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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

0.1

0.2

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0.4

0.5

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

0

0.1

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0.6

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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0.00 0.40 0.80 1.20 1.60 2.00

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

• ANSYS is committed to providing and supporting “best in class” technology in dense and dilute multiphase

• Continue to improve speed and fidelity through experimental validation of results.

• Have the most comprehensive and advanced collection of multiphase tools of any commercially available CFD code.

Summary

THANK YOU!

Questions?

Please contact:

mohammed.azhar@ansys.comphil.stopford@ansys.com