Hydrodynamic vortex separators (HDVSs) are used in wastewater treatment to separate solids from wastewater. The aim of this research is to devise a CFD-based methodology that optimises their performance through modification of their design. A validation study is performed to assess whether OpenFOAM can be used to reliably model the flow of water in an HDVS. The results of the simulations are compared with experimental readings, showing a good fit when the appropriate boundary layer height and turbulence model are used. The continuous adjoint method is employed to derive the adjoint equations, associated with the drift flux equations used to model the flow of wastewater. They are specialised to the typical boundary conditions of ducted flows and are coded using OpenFOAM. An optimal design is found for boundary conditions, corresponding to typical values used in practice, and is shown to improve the performance of a simplified initial design by 40%. This optimal design is subsequently subjected to a different hydraulic loading rate and dispersed-phase volume fraction at the inlet, to assess the performance variation in these circumstances. Though the optimal design removes all the solids when the dispersed-phase fraction is reduced at the inlet, initial results suggest that the design is sensitive to hydraulic loading rate and further tests are recommended before drawing more explicit conclusions. This is the first time the adjoint drift flux equations have been derived. It is also the first time they have been coded and applied to an HDVS to optimise its performance. The methodology developed in this thesis could be applied to any device that separates solids from liquid or two immiscible liquids, in order to optimise its performance.

La modélisation des systèmes mécatroniques nécessite le même type de méthodologie pour la conception et le prototypage de dispositifs mécatroniques. Une ingénierie unifiée et intégrée doit être déployée. Diverses approches sont actuellement proposées pour atteindre de la modélisation multi-physique comme la théorie des graphes, les approches équationnelles ou les techniques. Dans ce contexte, l’objectif de nos travaux de recherche est la conception d'une méthodologie appliquée aux modèles dynamiques multi-physiques à topologie dynamique. Pour une telle contribution, il est nécessaire de partir d’une approche existante. Cette approche porte sur la modélisation topologique puisqu’elle est basée sur les collections topologiques et les transformations. Cette approche topologique est utilisée pour modéliser les systèmes mécatroniques.Son point fort est la séparation de la topologie (loi d'interconnexion) et la loi de comportement (physique) qui permet la simplification de la modélisation de systèmes complexes que l'on peut décrire comme un ensemble d'interactions locales entre entités élémentaires. La thèse propose donc une nouvelle méthodologie nommée 4Mo(DS)2 qui se rapporte à la modélisation multi-niveaux, multi-domaines et multi-physiques basée sur des systèmes dynamiques qui ont des structures dynamiques. Cette méthodologie permet la modélisation topologique des modèles dynamiques multi-physiques à topologie dynamique pendant la phase de conception tout en prenant en compte les modifications topologiques, le contrôle et commande ainsi que l’intégration de la dimension deux dans leur structure topologique. / Mechatronic systems modelling requires the same type of methodology for the design and prototyping of mechatronic devices. Unified and integrated engineering must be deployed. Various approaches are currently proposed to achieve multi-physics modeling such as graph theory, equational approaches or techniques. In this context, the objective of our research work is the design of a methodology applied to dynamic multi-physical models with dynamic topology. For such a contribution, it is necessary to start from an existing approach. This approach focuses on topological modelling since it is based on topological collections and transformations. This topological approach is used to model mechatronic systems.Its strong point is the separation of topology (interconnection law) and behavior law (physical) which allows the simplification of the modeling of complex systems that can be described as a set of local interactions between elementary entities. The thesis therefore proposes a new methodology named 4Mo(DS)2 which relates to multilevel, multi-physical and multi-domain modeling based on dynamic systems that have dynamic structures. This methodology allows the topological modeling of dynamic multi-physical dynamic topology models during the design phase while taking into account topological modifications, control and command as well as the integration of dimension two into their topological structure.