera a convergência ao modelo final; porém, qualquer metodologia numérica deve ser extensivamente testada antes de ser utilizada nos escritórios de cálculo. Inicialmente mostra-se a lógica da análise de instabilidades provocadas pelo vento, resume-se a modelagem de tabuleiros de pontes para ensaios em túnel de vento e descreve-se o método numérico implementado no programa comercial de análise de pontes RM. Comparam-se dados disponíveis de testes de modelos reduzidos no túnel de vento com as estimativas de aproximação do Método da Vorticidade em Partículas (MVP). Confrontam-se resultados para casos clássicos, um estudo paramétrico, dados dos relatórios de três pontes Brasileiras já ensaiadas no Túnel de Vento Joaquim Blessmann do LAC – PPGEC/UFRGS: Paulicéia, Guamá e Roberto Marinho. Finalmente, considera-se o método experimental como preciso e julga-se o método numérico comparativamente, analisando a confiabilidade dos resultados e procurando definir a sua faixa de aplicabilidade. Examinando a variabilidade dos resultados, bastante baixa, definiu-se sua faixa de aplicação considerando os resultados obtidos como satisfatórios para projetos básicos e executivos de estruturas; necessitando, porém, para os casos especiais, de comprovação experimental em túnel de vento antes da sua execução. Exemplifica-se então o uso do método para alguns problemas de análises de seções. Os resultados e comparações corroboram verificações anteriores do método dos vórtices discretos para verdadeiras seções de pontes e mostram porque o seu uso vem se tornando cada vez mais aceitável. / The work has the objective to realize a comparative study between three methods to obtain bridge aerodynamic coefficients: analytic, experimental and numerical. The theme is motivated by the increasing need of knowledge about the aerodynamic behaviour of bridge decks in the early stages of the design process. The accuracy of a predictive tool will certainly accelerate the convergence to the final design. However, any numerical methodology must be extensively tested ascertain and hence validated before it becomes of current use by designers. Collaboration is made comparing wind tunnel data of reduced models and numerical estimations by a simplified approach. After a brief overview of wind loading and wind tunnel modeling, the bridge wind resistance design in the commercially available bridge design software package RM is shown. The Discrete Vortex Method and the implementation are shortly described. Initially, classical fluid problems are indicated together with the comparison of parametric cross sectional bridge shapes. After, three Brazilian large cablestayed bridge projects are presented as instance of analysis: Paulicéia, Guamá and Roberto Marinho. Bridges aerodynamic coefficients were experimentally obtained at the Boundary Layer Wind Tunnel Joaquim Blessmann at Universidade Federal do Rio Grande do Sul (UFRGS). Finally, experimental results are considered precise and those results evaluated with CFD are compared analyzing the liability and applicability. According to the results variability, quite low, we considered them appropriated for basic and final structural designs; needing, although, for special cases, of experimental probation in wind tunnel tests before the construction phase. Some CFD analysis problems of cross sections are then presented as application examples. The results and similitude corroborate earlier verifications of the method and this implementation, demonstrating why its use is becoming increasingly acceptable.