The paper presents an algorithm for the construction of an approximation of a highly nonlinear current-flux characteristic of a synchronous reluctance machine. Such an approximation is required in a Hamiltonian model of an electric machine and the constructed approximation is suited to be used in such a model. It employs a simplicial approximation based on irregular points sets in the spaces of currents and fluxes. The sets are constructed by the iterative insertion of new points. Initially the sets contain an arbitrarily small number of elements. The insertion is based on an approximation error calculation. Based on the sets containing possibly small number of elements, the proposed procedure leads to smooth and precise approximation. Due to the nonlinearity of the approximated characteristics, ambiguities can occur. A method for the triangulation refinement of the sets of currents and fluxes that eliminates them is also presented. In the paper, a reluctance machine model using the constructed approximation is described and compared with a model using the approximation based on regular sets.

The whirlpool separator, used for hot trub separation, is prevalent in the brewing industry. It is a kind of a hydrocyclone inside of which a tea leaf effect occurs, which is sediment accumulation into a cone shape at the central part of the tank’s bottom. This manner of sediment accumulation is caused by the secondary flow occurring in the so-called Ekman boundary layer. This article is a summary of the research, which has been conducted for many years and involved observation, simulation and experimental research on the recognition and formation of the secondary flow accumulating the sediment cone. Secondary flows occurring in a whirlpool were identified through CFD simulation and PIV experiments, and are presented in this paper. Based on their location and direction, an attempt to determine their impact on the separation process taking place in the whirlpool has been made. The secondary flow identification methods proposed in this paper can be successfully applied in other solutions, e. g. structural ones, which involve rotational-flow-based separation.