Level set-based topology optimization of steady state incompressible viscous flows under outflow rate inequality constraint

Abstract

Historically, fluidic devices such as switches, amplifiers, and oscillators, have an advantage, compared with electronic devices, in terms of maintenance-free operation and operating life. Therefore, prior to the great progress in electronic technologies that has occurred during the past several decades, the structure and function of fluidic devices were the subject of extensive research. In particular, the structures of these fluidic devices are often composed of complicated flow channel layouts. Recently, fluidic devices are again attracting significant attention, stimulated by progress in the development of MEMS technologies. In this study, to develop an energy-efficient structure for a MEMS-scale fluidic device, we apply a topology optimization method to an optimal design problem for a steady state incompressible viscous flow field. We use a level set-based topology optimization method incorporating the concept of the phase field method for the topology optimization so that clear boundaries between the solid and fluid domains are expressed in the optimal configurations. To define the topology optimization problem for a fluid regime, the expressions of the primary and adjoint problems are formulated concretely, to minimize viscous energy dissipation. Moreover, to ensure the intended design outflow rate at a designated outlet, the optimization problem includes an outflow rate inequality constraint in this paper. Following the concept of the standard adjoint variable method, a stable optimization process that satisfies the outflow rate inequality constraint is achieved. Two numerical examples, one for two-terminal and the other for multi-terminal flow, are provided to demonstrate the usefulness of the proposed level set-based topology optimization method.