© fluent inc. 9/14/20151 fluent software training trn-98-006 modeling multiphase flows
TRANSCRIPT
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Outline
Definitions; Examples of flow regimes Description of multiphase models in FLUENT 5 and FLUENT 4.5 How to choose the correct model for your application Summary and guidelines
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Definitions Multiphase 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 phases One 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
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Flow Regimes
Multiphase flow can be classified by the following regimes:
Bubbly flow: Discrete gaseous or fluid bubbles in a continuous fluid
Droplet flow: Discrete fluid droplets in a continuous gas
Particle-laden flow: Discrete solid particles in a continuous fluid
Slug flow: Large bubbles (nearly filling cross-section) in a continuous fluid
Annular flow: Continuous fluid along walls, gas in center
Stratified/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
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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 are predicted by VOF model.
turbulent or laminar, dilute or dense, bubble or particle diameter (mainly for drag considerations).
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Multiphase Models
Four models for multiphase flows currently available in structured FLUENT 4.5
Lagrangian dispersed phase model (DPM) Eulerian Eulerian model Eulerian 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
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Dispersed Phase Model Appropriate for modeling particles, droplets, or bubbles
dispersed (at low volume fraction; less than 10%) in continuous fluid phase:
Spray dryers Coal and liquid fuel combustion Some 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 loading Computes steady and unsteady (FLUENT 5) particle tracks.
Particle trajectories in a spray dryer
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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 gradients rotating reference frames temperature gradients Brownian motion (FLUENT 5) Saffman lift (FLUENT 5) user defined
Particle Trajectory Calculations
ppppp Fguuf
dt
ud //)()(drag
F
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Coupling Between Phases One-Way Coupling
Fluid phase influences particulate phase via drag and turbulence transfer. Particulate phase have no influence on the gas phase.
Two-Way Coupling Fluid 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 cooling Droplet evaporation Droplet boiling Devolatilization Surface combustion
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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
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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
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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:
drag external force laws for reacting particles and droplets customized switching between laws output for sample planes erosion/accretion rates access to particle definition at injection time scalars associated with each particle and access at each particle time step
(possible to integrate scalar variables over life of particle)
FLUENT 5
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Eulerian-Eulerian Multiphase ModelFLUENT 4.5
10s 70s 120s
waterwater
airair
Becker et al. 1992
Locally Aerated Bubble Column
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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 Boiling Separators Aeration
Inappropriate for modeling stratified or free-surface flows.
Volume fraction of water
Stream functioncontours for water
Boiling water in a container
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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
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Eulerian Multiphase Model
Can solve for multiple species and homogeneous reactions in each phase.
Heterogeneous reactions can be done through UDS.
Allows for heat and mass transfer between phases.
Turbulence models for dilute and dense phase regimes.
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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
sat
vsatvvll T
TTrm
1212 rm
r
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Eulerian Multiphase Model: Turbulence Time 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-model: Dispersed turbulence model (default) appropriate when both of these
conditions are met: Number of phases is limited to two:
Continuous (primary) phase Dispersed (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.
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Eulerian Granular Multiphase Model: FLUENT 4.5
Volume fraction of air2D fluidized bed with a central jet
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Eulerian Granular Multiphase Model: Extension of Eulerian-Eulerian model for flow of granular
particles (secondary phases) in a fluid (primary)phase Appropriate for modeling:
Fluidized beds Risers Pneumatic lines Hoppers, standpipes Particle-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
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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 applications Syamlal -good for a wide range of applications Sinclair -good for dilute and dense pneumatic
transport lines and risers
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Eulerian Granular Multiphase Model Frictional viscosity pushes the limit into the plastic regime.
Hoppers, standpipes Several choice of drag laws:
Drag laws can be modified using UDS. Heat transfer between phases is the same as in Eulerian/Eulerian multiphase 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
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Algebraic Slip Mixture ModelFLUENT 5
Courtesy of Fuller Company
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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.
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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
))((t
uuuga m
mm
drag
f
ppm
p fd
18
)( 2
dragf
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Oil-Water Separation
Fluent 5 Results with ASMM Fluent v4.5 Eulerian Multiphase
Courtesy ofArco Exploration & Production TechnologyDr. Martin de Tezanos Pinto
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Cavitation Model ( Fluent 5) Predicts cavitation inception and approximate extension of cavity bubble. Solves for the momentum equation of the mixture Solves for the continuity equation of the mixture Assumes no slip velocity between the phases Solves 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 properties Solve for change of bubble size
l
v pp
dt
dR
3
)(2
l
vvv pp
Rm
3
)(23
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Volume of Fluid Model Appropriate for flow where Immiscible
fluids have a clearly defined interface. Shape of the interface is of interest
Typical problems: Jet breakup Motion of large bubbles in a liquid Motion 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
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Volume Fraction Assumes that each control volume contains just one phase (or the
interface between phases). For volume fraction of kth fluid, three conditions are possible:
k = 0 if cell is empty (of the kth fluid)
k = 1 if cell is full (of the kth fluid)
0 < k < 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 Sk
.
Multiple interfaces can be simulated Can not resolve details of the interface smaller than the mesh size
kj
k
ikt
ux
S
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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
x
u
x
u
xx
Puu
xu
t
)()()(
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Formulations of VOF Model Time-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 conditions There 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
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Comparison of Different Front Tracking Algorithms
2nd order upwind Donor - Acceptor
Geometric reconstruction Geometric reconstruction with tri mesh
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Surface Tension
Cylinder of water (5 x 1 cm) is surrounded by air in no gravity Surface is initially perturbed so that the diameter is 5% larger on ends The disturbance at the surface grows because of surface tension
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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.
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Choosing a Multiphase Model: Fluid-Fluid Flows (1)
Bubbly flow examples: Absorbers Evaporators Scrubbers Air lift pumps
Droplet flow examples: Atomizers Gas cooling Dryers
Slug flow examples: Large bubble motion in pipes or tanks
Separated flows free surface, annular flows, stratified flows, liquid films
CavitationFlotationAerationNuclear reactors
Combustors Scrubbers Cryogenic pumping
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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.
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Choosing a Multiphase Model: Particle-Laden Flow
Examples: Cyclones Slurry transport Flotation Circulating bed reactors
Dust collectors Sedimentation Suspension Fluidized 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..
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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 0.001 Set normalizing density equal to physical density Compute a transient solution
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Solution Strategies (VOF) For explicit formulations for best and quick results:
use geometric reconstruction or donor-acceptor use 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
solver solve 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 cells PRESTO (only for quads and hexes)
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Summary Modeling 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.
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Conservation equations Conservation of mass
Conservation of momentum
Conservation of enthalpy
qqqqqqqqqqqqq FPuuut
)(
n
ppqqqqqq mu
t 1
)(1
pqpq
n
ppq umR
qqqk
q
qqqqqqqq squdt
dphuh
t
.:)()(
)(1
pqpq
n
ppq hmQ
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Constitutive Equations
Frictional Flow Particles are in enduring contact and momentum transfer is through
friction Stresses from soil mechanics, Schaeffer (1987)
Description of frictional viscosity
is the second invariant of the deviatoric stress tensor
frictskinscollss ,,, ,max
)0( su
2
, 2
sin
I
Psfricts
2I
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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
)()(, sss
ff
f
fsvmfsvm uut
uuu
t
uCK
)()(, fsffsLfsk uuuCK
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Eulerian Multiphase Model: Turbulence The transport equations for the model are of the form
Value of the parameters
k
kkkkkkk
k
tk
kkkkkkkkk
Gkkukt
)(
kkkkk
k
kk
tk
kkkkkkkkk
cGck
ut
}{)( 21
3.192.144.13.1109.0321 cccc k
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Comparison of Drag Laws
Fluid-solid drag functions
0
2
4
6
8
10
12
14
0.01 0.06 0.12 0.17 0.23 0.28 0.34 0.39 0.45 0.5 0.56
Solids volume fraction
f
Syamlal-O'Brien
Schuh et al.
Gidaspow A
Gidaspow B
Wen and Yu
Di 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'Brien
Schuh et al.
Gidaspow A
Gidaspow B
Wen and Yu
Di Felice
Relative Reynolds number 1 and 1000Particle diameter 0.001 mm
Arastoopour
Arastoopour
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Drag Force Models
Fluid-fluid drag functions
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
10 2460 4910 7360 9810 12260 14710
Re
CdSchiller and Naumann
Schuh et al.
Morsi et Alexander
1000Re44.0
1000ReRe15.0124 687.0
DC
2500Re4008.0
2500Re200Re/Re0135.0Re914.024
200Re0Re15.0124282.0
687.0
DC
(Re)are,,whereReRe 3212
321 faaa
aaaCD
Schiller and Naumann
Schuh et al.
Morsi and Alexander
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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/Eulerian model
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Heterogeneous Reactions in FLUENT4.5
Problem Description Two 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, L2 solid 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)
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Heterogeneous Reactions in FLUENT 4.5
In usrmst.F calculate the net mass transfer between phases as a result of reactions
– Reactions could be two ways Assign 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.F Adjust 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.
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Heterogeneous Reactions in FLUENT 4.5
Compile your version of the code Run Fluent and set up the case :
Enable time dependent, multiphase, temperature and species calculations. Define phases Enable mass transfer and multi-component multi-species option. Define species, homogeneous reactions within each phases Define properties Enable user defined mass transfer
GOOD LUCK!!
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Particle size
Descriptive terms Size range Example
Coarse solid 5 - 100 mm coal
Granular solid 0.3 - 5 mm sugar
Coarse powder 100-300 m salt, sand
Fine powder 10-100 m FCC catalyst
Super fine powder 1-10 m face powder
Ultra fine powder ~1 m paint pigments
Nano Particles ~1e-3 m molecules
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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 number Mass flow rates and exchange source terms for each injection are
divided equally among the multiple stochastic tracks.
iii uuu 'iu'
32' k
iu
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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.
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Stochastic vs. Cloud Tracking Stochastic 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.
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Granular Flow Regimes
Elastic Regime Plastic Regime Viscous Regime
Stagnant Slow flow Rapid flow
Stress is strain Strain rate Strain rate dependent independentdependent
Elasticity Soil mechanicsKinetic theory
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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
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Sample Planes and Particle Histograms
As 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.