Evaporation is used in the dairy industry to reduce the production costs of powder production (including milk powder) as it is more energy efficient to remove water by evaporation than by drying. There are significant economic reasons why gaining a greater understanding of the complex interactions occurring between the liquid and vapour phases in evaporators is advantageous. The multiphase flows in industrial dairy falling film evaporators were studied. Several computational fluid dynamic (CFD) models were created using Ansys CFX 10. Two case studies were chosen. The first case involved modelling the dispersed droplets that require separation from the water vapour evaporated from the feed of the evaporator. The CFD results were able to show that fouling was not caused by a lack of separation. The predicted separation agreed with experimental measurements. The atomisation process was found to be critical in the prediction of the separation. The atomisation process is not well understood and introduced the greatest error to the model. A plug flow assumption is currently used as a basis for the design the separators. The CFD solutions found no validity to this assumption. The second case study aimed to model and solve the distribution of the feed into the heat transfer tubes at the top of the falling film evaporators. The goal of this study was to be able to accurately predict wetting of the tubes. The volume of fluid (VOF) method using the continuum surface force method (CSF) to account for surface tension was chosen to model the system. The poor curvature estimate of the CSF method was found to produce parasitic currents that limited the stability of the solutions. Small VOF timesteps prevented the solver from diverging and the parasitic currents would oscillate the interface around the correct location. The small timesteps required significantly more computational power than was available and the model for the distribution process could not be solved. The CSF VOF method showed considerable promise, particularly because it can predict free surface topography without user input. There are still questions about numerical creeping of films, but the method was able to correctly predict several different surface tension and contact angle dominated film flows expected to be needed to accurately model the distribution of the falling film evaporator. Validated solutions of jet, meniscus, sessile, "overfall" and 3-D weir models were obtained and these agreed with published results in literature. A 2-D weir solution showed qualitative agreement with the expected form of the film. A 2-D hydraulic jump model without surface tension was created and agreed with experimental work in the literature to within 22%. The 3-D hydraulic jump solution only showed partial agreement with published experimental, the solutions were not mesh independent and not well converged so few conclusions can be drawn. The solutions of a rivulet model showed qualitative similarities with experimental work. The predicted wetting rate did not agree with values in the published literature because the spatial domain modelled was believed to be too narrow. An extended model of rivulet flow agreed with the idealised rivulet profile in literature and the predicted wetting rate agreed with some of the published literature. Again the solutions were not mesh independent so few conclusions can be confirmed.

Les travaux présentés dans ce manuscrit se concentrent sur l'approximation numérique des équations de la magnétohydrodynamique (MHD) et sur leur stabilisation pour des problèmes caractérisés par des nombres de Reynolds cinétique élevés ou par des écoulements multiphasiques. Nous validons numériquement un nouveau modèle de Simulation des Grandes Echelles (ou Large Eddy Simulations, LES), dit de viscosité entropique, sur des écoulements de cylindre en précession ou créés par des turbines contra-rotatives (écoulement de Von Kármán). Ces études sont réalisées avec le code MHD SFEMaNS développé par J.-L. Guermond et C. Nore depuis 2002 pour des géométries axisymétriques. Ce code est basé sur une décomposition spectrale dans la direction azimutale et des éléments finis de Lagrange dans un plan méridien. Nous adaptons une méthode de pseudo-pénalisation pour prendre en compte des turbines en mouvement, ce qui étend le code SFEMaNS à des géométries quelconques. Nous présentons aussi une méthode originale d'approximation des équations de Navier-Stokes à densité variable qui utilise la quantité de mouvement comme variable et la viscosité entropique pour stabiliser les équations de la masse et du mouvement. / The investigations presented in this manuscript focus on the numerical approximation of the magnetohydrodynamics (MHD) equations and on their stabilization for problems involving either large kinetic Reynolds numbers or multiphase flows. We validate numerically a new Large Eddy Simulation (LES) model, called entropy viscosity, on flows driven by precessing cylindrical containers or counter-rotating impellers (Von Kármán flow). These studies are performed with SFEMaNS MHD-code developed by J.-L. Guermond and C. Nore since 2002 for axisymmetric geometries. This code is based on a spectral decomposition in the azimuthal direction and a Lagrange finite element approximation in a meridian plane. We adapt a pseudo-penalization method to report the action of rotating impellers that extends the range of SFEMaNS's applications to any geometry. We also present an original approximation method of the Navier-Stokes equations with variable density. This method uses the momentum as variable and stabilizes both mass and momentum equations with the same entropy viscosity.