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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.

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Quasi-hom-Lie algebras (qhl-algebras) were introduced by Larsson and Silvestrov (2004) as a generalisation of hom-Lie algebras, which are a deformation of Lie algebras. Lie algebras are defined by an operation called bracket, [·,·], and a three-term Jacobi identity. By the theorem from Hartwig, Larsson, and Silvestrov (2003), this bracket and the three-term Jacobi identity are deformed into a new bracket operation, <·,·>, and a six-term Jacobi identity, making it a quasi-hom-Lie algebra. Throughout this thesis we deform the Lie algebra sl2(F), where F is a field of characteristic 0. We examine the quasi-deformed relations and six-term Jacobi identities of the following polynomial algebras: F[t], F[t]/(t2), F[t]/(t3), F[t]/(t4), F[t]/(t5), F[t]/(tn), where n is a positive integer ≥2, and F[t]/((t-t0)3). Larsson and Silvestrov (2005) and Larsson, Sigurdsson, and Silvestrov (2008) have already examined some of these cases, which we repeat for the reader's convenience. We further investigate the following σ-twisted derivations, and how they act in the different cases of mentioned polynomial algebras: the ordinary differential operator, the shifted difference operator, the Jackson q-derivation operator, the continuous q-difference operator, the Eulerian operator, the divided difference operator, and the nilpotent imaginary derivative operator. We also introduce a new, general, σ-twisted derivation operator, which is σ(t) as a polynomial of degree k.

Indiana University-Purdue University Indianapolis (IUPUI) / This paper is a study of the dynamics of a new family of maps from the complex plane to itself, which we call twisted tent maps. A twisted tent map is a complex generalization of a real tent map. The action of this map can be visualized as the complex scaling of the plane followed by folding the plane once. Most of the time, scaling by a complex number will \twist" the plane, hence the name. The "folding" both breaks analyticity (and even smoothness) and leads to interesting dynamics ranging from easily understood and highly geometric behavior to chaotic behavior and fractals.

A presente dissertação trata de um estudo teórico-experimental sobre escoamento monofásico e bifásico no interior de tubos com fitas retorcidas. Esta técnica tem sido utilizada há várias décadas para a intensificação de troca de calor para escoamento monofásico e evaporação convectiva no interior de tubos. No entanto, com sua utilização, o aumento do coeficiente de troca de calor é acompanhado pelo incremento da perda de pressão. Portanto a compreensão dos fenômenos relacionados aos incrementos da perda de pressão e troca de calor são fundamentais para engenheiros projetistas. Neste estudo, inicialmente, é apresentada uma extensa revisão bibliográfica sobre padrões de escoamento, modelos para estimativa de fração de vazio e metodologias para previsão da perda de pressão em tubos com e sem fitas retorcidas para escoamentos bifásicos e monofásicos. Foram realizados experimentos em bancada experimental utilizando seção de testes com diâmetro interno de 15,9 mm e dois metros de comprimento com fitas apresentando razões de retorcimento de 3, 4, 9, 14 e , a última correspondente ao tubo sem inserto. Os experimentos foram executados para o refrigerante R134a, velocidades mássicas entre 75 e 250 kg/m²s, e títulos de vapor entre 5 e 95% no caso de escoamentos bifásicos. Resultados foram levantados para velocidades mássicas entre 100 e 450 kg/m²s para escoamentos monofásicos. Durante os ensaios foram levantados resultados de perda de pressão e identificados subjetivamente os respectivos padrões de escoamento. Como resultado final deste estudo é proposta uma correlação para previsão da perda de pressão durante o escoamento no interior de tubos com fitas retorcidas. / A theoretical and experimental study on single and two-phase flow inside tubes with twisted tapes inserts is presented. Twisted tape inserts have been used for decades as a technique of heat transfer enhancement. However, their heat transfer enhancement is accompanied by an increase of the pressure drop. Therefore, understanding the pressure drop and heat transfer mechanisms is fundamental for heat exchanger designers in order to optimize these devices when using twisted-tape inserts. Based on these aspects the present study concerns single and two-phase flows inside tubes with twisted tapes. Experiments were performed in an experimental apparatus for a 15.9 mm ID and twisted tape with twist ratios of 3, 4, 9, 14 and , the last one corresponding to a plain tube without tape. For two-phase flow, experiments were conducted for R134a, mass velocities from 75 to 250 kg/m²s and vapor qualities from 5 to 95%. In case of single-phase flow, experiments were performed for mass velocities from 100 to 450 kg/m²s. The experimental campaign was focused on pressure drop and flow pattern subjective identification. Additionally an extensive literature review on flow patterns, superficial void fraction, and methodologies for prediction of the pressure drop in plain tubes with and without twisted-tape inserts during single and two-phase flow is presented. As final result, a correlation for prediction of pressure drop during flow inside tubes with twisted tape inserts is proposed.

L'objectiu més important del tractament de conductes és reduir al mínim el nombre de microorganismes i residus patològics a l'interior del sistemes de conductes per prevenir o tractar la periodontitis apical. La instrumentació completa de la regió apical s'ha considerat durant molt temps com un component essencial en el procés de neteja i conformació. Durant molts anys s'ha descrit la zona apical com la zona més crítica de la fase d'instrumentació. El transport apical implica una deformació iatrogènica de l'anatomia originària del conducte, això produeix una preparació difícil de segellar correctament predisposant a una major filtració que pot comprometre el correcte segellat apical. Per a la realització d'aquest treball s'han fet servir cinc sistemes d'instruments rotatoris, per avaluar el transport produït en arrels mesials de molars mandibulars, mitjançant la tècnica de superposició radiogràfica. S'han triat aquests cinc sistemes per les seves característiques de disseny i fabricació. La tècnica de superposició radiogràfica és una tècnica que ens proporciona la deformació apical dels conductes en dues dimensions d'una forma eficaç i amb un baix cost. La hipòtesi que es planteja en aquest estudi és que no hi haurà diferències estadísticament significatives en comparar el transport apical produït per cinc sistemes rotatoris de níquel titani en arrels mesials de primers molars mandibulars instrumentats fins a un calibre apical de 40.04. L'objectiu principal d'aquest estudi és comparar el transport apical produït pels diferent sistemes. Al seu torn de forma específica s'ha avaluat el transport apical produït per cada un dels sistemes d'instruments rotatoris de níquel titani. Els resultats obtinguts conclouen que no hi ha diferències estadísticament significatives en el transport apical produït pels diferents sistemes, encara que aquests tenen diferències de disseny i fabricació. Aquests resultats determinen que els cinc sistemes són segurs vàlids per al seu ús, ja que tots produeixen una preparació centrada en el conducte amb una mínima deformació del terç apical del conducte. En conclusió, la instrumentació de la regió apical és un repte per al professional, ja que és la zona del conducte on hi ha un major nombre d'irregularitats i on és més difícil aconseguir una correcta neteja i conformació. Conèixer i usar els instruments de forma adequada és indispensable per no produir deformacions en el terç apical que ens puguin fer fracassar el tractament per un segellat inadequat.

The present study describes the flow characteristics of swirling flows induced by twisted tape inserts in circular pipes. The study is focused on the secondary flow which is investigated experimentally and with numerical models. The results are expected to improve the paper manufacturing process by identifying and removing the detrimental secondary flow. Experimental tests show for the first time the existence of two co-rotating helical vortices superimposed over the main swirling flow, downstream of twisted tapes. The close proximity of the two co-rotating vortices creates a local counter-rotating flow at the pipe centerline. The flow is analyzed using LDV measurements and high speed camera visualization with fine air bubbles seeding which confirm that the helical vortices are stable. After extracting the characteristic tangential velocity profiles of the main vortex and of the two secondary vortices, it was observed that the maximum tangential velocity of all three vortices is the same, approximately half of the bulk velocity. The winding of the helical vortices is in the swirl direction and the pitch of the helical vortices is found to be independent of the inlet velocity. The experimental findings are confirmed by numerical simulations. The numerical results show that the helical vortices originate inside the swirler and evolve from single co-rotating vortices on each side of the tape. The flow characteristics are analyzed in detail. Swirlers with multiple twists and multiple chambers are shown to have less stable secondary motion and could be employed in applications were the secondary motion is detrimental.