2. Numerical Modeling and Simulations

The design of engineering processes and equipment was traditionally accomplished in the past by experimentation, the construction of prototypes, and the building of pilot plants. These methods are time-consuming and labor-intensive and, in the beginning of the twenty-first century, have been proven to be very expensive. In the last two decades, modeling and computer simulations are increasingly used for the design of equipment and processes. The main advantage of computer simulations is that they require significantly less time and resources than the building, testing, and optimization of prototypes and pilot plants. The main disadvantage of simulations is that, oftentimes, the modeling does not accurately describe the actual engineering system to be built and some or all the testing results suffer from inaccuracies. This appears to be a temporary drawback to the simulation methods, because it is mainly due to the fact that numerical simulations are novel and recently developed methods in science and engineering. This chapter begins with sections on the desired attributes of mathematical models, in general, and continues with the four classifications of the coupling methods between the carrier fluid and the particles. A short description follows on the modeling of the flow of the carrier phase as laminar, turbulent, or transitional flow. A large part of the chapter is devoted to the methods of modeling of the suspension of particles as homogeneous mixture, point sources for momentum and energy transfer, discrete particles, or continua (two-fluid models). The complex interactions of particles with walls and the modeling of collision processes between particles and walls and between two or more particles are presented in detail. Finally the chapter examines critically the methods used most frequently for the numerical treatment of the boundaries in momentum and energy particle–fluid interactions, such as the Body-Fitted Coordinates, the Front Tracking Method, the Lattice Boltzmann Method, and the Immersed Boundary Method.