Computational Fluid Dynamics (CFD) and Multiphase...

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Computational Fluid Dynamics (CFD) and Computational Fluid Dynamics (CFD) and

Multiphase Flow ModellingMultiphase Flow Modelling

Telemark University College, PO. Box 203, NTelemark University College, PO. Box 203, N--3901, Porsgrunn, 3901, Porsgrunn, NorwayNorway

AssociateAssociate Professor Britt M. Halvorsen (Dr. Professor Britt M. Halvorsen (Dr. IngIng ) )

Amaranath S. KumaraAmaranath S. Kumara ((PhDPhD Student)Student)

Telemark University CollegeTelemark University College

WhatWhat is CFD?is CFD?

The results of CFD analyses are relevant in:The results of CFD analyses are relevant in:

�� ConceptualConceptual studies of studies of newnew designsdesigns

�� DetailedDetailed productproduct developmentdevelopment

�� TroubleshootingTroubleshooting

�� RedesignRedesign

CFD CFD analysisanalysis complementscomplements testing and testing and experimentationexperimentation

�� ReducesReduces the total the total efforteffort requiredrequired in the in the experimentexperiment design and datadesign and data

acquisitionacquisition

Computational Fluid Computational Fluid DynamicsDynamics (CFD) is the (CFD) is the sciencescience of predicting:of predicting:

�� Fluid flowFluid flow

�� Heat and mass transferHeat and mass transfer

�� ChemicalChemical reactionsreactions and related phenomena by solving numerically the and related phenomena by solving numerically the

set of set of governinggoverning mathematicalmathematical equations.equations.

Conservation of mass, momentum, energy, species, etc.


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HowHow DoesDoes CFD Work?CFD Work?

FLUENT solvers are based on the finite volume method

� Domain is discretized onto a finite set

of control volumes (or cells).

� General conservation (transport) equations

for mass, momentum, energy, species, etc.

are solved on this set of control volumes.

� Partial differential equations are

discretized into a system of algebraic

equations

� All algebraic equations are then solved

numerically to render the solution field

Control Control volumesvolumes in a pipe in a pipe sectionsection

Equation VariableEquation Variable

ContinuityContinuity 11

X momentum uX momentum u

Y momentum vY momentum v

Z momentum wZ momentum w

EnergyEnergy hh


WhatWhat is Turbulence?is Turbulence?

�� Unsteady, Unsteady, irregularirregular motionmotion in which in which transportedtransported quantitiesquantities (mass, momentum, (mass, momentum,

scalarscalar speciesspecies)) fluctuatefluctuate in time and in time and spacespace

Small structuresLarge structures

�� ContainsContains a a widewide range of turbulent eddy range of turbulent eddy sizessizes ((scalesscales spectrumspectrum))

�� Fluid properties and velocity Fluid properties and velocity exhibitexhibit randomrandom variationsvariations

�� StatisticalStatistical averaging results in averaging results in accountableaccountable, turbulence related transport, turbulence related transport

mechanismsmechanisms

�� This This characteristiccharacteristic allowsallows for turbulence modelingfor turbulence modeling

Turbulent JetTurbulent Jet Energy Energy

CascadeCascade


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Dinosaur meshDinosaur mesh

Pressure field on a dinosaurPressure field on a dinosaur

CFD Modeling CFD Modeling OverviewOverview


Multiphase Multiphase ModellingModelling

�� A phase is a A phase is a classclass of matter with a of matter with a definabledefinable boundary and a boundary and a

particularparticular dynamicdynamic responseresponse to the to the surroundingsurrounding flow/flow/potentialpotential

fieldfield

Introduction Introduction

�� Phases are Phases are generallygenerally identifiedidentified by solid, liquid or by solid, liquid or gaseousgaseous

statesstates of matter of matter butbut cancan alsoalso referrefer to other forms:to other forms:

Materials with Materials with differentdifferent chemicalchemical properties properties butbut in thein the

same same statestate or phase (i.e. or phase (i.e. liquidliquid--liquidliquid, , suchsuch as, as, oiloil--waterwater))

�� The fluid system is The fluid system is defineddefined by a by a primaryprimary and multiple and multiple secondarysecondary phasesphases

ThereThere maymay be be severalseveral secondary phase secondary phase denotingdenoting particles with particles with differentdifferent sizessizes

�� In In contrastcontrast, , multimulti--componentcomponent flow (flow (speciesspecies transport) transport) refersrefers to flow that to flow that cancan bebe

characterizedcharacterized by a single velocity and temperature by a single velocity and temperature fieldfield for all for all speciesspecies


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ChoosingChoosing a Multiphase Modela Multiphase Model

�� In order to In order to selectselect the appropriate model, users must know the appropriate model, users must know a a priori priori the the

characteristicscharacteristics of the flow in terms of the following:of the flow in terms of the following:

Flow regimeFlow regime

�� Particulate (bubbles, droplets or solid particles in continuousParticulate (bubbles, droplets or solid particles in continuous phase)phase)

�� Stratified (fluids Stratified (fluids separatedseparated by interface with by interface with lengthlength scalescale

comparablecomparable to domain to domain lengthlength scalescale))

�� Multiphase turbulence modelingMultiphase turbulence modeling

�� For particulate flow, one For particulate flow, one cancan estimateestimate::

�� Particulate loading (Particulate loading (ββ))

�� Stokes number (St)Stokes number (St)

Where and

cc

dd

ραραβ =


Multiphase Flow RegimesMultiphase Flow Regimes

�� Particle Particle –– laden flow laden flow –– cyclone cyclone

separators, air classifiers, separators, air classifiers,

dust collectors, dustdust collectors, dust--laden laden

environmental flowsenvironmental flows

�� Fluidized beds Fluidized beds –– Fluidized bed reactorsFluidized bed reactors

Gas-Liquid

Liquid-Liquid

�� Bubbly flow Bubbly flow –– absorbers, evaporators, absorbers, evaporators,

sparging devicessparging devices

�� Droplet flow Droplet flow –– atomizers, combustorsatomizers, combustors

�� Slug flow Slug flow –– offshore pipe linesoffshore pipe lines

�� Stratified flow Stratified flow –– freefree--surface flowsurface flow

Gas-Solid

�� Slurry flow Slurry flow –– Particle flow in liquids, Particle flow in liquids,

solids suspension, solids suspension,

sedimentation, andsedimentation, and

hydrotransporthydrotransport

Liquid-Solid


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Multiphase Flow ModelsMultiphase Flow Models

""No universal multiphase model for all regimesNo universal multiphase model for all regimes""

� Volume of Fluid model (VOF)

Direct method of predicting interface shape

between immiscible phases

� Eulerian Model

Model resulting from averaging of VOF model

applicable to dispersed flows

� Mixture Model

Simplification of Euler model; applicable when

inertia of dispersed phase is small

� Lagrangian Dispersed Phase Model (DPM)Lagrangian particle/bubble/droplet tracking

Dispersed flowDispersed flow

Stratified FlowStratified Flow

Dilute FlowDilute Flow


The Volume of Fluid Model (VOF)The Volume of Fluid Model (VOF)


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The Volume of Fluid (VOF) ModelThe Volume of Fluid (VOF) Model

�� The VOF model is designed to track the The VOF model is designed to track the positionposition of the interface of the interface

between between twotwo or more immiscible fluids.or more immiscible fluids.

�� Tracking is Tracking is accomplishedaccomplished by by solutionsolution of phase of phase continuitycontinuity equation equation ––

resulting volume fraction abrupt resulting volume fraction abrupt changechange pointspoints outout the interface locationthe interface location

�� A mixture fluid momentum equation is A mixture fluid momentum equation is solvedsolved using mixture material using mixture material

properties. properties. ThusThus the mixture fluid material properties the mixture fluid material properties experienceexperience jump jump

acrossacross the interface.the interface.

�� Turbulence and Turbulence and energyenergy equations are equations are alsoalso solvedsolved for mixture fluid.for mixture fluid.

�� Surface tension and Surface tension and wallwall adhesionadhesion effectseffects cancan be be takentaken intointo accountaccount..

Phases Phases cancan be be compressiblecompressible and be and be mixturesmixtures of of speciesspecies


Applicability of VOF modelApplicability of VOF model

�� Flow regime Flow regime -- Slug flow, stratified/freeSlug flow, stratified/free--surface flowsurface flow

�� Volume loading Volume loading -- Dilute to denseDilute to dense

�� Particulate loading Particulate loading -- Low to highLow to high

�� Turbulence modeling Turbulence modeling -- Weak to moderate coupling between phasesWeak to moderate coupling between phases

�� Stokes number Stokes number -- All rangesAll ranges

�� Application examplesApplication examples

•• Large slug flowsLarge slug flows

•• FillingFilling

•• Offshore separator sloshingOffshore separator sloshing

•• BoilingBoiling

•• CoatingCoating


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Summary Summary -- VOFVOF

�� Available in conjunction with most other FLUENT modelsAvailable in conjunction with most other FLUENT models

�� VOF is an Eulerian fixedVOF is an Eulerian fixed--grid techniquegrid technique

�� VOF is numerically robust and accurateVOF is numerically robust and accurate

Not available with the following reacting flow models:Not available with the following reacting flow models:

•• Eddy dissipation conceptEddy dissipation concept

•• Premixed, nonPremixed, non--premixed, partially premixedpremixed, partially premixed

•• Composition PDFComposition PDF

•• NOx and sootNOx and soot


The Eulerian Multiphase ModelThe Eulerian Multiphase Model


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The Eulerian Multiphase ModelThe Eulerian Multiphase Model

�� The Eulerian multiphase model is a result of averaging of NS eqThe Eulerian multiphase model is a result of averaging of NS equationsuationsover the volume including arbitrary particles + continuous phaseover the volume including arbitrary particles + continuous phase

�� The result is a set of conservation equations for each phase (cThe result is a set of conservation equations for each phase (continuousontinuousphase + N particle phase + N particle ““mediamedia””))

�� Both phases coexist simultaneously: conservation equations for Both phases coexist simultaneously: conservation equations for eacheachphase contain singlephase contain single--phase terms (pressure gradient, thermalphase terms (pressure gradient, thermalconduction etc.) + interfacial termsconduction etc.) + interfacial terms

�� Interfacial terms express interfacial momentum (drag), heat andInterfacial terms express interfacial momentum (drag), heat and massmassexchange. These are nonlinearly proportional to degree of mechanexchange. These are nonlinearly proportional to degree of mechanicalical(velocity difference between phases), thermal (temperature diffe(velocity difference between phases), thermal (temperature difference).rence).Hence equations are harder to convergeHence equations are harder to converge

�� AddAdd--on models (turbulence etc.) are availableon models (turbulence etc.) are available


Applicability of Eulerian modelApplicability of Eulerian model

�� Flow regime Flow regime -- Bubbly flow, droplet flow, slurry flow, fluidized beds, Bubbly flow, droplet flow, slurry flow, fluidized beds,

particleparticle--laden flowladen flow

�� Volume loading Volume loading -- Dilute to denseDilute to dense

�� Particulate loading Particulate loading -- Low to highLow to high

�� Turbulence modeling Turbulence modeling -- Weak to strong coupling between phasesWeak to strong coupling between phases

�� Stokes number Stokes number -- All rangesAll ranges


•• Fluidized bedsFluidized beds

•• High particle loading flowsHigh particle loading flows

•• SlurrySlurry flowsflows

•• SedimentationSedimentation

•• HydrotransportHydrotransport

•• RisersRisers

•• Packed bed reactorsPacked bed reactors

Bubbling Fluidized Bubbling Fluidized

bedsbeds


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Summary Summary –– Eulerian modelEulerian model

�� Euler model is a powerful tool to model dispersed flowsEuler model is a powerful tool to model dispersed flows

�� Accuracy is determined by accuracy of interfacial termsAccuracy is determined by accuracy of interfacial terms

�� The interfacial terms are usually nonlinear so convergence is oThe interfacial terms are usually nonlinear so convergence is often ften

difficultdifficult

•• Try solving the case using the unsteady solverTry solving the case using the unsteady solver

•• Be careful with your choice of particle diameterBe careful with your choice of particle diameter

�� Boundary conditions Boundary conditions

•• Remember that VOF and physical velocity are Remember that VOF and physical velocity are meaninglessmeaningless. . RatherRather, ,

their roduct (superficial velocity) is related to volume flow ratheir roduct (superficial velocity) is related to volume flow rate (i.e. te (i.e.

reality).reality).

•• Backflow volume fraction of phases is Backflow volume fraction of phases is importantimportant..


The Mixture ModelThe Mixture Model


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The Mixture ModelThe Mixture Model

�� The mixture model is a The mixture model is a simplifiedsimplified Eulerian approach for modeling Eulerian approach for modeling nn--phasephase

flowsflows

�� The simplification is based on the The simplification is based on the assumptionassumption that the Stokes number is smallthat the Stokes number is small

(particle and primary fluid velocity is (particle and primary fluid velocity is nearlynearly equalequal in both magnitude andin both magnitude and

direction)direction)

�� Solves the mixture momentum equation (for massSolves the mixture momentum equation (for mass--averaged mixture velocity)averaged mixture velocity)

and prescribes relative velocities to describe the dispersed phaand prescribes relative velocities to describe the dispersed phasesses

•• InterphaseInterphase exchange terms exchange terms dependdepend on relative (slip) velocities which areon relative (slip) velocities which are

algebraicallyalgebraically determined based on the determined based on the assumptionassumption that St << 1. This that St << 1. This

meansmeans that phase that phase separationseparation cannotcannot be be modeledmodeled using the mixture using the mixture

modelmodel

•• Turbulence and Turbulence and energyenergy equations are equations are alsoalso solvedsolved for the mixture for the mixture ifif requiredrequired

�� Solves a volume fraction transport equation for each secondarySolves a volume fraction transport equation for each secondary phase.phase.

�� A submodel for cavitation is availableA submodel for cavitation is available


Applicability of Mixture modelApplicability of Mixture model


•• Gas spargingGas sparging

•• HydrocyclonesHydrocyclones

•• Bubble Bubble columncolumn reactorsreactors

•• Solid suspensionsSolid suspensions

�� Flow regime Flow regime -- Bubbly, droplet, and slurry flowsBubbly, droplet, and slurry flows

�� Volume loading Volume loading -- Dilute to moderately denseDilute to moderately dense

�� Particulate Loading Particulate Loading -- Low to moderateLow to moderate

�� Turbulence modeling Turbulence modeling -- Weak coupling between phasesWeak coupling between phases

�� Stokes Number Stokes Number -- St << 1St << 1


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Summary Summary -- Mixture modelMixture model

�� Simple approachSimple approach

�� Easy to useEasy to use

�� Applicable to many multiphase flow problemsApplicable to many multiphase flow problems

�� Consider restrictionsConsider restrictions


Discrete Phase Model (DPM)Discrete Phase Model (DPM)


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�� Trajectories of particles/droplets/Trajectories of particles/droplets/bubblesbubbles are computed in a Lagrangian are computed in a Lagrangian

frameframe•• ParticlesParticles cancan exchange heat, mass, and momentum with the continuous gas exchange heat, mass, and momentum with the continuous gas

phasephase

•• EachEach trajectory trajectory representsrepresents a a groupgroup of particles of the same initial propertiesof particles of the same initial properties

•• ParticleParticle--particleparticle interactionsinteractions are are neglectedneglected

•• TurbulentTurbulent dispersion dispersion cancan be be modeledmodeled using using eithereither stochasticstochastic tracking or a tracking or a

““particle cloudparticle cloud”” modelmodel

� Numerous sub-modeling capabilities are available:• Heating/cooling of the discrete phase

• Vaporization and boiling of liquid droplets

• Volatile evolution and char combustion for combusting particles

• Droplet breakup and coalescence using spray models

• Erosion/Accretion

Discrete Phase Model (DPM)Discrete Phase Model (DPM)


Applicability of DPMApplicability of DPM


•• Spray Spray dryersdryers

•• CyclonesCyclones

•• Particle Particle separationseparation

and and classificationclassification

•• Aerosol dispersionAerosol dispersion

•• Liquid Liquid fuelfuel

•• CoalCoal combustioncombustion

�� Flow regime Flow regime -- Bubbly flow, droplet flow, particleBubbly flow, droplet flow, particle--laden flowladen flow

�� Volume loading Volume loading -- Must be dilute (volume fraction < 12%)Must be dilute (volume fraction < 12%)

�� Particulate Loading Particulate Loading -- Low to moderateLow to moderate

�� Turbulence modeling Turbulence modeling -- Weak to strong coupling between phasesWeak to strong coupling between phases

�� Stokes Number Stokes Number -- All ranges of Stokes numberAll ranges of Stokes number


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SummarySummary

CFD Modelling of Multiphase Flow SystemsCFD Modelling of Multiphase Flow Systems

�� Choose an appropriate model for your application based on flowChoose an appropriate model for your application based on flow

regime, volume loading, particulate loading, turbulence, and regime, volume loading, particulate loading, turbulence, and Stokes Stokes

numbernumber

•• Use VOF for Use VOF for freefree surface and stratified flowssurface and stratified flows

•• Use the Eulerian Use the Eulerian granulargranular model for high particle loading flowsmodel for high particle loading flows

•• Consider the Stokes number in low to moderate particle loadingConsider the Stokes number in low to moderate particle loading flowsflows

�� For St > 1, the mixture model is not applicable. For St > 1, the mixture model is not applicable. InsteadInstead, use , use eithereither DPM or EulerianDPM or Eulerian�� For St For St ≤≤ 1, all models are applicable. Use the 1, all models are applicable. Use the leastleast CPU CPU demandingdemanding model based on model based on

other requirementsother requirements

�� Strong coupling among phase equations Strong coupling among phase equations solvesolve betterbetter with with reducedreduced

underunder--relaxation factorsrelaxation factors

�� Users should understand the limitations and applicability of eUsers should understand the limitations and applicability of each modelach model


Thank youThank you ……..


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