Crystal size distribution dynamics in a classified crystallizer: Part I. Experimental and theoretical study of cycling in a potassium chloride crystallizer
Cycles in particle size and slurry density were experimentally observed in a mixed suspension, potassium chloride crystallizer equipped with a fines dissolver and having nonrepresentative product withdrawal. Cycling behavior was achieved with a product crystal elutriator but was also observed with changes in the orientation of the product removal tube, indicating that instability was induced by product classification. Simulation of the unstable runs with a dynamic model showed crystal size distribution (CSD) limit cycles of similar period using nucleation kinetics and process conditions measured experimentally. The computer simulation showed no tendency towards cycling for the stable runs.
Battery models play important roles in battery manufacturing, design, safe operation, and many of its applications, such as in providing power sources of electric vehicles due to the high energy density, long life, and high cell voltage. Unlike the detection of impedance spectrum in a short linear interval, the I-V characteristic of lithium-ion batteries presents strongly nonlinearity such as the serious polarization in both ends of charging /discharging. To modeling the nonlinear characteristic of real battery accurately, this paper proposes a variable-order fractional equivalent circuit model that provides a novel and effective trade-off of model accuracy and simplicity. The proposed method is verified under the working conditions of pulse and constant current charging /discharging, where the maximum model error is less than 1.8%.