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## Über dieses Buch

This book concerns the most up-to-date advances in computational transport phenomena (CTP), an emerging tool for the design of gas-solid processes such as fluidized bed systems. The authors examine recent work in kinetic theory and CTP and illustrate gas-solid processes’ many applications in the energy, chemical, pharmaceutical, and food industries. They also discuss the kinetic theory approach in developing constitutive equations for gas-solid flow systems and how it has advanced over the last decade as well as the possibility of obtaining innovative designs for multiphase reactors, such as those needed to capture CO2 from flue gases. Suitable as a concise reference and a textbook supplement for graduate courses, Computational Transport Phenomena of Gas-Solid Systems is ideal for practitioners in industries involved with the design and operation of processes based on fluid/particle mixtures, such as the energy, chemicals, pharmaceuticals, and food processing.

## Inhaltsverzeichnis

### Chapter 1. Conservation Laws for Multiphase Flow

Abstract
In this chapter, the derivation of the basic equations for conservation of mass, momentum, and energy for a multiphase system is presented. It is assumed that the systems for which conservation equations are derived consist of a sufficient amount of disperse phases (e.g., particles) that discontinue and can be smoothed out. This means derivatives of various properties exist and are continuous. Thus, for any property per unit volume, the Reynolds transport theorem is used.
Hamid Arastoopour, Dimitri Gidaspow, Emad Abbasi

### Chapter 2. Conservation and Constitutive Equations for Fluid–Particle Flow Systems

Abstract
Chapter 1 presented general forms of conservation equations; this chapter presents mass and momentum conservation equations and constitutive and boundary conditions for fluid–particle flow systems. The conservation equations and constitutive relations are general and can be applied to all regimes of fluid–particle flow from a very dilute particle volume fraction to the packed bed regime.
The background and fundamentals of the kinetic theory approach for derivation of the conservation and constitutive equations are presented for the regimes when particle collision is dominant.
In addition, the kinetic theory approach has been extended to multi-type particulate flow, assuming a non-Maxwellian velocity distribution and energy non-equipartition. Each group or type of particle is represented by a phase, with an average velocity and a granular temperature. Then, the multi-type governing equations are successfully applied to describe numerical simulation of a simple shear flow of a mixture of two particle groups with different properties.
In dense granular flows, in addition to the kinetic and collisional stresses (described by the kinetic theory), the frictional stresses must be considered, which, in dense flow of particles, have a dominant effect. Thus, the frictional behavior of granular matter is also discussed based on soil mechanics principles. Finally, the generalized forms of governing equations and constitutive relations for all particle phase flow regimes are presented in Tables 2.1 and 2.2.
Hamid Arastoopour, Dimitri Gidaspow, Emad Abbasi

### Chapter 3. Homogeneous and Nonhomogeneous Flow of the Particle Phase

Abstract
Gas–particle flows are inherently oscillatory, and they manifest in nonhomogeneous structures. Thus, if one sets out to solve the microscopic two-fluid model equations for gas-particle flows, grid sizes of less than 10-particle diameter become essential. For most devices of practical (commercial) interest, such fine spatial grids and small time steps require significant computational time. Thus, the effect of the large-scale structures using coarse grids must be accounted for through appropriate modifications of the closures (i.e., drag model). Qualitatively, this is equivalent to an effectively larger apparent size for the particles.
In this chapter, two approaches are discussed that have gained significant attention in the literature: filtering (subgrid) and energy minimization multi-scale (EMMS).
Hamid Arastoopour, Dimitri Gidaspow, Emad Abbasi

### Chapter 4. Polydispersity and the Population Balance Model

Abstract
In this chapter, an introduction to the concept of polydispersity in multiphase systems and the numerical solution of coupled computational fluid dynamics (CFD) and population balance equation (PBE) using CFD computer codes are presented. PBE is a balance equation based on the number density function and accounts for the spatial and temporal evolutions of particulate phase internal variable distribution function in a single control volume. Solutions based on the different method of moments (MOM) are also presented. The Finite size domain Complete set of trial functions Method of Moments (FCMOM) and the implementation of FCMOM in a CFD code are discussed in more detail. Finally, the validation and verification of FCMOM for three processes of linear growth, homogeneous aggregation, and nonhomogeneous aggregation in emulsion flow are presented.
Hamid Arastoopour, Dimitri Gidaspow, Emad Abbasi

### Chapter 5. Case Studies

Abstract
In this chapter, three case studies are presented: the first case presents computational fluid dynamics (CFD) modeling and simulation of a pharmaceutical bubbling bed drying process. The mathematical model used in Case1 is composed of the continuity, momentum, energy, and species transfer equations to simulate the flow pattern and heat and mass transfer in the pharmaceutical drying processes based on bubbling fluidized beds. Case 2 presents CFD modeling and simulation of a reactive gas–solid system in the riser section of a circulating fluidized bed (CFB) reactor representing a CO2 capture process using solid sorbents. In Case 3, a two-way coupled computational fluid dynamics-population balance equation (CFD-PBE) is presented following the second case where the density distribution of the solid phase is changing due to the chemical reaction (i.e., carbon capture) between the solid and gas phases.
Hamid Arastoopour, Dimitri Gidaspow, Emad Abbasi

### Backmatter

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