Topological optimization method considering compressible turbulent flow and fluid-structure interaction in the design of labyrinth seals

Abstract

This work is part of the scope of the thematic project Research Centre for Greenhouse Gas Innovation (RCG2I) (BG E&P Brasil (Shell) - CPE), proc. FAPESP nº 2020/15230-5 (05/2021 a 04/2026). The center, based on the University of São Paulo, is the result of a partnership with FAPESP in supporting high-level scientific research to study the use and applications involving Greenhouse Gases (GHG), such as methane (CH4) and carbon dioxide (CO2). Efficiency in transporting GHG using compressors must be improved, and in this way, the RCGI researchers are applying numerical analysis and optimization methods to improve the performance of compressor components such as labyrinth seal or impeller. Particularly, labyrinth seals optimization makes it possible to reduce GHG leakage, contributing to the reduction of CO2 emissions. Topology Optimization (TO) is gaining more and more space in industrial projects where the balance between maximizing performance and reducing costs is sought. This tool emerged in Engineering to improve mechanical system designs and has high freedom compared to shape and parametric optimizations, allowing non-intuitive solutions to be generated from certain initial domains. With the advancement of additive manufacturing technologies, in recent years, it was possible to manufacture complex projects created by the topology optimization method, making this method more relevant and present in different areas of Engineering, including flow machines. In the design of components flow machines, it is necessary to include in the topology optimization problem the compressibility and turbulence of the flow and the resonance frequency considering the fluid-structure coupling. Thus, in this work, the topology optimization method will be applied in the design of labyrinth seals subjected to compressible and turbulent rotary flow, considering a resonance frequency constraint based on fluid-structure coupling. Initially, the perfect gas model will be used. For that, a topology optimization formulation that considers turbulence for compressible flow will be used, based on the Topology Optimization of Binary Structures (TOBS) approach, which uses binary variables, allowing a clear definition of the solid-fluid interface. The multi-objective function will maximize pressure loss, or energy dissipation by the fluid, maximizing vorticity and entropy generation. The Finite Element Method (FEM) will be used to solve the equilibrium equations. The results to be presented will be the design of a Smart Labyrinth Seals for operation in subsonic and turbulent compressible regimes considering a resonance frequency restriction by the fluid-structure coupling. The results obtained can be manufactured by additive manufacturing techniques in a 3D printer. (AU)