Método de otimização topológica aplicado a escoamentos incompressíveis integrando o método de volumes finitos (MVF) e o método de elementos finitos (MEF)

Abstract

This work proposes the creation of a new topological optimization methodology, applied to incompressible flows. This methodology proposes the union of the OpenFOAM software, which uses the finite volume method to solve the Navier-Stokes equation, together with the Topological Optimization Method (TOM), which uses the finite element method to solve it. . The optimization methodology is applied to the study and design of hydrodynamic components, such as diffusers, mixers and valves, seeking to optimize these equipment. Computational flow modeling tools, better known as Computational Fluid Dynamics (CFD), are tools with great ability to simulate with good accuracy, important features in the field of fluid mechanics, being a powerful tool that covers a wide range of areas industrial and non-industrial application. Another tool that has been gaining ground in several areas is the MOT. MOT is a computational method that allows to obtain an optimized design of a system, through the distribution of a limited amount of material in a given design domain. In this case, the MOT is applied to a porous solid domain, allowing to obtain the optimized topology (optimal shape) of a geometry where its final optimized shape is controlled by a variable that has a single value that varies from cell to cell of the mesh, updated throughout the iterative process, referred to as the design variables. As the advantages of using both tools are evident, the project presented here proposes to unite these tools in an optimization methodology, this methodology being applicable to cases where the flow is single-phase and incompressible. The implementation of the optimization methodology is carried out in the form of coupled computational routines, integrating the OpenFOAM software, which solves the Navier-Stokes equations, using the finite volume method, and the topological optimization method ( MOT), which uses the finite element method in its resolution. The MOT routine is executed in a generic copiler, which reads the Matlab language. As a way of attesting the effectiveness of the optimization methodology proposed here, the optimization methodology was applied to some geometries with already consolidated results in the area of topological optimization. The geometries used were the nozzle, elbow, double channel and multi-outlet devices. Comparing the results obtained by this project with the results found in the literature, the optimized geometries obtained showed a very close similarity with the literature, in some cases such as the nozzle, elbow and double channel the results were identical to the literature. In general, device optimization, using MOT together with the OpenFOAM software, proved to be viable and efficient in the process of optimizing hydrodynamic devices.