(137b) A Comparison of Numerical Optimization Methods for Cyclone Separators

Authors: 
Martignoni, W. P., University of Blumenau
Luciano, R. D., University of Blumenau
Rosa, L. M. D., Regional University of Blumenau
Meier, H. F., University of Blumenau
Cyclone separators, more commonly known as cyclones, are widely used in the industry with multiple different purposes. The most common usage is in gas-solid separation. In order to find the best possible performance for this equipment, optimization procedures are conducted with mathematical models. Studies that employ optimization techniques to cyclones have demonstrated the existence of geometries with better characteristics than those with classical dimensions, such as the Lapple or Stairmand geometries. Although there are several mathematical optimization methods available in the literature, to the authors’ knowledge no comparison has been made to evaluate which optimization method is more adequate specifically for cyclone separators. This is important as some optimization methods will be significantly more efficient than others, depending on the topology of the objective function and on the computational cost of the model for the objective function utilized. As an example for cyclone separators, in cases where the computational cost of the mathematical model used is negligible (e.g. when using meta-models or simple empirical models), the number of objective function calls is not important as its impact on the total optimization time will most likely be negligible. On the other hand, if the model is costly such as in the computational fluid dynamics approach, the total time taken by the procedure will heavily depend on the function call efficiency of the optimization method. This paper therefore describes the comparison of different optimization methods for cyclone geometry optimization studies, evaluating mainly the number of objective function calls and the quality of the results. For this purpose, the semi-empirical model of Muschelknautz is chosen as mathematical cyclone model due to its reduced computational cost added to its good prediction and extrapolation capabilities. It is assumed that this model is sufficiently representative of the behavior that other good fidelity cyclone models will have with optimization methods. The six optimization methods compared include the derivative-free COBYLA, Nelder-Mead and Powell methods. Results show that, even with the relatively limited sample of six methods tested, the choice of optimization method has a big impact on the total computational time required by the complete procedure. Overall the COBYLA method is shown to be the indicated one for cyclone optimization studies, with consistent results and a low number of objective function evaluations required.