Introygffhhffduction_to_Aerodynamics1.pptx

© Fluent Inc. 12/26/25
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Fluent Software Training
TRN-99-003
Modeling Multiphase Flows

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TRN-99-003
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/domain
Volume 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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TRN-99-003
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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TRN-99-003
Dispersed Phase 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
p
p
p
p
p
F
g
u
u
f
dt
u
d



 /
/
)
(
)
(
drag











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TRN-99-003
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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TRN-99-003
 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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TRN-99-003
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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TRN-99-003
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 Model
FLUENT 4.5
10s 70s 120s
water
air
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 function
contours for water
Boiling water in a container

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TRN-99-003
 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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TRN-99-003
 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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TRN-99-003
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
sat
l
l
l
v
v
T
T
T
r
m





 
sat
v
sat
v
v
l
l
T
T
T
r
m





1
2
12 

r
m 

r

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TRN-99-003
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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TRN-99-003
Eulerian Granular Multiphase Model:
FLUENT 4.5
Volume fraction of air
2D fluidized bed with a central jet

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 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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TRN-99-003
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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TRN-99-003
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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TRN-99-003
Algebraic Slip Mixture Model
FLUENT 5
Courtesy of
Fuller Company

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TRN-99-003
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 junction
Water volume fraction
 If possible, always choose the fluid with higher density as the primary
phase.

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TRN-99-003
 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
p
rel a
u 



))
(
(
t
u
u
u
g
a m
m
m












drag
f
p
p
m
p
f
d




18
)
( 2


drag
f

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TRN-99-003
Oil-Water Separation
Fluent 5 Results with ASMM Fluent v4.5 Eulerian Multiphase
Courtesy of
Arco Exploration & Production Technology
Dr. Martin de Tezanos Pinto

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TRN-99-003
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 p
p
dt
dR

3
)
(
2 

l
v
v
v p
p
R
m



3
)
(
2
3 



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TRN-99-003
Cavitation model

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TRN-99-003
VOF Model

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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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TRN-99-003
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 Sk
.
 Multiple interfaces can be simulated
 Can not resolve details of the interface smaller than the mesh size





k
j
k
i
k
t
u
x
S
 

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TRN-99-003
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 .
j
j
i
j
j
i
i
j
j
i
i
j F
g
x
u
x
u
x
x
P
u
u
x
u
t






 
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
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







)
(
)
(
)
(

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TRN-99-003
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
Decreasing
Accuracy

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TRN-99-003
Comparison of Different Front Tracking Algorithms
2nd order upwind Donor - Acceptor
Geometric reconstruction Geometric reconstruction
with tri mesh

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TRN-99-003
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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TRN-99-003
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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TRN-99-003
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
Cavitation
Flotation
Aeration
Nuclear reactors
 Combustors
 Scrubbers
 Cryogenic pumping

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TRN-99-003
Gas-Liquid Flows (2)
Volume fraction Model Comments
Less 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 of
primary phase is much less than the density of the
secondary phase, restricts to applications with small
diameter and low volume fraction of the Seconday
phase.
For large bubbles either use Vof or modify the Drag
law. Ignores bubble coalescence or interaction.
All Values VOF Bubbles should span across several cells.Applicable
to separated flows: free surface flows, annular flows,
liquid films, stratified flows.

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TRN-99-003
Particle-Laden Flow
 Examples:
 Cyclones
 Slurry transport
 Flotation
 Circulating bed reactors
 Dust collectors
 Sedimentation
 Suspension
 Fluidized bed reactors
Volume fraction Model Comments
Less than 10% DPM
ASMM
Ignores bubble coalescence or particle-particle
interaction
Only one solid size. More efficient than DPM. For
liquid-solid applications can be used for higher
volume fraction of solids but well below packing
limit.
All values Eulerian
Granular
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














q
q
q
q
q
q
q
q
q
q
q
q
q
F
P
u
u
u
t



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






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 )
(




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

n
p
pq
q
q
q
q
q
m
u
t 1


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
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)
(
1
pq
pq
n
p
pq
u
m
R
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q
q
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k
q
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)
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(
1
pq
pq
n
p
pq
h
m
Q 




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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
 
frict
s
kin
s
coll
s
s ,
,
,
,
max 


 

)
0
( 
 s
u

2
,
2
sin
I
Ps
frict
s

 
2
I

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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






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(
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(
, s
s
s
f
f
f
f
s
vm
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u
t
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t
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C
K

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(
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(
, f
s
f
f
s
L
fs
k
u
u
u
C
K







 


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TRN-99-003
Eulerian Multiphase Model: Turbulence
 The transport equations for the model are of the form
 Value of the parameters


k
k
k
k
k
k
k
k
k
t
k
k
k
k
k
k
k
k
k
k
G
k
k
u
k
t























 )
(

k
k
k
k
k
k
k
k
t
k
k
k
k
k
k
k
k
k
k
c
G
c
k
u
t

















 













}
{
)
( 2
1

3
.
1
92
.
1
44
.
1
3
.
1
1
09
.
0
3
2
1 



 
 c
c
c
c k

48
TRN-99-003
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 1000
Particle diameter 0.001 mm
Arastoopour
Arastoopour

49
TRN-99-003
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
Cd
Schiller and Naumann
Schuh et al.
Morsi et Alexander
 







1000
Re
44
.
0
1000
Re
Re
15
.
0
1
24 687
.
0
D
C
 
 













2500
Re
4008
.
0
2500
Re
200
Re
/
Re
0135
.
0
Re
914
.
0
24
200
Re
0
Re
15
.
0
1
24
282
.
0
687
.
0
D
C
(Re)
are
,
,
where
Re
Re
3
2
1
2
3
2
1 f
a
a
a
a
a
a
CD 


Schiller and Naumann
Schuh et al.
Morsi and Alexander

50
TRN-99-003
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 Elimination
Algorithm v4.5
Implicit/Full Elimination
Algorithm v4.5
TDMA Coupled
Algorithm v4.5
TDMA Coupled
Algorithm v4.5
Multiphase Flow Solution
Algorithms
Multiphase Flow Solution
Algorithms
Only Eulerian/Eulerian
model

51
TRN-99-003
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)

52
TRN-99-003
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.

53
TRN-99-003
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!!

54
TRN-99-003
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

55
TRN-99-003
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.
i
i
i u
u
u '


i
u'
3
2
' k
i
u 



56
TRN-99-003
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.

57
TRN-99-003
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.

58
TRN-99-003
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

59
TRN-99-003
Flow regimes

60
TRN-99-003
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 T
pq pq p q
 
Boiling water in a container:
contours of water temperature

61
TRN-99-003
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.

Introygffhhffduction_to_Aerodynamics1.pptx

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