Topology optimization method applied to the design of liquid flow channels with dispersed bubbles

Resumo

A novel topology optimization formulation for the design of channels considering two-phase flow is developed in the present study. The considered cases comprise steady-state laminar flow, consisting of a liquid phase with dispersed gas bubbles. The optimization problem consists in defining the flow channel of liquid with bubbles that minimizes an objective function, for instance, the energy dissipation. The design variables represent the Darcy’s forces in each point of the computational domain and are optimized in order to control the flow velocity. Bubbles can affect the flow field by variating the flow properties and causing flow separation. Thereby, changing the gas concentration by optimizing the flow path is useful in many engineering applications, such as turbomachines, heat exchangers, and chemical reactors. To simulate the dispersed two-phase flow, the two-fluid Euler-Euler model is applied, in which the two phases are treated as interpenetrating media, tracking the averaged concentration of the phases. Models of momentum exchange between phases are used to simulate the behavior of bubbles in a continuous approach. The governing equations are solved by the finite element method using the FEniCS open source platform. The optimization formulation is implemented using the same platform, with automatic differentiation to solve the adjoint problem for calculating the derivative and the interior point optimization algorithm to update the design variables. The results account for optimization examples to demonstrate the validity and applicability of this approach.