Solidification of Double-Diffusive Flows Using Thermo-Magneto-Hydrodynamics and Optimization

Abstract

A multilevel approach, based on our previously developed hybrid optimizer, is presented for solving a problem that consists of a solidifying thermosolutal flow in a square cavity subjected to variable thermal and magnetic boundary conditions. The objective is to reduce the standard deviations of the vorticity within the liquid region as well as reduce the liquid area over the entire domain. Thus, the optimization problem is formulated to simultaneously find thermal and magnetic boundary conditions that must induce such prescribed solute concentration and velocity profiles. The optimizer is based on several deterministic and evolutionary techniques with automatic switching among them, combining the best feature of each algorithm. A radial basis function based response surface scheme is implemented to reduce the overall computing time.

Keywords:

• Flow control
• Hybrid optimization
• Inverse problems
• Magnetohydrodynamics
• Materials processing
• Numerical methods
• Smart manufacturing
• Solidification
• Solute transport

ACKNOWLEDGMENTS

This work was partially funded by CNPq (agency for the fostering of science from the Brazilian government). The first author is grateful also for the financial support obtained from Florida International University. Both authors are grateful for the partial financial support provided by the AFOSR grant FA9550-06-1-0170 monitored by Dr. Todd E. Combs and Dr. Fariba Fahroo and by the ARO grant 50486-MS-H monitored by Dr. William M. Mullins.