Liquid films falling under the influence of gravity are widely encountered in a variety of industrial two-phase flow applications (distillation columns, nuclear reactor cores, etc.). In addition, the falling annular film represents a fundamental limiting case of the annular flow regime of two-phase gas-liquid flows. The literature on annular falling films is dominated by studies concerning the average film thickness. Information on more detailed characteristics of the film thickness variations and information on the velocity profile within the film and wall shear stress are much less common. The statistical description of the film thickness is complicated by the fact that practically all flows of interest occur in the turbulent regime. Due to the complex and unsteady nature of the turbulent annular falling film, no complete theories or models have yet been developed on the subject. Experimental studies are needed to gain insight into the basic mechanisms that govern this complex flow.<p>The primary purpose of this thesis research was to characterise the film thickness of falling annular films at high and very high Reynolds numbers using non-intrusive imaging techniques. Another objective was to develop ray-tracing techniques to reduce optical distortion and obtain high-quality experimental data. <p>Instantaneous film thickness measurements of falling annular films were extracted at five different Reynolds numbers in the range Re = 1000 ~ 6000 for the fully developed turbulent regime using an automated optical measurement technique. From visual observation of the images obtained it was found that waves were not axisymmetric, i.e., there was substantial azimuthal variation in film thickness. The turbulent waves appeared to be similar in appearance to very large breaking ocean waves driven by strong winds. The random nature of these falling annular films was subjected to statistical analysis.<p>Statistical characteristics of film thickness were studied at Reynolds numbers in the range Re = 1000 ~ 6000. A correlation for dimensionless mean film thickness was obtained in the turbulent flow regime. The dimensionless mean film thickness obtained here was found to be in reasonable agreement with the other established experimental and theoretical studies. It was shown that the Reynolds number influences the statistical characteristics of film thickness such as standard deviation and coefficient of variation. The additional data obtained here shows that the standard deviation continues to increase in proportion to the mean film thickness in the turbulent regime. In other words, in the lower turbulent zones the films are thin and less wavy, whereas in the higher turbulent zones the films are thicker and extremely wavy in nature.<p>The probability density distributions were also obtained. It was found that the measured probability density distributions were asymmetric. They all had a maximum peak and were skewed to the right hand side with a long tail that stretched to over six times the peak value. The maximum peak could be considered to represent the modal value of the film thickness or the substrate film thickness. The increase in skewness and the decrease in the height of the peak with liquid Reynolds number could be attributed to the presence of large disturbance waves which ride on the substrate film. This enhances the waviness of the film.<p>A common problem in imaging flows in cylindrical tubes is the optical distortion caused by the wall curvature. To minimize this problem the cylindrical tube was surrounded by an optical correction box with flat walls filled with water. In addition, an advanced ray tracing model was employed to reduce optical distortion effects in the cylindrical tube. This technique increased the accuracy of the imaging technique and enabled quantitative measurements of film thickness to be made.

Liquid films falling under the influence of gravity are widely encountered in a variety of industrial two-phase flow applications (distillation columns, nuclear reactor cores, etc.). In addition, the falling annular film represents a fundamental limiting case of the annular flow regime of two-phase gas-liquid flows. The literature on annular falling films is dominated by studies concerning the average film thickness. Information on more detailed characteristics of the film thickness variations and information on the velocity profile within the film and wall shear stress are much less common. The statistical description of the film thickness is complicated by the fact that practically all flows of interest occur in the turbulent regime. Due to the complex and unsteady nature of the turbulent annular falling film, no complete theories or models have yet been developed on the subject. Experimental studies are needed to gain insight into the basic mechanisms that govern this complex flow.<p>The primary purpose of this thesis research was to characterise the film thickness of falling annular films at high and very high Reynolds numbers using non-intrusive imaging techniques. Another objective was to develop ray-tracing techniques to reduce optical distortion and obtain high-quality experimental data. <p>Instantaneous film thickness measurements of falling annular films were extracted at five different Reynolds numbers in the range Re = 1000 ~ 6000 for the fully developed turbulent regime using an automated optical measurement technique. From visual observation of the images obtained it was found that waves were not axisymmetric, i.e., there was substantial azimuthal variation in film thickness. The turbulent waves appeared to be similar in appearance to very large breaking ocean waves driven by strong winds. The random nature of these falling annular films was subjected to statistical analysis.<p>Statistical characteristics of film thickness were studied at Reynolds numbers in the range Re = 1000 ~ 6000. A correlation for dimensionless mean film thickness was obtained in the turbulent flow regime. The dimensionless mean film thickness obtained here was found to be in reasonable agreement with the other established experimental and theoretical studies. It was shown that the Reynolds number influences the statistical characteristics of film thickness such as standard deviation and coefficient of variation. The additional data obtained here shows that the standard deviation continues to increase in proportion to the mean film thickness in the turbulent regime. In other words, in the lower turbulent zones the films are thin and less wavy, whereas in the higher turbulent zones the films are thicker and extremely wavy in nature.<p>The probability density distributions were also obtained. It was found that the measured probability density distributions were asymmetric. They all had a maximum peak and were skewed to the right hand side with a long tail that stretched to over six times the peak value. The maximum peak could be considered to represent the modal value of the film thickness or the substrate film thickness. The increase in skewness and the decrease in the height of the peak with liquid Reynolds number could be attributed to the presence of large disturbance waves which ride on the substrate film. This enhances the waviness of the film.<p>A common problem in imaging flows in cylindrical tubes is the optical distortion caused by the wall curvature. To minimize this problem the cylindrical tube was surrounded by an optical correction box with flat walls filled with water. In addition, an advanced ray tracing model was employed to reduce optical distortion effects in the cylindrical tube. This technique increased the accuracy of the imaging technique and enabled quantitative measurements of film thickness to be made.

Gas-liquid annular two phase flow in pipes is important in the oil and gas, nuclear and the process industries. It has been identified as one of the most frequently encountered flow regimes and many models (empirical and theoretical) for the film flow and droplet behaviour for example have been developed since the 1950s. However, the behaviour in large pipes (those with diameter greater than 100 mm) has not been fully explored. As a result, the two- phase flow characteristics, data, and models specifically for such pipes are scarce or non-existent such that those from smaller pipes are extrapolated for use in design and operation. Many authors have cautioned against this approach since multiphase pipe flow behaviour is different between small and large pipes. For instance the typical slug flows seem not to occur in vertical upwards flows when the pipe diameter exceeds 100 mm. It is therefore imperative that theoretical models and empirical correlations for such large diameter pipes are specifically developed.

This thesis deals with the dynamics of a thin liquid film falling down a heated plate. The heating yields surface tension gradients that induce thermocapillary stresses on the free surface, thus affecting the stability and the evolution of the film. Accounting for the coherence of the flow due to viscosity, two main approaches that reduce the dimensionality of the original problem are usually considered depending on the flow rate (as measured by the Reynolds number): the `long wave' asymptotic expansion for small Reynolds numbers and the `integral boundary layer' approximation for moderate Reynolds numbers. The former suffers from singularities and the latter from incorrectness of the instability threshold for the occurrence of hydrodynamic waves. Thus, the aim of this thesis is twofold: in a first part, we define quantitatively the validity of the `long wave' evolution equation (Benney equation) for the film thickness h including the thermocapillary effect; and in a second part, we improve the `integral boundary layer' approach by combining a gradient expansion to a weighted residual method. In the first part, we further investigate the Benney equation in its validity domain in the case of periodically inhomogeneous heating in the streamwise direction. It induces steady-state deformations of the free surface with increased transfer rate in regions where the film is thinner, and also in average. The inhomogeneities of the heating also modify the nature of travelling wave solutions at moderate temperature gradients and allows for suppressing wave motion at larger ones. Moreover, large temperature gradients (for instance positive ones) in the streamwise direction produce large local film thickening that may in turn become unstable with respect to transverse disturbances such that the flow may organize in rivulet-like structures. The mechanism of such instability is elucidated via an energy analysis. The main features of the rivulet pattern are described experimentally and recovered by direct numerical simulations. In the second part, various models are obtained, which are valid for larger Reynolds numbers than the Benney equation and account for second-order viscous and inertial effects. We then elaborate a strategy to select the optimal model in terms of linear stability properties and existence of nonlinear solutions (solitary waves), for the widest possible range of parameters. This model -- called reduced model -- is a system of three coupled evolution equations for the local film thickness h, the local flow rate q and the surface temperature Ts. Solutions of this model indicate that the interaction of the hydrodynamic and thermocapillary modes is non-trivial, especially in the region of large-amplitude solitary waves. Finally, the three-dimensional evolution of the solutions of the reduced model in the presence of periodic forcing and noise compares favourably with available experimental data in isothermal conditions and with direct numerical simulations in non-isothermal conditions. ------------------------------------------------ Cette thèse analyse la dynamique d'un film mince s'écoulant le long d'une paroi chauffée. Le chauffage crée des gradients de tension superficielle qui induisent des tensions thermocapillaires à la surface libre, altérant ainsi la stabilité et l'évolution du film. Grâce à la cohérence de l'écoulement assurée par la viscosité, deux approches permettant de réduire la dimensionnalité du problème original sont habituellement considérées suivant le débit (mesuré par le nombre de Reynolds): l'approximation asymptotique dite `longues ondes' pour les faibles nombres de Reynolds et l'approximation `intégrale couche limite' pour les nombres de Reynolds modérés. Cependant, la première approximation souffre de singularités et la dernière de prédictions imprécises du seuil de stabilité des ondes hydrodynamiques à la surface du film. Le but de cette thèse est donc double: dans une première partie, il s'agit de déterminer, de manière quantitative, la validité de l'équation d'évolution `longues ondes' (ou équation de Benney) pour l'épaisseur du film h, en y incluant l'effet thermocapillaire; et dans une seconde partie, il s'agit d'améliorer l'approche `intégrale couche limite' en combinant un développement en gradients avec une méthode aux résidus pondérés. Dans la première partie, nous étudions l'équation de Benney, dans son domaine de validité, dans le cas d'un chauffage inhomogène et périodique dans la direction de l'écoulement. Cela induit des déformations permanentes de la surface libre avec un accroissement du transfert de chaleur dans les régions où le film est plus mince, mais aussi en moyenne. Un chauffage inhomogène modifie également la nature des solutions d'ondes progressives pour des gradients de températures modérés et conduit même à leur suppression pour des gradients de températures plus importants. De plus, ceux-ci, lorsqu'ils sont par exemple positifs le long de l'écoulement, produisent des épaississements localisés du film qui peuvent à leur tour devenir instables par rapport à des perturbations suivant la direction transverse à l'écoulement. Ce dernier s'organise alors sous forme d'une structure en rivulets. Le mécanisme de cette instabilité est élucidé via une analyse énergétique des perturbations. Les principales caractéristiques des structures en rivulets sont décrites expérimentalement et retrouvées par l'intermédiaire de simulations numériques. Dans la seconde partie, nous dérivons une famille de modèles valables pour des nombres de Reynolds plus grands que l'équation de Benney, qui prennent en compte les effets visqueux et inertiels du second ordre. Nous élaborons ensuite une stratégie pour sélectionner le modèle optimal en fonction de ses propriétés de stabilité linéaire et de l'existence de solutions non-linéaires (ondes solitaires), et ce pour la gamme de paramètres la plus large possible. Ce modèle -- appelé modèle réduit -- est un système de trois équations d'évolution couplées pour l'épaisseur locale de film h, le débit local q et la température de surface Ts. Les solutions de ce modèle indiquent que l'interaction des modes hydrodynamiques et thermocapillaires n'est pas triviale, spécialement dans le domaine des ondes solitaires de grande amplitude. Finalement, l'évolution tri-dimensionnelle des solutions du modèle réduit en présence d'un forçage périodique ou d'un bruit se compare favorablement aux données expérimentales disponibles en conditions isothermes, ainsi qu'aux simulations numériques directes en conditions non-isothermes

Cette thèse est consacrée à trois différentes équations d’évolution non-linéaires dans le cadre de mécanique des fluides : le système fluide-solide, le système de Boussinesq et un modèle de films liquides. Pour le système fluide-solide, nous étudions l’évolution d’un petit solide en mouvement dans un fluide newtonien incompressible dans le cas où l’obstacle se contracte vers un point. En supposant que la densité du solide tend vers l’infini, nous montrons la convergence des solutions du système fluide-solide vers une solution des équations de Navier-Stokes dans $\mathbb{R}^d$ , avec $d^2$ et 3. Pour le problème de convection, nous travaillons sur l’unicité des solutions ‘mild’ du système de Boussinesq et généralise de plusieurs manières différentes des résultats classiques d’unicité pour les équations de Navier-Stokes. Dans la dernière partie, nous exposons nos contributions à l’étude des interface 2D de films liquides en dimension trois. Nous montrons qu’une variante 2D, non-local, de l’équation de Kuramoto-Sivashinsky admet un attracteur globale compact et obtenons enfin une majoration du nombre d’oscillations spatiales des solutions / This thesis is devoted to three different non-linear evolution equations in fluid mechanics : the fluid-solid system, the Boussinesq system and a falling films model. For the fluid-solid system, we study the evolution of a small moving solid in incompressible viscous fluid in the case the obstacle converges to a point. Assuming that the density of the solid tends to infinity, we prove that the rigid body has no influence on the limit equation by showing the convergence of solutions of the fluid-solid system towards to a solution of the Navier-Stokes equations in the full $\mathbb{R}^d$ , avec $d^2$ et 3. For the convection problem, we provide several uniqueness classes on the velocity and the temperature and generalize some classical uniqueness result for ‘mild’ solutions of the Navier-Stokes equations. We then work on a falling films model in three dimensions (2D interface). We show that a non-local variant of the Kuramoto-Sivashinsky equation admits a compact global attractor and we study the number of spatial oscillations of the solutions

This thesis deals with the dynamics of a thin liquid film falling down a heated plate. The heating yields surface tension gradients that induce thermocapillary stresses on the free surface, thus affecting the stability and the evolution of the film. Accounting for the coherence of the flow due to viscosity, two main approaches that reduce the dimensionality of the original problem are usually considered depending on the flow rate (as measured by the Reynolds number): the `long wave' asymptotic expansion for small Reynolds numbers and the `integral boundary layer' approximation for moderate Reynolds numbers. The former suffers from singularities and the latter from incorrectness of the instability threshold for the occurrence of hydrodynamic waves. Thus, the aim of this thesis is twofold: in a first part, we define quantitatively the validity of the `long wave' evolution equation (Benney equation) for the film thickness h including the thermocapillary effect; and in a second part, we improve the `integral boundary layer' approach by combining a gradient expansion to a weighted residual method. <p>In the first part, we further investigate the Benney equation in its validity domain in the case of periodically inhomogeneous heating in the streamwise direction. It induces steady-state deformations of the free surface with increased transfer rate in regions where the film is thinner, and also in average. The inhomogeneities of the heating also modify the nature of travelling wave solutions at moderate temperature gradients and allows for suppressing wave motion at larger ones.<p>Moreover, large temperature gradients (for instance positive ones) in the streamwise direction produce large local film thickening that may in turn become unstable with respect to transverse disturbances such that the flow may organize in rivulet-like structures. The mechanism of such instability is elucidated via an energy analysis. The main features of the rivulet pattern are described experimentally and recovered by direct numerical simulations.<p>In the second part, various models are obtained, which are valid for larger Reynolds numbers than the Benney equation and account for second-order viscous and inertial effects. We then elaborate a strategy to select the optimal model in terms of linear stability properties and existence of nonlinear solutions (solitary waves), for the widest possible range of parameters. This model -- called reduced model -- is a system of three coupled evolution equations for the local film thickness h, the local flow rate q and the surface temperature Ts. Solutions of this model indicate that the interaction of the hydrodynamic and thermocapillary modes is non-trivial, especially in the region of large-amplitude solitary waves.<p>Finally, the three-dimensional evolution of the solutions of the reduced model in the presence of periodic forcing and noise compares favourably with available experimental data in isothermal conditions and with direct numerical simulations in non-isothermal conditions.<p><p>------------------------------------------------<p><p>Cette thèse analyse la dynamique d'un film mince s'écoulant le long d'une paroi chauffée. Le chauffage crée des gradients de tension superficielle qui induisent des tensions thermocapillaires à la surface libre, altérant ainsi la stabilité et l'évolution du film. Grâce à la cohérence de l'écoulement assurée par la viscosité, deux approches permettant de réduire la dimensionnalité du problème original sont habituellement considérées suivant le débit (mesuré par le nombre de Reynolds): l'approximation asymptotique dite `longues ondes' pour les faibles nombres de Reynolds et l'approximation `intégrale couche limite' pour les nombres de Reynolds modérés. Cependant, la première approximation souffre de singularités et la dernière de prédictions imprécises du seuil de stabilité des ondes hydrodynamiques à la surface du film. Le but de cette thèse est donc double: dans une première partie, il s'agit de déterminer, de manière quantitative, la validité de l'équation d'évolution `longues ondes' (ou équation de Benney) pour l'épaisseur du film h, en y incluant l'effet thermocapillaire; et dans une seconde partie, il s'agit d'améliorer l'approche `intégrale couche limite' en combinant un développement en gradients avec une méthode aux résidus pondérés.<p>Dans la première partie, nous étudions l'équation de Benney, dans son domaine de validité, dans le cas d'un chauffage inhomogène et périodique dans la direction de l'écoulement. Cela induit des déformations permanentes de la surface libre avec un accroissement du transfert de chaleur dans les régions où le film est plus mince, mais aussi en moyenne. Un chauffage inhomogène modifie également la nature des solutions d'ondes progressives pour des gradients de températures modérés et conduit même à leur suppression pour des gradients de températures plus importants. De plus, ceux-ci, lorsqu'ils sont par exemple positifs le long de l'écoulement, produisent des épaississements localisés du film qui peuvent à leur tour devenir instables par rapport à des perturbations suivant la direction transverse à l'écoulement. Ce dernier s'organise alors sous forme d'une structure en rivulets. Le mécanisme de cette instabilité est élucidé via une analyse énergétique des perturbations. Les principales caractéristiques des structures en rivulets sont décrites expérimentalement et retrouvées par l'intermédiaire de simulations numériques. <p>Dans la seconde partie, nous dérivons une famille de modèles valables pour des nombres de Reynolds plus grands que l'équation de Benney, qui prennent en compte les effets visqueux et inertiels du second ordre. Nous élaborons ensuite une stratégie pour sélectionner le modèle optimal en fonction de ses propriétés de stabilité linéaire et de l'existence de solutions non-linéaires (ondes solitaires), et ce pour la gamme de paramètres la plus large possible. Ce modèle -- appelé modèle réduit -- est un système de trois équations d'évolution couplées pour l'épaisseur locale de film h, le débit local q et la température de surface Ts. Les solutions de ce modèle indiquent que l'interaction des modes hydrodynamiques et thermocapillaires n'est pas triviale, spécialement dans le domaine des ondes solitaires de grande amplitude. Finalement, l'évolution tri-dimensionnelle des solutions du modèle réduit en présence d'un forçage périodique ou d'un bruit se compare favorablement aux données expérimentales disponibles en conditions isothermes, ainsi qu'aux simulations numériques directes en conditions non-isothermes<p> / Doctorat en sciences appliquées / info:eu-repo/semantics/nonPublished