Modeling and simulation of population balances for particulate processes

This work focuses on the modeling and numerical approximations of population balance equations (PBEs) for the simulation of different phenomena occurring in process engineering. The population balance equation (PBE) is considered to be a statement of continuity. It tracks the change in particle size distribution as particles are born, die, grow or leave a given control volume. In the population balance models the one independent variable represents the time, the other(s) are property coordinate(s), e.g., the particle volume (size) in the present case. They typically describe the temporal evolution of the number density functions and have been used to model various processes such as granulation, crystallization, polymerization, emulsion and cell dynamics. The semi-discrete high resolution schemes are proposed for solving PBEs modeling one and two-dimensional batch crystallization models. The schemes are discrete in property coordinates but continuous in time. The resulting ordinary differential equations can be solved by any standard ODE solver. To improve the numerical accuracy of the schemes a moving mesh technique is introduced in both one and two-dimensional cases ...

Optimum Design of Electromagnets for Magnetic Levitation of Transport Systems based on the Inverse Problem Solutions

Article is devoted to design of optimum electromagnets for magnetic levitation of transport systems. The method of electromagnets design based on the inverse problem solution of electrical equipment is offered. The method differs from known by introducing a stage of minimization the target functions providing the stated levitation force and magnetic induction in a gap, and also the mass of an electromagnet. Initial values of parameters are received, using approximate formulas of the theory of electric devices and electrical equipment. The example of realization of a method is given. The received results show its high efficiency at design. It is practical to use the offered method and the computer program realizing it as a part of system of the automated design of electric equipment for transport with a magnetic levitation.