**1. Introduction**

234 Computational Simulations and Applications

A spectral method DNS is carried in a channel reaction flow. The results are used for turbulent model research. It is shown that the ASSCM SGS model value is close to the exact

The ASOM RANS turbulent combustion model is tested by LES and DNS results. Though this model is simple, its value has same trend with the exact value and quite close to the exact value sometimes. It can give quick and roughly prediction for average parameters but

The correlations in turbulent combustion model are studied in DNS, the temperature fluctuation is very important. The RANS equations were modelled. The near wall damping

Colucci P J, Jaberi F A, Givi P. Filtered density function for large eddy simulation of

DesJardin P E, Frankel S H. Two-dimensional large eddy simulation of soot formation in the

Gao F, Obrien E E. A large-eddy simulation scheme for turbulent reacting flows. Phys Fluids

Giacomazzi E, Battaglia V, Bruno C. The coupling of turbulence and chemistry in a

James S, Jaberi F A. Large scale simulations of two-demensional nonpremixed methane jet

Jones W P. Large eddy simulation of turbulent combustion processes. Computer Physics

Kawamura H, Abe H, Shingai K. DNS of turbulence and heat transport in a channel flow

Renfro M W, Chaturvedy A, King G B. Comparison of OH time-series measurements and

Westbrook C K, Dryer F L. Simplified Reaction Mechanisms for the Oxidation of Hydrocarbon Fuels in Flames, Combust. Sci. Tech. 1981, 27(1-2): 31-43 Xu C, Toonder J M J, Nieuwstadt F T M, et al. Origin of high kurtosis levels in the viscous

Yaga M, Endo H, Yamamoto T, et al. Modeling of eddy characteristic time in LES for

Zhang Z S, Cui G X, Xu C X, Theory and modelling of turbulence, Beijing, Qsinghua

near-field of strongly radiating nonpremixed acetylene-air turbulent jet flame.

premixed bluff-body flame as studied by LES. Combustion and Flame, 2004,

with different Reynolds and Prandtl numbers and boundary conditions. In: Nagano Y, Hanjalic K, Tsuji, eds. 3rd Int. Symp. on Turbulence, Heat and Mass

large-eddy simulations in hydrogen jet flames. Combustion and Flame, 2004,

sublayer. Direct numerical simulation and experiments. Physics of Fluids, 1996,

calculating turbulent diffusion flame. International Journal of Heat and Mass

turbulent reacting flows. Physics of Fluids, 1998, 10(2):499~515

value mainly, so ASSOM model is reasonable again.

modification can improve the prediction ability of SGS model.

Combustion and Flame, 1999, 119:121~123

flames. Combustion and Flame, 2000, 123:465~487

Communications, 2002, 147:533~537

Transfer. Tokyo, 2000. 15~32

Transfer, 2002, 45:2343~2349

University Press, 2005

A, 1993, 5(6):1282~1284

138:320~335

139:142~151

8(7):1938~1944

not RMS value.

**7. References** 

Gas-solid fluidized beds are widely applied in chemical processes such as drying, combustion, synthesis of fuels, granulation, polymerization etc. They have several advantageous properties including; excellent heat and mass transfer, nearly isothermal conditions due to intense gas-solid mixing, large gas-solid surface area, smooth transport of solids, uniform solid product in batch processes, and possibility of continuous and largescale operations. On the other hand, these reactors have several drawbacks that provide a strong motivation for further studies and developments. These include; difficulty in scalingup and design, erosion of vessel and internals, formation of agglomerates, non-uniform products due to non-uniform solids residence time during continuous operation, and high particle entrainment. These drawbacks are bottlenecks for practitioners to reliably design and scale-up commercial fluidized bed reactors. The main reason for this is that the gassolid multiphase flow dynamics coupled with heat and mass transfer and chemical reactions that occur in these systems are very complex and not yet fully understood.

In bubbling gas-solid fluidized beds, bubble characteristics such as size, shape, velocity, distribution have a vital influence on the hydrodynamics of bed and hence on its performance as a chemical reactor and/or a heat exchange unit. The extent of gas-solid mixing and segregation, heat and mass transfer as well as reaction conversion are governed by the number, size and motion of bubbles passing through the bed (Kunii & Levenspiel, 1991). Therefore, fundamental understanding of the hydrodynamics of fluidized beds thereafter their heat and mass transfer as well as chemical conversion come only after a sound understanding of bubbling behaviour is achieved. However, prediction of bubble characteristics is extremely complex as bubbles can grow, coalesce, split or even disappear as they move from the distributor where they are formed to the top of the bed where they finally erupt. Moreover, bubble characteristics vary with geometric construction of the bed and operating conditions. In many applications, heat exchanger tubes are inserted to enhance the rate of heat and mass transfer and chemical conversion, control the operating temperature, promote good mixing and reduce gulf circulation of solids. In these systems, the bubbling behaviour is also strongly influenced by the geometry and arrangement of the internals (Yates et al., 1990; Hull et al., 1999; Asegehegn et al., 2011a). Therefore,

Numerical Simulation of Dense

be performed, using less computation time.

Chiesa et al., 2005; van der Hoef et al., 2008)

**2. The Eulerian two-fluid model** 

Kuipers & van Swaaij, 1998).

Gas-Solid Multiphase Flows Using Eulerian-Eulerian Two-Fluid Model 237

Practically the motion of gas-particle flow systems present in fluidized beds should be expressed at least by the Eulerian-Lagrangian approach with the Newtonian equations of motion for the suspended particles. However, when the system comprises a large number of closely spaced particles, as in the case of fluidized bed, the problem is far too difficult to allow direct solution by tracking individual particles. Despite the rapid growth in computer capacity, it is only possible to track less than 106 particles (much less than the practical number of particles found in industrial scale fluidized beds) using the DPM. Since both CPU time and the required memory scales linear with the number of particles, it is obvious that DPM simulations of engineering size fluidized beds are beyond the capability of commercially available computer facilities within the foreseeable future. Therefore, DPM is not a natural choice for hydrodynamic modelling of gas-solid systems. For practical purposes, it is necessary to seek some way of simplifying it so that it can be described by a relatively small number of partial differential equations. One way of simplifying this problem is to replace the point mechanical and fluid mechanical variables by an appropriate locally average value of the corresponding variables to formulate the integral balances for mass, momentum and energy for a fixed control volume containing both phases. Hence describing the motion of the fluid and particles as though they were interpenetrating continua (Anderson and Jackson, 1967). In such continuum model, the equations are a generalization of the Navier-Stokes equations for interacting continua. This means that instead of knowing the positions and velocities of each particle, only the volume fraction of each phase and the average volume flow pattern are known. Though the local instantaneous value of variables vary rapidly on a scale comparable with the particle spacing the averaged variables are smoothed by averaging over regions large compared with the particle spacing but small compared with the size of complete system. The main advantage of this model is that the averaging techniques allow us to use relatively coarser grids and longer time steps so that the computational effort is significantly reduced, hence larger scale simulations can

In fact, the continuum model suffers from some limitations in modelling of the gas-solid flow. It does not provide information about the hydrodynamics of individual particles and thus has limitations in predicting certain discrete flow characteristics such as particle size and density effect. Nevertheless, it remains the only feasible approach for performing parametric investigation and scale-up and design studies of industrial scale systems and dense gas-solid beds (van Wachem et al., 2001; van der Hoef et al., 2008). Detail comparisons of the DPM and the TFM can be found elsewhere in the literature (e.g., Gera et al., 1998;

Most literatures give tribute to the paper by Davidson (1961) as the first to apply the concept of hydrodynamic model in fluidized beds in his analysis of a single isolated bubble rising in an unbounded fluidized bed. However, Anderson & Jackson (1967) were the first to formulate the complete CFD TFM for gas-solid multiphase flows in the mid 60's. Since then many have made significant efforts to develop detailed microbalance models to study the complex hydrodynamics of gas-fluidized beds (e.g., Gidaspow, 1994; Enwald et al., 1996;

Owing to the continuum description of the particulate suspension, the TFM requires additional closure laws for the solid rheology. Two of the most important transport

fundamental understating of the bubble hydrodynamics is necessary for better understanding of the complex gas-solid flow dynamics. This will lead to better optimize and improve the design, scale-up and operation procedure of the systems as well as to extend their use to novel applications.

Several experimental techniques have been developed for the past several decades in an attempt to measure and understand the bubble characteristics in laboratory-scale fluidized beds. Unfortunately, these laboratory-scale data do not necessarily scale-up accurately. To better understand the hydrodynamics in a commercial-scale fluidized bed reactor, it is necessary to study a vessel of that size. However, such experiments are not only prohibitive due to their capital and operational cost but also provide little information on the bubbling properties of the bed. In case of parametric studies, it is not practical or even impossible to vary the geometry and operating conditions of commercial-scale fluidized beds during experimentation. Moreover, due to the harsh environment and opaque nature of gas-solid flow structure of fluidized beds, it is difficult to observe the flow structure of the bed using many of the experimental techniques developed so far. Thus, together with the development of dedicated experimental techniques the development of fundamental hydrodynamic models is of utmost importance to achieve a better understanding of fluidization. Eventually this will lead to the improvement of existing processes, improved scale-up and the design of more efficient future processes. In recent years, together with rapid development of high performance computers and numerical algorithms, the rapid growth of interest in understanding the physical mechanisms responsible for the complex behaviour of gas-solid systems has helped to spark the development of fundamental approaches based on Computational Fluid Dynamics (CFD). Though empirical correlations are still largely used for designing gas-solid fluidized beds, these CFD models have been seen as fundamental tools in the study of the hydrodynamics and to aid in the design process of these systems. Numerical models are more flexible and less expensive specially when performing parametric studies for different bed geometries and operating conditions. Moreover, they provide extensive data for bubble characteristics for the entire cross section of the bed regardless of the complexity of bed geometry and operating conditions. However, further model development and validation of the models are still needed. It is believed that such validated CFD models can contribute to the successful understanding of bubble characteristics hence the design and optimization of these industrially relevant reactors.

Broadly speaking, there are two types of CFD models for gas-solid multiphase flow simulations that are widely applied today; namely, the Discrete Particle Model (DPM) and the Two-Fluid Model (TFM). In the DPM approach, which is based on the Eulerian-Lagrangian approach (Tsuji et al., 1993; Hoomans et al., 1996), the gas phase is treated as a continuous phase described by locally averaged Navier-Stokes equations on a computational cell scale, whereas the motion of particles is modelled as a discrete phase, described by Newton's laws of motion on an individual particle scale. A comprehensive review of the state of the Eulerian-Lagrangian model with a detailed description and governing equations as well as their application in the study of fluidized beds can be found elsewhere in the literature (e.g. Deen et al., 2007). In the TFM, which is based on the Eulerian-Eulerian approach (Anderson & Jackson, 1967), both the gas and solid phases are treated as fully interpenetrating continua. They are described by separate conservation equations for mass and momentum with appropriate interaction term between the phases included as a source terms in the conservation equations to couple the two phases.

fundamental understating of the bubble hydrodynamics is necessary for better understanding of the complex gas-solid flow dynamics. This will lead to better optimize and improve the design, scale-up and operation procedure of the systems as well as to extend

Several experimental techniques have been developed for the past several decades in an attempt to measure and understand the bubble characteristics in laboratory-scale fluidized beds. Unfortunately, these laboratory-scale data do not necessarily scale-up accurately. To better understand the hydrodynamics in a commercial-scale fluidized bed reactor, it is necessary to study a vessel of that size. However, such experiments are not only prohibitive due to their capital and operational cost but also provide little information on the bubbling properties of the bed. In case of parametric studies, it is not practical or even impossible to vary the geometry and operating conditions of commercial-scale fluidized beds during experimentation. Moreover, due to the harsh environment and opaque nature of gas-solid flow structure of fluidized beds, it is difficult to observe the flow structure of the bed using many of the experimental techniques developed so far. Thus, together with the development of dedicated experimental techniques the development of fundamental hydrodynamic models is of utmost importance to achieve a better understanding of fluidization. Eventually this will lead to the improvement of existing processes, improved scale-up and the design of more efficient future processes. In recent years, together with rapid development of high performance computers and numerical algorithms, the rapid growth of interest in understanding the physical mechanisms responsible for the complex behaviour of gas-solid systems has helped to spark the development of fundamental approaches based on Computational Fluid Dynamics (CFD). Though empirical correlations are still largely used for designing gas-solid fluidized beds, these CFD models have been seen as fundamental tools in the study of the hydrodynamics and to aid in the design process of these systems. Numerical models are more flexible and less expensive specially when performing parametric studies for different bed geometries and operating conditions. Moreover, they provide extensive data for bubble characteristics for the entire cross section of the bed regardless of the complexity of bed geometry and operating conditions. However, further model development and validation of the models are still needed. It is believed that such validated CFD models can contribute to the successful understanding of bubble characteristics hence the design and optimization of these industrially relevant reactors. Broadly speaking, there are two types of CFD models for gas-solid multiphase flow simulations that are widely applied today; namely, the Discrete Particle Model (DPM) and the Two-Fluid Model (TFM). In the DPM approach, which is based on the Eulerian-Lagrangian approach (Tsuji et al., 1993; Hoomans et al., 1996), the gas phase is treated as a continuous phase described by locally averaged Navier-Stokes equations on a computational cell scale, whereas the motion of particles is modelled as a discrete phase, described by Newton's laws of motion on an individual particle scale. A comprehensive review of the state of the Eulerian-Lagrangian model with a detailed description and governing equations as well as their application in the study of fluidized beds can be found elsewhere in the literature (e.g. Deen et al., 2007). In the TFM, which is based on the Eulerian-Eulerian approach (Anderson & Jackson, 1967), both the gas and solid phases are treated as fully interpenetrating continua. They are described by separate conservation equations for mass and momentum with appropriate interaction term between the phases

included as a source terms in the conservation equations to couple the two phases.

their use to novel applications.

Practically the motion of gas-particle flow systems present in fluidized beds should be expressed at least by the Eulerian-Lagrangian approach with the Newtonian equations of motion for the suspended particles. However, when the system comprises a large number of closely spaced particles, as in the case of fluidized bed, the problem is far too difficult to allow direct solution by tracking individual particles. Despite the rapid growth in computer capacity, it is only possible to track less than 106 particles (much less than the practical number of particles found in industrial scale fluidized beds) using the DPM. Since both CPU time and the required memory scales linear with the number of particles, it is obvious that DPM simulations of engineering size fluidized beds are beyond the capability of commercially available computer facilities within the foreseeable future. Therefore, DPM is not a natural choice for hydrodynamic modelling of gas-solid systems. For practical purposes, it is necessary to seek some way of simplifying it so that it can be described by a relatively small number of partial differential equations. One way of simplifying this problem is to replace the point mechanical and fluid mechanical variables by an appropriate locally average value of the corresponding variables to formulate the integral balances for mass, momentum and energy for a fixed control volume containing both phases. Hence describing the motion of the fluid and particles as though they were interpenetrating continua (Anderson and Jackson, 1967). In such continuum model, the equations are a generalization of the Navier-Stokes equations for interacting continua. This means that instead of knowing the positions and velocities of each particle, only the volume fraction of each phase and the average volume flow pattern are known. Though the local instantaneous value of variables vary rapidly on a scale comparable with the particle spacing the averaged variables are smoothed by averaging over regions large compared with the particle spacing but small compared with the size of complete system. The main advantage of this model is that the averaging techniques allow us to use relatively coarser grids and longer time steps so that the computational effort is significantly reduced, hence larger scale simulations can be performed, using less computation time.

In fact, the continuum model suffers from some limitations in modelling of the gas-solid flow. It does not provide information about the hydrodynamics of individual particles and thus has limitations in predicting certain discrete flow characteristics such as particle size and density effect. Nevertheless, it remains the only feasible approach for performing parametric investigation and scale-up and design studies of industrial scale systems and dense gas-solid beds (van Wachem et al., 2001; van der Hoef et al., 2008). Detail comparisons of the DPM and the TFM can be found elsewhere in the literature (e.g., Gera et al., 1998; Chiesa et al., 2005; van der Hoef et al., 2008)
