Development of topological optimization schemes controlling the trajectories of multiple particles in fluid

Abstract

This paper describes the development of a new topology optimization framework that controls, captures, isolates, switches, or separates particles depending on their material properties and initial locations. Controlling the trajectories of particles in laminar fluid has several potential applications. The fluid drag force, which depends on the fluid and particle velocities and the material properties of particles, acts on the surfaces of the particles, thereby affecting the trajectories of the particles whose deformability can be neglected. By changing the drag or inertia force, particles can be controlled and sorted depending on their properties and initial locations. In several engineering applications, the transient motion of particles can be controlled and optimized by changing the velocity of the fluid. This paper presents topology optimization schemes to determine optimal pseudo rigid domains in fluid to control the motion of particles depending on their properties, locations, and geometric constraints. The transient sensitivity analysis of the positions of particles can be derived with respect to the spatial distributed design variables in topology optimization. The current optimization formulations are evaluated for effectiveness based on different conditions. The experimental results indicate that the formulations can determine optimal fluid layouts to control the trajectories of multiple particles.

A new density filter for pipes for fluid topology optimization

“…2018; Andreasen 2020; Picelli et al. 2020; Yoon 2020; Yoon & So 2021). In Borrvall & Petersson (2003), topology optimization was proposed to minimize the fluid energy dissipation in Stokes flow.…”

“…A variety of other fluid topology optimization schemes were reviewed in Chen (2016). Recently, topology optimization has been used to control particles suspended in fluid (Andreasen 2020; Yoon 2020; Yoon & So 2021; Yoon 2022; Choi & Yoon 2023). In Yoon (2020) and Andreasen (2020), a topology optimization was conducted to control particles in steady-state fluid, and the sensitivity was derived.…”

“…In Yoon (2020) and Andreasen (2020), a topology optimization was conducted to control particles in steady-state fluid, and the sensitivity was derived. Multiple particles in fluid were controlled through topology optimization using the SHAKE algorithm (Yoon & So 2021). The topology optimization of particles in unsteady fluid flow was presented in Yoon (2022).…”

“…As stated above, fluid topology optimization is an actively studied field. Among these investigations, the new density filter can be applied to both traditional fluid topology optimization and fluid–particle topology optimization, which is also actively being researched (Andreasen 2020; Yoon 2020; Yoon & So 2021; Yoon 2022; Choi & Yoon 2023). Recent studies in the field of topology optimization have explored a wide range of areas, including the optimization of fluid systems and the control of particles within a fluid.…”

“…The Lagrangian is defined as follows: For the sensitivity analysis, the differentiation of the Lagrangian is evaluated as follows: After the arrangement of the terms in the (A14), the sensitivity can be summarized as (A15) with the adjoint sensitivity (A16) and (A17). See Yoon (2020) and Yoon & So (2021) for more detailed derivations For the numerical calculation of the time integration, the Newmark scheme (, ) is implemented in this paper. In the computation of the transient particle motion and the adjoint variable, the Newmark scheme is also employed.…”