La conception des nacelles doit répondre à des contraintes géométriques d’encombrement mais aussi à des spécifications motoristes qui précisent les niveaux de performance exigés. Au sol, l’une des principales contraintes imposées par le motoriste concerne le niveau de distorsion de pression totale dans le plan fan quand la nacelle est soumise à un vent de travers. Dans le cas le plus limitant, c’est-à-dire lorsque la direction du vent est perpendiculaire à l’axe de la nacelle, il se produit un décollement au niveau de l’entrée d’air côté vent. L’hétérogénéité de l’écoulement crée des efforts instationnaires sur les aubes du fan. Ces efforts peuvent amener à un régime de pompage endommageant ainsi le moteur. De plus, la tendance actuelle est de réaliser des nacelles courtes, réduisant la distance qu’à l’écoulement pour s’homogénéiser avant d’impacter le fan, conduisant à un couplage entre le décollement et le fan. Le but de cette étude est de simuler numériquement l’écoulement intervenant dans une nacelle courte soumise à un vent de travers et d’étudier l’impact de la présence du fan. Tout d’abord, la définition de la distorsion est basée sur les grandeurs totales. Ainsi, la compréhension du comportement des grandeurs totales au voisinage d’une paroi et l’influence des paramètres numériques sur leur évolution est nécessaire. Une approche analytique et numérique sur plaque plane a permis d’évaluer le comportement des grandeurs totales à la frontière externe de la couche limite et l’influence des paramètres numériques RANS sur leur évolution. Cette étude a permis de choisir les paramètres numériques utilisés pour la simulation de la nacelle. Pour faire ressortir l’influence du fan sur la distorsion, deux types de simulations ont été menés : une simulation de nacelle isolée et une simulation de l’ensemble complet nacelle/fan respectivement comparées à un essai en soufflerie sur une maquette de nacelle isolée et à un essai de moteur complet à échelle 1 :1 réalisé en « soufflerie » à veine ouverte. La description correcte de la distorsion nécessite de prendre en compte les phénomènes de transition. Une méthode innovante de prise en compte de la transition par équations de transport est utilisée. Comme le coût de calcul de l’ensemble complet est prohibitif, la question du découplage du calcul en injectant une distorsion, issue d’une simulation de nacelle isolée, dans un calcul de fan isolé est discutée. La distorsion par vent de travers intervient lorsque l’avion est au sol. Par conséquent, l’impact de la présence du sol est étudié dans le cas de la nacelle isolée. Enfin, le critère de distorsion utilisé présente plusieurs défauts importants et peut être remis en cause. Une nouvelle méthode de mesure et de calcul estétudiée. / Inlet design must fulfill geometrical constraints and engine requirements. One of these requirementsis the homogeneity of the flow impacting the fan which is quantified by the distortionlevels of stagnation pressure. When the airplane is on the ground and ready to take-off, crosswindconditions are critical for the distorsion level. The most critical case is when the wind directionis normal to the engine axis. Subsonic and supersonic separations occur near the inlet lip. Theso-created heterogeneity produces an unsteady stress on the fan blades which can lead to surge.Furthermore, short inlets are designed nowadays reducing the distance available for the flow tohomogenize before the fan leading to a coupling between the fan and the separated flow region.The aim of this study is to numerically predict the flow in a short inlet under crosswind conditionsand to investigate the fan influence on the distortion. First of all, the distortion definition isbased on stagnation quantities. Therefore, the stagnation quantities behavior and the numericalparameters influence must be investigated. The behavior of the stagnation quantities near theboundary layer edge is studied with analytical and numerical approaches. The numerical parameterschosen for the inlet simulation come from the so-obtained results obtained. In order tohighlight the fan influence on the distortion, two kinds of simulations were proceeded and comparedto experimental results : an isolated inlet simulation and a inlet/fan simulation. To correctlypredict the distortion, transition has to be be taken into account. Therefore an innovative solutionusing transport equations is used. As the computation cost for the inlet/fan computation isprohibitive, the decoupling which consists in injecting on a isolated fan the distortion obtainedduring a isolated inlet computation, is discussed. In fact, crosswind conditions occur when theairplane is on the ground, thus, the ground influence over the inlet distortion is studied for anisolated inlet. Finally, the distortion criterion used in this study has evidenced some strong defectsand can be questioned. Another approach of measurement with another criterion definitionis investigated.

Neste trabalho, é apresentada a simulação de escoamentos compressíveis turbulentos no entorno de corpos móveis rígidos ou deformáveis empregando-se técnicas adaptativas. As simulações numéricas são conduzidas utilizando-se o método dos elementos finitos. A discretização espaço-temporal é desenvolvida através do método das linhas ou direções características (Characteristic-Based Split - CBS) e a modelagem da turbulência é feita através de um modelo de Simulação de Grandes Escalas (SGE, ou na terminologia em inglês, Large Eddy Simulation – LES) com o coeficiente de Smagorinsky variável no tempo e espaço (SGE ou LES dinâmico). A análise estrutural de corpos deformáveis imersos no fluido é realizada através de um modelo de elementos finitos triangulares para análise de placas e cascas com não linearidade geométrica, usando materiais elásticos com comportamento linear. Conjuntamente, um método de adaptação anisotrópica transiente de malhas é empregado para obter resultados com boa resolução a baixos custos computacionais. A consideração do movimento relativo de corpos imersos no escoamento é feita através de um método híbrido de movimento da malha que emprega interpolação com funções de base radial. Exemplos bidimensionais e tridimensionais são apresentados de forma a validar cada uma das metodologias desenvolvidas. Por fim, exemplos de simulações complexas são investigados, comparando-se os resultados obtidos com resultados experimentais e numéricos presentes na literatura. / In this work, the simulation of compressible turbulent flows around rigid and flexible moving bodies is presented using adaptative techniques. The numerical simulations are solved employing the finite element method. The space-time discretization is performed using the Characteristic-Based Split scheme (CBS) and turbulence is modelled with Large Eddy Simulation (LES) and a dynamic Smagorinsky sub-grid model. The structural analysis of deformable bodies immersed on the flow is performed using a triangular finite element model for the analysis of geometrically non-linear elastic plates and shells. An anisotropic mesh adaptation algorithm for transient simulations is coupled with the solver to achieve results with good resolution and low computational costs. The consideration of the relative movement of immersed bodies on the flow is performed employing an hybrid method of mesh movement based on radial basis function interpolation. Twodimensional and three-dimensional examples are presented in order to validate the proposed methodologies. Finally, complex simulations are investigated, where results are compared with experimental and numerical data available in the literature.

Made available in DSpace on 2014-12-17T14:58:17Z (GMT). No. of bitstreams: 1 FelipePMA_DISSERT.pdf: 3715487 bytes, checksum: 630bbbaabad6ec787270701f99c61fb0 (MD5) Previous issue date: 2012-04-18 / A critical problem in mature gas wells is the liquid loading. As the reservoir pressure decreases, gas superficial velocities decreases and the drag exerted on the liquid phase may become insufficient to bring all the liquid to the surface. Liquid starts to drain downward, flooding the well and increasing the backpressure which decreases the gas superficial velocity and so on. A popular method to remedy this problem is the Plunger Lift. This method consists of dropping the "plunger"to the bottom of the tubing well with the main production valve closed. When the plunger reaches the well bottom the production valve is opened and the plunger carry the liquid to the surface. However, models presented in literature for predicting the behavior in plunger lift are simplistic, in many cases static (not considering the transient effects). Therefore work presents the development and validation of a numerical algorithm to solve one-dimensional compressible in gas wells using the Finite Volume Method and PRIME techniques for treating coupling of pressure and velocity fields. The code will be then used to develop a dynamic model for the plunger lift which includes the transient compressible flow within the well / Um problema cr?tico em po?os maduros de g?s ? a carga l?quida. Quando a press?o do reservat?rio diminui, a velocidade superficial diminui e o arrasto exercido na fase l?quida pode se tornar insuficiente para trazer todo o l?quido para a superf?cie. O l?quido come?a a drenar para baixo, afogando o po?o e aumentando a contrapress?o, a qual diminui a velocidade superficial, e assim por diante. Um m?todo popular para remediar esse problema ? o plunger lift. Esse m?todo consiste em derrubar um plunger na fundo coluna de produ??o com a v?lvula principal fechada. Quando o plunger alcan?a o fundo do po?o a v?lvula de produ??o ? aberta e o plunger carrega o l?quido para a superf?cie. Atualmente, os modelos presentes na literatura para prever o comportamento do plunger s?o simplistas, em muitos casos est?ticos (n?o consideram efeitos transientes). Assim, esse trabalho apresenta e valida um algor?timo num?rico para resolver escoamentos em po?os de g?s usando o M?todo dos Volumes Finitos e a t?cnica PRIME para tratar o acoplamento da press?o e velocidade. Esse modelo ser? usado para desenvolver modelos din?micos para plunger lift que incluem efeitos transientes e compress?veis nos escoamentos em po?os

Neste trabalho, é apresentada a simulação de escoamentos compressíveis turbulentos no entorno de corpos móveis rígidos ou deformáveis empregando-se técnicas adaptativas. As simulações numéricas são conduzidas utilizando-se o método dos elementos finitos. A discretização espaço-temporal é desenvolvida através do método das linhas ou direções características (Characteristic-Based Split - CBS) e a modelagem da turbulência é feita através de um modelo de Simulação de Grandes Escalas (SGE, ou na terminologia em inglês, Large Eddy Simulation – LES) com o coeficiente de Smagorinsky variável no tempo e espaço (SGE ou LES dinâmico). A análise estrutural de corpos deformáveis imersos no fluido é realizada através de um modelo de elementos finitos triangulares para análise de placas e cascas com não linearidade geométrica, usando materiais elásticos com comportamento linear. Conjuntamente, um método de adaptação anisotrópica transiente de malhas é empregado para obter resultados com boa resolução a baixos custos computacionais. A consideração do movimento relativo de corpos imersos no escoamento é feita através de um método híbrido de movimento da malha que emprega interpolação com funções de base radial. Exemplos bidimensionais e tridimensionais são apresentados de forma a validar cada uma das metodologias desenvolvidas. Por fim, exemplos de simulações complexas são investigados, comparando-se os resultados obtidos com resultados experimentais e numéricos presentes na literatura. / In this work, the simulation of compressible turbulent flows around rigid and flexible moving bodies is presented using adaptative techniques. The numerical simulations are solved employing the finite element method. The space-time discretization is performed using the Characteristic-Based Split scheme (CBS) and turbulence is modelled with Large Eddy Simulation (LES) and a dynamic Smagorinsky sub-grid model. The structural analysis of deformable bodies immersed on the flow is performed using a triangular finite element model for the analysis of geometrically non-linear elastic plates and shells. An anisotropic mesh adaptation algorithm for transient simulations is coupled with the solver to achieve results with good resolution and low computational costs. The consideration of the relative movement of immersed bodies on the flow is performed employing an hybrid method of mesh movement based on radial basis function interpolation. Twodimensional and three-dimensional examples are presented in order to validate the proposed methodologies. Finally, complex simulations are investigated, where results are compared with experimental and numerical data available in the literature.

A investigação dos mecanismos de instabilidade pode ter um papel importante no entendimento do processo laminar para turbulento de um escoamento. Análise de instabilidade de uma camada limite de uma linha de estagnação compressível foi realizada no contexto de teoria linear BiGlobal. O estudo dos mecanismos de instabilidade deste escoamento pode proporcionar uma visão útil no desenho aerodinâmico das asas. Um novo procedimento foi desenvolvido e implementado computacionalmente de maneira sequencial e paralela para o estudo de instabilidade BiGlobal. O mesmo baseia-se em formar a matriz esparsa associada ao problema discretizado por dois métodos: pontos de colocação de Chebyshev-Gauss-Lobatto e diferenças finitas, além das combinações destes métodos. Isto permitiu o uso de bibliotecas computacionais eficientes para resolver o sistema linear associado ao problema de autovalor utilizando o algoritmo de Arnoldi. O desempenho do método numérico e código computacional proposto são analisados do ponto de vista do uso de métodos de ordenação dos elementos da matriz, coeficientes de preenchimento, memória e tempo computacional a fim de determinar a solução mais eficiente para um problema físico geral com técnicas de matrizes esparsas. Um estudo paramétrico da instabilidade da camada limite de uma linha de estagnação foi realizado incluindo o estudo dos efeitos de compressibilidade. O excelente desempenho código computacional permitiu obter as curvas neutras e seus respectivos valores críticos para a faixa de número de Mach 0 \'< OU =\' Ma \'< OU =\' 1. Os resultados confirmam a teoria assintótica apresentada por (THEOFILIS; FEDOROV; COLLIS, 2004) e mostram que o incremento do número de Mach reduz o numero de Reynolds crítico e a faixa instável do número de ondas. / Investigation of linear instability mechanisms is essential for understanding the process of transition from laminar to turbulent flow. An algorithm for the numerical solution of the compressible BiGlobal eigenvalue problem is developed. This algorithm exploits the sparsity of the matrices resulting from the spatial discretization of the enigenvalue problem in order to improve the performance in terms of both memory and CPU time over previous dense algebra solutions. Spectral collocation and finite differences spatial discretization methods are implemented, and a performance study is carried out in order to determine the best practice for the efficient solution of a general physical problem with sparse matrix techniques. A combination of spectral collocation and finite differences can further improve the performance. The code developed is then applied in order to revisit and complete the parametric analyses on global instability of the compressible swept Hiemenz flow initiated in (THEOFILIS; FEDOROV; COLLIS, 2004) and obtain neutral curves of this flow as a function of the Mach number in the 0 \'< OU =\' Ma \'< OU =\' 1 range. The present numerical results fully confirm the asymptotic theory results presented in (THEOFILIS; FEDOROV; COLLIS, 2004). This work presents a complete parametric study of the instability properties of modal three dimensional disturbances in the subsonic range for the flow conguration at hand. Up to the subsonic maximum Mach number value studied, it is found that an increase in this parameter reduces the critical Reynolds number and the range of the unstable spanwise wavenumbers.

As aplicações aeroespaciais estão frequentemente associadas a escoamentos compressíveis com altíssimos números de Reynolds. No entanto, existem no contexto aeroespacial importantes aplicações que envolvem escoamentos compressíveis a Reynolds relativamente baixos. Entre eles se destacam o escoamento em pás de turbina a gás e ao redor de dispositivos de alta sustentação como eslates e flapes em grandes ângulos de ataque. Pode-se destacar também o processo de combustão supersônica que está intimamente ligado e é fortemente beneficiado pelo presente estudo. Nas aplicações aerodinâmicas em baixos números de Reynolds frequentemente uma parcela significativa do escoamento se apresenta no regime de transição para turbulência, ou nos estágios iniciais do escoamento turbulento. O objetivo do presente projeto é a simulação numérica direta de escoamentos compressíveis transicionais com desenvolvimento de um código para simulação em três dimensões de escoamentos alto subsônicos. O escoamento a ser estudado no projeto é a evolução linear e não linear de trens de onda e pacotes de onda em uma camada de mistura compressível. A solução das equações de Navier-Stokes é obtida através do método das diferenças finitas. As derivadas espaciais são resolvidas através de um método compacto de sexta ordem, enquanto que as derivadas temporais são resolvidas através do método de Runge-Kutta de quarta ordem. Os métodos de aproximação foram modificados para trabalhar com malhas não uniformes visando refinar a malha em pontos em que o fenômeno ocorre e, consequentemente, reduzir o custo computacional. A investigação numérica inicia-se com a análise da taxa de amplificação dos trens de ondas fortemente modulados em regime linear. Os resultados obtidos foram comparados favoravelmente com a teoria linear. Os testes foram estendidos para a análise não linear, e consequentemente, foi possível reproduzir os fenômenos clássicos de instabilidade hidrodinâmica através da evolução dos trens de ondas oblíquos. / Aerospace applications are frequently associated with compressible flows at relatively high Reynolds number. Nevertheless important applications involve compressible flows at relatively low Reynolds number in the aerospace context. Among them, the flow on gas turbine blades and high lift devices such as slats and flaps at high angle of attack are particulary important. Besides, progress in aeroespace research is dependent on developing more efficient propulsion systems. In aerodynamic applications at low Reynolds number, often a substancial portion of the flow is in the transition regime, or in the initial stages of a turbulent flow. The objective of the present study is the Direct Numerical Simulation of three-dimensional transition of compressible flows in a mixing layer. Inspired on the worked devoted to modulated waves, the current work investigates the linear and nonlinear temporal evolution of wavetrains in this phenomenon. The Navier-Stokes equations were solved with a sixth-order compact finite-difference schemes. The time integration was performed by a fourth-order Runge-Kutta scheme. Moreover, the methods to solve the spatial derivatives were modified to work with non-uniform grids. This technique was implemented with the objective to improve the resolution of the grid where the phenomenon occurs and to reduce the computational cost. The numerical investigation starts with an analysis of the growth rate of the wavetrains in linear regime to verify the numerical code. The results compared favourably with linear theory. Tests were also performed in the nonlinear regime to simulate the oblique wavetrains and it was possible to reproduce the classical hydrodynamic instability phenomena.

Dans les installations nucléaires, les explosions, qu’elles soient d’origine interne ou externe, peuvent entrainer la rupture du confinement et le rejet de matières radioactives dans l’environnement. Il est donc fondamental, dans un cadre de sûreté de modéliser ce phénomène. L’objectif de cette thèse est de contribuer à l’élaboration de schémas numériques performants pour résoudre ces modèles complexes. Les travaux présentés s’articule autour de deux axes majeurs : le développement de schémas volumes finis consistants pour les équations d’Euler compressible qui modélise les ondes de choc et celui de schémas performants pour la propagation d’interfaces comme le front de flamme lors d'une déflagration. La discrétisation spatiale est de type mailles décalées pour tous les schémas développés. Les schémas pour les équations d'Euler se basent sur une formulation en énergie interne qui permet de préserver sa positivité ainsi que celle de la masse volumique. Un bilan d'énergie cinétique discret peut être obtenu et permet de retrouver un bilan d'énergie totale par l'ajout d'un terme de correction dans le bilan d'énergie interne. Le schéma ainsi construit est consistant au sens de Lax avec les solutions faibles entropiques des équations continues. On utilise les propriétés des équations de type Hamilton-Jacobi pour construire une classe de schémas volumes finis performants sur une large variété de maillages modélisant la propagation du front de flamme. Ces schémas garantissent un principe du maximum et possèdent des propriétés importantes de monotonie et consistance qui permettent d'obtenir un résultat de convergence. / In nuclear facilities, internal or external explosions can cause confinement breaches and radioactive materials release in the environment. Hence, modeling such phenomena is crucial for safety matters. The purpose of this thesis is to contribute to the creation of efficient numerical schemes to solve these complex models. The work presented here focuses on two major aspects: first, the development of consistent schemes for the Euler equations which model the blast waves, then the buildup of reliable schemes for the front propagation, like the flame front during the deflagration phenomenon. Staggered discretization is used in space for all the schemes. It is based on the internal energy formulation of the Euler system, which insures its positivity and the positivity of the density. A discrete kinetic energy balance is derived from the scheme and a source term is added in the discrete internal energy balance equation to preserve the exact total energy balance. High order, MUSCL-like interpolators are used in the discrete momentum operators. The resulting scheme is consistent (in the sense of Lax) with the weak entropic solutions of the continuous problem. We use the properties of Hamilton-Jacobi equations to build a class of finite volume schemes compatible with a large number of meshes to model the flame front propagation. These schemes satisfy a maximum principle and have important consistency and monotonicity properties. These latters allows to derive a convergence result for the schemes based on Cartesian grids.

On s’intéresse à la simulation d’écoulements compressibles multi-matériaux et, notamment, aux interactions fluide/structure dans les régimes transitoires et en dynamique rapide. Le but est de pouvoir décrire l’évolution de matériaux de lois de comportement très différentes à l’aide d’un modèle unique. Les milieux sont seulement différenciés par leurs équations d’état et sont séparés par une interface dite sharp. Les matériaux peuvent être des fluides ou des solides élastiques et sont soumis à de grandes déformations. Le modèle est écrit dans le formalisme eulérien. Le schéma numérique est résolu sur des grilles cartésiennes pour des simulations en trois dimensions.Une extension du modèle permet de décrire les déformations plastiques des solides. / We are interested in the simulation of compressible multimaterial flows and especially influid/structure interactions in transient states and fast dynamics. We aim to describe the evolution of materials of very different constitutive laws with an unified model. The materials are only differentiated by their own constitutive laws and are separated by a sharp interface. They can be as well fluids or elastic solids and under go large de formations. The model is written in the Eulerian framework. The numerical scheme is solved on Cartesian grids for simulations in three dimensions. An extension of the elastic model is added to describe the plastic deformations of solids.

Minimizing numerical dissipation without compromising the robust shock-capturing attributes remains an outstanding challenge in the design of numerical methods for high-speed compressible flows. The conflicting requirements of low and high numerical dissipation for accurate resolution of discontinuous and smooth flow features, respectively, are the principal reason behind this challenge. In this work we pursue a recently proposed novel strategy of combining adaptive mesh redistribution with conservative high-order shock-capturing finite-volume discretization methodology to overcome this challenge. In essence, we perform high-order finite-volume WENO (weighted essentially non oscillatory) reconstruction on a continuously moving grid the nodes of which are repositioned adaptively in such a way that maximum spatial resolution is achieved in regions associated with sharpest flow gradients. Moreover, to reduce computational expense, the finite-volume WENO discretization strategy is combined with the midpoint quadrature so that only one reconstruction along each intercool location is necessary. To estimate a monotone upwind flux, a rotated HLLC (Harten-Lax-vanLeer-contact resolving) Riemann solver is employed at each intercool location with the state variables estimated from the high-order WENO reconstruction procedure. The effectiveness of this adaptive high-order discretization methodology is assessed on the well-known double Mach reflection test case for reconstruction orders ranging from five to eleven. We find that the resolution of the intricate flow features such as the wall-jet improves progressively with the reconstruction order, which is indicative of the reduced dissipation level of the adaptive high-order WENO discretization. The adaptive discretization methodology is applied to simulate a flow configuration consisting of a Mach 3 supersonic jet injected in a Mach 2 supersonic crossflow of similar ideal gas. It is found that the flow characteristics and especially features that are formed as a result of the Kelvin-Helmholtz instability are strongly influenced by the reconstruction order. The influence of the jet inclination angle on the overall flow features is analyzed.

Experiments are done using a smooth solid rigid homogeneous acrylic sphere rolling on an inclined plane which is submerged in water. The motivation for these experiments comes from a need to understand a class of solid-fluid interaction problems that include sediment transport, movement of gravel on ocean floor and river bed due to water currents. Experiments are performed in a glass water tank 15 cm wide by 14 cm deep by 61 cm long which can be tilted to desired angle. The sphere is released from rest on the inclined false bottom of the tank in quiescent water. Our experimental study has twofold aim: (1)to study the boundary layer separation, the three-dimensional eddying motion in the wake and the near-wake structure and(2) to establish hydrodynamic force coefficients by analyzing kinematical data of the sphere motion from start to till it attains terminal velocity. Experiments are carried out at moderate Reynolds number Rearound1500. Previous studies on the first problem exist in the literature for Reup to 350. Previous studies on the second problem do not clearly define the added-mass coefficient and the influence of the water tank side-walls on the drag coefficient. In the first study, the characterization of the wake is done using flow visualization methods (fluoresce in dye visualization and particle streak visualization) and Particle Image Velocimetry (PIV). Laser light sheet obtained from an argon ion continuous laser beam is taken in different orientations to illuminate the fluoresce in dye or 14 m silver-coated hollow glass spheres. These experiments show that the wake behind the rolling sphere up to 1.6 diameters (or 1.6D) downstream is confined within height 1.2Dand width1.2D. At about 1.8Ddownstream, the wake sways alternately on either side of the equatorial plane, moving in lateral-vertical direction and moving out of the confining region; this gives zigzag appearance to the wake. Also in these experiments, we observe that the flow separations from the surface of the rolling sphere show three separation zones. The eddies shed from the primary separation surface on the upper hemisphere are symmetrical about the equatorial plane with Strouhal number St=1.0. The primary separation is affected by the symmetrical secondary separations on the rear surface in the piggyback region — it is the region near the upper rear surface of the sphere behind the transverse equatorial plane and below the primary separation surface. The lower eddies below the primary separation zone are shed alternately on either side of the equatorial plane with shedding frequency St=0.5. Our experiments show that there is a viscous blockage of width 0.4Dat the crevice near the point of contact. On either side of the viscous blockage at the crevice, we see weak symmetric eddies. Based on our experimental observations, we proceed to build a simple physical model of the separated flow on the surface of the rolling sphere. In the second study, the motion of the sphere is photographed and paired data of the displacement and time is obtained for the sphere motion from the start of motion till terminal velocity is reached at about 4.5 sphere diameters from the point of release of the sphere. Equation of motion of the sphere is solved numerically treating added-mass coefficient Ca and drag coefficient Cd as parameters. Experimental data is fitted on these solutions and the best fit gives the values of the force coefficients. Theoretical value of Ca equal to 0.621 is confirmed experimentally. Value of Cd is found to be 1.23 at Re=990 and it is 1.06 at Re= 1900. Side-wall effects become important for ratio of diameter of sphere to width of tank greaterthan0.20.