Discrete Topology Optimization of Stepped Labyrinth Seal using Velocity Components within Laminar Swirl Flow Regime

Resumo

Recent improvements in computational tools and additive manufacturing techniques have expanded possibilities for fluidic device design, particularly in an industrial context. Among these innovations, gas labyrinth seals have emerged as promising passive mechanisms for sealing, crucial for maintaining the performance of rotating machinery and mitigating environmental impact. However, the systematic labyrinth seal design is challenging and requires additional methodology tailoring of the traditional approaches. These challenges include: i) the risk of converging to suboptimal solutions due to the closure of fluid inlets/outlets when maximizing the energy dissipation directly, and ii) the absence of labyrinth-like flow path when using full fluid initial guess for the design domain. This paper aims to address these key challenges by using discrete topology optimization. We demonstrate the potential of the TOBS (Topology Optimization of Binary Structures) method to provide innovative designs and solve the aforementioned issues. One of the main advantages of this discrete approach is the explicitly defined domains during the entire optimization due to the absence of intermediate density values (e.g., gray-scale region), consequently easing the prototype manufacturing and allowing straightforward boundary identification. In addition, the material interpolation models can be expressed in linear form without penalty factors due to the discrete nature of the optimization problem formulation. In this work the topology optimization problem is to maximize the flow velocity components subjected to a volume fraction constraint assuming incompressible laminar swirl flow with test bench dimensions. The sensitivity field of objective functions is computed via the adjoint method through automatic differentiation. In our approach, the fluid flow governing equations are solved in the inertial reference frame using the Finite Element Method and the optimization problem via Integer Linear Programming. Discretization of the problem involves utilizing adaptive smoothed boundary fitting mesh captured via isosurface techniques. Finally, the optimized topologies are demonstrated for a stepped seal and compared with benchmark configurations from literature.