Extended discrete element method

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Spatial and temporal temperature distribution in a spherical particle with heating that varies over time

The Advanced Discrete Element Method ( English extended discrete element method ) or XDEM is in the numerical analysis , an approach that the movement of granular materials or particles as by the classical discrete element method (DEM) (Cundall and Allen) is expanded to include additional properties such as the thermodynamic state, mechanical stress / strain or electromagnetic fields for each particle. In contrast to continuum mechanics , the XDEM resolves the particle phase with the various processes belonging to a particle. While the discrete element method describes the position and orientation of the particles in space and time, the extended discrete element method also calculates properties such as temperature and / or species distributions or mechanical interaction with structures.

Historical review

The molecular dynamics as et in the late 50s by Alder al. and was developed by Rahman in the early 60s, can be seen as a first step towards the Extended Discrete Element method, although the forces due to contacts between particles have only been replaced by potentials such as Lennard-Jones potentials of molecules or atoms to describe the interaction . Similarly, the fluid dynamic interaction between particles moving in a fluid was investigated. The fluid mechanical drag forces due to the relative speed between the particles and the surrounding fluid were viewed as additional forces that act on the particles. With this multiphase flow approach consisting of a solid and gaseous phase, the particle phase is recorded using discrete methods, while the gaseous or liquid phase is described using continuum mechanical methods. This approach is therefore called the combined continuum and discrete model (CCDM) as it was used by Kawaguchi et al., Hoomans, Xu 1997 and Xu 1998. Since the solid phase consisting of particles is described discretely, there are no constitutive laws, which leads to a better understanding of fundamental physics. This is demonstrated by Zhu 2007 et al. and Zhu 2008 et al. confirmed in their review of the literature on particulate flows modeled with CCDM. CCDM was developed in the last two decades and describes the granular phase with the discrete element method (DEM) while the gaseous or liquid phase is treated with the Navier-Stokes equations. It has thus established itself as an effective method to investigate interactions between a particle and a fluid phase, as in the literature review by Yu and Xu, Feng and Yu and Deen et al. is pictured. Based on the CCDM method, the characteristic properties of spouted or fluidized beds were determined by Gryczka et al. detected.

The theoretical basis for XDEM was laid by Peters, who calculated the combustion of wood chips on a moving grate. This concept was later adopted by Simsek et al. adopted to describe a grate furnace . Applications for the blast furnace have been reported by Shungo et al. carried out. Today the numerical simulation of the injection processes of liquids such as diesel in a gaseous medium is a standard tool for a large number of CFD codes such as Star-CD from CD-adapco , Ansys and AVL -Fire. Drops that arise during atomization are described using a zero-dimensional approach in order to determine the mass and heat transfer into the gas phase.

methodology

Sequential concept for discrete-continuous applications.

Numerous requirements in engineering exist and are emerging that contain a continuous and discrete phase at the same time and therefore cannot be solved with sufficient accuracy with either continuous or discrete methods alone. For this reason, XDEM was developed to be an excellent platform for coupling discrete and continuous phases for a very large number of applications. Although research and development of numerical methods in the fields of discrete and continuous solution methods continues, these tools have now reached a high level of development. There are two concepts for coupling discrete and continuous solvers:

  • Monolithic concept : The equations describing the multi-phase application are treated simultaneously and result in a comprehensive solution to the problem.
  • Sequential concept : The equations that describe the discrete and continuous phases are solved separately and sequentially by specially developed methods, whereby the results of a set of equations are made available for the remaining ones.

The first concept requires a solver that captures the entire physical properties of the system and therefore places great demands on the implementation. However, there are scenarios for which the matrix coefficients of coupled differential equations cannot be determined or can only be determined with great effort. For this reason, the sequential concept as a coupling between different solvers that represent the discrete and continuous phases shows great advantages over the monolithic approach. It offers a great deal of freedom for coupling a variety of solvers. In addition, a more modular software is retained, which allows individually adapted solution methods. However, the sequential concept requires stable and sufficiently precise couplings between the individual modules. Within the sequential concept for XDEM, the results for continuous problems are calculated by solving the relevant conservation equations. Properties such as temperature of individual particles are also found by solving the associated equations for the particle, which represents the internal distribution of the relevant variables in space and time. Essential conservation principles with the associated variables that apply to the particles are summarized in the following table:

Conservation Principles
Conservation law equation variable
Mass (compressible medium) continuity Pressure / density
Linear impulse Navier-Stokes speed
energy energy temperature
species Species transport Mass fractions
Charge, electricity Maxwell electric / magnetic field, electric displacement field

The solution of these equations defines the three-dimensional and unsteady field for the relevant variables such as temperature or species. However, the resolution in particular in spatial dimensions is limited by the fact that the equations have to be solved for a large number of particles. As a result, the spatial resolution is usually reduced to a representative dimension, which results in sufficient accuracy and is proven by Man and Byeong, while the unsteady character of Lee et al. is highlighted.

Applications

Deformation of a conveyor belt due to impacting particles.

Applications that include a continuous as well as discrete phase occur in the pharmaceutical industry such as tablet production, food industry, mining, construction and agricultural machinery, metal extraction, energy generation and systems biology. Some prominent examples are coffee beans, corn flakes, nuts, coal, sand, renewable fuels like biomass and fertilizers. Originally, according to Hoomans, such studies were limited to simple flow configurations. However, Chu and Yu were able to demonstrate that the method can be applied to complex flow configurations such as a fluidized bed, conveyor belt or cyclone. Similarly, Zhou et al. applied the CCDM approach to the complex geometry of a coal powder combustion and Chu et al. modeled the flow of air, coal dust and magnetite particles of various sizes.

The CCDM approach was also used for fluidized beds as researched by Rowe and Nienow and Feng and Yu and investigated by Feng and Yu to investigate the chaotic movement of particles in fluidized beds. Kafuia et al. also describe particle continuum fluid modeling for fluidized beds. Other applications of XDEM include thermal conversion of biomass on forward and reverse grates. Heat transfer in a fixed bed reactor was also investigated for hot air flowing through a fixed bed, whereby the particles experience different heat transfer due to their distribution and position. The deformation of a conveyor belt due to impacting granular materials is an application from stress and strain analysis.

  • Distribution of the surface temperature of particles on a return grate

  • Reaction progress of the pyrolysis of straw on a moving grate

  • Distribution of the porosity and particle temperature in a fixed bed reactor

Literature review

  1. ↑ PA Cundall, ODL Strack: A discrete numerical model for granular assemblies . In: Geotechnique . 29, 1979, pp. 47-65.
  2. ^ MP Allen, DJ Tildesley: Computer Simulation of Liquids . Clarendon Press Oxford, 1990.
  3. ^ BJ Alder, TE Wainwright: Studies in Molecular Dynamics. I. General Method . In: J. Chem. Phys. . 31, 1959, p. 459.
  4. ^ A. Rahman: Correlations in the Motion of Atoms in Liquid Argon . In: Phys. Rev. . 136, 1964.
  5. ↑ T. Kawaguchi, Y. Tsuji, T. Tanaka: Discrete particle simulation of two-dimensional fluidized bed . In: Powder Technol. . 77, 1993.
  6. ↑ BPB Hoomans, JAM Kuipers, WJ Briels, WPM Van Swaaij: Discrete particle simulation of bubble and slug formation in a two-dimensional gas-fluidized bed: A hard-sphere approach . In: Chem. Eng. Sci. . 51, 1996.
  7. ^ BH Xu, AB Yu: Numerical simulation of the gas-solid flow in a fluidized bed by combining discrete particle method with computational fluid dynamics . In: Chemical Engineering Science . 52, 1997, p. 2785.
  8. ↑ BH Xu, AB Yu: Comments on the paper numerical simulation of the gas-solid flow in a fluidized bed by combining discrete particle method with computational fluid dynamics . In: Chemical Engineering Science . 53, 1998, pp. 2646-2647.
  9. ↑ HP Zhu, ZY Zhou, RY Yang, AB Yu: Discrete particle simulation of particulate systems: Theoretical developments . In: Chemical Engineering Science . 62, 2007, pp. 3378-3396.
  10. ↑ HP Zhu, ZY Zhou, RY Yang, AB Yu: Discrete particle simulation of particulate systems: A review of major applications and findings . In: Chemical Engineering Science . 63, 2008, pp. 5728-5770.
  11. ↑ BH Xu, AB Yu: Particle-scale modeling of gas-solid flow in fluidization . In: Journal of Chemical Technology and Biotechnology . 78, 2003, pp. 111-121.
  12. ↑ YQ Feng, Yu AB, AB Yu, A. Vince: Assessment of model formula tions in the discrete particle simulation of gas-solid flow . In: Industrial & Engineering Chemistry Research . 43, 2004, pp. 8378-8390.
  13. ↑ NG Deen, MVS Annaland, MA Van Der Hoef, JAM Kuipers: Review of discrete particle modeling of fluidized beds . In: Chemical Engineering Science . 62, 2007, pp. 28-44.
  14. ↑ O. Gryczka, S. Heinrich, NS Deen, M. van Sint Annaland, JAM Kuipers, M. Mörl: CFD modeling of a prismatic spouted bed with two adjustable gas inlets . In: Canadian Journal of Chemical Engineering . 87, 2009, pp. 318-328.
  15. ↑ B. Peters: Classification of combustion regimes in a packed bed based on the relevant time and length scales . In: Combustion and Flame . 116, 1999, pp. 297-301.
  16. ↑ B. Peters: Measurements and application of a discrete particle model (DPM) to simulate combustion of a packed bed of individual fuel particles . In: Combustion and Flame . 131, 2002, pp. 132-146.
  17. ↑ E. Simsek, B. Brosch, S. Wirtz, V. Scherer, F. Krüll: Numerical simulation of grate firing systems using a coupled CFD / Discrete Element Method (DEM) . In: Powder Technology . 193, 2009, pp. 266-273.
  18. ↑ Shungo Natsui, Shigeru Ueda, Zhengyun Fan, Nils Andersson, Junya Kano, Ryo Inoue, Tatsuro Ariyama: Characteristics of solid flow and stress distribution including asymmetric phenomena in blast furnace analyzed by discrete element method . In: ISIJ International . 50, 2010, pp. 207-214.
  19. ↑ YH Man, RC Byeong: A numerical study on the combustion of a single carbon particle entrained in a steady flow . In: Combustion and Flame . 97, 1994, pp. 1-16.
  20. ↑ JC Lee, RA Yetter, FL Dryer: Numerical simulation of laser ignition of an isolated carbon particle in a quiescent environment . In: Combustion and Flame . 105, 1996, pp. 591-599.
  21. ↑ BPB Hoomans, JAM Kuipers, WJ Briels, WPM Van Swaaij: Discrete particle simulation of bubble and slug formation in a two-dimensional gas-fluidized bed: A hard-sphere approach . In: Chem. Eng. Sci. . 51, 1996.
  22. ↑ KW Chu, AB Yu: Numerical simulation of complex particle-fluid flows . In: Powder Technology . 179, 2008, pp. 104-114.
  23. ↑ H. Zhou, G. Mo, J. Zhao, K. Cen: DEM-CFD simulation of the particle dispersion in a gas-solid two-phase flow for a fuel-rich / lean burner . In: Fuel . 90, 2011, pp. 1584-1590.
  24. ↑ KW Chu, B. Wang, AB Yu, A. Vince, GD Barnett, PJ Barnett: CFD-DEM study of the effect of particle density distribution on the multiphase flow and performance of dense medium cyclone . In: Minerals Engineering . 22, 2009, pp. 893-909.
  25. ↑ PN Rowe, AW Nienow: Particle mixing and segregation in gas fluidized beds: A review . In: Powder Technology . 15, 1976, pp. 141-147.
  26. ↑ YQ Feng, Yu AB, AB Yu, A. Vince: Assessment of model formula tions in the discrete particle simulation of gas-solid flow . In: Industrial & Engineering Chemistry Research . 43, 2004, pp. 8378-8390.
  27. ↑ YQ Feng, AB Yu: An analysis of the chaotic motion of particles of different sizes in a gas fluidized bed . In: Particuology . 6, 2008, pp. 549-556.
  28. ↑ KD Kafuia, C. Thornton, MJ Adams: Discrete particle-continuum fluid modeling of gas-solid fluidized beds . In: Chemical Engineering Science . 57, 2002, pp. 2395-2410.