Large-scale CFD–DEM simulations of fluidized granular systems
Introduction
Granular flows are characteristic to numerous natural phenomena and are part of many processes of the pharmaceutical and chemical industries. In these industrial processes granular flows have a critical impact on the product's performance and safety. For example, in continuous powder blending of active pharmaceutical ingredients (APIs) and excipients prior to tableting, the granular flow properties of the components determine the content uniformity of the tablets made later in the process. Only a detailed understanding of the influence of particle size, shape, surface texture and other properties on the mean and the fluctuating flow fields in granular flows allows a precise design and optimization of this manufacturing operation.
In recent years Discrete Element Model (DEM) simulations have increasingly been used to study flows of granular systems, e.g. Stewart et al. (2001), Bertrand et al. (2005), Remy et al., 2010a, Remy et al., 2010bSun and Sundaresan (2011), Moon et al. (2006), etc. In these simulations the interaction between the solid and the fluid phase is typically neglected and only particle–particle contacts are considered. However, in the pharmaceutical and other industries, fine granular materials are encountered (typically in the order of ten to several hundred microns), where both particle–particle interactions and fluid drag have significant contributions. Examples include fluid-bed drying, hopper filling/discharge, chute flows or die filling. Thus, accounting for fluid–particle interaction is necessary to correctly describe such processes, and to design and to scale-up industrial devices.
Combining Computational Fluid Dynamics (CFD) and Discrete Element Model (DEM) makes it possible to simulate fluidic-granular systems. In DEM, the motion of discrete particles is tracked by solving Newton's second law of motion and in CFD, the flow of a continuum fluid is simulated by solving the Navier–Stokes equations, based on the concept of local averaging. According to Zhou et al. (2010) and Feng and Yu (2004), the main advantage of CFD–DEM is that detailed particle-scale information is obtained, including particle trajectories and forces acting on individual particles. For example, in the study of fluid-bed catalytic crackers (risers) only in the last years it became clear that catalyst particles form complex clusters at the meso-scale, which strongly influences the reactor's behavior (see Zhang et al., 2008). Such information cannot be obtained in detail with the alternative method, such as the Two-Fluid Model (TFM), see related works of Hong et al. (2012), Bi and Li (2004), Li et al. (2012), or most experimental techniques, see for instance the works of Van Buijtenen et al. (2011) and Lekhal et al. (2006), where some experimental methods are discussed and used.
DEM simulations are computationally expensive, and their routine application is still limited to the analysis of several hundred thousand particles. However, as shown by Radeke et al. (2010), the computational performance of DEM simulations can be significantly improved by the newly available Compute United Device Architecture (CUDA) technology. Radeke et al. (2010) already performed DEM-simulations on readily available Graphics Processing Units (GPUs) with a particle number of about O(107) particles. Thus, a combination of CFD, executed on the Central Processing Units (CPUs), and DEM, executed on GPUs, is a promising high-performance method for coupled CFD–DEM simulations with up to 9 million particles per GB of GPU-Memory. As the two codes (CFD and DEM) run on separate platforms (i.e., CPUs and GPUs) the computing performance of each code is not affected by the other one. This is not a case in regularly parallelized CFD–DEM simulations, e.g. Kafui et al. (2011) for O(106) particles. Kafui et al. (2011) applied a semi-automatic parallelization of a CFD–DEM code in order to increase the CPU calculation performance with increasing number of CPU processors and showed a maximal speedup of 44, with 64 processing cores. The authors also showed that the increasing number of processors leads to a significant global communication overhead and to a degradation of the full CFD–DEM performance in comparison with the DEM alone and CFD alone.
The objective of the work is to present a new hybrid approach to solve CFD–DEM problems in gas–solid fluidized beds systems applying an efficient coupling method suitable for large-scale simulations. We are using CUDA technology for the particle simulation and introduce a coupling methodology with an existing CFD-code. The coupling of CFD and DEM is realized through particle–fluid interaction forces. Here, the drag force plays an important role for coupling between gas and solid phases, since next to field forces, it is the only accelerating force acting on a particle (Van der Hoef et al.,, Du et al., 2005). Several widely used models are described in the literature (e.g. Gidaspow, 1994, Syamlal and O'Brien, 1988, Di Felice, 1994, Koch and Hill, 2001). Several authors (e.g. Du et al., 2005) reviewed the models and demonstrated that the use of the Gidaspow model resulted in the best agreement with experimental observation, both qualitatively and quantitatively. Huilin and Gidaspow (1994) combined the Ergun (1952) equation for dense regimes and a correlation proposed by Wen and Yu (1966) for the more dilute regimes. In the last few years a model proposed by Beetstra et al. (2007a) was frequently applied. Similarly to Hill et al. (2001) and Koch and Hill (2001) Beetstra et al. (2007a) derived their model based on a wide range of data for particles Reynolds numbers of up to 1.000. Furthermore, they extended their model to random arrays of bi-disperse spheres and demonstrated that the model was valid for general poly-disperse systems. As such, it was more practical for general fluid bed simulations.
In presented work, coupling between the CFD code (AVL-Fire®) and our high-performance GPU-based DEM code was established based on the newly available Compute United Device Architecture (CUDA) technology (Radeke et al., 2010). The DEM code can simulate many millions of particles on readily available hardware, and the simulations may directly be visualized via a GUI using OpenGL display features. Data exchange between the codes was performed using AVL Code Coupling Interface (ACCI), a software component for co-simulations with an arbitrary number of instances of different simulation programs. Under this protocol the codes concurrently simulate the same time interval and continuously exchange information. In contrast to the coupling method used by Xu et al. (2012), which also performed a gas–solid flow simulation with CPU–GPU hybrid systems, our coupling method is more efficient and has lower memory requirements.
Validation of the numerical results with experimental data is an essential part of modeling and code development. This, however, is not straightforward as high-quality experimental data of fluidized beds (FBs) are scarce. A review of experimental techniques to capture the gas–solid distribution in fluidized beds, including direct two-dimensional visualization of dilute systems, voidage distributions in a cross section, as well as pressure and acoustic data, can be found in Van Ommen and Mudde (2008). The numerical results obtained in this work were validated against experimental and CFD–DEM simulation data of Link et al. (2004) and Van Buijtenen et al. (2011). Their experimental and CFD–DEM simulation studies were done in a pseudo-2D spout-fluid bed (i.e., a FB with low depth of only a few particle diameters) using non-intrusive measurement techniques Particle Image Velocimetry (PIV) and Positron Emission Particle Tracking (PEPT). In their work, the multiple-interacting-spouts regime was analyzed in detail (Van Buijtenen et al., 2011) for single-, double- and triple-spout fluidized beds. The experimental and CFD–DEM simulation data include profiles of the time-averaged vertical particle velocity and the time-averaged particle velocity fields. Pepiot and Desjardins (2012) reported that a 2D bed failed to fully reproduce the flow dynamics of a 3D bed and that the bed height in comparison to a 3D bed simulation was over-predicted, primarily due to the higher flow velocities in a 2D-system caused by a small distance between walls. Nevertheless, pseudo-2D spout fluid beds are widely used in the validation process of coupled CFD–DEM simulations Van Buijtenen et al. (2011). This strategy is also followed in our work. Thus, our objective was to model single-, double- and triple-spout beds and validates the code against the data by Van Buijtenen et al. (2011).
Section snippets
CFD–DEM model
The gas-phase (continuum) dynamics are described by the incompressible Newtonian fluid based on an Euler approach. In contrast, the dispersed phase (i.e., the particles) are treated as a collection on individual particles, whose movement is described by applying Newton's second law. Thus, the model is based on an Euler–Lagrange approach for a non-reactive flow.
The continuum and dispersed phases are strongly coupled via the momentum exchange between gas phase and particles. Due to a high packing
Test of implementation in CFD-code
Three common drag force models were presented in Section 2.2. In order to validate the implementation of the source term in the CFD-code and in a simple way to investigate the suitability of these models, a simple test case was analyzed. The system encompasses a fixed bed of spheres with a length L in a pipe with diameter D. The fixed boundary conditions were the inlet velocity u and the ambient pressure pout. The resulting pressure drop across the bed was monitored. The drag models were
Coupled CFD–DEM simulations
Numerical results of our coupled CFD–DEM simulations were verified against experimental data of Link et al. (2004) and Van Buijtenen et al. (2011). In their publications a pseudo-2D spout-fluid bed was studied using non-intrusive techniques, i.e., Particle Image Velocimetry (PIV) and Positron Emission Particle Tracking (PEPT). Simulation models were reported as well. The “multiple-interacting-spouts regime” was analyzed in detail in work of Van Buijtenen et al. (2011) for single-, double- and
Evaluation of the computational time
In addition to verifying the accuracy of the proposed method the computational efficiency of the algorithm was studied. For the computations an Intel Core i7 960 4×3.20 GHz CPU Computer and a single NVIDIA GeForce GTX 580 graphical card with 3 GB of memory was used. Five different cases with an increasing number of particles were considered, involving (i) 107,000, (ii) 428,000, (iii) 1,712,000, (iv) 6,848,000 and finally (v) 25,000,000 particles. The particle diameter was decreased in order to
Conclusion
This work presents a novel coupled CFD–DEM simulation algorithm, which concerns the coupling of an in-house DEM code and a commercial CFD code (AVL-Fire®). The data exchange between the codes was performed by applying a software component, AVL Code Coupling Interface (ACCI). The data mapping function may be used for mapping the quantities between different computational grids, e.g., a relatively complex CFD and a regular DEM mesh. The numerical results obtained in this work were verified using
Nomenclature
- CD
drag coefficient (dimensionless)
- D
diameter (m)
- dp
particle diameter (m)
- en,p→p
normal restitution coefficient, particle and particle (dimensionless)
- en,p→w
normal restitution coefficient, particle and wall (dimensionless)
- et,p→p
tangential restitution coefficient, particle and particle (dimensionless)
- et,p→w
tangential restitution coefficient, particle and wall (dimensionless)
- F
dimensionless drag force coefficient proposed by Beetstra et al.
- g
gravity (m/s²)
- I
unit matrix (dimensionless)
- Ip
particle moment of
Acknowledgments
The research work has been supported by the Austrian Research Promotion Agency (FFG), Land Steiermark and the Styrian Business Promotion Agency (SFG). The authors want to thank Dr. Peter Sampl (AVL GmbH), Dr. Wilfried Edelbauer (AVL GmbH), Dr. Stefan Radl (Institute for Process and Particle Engineering, Graz University of Technology), and Mr. Georg Neubauer (RCPE GmbH) for their support.
References (41)
- et al.
Numerical study of segregation using a new drag force correlation for polydisperse systems derived from Lattice-Boltzmann simulations
Chem. Eng. Sci.
(2007) - et al.
DEM-based models for the mixing of granular materials Chem. Eng. Sci.
(2005) - et al.
Multiscale analysis and modeling of multiphase chemical reactors
Adv. Powder Technol.
(2004) - et al.
Review of discrete particle modeling of fluidized beds
Chem. Eng. Sci.
(2007) The voidage functions for fluid-particle interaction system
Int. J. Multiphase Flow
(1994)- et al.
DEM–CFD modeling of a fluidized bed spray granulator
Chem. Eng. Sci.
(2011) - et al.
Influence of rolling friction on single spout fluidized bed simulation
Particuology
(2012) - et al.
Meso-scale structures of bidisperse mixtures of particles fluidized by a gas
Chem. Eng. Sci.
(2011) - et al.
An EMMS-based multi-fluid model (EFM) for heterogeneous gas–solid riser flows: Part I. Formulation of structure-dependent conservation equations
Chem. Eng. Sci.
(2012) - et al.
Parallelization of a Lagrangian–Eulerian DEM/CFD code for application to fluidized beds
Powder Technol.
(2011)