CFD-DEM

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The CFD-DEM model, or Computational Fluid Dynamics / Discrete Element Method model, is a process used to model or simulate systems combining fluids with solids or particles. In CFD-DEM, the motion of discrete solids or particles phase is obtained by the Discrete Element Method (DEM) which applies Newton's laws of motion to every particle, while the flow of continuum fluid is described by the local averaged Navier–Stokes equations that can be solved using the traditional Computational Fluid Dynamics (CFD) approach. The interactions between the fluid phase and solids phase is modeled by use of Newton's third law.

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The direct incorporation of CFD into DEM to study the gas fluidization process so far has been attempted by Tsuji et al. [1] [2] and most recently by Hoomans et al., [3] Deb et al. [4] and Peng et al. [5] A recent overview over fields of application was given by Kieckhefen et al. [6]

Parallelization

OpenMP has been shown to be more efficient in performing coupled CFD-DEM calculations in parallel framework as compared to MPI by Amritkar et al. [7] Recently, a multi-scale parallel strategy [8] is developed. Generally, the simulation domain is divided into many sub-domains and each process calculates only one sub-domain using MPI passing boundary information; for each sub-domain, the CPUs are used to solve the fluid phase while the general purpose GPUs are used to solve the movement of particles. However, in this computation method CPUs and GPUs work in serial. That is, the CPUs are idle while the GPUs are calculating the solid particles, and the GPUs are idle when the CPUs are calculating the fluid phase. To further accelerate the computation, the CPU and GPU computing can be overlapped using the shared memory of a Linux system. Thus, the fluid phase and particles can be calculated at the same time.

Reducing computation cost using Coarse Grained Particles

The computation cost of CFD-DEM is huge due to a large number of particles and small time steps to resolve particle-particle collisions. To reduce computation cost, many real particles can be lumped into a Coarse Grained Particle (CGP). [9] [10] The diameter of the CGP is calculated by the following equation:

where is the number of real particles in CGP. Then, the movement of CGPs can be tracked using DEM. In simulations using Coarse Grained Particles, the real particles in a CGP are subjected to the same drag force, same temperature and same species mass fractions. The momentum, heat and mass transfers between fluid and particles are firstly calculated using the diameter of real particles and then scaled by times. The value of is directly related to computation cost and accuracy. [11] When is equal to unity, the simulation becomes DEM-based achieving results that are of the highest possible accuracy. As this ratio increases, the speed of the simulation increases drastically but its accuracy deteriorates. Apart from an increase in speed, general criteria for selecting a value for this parameter is not yet available. However, for systems with distinct mesoscale structures, like bubbles and clusters, the parcel size should be small enough to resolve the deformation, aggregation, and breakage of bubbles or clusters. The process of lumping particles together reduces the collision frequency, which directly influences the energy dissipation. To account for this error, an effective restitution coefficient was proposed by Lu et al., [10] based on kinetic theory of granular flow, by assuming the energy dissipation during collisions for the original system and the coarse grained system are identical.

Related Research Articles

A discrete element method (DEM), also called a distinct element method, is any of a family of numerical methods for computing the motion and effect of a large number of small particles. Though DEM is very closely related to molecular dynamics, the method is generally distinguished by its inclusion of rotational degrees-of-freedom as well as stateful contact and often complicated geometries. With advances in computing power and numerical algorithms for nearest neighbor sorting, it has become possible to numerically simulate millions of particles on a single processor. Today DEM is becoming widely accepted as an effective method of addressing engineering problems in granular and discontinuous materials, especially in granular flows, powder mechanics, and rock mechanics. DEM has been extended into the Extended Discrete Element Method taking heat transfer, chemical reaction and coupling to CFD and FEM into account.

<span class="mw-page-title-main">Molecular dynamics</span> Computer simulations to discover and understand chemical properties

Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of the system. In the most common version, the trajectories of atoms and molecules are determined by numerically solving Newton's equations of motion for a system of interacting particles, where forces between the particles and their potential energies are often calculated using interatomic potentials or molecular mechanical force fields. The method is applied mostly in chemical physics, materials science, and biophysics.

<span class="mw-page-title-main">Computational fluid dynamics</span> Analysis and solving of problems that involve fluid flows

Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid with surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can be achieved, and are often required to solve the largest and most complex problems. Ongoing research yields software that improves the accuracy and speed of complex simulation scenarios such as transonic or turbulent flows. Initial validation of such software is typically performed using experimental apparatus such as wind tunnels. In addition, previously performed analytical or empirical analysis of a particular problem can be used for comparison. A final validation is often performed using full-scale testing, such as flight tests.

In plasma physics, the particle-in-cell (PIC) method refers to a technique used to solve a certain class of partial differential equations. In this method, individual particles in a Lagrangian frame are tracked in continuous phase space, whereas moments of the distribution such as densities and currents are computed simultaneously on Eulerian (stationary) mesh points.

<span class="mw-page-title-main">Smoothed-particle hydrodynamics</span> Method of hydrodynamics simulation

Smoothed-particle hydrodynamics (SPH) is a computational method used for simulating the mechanics of continuum media, such as solid mechanics and fluid flows. It was developed by Gingold and Monaghan and Lucy in 1977, initially for astrophysical problems. It has been used in many fields of research, including astrophysics, ballistics, volcanology, and oceanography. It is a meshfree Lagrangian method, and the resolution of the method can easily be adjusted with respect to variables such as density.

<span class="mw-page-title-main">Fluidized bed</span>

A fluidized bed is a physical phenomenon that occurs when a solid particulate substance is under the right conditions so that it behaves like a fluid. The usual way to achieve a fluidized bed is to pump pressurized fluid into the particles. The resulting medium then has many properties and characteristics of normal fluids, such as the ability to free-flow under gravity, or to be pumped using fluid technologies.

<span class="mw-page-title-main">Lattice Boltzmann methods</span> Class of computational fluid dynamics methods

The lattice Boltzmann methods (LBM), originated from the lattice gas automata (LGA) method (Hardy-Pomeau-Pazzis and Frisch-Hasslacher-Pomeau models), is a class of computational fluid dynamics (CFD) methods for fluid simulation. Instead of solving the Navier–Stokes equations directly, a fluid density on a lattice is simulated with streaming and collision (relaxation) processes. The method is versatile as the model fluid can straightforwardly be made to mimic common fluid behaviour like vapour/liquid coexistence, and so fluid systems such as liquid droplets can be simulated. Also, fluids in complex environments such as porous media can be straightforwardly simulated, whereas with complex boundaries other CFD methods can be hard to work with.

<span class="mw-page-title-main">Fluid–structure interaction</span>

Fluid–structure interaction (FSI) is the interaction of some movable or deformable structure with an internal or surrounding fluid flow. Fluid–structure interactions can be stable or oscillatory. In oscillatory interactions, the strain induced in the solid structure causes it to move such that the source of strain is reduced, and the structure returns to its former state only for the process to repeat.

<span class="mw-page-title-main">Meshfree methods</span> Methods in numerical analysis not requiring knowledge of neighboring points

In the field of numerical analysis, meshfree methods are those that do not require connection between nodes of the simulation domain, i.e. a mesh, but are rather based on interaction of each node with all its neighbors. As a consequence, original extensive properties such as mass or kinetic energy are no longer assigned to mesh elements but rather to the single nodes. Meshfree methods enable the simulation of some otherwise difficult types of problems, at the cost of extra computing time and programming effort. The absence of a mesh allows Lagrangian simulations, in which the nodes can move according to the velocity field.

The material point method (MPM) is a numerical technique used to simulate the behavior of solids, liquids, gases, and any other continuum material. Especially, it is a robust spatial discretization method for simulating multi-phase (solid-fluid-gas) interactions. In the MPM, a continuum body is described by a number of small Lagrangian elements referred to as 'material points'. These material points are surrounded by a background mesh/grid that is used to calculate terms such as the deformation gradient. Unlike other mesh-based methods like the finite element method, finite volume method or finite difference method, the MPM is not a mesh based method and is instead categorized as a meshless/meshfree or continuum-based particle method, examples of which are smoothed particle hydrodynamics and peridynamics. Despite the presence of a background mesh, the MPM does not encounter the drawbacks of mesh-based methods which makes it a promising and powerful tool in computational mechanics.

A CFD-DEM model is suitable for the modeling or simulation of fluid-solids or fluid-particles systems. In a typical CFD-DEM model, the phase motion of discrete solids or particles is obtained by the Discrete Element Method (DEM) which applies Newton's laws of motion to every particle and the flow of continuum fluid is described by the local averaged Navier–Stokes equations that can be solved by the traditional Computational Fluid Dynamics (CFD). The model is first proposed by Tsuji et al. The interactions between the fluid phase and solids phase is better modeled according to Newton's third law.

In computational fluid dynamics, the immersed boundary method originally referred to an approach developed by Charles Peskin in 1972 to simulate fluid-structure (fiber) interactions. Treating the coupling of the structure deformations and the fluid flow poses a number of challenging problems for numerical simulations. In the immersed boundary method the fluid is represented in an Eulerian coordinate system and the structure is represented in Lagrangian coordinates. For Newtonian fluids governed by the Navier–Stokes equations, the fluid equations are

In particle segregation, particulate solids, and also quasi-solids such as foams, tend to segregate by virtue of differences in the size, and also physical properties such as volume, density, shape and other properties of particles of which they are composed. Segregation occurs mainly during the powder handling and it is pronounced in free-flowing powders. One of the effective methods to control granular segregation is to make mixture's constituents sticky using a coating agent. This is especially useful when a highly active ingredient, like an enzyme, is present in the mixture. Powders that are inherently not free flowing and exhibit high levels of cohesion/adhesion between the compositions are sometimes difficult to mix as they tend to form agglomerates. The clumps of particles can be broken down in such cases by the use of mixtures that generate high shear forces or that subject the powder to impact. When these powders have been mixed, however, they are less susceptible to segregation because of the relatively high inter-particulate forces that resist inter-particulate motion, leading to unmixing.

<span class="mw-page-title-main">Bubble column reactor</span>

A bubble column reactor is a chemical reactor that belongs to the general class of multiphase reactors, which consists of three main categories: trickle bed reactor, fluidized bed reactor, and bubble column reactor. A bubble column reactor is a very simple device consisting of a vertical vessel filled with water with a gas distributor at the inlet. Due to the ease of design and operation, which does not involve moving parts, they are widely used in the chemical, biochemical, petrochemical, and pharmaceutical industries to generate and control gas-liquid chemical reactions.

The multiphase particle-in-cell method (MP-PIC) is a numerical method for modeling particle-fluid and particle-particle interactions in a computational fluid dynamics (CFD) calculation. The MP-PIC method achieves greater stability than its particle-in-cell predecessor by simultaneously treating the solid particles as computational particles and as a continuum. In the MP-PIC approach, the particle properties are mapped from the Lagrangian coordinates to an Eulerian grid through the use of interpolation functions. After evaluation of the continuum derivative terms, the particle properties are mapped back to the individual particles. This method has proven to be stable in dense particle flows, computationally efficient, and physically accurate. This has allowed the MP-PIC method to be used as particle-flow solver for the simulation of industrial-scale chemical processes involving particle-fluid flows.

<span class="mw-page-title-main">Extended discrete element method</span>

The extended discrete element method (XDEM) is a numerical technique that extends the dynamics of granular material or particles as described through the classical discrete element method (DEM) by additional properties such as the thermodynamic state, stress/strain or electro-magnetic field for each particle. Contrary to a continuum mechanics concept, the XDEM aims at resolving the particulate phase with its various processes attached to the particles. While the discrete element method predicts position and orientation in space and time for each particle, the extended discrete element method additionally estimates properties such as internal temperature and/or species distribution or mechanical impact with structures.

<span class="mw-page-title-main">MOOSE (software)</span>

MOOSE is an object-oriented C++ finite element framework for the development of tightly coupled multiphysics solvers from Idaho National Laboratory. MOOSE makes use of the PETSc non-linear solver package and libmesh to provide the finite element discretization.

Computational Fluid Dynamics (CFD) modeling and simulation for phase change materials (PCMs) is a technique to analyze the performance and behavior of PCMs. The CFD models have been successful in studying and analyzing the air quality, natural ventilation and stratified ventilation, air flow initiated by buoyancy forces and temperature space for the systems integrated with PCMs. Simple shapes like flat plates, cylinders or annular tubes, fins, macro- and micro-encapsulations with containers of different shape are often modeled in CFD software's to study.

Quadrature-based moment methods (QBMM) are a class of computational fluid dynamics (CFD) methods for solving Kinetic theory and is optimal for simulating phases such as rarefied gases or dispersed phases of a multiphase flow. The smallest "particle" entities which are tracked may be molecules of a single phase or granular "particles" such as aerosols, droplets, bubbles, precipitates, powders, dust, soot, etc. Moments of the Boltzmann equation are solved to predict the phase behavior as a continuous (Eulerian) medium, and is applicable for arbitrary Knudsen number and arbitrary Stokes number . Source terms for collision models such as Bhatnagar-Gross-Krook (BGK) and models for evaporation, coalescence, breakage, and aggregation are also available. By retaining a quadrature approximation of a probability density function (PDF), a set of abscissas and weights retain the physical solution and allow for the construction of moments that generate a set of partial differential equations (PDE's). QBMM has shown promising preliminary results for modeling granular gases or dispersed phases within carrier fluids and offers an alternative to Lagrangian methods such as Discrete Particle Simulation (DPS). The Lattice Boltzmann Method (LBM) shares some strong similarities in concept, but it relies on fixed abscissas whereas quadrature-based methods are more adaptive. Additionally, the Navier–Stokes equations(N-S) can be derived from the moment method approach.

The Cohesion number (Coh) is a useful dimensionless number in particle technology by which the cohesivity of different powders can be compared. This is especially useful in DEM simulations of granular materials where scaling of the size and stiffness of the particles are inevitable due to the computationally demanding nature of the DEM modelling.

References

  1. ↑ Tsuji, Y.; Kawaguchi, T.; Tanaka, T. (1993). "Discrete particle simulation of two-dimensional fluidized bed". Powder Technology. Elsevier BV. 77 (1): 79–87. doi:10.1016/0032-5910(93)85010-7. ISSN   0032-5910.
  2. ↑ Tsuji, Y.; Tanaka, T.; Ishida, T. (1992). "Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe". Powder Technology. Elsevier BV. 71 (3): 239–250. doi:10.1016/0032-5910(92)88030-l. ISSN   0032-5910.
  3. ↑ Hoomans, B.P.B.; Kuipers, J.A.M.; Briels, W.J.; van Swaaij, W.P.M. (1996). "Discrete particle simulation of bubble and slug formation in a two-dimensional gas-fluidised bed: A hard-sphere approach". Chemical Engineering Science. Elsevier BV. 51 (1): 99–118. doi:10.1016/0009-2509(95)00271-5. ISSN   0009-2509. S2CID   17460834.
  4. ↑ Deb, Surya; Tafti, Danesh (2014). "Investigation of flat bottomed spouted bed with multiple jets using DEM–CFD framework". Powder Technology. Elsevier BV. 254: 387–402. doi:10.1016/j.powtec.2014.01.045. ISSN   0032-5910.
  5. ↑ Peng, Z.; Doroodchi, E.; Luo, C.; Moghtaderi, B. (2014). "Influence of void fraction calculation on fidelity of CFD-DEM simulation of gas-solid bubbling fluidized beds". AIChE J. 60 (6): 2000. doi:10.1002/aic.14421.
  6. ↑ Kieckhefen, P.; Pietsch, S.; Dosta, M.; Heinrich, S. (2020). "Possibilities and Limits of Computational Fluid Dynamics–Discrete Element Method Simulations in Process Engineering: A Review of Recent Advancements and Future Trends". Annual Review of Chemical and Biomolecular Engineering. 11: 397–422. doi:10.1146/annurev-chembioeng-110519-075414. PMID   32169000. S2CID   212707563.
  7. ↑ Amritkar, Amit; Deb, Surya; Tafti, Danesh (2014). "Efficient parallel CFD-DEM simulations using OpenMP". Journal of Computational Physics. 256: 501. Bibcode:2014JCoPh.256..501A. doi:10.1016/j.jcp.2013.09.007.
  8. ↑ Lu, L.; Xu, J.; Ge, W.; Gao, G.; Jiang, Y.; Zhao, M.; Liu, X.; Li, J. (2016). "Computer virtual experiment on fluidized beds using a coarse-grained discrete particle method—EMMS-DPM". Chemical Engineering Science. 155: 314–337. doi:10.1016/j.ces.2016.08.013.
  9. ↑ Lu, L.; Yoo, K.; Benyahia, S. (2016). "Coarse-Grained-Particle Method for Simulation of Liquid–Solids Reacting Flows". Industrial & Engineering Chemistry Research. 55 (39): 10477–10491. doi:10.1021/acs.iecr.6b02688. OSTI   1477859.
  10. 1 2 Lu, L.; Xu, J.; Ge, W.; Yue, Y. (2014). "EMMS-based discrete particle method (EMMS–DPM) for simulation of gas–solid flows". Chemical Engineering Science. 120: 67–87. doi:10.1016/j.ces.2014.08.004.
  11. ↑ Lu, L.; Konan, A.; Benyahia, S. (2017). "Influence of grid resolution, parcel size and drag models on bubbling fluidized bed simulation". Chemical Engineering Journal. 326: 627–639. doi: 10.1016/j.cej.2017.06.002 . OSTI   1404697.
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