Topology optimization of passively moving rigid bodies in unsteady flows

TL;DR

This paper introduces a topology optimization framework for passively moving rigid bodies in unsteady flows, coupling fluid dynamics with rigid-body motion to optimize shapes for fluid-force-induced movement.

Contribution

It presents a novel passive motion-based topology optimization method, coupling fluid-structure interaction with shape optimization for unsteady flow scenarios.

Findings

Optimized shapes effectively harness fluid forces for passive movement.

The method successfully handles 2D and 3D problems with translational and rotational motions.

Insights into the physical effectiveness and limitations of the optimized designs.

Abstract

This study proposes the topology optimization method for moving rigid bodies subjected to forces from fluid flow, such as sails and turbines, with an unsteady time-dependent formulation. Unlike existing topology optimization frameworks in which rigid-body motion drives the flow, which is referred to as $\textit{active}$, the present study considers rigid-body motion induced by fluid forces, i.e., $\textit{passive}$. The equations of motion governing the rigid-body dynamics are solved in a coupled manner with the continuity equation and the momentum conservation equations. The rigid body is represented on a design grid that is separated from the analysis grid on which the state and adjoint fields are defined. After updating the rigid body motion, the body is mapped onto the analysis grid. The fluid equations are solved using the lattice kinetic scheme, an extended version of the lattice Boltzmann method, owing to its suitability for unsteady flows. Design sensitivities based on the adjoint variable method are presented and applied to two- and three-dimensional problems involving translational and rotational motions. The optimized shapes for each problem are discussed from a physical perspective and compared with a reference shape or their binarized counterparts, providing insights into the effectiveness of the proposed method as well as its limitations.