© Fluent Inc. 10/28/20051
Fluent Software TrainingTRN-98-006
Modeling Multiphase Flows
© Fluent Inc. 10/28/20052
Fluent Software TrainingTRN-98-006
Outline
Definitions; Examples of flow regimesDescription of multiphase models in FLUENT 5 and FLUENT 4.5How to choose the correct model for your applicationSummary and guidelines
© Fluent Inc. 10/28/20053
Fluent Software TrainingTRN-98-006
DefinitionsMultiphase flow is simultaneous flow of
Matters with different phases( i.e. gas, liquid or solid).Matters with different chemical substances but with the same phase (i.e. liquid-liquid like oil-water).
Primary and secondary phasesOne of the phases is considered continuous (primary) and others (secondary) are considered to be dispersed within the continuous phase.
A diameter has to be assigned for each secondary phase to calculate its interaction (drag) with the primary phase (except for VOF model).
Dilute phase vs. Dense phase;Refers to the volume fraction of secondary phase(s)
Volume fraction of a phase = Volume of the phase in a cell/domainVolume of the cell/domain
© Fluent Inc. 10/28/20054
Fluent Software TrainingTRN-98-006
Flow RegimesMultiphase flow can be classified by the following regimes:
Bubbly flow: Discrete gaseous or fluid bubbles in a continuous fluidDroplet flow: Discrete fluid droplets in a continuous gas Particle-laden flow: Discrete solid particles in a continuous fluidSlug flow: Large bubbles (nearly filling cross-section) in a continuous fluidAnnular flow: Continuous fluid along walls, gas in centerStratified/free-surface flow: Immiscible fluids separated by a clearly-defined interface
bubbly flow droplet flow particle-laden
flow
slug flow
annular flow free-surface flow
© Fluent Inc. 10/28/20055
Fluent Software TrainingTRN-98-006
Flow Regimes
User must know a priori what the flow field looks like:Flow regime,
bubbly flow , slug flow, etc.Model one flow regime at a time.
– Multiple flow regime can be predicted if they are predicted by one model e.g. slug flow and annular flow may coexist since both arepredicted by VOF model.
turbulent or laminar,dilute or dense,bubble or particle diameter (mainly for drag considerations).
© Fluent Inc. 10/28/20056
Fluent Software TrainingTRN-98-006
Multiphase Models
Four models for multiphase flows currently available in structured FLUENT 4.5
Lagrangian dispersed phase model (DPM)Eulerian Eulerian modelEulerian Granular model Volume of fluid (VOF) model
Unstructured FLUENT 5 Lagrangian dispersed phase model (DPM)Volume of fluid model (VOF)Algebraic Slip Mixture Model (ASMM)Cavitation Model
© Fluent Inc. 10/28/20057
Fluent Software TrainingTRN-98-006
Dispersed Phase Model
© Fluent Inc. 10/28/20058
Fluent Software TrainingTRN-98-006
Dispersed Phase ModelAppropriate for modeling particles, droplets, or bubbles dispersed (at low volume fraction; less than 10%) in continuous fluid phase:
Spray dryersCoal and liquid fuel combustionSome particle-laden flows
Computes trajectories of particle (or droplet or bubble) streams in continuous phase.Computes heat, mass, and momentum transfer between dispersed and continuous phases.Neglects particle-particle interaction.Particles loading can be as high as fluid loadingComputes steady and unsteady (FLUENT 5) particle tracks.
Particle trajectories in a spray dryer
© Fluent Inc. 10/28/20059
Fluent Software TrainingTRN-98-006
Particle trajectories computed by solving equations of motion of the particle in Lagrangian reference frame:
where represents additional forces due to:virtual mass and pressure gradientsrotating reference framestemperature gradientsBrownian motion (FLUENT 5)Saffman lift (FLUENT 5)user defined
Particle Trajectory Calculations
ppppp Fguuf
dtud
ρρρρ //)()(drag +−+−=
F
© Fluent Inc. 10/28/200510
Fluent Software TrainingTRN-98-006
Coupling Between PhasesOne-Way Coupling
Fluid phase influences particulate phase via drag and turbulence transfer.Particulate phase have no influence on the gas phase.
Two-Way CouplingFluid phase influences particulate phase via drag and turbulence transfer.Particulate phase influences fluid phase via source terms of mass, momentum, and energy.Examples include:
Inert particle heating and coolingDroplet evaporationDroplet boilingDevolatilizationSurface combustion
© Fluent Inc. 10/28/200511
Fluent Software TrainingTRN-98-006
To determine impact of dispersed phase on continuous phase flow field, coupled calculation procedure is used:
Procedure is repeated until both flow fields are unchanged.
DPM: Calculation Procedure
continuous phase flow field calculation
particle trajectory calculation
interphase heat, mass, and momentum exchange
© Fluent Inc. 10/28/200512
Fluent Software TrainingTRN-98-006
Turbulent Dispersion of Particles
Dispersion of particle due to turbulent fluctuations in the flow can be modeled using either:
Discrete Random Walk Tracking (stochastic approach)
Particle Cloud Tracking
© Fluent Inc. 10/28/200513
Fluent Software TrainingTRN-98-006
User Defined Function Access in DPM
User defined functions (UDF’s) are provided for access to the discrete phase model. Functions are provided for user defined:
dragexternal forcelaws for reacting particles and dropletscustomized switching between laws output for sample planeserosion/accretion ratesaccess to particle definition at injection timescalars associated with each particle and access at each particle time step (possible to integrate scalar variables over life of particle)
FLUENT 5
© Fluent Inc. 10/28/200514
Fluent Software TrainingTRN-98-006
Eulerian-Eulerian Multiphase ModelFLUENT 4.5
10s 70s 120s
waterwater
airair
Becker et al. 1992
Locally Aerated Bubble Column
© Fluent Inc. 10/28/200515
Fluent Software TrainingTRN-98-006
Eulerian Multiphase Model
Appropriate for modeling gas-liquid or liquid-liquid flows (droplets or bubbles of secondary phase(s) dispersed in continuous fluid phase (primary phase)) where:
Phases mix or separate Bubble/droplet volume fractions from 0 to 100%
Evaporation BoilingSeparatorsAeration
Inappropriate for modeling stratified or free-surface flows.
Volume fraction of water
Stream functioncontours for water
Boiling water in a container
© Fluent Inc. 10/28/200516
Fluent Software TrainingTRN-98-006
Eulerian Multiphase Model
Solves momentum, enthalpy, continuity, and species equations for each phase and tracks volume fractions.Uses a single pressure field for all phases.Interaction between mean flow field of phases is expressed in terms of a drag, virtual and lift forces.
Several formulations for drag is provided.Alternative drag laws can be formulated via UDS.Other forces can be applied through UDS. Gas sparger in a mixing tank:
contours of volume fraction with velocity vectors
© Fluent Inc. 10/28/200517
Fluent Software TrainingTRN-98-006
Eulerian Multiphase Model
Can solve for multiple species and homogeneous reactions in eachphase.
Heterogeneous reactions can be done through UDS.
Allows for heat and mass transfer between phases.
Turbulence models for dilute and dense phase regimes.
© Fluent Inc. 10/28/200518
Fluent Software TrainingTRN-98-006
Mass Transfer
Evaporation/Condensation. For liquid temperatures ≥ saturation temperature, evaporation rate:
For vapor temperatures ≤ saturation temperature, condensation rate:
User specifies saturation temperature and, if desired, “time relaxation parameters” rl and rv . (Wen Ho Lee (1979))
Unidirectional mass transfer, is constant
User Defined Subroutine for mass transfer
( )sat
satlllvv T
TTrm −=
ρα
( )sat
vsatvvll T
TTrm −=
ρα
1212 ραrm =
r
© Fluent Inc. 10/28/200519
Fluent Software TrainingTRN-98-006
Eulerian Multiphase Model: TurbulenceTime averaging is needed to obtain smoothed quantities from the space averaged instantaneous equations.Two methods available for modeling turbulence in multiphase flows within context of standard k-ε model:
Dispersed turbulence model (default) appropriate when both of these conditions are met:
Number of phases is limited to two: Continuous (primary) phaseDispersed (secondary) phase
Secondary phase must be dilute.Secondary turbulence model appropriate for turbulent multiphase flows involving more than two phases or a non-dilute secondary phase.
Choice of model depends on importance of secondary-phase turbulence in your application.
© Fluent Inc. 10/28/200520
Fluent Software TrainingTRN-98-006
Eulerian Granular Multiphase Model:FLUENT 4.5
Volume fraction of air2D fluidized bed with a central jet
© Fluent Inc. 10/28/200521
Fluent Software TrainingTRN-98-006
Eulerian Granular Multiphase Model:Extension of Eulerian-Eulerian model for flow of granular particles (secondary phases) in a fluid (primary)phaseAppropriate for modeling:
Fluidized bedsRisersPneumatic linesHoppers, standpipesParticle-laden flows in which:
Phases mix or separate
Granular volume fractions can vary from 0 to packing limit
Circulating fluidized bed, Tsuo and Gidaspow(1990).
Solid velocity profiles Contours of solid volume fraction
© Fluent Inc. 10/28/200522
Fluent Software TrainingTRN-98-006
Eulerian Granular Multiphase Model: Overview
The fluid phase must be assigned as the primary phase. Multiple solid phase can be used to represent size distribution.Can calculate granular temperature (solids fluctuating energy) for each solid phase.Calculates a solids pressure field for each solid phase.
All phases share fluid pressure field.Solids pressure controls the solids packing limit
Solids pressure, granular temperature conductivity, shear and bulk viscosity can be derived based on several kinetic theory formulations.
Gidaspow -good for dense fluidized bed applicationsSyamlal -good for a wide range of applicationsSinclair -good for dilute and dense pneumatic transport lines
and risers
© Fluent Inc. 10/28/200523
Fluent Software TrainingTRN-98-006
Eulerian Granular Multiphase ModelFrictional viscosity pushes the limit into the plastic regime.
Hoppers, standpipesSeveral choice of drag laws:
Drag laws can be modified using UDS.Heat transfer between phases is the same as in Eulerian/Eulerianmultiphase model.Only unidirectional mass transfer model is available.
Rate of mass transfer can be modified using UDS.Homogeneous reaction can be modeled.
Heterogeneous reaction can be modeled using UDS.
Can solve for enthalpy and multiple species for each phase.Physically based models for solid momentum and granular temperature boundary conditions at the wall.Turbulence treatment is the same as in Eulerian-Eulerian model
Sinclair model provides additional turbulence model for solid phase
© Fluent Inc. 10/28/200524
Fluent Software TrainingTRN-98-006
Algebraic Slip Mixture ModelFLUENT 5
Courtesy of Fuller Company
© Fluent Inc. 10/28/200525
Fluent Software TrainingTRN-98-006
Algebraic Slip Mixture Model
Can substitute for Eulerian/Eulerian, Eulerian/Granular and Dispersed phase models Efficiently for Two phase flow problems:
Fluid/fluid separation or mixing:Sedimentation of uniform size particles in liquid.Flow of single size particles in a Cyclone.
Applicable to relatively small particles (<50 microns) and low volume fraction (<10%) when primary phase density is much smaller than the secondary phase density.
Air-water separation in a Tee junctionWater volume fraction
If possible, always choose the fluid with higher density as the primary phase.
© Fluent Inc. 10/28/200526
Fluent Software TrainingTRN-98-006
Solves for the momentum and the continuity equations of the mixture.Solves for the transport of volume fraction of secondary phase.Uses an algebraic relation to calculate the slip velocity between phases.It can be used for steady and unsteady flow.
is the drag function
ASMM
prel au τ=
))((t
uuuga mmm ∂
∂+∇⋅−=
dragf
ppmp f
dμρρ
τ18
)( 2−=
dragf
© Fluent Inc. 10/28/200527
Fluent Software TrainingTRN-98-006
Oil-Water Separation
Fluent 5 Results with ASMM Fluent v4.5 Eulerian Multiphase
Courtesy ofArco Exploration & Production TechnologyDr. Martin de Tezanos Pinto
© Fluent Inc. 10/28/200528
Fluent Software TrainingTRN-98-006
Cavitation Model ( Fluent 5)Predicts cavitation inception and approximate extension of cavity bubble.Solves for the momentum equation of the mixtureSolves for the continuity equation of the mixtureAssumes no slip velocity between the phasesSolves for the transport of volume fraction of vapor phase.
Approximates the growth of the cavitation bubble using Rayleigh equation
Needs improvement: ability to predict collapse of cavity bubbles
Needs to solve for enthalpy equation and thermodynamic propertiesSolve for change of bubble size
l
v ppdtdR
ρ3)(2 −
=l
vvv ppR
mρ
αρ3
)(23 −=
© Fluent Inc. 10/28/200529
Fluent Software TrainingTRN-98-006
Cavitation model
© Fluent Inc. 10/28/200530
Fluent Software TrainingTRN-98-006
VOF Model
© Fluent Inc. 10/28/200531
Fluent Software TrainingTRN-98-006
Volume of Fluid ModelAppropriate for flow where Immiscible fluids have a clearly defined interface.
Shape of the interface is of interestTypical problems:
Jet breakupMotion of large bubbles in a liquidMotion of liquid after a dam break (shown at right)Steady or transient tracking of any liquid-gas interface
Inappropriate for:Flows involving small (compared to a control volume) bubbles
Bubble columns
© Fluent Inc. 10/28/200532
Fluent Software TrainingTRN-98-006
Volume FractionAssumes that each control volume contains just one phase (or theinterface between phases).
For volume fraction of kth fluid, three conditions are possible:εk = 0 if cell is empty (of the kth fluid)εk = 1 if cell is full (of the kth fluid)0 < εk < 1 if cell contains the interface between the fluids
Tracking of interface(s) between phases is accomplished by solution of a volume fraction continuity equation for each phase:
Mass transfer between phases can be modeled by using a user-defined subroutine to specify a nonzero value for Sεk .
Multiple interfaces can be simulatedCan not resolve details of the interface smaller than the mesh size
∂ε∂
∂ε∂ ε
kj
k
ikt
ux
S+ =
© Fluent Inc. 10/28/200533
Fluent Software TrainingTRN-98-006
VOF
Solves one set of momentum equations for all fluids.
Surface tension and wall adhesion modeled with an additional source term in momentum eqn.
For turbulent flows, single set of turbulence transport equations solved.
Solves for species conservation equations for primary phase .
jji
j
j
i
ijji
ij Fg
xu
xu
xxPuu
xu
t++++−=+ ρ
∂∂
∂∂
μ∂∂
∂∂ρ
∂∂ρ
∂∂ )()()(
© Fluent Inc. 10/28/200534
Fluent Software TrainingTRN-98-006
Formulations of VOF ModelTime-dependent with a explicit schemes:
geometric linear slope reconstruction (default in FLUENT 5)Donor-acceptor (default in FLUENT 4.5)
Best scheme for highly skewed hex mesh.Euler explicit
Use for highly skewed hex cells in hybrid meshes if default scheme fails.Use higher order discretization scheme for more accuracy.
Example: jet breakup
Time-dependent with implicit scheme:Used to compute steady-state solution when intermediate solution is not important.
More accurate with higher discretization scheme.Final steady-state solution is dependent on initial flow conditionsThere is not a distinct inflow boundary for each phase
Example: shape of liquid interface in centrifuge
Steady-state with implicit scheme:Used to compute steady-state solution using steady-state method.
More accurate with higher order discretization scheme.Must have distinct inflow boundary for each phase
Example: flow around ship’s hull
DecreasingAccuracy
© Fluent Inc. 10/28/200535
Fluent Software TrainingTRN-98-006
Comparison of Different Front Tracking Algorithms
2nd order upwind Donor - Acceptor
Geometric reconstruction Geometric reconstruction with tri mesh
© Fluent Inc. 10/28/200536
Fluent Software TrainingTRN-98-006
Surface Tension
Cylinder of water (5 x 1 cm) is surrounded by air in no gravitySurface is initially perturbed so that the diameter is 5% larger on endsThe disturbance at the surface grows because of surface tension
© Fluent Inc. 10/28/200537
Fluent Software TrainingTRN-98-006
Wall Adhesion Wall adhesion is modeled by specification of contact angle that fluid makes with wall.
Large contact angle (> 90°) is applied to water at bottom of container in zero-gravity field.An obtuse angle, as measured in water, will form at walls. As water tries to satisfy contact angle condition, it detaches from bottom and moves slowly upward, forming a bubble.
© Fluent Inc. 10/28/200538
Fluent Software TrainingTRN-98-006
Choosing a Multiphase Model: Fluid-Fluid Flows (1)
Bubbly flow examples: AbsorbersEvaporatorsScrubbersAir lift pumps
Droplet flow examples: AtomizersGas coolingDryers
Slug flow examples: Large bubble motion in pipes or tanks
Separated flowsfree surface, annular flows, stratified flows, liquid films
CavitationFlotationAerationNuclear reactors
CombustorsScrubbersCryogenic pumping
© Fluent Inc. 10/28/200539
Fluent Software TrainingTRN-98-006
Choosing a Multiphase Model: Gas-Liquid Flows (2)
Volume fraction Model CommentsLess than 10% DPM
Cavitation
Ignores bubble coalescence or particle-particle interaction.
Inception of cavitation and its approximate extension.All Values ASMM
Eulerian
Applies to two phase flows only. If density ofprimary phase is much less than the density of thesecondary phase, restricts to applications with smalldiameter and low volume fraction of the Secondayphase.
For large bubbles either use Vof or modify the Draglaw. Ignores bubble coalescence or interaction.
All Values VOF Bubbles should span across several cells.Applicableto separated flows: free surface flows, annular flows,liquid films, stratified flows.
© Fluent Inc. 10/28/200540
Fluent Software TrainingTRN-98-006
Choosing a Multiphase Model: Particle-Laden Flow
Examples: CyclonesSlurry transport FlotationCirculating bed reactors
Dust collectorsSedimentationSuspensionFluidized bed reactors
Volume fraction Model CommentsLess than 10% DPM
ASMM
Ignores bubble coalescence or particle-particleinteraction
Only one solid size. More efficient than DPM. Forliquid-solid applications can be used for highervolume fraction of solids but well below packinglimit.
All values EulerianGranular
Solve in a transient manner..
© Fluent Inc. 10/28/200541
Fluent Software TrainingTRN-98-006
Solution Guidelines
All multiphase calculations: Start with a single-phase calculation to establish broad flow patterns.
Eulerian multiphase calculations:Use COPY-PHASE-VELOCITIES to copy primary phase velocities to secondary phases.Patch secondary volume fraction(s) as an initial condition.For a single outflow, use OUTLET rather than PRESSURE-INLET; for multiple outflow boundaries, must use PRESSURE-INLET for each.For circulating fluidized beds, avoid symmetry planes. (They promote unphysical cluster formation.)Set the “false time step for underrelaxation” to 0.001Set normalizing density equal to physical densityCompute a transient solution
© Fluent Inc. 10/28/200542
Fluent Software TrainingTRN-98-006
Solution Strategies (VOF)For explicit formulations for best and quick results:
use geometric reconstruction or donor-acceptoruse PISO algorithm with under-relaxation factors up to 1.0
reduce time step if convergence problem arises.To ensure continuity, reduce termination criteria to 0.001 for pressure in multi-grid solversolve VOF once per time-step
For implicit formulations:always use QUICK or second order upwind difference scheme for VOF equation.may increase VOF UNDER-RELAXATION from 0.2 (default ) to 0.5.
Use proper reference density to prevent round off errors.Use proper pressure interpolation scheme for hydrostatic consideration:
Body force weighted scheme for all types of cellsPRESTO (only for quads and hexes)
© Fluent Inc. 10/28/200543
Fluent Software TrainingTRN-98-006
SummaryModeling multiphase flows is very complex, due to interdependence of many variables.Accuracy of results directly related to appropriateness of model you choose:
For most applications with low volume fraction of particles, droplets, or bubbles, use ASMM or DPM model .For particle-laden flows, Eulerian granular multiphase model is best.For separated gas-liquid flows (stratified, free-surface, etc.) VOF model is best.For general, complex gas-liquid flows involving multiple flow regimes:
Select aspect of flow that is of most interest.Choose model that is most appropriate.Accuracy of results will not be as good as for others, since selected physical model will be valid only for some flow regimes.
© Fluent Inc. 10/28/200544
Fluent Software TrainingTRN-98-006
Conservation equationsConservation of mass
Conservation of momentum
Conservation of enthalpy
++⋅∇+∇−=⊗⋅∇+∂∂
qqqqqqqqqqqqq FPuuut
ρατααραρα )(
∑=⋅∇+∂∂
=
n
ppqqqqqq mu
t 1ραρα
)(1
pqpq
n
ppq umR +∑
=
++∇−∇+−=⋅∇+∂∂
qqqkq
qqqqqqqq squdt
dphuh
t.:)()( ταραρα
)(1
pqpq
n
ppq hmQ +∑
=
© Fluent Inc. 10/28/200545
Fluent Software TrainingTRN-98-006
Constitutive Equations
Frictional FlowParticles are in enduring contact and momentum transfer is through frictionStresses from soil mechanics, Schaeffer (1987)
Description of frictional viscosity
is the second invariant of the deviatoric stress tensor
[ ]frictskinscollss ,,, ,max μμμμ +=
)0( =∇ su
2, 2
sinI
Psfricts
ϕμ =
2I
© Fluent Inc. 10/28/200546
Fluent Software TrainingTRN-98-006
Interphase Forces (cont.)Virtual Mass Effect: caused by relative acceleration between phases Drew and Lahey (1990).
Virtual mass effect is significant when the second phase density is much smaller than the primary phase density (i.e., bubble column)
Lift Force: Caused by the shearing effect of the fluid onto the particle Drew and Lahey (1990).
Lift force usually insignificant compared to drag force except when the phases separate quickly and near boundaries
⎟⎠
⎞⎜⎝
⎛∇⋅+
∂∂
−∇⋅+∂
∂= )()(, ss
sff
ffsvmfsvm uu
tuuu
tu
CK ρα
)()(, fsffsLfsk uuuCK ×∇×−= ρα
© Fluent Inc. 10/28/200547
Fluent Software TrainingTRN-98-006
Eulerian Multiphase Model: TurbulenceThe transport equations for the model are of the form
Value of the parameters
ε−k
kkkkkkkk
tk
kkkkkkkkk
Gkkukt
Π+−+∇+⋅∇=⋅∇+∂∂ ερα
σμνραρα )(
kkkkkk
kk
tk
kkkkkkkkk
cGck
ut εεε
ε
εραεεσμνεραερα Π+−+∇+⋅∇=⋅∇+
∂∂ }{)( 21
3.192.144.13.1109.0321 εεεεμ σσ cccc k
© Fluent Inc. 10/28/200548
Fluent Software TrainingTRN-98-006
Comparison of Drag Laws
Fluid-solid drag functions
0
2
4
6
8
10
12
14
0.010.060.120.170.230.280.340.390.45 0.5 0.56
Solids volume fraction
f
Syamlal-O'BrienSchuh et al.Gidaspow AGidaspow BWen and YuDi Felice
Fluid-solid drag functions
0
50
100
150
200
250
300
0.01 0.07 0.13 0.19 0.25 0.31 0.37 0.43 0.49 0.55
Solids volume fraction
f
Syamlal-O'BrienSchuh et al.Gidaspow AGidaspow BWen and YuDi Felice
Relative Reynolds number 1 and 1000Particle diameter 0.001 mm
Arastoopour
Arastoopour
© Fluent Inc. 10/28/200549
Fluent Software TrainingTRN-98-006
Drag Force ModelsFluid-fluid drag functions
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
10 2460 4910 7360 9810 1226014710Re
CdSchiller and NaumannSchuh et al.Morsi et Alexander
( )⎩⎨⎧
>≤+
=1000Re44.01000ReRe15.0124 687.0
DC
( )( )
⎪⎩
⎪⎨
⎧
>>≤+
≤<+=
2500Re4008.02500Re200Re/Re0135.0Re914.024
200Re0Re15.0124282.0
687.0
DC
(Re)are,,whereReRe 3212
321 faaaaaaCD ++=
Schiller and Naumann
Schuh et al.
Morsi and Alexander
© Fluent Inc. 10/28/200550
Fluent Software TrainingTRN-98-006
Solution Algorithms for Multiphase Flows
Coupled solver algorithms (more coupling between phases)Faster turn around and more stable numerics
High order discretization schemes for all phases.More accurate results
Implicit/Full EliminationAlgorithm v4.5
Implicit/Full EliminationAlgorithm v4.5
TDMA CoupledAlgorithm v4.5
TDMA CoupledAlgorithm v4.5
Multiphase Flow SolutionAlgorithms
Multiphase Flow SolutionAlgorithms
Only Eulerian/Eulerianmodel
© Fluent Inc. 10/28/200551
Fluent Software TrainingTRN-98-006
Heterogeneous Reactions in FLUENT4.5
Problem DescriptionTwo liquid e.g. (L1,L2) react and make solids e.g. (s1,s2)Reactions happen within liquid e.g. (L1-->L2)Reactions happen within solid e.g. (s1--->s2)
Solution!Consider a two phase liquid (primary) and solid (secondary)
liquid has two species L1, L2solid has two species s1,s2
Reactions within each phase i.e. (L1-->L2) and (s1-->s2) can be set up as usual through GUI (like in single phase)For heterogeneous reaction e.g. (L1+0.5L2-->0.2s1+s2)
© Fluent Inc. 10/28/200552
Fluent Software TrainingTRN-98-006
Heterogeneous Reactions in FLUENT 4.5
In usrmst.Fcalculate the net mass transfer between phases as a result of reactions
– Reactions could be two waysAssign this value to suterm
– If the net mass transfer is from primary to secondary the value should be negative and vica versa.
The time step and mass transfer rate should be such that the net volume fraction change would not be more than 5-10%.
In urstrm.FAdjust the mass fraction of each species by assigning a source or sink value (+/-) according to mass transfer calculated above.Adjust the enthalp of each phase by the net amount of heat of reactions and enthalpy transfer due to mass transfer. Again this will be in a form of a source term.
© Fluent Inc. 10/28/200553
Fluent Software TrainingTRN-98-006
Heterogeneous Reactions in FLUENT 4.5
Compile your version of the codeRun Fluent and set up the case :
Enable time dependent, multiphase, temperature and species calculations.Define phasesEnable mass transfer and multi-component multi-species option.Define species, homogeneous reactions within each phasesDefine propertiesEnable user defined mass transfer
GOOD LUCK!!
© Fluent Inc. 10/28/200554
Fluent Software TrainingTRN-98-006
Particle size
Descriptive terms Size range ExampleCoarse solid 5 - 100 mm coalGranular solid 0.3 - 5 mm sugarCoarse powder 100-300 μm salt, sandFine powder 10-100 μm FCC catalystSuper fine powder 1-10 μm face powderUltra fine powder ~1 μm paint pigmentsNano Particles ~1e-3 μm molecules
© Fluent Inc. 10/28/200555
Fluent Software TrainingTRN-98-006
Discrete Random Walk Tracking
Each injection is tracked repeatedly in order to generate a statistically meaningful sampling.Turbulent fluctuation in the flow field are represented by defining an instantaneous fluid velocity:
where is derived from the local turbulence parameters:
and is a normally distributed random numberMass flow rates and exchange source terms for each injection aredivided equally among the multiple stochastic tracks.
iii uuu '+=iu '
32' k
iu ς=ς
© Fluent Inc. 10/28/200556
Fluent Software TrainingTRN-98-006
Cloud Tracking
The particle cloud model uses statistical methods to trace the turbulent dispersion of particles about a mean trajectory. The mean trajectory is calculated from the ensemble average of the equations of motion for the particles represented in the cloud. The distribution of particles inside the cloud is represented by a Gaussian probability density function.
© Fluent Inc. 10/28/200557
Fluent Software TrainingTRN-98-006
Stochastic vs. Cloud TrackingStochastic tracking:
Accounts for local variations in flow properties such as temperature, velocity, and species concentrations.Requires a large number of stochastic tries in order to achieve a statistically significant sampling (function of grid density).Insufficient number of stochastic tries results in convergence problems and non-smooth particle concentrations and coupling source term distributions. Recommended for use in complex geometry
Cloud tracking:Local variations in flow properties (e.g. temperature) get averaged away inside the particle cloud.Smooth distributions of particle concentrations and coupling source terms.Each diameter size requires its own cloud trajectory calculation.
© Fluent Inc. 10/28/200558
Fluent Software TrainingTRN-98-006
Granular Flow Regimes
Elastic Regime Plastic Regime Viscous Regime
Stagnant Slow flow Rapid flow
Stress is strain Strain rate Strain rate dependent independent
dependent
Elasticity Soil mechanics Kinetic theory
© Fluent Inc. 10/28/200559
Fluent Software TrainingTRN-98-006
Flow regimes
© Fluent Inc. 10/28/200560
Fluent Software TrainingTRN-98-006
Eulerian Multiphase Model: Heat Transfer
Rate of energy transfer between phases is function of temperature difference between phases:
Hpq (= Hqp) is heat transfer coefficient between pth phase and qth phase.
Can be modified using UDS.
( )Q H T Tpq pq p q= −
Boiling water in a container: contours of water temperature
© Fluent Inc. 10/28/200561
Fluent Software TrainingTRN-98-006
Sample Planes and Particle HistogramsAs particles pass through sample planes (lines in 2-D), their properties (position, velocity, etc.) are written to files. These files can then be read into the histogram plotting tool to plot histograms of residence time and distributions of particle properties. The particle property mean and standard deviation are also reported.