The CFD Simulations of a Fluidized Bed Crystallizer
Fluidized-bed crystallizer(FBC) is a kind of widely-used reactors across many industry branches, which has been used for long time. However, more accurate modeling tools for the design and scale-up of FBC are also required to obtain the high efficiency and low cost. The simulations using the multi-phase CFD and other coupling methods and models (DEM and PBM) are introduced in this report. Compared the simulated results with the experiment data, it is demonstrated that with the appropriate and comprehensive models, the CFD simulation could provide a relatively accurate prediction of flow pattern, particle distribution and velocity and local kinetic energy.
Thus, the choice of the coupling model is important and some efforts are still required in the future study.
Computational Fluid Dynamics(CFD), is a new interdisciplinary subject of fluid mechanics and computer science. Based on the numerical methods and data structures, it use the rapid calculation ability of the computers to solve the governing equations of fluid mechanics, so that the flow field can be predicted.
As for the application of CFD, it is routinely employed in so many fields such as the design of aircraft, turbomachinery, car and ship. Moreover, CFD is also applied in meteorology, oceanography, astrophysics, biology, oil recovery and architecture. Hence, CFD is gradually becoming an important tool in product design and development, and also a practical research method in various sciences.
CFD software usually refers to a commercial CFD program with a good human-computer interaction interface, which enables users to solve practical problems without being proficient in CFD-related theories. Nowadays, several commercial CFD software are available, such as FLUENT, CFD-ACE+ (CFDRC), Phoenis, CFX, Star-cd, etc.
The most important and basic consideration of CFD is how to treat continuous fluids in a discrete manner on a computer. One method is to discretize the spatial region into small cells to form a solid mesh or lattice, and then apply the appropriate algorithm to solve the continuity equation and equation of motion (Eulerian equation for inviscid fluids, Navier-Stokes equation for viscous fluids). In addition, such a grid may be irregular (for example, consisting of a triangle in two dimensions, a tetrahedron in three dimensions) or regular. Finally, if the problem is highly dynamic and spans a large range of scales, the grid itself should be dynamically time-adjustable, such as in adaptive mesh refinement methods.
As for the discretization methods, the Finite volume method(FVM) is the most common approach used in CFD codes. The FVM focus on the control volume and it has an advantage in memory usage and solution speed, especially for large problems, high Reynolds number turbulent flows, and source term dominated flows (like combustion).
Fluidized-bed crystallizers (FBC) is a kind of reactor to produce the large crystals, which was firstly applied to industry in the 1920s. As the figure 1 shows, based on the fluidized-bed principles, the FBC grows a mass of crystals suspended when the supersaturated solution flow upward through the whole working space. The suspended crystals will grown until the desired size is reached and then they will settle down to the bottom to be collected. As for the FBC, it is mostly applied on water treatment, fertilizer manufacture, fluoride removal and also the production of bottle polymers, fibers, and filaments.
Figure 1 Schematic diagram of FBC reactor
For the fluidized bed crystallizers, fluidization and crystallization simultaneously produce very complex phenomena, which requires a comprehensive study of process hydrodynamics to design the reactors with high efficiency. In addition, to design and optimize the multiphase reactors, accurate model of mixing behavior between the phases is necessary and essential.
For simplicity, the design of a fluidized bed crystallizer is usually based on a perfect size classification . In most modeling work of fluidized bed crystallizers, liquid flow is considered to be a plug flow or near plug flow regime. However, most practical crystallizer systems exhibit the macroscopic mixing behavior somewhere between the two extremes of the plug flow and the ideal mixed flow.
Computational Fluid Dynamics (CFD) is becoming an important tool for studying the hydrodynamic behavior of the conventional industrial crystallization processes. Many multi-phase simulations have applied the CFD to provide an insight on the hydrodynamics of the FBC.
The early CFD simulations for FBC operation are applied on 2007. The multi-fluid Eulerian CFD model was being used to investigate the hydrodynamics of the FBC. The solid and liquid phases are treated as a continuum of complete interpenetration. For each phase, the governing equations are the conservation of mass and momentum equations. These equations, as well as the appropriate boundary and initial conditions, are resolved by Fluent, with the use of laminar flow model in double precision mode.
As for the results of this kind of simulation, the relative distribution of the different phases could be obtained. This information is really helpful in fixing the size of the FBC, which can be an important factor affecting the total cost.
The volume fraction distribution of solid particles in different sizes is another finding of the simulation. It actually provides insight into the hydrodynamics of the FBC, which fills up the knowledge gap in developing the overall mechanical model.
However, The simulated result of the time-averaged distribution of solid volume fraction, does not match well with the experimental data, even if we could observe a similar trend . As for the FBC, the feed solution is in high velocity so the flow regime might fall into the transition or even the turbulence zone. Therefore, more rigorous numerical investigation, considering turbulent flow and interaction between phases, is required necessarily.
As for simulation of the turbulent flow, the model to describe turbulent fluid flow is required to be chosen initially. There are several models available, such as the standard k–ε model, the realizable k–ε model, the Re–stress model, the detached eddy simulation (DES), and the large eddy simulation (LES) .
To model the two-phase flow, an Eulerian multiphase model was mostly used with the standard k–ε method, because for isotropic flows with high Re, it is simple and suitable . The standard k–ε model need to be pay attention to that the flow must be fully turbulent flow so the effects of molecular viscosity could be neglected.
The turbulence kinetic energy (k) and its dissipation rate (ε) are obtained from the following equations:
Meanwhile, the momentum exchange between the phases are also considered by the calculation of the fluid–solid exchange coefficient Ksl：
All definitions of f include a drag function (CD) that is based on the relative Reynolds number (Res).
Figure 2 The distribution of size volume fractions for the polydispersed bed (a) d = 0.4 mm;
(b) d = 0.9 mm; (c) d = 1.8 mm; (d) d = 3 mm
Figure 3 Vectorial liquid velocity profiles for (a) pure water; (b) α= 10% d = 0.5 mm;
(c) α = 10% d = 1.5 mm; (d) α = 10% d = 0.4–3 mm.
Based on the results, several aspects of the FBC dynamics are analyzed by the multiphase CFD successfully. Therefore, the Eulerian multi-phase model with standard k–ε method was mostly validated.
For the polydispersed bed, as the diameter of solids increases, the expansion of bed decreases (figure 2). For the vectorial liquid velocity profiles, suspension fluidization is far from uniform. As figure 3 shows, the circulations loops are clearly presented. The position and the direction of the loops are totally different for different case. Thus, the assumption of piston flow in the modeling might not be feasible.
The PBM (Population balance model) describes the variation of PSD (particle size distribution) in a multi-phase flow system and it takes the particle growth and aggregation into account. In present work, the PBM is usually expressed by:
where n(L;x,t) was the length number density distribution, and the terms on the right side of equation, are the particle flux due to surface deposition and the birth and death rate of particle diameter due to aggregation, separately.
Figure 4 Schematic of simulation strategy
Initially, CFD consider several models, including Eulerian–Eulerian two-fluid model, Turbulent model, Empirical drag model, Species transport model and Heat transfer model. Based on this models, the solid volume fraction and solid velocity could be obtained. Then the PBM is coupled by evaluating Crystal grown mechanism and Shear aggregation kernel to get the crystal size-dependent growth rate and the crystal aggregation.
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The simulation results indicate that the particle growth description of CFD-PBM model is feasible and reasonable. Basic flow hydrodynamics are well validated for both uniform particle and polydisperse particle. The results show that when considering particle surface deposition and cluster removal, the simulated growth rate agrees well with the experimental data. In addition, during the evolution of particle growth, the defluidization phenomenon is also observed because the solid particles gradually settle and accumulate near the bottom of the bed.
In this section, a FBC was investigated using CFD-DEM (DEM: Discrete Element Method) simulations by focusing on the two-phase flow. DEM are relatively computationally intensive, which limits either the length of a simulation or the number of particles. Several DEM codes, as do molecular dynamics codes, take advantage of parallel processing capabilities (shared or distributed systems) to scale up the number of particles or length of the simulation.
An alternative to treating all particles separately is to average the physics across many particles and thereby treat the material as a continuum. In order to save computation time, for the current CFD-DEM simulation, assume that all particles are spherical.
In the DEM, the amount of the particles is an important parameter. For the study of considering 100,000 particles in the simplified setup, as figure 5 shows, the comparison with previous experimental data shows that CFD-DEM simulation is really suitable for predicting particle position and velocity. Particularly, the transition point between crystals going up to the top and crystals sinking down to the bottom is well simulated by the CFD-DEM.
Figure 5 Comparison of the average vertical velocity of the fluidized glass particles as a function of their radial position in the column from the experiment and the CFD-DEM simulation
A compromise must be made between the simulated process time and the number of simulated particles because the simulation is computationally challenging. Therefore, the CFD-DEM simulations are suitable to examine a short time-window in detail, instead of simulating the whole crystallization process. Moreover, usually the CFD-DEM simulations take 200,000 particles into account. Even if this is a high value in the simulation, it must be paid attention to that one crystallizer typically contains 170 million crystals in reality.
According to the above results of the CFD modeling, CFD is a very powerful and useful tool to understand the fundamentals of multi-phase fluidization system and to design multi-phase FBC. This technique could provide the prediction of flow patterns, local solids concentration and local kinetic energy values, taking into account the reactor shape. The coupling method and model, such as the DEM and PBM, provide their applicability and accuracy for the specific situations.
The basic principles of the CFD method for multiphase fluidization systems in FBC are mainly focused on the discussion of various multiscale models and the coupling theory of interaction forces. In order to get sufficient and accurate information, it is important to choose the suitable coupling models based on multiscale models, system conditions, reactor scale, etc. The figure 6 is a brief reference for researchers to find the appropriate models.
Figure 6 Four common multi-scale models applied to simulate gas–liquid–solid FBRs at various time and length scales at present. (DPM: discrete particle method; FT: front tracking; FC: front capturing)
At the same time, several efforts require to be focus in the future for the CFD on scale-up, design and control of FBCs: provide suitable laws for interphase momentum exchange between phases; consider the properties of transport-phenomena for numerical models and improve the measurement techniques to provide more accurate experimental data.
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