Closed-Loop Liquid Film Control with a 3D Spectral Solver

Hot-dip galvanization is an ubiquitous process involved in steel production, which consists in covering the alloy with a layer of molten zinc. Gas jets impinge on the surface in order to control the thickness in a procedure called jet wiping, however this causes instabilities that ultimately manifest themselves as ondulations on the final product. Being able to accurately simulate how a jet perturbs the liquid zinc layer on an upward moving substrate is thus essential to obtain a thin and smooth final coating. A 3D spectral solver has been improved and tested, it takes into account the surface tension terms and it features a perfectly matched layer. Some efforts have been made to make the solver faster, while being able to simulate a larger number of jets. Jet wiping is not the only control method that has been investigated: since the liquid zinc is paramagnetic at those temperatures the flow could also be controlled by electromagnets. These simulations are at the basis of the final aim of this work, which is to optimize the controllers characteristics and behavior in order to obtain the desired final coating. A fast solver is an essential aspect when trying to run machine learning simulations of such systems, on this note another idea that could speed up the time integration involves computing the Jacobian of the system. Some steps have been taken into this direction but dealing with simplified equations.