Projeto de hidrociclones usando otimização robusta e evolução diferencial

Abstract

Hydrocyclones are versatile equipment largely used in industry to remove or classify a discrete phase (liquid or solid) mixed in a continuous liquid phase, based on a centrifugal field and on the discrete phase’s size and density. These equipment, which are constituted by a cylindrical and a conical part, promote the separation process by the action of a centrifugal force that comes from the rotational movement of the mixture and they have their performance closely related to their geometric dimensions. The performance of these separators can be measured by the responses total efficiency (ET), liquid ratio (RL) and Euler number (Eu), which represent the classification and concentration capacity and the energy cost, respectively. These three responses are, normally, conflicting objectives in hydrocyclones project, therefore it is necessary to use an optimization method to find out the configurations that produce good performance equipment in all three characteristics. Besides that, it’s important to adopt a robustness insertion criterion to reach reliable results, as hydrocyclone dimensions may not be totally accurate due to fabrication process limitations and wear that occur with operation. Faced with this, the purpose of this work is to project hydrocyclones with high classification and concentration capacity and low energy cost, using robust optimization by differential evolution technique basing on experimental data. The robustness introduction effect on the empirical models was evaluated through the comparison between the determination coefficient and objective function values of the nominal and robust models, besides the realization of a comparative analysis of models’ sensibility. It was verified that an augmentation in the robustness parameter (δ) makes the value of determination coefficient and objective function get worse, besides that it was noticed that the two types of model were equally sensitive to parameter perturbation when the value of δ was low, however when the value of δ was high, the robust model was less impaired than the nominal one. Both models were used to execute the hydrocyclone dimensions optimization, with and without robustness, considering four cases: maximum ET and minimum RL (case 1); maximum ET and minimum Eu (case 2); minimum RL and minimum Eu (case 3); maximum ET, minimum RL and minimum Eu (case 4). The obtained hydrocyclones presented satisfying values of the concerning responses, inside the desired range, it was also verified that the augmentation in robustness parameter value causes the robust curves to distance from the nominal ones and it reduces the objectives space, which means a smaller optimum hydrocyclones variety. Some of the optimum hydrocyclones were chosen to be used as reference in experimental tests with equipment of similar dimensions to theirs. The experimental result showed that the tested separators had a good performance.