Topology optimization of fluid problems with a floating island exclusion constraint

Abstract

In topology optimization for fluid problems, the Brinkman model is commonly used to extend the Navier-Stokes equations to the entire fixed design domain. This model allows solutions where the solid domain exists in the fluid. However, such a structure implies a solid region floating in the fluid in a three-dimensional problem, and such a solution does not make engineering sense from a manufacturability standpoint. In this study, we propose an optimal design methodology for topology optimization of fluid problems with consideration of manufacturability introducing a fictitious physical model to realize constraints that prohibit floating solid regions. First, the formulation of governing equations of fluid and fictitious physical problem is discussed and a density-based topology optimization is described. Then, an optimization problem for Tesla valve, which is a check valve without moving parts, with a floating island exclusion constraint is formulated. As a numerical example, the proposed method provides two-dimensional optimal solutions which contain less floating solid regions compared to the original design.