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Licensed Unlicensed Requires Authentication Published by De Gruyter February 11, 2017

Discrete simulation of granular and particle-fluid flows: from fundamental study to engineering application

  • Wei Ge

    Wei Ge got his BSc in 1992 and his PhD in 1998, both from Harbin Institute of Technology, China. He has been a professor of chemical engineering at the Institute of Process Engineering, CAS, since 2006. He is engaged mainly in multiscale simulation of particle-fluid two-phase systems. He proposed pseudo-particle modeling and extended the EMMS model. As project leader, he developed the Mole series multiscale supercomputing systems to bridge simulation of molecular details to reactor performance. He is associate editor of Chem. Eng. Sci.

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    , Limin Wang

    Limin Wang got his PhD degree from Institute of Process Engineering (IPE), CAS, in 2008. From 2008 to 2009, he worked as a postdoctoral fellow in CNRS, France. He has been a professor of chemical engineering at the Institute of Process Engineering, CAS, since 2016. He is engaged mainly in mesoscale concept for turbulence modeling and simulation, lattice Boltzmann modeling for particle-fluid two-phase flows, and lattice- and particle- based methods for complex flows.

    , Ji Xu

    Ji Xu got his BSc in 2006 from Xi’an Jiaotong University and his PhD in 2012 from Institute of Process Engineering (IPE), CAS. He has been an associate professor of chemical engineering at IPE since 2015. He is engaged mainly in developing supercomputing methods for large-scale particle simulations, for example MD and DEM.

    , Feiguo Chen

    Feiguo Chen got his BSc in 2002 from Tsinghua University and his PhD in 2009 from CAS. He has been an associate professor of chemical engineering at Institute of Process Engineering, CAS, since 2012. He is engaged mainly in multiscale discrete simulation for multiphase systems.

    , Guangzheng Zhou

    Guangzheng Zhou got his PhD in 2010 from Institute of Process Engineering, CAS. He is engaged mainly in mesh-free simulation of granular flows and liquid-liquid two-phase flows. He designed some novel baffles based on DEM for the enhancement of powder mixing in tumbling blenders. He also proposed a revised model of surface tension based on SPH and revealed the inherent non-Newtonian properties of noncompressible SPH.

    , Liqiang Lu

    Liqiang Lu got his PhD in 2016 from Institute of Process Engineering, CAS. His research focuses on large-scale discrete particle simulation of fluid-particle systems using OpenFOAM and GPU-based DEM code. He proposed the EMMS-DPM coarse grained method for simulation of gas-solid flows using EMMS model and KTGFs. He is also interested in code optimization on Xeon Phi and GPUs and developed an online interactive gas solid flow simulation system. Since March 2016, he has been working as an ORISE postdoctoral researcher at the NETL Multiphase Flow Science Team, USA.

    , Qi Chang

    Qi Chang received his BSc and MSc in chemical engineering and technology from Tianjin University in 2009 and 2013, respectively, and is now pursuing his PhD study there and a visiting student at IPE now. He is now working on DNS of particle fluid flows.

    and Jinghai Li

    Jinghai Li established the EMMS model for gas-solid systems and generalized it into the EMMS paradigm of computation. He devotes himself to promoting mesoscience based on the EMMS principle of compromise in competition as an interdisciplinary science. He is vice president of the International Council for Science, vice chairman of the China Association of Science and Technology, and vice president of the Chinese Society of Chemical Engineering. He is editor-in-chief of Particuology. He holds memberships with CAS, TWAS, SATW, RAEng, and ATSE.

Abstract

Multiphase chemical reactors with characteristic multiscale structures are intrinsically discrete at the elemental scale. However, due to the lack of multiscale models and the limitation of computational capability, such reactors are traditionally treated as continua through straightforward averaging in engineering simulations or as completely discrete systems in theoretical studies. The continuum approach is advantageous in terms of the scale and speed of computation but does not always give good predictions, which is, in many cases, the strength of the discrete approach. On the other hand, however, the discrete approach is too computationally expensive for engineering applications. Developments in computing science and technologies and encouraging progress in multiscale modeling have enabled discrete simulations to be extended to engineering systems and represent a promising approach to virtual process engineering (VPE, or virtual reality in process engineering). In this review, we analyze this emerging trend and emphasize that multiscale discrete simulations (MSDS), that is, considering multiscale structures in discrete simulation through rational coarse-graining and coupling between discrete and continuum methods with the effect of mesoscale structures accounted in both cases, is an effective way forward, which can be complementary to the continuum approach that is being improved by multiscale modeling also. For this purpose, our review is not meant to be a complete summary to the literature on discrete simulation, but rather a demonstration of its feasibility for engineering applications. We therefore discuss the enabling methods and technologies for MSDS, taking granular and particle-fluid flows as typical examples in chemical engineering. We cover the spectrum of modeling, numerical methods, algorithms, software implementation and even hardware-software codesign. The structural consistency among these aspects is shown to be the pivot for the success of MSDS. We conclude that with these developments, MSDS could soon become, among others, a mainstream simulation approach in chemical engineering which enables VPE.

About the authors

Wei Ge

Wei Ge got his BSc in 1992 and his PhD in 1998, both from Harbin Institute of Technology, China. He has been a professor of chemical engineering at the Institute of Process Engineering, CAS, since 2006. He is engaged mainly in multiscale simulation of particle-fluid two-phase systems. He proposed pseudo-particle modeling and extended the EMMS model. As project leader, he developed the Mole series multiscale supercomputing systems to bridge simulation of molecular details to reactor performance. He is associate editor of Chem. Eng. Sci.

Limin Wang

Limin Wang got his PhD degree from Institute of Process Engineering (IPE), CAS, in 2008. From 2008 to 2009, he worked as a postdoctoral fellow in CNRS, France. He has been a professor of chemical engineering at the Institute of Process Engineering, CAS, since 2016. He is engaged mainly in mesoscale concept for turbulence modeling and simulation, lattice Boltzmann modeling for particle-fluid two-phase flows, and lattice- and particle- based methods for complex flows.

Ji Xu

Ji Xu got his BSc in 2006 from Xi’an Jiaotong University and his PhD in 2012 from Institute of Process Engineering (IPE), CAS. He has been an associate professor of chemical engineering at IPE since 2015. He is engaged mainly in developing supercomputing methods for large-scale particle simulations, for example MD and DEM.

Feiguo Chen

Feiguo Chen got his BSc in 2002 from Tsinghua University and his PhD in 2009 from CAS. He has been an associate professor of chemical engineering at Institute of Process Engineering, CAS, since 2012. He is engaged mainly in multiscale discrete simulation for multiphase systems.

Guangzheng Zhou

Guangzheng Zhou got his PhD in 2010 from Institute of Process Engineering, CAS. He is engaged mainly in mesh-free simulation of granular flows and liquid-liquid two-phase flows. He designed some novel baffles based on DEM for the enhancement of powder mixing in tumbling blenders. He also proposed a revised model of surface tension based on SPH and revealed the inherent non-Newtonian properties of noncompressible SPH.

Liqiang Lu

Liqiang Lu got his PhD in 2016 from Institute of Process Engineering, CAS. His research focuses on large-scale discrete particle simulation of fluid-particle systems using OpenFOAM and GPU-based DEM code. He proposed the EMMS-DPM coarse grained method for simulation of gas-solid flows using EMMS model and KTGFs. He is also interested in code optimization on Xeon Phi and GPUs and developed an online interactive gas solid flow simulation system. Since March 2016, he has been working as an ORISE postdoctoral researcher at the NETL Multiphase Flow Science Team, USA.

Qi Chang

Qi Chang received his BSc and MSc in chemical engineering and technology from Tianjin University in 2009 and 2013, respectively, and is now pursuing his PhD study there and a visiting student at IPE now. He is now working on DNS of particle fluid flows.

Jinghai Li

Jinghai Li established the EMMS model for gas-solid systems and generalized it into the EMMS paradigm of computation. He devotes himself to promoting mesoscience based on the EMMS principle of compromise in competition as an interdisciplinary science. He is vice president of the International Council for Science, vice chairman of the China Association of Science and Technology, and vice president of the Chinese Society of Chemical Engineering. He is editor-in-chief of Particuology. He holds memberships with CAS, TWAS, SATW, RAEng, and ATSE.

Acknowledgments

The authors would like to thank all members of the EMMS group for their contributions to the studies and developments reviewed in this article and for their collaboration and support in its preparation, especially Shiwen Liu, Xiaowen Liu, and Mengjie Du, for their help in the literature survey and drawing; Yanfeng Shi for editing; and Guoxian Gao for the visualization of some computational results. We would also like to thank Prof. Ying Hu of East China University of Science Technology for illuminative discussions on the theoretical background of the EMMS model. We are grateful to the financial support from the National Natural Science Foundation of China (grants 21225628, 21206167, 91434113, 91434201, 21106155, and 2110645), the CAS (grants XDA07080000 and QYZDB-SSW-SYS029 and CAS Interdisciplinary Innovation Team), and the National Program on Key Basic Research Project (grant 2015CB251402).

Appendix: The energy minimization multiscale (EMMS) model

The EMMS model was first proposed in Li (1987) and first published by Li et al. (1988). A more detailed and systematic description was given by the monograph of Li and Kwauk (1994). The original model is for a steady-state global description of the heterogeneous two-phase structures in concurrent-up gas-solid fluidization without considering the spatial distribution and temporal variation of the flow field, and only the vertical motion is considered. The physical picture of the model is shown in Appendix Figure A1; that is, the solids in gas-solid fluidization are either in the dense phase with voidage εc, superficial solid velocity Udf, and superficial velocity of the interstitial gas Uc (superficial velocities are the equivalent velocities corresponding to an empty cross-section, that is, the real velocities Vdc=Udc/(1–εc), Vc=Uc/εc) or in the dilute phases with voidage εf, superficial solid velocity Udf, and superficial velocity of the interstitial gas Uf. The dense phase is assumed to occur as discrete clusters with volume fraction of f and characteristic size of dcl. This dcl is taken as the diameter of a hydrodynamically equivalent spherical cluster in calculating the drag on its member particles.

Appendix Figure A1: Two-phase structure assumed in the EMMS model.
Appendix Figure A1:

Two-phase structure assumed in the EMMS model.

At given operation conditions, that is, the superficial gas velocity Ug and superficial solids velocity Ud, six hydrodynamic equations can be established for these eight variables, they are as follows:

(A1)Ug=Uf(1f)+Ucf,

and

(A2)Ud=Udf(1f)+Udcf,

representing the continuity equations of the fluid and solid phases;

(A3)FDf=34CDf1εfdpρfUsf2=Gf=(1εf)(ρpρf)g,

representing the balance of the effective weight of the dilute-phase solids and the drag from the dilute-phase gas (where CDf is the drag coefficient in the dilute phase, which is a function of the dilute-phase superficial slip velocity Usf=UfεfUdf/(1–εf) and εf);

(A4)FDc=34CDc1εcdpρfUsc2,
(A5)FDi=34CDi1dclρfUsi2,

and

(A6)FDc+FDi=Gc=(1εc)(ρpρf)g

representing the balance between the effective weight of the dense-phase solids and the drag from the dense-phase gas and from the bypassing the dilute-phase gas (where CDc is the drag coefficient in the dense phase, which is a function of the dense-phase superficial slip velocity Usc=UcεcUdc/(1–εc) and εc; and CDi is the drag coefficient of the dilute phase fluid to the dense phase solids, which is a function of the interphase superficial slip velocity Usi=(UfεfUdc/(1–εc))(1–f));

(A7)FDf+f1fFDi=FDc,

representing the balance between the pressure drops in the dense and dilute phases; and finally, an empiric correlation of dcl based on the assumption that it is inversely proportional to the energy input Nst, that is,

(A8)dcldp=g(Up1εmax(Umf+εmfUp1εmf))Nstρpρpρf(Umf+εmfUp1εmf)g,

where εmf is the minimum fluidization voidage and

(A9)Nst=Wstρp(1ε)

is the energy consumption rate for suspending and transporting the particles per unit mass of solids with

(A10)Wst=FDcUcf+FDfUf(1f)+FDiUf(1f).

Obviously, six equations are not enough to solve eight variables, therefore, to close the equation set, a stability condition is introduced to the model, that is, the minimization of Nst (Nst→min). It is first proposed for particle-fluid compromise regime but Ge and Li (2002a) later demonstrated that, effectively, it is applicable to choking prediction also. Zhang et al. (2005) and Hu et al. (2017) later demonstrated in systems with acceleration and concurrent-down flows that Nst/NT→min is a stability criterion effective in more general conditions. According to Li and Kwauk (1994), Nst is the portion in the total energy consumption NT=gUg(ρpρg)/ρp that can be consumed without causing mesoscale dynamic motion in the systems, while the rest Nd=NTNst is the additional consumption due to such dynamic motion, for example, the deformation, merging, and breakage of the bubbles and clusters in gas-solid flow, which inevitably causes the acceleration and deacceleration of the solids and, hence, their velocity fluctuations. To understand this remark, some further discussion is necessary.

[Correction added after online publication 16 November 2017: The original text of the sixth line of this paragraph was: …it is applicable to all flow regimes also.]

As discussed in Li and Kwauk (1994), Nst, or more directly, Wst, can be decomposed into three parts corresponding to the dense and dilute phases and the interphase, respectively. The first two parts are same to their counterparts in the three-phase breakdown of NT or WT, and the difference is only in the interphase. That is, (Wst)iPiUf(1–f)=FDiUf(1–f) and (WT)iPiUf=FDiUf. In other words, Wd=fFDiUf. In fact, Wst is calculated based on an idealized system without dynamic motion of the mesoscale structures. However, as demonstrated in DNS (Ma et al. 2006, Zhou et al. 2014), whenever these mesoscale structures are existent, they cannot be kept at steady states without causing such motion, because the forces at the interfaces between these structures are inevitably nonuniform. Therefore, to separate the contribution of the static structures to the energy consumption, they are calculated as fixed configurations of solids, which means that internal forces have to been introduced (artificially) to keep the configurations. In this case, as for single solid particles in the dense or dilute phases, the internal stress of the structures will distribute the pressure drop caused by FDi to the whole cross-section of the bed or element considered, not just the dilute phase as in the calculation of (NT)i. The differences between (NT)i and (Nst)i and then NT and Nst are hence produced.

It is interesting to note that Nst or Wst contains not only the energy dissipation (Ws=(Ws)c+(Ws)f+(Ws)iPcUscfPfUsf(1–f)+ΔPiUsf(1–f)), which is related to the entropy production rate employed in nonequilibrium thermodynamics, but also energy conversion from the enthalpy of the gas to the gravitational potential of the solids (Wt=WstWs, with (Wt)c=(Wst)c–(Ws)c, (Wt)f=(Wst)f–(Ws)f, and (Wt)i=(Wst)i–(Ws)i). Both Ns and Nt (or Ws and Wt) are considered as energy consumption, but the definition of consumption is actually application dependent and hence subjective. As shown in Appendix Figure A2, in concurrent-up flow, which was first considered in the original model, NT is positive and considered as the total energy input to be “consumed” by Nst and Nd, which are also positive but smaller than NT. But in concurrent-down flow, the release of gravitational potential from the solids, −Ntr, becomes the driving power with Nst and Nd as a whole actually store rather than consume energy. It seems that “energy conversion,” either “consumed” or “stored,” is a more general and suitable phrase instead of “energy consumption” for these energy-related terms. In this sense, the energy conversion involved in Nst will not cause the fluctuation of the solids, while Nd is responsible for that, and it is their magnitudes rather than signed values are really relevant to the stability criterion.

Appendix Figure A2: Breakdown of the energy transformation rates in gas-solid flow (downward arrows mean negative values).(A) Concurrent-up flow and (B) concurrent-down flow.
Appendix Figure A2:

Breakdown of the energy transformation rates in gas-solid flow (downward arrows mean negative values).

(A) Concurrent-up flow and (B) concurrent-down flow.

In fact, we can define in the framework of the EMMS model the total dissipation in the system, Nsdr=NTNtr=gUs(ρpρg)/ρp with Ntr=gUd(ρpρg)/ρp, which is roughly related to the mass-specific entropy production rate in the system σ with σ=Nsdr/T (where T is the real molecular temperature). In this sense, the original EMMS model is for a system with given σ, while Nst contains only part of the σ, that is, Ns/T. On the other hand, the total energy conversion involved for transporting the solids, Ntr, is meaningful only in creating the global velocity profile of the solids in which the part of Nt is actually responsible for the fluctuation of the solids due to this profile. That means, Ntr and Nt are only relevant to the stability criterion above certain scale, and for a local element where the effect of global flow distribution is negligible, the effective stability criteria may be different for being applicable to different flow regimes and directions. Note that Ns in this sense is the local dissipation in the system, without considering the additional dissipation caused by the temporal and spatial fluctuation of the flow variables. The minimization of dissipation is related to the minimum entropy production in nonequilibrium systems (Prigogine 1967); however, this effect may eventually coexist with maximum dissipation, and the whole system is in fact described by the compromise in competition of the two seemingly contradictive tendencies. This is the core thought of the EMMS principle (Li and Kwauk 2003) developed from the EMMS model.

[Correction added after online publication 16 November 2017: The original text of last four sentences of this paragraph was: That means, Ntr and Nt are only relevant to the stability criterion at the global scale, and for a local element where the effect of global flow distribution is negligible, the effective stability criterion is correspondingly (NstNt)/(NTNtr) = Ns/Nsdr → min, which is indifferently applicable to different flow regimes and directions. Note that Ns in this sense is the local dissipation in the system, without considering the additional dissipation caused by the temporal and spatial fluctuation of the flow variables. As discussed in Ge et al. (2007), the minimization of local dissipation is in accordance with the minimum entropy production in nonequilibrium systems (Prigogine 1967); however, this local effect may eventually lead to maximum entropy production at global scale, and the whole system is in fact described by the compromise in competition of the two seemingly contradictive tendencies. This is, however, consistent to the EMMS principle (Li and Kwauk 2003, Li et al. 2004, Ge et al. 2007) later developed from the EMMS model.]

This may propose very intriguing questions such as whether a similar relationship between σ→min and Nst→min exists as in the case of E→min for equilibrium systems at ground state and F=ETS→min or G=ETS+pV for higher temperatures, and whether Nst=NTNd=NsdrNd+Ntr(Nst=NsdrNd for systems without net reversible energy transformation, which is similar in form to F=ETS) can be understood from a new angle. One clue for this similarity is that if the energy consumption does not cause any relative motion between the solids, as assumed in the calculation of Nst, the solid subsystem itself is indeed equivalent to a system near zero temperature. In this case, the hydrodynamic forces between the particles are completely and uniquely defined by the configuration of the particles under given overall flow conditions; that is, they become, effectively, potential forces, while for the gas subsystem, the particle configuration determines Nst. Together with the gravitational potential, an effective energy Es can be defined for the solid phase in an equivalent equilibrium system, which can be related to Nst. In real systems where the relative motion between the solids are inevitable, the additional energy consumption Nd is related to intensity of such fluctuations and hence corresponds to the effective (granular) temperature Ts and entropy Ss in the equivalent equilibrium system. On the other hand, it can be expected from the physical conditions that σ→min may still applicable locally at the scale of single particles or fluid elements, so another interesting questions is how it leads to Nst→min through the hydrodynamic interactions among these particles and elements.

[Correction added after online publication 16 November 2017: The original text of the end of the first sentence of this paragraph was: …can be understood as a kind of “free entropy production rate”.]

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Received: 2015-12-25
Accepted: 2016-11-28
Published Online: 2017-2-11
Published in Print: 2017-11-27

©2017 Walter de Gruyter GmbH, Berlin/Boston

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