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m Glrx moved page Extended Discrete Element Method to Extended discrete element method: Capitalization. See Finite element method, Discrete element method |
capitalization, ref position, spacing, crlfs |
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The '''
| first1=P. A.
| last1=Cundall
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| volume=29
| pages=47–65
}}</ref> and Allen
| first1=M. P.
| last1=Allen
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| title=Computer Simulation of Liquids
| publisher=Claredon Press Oxford
| year=1990}}</ref>) 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.
[[File:Internal temperature distribution in a particle.png|thumb|An internal temperature distribution for a spherical particle versus radius and time under a time-varying [[heat flux]].]]
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==History==
Molecular
| first1=B. J.
| last1=Alder
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| year=1964
| volume=136
}}</ref> may be regarded as a first step toward the extended discrete element method, although
the forces due to collisions between particles were replaced by energy potentials e.g. [[Lennard-Jones]] potentials
of [[molecules]] and [[atoms]] as long range forces to determine interaction.
Similarly, the fluid dynamic interaction of particles suspended in a flow were investigated. The [[drag]] forces exerted on the particles by the relative velocity by them and the flow were treated as additional forces acting on the particles. Therefore, these [[multiphase flow]] phenomena including a solid e.g.~particulate and a gaseous or fluid phase resolve the particulate phase by discrete methods, while gas or liquid flow is described by continuous methods, and therefore, is labelled the combined continuum and discrete model (CCDM) as applied by Kawaguchi et al,<ref>{{cite journal
| first1=T.
| last1=Kawaguchi
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| year=1993
| volume=77
}}</ref>
| first1=B. P. B.
| last1=Hoomans
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| year=1996
| volume=51
}}</ref>
| first1=B. H.
| last1=Xu
| first2=A. B.
| last2=Yu
| title=Numerical simulation of the gas-solid flow in a fluidized bed by combining discrete particle method with computational fluid dynamics
| journal=Chemical Engineering Science
| year=1997
| volume=52
| pages=2785
}}</ref> and Xu
| first1=B. H.
| last1=Xu
| first2=A. B.
| last2=Yu
| title=Comments on the paper numerical simulation of the gas-solid flow in a fluidized bed by combining discrete particle method with computational fluid dynamics
| journal=Chemical Engineering Science
| year=1998
| volume=53
| pages=2646–2647
}}</ref>
a better understanding of the fundamentals. This was also concluded by Zhu 2007 et al.<ref>{{cite journal
| first1=H. P.
| last1=Zhu
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| volume=62
| pages=3378-3396
}}</ref> and Zhu 2008 et al.<ref>{{cite journal
| first1=H. P.
| last1=Zhu
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| volume=63
| pages=5728–5770
}}</ref> during a review on particulate flows modelled with the CCDM approach. It has seen a mayor development in last two decades and describes motion of the solid phase by the [[Discrete Element Method]] (DEM) on an individual particle scale and the remaining phases are treated by the [[Navier-Stokes]] equations. Thus, the method is recognized as an effective tool to investigate into the interaction between a particulate and fluid phase as reviewed by Yu and Xu,<ref>{{cite journal
| first1=B. H.
| last1=Xu
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| volume=78
| pages=111–121
}}</ref>
| first1=Y. Q.
| last1=Feng
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| volume=43
| pages=8378–8390
}}</ref> and Deen et al.
| first1=N. G.
| last1=Deen
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| volume=62
| pages=28–44
}}</ref>
| first1=O.
| last1=Gryczka
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}}</ref>.
The theoretical foundation for the
| first1=B.
| last1=Peters
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| volume=116
| pages=297-301
}}</ref>
| first1=B.
| last1=Peters
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| volume=131
| pages=132–146
}}</ref>
| first1=E.
| last1=Simsek
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| volume=193
| pages=266–273
}}</ref> to predict the furnace process of a grate firing system. Applications to the complex processes of a blast furnace have been attempted by Shungo et al.<ref>{{cite journal
| first1=Shungo
| last1=Natsui
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| volume=50
| pages=207–214
}}</ref>
codes such as Star-CD of [[CD-adapco]], [[Ansys]] and [[AVL]]-Fire. Droplets of a spray are treated by a zero-dimensional approach to account for heat and mass transfer to the fluid phase.
==Methodology==
Numerous challenges in engineering exist and evolve, that include a continuous and discrete phase simultaneously, and therefore, cannot be solved accurately by continuous or discrete approaches, only. Therefore, XDEM provides a platform, that couples discrete and continuous phases for a large number of engineering applications.
Although research and development of numerical methods in each domains of discrete and continuous solvers is still progressing, respective software tools have reached a high degree of maturity. In order to couple discrete and continuous approaches, two major concepts are available:
*'''Monolithic concept''': The equations describing multi-physics phenomena are solved simultaneously by a single solver producing a complete solution.
*'''Partitioned or staggered concept''': The equations describing multi-physics phenomena are solved sequentially by appropriately tailored and distinct solvers with passing the results of one analysis as a load to the next.
The former concept requires a solver that includes a combination of all physical problems involved, and therefore, requires a large implementation effort. However, there exist scenarios for which it is difficult to arrange the coefficients of combined [[differential equations]] in one [[matrix]]. A partitioned concept as a coupling between a number of solvers representing individual domains of physics offers distinctive advantages over a monolithic concept.
[[File:Staggered methodology for software coupling.png|thumb|Staggered methodology for discrete/continuous applications.]]
It inherently encompasses a large degree of flexibility by coupling an almost arbitrary number of solvers.
Furthermore, a more modular software development is retained that allows by far more specific solver techniques adequate to the
problems addressed. However, partitioned simulations impose stable and accurate coupling algorithms that convince by their pervasive character.
Within the staggered concept of XDEM, continuous fields are described by the solution the respective continuous (conservation) equations. Properties of individual particles such as temperature are also resolved by solving respective conservation equations that yields both a spatial and temporal internal distribution of relevant variables. Mayor conservation principles with their equations and variables to be solved for and that are employed to an individual particle within XDEM are listed in the
following table.
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|}
The solution of these equations in principle defines a three-dimensional and transient field of the relevant variables such as temperature or species. However, the application of these conservation principles to a large number of particles usually restricts the resolution to at most one representative dimension and time due to CPU time consumption. Experimental evidence
at least in reaction engineering supports the assumption of one-dimensionality as pointed out by Man and Byeong,<ref>{{cite journal
| first1=Y. H.
| last1=Man
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| volume=97
| pages=1–16
}}</ref> while the importance of a transient behaviour is stressed by Lee et al.<ref>{{cite journal
| first1=J. C.
| last1=Lee
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| volume=105
| pages=591–599
}}</ref>
| first1=J. C.
| last1=Lee
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| pages=591–599
}}</ref>
==Applications==
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[[File:Particles impacting on a conveyer belt.png|thumb|Deformation of a conveyor belt due to impacting granular material.]]
Problems that involve both a continuous and a discrete phase are important in applications as diverse as pharmaceutical industry e.g.~drug production, agriculture food and processing industry, mining, construction and agricultural machinery, metals manufacturing, energy production and systems biology. Some predominant examples are coffee, corn flakes, nuts, coal, sand, renewable fuels e.g.~biomass for energy production and fertilizer.
Initially, such studies were limited to simple flow configurations as pointed out by Hoomans,<ref>{{cite journal
| first1=B. P. B.
| last1=Hoomans
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| year=1996
| volume=51
}}</ref>
| first1=K. W.
| last1=Chu
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| volume=179
| pages=104–114
}}</ref> demonstrated that the method could be applied to a complex flow configuration consisting of a fluidized bed, conveyor belt and a cyclone. Similarly, Zhou et al.<ref>{{cite journal
| first1=H.
| last1=Zhou
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| volume=90
| pages=1584–1590
}}</ref> applied the CCDM approach to the complex geometry of fuel-rich/lean burner for pulverised coal combustion in a plant and Chu et al.<ref>{{cite journal
| first1=K. W.
| last1=Chu
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| volume=22
| pages=893–909
}}</ref> modelled the complex flow of air, water, coal and magnetite particles of different sizes in a dense medium [[cyclone]] (DMC).
The CCDM approach has also been applied to fluidised beds as reviewed by Rowe and Nienow<ref>{{cite journal
| first1=P. N.
| last1=Rowe
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| volume=15
| pages=141–147
}}</ref> and Feng and Yu
| first1=Y. Q.
| last1=Feng
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| volume=43
| pages=8378–8390
}}</ref> and applied by Feng and Yu
| first1=Y. Q.
| last1=Feng
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| volume=6
| pages=549–556
}}</ref> to the chaotic motion of particles of different sizes in a gas fluidized bed. Kafuia et al.<ref>{{cite journal
| first1=K. D.
| last1=Kafuia
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| volume=57
| pages=2395–2410
}}</ref> describe discrete particle-continuum fluid modelling of gas-solid fluidised beds. Further applications of XDEM include thermal conversion of biomass on a backward and forward acting grate. Heat transfer in a [[packed bed]] [[reactor]] was also investigated for hot air streaming upward through the packed bed to heat the particles, which dependent on position and size experience different heat transfer rates. The [[deformation]] of a conveyor belt due to impacting [[granular material]] that is discharged over a chute represents an application in the field of [[stress]]/[[strain]] analysis.
{|
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| [[File:Particle temperature in a packed bed reactor.png|thumb|Distribution of porosity inside the packed bed and particle temperature.]]
|}
==References==
{{Reflist|30em}}
{{Numerical PDE}}
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