**1. Introduction**

84 Mass Transfer in Chemical Engineering Processes

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**6. References** 

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Drying is inherently a cross and multidisciplinary area because it requires optimal fusion of transport phenomena and materials science and the objective of drying is not only to supply heat and remove moisture from the material but to produce a dehydrated product of specific quality (Mujumdar, 2004)[1]. There are two main modes of drying used in the heat drying or pelletization processes; namely, direct and indirect modes. Each mode of drying has its merits and disadvantages and the choice of dryer design and drying method varies according to the nature of the material to be handled, the final form of the product, and the operating and capital cost of the drying process.

The drying of various materials at different conditions in a wide variety of industrial and technological applications is a necessary step either to obtain products that serve our daily needs or to facilitate and enhance some of the chemical reactions conducted in many engineering processes. Drying processes consume large amounts of energy; any improvement in existing dryer design and reduction in operating cost will be immensely beneficial for the industry.

With the advance in technology and the high demands for large quantities of various industrial products, innovative drying technologies and sophisticated drying equipment are emerging and many of them remain to be in a developmental stage due to the ever increasing presence of new feedstock and wetted industrial products. During the past few decades, considerable efforts have been made to understand some of the chemical and physical changes that occur during the drying operation and to develop new methods for preventing undesirable quality losses. It is estimated that nearly 250 U.S. patents and 80 European patents related to drying are issued each year (Mujumdar, 2004)[1]. Currently, the method of drying does not end at the food processing industry but extends to a broad range of applications in the chemical, biochemical, pharmaceutical, and agricultural sectors. In a paper by Mujumdar and Wu (2008)[2], the authors emphasized on the need for cost effective solutions that can push innovation and creativity in designing drying equipment and showed that a CFD approach can be one of these solutions. The collective effort of their research work along with other researchers in the drying industry using mathematical

Numerical Simulation of Pneumatic and Cyclonic Dryers Using Computational Fluid Dynamics 87

As for the heat- and mass-transfer correlations used in commercial CFD packages, very few are provided and the implementation of modified correlations or newly added ones to those already presented or provided by a commercial software demands the need for user defined function subroutines (UDF). This method can become very complicated and usually require many hours of coding and debugging. Although the heat-transfer model capabilities are well improved and capture the heat-transfer mechanism to a reasonable extent, average Nusselt number correlations are used instead of local values. This in turn, reduces the accuracy of the solution results. Additionally, the nature of the CFD equations is approximated which captures the solution results based on approximated assumptions and not on the exact solutions. From a mass-transfer capabilities point of view, mass-transfer models still lack robustness and are hardly included in the current available commercial software. The physics behind these transfer mechanisms is rich and complex, and not entirely captured by CFD methods due to its reliance on experimental observations and correlated equations. Thus, although *qualitative* predictions might be attainable to a

Multiphase flow models have improved substantially during the past years due to a better understanding of the physical phenomena occurring in multiphase flow systems. An extensive research has also led to a better understanding of the kinetic theory for granular flow and therefore, better implementation of the mathematical formulations pertaining to the flow, heat, and mass transfer mechanisms occurring in multiphase flow systems. The present numerical models for multiphase flows incorporate two approaches: the Eulerian-Eulerian approach, and the Eulerian-Lagrangian approach. A decision on whether the Eulerian-Eulerian or Eulerian-Lagrangian formulation of the governing equations is to be used should be made prior to the numerical solution, simply because each formulation has its limitations and constraints. Numerical predictions obtained from each formulation are not identical, and the choice of a convenient formulation for a specific model relies on whether a dense or dilute system is being considered and the objectives of the numerical study. For instance, if the objective of the numerical model is to follow the trajectories of individual particles, then the Eulerian-Lagrangian formulation appears more convenient for a dilute system (volume fraction of 1% and less). However, for a dense system, this approach is computationally expensive and time consuming and requires powerful and high-speed computers. On the contrary, the Eulerian-Eulerian formulation can handle both dense and dilute systems; however, it cannot predict the local behavior of particles in the

The theory behind the Eulerian-Eulerian approach is based on the macroscopic balance equations of mass, momentum, and energy for both phases. Eulerian models assume both phases as two interpenetrating continuum (Enwald et al., 1996)[5] and permit the solution of the Navier-Stokes equations with the assumption of incompressibility for both the gas and dispersed phases. The gas phase is the primary or continuous phase while the solid phase is termed as the dispersed phase. Both phases are represented by their volume fractions and are linked through the drag force in the momentum equation as given by Wen and Yu[6] correlation for a dilute system, Ergun[7] correlation for a dense system, and Gidaspow et al.[8], which is a combination of both correlations for transition and fluctuating systems. An averaging technique for the field variables such as the gas and solid velocities, solid volume

reasonable extent, *quantitative* predictions are still the biggest challenge.

**2. Numerical models** 

flow field.

modeling for the simulation of the drying mechanism in commercial dryers demonstrated the CFD capabilities and usefulness for the design and understanding of drying equipment. In a recent paper by Jamaleddine and Ray (2010)[3], the authors presented a comprehensive review on the application of CFD for the design, study, and evaluation of lab-scale and industrial dryers. The use of different numerical methods such as the finite element, finite volume, and finite difference were fully discussed. Numerical models such as the Eulerian-Eulerian and Eulerian-Lagrangian, used for gas–solid multiphase flow systems were also discussed along with their merits, disadvantages, and the scope of their applicability. The application of Kinetic theory approach for granular flow was also discussed. The authors pointed out some of the merits and shortcomings of CFD methods in general, and the drying application, in particular. They argued that a key advantage of CFD methods in evaluating drying systems is that it makes it possible to evaluate geometric changes (different feed point layouts such as multiple entry points) and operating conditions with much less time (faster turnaround time) and expense (flexibility to change design parameters without the expense of hardware changes) than would be involved in laboratory testing. A second advantage is that CFD provides far more detailed output information (suited for trouble-shooting) and far better understanding of the dryer performance than can be obtained in a laboratory environment. By interpreting graphical predictions from a CFD solution, local conditions of all phases in the drying chamber can be evaluated and crucial information related to the dispersion of particulate material can be gathered.

Despite the fact that CFD methods can offer valuable information and a great deal of insight of the process, the use of CFD methods requires considerable expertise. Lack of in-depth knowledge of the CFD methods and insufficient proficiency in utilizing commercial CFD software packages are major concerns for implementing CFD solutions in unknown and unconventional systems. In addition, CFD models have inherent limitations and challenges. Massah et al. (2000)[4] indicated some of the computational challenges of CFD modeling in the drying applications of granular material as follows. First of all, most processes involve solids with irregular shapes and size distribution, which might not be easily captured by some models. Second, Eulerian-Eulerian CFD methods rely on the kinetic theory approach to describe the constituent relations for solids viscosity and pressure, which are based on binary collisions of smooth *spherical* particles and do not account for deviations in shape or size distribution. Finally, very little is known about the turbulent interaction between different phases; thus, CFD models might not have the ability of presenting the associated drag models for a specific case study especially when solids concentration is high. In addition to the above, note that CFD simulations of three-dimensional geometries are computationally demanding and might be costly and although in some cases, the computational effort can be reduced by modeling a two-dimensional representation of the actual geometry (mostly for axisymmetric systems), the realistic behaviour of the simulated system might not be fully captured. Some geometrical systems cannot be modeled using the above simplification and thus, the computational effort becomes a must. This argument also applies to models adopting the Eulerian-Lagrangian formulation for *dense systems* which determine the trajectories of particles as they travel in the computational domain. In addition, formulas describing cohesion and frictional stresses within solids assembly are also not well established in these models. Finally, changes in particle size due to attrition, agglomeration, and sintering are difficult to account for.

As for the heat- and mass-transfer correlations used in commercial CFD packages, very few are provided and the implementation of modified correlations or newly added ones to those already presented or provided by a commercial software demands the need for user defined function subroutines (UDF). This method can become very complicated and usually require many hours of coding and debugging. Although the heat-transfer model capabilities are well improved and capture the heat-transfer mechanism to a reasonable extent, average Nusselt number correlations are used instead of local values. This in turn, reduces the accuracy of the solution results. Additionally, the nature of the CFD equations is approximated which captures the solution results based on approximated assumptions and not on the exact solutions. From a mass-transfer capabilities point of view, mass-transfer models still lack robustness and are hardly included in the current available commercial software. The physics behind these transfer mechanisms is rich and complex, and not entirely captured by CFD methods due to its reliance on experimental observations and correlated equations. Thus, although *qualitative* predictions might be attainable to a reasonable extent, *quantitative* predictions are still the biggest challenge.
