AUTOMATED WORKFLOW FOR SPATIALLY RESOLVED PACKED BED

10th International Conference on CFD in Oil & Gas, Metallurgical and Process IndustriesSINTEF, Trondheim, NORWAY17-19th June 2014

CFD 2014

AUTOMATED WORKFLOW FOR SPATIALLY RESOLVED PACKED BED REACTORS WITHSPHERICAL AND NON-SPHERICAL PARTICLES

Thomas EPPINGER1⇤, Nico JURTZ1†, Ravindra AGLAVE2‡

1CD-adapco, Nordostpark 3-5, 90411 Nuremberg, Germany2CD-adapco, 11000 Richmond Avenue, Houston, TX, 77042, United States

⇤ E-mail: [email protected]† E-mail: [email protected]

‡ E-mail: [email protected]

ABSTRACTPacked bed reactors are widely used in the chemical and processindustry amongst others for highly exothermic or endothermic cat-alytic surface reactions. Such reactors are characterized by a smalltube to particle diameter ratio D/d to ensure a safe thermal manage-ment. For the design of such apparatuses the well-known correla-tions for packed bed reactors cannot be used, because these reactorsare dominated by the influence of the confining wall, which affectsthe porosity and the velocity field and as a result also the speciesand temperature distribution within the bed.For spatially resolved simulations of packed bed reactors a ran-domly packed bed has to be generated and meshed. Special atten-tion has to be paid on the mesh at the particle-particle and particle-wall contact points. We developed a method, which flattens theparticles locally in the vicinity of the contact points and we couldshow, that this method does not affect significantly the bed proper-ties and the fluid dynamics in terms of bed porosity, radial porositydistribution and pressure drop.Based on this published work we developed a workflow and a toolwhich allows an automated simulation: generation of a packed bedwith DEM (discrete element method), meshing and solving thetransport equations with a finite volume code. The whole workflowis done within the software package STAR-CCM+ by CD-adapco.The simulation time could be reduced significantly and depends onthe number of particles (typically 1-2 days for 1500 particles).Further we used the built-in DEM capability to generate randompackings of non-spherical particles like cylinders and Raschig rings,which are more often used in the chemical industry, as a composi-tion of spherical particles. For the meshing and the CFD calcula-tion these approximated shapes are replaced by their original exactshape.With the described workflow we have investigated spherical as wellas non-spherical packings with D/d between 2 and 10 and packingheights between 10d and 40d. The results are validated in terms ofbed porosity, radial porosity and velocity distribution and tempera-ture profiles with experimental results from literature.Based on these results the interplay between the flow field, thetemperature, the species distribution and the chemical reaction inpacked bed reactors can be investigated in detail.

Keywords: DEM, packed beds, chemical reactors, process indus-try, CFD, hydrodynamics .

NOMENCLATUREGreek Symbolsd Identity matrix, [�].l Thermal conductivity, [W/m2K].µ Dynamic viscosity, [Pas].n Poisson coefficient, [�].x Friction coefficient, [�].r Mass density, [kg/m3].t Stress tensor, [Pa].Q Dimensionless temperature, [�].

Latin Symbolsc Heat capacity, [J/kgK].d Particle diameter, [m].e Coefficient of restitution, [�].g Gravity vector, [m/s2].h Particle height, [m].p Pressure, [Pa].r Particle radius, [m].v Velocity vector, [m/s].vmag Velocity magnitude, [m/s].A Area, [m2].D Tube diameter, [m].E Young’s modulus, [Pa].H Total Enthalpy, [J].R Tube radius, [m].T Temperature, [K].Q̇ Heat flow, [W ].q̇ Heat flux, [W/m2].

Sub/superscriptse f f Effective.sl Sliding.r Rolling.t Turbulent.solid Solid phase.f luid Fluid phase.N Normal.T Tangential.

INTRODUCTIONPacked bed reactors are widely used in the chemical and pro-cess industry amongst others for catalyzed heterogeneous re-actions, adsorption processes, heat storage or filter applica-tions. They consist of a container - mostly a tube - which

T. Eppinger, N. Jurtz, R. Aglave

is filled with particles. Although a broad variety of industri-ally manufactured particle shapes exist most applications areusing spherical or cylindrical shaped particles.Based on the particle to diameter ratio D/d different nu-merical approaches can be used to describe fluid flow, heatand mass transfer. For large D/d (D/d > 10-20) a pseudo-homogeneous model approach can be used. In its simplestform a plug-flow velocity profile corrected with the bedporosity is assumed and physical properties like thermal con-ductivity are averaged based on the volume fraction of thesolid and fluid phase. This model was extended in the pastby several research groups to describe packed bed reactorsmore accurately.Packed bed reactors with small D/d (D/d < 10-20) are of-ten used for highly exothermic or endothermic catalytic reac-tions. These reactors are dominated by the wall effect: Dueto the confining wall the particles are only in point contactwith the wall which leads to a high porosity in the near wallregion and as a result to a high volumetric flow which actslike an isolating film and hinders the heat transport to or fromthe wall. For the design of these kind of reactors the pseudo-homogeneous approach fails because they are dominated bylocal effects and an exact description of the flow, temperatureand species distribution is needed.Due to the increasing computational power in the last yearsit is now possible to simulate such reactors in a spatiallyresolved way. First CFD simulations of packed beds withspherical particles were published in the end of the 1990sand in the last years a huge amount of research work waspublished.For a spatially resolved simulation two main challenges haveto be managed: Firstly an accurate description of the ran-domly packed bed is needed and secondly the meshing at thecontact points between particles and between the particlesand the wall has to be handled to avoid either highly skewedcells or a large number of cells due to local refinement in thevicinity of the contact points.There are several ways to obtain a description of the packingfor the CFD calculation. For ordered packings the position ofeach particle can easily be calculated analytically, which canthen be used to create a CAD description. Such a descriptioncan also be derived based on experimental MRT measure-ment of an existing packing. But there are also numericalmethods to generate a random packing. The Monte-Carlomethod basically positions particles randomly within the do-main and if this position fulfills a certain stability criteria theparticle is kept, otherwise the particle is removed. This isrepeated until the final packing height is reached. A secondnumerical method is based on the discrete element method(DEM) which was first described by (Cundall, 1979). In thismodel the particles are injected into the domain and New-ton’s law of motion is solved for each particle with consider-ation of all relevant forces acting on the particles. The DEMmethod has several advantages: It is inexpensive comparedto the experimental methods, computationally more efficientthan the Monte-Carlo method and the physical process of fill-ing is approximated, which can include obstacles or specialfeatures like macroscopic wall structures which can influencethe local void fraction distribution.Also for the second issue, the mesh generation in the vicinityof the contact points, several methods are known from litera-ture which are depicted in Figure 1. Shrinking the particles acertain amount, mostly in the range of 0.5-1 % of the particlediameter d, is a widely used technique (see e.g. (Nijemeis-land and Dixon, 2004) or (Bai et al., 2009)). As a result the

contact points disappear and cells can be generated in thegap. On the other hand the solid fraction and therefore theporosity of the packed bed is reduced, which influences thepressure drop significantly. A similar method is suggestedby (Guardo et al., 2005), but instead of shrinking he sug-gested to inflate the particles a certain amount. The contactpoints become contact lines or areas and the cell quality inthat region can be increased. But analogous to the shrinkingmethod the porosity is influenced significantly and a subse-quent correction is needed. (Ookawara et al., 2007) have pre-sented a method where the particles are bridged with a smallcylinder while (Eppinger et al., 2011) use a local flatteningtechnique: the particle surface is modified as soon as the nor-mal distance between the surfaces of two particles fall belowa prescribed value in such a way that a small gap is createdwhich can then be filled with a small number of cells with areasonable quality. The method by Ookawara as well as themethod by Eppinger has a reduced influence on the porosityand on the pressure drop because the packing is only modi-fied locally. Another advantage of the local flattening methodis, that it can be easily adapted to any kind of particle shapesand contact type like e.g. the contact line of cylindrical par-ticles which are in contact at their lateral surface.

Figure 1: Schematic overview of the different contact pointtreatment methods. Left: Shrinking the particles, middle:bridging the gap with a cylinder, right: local flattening of theparticles.

If heat transport in the packed bed is considered the heat con-duction between the solid particles has to be treated carefully.Generally the heat flow Q between two solids which are incontact at an area A can be described with following equa-tion

Q̇ = q̇⇤A =�lDT ⇤A (1)

where l is the thermal conductivity, q̇ is the heat flux and T isthe temperature. It is obvious that the amount of heat whichcan be transferred by conduction depends on the used contactpoint meshing method. For the shrinking and the local flat-tening method the heat transfer by conduction will be zerobecause there is no contact area while for the inflating andthe bridging method the heat transport by conduction will beoverpredicted. A more detailed discussion on this topic fol-lows.In this study an automated workflow for the simulation ofpacked bed reactors is presented. The workflow consistsmainly of a DEM simulation to create a random packing, aconversion step to create a CAD description out of the DEMdata, an automated mesh generation based on the CAD de-scription and the solver run including post-processing. Allsteps are controlled by a script to ensure convergence and

Automated Workflow for Spatially Resolved packed Bed Reactors with Spherical and Non-Spherical Particles/ CFD 2014

short calculation times. Some results of this workflow arepresented and validated with experimental data.

MODEL DESCRIPTION

For the investigation of spatially resolved 3 dimensionalpacked bed reactors we have developed an automated andfully numerical workflow based on CD-adapco’s finite vol-ume code STAR-CCM+. For the generation of a randompacking we used DEM and for the contact point treatmentthe local flattening method as described in detail in (Eppingeret al., 2011). A short summary and validation is given inthe next subsection. All single steps are concatenated witha java-macro, which on the one hand reduces the number ofpossible user errors and on the other hand reduces the sim-ulation time not only by reducing the idle time but also byadjusting the stopping criteria based on the given parameters.

Generation of a random packing

The generation of the random packing is done with the im-plemented DEM in STAR-CCM+. Monodisperse sphericalparticles are initialized randomly at the top of the tube andfall because of gravity to the bottom of the tube. For each ofthese particles Newton’s law of motion is solved which takesthe gravity and the interaction between the particles and be-tween the particles and the tube wall into account. Drag forceresulting from the interaction with the gas phase in the tube isneglected so that the following equations have to be solved:

midvi

dt= Fg +Â

npFc +Â

nbFc (2)

and

dIiwi

dt= Â

npTc +Â

nbTc (3)

where mi, vi, Ii and wi are the mass, velocity, mass momentof inertia and angular velocity of particle i, respectively. Fgis the gravitational force acting on particle i. Fc and Tc are,respectively, the contact force and the contact torque act-ing on particle i due to its neighbor particles np or neighborboundaries nb which are in contact with particle i. The con-tact forces and torques are calculated using a spring-dashpotmodel. For these simulations the non-linear Hertz-Mindlinmodel was used, where the forces and torques are calculatedas a function of the parameters stated in Table 1.

Table 1: Particle properties used for the DEM simulationProperty Symbol Unit ValueDensity r kg/m3 2500Norm. coeff. of restitution eN - 0.9Tang. coeff. of restitution eT - 0.5Poisson coefficient n - 0.235Young’s modulus E Pa 78.5e9Sliding friction coefficient xsl - 0.2Rolling friction coefficient xr - 0.002

The DEM simulation is stopped when all particles are in afinal stable position. This is assumed when the velocity ofall particles is below a given value (mostly a value of vmag <10�4m/s was used).For the generation of packings with non-spherical particlesthe composite particle model is used: Non-spherical parti-cles are approximated by a certain number of spheres, which

are fixed together and do not separate during the DEM sim-ulation. The composite particle model treats the individualspheres as separate entities only for contact detection whilefor the rest of the simulation it is a single object and forcesand torque are calculated with respect to the center of mass.An example for a cylindrical particle is shown in Figure 2.The simulation itself is conducted in the same way as forspherical particles.

Work Flow – Non-Spherical Particles

Figure 2: Example for packings with non-spherical particles:Left: Composite particle for the DEM simulation made of330 spheres and resulting randomly packed bed. Right: CADdescription of packed beds with different particle shapes (leftto right: full cylinders, Raschig-rings and 4-hole cylinders)based on the same DEM result.

Generation of a CAD description and meshing

The mesh generation process can be divided into two steps.Firstly the position and diameter of the centroid of thespheres of the randomly packed bed from the DEM simu-lation is extracted and in a subsequent step a CAD descrip-tion based on these data is generated. The whole tube canbe divided in three sections, the upstream region, the regionwith the packed bed, and a downstream region. The upstreampart is needed for the development of the flow profile whilethe downstream part is mainly to avoid backflow at the out-let boundary. To avoid the meshing problems at the contactpoints the local flattening method by (Eppinger et al., 2011)is used with the parameters given in table 2. All parametersare set relative to a given base size which gives a constantpolyhedral mesh quality for different sizes of the particles bychanging only one parameter.

Table 2: Settings for the meshing parametersProperty ValueBase size (bs) dSurface edge size (ses) on spheres 0.04-0.10 dSurface grow rate 1.3Number of prism layers 2Thickness of the prism layers 0.03 dMinimum distance between two surfaces 0.12 ses

In principle the mesh generation for non-spherical particlesis done in a similar same way but some additional steps has tobe included: Firstly the orientation of the non-spherical par-ticles in the packed bed is important and has to be exported


from the DEM simulation too. Secondly for the DEM simu-lation the shape of the non-spherical particle is approximatedby a certain number of spheres and therefore it is not an exactdescription. But for the CAD description the approximatedDEM shapes can be replaced with the exact shape. Thisis done by generating one non-spherical CAD-part which isthen cloned and positioned according to the exported DEMdata. The resulting packed bed for different particle shapesis depicted in Figure 2.

Simulation setupFor the steady state flow and heat transfer simulation in thisstudy the following governing equations for mass, momen-tum and energy are solved.Conservation of mass:

—rv = 0 (4)

where r is the mass density and v is the velocity vector.Conservation of momentum:

—rvv =�—p+—t +rg (5)

with pressure p, gravity vector g and the stress tensor t

t = µe f f [—v+—vT � 23(— ·v)d ] (6)

where d is the identity matrix and the effective viscosity µe f fcan be expressed as µe f f = µ +µt , the laminar and turbulentviscosity, respectively.Conservation of energy:

—(rHv) =�—q̇+— · (t ·v) (7)

with total enthalpy H and heat flux q̇.A schematic reactor overview is given in Figure 3. All CFD

Figure 3: Schematic reactor overview.

simulations are conducted in steady state with air as an idealgas with constant physical properties according to the rele-vant tables in the following subsections. Turbulence is mod-eled with the realizable k-e turbulence model using ’All y+-wall treatment’. If the heat transport in the solid phase wastaken into account a conformal mesh at the solid-fluid inter-face was created. At the inlet a constant plug flow profilewith a constant temperature is assumed. At the outlet a con-stant absolute pressure of 1.013 bar was specified. A constanttemperature was set at the heated wall.

Process automation

To decrease the total simulation time by reducing the idletime and to avoid user mistakes during the simulation setupthe whole process consisting of the previously described sin-gle steps is automated with a java-script. A summary aboutthe workflow described above for spherical as well as fornon-spherical particles is given in Figure 4, where the ad-ditional steps for non-spherical particles are highlighted inred. A GUI collects all relevant parameters and settings forthe DEM, the mesh and the CFD calculation. Based onthese data two scripts are generated. The first one gener-ated the packing geometry using DEM. The second scriptwhich starts automatically after the first one has terminated,generates the CAD geometry, the mesh and all numericaland physical settings for the CFD simulation. Several pa-rameters are calculated based on literature data, e.g. theexpected packing height, so that the particles are injectedclosely above this value to ensure all particles can be injectedand the distance which the particles have to travel are notneedlessly long. Also some standard post processing rou-tines are added like an automated area based calculation ofthe radial and axial porosity profiles and pressure drop.

Modeling of a

Reference DEM Particle

Generation of a random packing

Discrete Element Method CFD Simulation

Modeling one particle

in the CAD-Modeler

Import particle data into

CAD-Modeler

Meshing

CFD Simulation

Export position and orientation

of the particles

Work Flow – Non-Spherical Particles

Figure 4: Workflow for the whole process. The additionalsteps for non-spherical particles are highlighted in red.

RESULTS

In this section some results are presented with a focus onnon-spherical particles and heat transport. A detailed pre-sentation and validation against correlations on bed porosity,radial porosity distribution, pressure drop and velocity pro-files for packed beds with spherical particles can be found in(Eppinger et al., 2011) and (Zobel et al., 2012). For that rea-son only a few results for spherical particles are presented inthis paper.


Validation of bed porosity and local porosity distri-bution

(Mueller, 1992) investigated packed beds of monodispersespheres made of plexiglas in a cylindrical tube with D/d rang-ing from 2.02 to 7.99. The radial porosity profile was derivedby analysing a large number of radial annular layers of equalthickness and the local porosity of each layer is calculated asratio of the solid volume and the total volume of the layer.We reproduced this work numerically and found an excellentagreement between the numerical and the experimental re-sults for all investigated D/d-ratios as depicted exemplarilyin Figure 5 for D/d = 3.96.

Figure 5: Comparison of the radial porosity profile for amonodisperse packed bed with D/d = 3.96. Experimentaldata are taken from (Mueller, 1992).

A validation of the bed porosity, which is defined as ratio ofthe volume of the void in the packing and the volume of thatregion when no particles are present, and local radial poros-ity distribution for packed beds made of cylinders, Raschigrings and 4-hole cylinders was conducted against correlationsby (Dixon, 1988) and (Foumeny and Benyahia, 1991). Thegenerated packed beds are depicted in Figure 2. The tube di-ameter is D = 0.22m, the cylindrical particle diameter d andthe height h is d = h= 0.025m, which gives a D/d of 8.8. Thetotal bed height is approximately H = 0.55m. The bed poros-ity for all three particles shapes is shown in Figure 6. For allthree particle shapes the numerical results are between thevalues of both correlations.

Figure 6: Comparison of the bed porosity of packed bed withdifferent particle shapes.

A more detailed validation is shown in Figure 7 and 8 wherethe axial and circumferential averaged radial porosity profilefor cylinders and Raschig rings is depicted. The numericalresults are compared with experimental results by (Roshani,

1990) and (Giese et al., 1998), respectively and with numer-ical results by (Caulkin et al., 2012). Generally the agree-ment between experimental and the numerical data is quitehigh. For cylindrical particles this is especially given in thenear wall region up to a distance of approximately one parti-cle diameter, while with increasing distance to the confiningtube wall the randomness of the packed bed gets more im-portant and slight shifts in the amplitude and the frequencyof the decaying profile can be found. Also the results forRaschig rings agree well with the experimental data, the typ-ical decrease in porosity directly at the wall and at one, twoand three particle diameters away from the wall are predictedcorrectly.

Figure 7: Comparison of the radial porosity distribution of apacked bed with cylindrical particles.

Figure 8: Comparison of the radial porosity distribution of apacked bed with Raschig rings.

Validation of heat transportOne critical point of the simulation of packed bed reactorsis the accurate calculation of the temperature profile. Espe-cially the heat transport via conduction between the particlesand between the particles and the wall has to be examined be-cause the choice how the contact points are treated may influ-ence the result as already mentioned in the introduction. Tojudge the influence detailed experimental temperature datafrom within the packed bed is needed. Getting these datais not an easy task because of the accessibility for measure-ment devices or techniques. The research group of Anthony


Dixon has published several papers over the last years whichwe used to validate our simulation results. The experimentalsetup is a single packed tube with a steam-heated wall. An airflow enters the tube and in a first unheated zone of the packedbed the flow profile should develop while in the second zonethe air is heated through the wall with a constant tempera-ture. Temperature is measured with a thermocouple cross atthe outlet of the packed bed. To obtain temperature profileswithin the packed bed different bed heights were used. Moredetailed information can be found in (Nijemeisland, 2000),(Nijemeisland and Dixon, 2001) and (Dixon et al., 2012).A first validation is done against experimental data from(Nijemeisland, 2000) and (Nijemeisland and Dixon, 2001)where a packing of 44 nylon spheres with a diameter ofd = 25.4mm were placed in a regular arrangement in a tubewith diameter D = 50,8mm (D/d = 2) resulting in a packingheight of approximately H ⇡ 400mm like depicted in Figure9. The inlet velocity was varied in such a way that particleReynolds numbers in the range of Re = 373 upto Re = 1922were covered. For the simulation three different geometriesbased on the contact point treatment were generated. Thefirst geometry is based on the global shrinking method (1%of the diameter) and parameters are used according to (Nije-meisland and Dixon, 2001), therefore it is named in the fol-lowing ’Nijemeisland’. The second geometry is based on thebridging method with a bridging tube diameter of 10 % of thesphere diameter d and is named ’Ookawara’. And the thirdgeometry is based on the local flattening method according tothe description above and is named ’Eppinger’. The bound-ary layer resolution is varied between two layers and ’Ally+ treatment’ and seven layers and a ’Low Reynolds model’.The resulting polyhedral mesh contains approximately 700000 cells for the model with two layers and 1.5 million cellsfor the model with seven layers. The physical properties areset according to Table 3.

Table 3: Settings for the validation simulation according to(Nijemeisland and Dixon, 2001).

property valuel f luid 0.026 W/(m·K)lsolid 0.242 W/(m·K)r f luid 1.225 kg /m3

rsolid 1300 kg /m3

cp, f luid 1003.6 J/(kg·K)cp,solid 1000 J/(kg·K)Tinlet 298 KTwall 383 K

Figure 9: Sketch of the experimental and numerical setup.The heating zone starts behind the light green zone.

In Figure 10 detailed results of the dimensionless tempera-ture Q = (T �Tinlet)/(Twall �Tinlet) for Re = 986 is shown.

Figure 10: (a)-(c) Comparison of temperature data at the out-let of the packed bed for different contact point methods andexperimental data for Re = 986. (d) Best-fit curves based onthe results from (a)-(c).


Each dot in Figure 10(a)-(c) represents a temperature valueapproximately 5 mm above the top layer. The numerical re-sults show for all three methods a quit good agreement with aslight spread around the experimental range of data. The con-tact point treatment according to Nijemeisland or Ookawaraslightly underpredicts the temperature profile, especially to-wards the center of the tube. This can not be seen when thelocal flattening method is used. Similar results are found forRe = 373, 1724 and 1922, which are not depicted in this pa-per. For an easier comparison of the different simulations aleast square best-fit curve for Q is used with

Q =A

log( Br/R )

+C (8)

and fitting parameters A, B and C. In 10(d) it can be seenthat all models predict the temperature profile in the nearwall region quit accurately. Towards the center of the tubeall models underpredict the temperature with the largest de-viation for the global shrinking method while the local flat-tening with two layers gives the most accurate result. Similarresults are also found for Re = 373, 1724 and 1922, respec-tively which are depicted in Figure 11, 12 and 13. The

0.8

0.85

0.9

0.95

1

0 0.2 0.4 0.6 0.8 1

Θ [−

]

r/R [−]

Experimental Data

Nijemeisland 2−Layer


Ookawara 2−Layer

Ookawara 7−Layer

Eppinger 2−Layer

Eppinger 7−Layer

Figure 11: Best-fit curves based on the simulation results forRe = 373.

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

0 0.2 0.4 0.6 0.8 1

Θ [−

]

r/R [−]

Experimental Data



Ookawara 2−Layer

Ookawara 7−Layer

Eppinger 2−Layer

Eppinger 7−Layer


global shrinking method always underpredicts the tempera-ture profile, while the local flattening method gives a slightoverprediction for high Re numbers. For high Re numbersthe bridging method gives the most accurate results although

the particles are bridged with a cylinder with a relativelylarge diameter which increases the particle heat conduction.It can be concluded that for high Re number the heat trans-port by conduction does not play a significant role, at least inthis case, where the conductivity of the solid phase (nylon) isnot very high.A second validation was done against a similar investigation,but with D/d = 5.45 and a randomly packed bed made ofmonodisperse spherical particles. The remaining setup is thesame as in the previous one. For details see (Dixon et al.,2012) and Table 4. The numerical results in (Dixon et al.,2012) are derived by two different approaches for the contactpoint treatment. One is the global shrinking method and theother is a mixed approach consisting of the bridging methodin the near wall region and the local shrinking in the rest ofthe bed. When the particles are bridged an effective thermalconductivity for the solid phase is used to compensate theenhanced heat conduction due to the increased contact by anadditional heat transport resistance.

Table 4: Solid settings for the validation simulation accord-ing to (Dixon et al., 2012).

property valuelsolid 0.25 W/(m·K)rsolid 1140 kg /m3

cp,solid 1700 J/(kg·K)Tinlet 298 KTwall 373 K

In Figure 14 a comparison of the experimental and numericalresults taken from the paper with simulation results with thelocal flattening method and different mesh sizes is shown. Ithas to be noted that an increase in base size or in minimumsurface size leads directly to a mesh with fewer cells but alsoto a larger gap between the particles. The larger gap influ-ences the velocity field, especially a velocity increase can bedetected in the gap and as a result the heat transport is af-fected. With a finer mesh and a smaller gap the experimentalresults can be reproduced quite well with almost the sameaccuracy as the published numerical data. The deviation inthe near wall region between the numerical and the experi-mental results are attributed by the authors of the paper toeither a cold backflow or problems with the thermocouples.It can be concluded based on these simulations that with thelocal flattening method without further modifications like an

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

0 0.2 0.4 0.6 0.8 1

Θ [−

]

r/R [−]

Experimental Data



Ookawara 2−Layer

Ookawara 7−Layer

Eppinger 2−Layer

Eppinger 7−Layer



adjustment of the effective thermal conductivity the experi-mental results can be reproduced.

Validation heat transport

Figure 14: Radial temperature profile for a packed bed withD/d = 5.45 at a bed height of z = 0.48m.

Simulation timeBeside the accuracy of the results the calculation time for thesimulation is also of high interest, especially if such simu-lation should be used as a standard tool or method for thedesign of packed bed reactors. The calculation time dependson the mesh size and on the complexity of the physics; there-fore it is difficult to give exact numbers for the calculationtime. E.g. the mesh could be much coarser if only the pres-sure drop is of interest compared to a mesh for an accurateprediction of the heat transport. Furthermore the calculationtime of the packing generation depends not only on the phys-ical properties but also on the DEM time step size which de-pends heavily on the Young’s modulus and the particle size.But to give some rough ideas on the needed calculation timesome numbers are presented. The DEM generation of a ran-domly packed bed with 1500 cylindrical composite particles(h= d = 1cm) made of 330 spheres each needs around 1 hourfor particles made of rubber (Young’s modulus = 0.5 MPa)and around 24h for particles made of glass (Young’s modu-lus = 75800 MPa). Simulation was done using one CPU. Themesh size can be roughly estimated with 10000 volume cellsper particle. This leads in the example above to a total meshsize of 15 million cells. The generation of such a mesh takesapproximately 7 hours on a single CPU. The CFD calculationitself with the physical assumptions mentioned above and in-cluding heat transfer needs around 3 hours on 64 CPUs. Allin all such a simulation can be conducted within 24 hours.

CONCLUSIONIn this contribution we have shown and validated a com-pletely numerical and automated workflow for the simulationof three dimensional and spatially resolved packed beds ofspherical and non-spherical particles. The workflow is hid-den behind a GUI which collects all relevant parameter andgenerates a set of macros to control the process. This ap-proach is validated against

• bed porosity,

• radial porosity distribution,

• pressure drop,

• radial velocity profile and

• heat transport.

Additionally the automation leads to a reduced simulationtime by avoiding user mistakes during the setup and by con-trolling and terminating the simulations when necessary ordesired and therefore by reducing the idle time.With simulation times in the range of one to a few days 3dimensional and spatially resolved simulations are startingto be feasible for design studies and optimization of catalyticpacked bed reactors.


REFERENCESBAI, H. et al. (2009). “A coupled dem and cfd simulation

of flow field and pressure drop in fixed bed reactor with ran-domly packed catalyst particles”. Industrial & EngineeringChemistry Research, 48(8), 4060–4074.

CAULKIN, R. et al. (2012). “Predictions of porosity andfluid distribution through nonspherical-packed columns”.AIChE Journal, 58(5), 1503–1512.

CUNDALL, P.; STRACK, O. (1979). “a discrete numer-ical model for granular assemblies”. Géotechnique, 29, 47–65.

DIXON, A.G. (1988). “Correlations for wall and particleshape effects on fixed bed bulk voidage”. Can. J. Chem. Eng.,66(5), 705–708.

DIXON, A.G. et al. (2012). “Experimental validation ofhigh reynolds number cfd simulations of heat transfer in apilot-scale fixed bed tube”. Chemical Engineering Journal,200(0), 344 – 356.

EPPINGER, T. et al. (2011). “Dem-cfd simulations offixed bed reactors with small tube to particle diameter ra-tios”. Chemical Engineering Journal, 166(1), 324 – 331.

FOUMENY, E. and BENYAHIA, F. (1991). “Predictivecharacterization of mean voidage in packed beds”. Heat Re-covery Systems and CHP, 11(2-3), 127–130.

GIESE, M. et al. (1998). “Measured and modeled super-ficial flow profiles in packed beds with liquid flow”. AIChEJ., 44(2), 484–490.

GUARDO, A. et al. (2005). “Influence of the turbu-lence model in cfd modeling of wall-to-fluid heat transfer inpacked beds”. Chemical Engineering Science, 60(6), 1733 –1742.

MUELLER, G.E. (1992). “Radial void fraction distri-butions in randomly packed fixed beds of uniformly sizedspheres in cylindrical containers”. Powder Technology,72(3), 269 – 275.

NIJEMEISLAND, M. (2000). Verification Studies ofComputational Fluid Dynamics in Fixed Bed Heat Transfer.Master’s thesis, Worcester Polytechnic Institute.

NIJEMEISLAND, M. and DIXON, A.G. (2001). “Com-parison of cfd simulations to experiment for convective heattransfer in a gas-solid fixed bed”. Chemical EngineeringJournal, 82(1-3), 231 – 246.

NIJEMEISLAND, M. and DIXON, A.G. (2004). “Cfdstudy of fluid flow and wall heat transfer in a fixed bed ofspheres”. AIChE J., 50(5), 906–921.

OOKAWARA, S. et al. (2007). “High-fidelity dem-cfdmodeling of packed bed reactors for process intensification”.Proceedings of European Congress of Chemical Engineering(ECCE-6), Copenhagen.

ROSHANI, S. (1990). Elucidation of local and globalstructural properties of packed bed configurations. Ph.D.thesis, University of Leeds.

ZOBEL, N. et al. (2012). “Influence of the wall structureon the void fraction distribution in packed beds”. ChemicalEngineering Science, 71(0), 212 – 219.

Documents

AUTOMATED WORKFLOW FOR SPATIALLY RESOLVED PACKED BED