Topology optimization of fluid diodes based on integer linear programming.

• Autor(a) principal: Souza, Bruno Caldas de
• Data de Publicação: 2021
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: https://www.teses.usp.br/teses/disponiveis/3/3152/tde-18052021-134145/
• topic: Dinâmica dos fluidos (Simulação); Diodos fluídicos; Fenics; Finite element method; Fluid Diodes; Juntas labrintos; Labyrinth seal; Método dos elementos finitos; Métodos topológicos (Otimização); TOBS; Topology optimization

Fluid diodes are devices that inhibit the fluid to flow from one environment to another and allowing in some cases the opposite direction to occur. A well-known example is the Tesla valve. There is a particular type of fluid diode used to minimize leakage in turbines and compressors called labyrinth seals, which optimization can bring major improvement related to CO2 and CH4 emissions. Topology optimization is a powerful tool, which has already been applied to design some plane 2D fluid diodes. So, with this environmental issue in mind and in order to find new efficient labyrinth seals, the scope of this work is to develop a new formulation of topology optimization to obtain innovative and non-intuitive designs of fluid diodes focused on labyrinth seals. As a first contribution, the formulation of topology optimization proposed in this work is based on the integer linear programming. In the current implementation of topology optimization for fluids considering density methods, there are essentially two problems. First, the gray scale in the result makes it difficult to identify the fluid mesh outline, which can be a problem in some applications and also during the optimization process. Second, even for low Reynolds flow design problems, a continuation scheme of the material model penalty parameters is necessary to avoid gray scale and to obtain clear solid/fluid boundaries. This work proposes a new methodology that solves these two problems, that is, it avoids gray scale and obtains clearer solid and fluid boundaries. In the labyrinth seal design, on the other hand, it presents fixed parts (stator) and rotational parts (axis), as well as a second contribution, a classification algorithm is implemented to identify parts belonging to the shaft and, thus, apply rotational boundary conditions to every solid that appears during topolgy optimization. Finally, an objective function considering some fluid-structure interaction is defined to prevent the appearance of islands, which are very common in this type of project, however, they are not acceptable in axysymmetric designs of labyrinth seals. Thus the defined multi-objective function contains terms of dissipation energy, vorticity and structural functions. Regarding the geometry of the labyrinth seal, the problem is modeled with a 2D swirl finite element model. The calculation of sensitivities and the linearization of the problem for optimization in integer variables is described. Numerical implementation is done in Python with the aid of finite element libraries (FEniCS) to calculate the direct and adjoint problem. The IBM proprietary optimization library (CPlex) is used as an optimization algorithm. As results, optimized labyrinth seal designs obtained according to the project objective are presented, varying the rotation, leakage patterns and aspect ratio of the project domain.