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
MODELLING OF BUBBLE DYNAMICS IN SLAG DURING ITS HOT STAGE ENGINEERING
Y. WANG1*, L. CAO1,2, B. BLANPAIN1, M. VANIERSCHOT3, M. GUO1
1 KU LEUVEN Department of Materials Engineering, 3001 Leuven, BELGIUM
2 UINVERSITY OF SCIENCE AND TECHNOLOGY BEIJING State Key Laboratory of Advanced Metallurgy, 100083 Beijing, CHINA
3 KU LEUVEN Mechanical Engineering Technology TC, Campus Group T, 3001 Leuven, BELGIUM
* E-mail: yannan.wang@kuleuven.be
ABSTRACT
Silica-rich additives are injected into the slag with N2/O2 as carrier gas to stabilize free lime in BOF (Basic Oxygen Furnace) steelmaking slag. In order to understand the mixing behaviour of the additives, bubble dynamics and momentum transfer are to be clarified at first. The objective of this work is to investigate the bubble breakup and the injected momentum transfer. To this purpose, a Volume of Fluid (VOF) two phase model was developed using ANSYS FLUENT software to study the dynamic breakup process of the gas phase and the velocity attenuation along the injected axis. Particle Image Velocimetry (PIV) measurements were used to validate the corresponding computational modelling. The validation between experimental measurements and computational modelling is reasonable in the turbulence model. Bubble breakup begins very quickly in the region near the inlet. The momentum contained in the gas phase is dissipated within a short distance from the inlet.
Keywords: bubble breakup; momentum transfer;
computational modelling; particle image velocimetry
NOMENCLATURE Greek Symbols
Volume fraction.
k
Inverse effective Prandtl numbers.
Turbulent dissipation rate, [m2/s3].
Dynamic viscosity, [kg/m.s].
e Effective viscosity, [kg/m.s]. Mass density, [kg/m3].
Stress tensor.
Latin Symbols A Inlet area, [m2].
C,C1,C2 Constant, 0.0845, 1.42, 1.68, respectively.
F Momentum source term, [N/m3].
g Gravitational acceleration, [m/s2].
Gb Turbulence generation due to buoyancy.
Gk Turbulence generation due to mean velocity gradient.
k Turbulence kinetic energy, [m2/s2].
p Pressure, [Pa].
Q gas flow rate, [Nm3/min].
R Additional term.
S Turbulence dissipation rate source term.
Sk Turbulence kinetic energy source term.
t Time, [s].
T Temperature, [K].
uin Inlet velocity, [m/s].
u Velocity, [m/s].
YM Contribution of the fluctuating dilatation.
Sub/superscripts
o Operating condition.
s Standard condition.
INTRODUCTION
Currently, about 10 million tonnes of BOF (Basic Oxygen Furnace) slag is annually produced as a main by-product during steelmaking in Europe (Euroslag, 2017). Therefore, the use of BOF slag becomes a very urgent issue since it causes land occupation, environmental problems and resource waste. However, BOF slag valorization is restricted by its volume swelling during natural aging due to the presence of free lime (Liu et.al, 2016). In order to solve this problem, silica-rich additives, which are used to stabilize the free lime at high temperature, are injected into the liquid slag with nitrogen or oxygen gas as carrier gas through a top submerged lance. As a result, a buoyancy-driven flow in the slag pot is generated by gas injection, and the additives can move with the flow and react with free lime and other compounds.
In this whole process, the mixing efficiency is usually considered as one of the most important performance parameters, therefore, one of the main objectives is to attain a good mixing effect in the slag pot. To this end, it
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is beneficial to clearly understand the way that the injected gas affects the mixing characteristics.
Regarding this topic, bubble dynamics and momentum transport phenomena are closely involved. A large body of research has been directed at a similar topic in ladle metallurgy that is the interaction between gas bubble and liquid metal (e.g. Cloete et.al, 2009; Li et.al, 2008;
Olsen and Cloete, 2009). Based on the references, it can be predicted that the stirring and mixing of slag in a treatment is also mainly attributed to buoyant potential energy in the form of gas bubbles with different sizes formed by gas jet breakup. In other words, the gas breakup in the slag pot is very important to the flow pattern and mixing characteristics.
The purpose of the present study is to build a computational model to study the gas jet breakup and the momentum transfer in the slag pot. This can lay the foundation for the further investigation of mixing characteristics in the slag pot. In order to validate the turbulence modelling, Particle Image Velocimetry (PIV) measurements in a scaled cubic vessel was performed, and a detailed comparison between experimental and numerical results is made.
MODEL DESCRIPTION
For the sake of reducing the computational cost, only a transient two-dimensional and two-phase (g-l) model is developed in the present study. The Volume of Fluid (VOF) multiphase flow model is adopted to investigate the gas jet breakup due to the immiscible property and the sharp interface between gas bubble and liquid slag.
The RNG k-ε turbulence model is applied to study the turbulence characteristics in the slag pot.
Volume of Fluid Model
The VOF model is designed for two or more immiscible fluids which, in our case, are liquid slag and gas, respectively. In the VOF model, a single set of momentum equations is shared by the fluids, and the volume fraction of each of the fluids in each computational cell is tracked throughout the domain.
The continuity and momentum equations are listed as follows:
Continuity equation
0
u
t (1)
Momentum equation
gF
p
tu uu
(2) In the VOF model, all variables and properties are shared by the phases and represent volume-averaged values. Therefore, the variables and properties in any given control volume are either purely representative of one of the phases, or representative of a mixture of the phases, which depends on the volume fraction values. In our two-phase system, the volume fractions of slag and gas sum up to unity. The volume-averaged density and viscosity can be represented by the following mathematical equations.
gas 1
slag
(3)gas gas slag
slag
(4)
gas gas slag
slag
(5)
RNG k-ε Model
RNG k-ε turbulence model is derived from the instantaneous Navier-Stokes equations, using a statistical technique called “renormalization group”
(RNG) method. It has a similar form to the standard k-ε turbulence model, but includes several refinements. It is more appropriate for rapidly strained and swirling flows than the standard k-ε turbulence model, and it also provides an analytically derived differential formula for effective viscosity that accounts for low-Reynolds number effects (ANSYS, Inc., 2015).
The turbulence kinetics energy, k, and its dissipation rate, ε, in the RNG k-ε model are obtained from the following transport equations:
k M b
k j e k j
i i
S Y G
x G k x
x ku t k
(6)
S k R
C G C k G x C
x x u t
b k j
e j
i i
2 2 3
1
(7)
The effective turbulent viscosity is solved by
e C k2 (8)Geometry and Operational Conditions
The geometry in the model consists of a slag pot and a lance. The slag pot is in the shape of a tapered cylinder and the lance is a simple cylinder. Liquid slag is contained in the slag pot with a certain height. The lance is submerged into the liquid slag from the slag level to a specific depth in the centre position. The dimensions and physical properties and operational conditions are listed in Table 1, 2 and 3, respectively. Since it is a symmetrical geometry, only half of it was built. The total node number is around 36000, which is large enough to obtain a sharp interface between gas bubble and liquid slag. The geometry with the grid is depicted in Figure 1.
Table 1: Geometrical dimensions of the pot.
Top diameter, mm 3360
Bottom diameter, mm 2390
Height, mm 3558
Lance diameter, mm 40
Table 2: Physical properties.
Density of slag, kg/m3 3000
Density of air, kg/m3 0.567*
Viscosity of slag, kg∙m-1∙s-1 0.100 Viscosity of air, kg∙m-1∙s-1 8.9e-5 Surface tension of slag/gas, N/m 0.55
“*” indicates a lower air density due to the high temperature in real case.
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Table 3: Operating conditions.
Air flow rate, Nm3/min 3
Inlet velocity, m/s 50.0 to 84.5
Operating temperature, K 1873
Operating pressure, Pa 3e5 to 5e5
Lance depth, mm 1000
Height of slag level, mm 3000
Figure 1: Geometry with grid.
The heat transfer is not in the scope of this study, therefore, the temperature gradient is neglected, which means that a uniform temperature field is assumed in this simulation. The inlet velocity of air is calculated based on the following equation.
A Q T p
T p A
u Q s
s o
o s
in o
(9)
Numerical Method
This model is implemented in FLUENT 16.2. Velocity inlet and pressure outlet boundary conditions are adopted for this simulation. For the solution methods, the Pressure-Implicit with Splitting Operators (PISO) pressure-velocity coupling scheme is used, which is recommended for a transient problem. PISO scheme has its own advantages that allows higher under-relaxation values for both momentum and pressure, leading to less iterations and faster convergence. In the spatial discretization part, the PREssure Staggering Option (PRESTO!) scheme and second order upwind scheme are performed for pressure and momentum, respectively.
Convergence is monitored by means of the unscaled residual of the continuity equation. The reason is that the continuity equation is the most difficult one to converge.
In this study, it is considered that the residual of the continuity equation must drop at least 3 orders of magnitude to obtain a sufficient accuracy. Therefore, the convergence criterion less than 10-7 is chosen when the time step size is 1×10-4.
The simulations were uploaded to a High Performance Computing (HPC) cluster. 2-5 nodes with 40-100 processors were required for the simulations.
TURBULENCE MODEL VALIDATION
In order to validate the RNG k-ε turbulence model, PIV measurements and the corresponding simulations were conducted beforehand.
Experimental setup
In the measurements, paraffin oil and compressed air are used to form a two-phase system. The vessel made of transparent glass is cubic shape with dimensions of 135
× 135 × 195 mm. A glass pipe with inner diameter of 5 mm taken as the top lance is also placed in the centre of the vessel. The operating conditions and physical properties are listed in Table 4.
The flow field in the vessel is measured by Time- Resolved PIV (TR-PIV). Since the vessel is axisymmetric, only the left zone is of interest. It can also be easily predicted that the liquid mainly flows in the upper part based on two considerations, one of which is that the upper part liquid is driven by the rising air, and the other one is that the injected air cannot penetrate very deeply, so the liquid in the lower part is almost still.
Therefore, the selected area to be measured is located in the upper left part of the median plane, which is shown in Figure 2. A PIV laser (wavelength 527 nm, pulse energy 10 mJ @ 1000 Hz) from NewWave is employed to generate a laser sheet with a thickness of 0.5 mm which exactly overlaps the median plane of the vessel.
The flow is seeded with hollow PMMA particles of diameters between 20 and 50 µm. The particles are coated by Rhodamine B to exhibit fluorescence, which can help increase the signal to noise ratio when the back light of the laser sheet is filtered out by an optical filter.
In order to correct for light refraction, the PIV system was calibrated by means of placing a calibration plate in the measured flow field, and the plate exactly overlaps the laser sheet. The images are recorded by a CMOS camera (HighSpeedStar 5) with a resolution of 1024 × 1024 pixels. The calculation of velocity vector is processed by the Davis 8.1 software (LaVision GmbH).
Further data processing is executed by Matlab software (R2016a) using specific code.
The corresponding numerical simulation is established with the same multiphase flow model (VOF) and the turbulence model (RNG k-ε). The half meshing with around 5800 nodes is shown in Figure 4. The solution methods are also kept the same. These can ensure consistent approaches to the following simulation of flow field in the slag pot.
Table 4: Operating parameters and physical properties.
Air flow rate, NL/h 300
Inlet velocity, m/s 4.25
Submerged depth, m 0.044
Height of oil level, m 0.164
Density of oil, kg/m3 880
Density of air, kg/m3 1.225
Viscosity of oil, kg∙m-1∙s-1 0.065 Viscosity of air, kg∙m-1∙s-1 1.789e-5 Surface tension of oil/air, N/m 0.026
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Figure 2: Schematic of the experimental setup and the measured area: A (-0.063, 0.164); B (-0.005, 0.164); C (-0.005, 0.106); D (-0.063, 0.106); E (-0.063, 0.135); F (-0.005, 0.135).
Figure 3: Photograph of the experimental setup.
(1: laser generator; 2: highspeed camera; 3: paraffin oil with PMMA particles; 4: glass pipe; 5: rotameter)
Figure 4: Meshing of the computing domain.
RESULTS Model Validation
The turbulence model in numerical simulation is verified with experimental data by comparing the time-averaged velocity fields in the domain. The representative case with air flow rate of 300 NL/h is employed here, and the results are presented in Figure 5 and 6, respectively.
Figure 5: Comparison of the experimentally and numerically obtained time-averaged velocity fields (air flow rate: 300 NL/h). (a) velocity field of the PIV measurements and (b)
velocity field of the numerical simulations.
Figure 6: Axial velocity profile of the measured line EF shown in figure 2.
It can be seen from Figure 5 that a circulation zone consisting of a counter-clockwise rotating vortex is formed in the middle of the measured zone in the measurement, and a similar one can be observed in the corresponding numerical simulation, despite of a deviation of the location of the vortex centre. There may be a reason to explain it. Because a 2D axisymmetric model is used in this study, the domain will sweep 360 degree along x-axis by default, which makes the 368
computing domain more like a cylinder. However, the model in this study in a cubic one. This may be the reason for the deviation of the vortex centre. A further work of the corresponding 3D modelling will be established to determine the reason. It also can be observed that a large discrepancy appears in the very right region. This is because this measured region is very close to the gas pipe, and the gas bubbles rising along with this pipe posed serious influence on the measurement due to the refractive issues. In other words, the obtained data in the region close to the gas pipe is hardly reliable.
The axial velocity profile of the measured line shown in Figure 2 is depicted in Figure 6. Clearly, this is a big deviation in the right part, and the reason of it has been explained in the last paragraph. Apart from this, the rest seems acceptable since only minor errors appear. This may be attributed to the coarse meshing.
In conclusion, the results are still convincing since a similar circulation in the middle of the measured region and an acceptable quantitative validation can be observed, which means the flow patterns in the experiment and modelling resemble each other.
However, there is, for sure, some space to improve the model. Based on the above description, the influence of the gas injection on the flow field is reasonably validated.
Bubble Formation
In the slag valorization process, gas stirring is a key step.
When the gas is injected into the slag through a submerged top lance, the continuous gas phase splits into discrete gas bubbles that move upward with high velocity. Soon a conical plume consisting of gas bubbles and liquid is shaped in the upward path. It is the moving bubbles that transfer momentum to the surrounding liquid and make the system stirred. Hence, gas breakage into bubbles is very important for transport phenomena in multiphase flow. For our study, gas breakage is the precondition for a better mixing, and it is well worth being investigated.
Figure 7: Gas bubble formation represented by the gas volume fraction (a: 0.02 s; b: 0.3 s; c: 0.75 s; d: 1.58 s; e: 2.70
s).
Figure 7 shows the dynamic breakage process of the gas phase in the slag pot. As can be seen in Figure 7(a), the gas phase comes out of the inlet and forms an
approximate circle. The upper part of the circle is a little deformed due to the pressure difference along the bubble surface. Later a dumbbell shape with a narrow neck forms near the inlet as the pressure difference continues increasing. Finally the gas phase splits into several gas bubbles. The gas bubbles keep moving up and can break up into even smaller bubbles.
It can be concluded that the gas phase begins breakup very soon near the inlet region, where large velocity gradient and turbulence kinetics energy exist. This will be further described in the following section. The formed bubbles can have secondary or several times breakup caused by turbulent eddies during rising up.
Many studies in regard to bubble breakup can be found in chemical engineering, most of which, however, were performed in low temperature systems (e.g. Xing et.al, 2015; Luo and Svendsen, 1996; Hengel et.al, 2005).
Nonetheless, these existing studies can supply important references for further investigation.
Momentum Characteristics
In ladle metallurgy, the gas phase is injected from the bottom through plugs, and the gas flow rate is smaller compared to that in slag valorization. It has been proved that the injected momentum in ladle metallurgy is dissipated within a very short distance (Krishnapisharody and Irons, 2013). In Ausmelt TSL application, the gas phase is injected from the top via a top submerged lance. (Hoang et.al, 2009; Wood et.al, 2011). A violent stir can be obtained in the bath.
Therefore, it is necessary to make clear if the injected momentum in the slag valorization can make an important contribution to system stirring. Three cases with initial inlet velocity of 84.5, 62.5 and 50.0 m/s, respectively, are discussed here. The time-averaged velocity and instantaneous results of turbulent kinetic energy and dissipation rate along the axis at 10.0 s are presented in Figure 8, 9 and 10, respectively.
Figure 8: Velocity attenuation along the injected axis
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Figure 9: Attenuation of turbulence kinetic energy along the injected axis
Figure 10: Attenuation of turbulence dissipation rate along the injected axis
The penetration depth is increased with increasing inlet velocity, which is clearly shown in Figure 8. However, the penetration depth is still quite small compared to the distance between the inlet and the bottom wall which is 2 m. This is because the density difference between the gas phase and slag is huge. Even with a very large inlet velocity, e.g. 84.5 m/s, the penetration depth is small compared to the slag bath height.
In Figure 9 and 10, the turbulence kinetic energy and it dissipation rate are depicted along the injected axis. The attenuations are consistent with the velocity attenuation, so the turbulence kinetic energy is dissipated in a short distance, which corresponds to other researchers’ work mentioned previously. It can also be concluded that the turbulence kinetics energy and its dissipation rate are very unstable in this short distance according to the sharp peaks. Therefore, it can be imaged that turbulence in the adjacent area of the inlet is very violent. This can explain why the gas phase can split easily into bubbles in this region.
Now that it has been proved the injected momentum is limited in stirring the slag, it can be inferred that the flow is mainly driven by buoyancy of gas bubbles. This can be easily understood since the pressure difference between the top and bottom surfaces of bubbles is so large, which makes the bubble move upward with high velocity, and this high velocity can be transferred to the surrounding slag through interphase interactions. This is how gas bubbles drive liquid slag flow in the slag pot.
CONCLUSIONS
The turbulence model used in our numerical simulation is quantitatively validated by comparing the velocity fields obtained from experiment and simulation, and the result is reasonable.
VOF model can successfully capture the dynamic breakup process of the gas phase. In our study, the gas phase breaks up into gas bubbles very quickly in the region adjacent to the inlet and the formed bubbles can undergo secondary or several times breakage while rising up.
The injected momentum is found to be dissipated in a short distance, very close to the inlet as indicated with measurements of the velocity attenuation and turbulence kinetic energy attenuation. This is consistent with the findings in the ladle metallurgy.
ACKNOWLEDGEMENT
The financial support from IWT Grant 140514 (Belgium) and computer support from HPC (KU Leuven) are highly acknowledged. Yannan Wang and Lingling Cao want to thank the support of the China Scholarship Council (CSC).
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