La première partie de cette thèse traite du développement du code de simulation numérique directe YWC, principalement du développement des conditions aux limites. En effet, une forte contribution scientifique a été apportée aux conditions aux limites appelées "Three dimensional Navier-Stokes characteristic boundary condtions" (3D-NSCBC). Premièrement, la formulation de ces conditions aux arêtes et coins a été complétée, ensuite une extension de la formulation a été proposée pour supprimer les déformations observées en sortie dans le cas d'écoulements non-perpendiculaires à la frontière. <p>De plus, ces conditions ont été étendues au cas des gaz réels et une nouvelle définition du facteur de relaxation pour la pression a été proposée. Ce nouveau facteur de relaxation permet de supprimer les déformations observées en sortie pour des écoulements transcritiques. <p>Les résultats obtenus avec le code YWC ont ensuite été utilisés dans la seconde partie de la thèse pour développer une nouvelle méthode de tabulation basée sur l'analyse en composantes principales. Par rapport aux méthodes existante telles que FPI ou SLFM, la technique proposée, permet une identification automatique des variables à transporter et n'est, de plus, pas lié à un régime de combustion spécifique. Cette technique a permis d'effectuer des calculs d'interaction flamme-vortex en ne transportant que 5 espèces à la place des 9 requises pour le calcul en chimie détaillée complète, sans pour autant perdre en précision. <p>Finalement, dans le but de réduire encore le nombre d'espèces transportées, les techniques T-BAKED et HT-BAKED PCA ont été introduites. En utilisant une pondération des points sous-représentés, ces deux techniques permettent d'augmenter la précision de l'analyse par composantes principales dans le cadre des phénomènes de combustion.<p> / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

Cette thèse propose un algorithme efficace pour la simulation numérique des interactions houle-structure avec des solveurs CFD bi-phasiques. L'algorithme est basé sur le couplage de la théorie potentielle et des équations bi-phasiques de Navier-Stokes. C'est une extension de la méthode Spectral Wave Explicit Navier-Stokes Equations (SWENSE) pour les solveurs CFD bi-phasiques avec une technique de capture d'interface. Dans cet algorithme, la solution totale est décomposée en une composante incidente et une composante complémentaire. La partie incidente est explicitement obtenue avec des méthodes spectrales basées sur la théorie des écoulements potentiels ; seule la partie complémentaire est résolue avec des solveurs CFD, représentant l'influence de la structure sur les houles incidentes. La décomposition assure la précision de la cinématique des houles incidentes quel que soit le maillage utilisé parles solveurs CFD. Une réduction significative de la taille du maillage est attendue dans les problèmes typiques des interactions houle structure. Les équations sont présentées sous trois formes : la forme conservative, la forme non conservative et la forme Ghost of Fluid Method. Les trois versions d'équations sont implémentées dans OpenFOAM et validées par une série de cas de test. Une technique d'interpolation efficace pour reconstruire la solution des houles irrégulières donnée par la méthode Higher-Order Spectral (HOS) sur le maillage CFD est également proposée. / This thesis proposes an efficient algorithm for simulating wave-structure interaction with two-phase Computational Fluid Dynamics (CFD) solvers. The algorithm is based on the coupling of potential wave theory and two phase Navier-Stokes equations. It is an extension of the Spectral Wave Explicit Navier-Stokes Equations (SWENSE) method for generalized two-phase CFD solvers with interface capturing techniques. In this algorithm, the total solution isdecomposed into an incident and acomplementary component. The incident solution is explicitly obtained with spectral wave models based on potential flow theory; only the complementary solution is solved with CFD solvers, representing the influence of the structure on the incident waves. The decomposition ensures the accuracy of the incident wave’s kinematics regardless of the mesh in CFD solvers. A significant reduction of the mesh size is expected in typical wave structure interaction problems. The governing equations are given in three forms: the conservative form, the non conservative form, and the Ghost of Fluid Method (GFM) form. The three sets of governing equations are implemented in OpenFOAM and validated by a series of wave-structure interaction cases. An efficient interpolation technique to map the irregular wave solution from a Higher-Order Spectral (HOS) Method onto the CFD grid is also proposed.

A pectina é uma substância polissacarídica originada de plantas, que pode ser utilizada como agente gelificante, estabilizante de compotas, em bebidas láticas e iogurtes. A gelatina, proteína, nesse caso de origem bovina, é principalmente utilizada como agente gelificante, pois, forma hidrogéis por resfriamento. O processo de irradiação por radiação gama pode causar uma variedade de modificações nas macromoléculas algumas de aplicação industrial, como é o caso de reticulação. A resposta dinâmica de materiais viscoelásticos pode ser usada para dar informação sobre o aspecto estrutural de um sistema a nível molecular. No presente trabalho, pectina com diferentes graus de metoxilação, gelatina e a mistura de ambas foram empregados para estudar a sensibilidade à radiação por meio de medidas de viscosidade. Amostras de soluções de pectina de alto teor de metoxilação (ATM) 1%, pectina de baixo teor (BTM) 1%, gelatina 0,5%,1% e 2%, e a mistura de ambas a 1% e 2% foram irradiadas com raios gama em doses de até 15kGy e taxa de dose em torno de 2kGy/h. Após irradiação, a viscosidade foi medida dentro de um período de 48 h. A viscosidade da pectina ATM e BTM diminuiu drasticamente com o aumento da dose de radiação. A gelatina, entretanto, apresentou grande resistência à radiação. Na mistura de ambas, houve predomínio do comportamento esperado para a pectina. / Pectin is a polysaccharide substance of plant origin that may be used as gelling agent, stabilizer in jams, in yogurt drinks and lactic acid beverages. Gelatin, a protein from bovine origin, in this case, is mainly used as gelling agent due to hydrogel formation during cooling. The 60 Co-irradiation process may cause various modifications in macromolecules, some with industrial application, as reticulation. The dynamic response of viscoelastic materials can be used in order to give information about the structural aspect of a system at molecular level. In the present work samples of pectin with different degree of methoxylation, gelatin and the mixture of both were employed to study the radiation sensitivity by means of viscosity measurements. Solutions prepared with citric pectin with high methoxylation content (ATM) 1 por cent, pectin with low content (BTM) 1 por cent, gelatin 0.5 por cent, 1 por cent and 2 por cent, and the mixture 1 por cent and 2 por cent were irradiated with gamma rays at different doses, up to 15 kGy with dose rate about 2 kGy/h. After irradiation the viscosity was measured within a period of 48 h. The viscosity of ATM and BTM pectin solutions decreased sharply with the radiation dose. However, the gelatin sample presented a great radiation resistance. When pectin and gelatin solutions were mixed a predominance of pectin behavior was found.

A pectina é uma substância polissacarídica originada de plantas, que pode ser utilizada como agente gelificante, estabilizante de compotas, em bebidas láticas e iogurtes. A gelatina, proteína, nesse caso de origem bovina, é principalmente utilizada como agente gelificante, pois, forma hidrogéis por resfriamento. O processo de irradiação por radiação gama pode causar uma variedade de modificações nas macromoléculas algumas de aplicação industrial, como é o caso de reticulação. A resposta dinâmica de materiais viscoelásticos pode ser usada para dar informação sobre o aspecto estrutural de um sistema a nível molecular. No presente trabalho, pectina com diferentes graus de metoxilação, gelatina e a mistura de ambas foram empregados para estudar a sensibilidade à radiação por meio de medidas de viscosidade. Amostras de soluções de pectina de alto teor de metoxilação (ATM) 1%, pectina de baixo teor (BTM) 1%, gelatina 0,5%,1% e 2%, e a mistura de ambas a 1% e 2% foram irradiadas com raios gama em doses de até 15kGy e taxa de dose em torno de 2kGy/h. Após irradiação, a viscosidade foi medida dentro de um período de 48 h. A viscosidade da pectina ATM e BTM diminuiu drasticamente com o aumento da dose de radiação. A gelatina, entretanto, apresentou grande resistência à radiação. Na mistura de ambas, houve predomínio do comportamento esperado para a pectina. / Pectin is a polysaccharide substance of plant origin that may be used as gelling agent, stabilizer in jams, in yogurt drinks and lactic acid beverages. Gelatin, a protein from bovine origin, in this case, is mainly used as gelling agent due to hydrogel formation during cooling. The 60 Co-irradiation process may cause various modifications in macromolecules, some with industrial application, as reticulation. The dynamic response of viscoelastic materials can be used in order to give information about the structural aspect of a system at molecular level. In the present work samples of pectin with different degree of methoxylation, gelatin and the mixture of both were employed to study the radiation sensitivity by means of viscosity measurements. Solutions prepared with citric pectin with high methoxylation content (ATM) 1 por cent, pectin with low content (BTM) 1 por cent, gelatin 0.5 por cent, 1 por cent and 2 por cent, and the mixture 1 por cent and 2 por cent were irradiated with gamma rays at different doses, up to 15 kGy with dose rate about 2 kGy/h. After irradiation the viscosity was measured within a period of 48 h. The viscosity of ATM and BTM pectin solutions decreased sharply with the radiation dose. However, the gelatin sample presented a great radiation resistance. When pectin and gelatin solutions were mixed a predominance of pectin behavior was found.

This paper will analyze the effects of using hybrid optimization methods for optimizing objective functions that are determined by computational fluid dynamics solvers for compressible viscous flow for optimal design of airfoils. Previous studies on this topic by the authors had examined the application of deterministic optimization methods and stochastic optimization methods such as Simulated Annealing and Simultaneous Perturbation Stochastic Analysis (SPSA). The studies indicated that SPSA method has a greater or equal efficiency as compared with SA method in reaching optimal airfoil designs for the design problem in question. However, in some situations SPSA method has a tendency to demonstrate an oscillatory behavior in the vicinity of a local optima. To overcome this tendency, a hybrid method designed to take full advantage of SPSA’s high rate of reduction of the objective function at the inception of the design process to drive the design cycles towards the optimal zone at first, and then combining with other methods to perform the final stages of the convergence towards the optimal solutions is considered. SPSA method has been combined with the gradient-based Broydon-Fletcher-Goldfarb-Shanno (BFGS) method as well as Simulated Annealing method for the transonic inverse airfoil design problem that is concerned with the specification of a target airfoil surface pressure distribution and starting from an initial guess of an airfoil shape, the target airfoil shape is reached by way of minimization of a quantity that depends on the difference between the target and current airfoil surface pressure distribution. For a typical transonic flow test case, the effects of using hybrid optimization techniques such as SPSA+BFGS and SPSA+SA as opposed to using SPSA alone can be seen in Figure 1. After 800 design cycles using SPSA, the hybrid SPSA+SA method took 2521 function evaluations of SA while the SPSA+BFGS method took 271 function evaluations to reach similar values which are much better than that reached by using SPSA alone in the entire minimization process. Results indicate that both of the two hybrid methods have capability to find a global optimum more efficiently than the SPSA method. The paper will address issues related to hybridization and its impact on the optimal airfoil shape designs in various contexts. / Singapore-MIT Alliance (SMA)

These thesis review some recent results on the construction of very high order multidimensional upwind schemes for the solution of steady and unsteady conservation laws on unstructured triangular grids. We also consider the extension to the approximation of solutions to conservation laws containing second order dissipative terms. To build this high order schemes we use a sub-triangulation of the triangular Pk elements where we apply the distribution used for a P1 element. This manuscript is divided in two parts. The first part is dedicated to the design of the high order schemes for scalar equations and focus more on the theoretical design of the schemes. The second part deals with the extension to system of equations, in particular we will compare the performances of 2nd, 3rd and 4th order schemes. The first part is subdivided in four chapters: The aim of the second chapter is to present the multidimensional upwind residual distributive schmes and to explain what was the status of their development at the beginning of this work. The third chapter is dedicated to the first contribution: the design of 3rd and 4th order quasi non-oscillatory schemes. The fourth chapter is composed of two parts: We start by understanding the non-uniformity of the accuracy of the 2nd order schemes for advection-diffusion problem. To solve this issue we use a Finite Element hybridisation. This deep study of the 2nd order scheme is used as a basis to design a 3rd order scheme for advection-diffusion. Finally, in the fifth chapter we extend the high order quasi non-oscillatory schemes to unsteady problems. In the second part, we extend the schemes of the first part to systems of equations as follows: The sixth chapter deals with the extension to steady systems of hyperbolic equations. In particular, we discuss how to solve some issues such as boundary conditions and the discretisation of curved geometries. Then, we look at the performance of 2nd and 3rd order schemes on viscous flow. Finally, we test the space-time schemes on several test cases. In particular, we will test the monotonicity of the space-time non-oscillatory schemes and we apply residual distributive schemes to acoustic problems.

The surface oscillations in a deformable wall are known to induce an instability in the adjacent flow even in the absence of inertia. This instability, if understood properly, can be exploited to generate a well-mixed flow pattern with improved transport coefficients in microfluidic systems, wherein the benefits of inertial instabilities can not be realised. In order to utilise the wall deformability in micro-devices as well as other biotechnological applications, the quantitative knowledge of the critical parameter for the on-set of instability and the nature of bifurcation in the region of transition point are essential. With this objective, a major portion of this thesis deals with the stability analysis of flow past a flexible surface. For Newtonian flow over a deformable solid medium, the analyses of hydrodynamic stability in two flow regimes are presented: the viscous mode instability in the limit of zero Reynolds number, and the wall mode instability in the limit of high Reynolds number. The flexible solid in both analyses is described as a neo-Hookean solid continuum of finite thickness. The previous work on viscous instability using the same solid model ignored the viscous dissipation in the solid. In the present study, a purely elastic neo-Hookean model is augmented to incorporate the viscous stresses accounting for the dissipative mechanism in an aqueous gel-like solid medium. The linear stability analysis for this neo-Hookean viscoelastic solid shows a dramatic influence of solid viscosity on the stability behaviour. The important parameter here is where ηr is the solid viscosity relative to the fluid viscosity and H is the solid-to-fluid thickness ratio. While the effect solid viscosity is stabilizing for a further increase in viscosity in the regime reduces the critical shear rate for transition, indicating a destabilizing influence of solid viscosity. The weakly nonlinear analysis indicates that the bifurcation is subcritical for most values of H when ηr =0. However, for non-zero solid viscosity, the analysis reveals a range of ηr for which the nature of bifurcation is supercritical. The results are in contrast to the behaviour for the Hookean (linear) elastic solid, for which the effect of solid viscosity is always stabilising and the bifurcation is subcritical for all values of H and ηr. For the wall mode instability, critical parameters for the linear and the neo-Hookean elastic solid are found to be very close. The weakly nonlinear analysis of the wall mode instability shows that the instability is driven to a supercritically stable branch, indicating the possibility of a stable complex flow pattern which is ) correction to the base flow. The amplitude of the supercritically bifurcated equilibrium state, A1e, is derived in the vicinity of the critical point, and its scaling with the flow Reynolds number is obtained. The nonlinear analysis is also carried out using the asymptotic analysis in small parameter Re−1/3. The asymptotic results are found to be in good agreement with the numerical solutions for For a polymeric flow over a deformable solid medium, the viscous instability is analysed by extending the viscous mode for the Newtonian fluid to the fluid with finite elasticity. The viscoelastic fluid is described by an Oldroyd-B model which introduces two additional parameters: the Weissenberg number, W , and β, the ratio of solvent-to-solution viscosity. The polymer viscosity parameter β is an indirect measure of polymer concentration with the extreme cases of β =1 representing the Newtonian fluid and β =0the upper convected Maxwell fluid. The analysis considers both the linearly elastic and the neo-Hookean models to describe the deformable solid. The analysis reveals the presence of two classes of modes: the finite wavelength modes and the shortwave modes. The behaviour of the finite wavelength modes is similar for both the models of solid medium. The effect of increasing fluid Weissenberg number and also increasing polymer concentration (achieved by reducing β below 1) on the finite wavelength instability is stabilising. The viscous instability ceases to exist for W larger than a certain maximum value Wmax. The behaviour of the shortwave mode is remarkably different for both the models of solid. Using the shortwave asymptotic, the differences are elucidated and it is shown that the shortwave instabilities in both the models are qualitatively different modes. For a linear elastic solid model, the shortwave mode is attributed to the normal-stresses in polymeric fluid with high Weissenberg number. This mode does not exist for the Newtonian flow and is a downstream travelling disturbance wave. On the other hand, the shortwave mode for the neo-Hookean model is attributed to the normal-stress difference in the elastic solid. Hence, this mode does exist for the Newtonian fluid and is an upstream travelling disturbance wave. The role of polymer concentration in the criticality of finite wavelength and shortwave modes is examined for a wide range of Weissenberg number. The results are condensed in a map showing the stability boundaries in parametric space covering β, W and H. The weakly nonlinear analysis reveals that the bifurcation of linear instability is subcritical when there is no dissipation in the solid. The nature of bifurcation, however, changes to supercritical when the viscous effects in the solid are taken into account. The final problem of this thesis deals with the flow past a rigid surface. Here, the stability of base profile in a plane Couette flow of dilute polymeric fluid is studied at moderate Reynolds number. Three variants of Oldroyd-B model have been analysed, viz. the classical Oldroyd-B model, the diffusive Oldroyd-B model, and the non-homogeneous Oldroyd-B model. The Newtonian wall modes are modified marginally for the polymeric fluid described by the classical Oldroyd-B model. The Oldroyd-B model with artificial diffusivity introduces the additional ‘diffusive modes’ which scale with P´eclet number. The diffusive modes become the slowest decaying modes, in comparison to the wall modes, for large wavenumber disturbances. For these two models, the polymeric flow is linearly stable. Using the equilibrium flow method, wherein the nonlinear flow is assumed to be at the transition point, the finite amplitude disturbances are analysed, and the threshold energy necessary for subcritical transition is estimated. The third variant of Oldroyd-B model accounts for non-homogeneous polymer concentration coupled with the stress field. This model exhibits an instability in the linear analysis. The ‘concentration mode’ becomes unstable when the fluid Weissenberg number exceeds a certain transition value. This instability is driven by the stress-induced fluctuations in polymer number density.

In this thesis we describe the development of Reynolds- averaged Navier Stokes code for the flow past two- dimensional configuration. Particularly, emphasis has been laid on the study of low Reynolds number airfoil aerodynamics. The thesis consists of five chapters covering the back ground history, problem formulation, method of solution and discussion of the results and conclusion. Chapter I deals with a detailed background history of low Reynolds number aerodynamics, problem associated with it, state of the art, its importance in practical applications in aircraft industries. Chapter II describes the mathematical model of the flow physics and various levels of approximations. Also it gives an account of complexity of the equations at low Reynolds number regarding flow separation, transition and reattachment. Chapter III describes method of solution, numerical algorithm developed, description of various upwind schemes, grid system, finite volume discrieti-zation of the governing equations described in Chapter II. Chapter IV describes the application of the newly developed Navier Stokes code for the test cases from GAMM Workshop proceedings. Also it describes validation of the code for Euler solutions, Blasius solution for the flow past flat plate and compressible Navier Stokes solution for the flow past NACA 0012 Airfoil at low Reynolds number. Chapter V describes the application of the Navier Stokes code for the more test cases of current practical interest . In this chapter laminar separation bubble characteristics are investigated in detail regarding formation, growth and shedding in an unsteady environment. Finally the conclusion is drawn regarding the robustness of the newly developed code in predicting the airfoil aerodynamic characteristics at low Reynolds number both in steady and unsteady environment. Lastly, suggestion for future work has been highlighted.

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