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Optimization methods are commonly used to develop new products and are also an importantstep in more incremental design improvements. In the maritime industry, these methodsare often used to create more ecient vessels and to ful ll the environmental requirementsimposed by the IMO. In recent years, the adjoint method have been used more frequently.This method can be used to predict the inuence of some input parameters on a quantityin a Computational Fluid Dynamics (CFD) simulation.In this project, the adjoint method has been investigated and applied on a relevant case;how it can be used to reduce the drag of a twisted rudder by changing the twist angles.STAR-CCM+ has been used to perform the CFD and adjoint simulations. These resultshave been imported to CAESES, a CAD-modeler, which connects the adjoint results to thedesign parameters. The adjoint results indicate a possible change of the design parameter,the twist angle is modi ed based on these results and a new geometry of the rudder is constructedin CAESES. Furthermore, the numerical results indicates that the method can beused to reduce the drag on the rudder. One of the cases in the project achieved a reductionof the rudder drag by 3.35 % and the total drag decreased with 0.18 %. However, the othertwo cases did not achieve a reduction of the drag and hence further investigations needs tobe done.The adjoint method have the possibility to be a good optimization alternative for developmentof new products or in engineering-to-order processes. The option of connecting theadjoint results to design parameters is a great advantage. On the other hand, the method inthis project is not reliable and the reason for the contradictory results needs to be studiedfurther. / Optimeringsmetoder är vanligt förekommande när nya produkter utvecklas och är också ett viktigt steg i inkrementella designförbättringar. I sjöfartsindustrin används dessa metoder för att skapa effektivare fartyg och för att uppfylla miljökraven framtagna av IMO. På senare år har adjointmetoden börjat användas mer. Metoden kan användas för att förutspåindataparametrars inverkan på en kvantitet i en strömningsmekanisk beräkning, även kallat CFD. I det här projektet ska adjointmetoden utvärderas och hur den kan användas för att reducera motståndet på ett tvistat roder genom att ändra tvist vinklarna. STAR-CCM+ har använts för att utföra CFD- och adjointberäkningarna. Dessa resultat importerades till en CAD-modellerare, CAESES, som kopplar adjointresultaten till designvariabler. Resultaten från adjointsimuleringen indikerar en möjlig förändring av designvariabeln, som sedan ändras utefter detta resultat och en ny rodergeometri genereras av CAESES. De numeriska resultaten indikerar att adjointmetoden kan användas för att reducera motståndet på ett tvistat roder. I ett av fallen i projektet reducerades motståndet med 3,35 % och det totala motståndet för hela fartyget reducerades med 0,18 %. Däremot så påvisade två andra fall ingen förändring av rodermotståndet och anledningen till detta kräver ytterligare unders ökningar. Adjointmetoden har möjligheterna att bli ett bra alternativ i en optimeringsprocess och för utveckling av nya produkter. Möjligheten att koppla adjointresultaten till designvariabler är också en stor fördel. Däremot så är metoden i detta projekt inte så tillförlitlig och anledningen till de motsägelsefulla resultaten måste studeras ytterligare.

A time spectral and coupled adjoint based sensitivity analysis of rotor blade is carried out in this study. The time spectral method is an efficient technique to solve unsteady periodic problems by transforming unsteady equation of motion to a steady state one. Due to the availability of the governing equations in the steady form, the steady form of the adjoint equations can be applied for the sensitivity analysis of the coupled fluid-structure system. An expensive computational time and memory requirement for the unsteady adjoint sensitivity analysis is thus avoided. A coupled analysis of fluid, structural, and flight dynamics is carried out through a CFD/CSD/CA coupling procedure that combines FSI analysis with enforced trim condition. Coupled sensitivity analysis results and their validations are presented and compared with aerodynamics only sensitivity analysis results. The fluid-structure coupled adjoint based sensitivity analysis will be applied to the shape optimization of a rotor blade in the future work. Minimization of required power is the objective of the optimization problem with constraints on thrust and drag of the rotor. The bump functions are considered as the design variables. Rotor blade shape changes are obtained by using the bump function on the surface of the airfoil sections along the span. / Doctor of Philosophy / The work in this dissertation is motivated by the reducing the computational cost at the early design stage with guaranteed accuracy. In the research, the author proposes that the goal can be achieve through coupled adjoint based sensitivity analysis using a fluid structure interaction in time spectral form. Adjoint based sensitivity analysis is very efficient for solving design problems with a large number of design variables. The time spectral approach is used to overcome inefficient calculation of rotor flows by expressing flow and structural state variables as Fourier series with small number of harmonics. The accuracy and the efficiency of flow solver are examined by simulating UH-60A forward flight condition. A significant reduction in the computational cost is achieved by its Fourier series form of the periodic time response and the assumption of periodic steady state. A good agreement between time accurate and time spectral analysis is noted for the high speed forward flight condition of UH-60A configuration. Prediction from both methods also agree quite well with the experimental data. The adjoint based sensitivity analysis results are compared with the finite difference sensitivity analysis results. Even with presence of small discrepancies, these two results show a good agreement to each other. Coupled sensitivity analysis includes not only the effect of fluid state changes but also the contribution of structural deformation.

Ao longo da última década o método adjunto tem sido consolidado como uma das mais versáteis e bem sucedidas ferramentas de otimização aerodinâmica e projeto inverso na Dinâmica dos Fluidos Computacional. Ele se tornou uma área de pesquisa por si só, criando uma grande variedade de aplicações e uma literatura prolífica. Entretanto, alguns aspectos relevantes do método permanecem ainda relativamente pouco explorados na literatura. Como é o caso das condições de contorno adjuntas e, mais especificamente, com respeito a fronteiras permeáveis. Esta dissertação discute detalhadamente uma nova forma de tratar o problema de contorno, que tem como objetivo assegurar que as equações adjuntas sejam bem-postas. O principal objetivo da otimização aerodinâmica consiste na tentativa de minimizar (ou maximizar) uma determinada medida de mérito. As aplicações de projeto inverso são desenvolvidas para escoamentos Euler 2-D ao redor de aerofólios, representados com a parametrização CST (Class-Shape function Transformation) proposta por Kulfan e Bussoletti (2006), em regime de vôo transônico e com domínio discretizado por malhas não-estruturadas de triângulos através de um ciclo de projeto, que utiliza o método steepest descent como algoritmo de busca da direção que minimiza (ou maximiza) a função de mérito. As equações adjuntas são derivadas na sua formulação contínua e suas condições de contorno são determinadas por equações diferenciais características adjuntas e relações de compatibilidade compatíveis com as variações realizáveis da física do escoamento. As variáveis adjuntas são, então, vistas como forças de vínculo generalizadas, que asseguram a realizabilidade de variações do escoamento. / Over the last decade the adjoint method has been consolidated as one of the most versatile and successful tools of aerodynamic optimization and inverse design in Computational Fluid Dynamics. It has become a research area of its own, spawning a large variety of applications and a prolific literature. Yet, some relevant aspects of the method remain relatively less explored in the literature. Such is the case with the adjoint boundary conditions and, more specifically, with regard to permeable boundaries. This dissertation discusses at length a novel approach to the boundary problem, which aims at ensuring the well-posedness of the adjoint equations. The main goal of aerodynamic optimization consists in attempting to minimize (or maximize) a certain mesure of merit. The inverse design applications are developed for 2-D Euler flows around airfoils, represented with the CST (Class-Shape function Transformation) parameterization proposed by Kulfan and Bussoletti (2006), in the transonic flight regime and domain discretized by triangle unstructured meshes in a design loop which makes use of the steepest descent method as search direction that minimizes (or maximizes) the mesure of merit. Adjoint equations are derived in the continuous formulation and their boundary conditions are determined by adjoint characteristic differential equations and compatibility relations. The latter are derived so as to be compatible with the realizable variations of physical quantities. The adjoint variables are seen as generalized constraint forces, which ensure the realizability of flow variations.

Um desafio constante no projeto aerodinâmico de uma superfície é obter a forma geométrica que permite, baseado em uma determinada medida de mérito, o melhor desempenho possível. No contexto de projeto de aeronaves de transporte, o desempenho ótimo em cruzeiro é a principal meta do projetista. Nesse cenário, o uso da Dinâmica do Fluidos Computacional como não só uma ferramenta de análise mas também de síntese torna-se uma forma atrativa para melhorar o projeto de aeronaves que é uma atividade dispendiosa em termos de tempo e recursos financeiros. O método adotado para projeto aerodinâmico é baseado na teoria de controle ótimo. Essa abordagem para o problema de otimização aerodinâmica foi inicialmente proposta por Jameson (1997) e é chamada de método adjunto. Esse método apresenta uma grande diminuição de custo computacional se comparado com a abordagem de diferenças finitas para a otimização baseada em gradiente. Essa dissertação apresenta o método adjunto contínuo aplicado às equações de Euler. Tal método está inserido no contexto de um ciclo de projeto inverso aerodinâmico. Nesse ciclo, tanto o código computacional de solução das equações do escoamento quanto o código de solução das equações adjuntas foram desenvolvidos ao longo desse trabalho. Além disso, foi adotada uma metodologia de redução do gradiente da função de mérito em relação às variáveis de projeto. O algorítmo utilizado para a busca do mínimo da função de mérito é o steepest descent. Os binômios de Bernstein foram escolhidos para representar a geometria do aerofólio de acordo com a parametrização proposta por Kulfan e Bussoletti (2006). Apresenta-se um estudo dessa parametrização mostrando suas características relevantes para a otimização aerodinâmica. Os resultados apresentados estão divididos em dois grupos: validação do ciclo de projeto inverso e aplicações práticas. O primeiro grupo consiste em exercícios de projeto inverso nos quais são estabelecidas distribuições de pressão desejadas obtidas a partir de geometrias conhecidas, desta forma garante-se que tais distribuições são realizáveis. No segundo grupo, porém, as distribuições desejadas são propostas pelo projetista baseado em sua experiência e, portanto, não sendo garantida a realizabilidade dessas distribuições. Em ambos os grupos, incluem-se resultados nos regimes de escoamento transônico e subsônico incompressível. / A constant endeavor in aerodynamic design is to find the shape that yields optimum performance, according to some context-dependent measure of merit. In particular for transport aircrafts, an optimum cruise performance is usually the designers main goal. In this scenario the use of the Computational Fluid Dynamics (CFD) technique as not only an analysis tool but as a design tool becomes an attractive aid to the time and financial resource consuming activity that is aircraft design. The method adopted for aerodynamic design is based on optimal control theory. This approach to the design problem was first proposed by Jameson (1997) and it is called adjoint method. It shows a great computational cost advantage over the finite difference approach to gradient-based optimization. This dissertation presents an Euler adjoint method implemented in context of an inverse aerodynamic design loop. In this loop both the flow solver and the adjoint solver were developed during the course of this work and their formulation are presented. Further on, a gradient reduction methodology is used to obtain the gradient of the cost function with respect to the design variables. The method chosen to drive the cost function to its minimum is the steepest descent. Bernstein binomials were chosen to represent the airfoil geometry as proposed by Kulfan and Bussoletti (2006). A study of such geometric representation method is carried on showing its relevant properties for aerodynamic optimization. Results are presented in two groups: inverse design loop validation and practical application. The first group consists of inverse design exercises in which the target pressure distribution is from a known geometry, this way such distribution is guaranteed to be realizable. On the second group however, the target distribution is proposed based on the designers knowledge and its not necessarily realizable. In both groups the results include transonic and subsonic incompressible conditions.

Ao longo da última década o método adjunto tem sido consolidado como uma das mais versáteis e bem sucedidas ferramentas de otimização aerodinâmica e projeto inverso na Dinâmica dos Fluidos Computacional. Ele se tornou uma área de pesquisa por si só, criando uma grande variedade de aplicações e uma literatura prolífica. Entretanto, alguns aspectos relevantes do método permanecem ainda relativamente pouco explorados na literatura. Como é o caso das condições de contorno adjuntas e, mais especificamente, com respeito a fronteiras permeáveis. Esta dissertação discute detalhadamente uma nova forma de tratar o problema de contorno, que tem como objetivo assegurar que as equações adjuntas sejam bem-postas. O principal objetivo da otimização aerodinâmica consiste na tentativa de minimizar (ou maximizar) uma determinada medida de mérito. As aplicações de projeto inverso são desenvolvidas para escoamentos Euler 2-D ao redor de aerofólios, representados com a parametrização CST (Class-Shape function Transformation) proposta por Kulfan e Bussoletti (2006), em regime de vôo transônico e com domínio discretizado por malhas não-estruturadas de triângulos através de um ciclo de projeto, que utiliza o método steepest descent como algoritmo de busca da direção que minimiza (ou maximiza) a função de mérito. As equações adjuntas são derivadas na sua formulação contínua e suas condições de contorno são determinadas por equações diferenciais características adjuntas e relações de compatibilidade compatíveis com as variações realizáveis da física do escoamento. As variáveis adjuntas são, então, vistas como forças de vínculo generalizadas, que asseguram a realizabilidade de variações do escoamento. / Over the last decade the adjoint method has been consolidated as one of the most versatile and successful tools of aerodynamic optimization and inverse design in Computational Fluid Dynamics. It has become a research area of its own, spawning a large variety of applications and a prolific literature. Yet, some relevant aspects of the method remain relatively less explored in the literature. Such is the case with the adjoint boundary conditions and, more specifically, with regard to permeable boundaries. This dissertation discusses at length a novel approach to the boundary problem, which aims at ensuring the well-posedness of the adjoint equations. The main goal of aerodynamic optimization consists in attempting to minimize (or maximize) a certain mesure of merit. The inverse design applications are developed for 2-D Euler flows around airfoils, represented with the CST (Class-Shape function Transformation) parameterization proposed by Kulfan and Bussoletti (2006), in the transonic flight regime and domain discretized by triangle unstructured meshes in a design loop which makes use of the steepest descent method as search direction that minimizes (or maximizes) the mesure of merit. Adjoint equations are derived in the continuous formulation and their boundary conditions are determined by adjoint characteristic differential equations and compatibility relations. The latter are derived so as to be compatible with the realizable variations of physical quantities. The adjoint variables are seen as generalized constraint forces, which ensure the realizability of flow variations.

Hydrodynamic vortex separators (HDVSs) are used in wastewater treatment to separate solids from wastewater. The aim of this research is to devise a CFD-based methodology that optimises their performance through modification of their design. A validation study is performed to assess whether OpenFOAM can be used to reliably model the flow of water in an HDVS. The results of the simulations are compared with experimental readings, showing a good fit when the appropriate boundary layer height and turbulence model are used. The continuous adjoint method is employed to derive the adjoint equations, associated with the drift flux equations used to model the flow of wastewater. They are specialised to the typical boundary conditions of ducted flows and are coded using OpenFOAM. An optimal design is found for boundary conditions, corresponding to typical values used in practice, and is shown to improve the performance of a simplified initial design by 40%. This optimal design is subsequently subjected to a different hydraulic loading rate and dispersed-phase volume fraction at the inlet, to assess the performance variation in these circumstances. Though the optimal design removes all the solids when the dispersed-phase fraction is reduced at the inlet, initial results suggest that the design is sensitive to hydraulic loading rate and further tests are recommended before drawing more explicit conclusions. This is the first time the adjoint drift flux equations have been derived. It is also the first time they have been coded and applied to an HDVS to optimise its performance. The methodology developed in this thesis could be applied to any device that separates solids from liquid or two immiscible liquids, in order to optimise its performance.

Cette étude s’inscrit dans le cadre de l’inspection en service des soudures des réacteurs nucléaires de génération IV, en vue de contribuer à la démonstration de sûreté. La structure anisotrope et hétérogène des soudures multipasses en acier inoxydable austénitique rend leur contrôle ultrasonore difficile. Ainsi, afin d'interpréter correctement les signaux mesurés et de caractériser les défauts potentiels, une description de la soudure est utilisée. Elle constitue la connaissance a priori introduite dans la méthode de l'Energie Topologique. L’étude réalisée se décline en deux temps : le développement de la méthode en milieu borné et sa comparaison avec le Matched Field Processing, puis son application au cas de soudures réelles. L'extension de la méthode de l'Energie Topologique aux milieux bornés isotropes et homogènes vise à tirer parti des réflexions multiples. Plusieurs solutions du problème numérique de propagation, obtenues pour différentes conditions aux frontières, sont judicieusement associées afin de sélectionner les échos de diffraction porteurs d'information. Selon le type de défaut à imager des énergies topologiques spécifiques sont définies. La technique est introduite analytiquement avant d'être validée numériquement puis expérimentalement.Dans un second temps, la méthode est appliquée au milieu complexe de la soudure. La procédure est testée expérimentalement sur des soudures réelles afin d'évaluer les performances en localisation. Cependant, en raison de la variabilité de la structure, la qualité de l'image peut se dégrader selon les cas d'étude. La possibilité de générer des sources arbitraires permet de pallier en grande partie cette difficulté. / The present study has been done as part of the in-service inspection of weld structure belonging to generation IV nuclear reactors. It aims at checking both the safety and integrity of these components. The anisotropic and heterogeneous structure of austenitic stainless steel welds disturbs the ultrasonic non destructive testing. Thus, a weld description model is necessary to properly analyze the ultrasonic measured signals and to characterize potential flaws. The weld model makes a priori knowledge up in the Topological Energy method. The study is divided into two parts: development of the method in a bounded medium and comparison with the Matched Field Processing method, and then its application to real weld structures.The work firstly focuses on expanding the Topological Energy method to isotropic and homogeneous bounded medium to take advantage of multiple reflections between the flaw and edges. For that, different conditions are numerically applied to boundaries. By adding up these conditions it becomes possible to select the appropriate scattering signal. Modified topological energies are defined according to the type of analyzed flaws. The approach is analytically demonstrated before being validated firstly from synthetical data and then from experimental data.The second part deals with the application of the method to the complex weld structure. The process is experimentally tested on welds in order to evaluate efficiency of flaws localization. However, the image's quality can be deteriorated because of variability of the structure. By generating arbitrary ultrasonic source this difficulty is mostly overcame.

Um desafio constante no projeto aerodinâmico de uma superfície é obter a forma geométrica que permite, baseado em uma determinada medida de mérito, o melhor desempenho possível. No contexto de projeto de aeronaves de transporte, o desempenho ótimo em cruzeiro é a principal meta do projetista. Nesse cenário, o uso da Dinâmica do Fluidos Computacional como não só uma ferramenta de análise mas também de síntese torna-se uma forma atrativa para melhorar o projeto de aeronaves que é uma atividade dispendiosa em termos de tempo e recursos financeiros. O método adotado para projeto aerodinâmico é baseado na teoria de controle ótimo. Essa abordagem para o problema de otimização aerodinâmica foi inicialmente proposta por Jameson (1997) e é chamada de método adjunto. Esse método apresenta uma grande diminuição de custo computacional se comparado com a abordagem de diferenças finitas para a otimização baseada em gradiente. Essa dissertação apresenta o método adjunto contínuo aplicado às equações de Euler. Tal método está inserido no contexto de um ciclo de projeto inverso aerodinâmico. Nesse ciclo, tanto o código computacional de solução das equações do escoamento quanto o código de solução das equações adjuntas foram desenvolvidos ao longo desse trabalho. Além disso, foi adotada uma metodologia de redução do gradiente da função de mérito em relação às variáveis de projeto. O algorítmo utilizado para a busca do mínimo da função de mérito é o steepest descent. Os binômios de Bernstein foram escolhidos para representar a geometria do aerofólio de acordo com a parametrização proposta por Kulfan e Bussoletti (2006). Apresenta-se um estudo dessa parametrização mostrando suas características relevantes para a otimização aerodinâmica. Os resultados apresentados estão divididos em dois grupos: validação do ciclo de projeto inverso e aplicações práticas. O primeiro grupo consiste em exercícios de projeto inverso nos quais são estabelecidas distribuições de pressão desejadas obtidas a partir de geometrias conhecidas, desta forma garante-se que tais distribuições são realizáveis. No segundo grupo, porém, as distribuições desejadas são propostas pelo projetista baseado em sua experiência e, portanto, não sendo garantida a realizabilidade dessas distribuições. Em ambos os grupos, incluem-se resultados nos regimes de escoamento transônico e subsônico incompressível. / A constant endeavor in aerodynamic design is to find the shape that yields optimum performance, according to some context-dependent measure of merit. In particular for transport aircrafts, an optimum cruise performance is usually the designers main goal. In this scenario the use of the Computational Fluid Dynamics (CFD) technique as not only an analysis tool but as a design tool becomes an attractive aid to the time and financial resource consuming activity that is aircraft design. The method adopted for aerodynamic design is based on optimal control theory. This approach to the design problem was first proposed by Jameson (1997) and it is called adjoint method. It shows a great computational cost advantage over the finite difference approach to gradient-based optimization. This dissertation presents an Euler adjoint method implemented in context of an inverse aerodynamic design loop. In this loop both the flow solver and the adjoint solver were developed during the course of this work and their formulation are presented. Further on, a gradient reduction methodology is used to obtain the gradient of the cost function with respect to the design variables. The method chosen to drive the cost function to its minimum is the steepest descent. Bernstein binomials were chosen to represent the airfoil geometry as proposed by Kulfan and Bussoletti (2006). A study of such geometric representation method is carried on showing its relevant properties for aerodynamic optimization. Results are presented in two groups: inverse design loop validation and practical application. The first group consists of inverse design exercises in which the target pressure distribution is from a known geometry, this way such distribution is guaranteed to be realizable. On the second group however, the target distribution is proposed based on the designers knowledge and its not necessarily realizable. In both groups the results include transonic and subsonic incompressible conditions.

Au cours des processus de conception,l’optimisation de formes apporte aux industriels dessolutions pour l’amélioration des performances desproduits. En particulier, les structures minces quiconstituent environ 70% d’un véhicule, sont une préoccupationdans l’industrie automobile. La plupartdes méthodes d’optimisation pour ces structures surfaciquesprésentent certaines limites et nécessitent desexpertises à chaque niveau de la procédure d’optimisation.L’objectif de cette thèse est de proposer une nouvellestratégie d’optimisation de formes pour les coquesminces. L’approche présentée consiste à exploiter leséquations de coques du modèle de Koiter en se basantsur une analyse isogéométrique. Cette méthode permetde réaliser des simulations sur la géométrie exacteen définissant la forme à l’aide de patchs CAO. Lesvariables d’optimisation choisies sont alors les pointsde contrôle permettant de piloter leur forme. La définitiondes patchs permet également de dégager ungradient de forme pour l’optimisation à l’aide d’uneméthode adjointe.Cette méthode a été appliquée pour des critères mécaniquesissus des bureaux d’études Renault. Des résultatsd’optimisation pour un critère de compliance sontprésentés. La définition et l’implémentation de critèresvibro-acoustiques sont discutés à la fin de cette thèse.Les résultats obtenus témoignent de l’intérêt de la méthode.Toutefois, de nombreux développements serontnécessaires avant d’être en mesure de l’appliquer dansl’industrie. / During the design process, optimizationof shapes offers manufacturers solutions for improvingproducts performances. In particular, thin shellstructures that represent about 70 % of a vehicle, area concern in the automotive industry. Most optimizationmethods for surface structures have limitationsand require expertise at every level of the optimizationprocedure.The aim of this thesis is to propose a new strategyfor the shape optimization of thin shell structures.The approach presented rely on using the Koiter’sshell model based on an isogeometric analysis. Thismethod allows for simulations on the exact geometryby defining the shape using CAD patches. Selectedoptimization variables are the control points used tocontrol the shape of the CAD patches. Variations ofthese points allows to scan a wide design space withfew parameters. The definition of patchs also enablesto find a gradient with respect to the shape for theoptimization by using the adjoint state method.This method was applied to mechanical criteria fromthe Renault design offices. Optimization results for acompliance criterion are presented. The definition andimplementation of vibro-acoustic criteria are discussedat the end of this thesis. The results demonstratethe interest of the method. However, many developmentswill be needed before being able to apply it inthe industry.