Expensive multi-objective optimization of electromagnetic mixing in a liquid metal
- PDF / 2,697,059 Bytes
- 25 Pages / 439.37 x 666.142 pts Page_size
- 20 Downloads / 185 Views
Expensive multi‑objective optimization of electromagnetic mixing in a liquid metal Sebastian Prinz1 · Jana Thomann2 · Gabriele Eichfelder2 · Thomas Boeck1 · Jörg Schumacher1 Received: 12 December 2019 / Revised: 29 May 2020 / Accepted: 7 September 2020 © The Author(s) 2020
Abstract This paper presents a novel trust-region method for the optimization of multiple expensive functions. We apply this method to a biobjective optimization problem in fluid mechanics, the optimal mixing of particles in a flow in a closed container. The three-dimensional time-dependent flows are driven by Lorentz forces that are generated by an oscillating permanent magnet located underneath the rectangular vessel. The rectangular magnet provides a spatially non-uniform magnetic field that is known analytically. The magnet oscillation creates a steady mean flow (steady streaming) similar to those observed from oscillating rigid bodies. In the optimization problem, randomly distributed mass-less particles are advected by the flow to achieve a homogeneous distribution (objective function 1) while keeping the work done to move the permanent magnet minimal (objective function 2). A single evaluation of these two objective functions may take more than two hours. For that reason, to save computational time, the proposed method uses interpolation models on trust-regions for finding descent directions. We show that, even for our significantly simplified model problem, the mixing patterns vary significantly with the control parameters, which justifies the use of improved optimization techniques and their further development. Keywords Multi-objective optimization · Expensive optimization · Trust-region method
* Gabriele Eichfelder gabriele.eichfelder@tu‑ilmenau.de 1
Institut für Thermo‑ und Fluiddynamik, Technische Universität Ilmenau, Postfach 100565, 98684 Ilmenau, Germany
2
Institut für Mathematik, Technische Universität Ilmenau, Postfach 100565, 98684 Ilmenau, Germany
13
Vol.:(0123456789)
S. Prinz et al.
1 Introduction The use of electromagnetic induction to manipulate electrically conducting fluids is common in industrial applications, most notably in metallurgy, where timedependent magnetic fields are used to generate a stirring motion inside a molten metal that is supposed to mix additives. A homogeneous distribution of these additives is desired since it usually has a strong influence on the quality of the final ingot. The electromagnetic forcing is then achieved by rotating magnetic fields that are, for example, generated by electromagnets (Eckert et al. 2007; Davidson 2001; Ben-David et al. 2014). Permanent magnets offer an interesting alternative to resistive electromagnets since they do not require a continuous supply of electrical currents to generate the electromagnet’s magnetic field. A possible scenario of generating a stirring motion inside a liquid metal is either by moving one or more permanent magnets with respect to the liquid metal (Prinz et al. 2016; Rivero et al. 2016; Beltrán et al. 2010) or by injecting
Data Loading...
