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© 2011 ANSYS, Inc. February 23, 20121
Multiphase Flows
Mohammed AzharPhil Stopford
© 2011 ANSYS, Inc. February 23, 20122
Outline
•VOF Model– VOF Coupled Solver
– Free surface flow applications
•Eulerian Model– DQMOM
– Boiling Model enhancements
– Multi-fluid flow applications
•Coupled CFD/DEM
© 2011 ANSYS, Inc. February 23, 20123
VOF Model: New in FLUENT 14
•Coupled VOF Solver– Solves the momentum, pressure based continuity and volume fraction
equations together.
– Coupled VOF solver aims to achieve faster steady state solution compared to segregated method of solving equations.
© 2011 ANSYS, Inc. February 23, 20124
•Select “Coupled” scheme as Pressure-velocity Coupling• Enable “Coupled with Volume Fraction” option
“Volume Fraction Courant Number ” provides the additional implicit under-relaxation for VOF equation. (could help for numerically sensitive cases)
TUI
Recommendations for higher order momentum schemes- Lower under-relaxation for momentum- Disable high order Rhie-Chow flux through solve >set > numerics
Coupled VOF Solver
© 2011 ANSYS, Inc. February 23, 20125
Free Surface Flow Around the Container Ship
8.533M cellshalf model
Cutcell mesh was created by TGrid
© 2011 ANSYS, Inc. February 23, 20126
Free Surface Flow Around the Container Ship
Coupled VOFSegregated VOF
• Segregated VOF converges in 1450 iterations
• Coupled VOF converges in 500 iterations
© 2011 ANSYS, Inc. February 23, 20127
The free surface level plot clearly shows that segregated VOF run matches well with coupled VOF run and experimental result after 1450 iterations but not after 500 iterations.
Free Surface Flow Around the Container Ship
© 2011 ANSYS, Inc. February 23, 20128
Eulerian Model: News in FLUENT 14
•DQMOM for population balance models
•Critical Heat flux (CHF) model
© 2011 ANSYS, Inc. February 23, 20129
DQMOM usage
•Problem– Cumulative size distribution of droplets at
inlet available
– It is desired to convert the size distribution into inputs required by DQMOM (volume fraction and moment-4 values)
•Solution– Use the “Generate DQMOM Values” to
obtain relevant inputs for DQMOM
•Target application– Ease of use for DQMOM problems
© 2011 ANSYS, Inc. February 23, 201210
Modeling spray injection using DQMOM
• Problem
– Diesel type spray from Madsen thesis
– N-hexane injected into nitrogen gas
– Injection velocity = 127 m/s
– Nozzle diameter = 127 mu-m
• Modeling details
– Population balance model in Fluent
– WAVE breakup model for breakage frequency
– Equi-sized binary breakage or parabolic breakage pdf
© 2011 ANSYS, Inc. February 23, 201211
Mesh
•2 cells in the nozzle exit
•218x55 cells
•k-epsilon per phase turbulence model with turbulent dispersion turned on
© 2011 ANSYS, Inc. February 23, 201212
Comparison between homogeneous and inhomogenous model
© 2011 ANSYS, Inc. February 23, 201213
Results
Shape of the spray Velocity vectors for the spray
© 2011 ANSYS, Inc. February 23, 201214
Comparison with experiments
Comparison with experiments at x/d=400Wu et al
© 2011 ANSYS, Inc. February 23, 201215
Boiling models in Fluent14
•We have three different models available in R14
•RPI Boiling model– Applicable to sub-cooled nucleate boiling
•Non-equilibrium Boiling– Extension of RPI to take care of saturated
boiling
•Critical Heat Flux– Extension of RPI to take care of boiling crisis
© 2011 ANSYS, Inc. February 23, 201216
Testing the CHF model
CHF model of FluentExperimental data from Hoyer• Area of influence – Kenning • Bubble departure frequency –Cole•Turbulent drift force - Simonin
© 2011 ANSYS, Inc. February 23, 201217
RPI paper validation case
Temperature in KVoid fraction
0.0
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0.0 0.5 1.0 1.5 2.0
Experiments
ANSYS CFD (Fluent)
RPI_paper
Vertical pipeLength: 2 mDiameter: 15.4 mmHeat Flux: 570 kW/m2
Mass Flux: 900 kg/m2-sOperating pressure: 4.5 MpaResults from Bartolomei experiments
Axial distribution of Average void fraction
© 2011 ANSYS, Inc. February 23, 201218
default settings for boiling model
© 2011 ANSYS, Inc. February 23, 201219
Results with default settings
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0.00 0.40 0.80 1.20 1.60 2.00
Experiments
RPI_paper
F14
F14_adapted
F14_2level_adapted
F13
Axial distribution of Average void fraction
© 2011 ANSYS, Inc. February 23, 201220
Results with various sub models other than defaults
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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
F14 default settings
F14, const. AOI =2
F14, Unal, Const. AOI=2
F14, Kocamustafa, Const. AOI=2
RPI paper
Experiements
Axial distribution of Average void fraction
© 2011 ANSYS, Inc. February 23, 201221
Observations
1. Mesh dependency
2. Excessive vapor generation close to “Onset of boiling”
© 2011 ANSYS, Inc. February 23, 201222
Reason for Mesh dependency
•qf = Single phase heat transfer to liquid – Grid independent as it uses a heat transfer coefficient for liquid calculated by
Fluent internally
•qe = Evaporation heat flux, f(Twall – Tsat)– Grid independent as it does not use liquid temperature from the cell next to the
wall
•qq = Quenching heat flux, f(Twall – Tliq)– Grid dependent component
qefwall qqqq
© 2011 ANSYS, Inc. February 23, 201223
Solution used in CFX at R12
•qq = Quenching heat flux, f(Twall – Tliq)
• In CFX, an approach was developed to make this component grid independent
•Based on the temperature in the cell next to the wall and its Y+, they estimate liquid temperature at Y+=250 and use this in the above correlation
•This option is available in Fluent at R14 as Quenching ‘Correction Model’
© 2011 ANSYS, Inc. February 23, 201224
Quenching correction options in Fluent14
© 2011 ANSYS, Inc. February 23, 201225
Results with various options for quenching
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0 0.5 1 1.5 2 2.5
F14 default settings
F14 with fixed y+=250
F14 with fixed temp = (Tsat - 3) K
Axial distribution of Average void fraction
© 2011 ANSYS, Inc. February 23, 201226
Checking grid independence for quenching correction option Y+=250
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0.00 0.40 0.80 1.20 1.60 2.00
Experiments
RPI_paper
F14, fixed Y+ = 250
F14_adapted, fixed Y+=250
F14 2 level adapted, fixed Y+=250
Axial distribution of Average void fraction
© 2011 ANSYS, Inc. February 23, 201227
Results with Wall lubrication
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Experiments
RPI_paper
F14, fixed Y+ = 250
F14_adapted,fixed Y+=250,WL
F14 2 level adapted, fixed Y+=250, WL
Axial distribution of Average void fraction
© 2011 ANSYS, Inc. February 23, 201228
Coupled Fluid and DEM
•At high volume fraction of particles particle-particle interaction becomes important.
– With or Without Interaction with Fluid Flow
© 2011 ANSYS, Inc. February 23, 201229
Theory: Soft Sphere DEM
Discrete Element Method: DEM
• Cundall and Strack (1979)
Soft Sphere Approach
• Contact forces computed from deformation.
• Overlap of ideal spheres used as the measure for deformation.
• Newtons 2nd law integrated in time.
– Allows for N-body interaction.
• Rigidity of materials determines time scale for integration.
* not to scale, greatly exaggerated
r1
r2
overlap*
Particle 1:mass m1
position x1
velocity v1
Particle 2:mass m2
position x2
velocity v2
© 2011 ANSYS, Inc. February 23, 201230
Theory: Soft Sphere DEM (cont’d)
Forces in Newtons 2nd law collected from pairwise interaction.
Collision laws defined for pairs of collision partners.
Implemented Force Laws
• Spring
• Spring-Dashpot
• Friction
These forces enter the equation of motion for the particle through Fother
* not to scale, greatly exaggerated
r1
r2
overlap*
Particle 1:mass m1
position x1
velocity v1
Particle 2:mass m2
position x2
velocity v2
F1
F2
12
1 )(
FF
xx
xxn
nkF
ij
ij
n
coll
losscollloss
t
m
K
mft
mm
mmmf
ln2
ln
12
12
21
2112
22
nkF1
Spring Model Spring-dashpot Model
© 2011 ANSYS, Inc. February 23, 201231
Fluidized Bed: Base CaseDimension
• 0.2 * 0.2 * 0.4 m cube.
• 16K Hex cells.
BC• Bottom: Velocity Inlet=0.5 m/s
• Top: Pressure Outlet=1 atm
DPM• Particle diameter = 750 micron
• 15K Parcels
• Volume Ratio of single mesh cell to single parcel = 5.5
DEM + DDPM• Spring-Dashpot: K = 100
Eta = 0.8 (particle-particle), 1 (particle-boundary)
• Friction: Mu-stick = 0.5, Mu-glide = 0.2, Mu-limit = 0.1, Vel-glide = 4.6, Vel-limit = 20, Slope-limit = 2
• Node based averaging (Beta)
• Particle time step size = 2e-4 sec
• No. of continuous phase iterations per DPM iteration = 200
• Update DPM sources every flow iteration
• Drag Law = Wen-Yu
© 2011 ANSYS, Inc. February 23, 201232
Fluidized Bed: Base Case
Solver Settings• PC SIMPLE
• Node based Gradients
• Bounded Second Order Implicit
• Momentum, Volume Fraction: QUICK
• URF: Pressure = 0.9, Momentum = 0.2, Volume Fraction, DPM = 1
© 2011 ANSYS, Inc. February 23, 201233
Fluidized Bed: Base Case
Simulation results• Pressure drop balanced by the
weight of the bed• Realistic bubbling frequency• No need for carefully tweaking
of parameters: Robust results.
Note Postprocessing: Showing only a slice from the full bed.
© 2011 ANSYS, Inc. February 23, 201234
Compare
• K = 100 N/m
• K = 1000 N/m
Time step: 5e-5 s
Results independent of K
K = 100 N/m sufficient
Fluidized Bed: Spring Constant Variation
© 2011 ANSYS, Inc. February 23, 201235
A blind challenge problem on modeling a bubbling fluidized bed of FCC particles with a Particle Size Distribution (PSD).
Cf. https://www.mfix.org/challenge/
Dimensions: 0.91m x 0.91 m x 7.41m
Particle content: 1351kg initially
“Fine Particles” have diameter < 45 μm
Comparison:
• 12% fine particles
• 3% fine particles
PSDs have similar mean average diameter of 85μm and 89μm. Fluidization differences from details of PSD.
Fluidized Bed: NETL Challenge 2011
© 2011 ANSYS, Inc. February 23, 201236
Mesh: 91k cells
Fluid/Particle Time Step: 0.5 ms
12% fines: initially about 512k parcels
3% fines: ditto
Spring-Dashpot and Friction forces with default values for particle-particle and particle-boundary collisions.
Able to simulate 16s of flow time in a day on 12 processors with a complete PSD.
Fluidized Bed: NETL Challenge 2011
12% fines 3% fines
© 2011 ANSYS, Inc. February 23, 201237
Proppants are used to prop open artificial fractures created in the rock of gas fields.
The placement of proppants at appropriate locations is essential for a successful fracturing operation.
Case
• Dimensions: 3m x 0.3m x 0.03m (width x height x depth)
• Particle content: 444k parcels, 8.9kg at 10s .
• Spring-Dashpot and friction force with default values except K = 100 N/m for particle-particle and particle-wall collisions.
• Fluid Time Step: 2e-3s, Particle Tracking Time Step: 2.5e-4s
• Particle volume fraction at injection surface about 0.07 .Using staggering in time and space on injection surface.
Proppant Transport
*
* colored by VOF
© 2011 ANSYS, Inc. February 23, 201238
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Summary