Método de otimização topológica aplicado a escoamentos incompressíveis laminares transientes bidimensionais

Abstract

Since before the beginning of industrial activity in the world, the flow of fluids has played an important role in the development of humanity. The importance of the study and knowledge of the phenomena of fluid flow are fundamental for the development of new technologies in the field of engineering and medicine. This work aims to implement topological optimization in two-dimensional laminar transient flows. First, all the flow conditions and their variations in time are calculated from the Navier-Stokes equation, and the finite element method is implemented to approximate the differential equations. Then, the topological optimization process is started, using as objective the minimization of the pressure drop in a predefined domain, in which a model of material in porous medium is used; a method based on the objective function gradient is used to define the sensitivity analysis. The concept of permeability is seen throughout the development, in which each element is interpolated between fluid and solid in an iterative process, so that in each update the objective of reducing energy loss along a domain is optimized, in which the final result of this process is the optimal geometry for the proposed problem.