Wanger Institute for Sustainable Energy Research (WISER), Illinois Institute of Technology, Chicago, IL, USA
Received Date: May 09, 2013; Accepted Date: May 10, 2013; Published Date: May 13, 2013
Citation: Arastoopour H (2013) Computational Fluid Dynamics (CFD) Application in Fluid/Particle Flow Systems. J Powder Metall Min 2:e110. doi: 10.4172/2168-9806.1000e110
Copyright: © 2013 Arastoopour H. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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The widespread industrial application of fluid/particle flow systems demands an increase in the overall development and enhancement of such systems. In spite of recent advances in computational capability, development of more general simulations, and design and scale-up tools for particle flow systems continues to pose a considerable challenge due to the complexity of flow pattern. Prior to the 1980s, research in fluid/ particle systems was mainly focused on the development of both overall flow measurements and the correlation and equations for the main flow parameter. During the last three decades, significant advances have been made in the development of Computational Fluid Dynamics (CFD) approach to fluid/particle flow systems. CFD approach is considered to be one of the major contributors to the Design and Scale-up and in turn economical feasibility of the processes deal with fluid/ particle flows. In addition, CFD has played a significant role in shortening the gap between fluid/ particle processes laboratory-scale and commercialscale. However, further research in the areas of reducing computational time and performing additional model verification through simulation of commercial-scale processes will be necessary to obtain successful widespread industrial application of a computational fluid dynamics approach to fluid/particle flow systems.
The first attempt in mathematical modeling of the fluid/particle flow systems based on CFD is attributed to [1,2] for developing Eulerian/ Eulerian two-fluid governing equations. Later on, several attempts were made to modify the one-dimensional flow equation and to simulate flow in a vertical pneumatic conveying system . Arastoopour et al.  considered particles of each size as a separate phase, developed an experimentally verified particle-particle collision equation, introduced it in one-dimensional equations, and successfully compared the calculated flow parameters with the experimental data for flow of dilute gas/particle systems. However, in a more concentrated gas/particle flow system, the radial distribution of phase velocities due to wall interaction becomes a contributing factor to the flow. This can be characterized by using a two- or three-dimensional fluid/particle flow models and realistic boundary conditions [5,6]. In fluid/particle flow systems, particles create structures including regions near the wall in the form of clusters or sheets. This is mainly attributed to significant particle collision and interaction that should be considered in the formulation of fluid/ particle flow equations. This finding motivated several investigators to develop a theory of particle interaction and collision based on the  kinetic theory approach [8-11]. The kinetic theory approach, which is based on the oscillation of the particles, uses a granular temperature equation to determine the turbulent kinetic energy of the particles, assumes a distribution function for instantaneous particle velocity, and defines a constitutive equation based on particle collision, interaction, and fluctuation . In fact, the kinetic theory approach for granular flow allows the determination of, for example, particle phase stress, pressure, and viscosity in place of the empirical equations [13,14]. Since the developmental stage of granular theory, there have been several modifications to the constitutive equations such as: Ocone et al. , who considered forces exerted between particles during sustained rolling and sliding contacts; Louge et al. , who considered effects of both gas turbulence and particle collision; and Kim and Arastoopour , who considered the cohesiveness of the particles according to the Geldart  classification and extended the kinetic theory model for cohesive particles. Jenkins and Mancini  extended the kinetic theory of dense gases to a binary mixture of idealized granular material for the low dissipation case. Iddir et al.  and Iddir et al.  then extended the kinetic theory for granular flow for mixtures of multi-type particles assuming a non-Maxwellian velocity distribution and energy non-equipartition. Each type of particle was considered as a separate phase with different velocity and granular temperature. Later, this model was incorporated in the MFIX Code  and used to study the flow of multi-type particles in the riser section of the circulating fluidized bed systems . However, further research is needed to extend the kinetic theory for particles of different shapes and surface properties, to develop more realistic boundary conditions for the particle phase, and to obtain a more accurate expression for interaction between fluid turbulence and particle fluctuation.
To account for continuous variation in particle size density distribution due to phenomena such as chemical reaction, agglomeration, breakage, attrition, and growth, with less required computational time for numerical simulation, a new approach to solve Population Balance Equations (PBE) linked with CFD is needed. PBE is a balance equation based on the number density function that accounts for the spatial and temporal evolutions of the particulate phase internal variable distribution function in a single control volume . This equation is an integro-differential equation that involves both integrals and derivatives of the distribution functions. The most promising method of solution at the present time for CFD/PBE equations is the method of moments. The method of moments [25,26] is based on solving the distribution function transport equation in terms of its lower order moments. Some of the variables in the population balance equation (PBE) need to be calculated from the CFD model and, in turn, solution of the population balance gives some of the phase properties needed in the CFD model. Therefore, PBE and CFD need to crosstalk via a two-way coupling. In recent years, [27,28] introduced a new version of method of moments called Finite size domain Complete set of trial functions Method of Moments (FCMOM). In FCMOM, the size distribution function is presented as an explicit series expansion by a complete system of orthonormal functions. This means no specific assumption for the size distribution function is needed using the FCMOM approach. However, further research is needed to develop more accurate models to account for variation of particle properties during the processes such as physical properties, rate of reaction, nucleation and growth, rate of breakage and attrition, and rate of agglomeration incorporated in the PBE equation. Furthermore, further research in obtaining more robust numerical schemes using the method of moments is needed for obtaining simulation of the entire three-dimensional process in less required computational time.
Another approach to simulate a gas/particle flow system is the Distinct Element Method, which is based on an equation of motion for each individual particle . Thus, in principle, individual particle size, shape, and density can be introduced directly into the equation without relying on theories, such as the kinetic theory, or correlations based on experimental data to provide closure for the governing equations. However, this approach requires huge computational time when many particles exist in a system such as a fluidized bed.
In summary, the computational fluid dynamics (CFD) approach has placed itself as an advanced tool for the simulation, design, and scale-up of fluid/particles processes that include chemical reaction, particle properties distribution variation, and heat and mass transfer. At the present time, the kinetic theory approach with experimentally verified interfacial forces and method of moments as a solution tool is the most promising method to describe chemical, material, and biological processes that include fluid/particle flows. To obtain realistic simulation and design parameters, three- dimensional transient numerical simulation of the entire system including the reactors, piping, valves, cyclones, and standpipes is essential. This requires a very powerful computational facility to perform the most efficient parallel processing calculations and robust numerical schemes for better and faster convergence. Future research topics in this area may include: further development of the constitutive equations for the particulate phase including the effect of particle shape, and development of more accurate models for particles variation properties such as physical properties, rate of reaction, nucleation and growth, rate of breakage and attrition, and rate of agglomeration. Further improvement in particle phase boundary conditions, interparticle forces, fluid/particle drag force, and turbulence interaction between fluid and particle phases could also be excellent future research topics in this area. In addition, more advanced research in numerical techniques, specifically in the method of moments and parallel processing of the CFD/PBE codes, is needed to obtain more realistic simulation of the entire three-dimensional process with complex geometry in a reasonable computational time.
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