2
Proceedings of the 12
thInternational Conference on Computational Fluid Dynamics in the Oil & Gas, Metallurgical and Process Industries
SINTEF
PROCEEDINGS
Progress in Applied CFD –
CFD2017
Editors:
Jan Erik Olsen and Stein Tore Johansen
Progress in Applied CFD – CFD2017
Proceedings of the 12
thInternational Conference on Computational Fluid Dynamics in the Oil & Gas, Metallurgical and Process Industries
SINTEF Proceedings
SINTEF Academic Press
SINTEF Proceedings no 2
Editors: Jan Erik Olsen and Stein Tore Johansen Progress in Applied CFD – CFD2017
Selected papers from 10th International Conference on Computational Fluid Dynamics in the Oil & Gas, Metal lurgical and Process Industries
Key words:
CFD, Flow, Modelling
Cover, illustration: Arun Kamath
ISSN 2387-4295 (online) ISBN 978-82-536-1544-8 (pdf)
© Copyright SINTEF Academic Press 2017
The material in this publication is covered by the provisions of the Norwegian Copyright Act. Without any special agreement with SINTEF Academic Press, any copying and making available of the material is only allowed to the extent that this is permitted by law or allowed through an agreement with Kopinor, the Reproduction Rights Organisation for Norway. Any use contrary to legislation or an agreement may lead to a liability for damages and confiscation, and may be punished by fines or imprisonment
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SINTEF Proceedings
SINTEF Proceedings is a serial publication for peer-reviewed conference proceedings on a variety of scientific topics.
The processes of peer-reviewing of papers published in SINTEF Proceedings are administered by the conference organizers and proceedings editors. Detailed procedures will vary according to custom and practice in each scientific community.
PREFACE
This book contains all manuscripts approved by the reviewers and the organizing committee of the 12th International Conference on Computational Fluid Dynamics in the Oil & Gas, Metallurgical and Process Industries. The conference was hosted by SINTEF in Trondheim in May/June 2017 and is also known as CFD2017 for short. The conference series was initiated by CSIRO and Phil Schwarz in 1997.
So far the conference has been alternating between CSIRO in Melbourne and SINTEF in Trondheim.
The conferences focuses on the application of CFD in the oil and gas industries, metal production, mineral processing, power generation, chemicals and other process industries. In addition pragmatic modelling concepts and bio‐mechanical applications have become an important part of the conference. The papers in this book demonstrate the current progress in applied CFD.
The conference papers undergo a review process involving two experts. Only papers accepted by the reviewers are included in the proceedings. 108 contributions were presented at the conference together with six keynote presentations. A majority of these contributions are presented by their manuscript in this collection (a few were granted to present without an accompanying manuscript).
The organizing committee would like to thank everyone who has helped with review of manuscripts, all those who helped to promote the conference and all authors who have submitted scientific contributions. We are also grateful for the support from the conference sponsors: ANSYS, SFI Metal Production and NanoSim.
Stein Tore Johansen & Jan Erik Olsen
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Organizing committee:
Conference chairman: Prof. Stein Tore Johansen Conference coordinator: Dr. Jan Erik Olsen Dr.
Bernhard Müller
Dr.Sigrid Karstad Dahl Dr.Shahriar Amini Dr.Ernst Meese Dr.Josip Zoric Dr.Jannike Solsvik Dr.Peter Witt
Scientific committee:
Stein Tore Johansen, SINTEF/NTNU Bernhard Müller, NTNU
Phil Schwarz, CSIRO
Akio Tomiyama, Kobe University
Hans Kuipers, Eindhoven University of Technology Jinghai Li, Chinese Academy of Science
Markus Braun, Ansys Simon Lo, CD‐adapco
Patrick Segers, Universiteit Gent Jiyuan Tu, RMIT
Jos Derksen, University of Aberdeen Dmitry Eskin, Schlumberger‐Doll Research Pär Jönsson, KTH
Stefan Pirker, Johannes Kepler University Josip Zoric, SINTEF
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CONTENTS
PRAGMATIC MODELLING ... 9
On pragmatism in industrial modeling. Part III: Application to operational drilling ... 11
CFD modeling of dynamic emulsion stability ... 23
Modelling of interaction between turbines and terrain wakes using pragmatic approach ... 29
FLUIDIZED BED ... 37
Simulation of chemical looping combustion process in a double looping fluidized bed reactor with cu‐based oxygen carriers ... 39
Extremely fast simulations of heat transfer in fluidized beds ... 47
Mass transfer phenomena in fluidized beds with horizontally immersed membranes ... 53
A Two‐Fluid model study of hydrogen production via water gas shift in fluidized bed membrane reactors ... 63
Effect of lift force on dense gas‐fluidized beds of non‐spherical particles ... 71
Experimental and numerical investigation of a bubbling dense gas‐solid fluidized bed ... 81
Direct numerical simulation of the effective drag in gas‐liquid‐solid systems ... 89
A Lagrangian‐Eulerian hybrid model for the simulation of direct reduction of iron ore in fluidized beds... 97
High temperature fluidization ‐ influence of inter‐particle forces on fluidization behavior ... 107
Verification of filtered two fluid models for reactive gas‐solid flows ... 115
BIOMECHANICS ... 123
A computational framework involving CFD and data mining tools for analyzing disease in cartoid artery ... 125
Investigating the numerical parameter space for a stenosed patient‐specific internal carotid artery model ... 133
Velocity profiles in a 2D model of the left ventricular outflow tract, pathological case study using PIV and CFD modeling ... 139
Oscillatory flow and mass transport in a coronary artery ... 147
Patient specific numerical simulation of flow in the human upper airways for assessing the effect of nasal surgery ... 153
CFD simulations of turbulent flow in the human upper airways ... 163
OIL & GAS APPLICATIONS ... 169
Estimation of flow rates and parameters in two‐phase stratified and slug flow by an ensemble Kalman filter ... 171
Direct numerical simulation of proppant transport in a narrow channel for hydraulic fracturing application ... 179
Multiphase direct numerical simulations (DNS) of oil‐water flows through homogeneous porous rocks ... 185
CFD erosion modelling of blind tees ... 191
Shape factors inclusion in a one‐dimensional, transient two‐fluid model for stratified and slug flow simulations in pipes ... 201
Gas‐liquid two‐phase flow behavior in terrain‐inclined pipelines for wet natural gas transportation ... 207
NUMERICS, METHODS & CODE DEVELOPMENT ... 213
Innovative computing for industrially‐relevant multiphase flows ... 215
Development of GPU parallel multiphase flow solver for turbulent slurry flows in cyclone ... 223
Immersed boundary method for the compressible Navier–Stokes equations using high order summation‐by‐parts difference operators ... 233
Direct numerical simulation of coupled heat and mass transfer in fluid‐solid systems ... 243
A simulation concept for generic simulation of multi‐material flow, using staggered Cartesian grids ... 253
A cartesian cut‐cell method, based on formal volume averaging of mass, momentum equations ... 265
SOFT: a framework for semantic interoperability of scientific software ... 273
POPULATION BALANCE ... 279
Combined multifluid‐population balance method for polydisperse multiphase flows ... 281
A multifluid‐PBE model for a slurry bubble column with bubble size dependent velocity, weight fractions and temperature ... 285
CFD simulation of the droplet size distribution of liquid‐liquid emulsions in stirred tank reactors ... 295
Towards a CFD model for boiling flows: validation of QMOM predictions with TOPFLOW experiments ... 301
Numerical simulations of turbulent liquid‐liquid dispersions with quadrature‐based moment methods ... 309
Simulation of dispersion of immiscible fluids in a turbulent couette flow ... 317
Simulation of gas‐liquid flows in separators ‐ a Lagrangian approach ... 325
CFD modelling to predict mass transfer in pulsed sieve plate extraction columns ... 335
BREAKUP & COALESCENCE ... 343
Experimental and numerical study on single droplet breakage in turbulent flow ... 345
Improved collision modelling for liquid metal droplets in a copper slag cleaning process ... 355
Modelling of bubble dynamics in slag during its hot stage engineering ... 365
Controlled coalescence with local front reconstruction method ... 373
BUBBLY FLOWS ... 381
Modelling of fluid dynamics, mass transfer and chemical reaction in bubbly flows ... 383
Stochastic DSMC model for large scale dense bubbly flows ... 391
On the surfacing mechanism of bubble plumes from subsea gas release ... 399
Bubble generated turbulence in two fluid simulation of bubbly flow ... 405
HEAT TRANSFER ... 413
CFD‐simulation of boiling in a heated pipe including flow pattern transitions using a multi‐field concept ... 415
The pear‐shaped fate of an ice melting front ... 423
Flow dynamics studies for flexible operation of continuous casters (flow flex cc) ... 431
An Euler‐Euler model for gas‐liquid flows in a coil wound heat exchanger ... 441
NON‐NEWTONIAN FLOWS ... 449
Viscoelastic flow simulations in disordered porous media ... 451
Tire rubber extrudate swell simulation and verification with experiments ... 459
Front‐tracking simulations of bubbles rising in non‐Newtonian fluids ... 469
A 2D sediment bed morphodynamics model for turbulent, non‐Newtonian,
particle‐loaded flows ... 479
METALLURGICAL APPLICATIONS ... 491
Experimental modelling of metallurgical processes ... 493
State of the art: macroscopic modelling approaches for the description of multiphysics phenomena within the electroslag remelting process ... 499
LES‐VOF simulation of turbulent interfacial flow in the continuous casting mold ... 507
CFD‐DEM modelling of blast furnace tapping ... 515
Multiphase flow modelling of furnace tapholes ... 521
Numerical predictions of the shape and size of the raceway zone in a blast furnace ... 531
Modelling and measurements in the aluminium industry ‐ Where are the obstacles? ... 541
Modelling of chemical reactions in metallurgical processes ... 549
Using CFD analysis to optimise top submerged lance furnace geometries ... 555
Numerical analysis of the temperature distribution in a martensic stainless steel strip during hardening ... 565
Validation of a rapid slag viscosity measurement by CFD ... 575
Solidification modeling with user defined function in ANSYS Fluent ... 583
Cleaning of polycyclic aromatic hydrocarbons (PAH) obtained from ferroalloys plant ... 587
Granular flow described by fictitious fluids: a suitable methodology for process simulations ... 593
A multiscale numerical approach of the dripping slag in the coke bed zone of a pilot scale Si‐Mn furnace ... 599
INDUSTRIAL APPLICATIONS ... 605
Use of CFD as a design tool for a phospheric acid plant cooling pond ... 607
Numerical evaluation of co‐firing solid recovered fuel with petroleum coke in a cement rotary kiln: Influence of fuel moisture ... 613
Experimental and CFD investigation of fractal distributor on a novel plate and frame ion‐exchanger ... 621
COMBUSTION ... 631
CFD modeling of a commercial‐size circle‐draft biomass gasifier ... 633
Numerical study of coal particle gasification up to Reynolds numbers of 1000 ... 641
Modelling combustion of pulverized coal and alternative carbon materials in the blast furnace raceway ... 647
Combustion chamber scaling for energy recovery from furnace process gas: waste to value ... 657
PACKED BED ... 665
Comparison of particle‐resolved direct numerical simulation and 1D modelling of catalytic reactions in a packed bed ... 667
Numerical investigation of particle types influence on packed bed adsorber behaviour ... 675
CFD based study of dense medium drum separation processes ... 683
A multi‐domain 1D particle‐reactor model for packed bed reactor applications ... 689
SPECIES TRANSPORT & INTERFACES ... 699
Modelling and numerical simulation of surface active species transport ‐ reaction in welding processes ... 701
Multiscale approach to fully resolved boundary layers using adaptive grids ... 709
Implementation, demonstration and validation of a user‐defined wall function for direct precipitation fouling in Ansys Fluent ... 717
FREE SURFACE FLOW & WAVES ... 727 Unresolved CFD‐DEM in environmental engineering: submarine slope stability and
other applications... 729 Influence of the upstream cylinder and wave breaking point on the breaking wave
forces on the downstream cylinder ... 735 Recent developments for the computation of the necessary submergence of pump
intakes with free surfaces ... 743 Parallel multiphase flow software for solving the Navier‐Stokes equations ... 752
PARTICLE METHODS ... 759 A numerical approach to model aggregate restructuring in shear flow using DEM in
Lattice‐Boltzmann simulations ... 761 Adaptive coarse‐graining for large‐scale DEM simulations ... 773 Novel efficient hybrid‐DEM collision integration scheme ... 779 Implementing the kinetic theory of granular flows into the Lagrangian
dense discrete phase model ... 785 Importance of the different fluid forces on particle dispersion in fluid phase
resonance mixers ... 791 Large scale modelling of bubble formation and growth in a supersaturated liquid ... 798
FUNDAMENTAL FLUID DYNAMICS ... 807 Flow past a yawed cylinder of finite length using a fictitious domain method ... 809 A numerical evaluation of the effect of the electro‐magnetic force on bubble flow
in aluminium smelting process ... 819
A DNS study of droplet spreading and penetration on a porous medium ... 825
From linear to nonlinear: Transient growth in confined magnetohydrodynamic flows ... 831
10
GRANULAR FLOW DESCRIBED BY FICTITIOUS FLUIDS:
A SUITABLE METHODOLOGY FOR PROCESS SIMULATIONS
Manuel SPARTA*, Svenn Anton HALVORSEN Teknova AS, 4612 Kristiansand, NORWAY
* E-mail: [email protected]
ABSTRACT
The flow of granular materials is often present in metallurgical reactors. Metallurgical simulations are typically multidisci- plinary and the granular flow will often have a significant effect on the temperature distribution. The flow of bulk materials exhibits patterns that can be very different from fluid flows.
Standard fluid flow methods are not applicable to describe such flows.
For simple bulk flows with plug flow sections and mass flow hoppers, a reasonable flow field can, however, be computed with a standard CFD tool. The trick is to apply appropriate, non- standard, moving wall boundary conditions.
This simple approach does not work for complex flow cases, including sections with one or more free boundaries. For such cases, we apply the Discrete Element Method (DEM), which has emerged to be the preferred choice for simulation of granular flow. A suitable method has been developed to compute the volume averaged flow field by DEM and then import it into a code for multiphysics simulations.
To reduce the high computational cost of DEM simulations a hybrid approach is recommended. DEM simulations are then used for the complex flow regions while the simple model is used wherever applicable. In the multiphysics program the flow field is forced to be equal, or very close to, the DEM results by applying a suitable volume force.
Keywords: Granular flow, Fictitious fluids, Standard CFD software, Process metallurgy.
NOMENCLATURE
Total flow, [m3/s]
Cross section, [m2]a Characteristic length, [m]
z Vertical coordinate, [m]
u Velocity, [m/s]
(z)
w Average vertical velocity, [m/s]
u radial component of the velocity, [m/s]
w vertical component of the velocity, [m/s]
K
Force factor, [Ns/m4] s Total flow scaling factor, [1]INTRODUCTION
The flow of granular material is ubiquitous in metal production with the transport of ores and carbonaceous materials in furnaces being a primary example. Granular flows exhibit patterns that can be very different from fluid flows (Jenike, 1964). For example, arc formation can clog outlets, small change in the hopper angle may result in the transition from funnel flow (with stagnant areas) to mass flow (with flow in the whole cross section). If obstacles are present, upstream stagnant zones and empty cavities downstream are easily formed.
All these effects can sum up counterintuitively, to the extent that the placement of obstacles can increase the flow rate (obstacles are routinely inserted before outlet opening in silos). These unique features imply that standard fluid models do not provide good approximations to granular flow. Significant efforts have been spent to derive numerical models for granular materials (for a recent review we refer to the work of Tang et al. (2015)), but such methods may not be implemented in common multiphysics programs.
Metallurgical simulations are typically multidisciplinary and the granular flow will often have a significant effect on the temperature distribution. For many applications, the general flow patterns are essential, while details can be neglected. It is most convenient if these patterns can be available within the computational tool you normally apply for multidisciplinary simulations.
We follow the the spirit of application-driven pragmatic modeling, i.e. deriving simplest possible model which can give fast, and sufficiently accurate answers (c.f. Zoric et al. 2014). We started to test whether standard CFD tools might be suitably adapted, to describe granular flow.
This article is organized as follows, a fictitious model geometry showing some challenges of a metallurgic reactor is presented. In first approximation, we attempt to enforce a granular-like flow applying available boundary conditions. Secondly, we show how to derive a template flow using Discrete Element Methods simulations and import it into a Multiphysics environment. Finally, we discuss the capabilities of a hybrid approach. All our testing is done in COMSOL Multiphysics (COMSOL, 2016), which is the tool that we routinely use.
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Model Geometry
After some initial trials, we chose to test our ideas on an axially symmetric geometry shown in Figure 1. This geometry is not based on any real reactor, but was designed to test some common patterns for granular flow:
a) A straight section at the top where plug flow is expected
b) A mass flow hopper
c) Another straight section with plug flow d) A sharp widening of the domain where there
will be a free surface, given by the angle of repose for the bulk material.
e) Stagnant (non-moving) particles on top of an obstacle (grey section)
f) A cavity just beneath the obstacle
Figure 1: Geometry of the cylindrical model investigated. Areas of interest are highlighted: a) Plug
flow zone b) Mass flow hopper c) Plug flow zone d) Abrupt widening with a free surface e) Stagnant particles on top of an obstacle f) Cavity right underneath
the obstacle.
SIMULATIONS
Simple adaptation of viscous flow
First we considered the upper part of our test reactor, consisting of sections a), b), and c). The flow here is comparatively simple with plug flow in a) and c) and a velocity gradient in b).
For our case, we set the velocity in the hopper center to be roughly twice as big as at the wall. This seems realistic for particulate flow (Jenike, 1964). Further, a parabolic velocity profile seems reasonable here. Hence, the flow field in b) should be properly described by viscous laminar flow.
We then applied boundary conditions to achieve the desired flow patterns for the upper sections.
For the vertical walls, there are two options:
1) Slip condition – Wall without friction. The flow is only forced to move parallel to the wall.
2) No slip and a moving wall with a prescribed vertical velocity, given by the plug flow require- ment. The viscous fluid will then match the velocity of the wall.
For a long straight section of fluid domain, the 2 approaches show the same result, plug flow. We favor, however, the second option as the boundary condition then plays an active role near geometrical transitions.
For the hopper section, we again rely on the moving wall condition. The first step is to compute the average vertical velocity as a function of the z-coordinate.
z
zw
(1)
where
is the total flow, and
z is the horizontal cross section area.Then, we let the vertical velocity at the wall be equal to the average velocity scaled by a suitable factor, in our case 2/3 worked well. An appropriate radial component is set to ensure that the flow is parallel to the wall, hence the wall velocity at the hopper wall is equal to:
tan( )
2 3 3 ,
2w z w z
uf (2)
where is the hopper angle.
The flow field obtained with this setup is shown in Figure 2, where the total flow rate is set to 1 m3/h. The first panel shows the radial component of the flow velocity and, as expected, this is zero except in the hopper. The vertical component has a flat profile in the zones a) and c) as described by the plug flow and the acceleration occurs in the hopper.
Figure 2: Top section of the model system, flow obtained imposing “No Slip condition” and prescribed
wall velocities.
The simple approach gives a realistic particulate flow field. A fictitious fluid flow is computed as the boundary conditions are not realistic for viscous flow.
For a given geometry it is sufficient with one CFD computation. If the results for another value of the total flow is required, the computed velocities are simply multiplied with the appropriate factor, to get the correct total flow. Granular flow is gravity driven and does not change pattern significantly as long as the motion is sufficiently small, i.e. inertia effects can be neglected.
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Flow at a free boundary
While laminar viscous flow worked well with adapted boundary conditions, this approach failed to describe the conditions at the free boundary in region d). At the free surface, there will be a thin layer, a few particle diameters thick, where the particles will move at a comparatively high speed (Shinohara, 1987 and Williams, 1976). Below this layer, the bulk velocity will be much slower. Such sharp change in the fluid velocity cannot be described by simply adapting the boundary conditions for a viscous fluid.
We tried to add one or more inner walls to enforce a suitable boundary layer at the free surface, but were not able to adapt a reasonable bulk flow pattern. We cannot preclude that such a procedure may succeed, but based on our trials, it does not look promising.
Application of Discrete Element Model (DEM) To obtain an accurate description of the problematic areas d)-f) we turn to the use of a Discrete Element Method simulations.
The Discrete Element Method (DEM) was first introduced by Cundall and Strack (1979) and in recent years, thanks to increasing of computational power and the development of efficient programs, it has become wildly used to investigate granular flow. In a nutshell, DEM predicts the bulk properties of a granular flow by analyzing the time propagation of position and momentum of each individual particle. Each particle is represented by a simple and well defined geometrical entity in most cases a sphere. The translational and angular accelerations are computed as the result of the corresponding momentum balances (Ariyama et al., 2014; Guo and Curtis, 2015). Realistic simulations involve, however, a huge number of particles and the computational time may be correspondingly high.
Furthermore, the method can be appropriate to obtain the flow patterns, but it is unsuitable to include in multidisciplinary iterations. For the latter case, our special application of standard CFD software is clearly preferable.
For our case, the workflow is organized as follows:
• Set up and run a DEM simulation for a suitable 3D model of the system under investigation, c.f.
Appendix A.
• By means of space and time averaging, turn the information of the DEM snapshots into a discretized flow field (Appendix B).
• Import the computed flow field into COMSOL Multiphysics.
The detailed description of the DEM simulation can be found in Appendix A. Briefly, the 3D model for the system of interest is constructed starting from the 2D axisymmetric model. Auxiliary structural elements functional to the keep the operation during the DEM simulation steady (see Figure 3) are added. In this case, a sufficiently large reservoir of particles was introduced above section a), to ensure particles flowing uniformly into our test reactor. A hopper section was applied, but a cylindrical region could alternatively have been chosen.
The lower part was extended and a flat plate was introduced. This plate was lowered at a constant speed,
to control the gravity driven flow. The vertical velocity at the bottom was set to 0.01 m/s. This seems like an unreasonable high flow, but as already stated: the flow patterns do not depend on the speed, as long as inertia effect can be neglected.
A 200 s simulation time was applied and a snapshot of the system was taken every 0.04 s. Each snapshot contains for each particle its Cartesian coordinates, radius and velocity in Cartesian components.
The free surface is clearly visible in Figure 3. The model also showed a void beneath the obstacle, section f). This void is not visible as the figure is in 3D, i.e. just beneath the obstacles we see the particles behind the void.
Figure 3: Left side: 3D model of the reactor walls. The original area of interest is highlighted with a red box.
Auxiliary feeder and output sections are marked with light blue. Right: Snapshot of the DEM simulation.
After a sufficiently long simulation, the information collected in the snapshots are transformed into a suitable flow field. Details of this steps are given in Appendix B.
Briefly, for one snapshot, particle velocities in 3D space are projected into a fine grid (grid elements smaller than the particles) in a 2D subdomain as shown in Figure 4 (space average). Subsequently, the information from several snapshots is combined (time average) and this greatly reduces the granularity of the field as seen in Figure 4.
The time average results are adjusted to ensure that the flow is correct at each level and smoothed using convolutions with a 5x5 Gaussian kernel (Davies, 1990) as shown in Figure 5.
The result of the procedure is shown in Figure 6 were the radial and vertical component of the flow velocity are depicted. Both components have the expected characteristics, the radial term vanishes in all the straight 595
sections and it assumes relatively large values only at the widening of the domain in the d) zone.
Figure 4: Left: The particles on the 3D DEM model are projected into a grid in the 2D subspace. Right: Details
of the projection of one DEM snapshot.
Figure 5: Detail of the vertical component of the flow field, smoothing with Gaussian convolution. Effect of
subsequent applications (k) of the filter.
The voids in sections d) and f) are shown as regions of zero velocities. Observe that the highest velocity is not shown at the free surface in zone d), but slightly below.
At the free surface, the particles will flow at the highest velocity. We have, however, computed the average volume flow. Since there are fewer particles found at the free boundary than slightly below, the average volume flow is diminished very close to the boundary. Further, the center of the particles will always be at least one radius away from the void region. Hence, moving towards the free boundary, a smaller and smaller fraction of a particle can be present. The average volume velocity will then gradually be lowered and reaching zero at the boundary. This latter effect also causes the average velocity to approach zero at any boundary, c.f. Figure 5 for k = 0. A stagnant zone is visible in the vertical component of the velocity in the e) zone.
Figure 6: Components of the velocity field extracted from a DEM simulation. Left: radial component, Right:
vertical component.
The data are saved in a text file that can be imported via the interpolated function feature of COMSOL. Here, after re-scaling with the appropriate total flow, the velocities can be natively used in multiphysics applications.
Having the fictitious fluid velocities obtained with DEM it is interesting to evaluate the performance of the approach based on wall speeds. The flows, apart from a scaling factor due to the higher DEM flow, are qualitatively similar (see Figure 2 and Figure 6). The only obvious difference is that with DEM one always obtains a boundary effect near walls whereas the simple approach gives a homogeneous velocity profile. Since the total flow is exact in both cases, the simple approach overestimates the fluid velocities near the boundaries (approximately 2-3 particle radiuses) and slightly underestimate elsewhere.
Hybrid approach
In the previous section, we demonstrated how to construct and analyze a DEM simulation to obtain a bulk flow field that can be used within COMSOL. An obvious disadvantage is that the DEM simulation can be costly in terms of resources and computational time when applied to metallurgical systems. One possible solution is to use the DEM approach only for the zones that are foreseen to be problematic. In the example considered in this work, an experienced practitioner may realize that the section comprising the zones d) and e) and the region including zone f) require DEM treatment. An ad hoc sub-model can then be extracted and treated with the outlined DEM procedure (see Figure 7). We found that the smaller DEM model only required half the simulation time.
596
Once the DEM simulation is processed as described above, the resulting flow field is mapped back into the original geometry and it is used as a “flow template”.
Within the two applicable regions we add a volume force that will force the flow to be equal, or very close to the DEM flow field. We applied stationary simulation and a proportional controller, that is we used the volume forces:
r z K
s u u
Fr , DEM (3)
r z K
s w w
Fz , DEM (4) where uDEM, and wDEMare the velocity components from DEM,
K
is a suitable large number and s is the scaling factor to ensure that the DEM total flow matches the CFD simulation. Other methods can be applied.Figure 7: 1) Problematic sections of the system are identified. 2) A subsystem is constructed. 3) Snapshot of
the DEM simulation.
To avoid discontinuities, we recommend the use of a smoothing function in the transition between forced (velocities from DEM) and free zones.
The results of the hybrid procedure are shown in Figure 8 where the velocity components of the fictitious fluid flow are shown. These are in excellent agreement with the DEM results of Figure 6 (apart from a scaling factor since the DEM simulation have applied a higher flow).
In this example, the complexity/cost of the DEM calculation is reduced by only a factor of 2. While this may not justify the use of a hybrid approach, it demonstrates that complex systems can be partitioned in subdomains to be solved individually. A model can then be incrementally improved by adding subsequent sections where flow velocities are DEM-derived.
There are small details that the approach cannot cover.
For example, the simplified approach imposes a uniform velocity across any cross section of any straight domain.
This is in contrast with the DEM results that predict a small boundary effect at the walls. As explained above, the velocity will approach zero at any (non-moving) boundary. For this reason, at the transition between the forced and free zones, small artefacts in the fluid flow can occur.
Figure 8: Components of the velocity field extracted from a DEM simulation.
CONCLUSIONS
For comparatively simple bulk flow like plug flow sections and mass flow hoppers, a reasonable flow field can be computed applying viscous laminar flow with appropriate moving wall boundary conditions.
This simple approach does not work for more complex flows, e.g. regions with a free boundary. The flow field must then be found by other methods, for instance a DEM simulation.
A suitable method has been developed to average DEM results and import the flow field into a program for Multiphysics simulations.
To reduce the computational cost of DEM simulations a hybrid approach is recommended. DEM simulations are then used for the complex flow regions while the simple model is used wherever applicable.
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APPENDIX A – DEM CALCULATION
The descriptions of complex flow zones in the granular flow calls for the use of DEM simulations. The first step in this endeavor is the construction of a 3D mesh. Having the 2D axisymmetric projection of the fluid domain already implemented in COMSOL greatly simplifies this operation and the 3D model of the wall is obtained by revolving the trace of the fluid domain, obtaining a volume of approximately 19 m3. At this stage, the 3D model should be equipped with a feeder zone and output zone designed to keep the flow steady and control with precision the flux. These two features are shown in the left panel of Figure 3. The DEM simulation was carried out using LIGGGHTS® (Kloss et al., 2012). The particles have density equal to 1000 kg/m3 and a radius normally distributed around the mean value 3 cm (standard deviation 1 cm). The granular model “Hertz”
was used to compute the frictional force between two granular particles; the evolution of the tangential overlap during particles - particle contact is used to modify the spring part of the tangential. Finally, an additional torque contribution is added via the epsd2 rolling friction model.
The following material properties and interactions were used for the simulation: Young’s modulus 4.7*109 Pa;
Poisson’s ratio 0.35; coefficient of restitution 0.43;
coefficient of friction 0.73, coefficient of rolling friction 0.21. The time step was set to 10-5 s. The right panel of Figure 3 depicts a snapshot of the DEM simulations with the system loaded with approximately 134000 spherical particles. While this number of particles is representative
of an industrial application using rather lumpy material, DEM simulations employing large particles are common in the field (see e.g. Natsui et al., 2009) and Corse Grain approximations are emerging as a viable tool to reduce computational costs (Sakai, 2016). After equilibration of the loaded particles, 200 s simulation was performed and a snapshot was saved every 4000 time steps. During this time the wall at the bottom of the system was moving downward at a constant speed of 0.01 m/s, corresponding to a flow of 4.2*10-2 m3/s. These values exceed normal metallurgical operational conditions but ensures that each particle travels enough space to be able to collect a representative picture with a relative short simulation.
For reference, the DEM calculations took approximately 4 days on a standard desktop PC.
APPENDIX B – HOMOGENEIZATION
This appendix describes the transformation of the information collected in the DEM snapshots into the flow field of a fictitious fluid.
The first step to be accomplished is the space averaging as depicted in Figure 4. In practice, the Cartesian coordinates and velocity components for each particle are transformed in cylindrical coordinates and projected into the 2D subspace of the axisymmetric model. The projection occurs over a discretized grid whose elements are smaller than the particles. The space average takes into consideration both the volume of the particle and the total volume extruded over the projection itself.
A detail of the outcome of the space average is shown in the right panel of Figure 4 where the magnitude of the vertical component of the velocity is rendered. Although the space averaging successfully collects all the information of the 3D model and translated it into a bidimensional field component, the granular nature of the system is still evident and “shadows” of the individual particles are still visible.
The second step consists of combining data from several snapshots into a time average. In the specific case, we used 450 snapshots collected every 0.4 s in the range 20- 200 s of the DEM simulation.
At this stage, it is important to realize that the approach so far does not include the movement of the “empty”
fraction of the bulk. A possible solution is to scale all the velocities with a factor inversely proportional to the packing density of the system. Alternatively, the bulk flux (imposed in the DEM simulation), can be used to scale the flux for each row of the grid in the 2D subspace.
An example of the results at this stage is shown in the top left section of Figure 5. Although the flux of the fictitious fluid is now exact by design, some noise is still present in the flow fields and small artefacts emerge near the walls (see vertical striations in Figure 5). This can be corrected using a smoothing function. Here we use repeated convolutions with a 5x5 Gaussian kernel (Davies, 1990).
The operations described in this section refer to a 2D axisymmetric COMSOL simulation. However, only small modifications of the projection function and smoothing procedure are needed to address Cartesian 2D and full 3D cases.
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