Topology Optimization of Fluid Problems Considering Self-Supporting Property: 3D Design of Fluid Diodes
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Most research on topology optimization of fluid problems uses Brinkman penalization for design representation, in which the solid domains are represented as porous media by introducing a fictitious body force. Although this model has been used widely and successfully, there is no guarantee to obtain a solution with a self-supporting structure. In other words, a solution may include a floating solid island which is surrounded by the fluid entirely. Since these kinds of structures cannot be manufactured, development costs for design modification will be inevitable. Therefore, in this research, we propose a new formulation for density-based fluid topology optimization considering self-supporting property. The proposed methodology introduces a fictitious physical problem that originates from heat conduction problems to detect a floating solid island and imposes a geometric constraint for penalizing the floating regions. As an example of problems in which floating solids will emerge, the three-dimensional design problem of fluid diodes is investigated. We will show that our framework can obtain a solution with self-supporting property while the solution maintains its performance. Numerical computations are performed using OpenFOAM, a C++ toolbox for the finite volume method discretization.
