Gas-particle flows in vertical risers are involved in many industrial scale fluidized bed applications such as catalytic cracking, fossil or biomass combustion. Risers flows are often simulated by two-fluid model equations coupled with closures developed in the frame the kinetic theory of granular media. However, two-fluid model discretized over coarse mesh with respect to particle clustering size are performed for large units because of limited computational resources. Now, it is well established that meso-scales cancelled out by coarse mesh simulations have dramatic effect on overall behaviour of flows. This study proposed a sub-grid modeling approach for effective drag force and particle stresses which accounts for the effects of unresolved structures on the resolved flows

Fede, Pascal

Simonin, Olivier

Özel, Ali

English

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To cite this version : Özel, Ali and Fede, Pascal and Simonin, Olivier Aposteriori study of filtered Euler-Euler two-phase model using a high resolution simulation of a 3D periodic circulating fluidized bed. In: 2012 AIChE Annual meeting, 28 October 2012 - 02 November 2012 (Pittsburgh, United States). Open Archive TOULOUSE Archive Ouverte (OATAO)OATAO is an open access repository that collects the work of Toulouse researchersand makes it freely available over the web where possible.  This is an author-deposited version published in : http://oatao.univ-toulouse.fr/Eprints ID : 10370 Any correspondance concerning this service should be sent to the repositoryadministrator: staff-oatao@listes-diff.inp-toulouse.frA POSTERIORI STUDY OF FILTERED EULER-EULER TWO-PHASEMODEL USING A HIGH RESOLUTION SIMULATION OF A 3-DPERIODIC CIRCULATING FLUIDIZED BEDAli Ozel, Pascal Fede, Olivier Simonin,Institut de Mécanique des Fluides de Toulouse, Toulouse, FranceIntroductionGas-particle flows in vertical risers are involved in many industrial scale fluidized bed appli-cations such as catalytic cracking, fossil or biomass combustion. Risers flows are often simulated bytwo-fluid model equations coupled with closures developed in the frame the kinetic theory of granularmedia (1–4). However, two-fluid model discretized over coarse mesh with respect to particle clusteringsize are performed for large units because of limited computational resources (5, 6). Now, it is wellestablished that meso-scales cancelled out by coarse mesh simulations have dramatic effect on overallbehaviour of flows (6–9).Several attempts of the extension of two-fluid model by accounting for these unresolved struc-tures have been done for coarse mesh simulations through different ways (6). In the framework ofthe filtered two-fluid model, Sundaresan and co-workers (7) performed highly resolved simulationsof kinetic theory based two-fluid model equations for gas-particle flow in 2-D and 3-D periodic do-main and it was stated that the existence of meso-scale structures causes overestimation of the dragforce and underestimation of the particle agitation production and dissipation. Following this study,(10) proposed an ad-hoc sub-grid models for effective drag force and particle stresses which accountsfor the effects of unresolved structures on the resolved flows. (8, 11) presented a filtering approachmethodology to construct closures for the effective drag force and the effective particle stresses. (9)proposed an effective drag model dependent on the filter size and the solid volume fraction for 2-Dbubbling fluidized bed.Such high resolutions simulations using the standard two-fluid model (1, 2) were performed by(12) for a 3-D periodic circulating fluidized bed (PCFB) where typical FCC particles (dp = 75µm,ρp = 1500 kg/m3) were interacting with the ambient gas (ρg = 1.186 kg/m3, µg = 1.8× 10−5 Pa.s).The mean gas-solid flow were periodically driven along the opposite direction of gravity and concern-ing the transfers between the phases with non-reactive isothermal flow, the drag and buoyancy forceswere accounted for the momentum transfer. The effect of the fluctuations of the gas velocity at smallscales was neglected. The computational domain is shown in Figure 1. (12) refined computationalgrids to get mesh-independent result in which statistical quantities do not change with any furthermesh refinement. Instantaneous particle volume fraction fields in the periodic circulating fluidizedbed for different mesh resolutions are shown in Figure 2. This result were then filtered by volumeaveraging and used to perform a priori analyses on the filtered phase balance equations. Consistent re-sults with previous studies were obtained. The physical identification of over-prediction of drag forcewas determined and these results show that filtered momentum equation could be computed on coarsegrid simulation but must take into account the particle to fluid drift velocity (sub-grid drift velocity)due to the sub-grid correlation between the local fluid velocity and the local particle volume fraction(9, 12, 13). Closure relation is needed for the sub-grid drift velocity and several models were pro-posed, herein, we discuss only the Functional model (see (12) for other models). Additionally, (12)proposed to use the Yoshizawa model (14) for the trace of particle sub-grid stress tensor and the stan-dard compressible Smagorinsky model (15) as in the single phase flows for the anisotropic parts ofstresses.The objective of the present study is to verify these models in posteriori studies. For posterioristudies, mesh independent of a 3-D PCFB was used as a reference for making comparisons. The numer-ical simulations have been carried out using an unsteady Eulerian multi-fluid approach implementedin the unstructured parallelized code NEPTUNE_CFD V1.07@Tlse. NEPTUNE_CFD is a multiphaseflow software developed in the framework of the NEPTUNE project, financially supported by CEA(Commissariat à l’Energie Atomique), EDF (Electricité De France), IRSN (Institut de Radioprotectionet de Sûreté Nucléaire) and AREVA-NP.!!"#$%&&!'!(#$%$&)*!'!(#$%$&)*!'!+!,-..!!!/#0%12!'34&!56+!+!789:;<:6:=>!!"!!!#!!!$!Figure 1: The periodic circulating fluidized bed (PCFB).Figure 2: Instantaneous particle volume fraction field in the periodic circulating fluidized bed fordifferent mesh resolutions. From right to left, the mesh resolution increases. White color correspondsto αp = 0. Black color corresponds to αp,max = 0.64.Particulate Sub-grid ModelsFunctional ModelThe proposed model for the effective drag term is given byαpρpτpVr,β =ρpτ˜p[1 +Kββh(αp)f(∆∗)]αp(U˜g,β − U˜p,β)(1)where the subscript β is used to indicate that there is no implicit summation, Kββ is the model constant,h(αp) and f(∆∗) are two independent functions. h(αp) is the solid volume fraction dependency ofthe model and the following suggested form of this function is obtained from high resolution PCFBsimulation:h(αp) = −tanh(αpCh,1)√αpαp,max(1−αpαp,max)2(2)(1− Ch,2αpαp,max+ Ch,3(αpαp,max)2)with constants Ch,1, Ch,2 and Ch,3 0.1, 1.88, 5.16, respectively. The maximum volume fraction of solidphase αp,max is set to 0.64. The dependence of model on the filter width is given by:f(∆∗) =∆∗2Cf,1 +∆∗2(3)with the constant Cf,1 equal to 0.15 and ∆∗is given by∆∗=∆τ˜p |V˜r|(4)where τ˜p is the filtered relaxation time, |V˜r| is the magnitude of the filtered relative velocity and ∆ isthe filter width. The constant Kββ is dynamically calculated and averaged over the domain to avoidnumerical instabilities (12).SGS Particle Stress ModelsThe particle sub-grid stress tensor σsgsp,ij can be decomposed into deviatoric and spherical parts.(15) model can be proposed for the anisotropic parts of stresses and (14) model can be used for thetrace of stress tensor as follows:σsgsp,ij = σ∗p,ij +13σp,kkδij (5)= −C2s∆2|S˜∗p |S˜∗p,ij + CY∆2|S˜∗p |2δij (6)with S˜∗p,ij the trace free strain rate tensor of the filtered particle velocity and given byS˜∗p,ij =∂U˜p,i∂xj+∂U˜p,j∂xi−23∂U˜p,k∂xkδij. (7)|S˜∗p | is the norm of S˜∗p,ij and defined by |S˜∗p |2 = 1/2S˜∗p,ijS˜∗p,ij . The constants Cs and Cy are dynamicallycalculated by performing domain averaging along the mean flow (16).Results and DiscussionsGlobal QuantitiesTo investigate the dynamic behaviour of particles in the PCFB, (12) defined the statistic quan-tities averaged over domain and in time such as; particle agitation, relative velocity weighted by solidvolume fraction and volumetric solid flux along the mean flow direction (see (12) for the procedure tocalculate domain statistics for different mesh resolutions). Here, we discuss only the averaged volumet-ric solid flux obtained by the standard two-fluid model (TFM) and filtered-two fluid model (LES-TFM;−0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.02  0.04  0.06  0.08  0.1  0.12  0.14  0.16  0.18y1x1Figure 3: The influence of mesh size the non-dimensional total volumetric mass flux , < Gs >twhereGs,o corresponds to the homogeneous case and Gs,conv corresponds to the converged case. : TFMsimulations.  ; LES-TFM simulations for three mesh resolutions: coarse (24 × 24 × 192, F r−1∆=0.175), moderate (32× 32× 256, F r−1∆= 0.128) and fine (40× 40× 320, F r−1∆= 0.104).the Functional model for the effective drag model and the Yoshizawa+Smagorinsky models for the ef-fective particle stresses). The coarsest mesh resolution composed of 110 000 cells (24×24×192, ∆x =∆y = ∆z = 1.145×10−3mwith inverse Froude number, Fr−1∆= 0.175). The highest mesh resolutioncase consists of approximately 17 million cells (128×128×1024 , ∆x = ∆y = ∆z = 0.215×10−3mwith inverse Froude number, Fr−1∆= 0.032). The inverse Froude number Fr−1∆based on the meshsize is given byFr−1∆=(∆x∆y∆z)1/3(τStp )2 ||g||(8)with Stoke’s relaxation time τStp given byρpρgd2p18νgand ||g|| is the norm of the gravity acceleration. Thecharacteristic length scale (τStp )2 ||g|| was set to 0.0066m. For LES-TFM simulations, the filter widthis given by ∆ = (∆x∆y∆z)1/3.The non-dimensional solid fluxes obtained from LES-TFM simulations for three mesh reso-lutions: coarse (24 × 24 × 192, F r−1∆= 0.175), moderate (32 × 32 × 256, F r−1∆= 0.128), fine(40× 40× 320, F r−1∆= 0.104) and mesh dependency study of non-dimensional fluxes obtained fromTFM simulations are shown in Figure 3. Solid fluxes were predicted very well by LES-TFM simula-tions. However, there is slight mesh dependency of the proposed models. The time-domain averagedof models’ constants Kββ , Cs and Cy for coarse, moderate and fine mesh resolutions are given in Table1. Instantaneous solid volume fraction in PCFB obtained from TFM simulations for different meshTable 1: Time-averaged of models’ constants Kββ, (where β = x, y, z), Cs and Cy for coarse, moder-ate and fine mesh resolutions.Fr−1∆< Kxx >t, < Kyy >t< Kzz >t< Cs >t< Cy >t0.175 5.23 4.86 0.010 0.0440.128 5.10 4.92 0.014 0.0430.104 4.82 4.96 0.007 0.038resolutions; Fr−1∆= 0.128 and Fr−1∆= 0.032 are shown in Figure 4. Coarse mesh simulation withFigure 4: Instantaneous of solid volume fraction in the PCFB. White color corresponds to αp = 0.Black color corresponds to αp,max = 0.64. left: TFM with mesh resolution, Fr−1∆= 0.032 (128 ×128×1024), centre: TFM with mesh resolution, Fr−1∆= 0.128 (32×32×256), right: LES-TFM withmesh resolution, Fr−1∆= 0.128 (32× 32× 256).Fr−1∆= 0.128 can not predict segregation along the center-line in the PFCB. In this figure, coarse meshsimulations with Fr−1∆= 0.128 by LES-TFM are also shown. The LES-TFM simulation is capable tocapture segregation of particles along the centre line even for coarse mesh simulation.ConclusionIn this study, we performed Euler-Euler two-phase model simulations by using the effectivedrag force and the effective sub-grid stresses models for gas-solid flow in a 3-D periodic circulatingfluidized bed over relatively coarse mesh with respect to the particle clustering size. The results showthat the overall hydrodynamic behaviour is accurately predicted as comparing with mesh independentresult of the same flow configuration. Further step is to perform simulations by using proposed andavailable models in the literature (e.g. (8, 11) and (9)) for the industrial-scaled fluidized bed appli-cation, make comparisons between models’ predictions and validations with available experimentaldata.AcknowledgementsThis work was performed using HPC resources from GENCI-CINES (Grant 2012-x2012026012).References1. G. Balzer, A. Boëlle, and O. Simonin. Eulerian gas-solid flow modelling of dense fluidizedbed. In FLUIDIZATION VIII, Proc. International Symposium of the Engineering Foundation,pages 409–418, 1995.2. A. Gobin, H. Neau, O. Simonin, J.-R. Llinas, V. Reiling, and J.-L. Selo. Fluid dynamic nu-merical simulation of a gas phase polymerization reactor. International Journal for NumericalMethods in Fluids, 43(10-11):1199–1220, 2003.3. D. Gidaspow, J. Jung, and R. K. Singh. Hydrodynamics of fluidization using kinetic theory: anemerging paradigm: 2002 Flour-Daniel lecture. Powder Technology, 148(2-3):123–141, 2004.4. M.A. van der Hoef, M. van Sint Annaland, N.G. Deen, and J.A.M. Kuipers. Numerical sim-ulation of dense gas-solid fluidized beds: a multiscale modeling strategy. Annual Review ofFluid Mechanics, 40(1):47–70, 2008.5. S. Sundaresan. Modeling the hydrodynamics of multiphase flow reactors: Current status andchallenges. AIChE Journal, 46(6):1102–1105, 2000.6. J. Wang. A review of eulerian simulation of geldart A particles in gas-fluidized beds. IndustrialEngineering Chemistry Research, 48(12):5567–5577, 2009.7. K. Agrawal, P.N. Loezos, M. Syamlal, and S. Sundaresan. The role of meso-scale structuresin rapid gas–solid flows. Journal of Fluid Mechanics, 445:151–185, 2001.8. Y. Igci, A. T. Andrews, S. Sundaresan, S. Pannala, and T. O’Brien. Filtered two-fluid modelsfor fluidized gas-particle suspensions. AIChE Journal, 54(6):1431–1448, 2008.9. J.-F. Parmentier, O. Simonin, and O. Delsart. A functional subgrid drift velocity model forfiltered drag prediction in dense fluidized bed. AIChE Journal, 58(4):1084–1098, 2012.10. A.T. IV Andrews, P. N. Loezos, and S. Sundaresan. Coarse-grid simulation of gas-particleflows in vertical risers. Industrial Engineering Chemistry Research, 44(16):6022–6037, 2005.11. Y. Igci and S. Sundaresan. Constitutive models for filtered Two-Fluid models of fluidizedGas–Particle flows. Industrial & Engineering Chemistry Research, 0(0), 10.1021/ie200190q.12. A. Ozel. Development of Large Eddy Simulation Approach for Simulation of Circulating Flu-idized Beds. PhD thesis, Université de Toulouse, Toulouse, France, 2011.13. A. Ozel, J.-F. Parmentier, O. Simonin, and P. Fede. A priori test of effective drag modelingfor filtered two-fluid model simulation of circulating and dense gas-solid fluidized beds. In7th International Conference on Multiphase Flow - ICMF 2010 Proceedings. InternationalConference on Multiphase Flow (ICMF), 2010.14. A. Yoshizawa. Statistical theory for compressible turbulent shear flows, with the applicationto subgrid modeling. Physics of Fluids, 29(7):2152, 1986.15. J. Smagorinsky. General circulation experiments with the primitive equations. MonthlyWeather Review, 91(3):99–164, March 1963.16. M. Germano, U. Piomelli, P. Moin, and W.H. Cabot. A dynamic subgrid-scale eddy viscositymodel. Physics of Fluids A: Fluid Dynamics, 3(7):1760, 1991.

A dynamic subgrid-scale eddy viscosity model.

A priori test of effective drag modeling for ﬁltered two-ﬂuid model simulation of circulating and dense gas-solid ﬂuidized beds.

A review of eulerian simulation of geldart A particles in gas-ﬂuidized beds.

Coarse-grid simulation of gas-particle ﬂows in vertical risers.

Constitutive models for ﬁltered Two-Fluid models of ﬂuidized Gas–Particle ﬂows.

Development of Large Eddy Simulation Approach for Simulation of Circulating Fluidized Beds.

Eulerian gas-solid ﬂow modelling of dense ﬂuidized bed.

Filtered two-ﬂuid models for ﬂuidized gas-particle suspensions.

Fluid dynamic numerical simulation of a gas phase polymerization reactor.

General circulation experiments with the primitive equations.

Hydrodynamics of ﬂuidization using kinetic theory: an emerging paradigm:

Modeling the hydrodynamics of multiphase ﬂow reactors: Current status and challenges.

Numerical simulation of dense gas-solid ﬂuidized beds: a multiscale modeling strategy.

Statistical theory for compressible turbulent shear ﬂows, with the application to subgrid modeling.

The role of meso-scale structures in rapid gas–solid ﬂows.

A posteriori study of filtered Euler-Euler two-phase model using a high resolution simulation of a 3D periodic circulating fluidized bed

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A posteriori study of filtered Euler-Euler two-phase model using a high resolution simulation of a 3D periodic circulating fluidized bed

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