Multi-objective Bayesian shape optimization of an industrial hydrodynamic separator using unsteady Eulerian-Lagrangian simulations

Abstract

Abstract The shape of a hydrodynamic particle separator has been optimized using a parallelized and robust formulation of Bayesian optimization, with data from an unsteady Eulerian flow field coupled with Lagrangian particle tracking. The uncertainty due to the mesh, initial conditions, and stochastic dispersion in the Eulerian-Lagrangian simulations was minimized and quantified. This was then translated across to the error term in the Gaussian process model and the minimum probability of improvement infill criterion. An existing parallelization strategy was modified for the infill criterion and customized to prefer exploitation in the decision space. In addition, a new strategy was developed for hidden constraints using Voronoi penalization. In the approximate Pareto Front, an absolute improvement over the base design of $$14\%$$ 14 % in the underflow collection efficiency and $$10\%$$ 10 % in the total collection efficiency was achieved, which resulted in the filing of a patent.* The corresponding designs were attributed to the effective distribution of residence time between the trays via the removal of a vertical plume. The plume also reduced both efficiencies by creating a flow path in a direction that acted against effective settling. The concave down and offset tray shapes demonstrated the value of Bayesian optimization in producing useful and non-intuitive designs. Graphic abstract