modeling multiphase flows with heat and mass transfer · modeling multiphase flows with heat and...
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Modeling Multiphase Flows with Heat and Mass Transfer
Presented byAndrey Troshko
Contributors:Adam Anderson
Kumar DhanasekharanPeter Spicka
Srinivasa Mohan
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Objective• There is an increasing interest across industries to
model complex multiphase flows including interphasic heat and mass transfer
• This complexity requires more realistic models of momentum, heat and mass exchange between phases
• The objective is– Provide some examples of simulated multiphase flows
highlighting new capabilities of Fluent 6.1– Gain a feedback from you on your needs and priorities in
this area
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Idea of presentation• Main challenge of multiphase flows is modeling of
interphasic terms which describe exchange of mass, momentum and heat between phases
• There are very few “universal” models for these interfacial terms so hardwiring them into standard code is not feasible so all but one examples below will use UDF
• Before examples, we provide a set of multiphase equations with interfacial terms and explain main idea behind models implemented in the examples
• We will also provide brief summary on each of presented models
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Outline• Underlying equations• Examples
– Nucleate subcooled boiling model• Example 1 Boiling flow in nuclear reactor• Example 2 Pool boiling curve benchmark• Example 3 Pool boiling in cylindrical vessel
– Coalescence and break up model• Example 4 Flow in bio reactor
– Heterogeneous reaction• Example 5 Ozone decomposition in fluidized bed
– Condensation• Example 6 Mist formation in condenser
– Gas assisted molding• Example 7 Molding flow in fridge handle
Euler
Mixture
VOF
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Outline• Equations• Examples
– Nucleate subcooled boiling model• Example 1 Boiling flow in nuclear reactor• Example 2 Pool boiling curve benchmark• Example 3 Pool boiling in cylindrical vessel
– Coalescence and break up model• Example 4 Flow in bio reactor
– Heterogeneous reaction• Example 5 Ozone decomposition in fluidized bed
– Condensation• Example 6 Mist formation in condenser
– Gas assisted molding• Example 7 Molding flow in fridge handle
Euler
Mixture
VOF
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Equations
MixtureMixtureMixturePhaseVOF
MixtureMixtureMixturePhaseMixture
PhasePhasePhasePhaseEuler
Scalar equation
Energyequations
Momentum equation
Mass equation
Model /equation
• Models and equations available in Fluent 6.1
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Equations: mass of phase q
( ) ( ) ∑=
=⋅∇+∂∂ n
ppqqqqqq mv
t 1
&rραρα
( ) ( ) vapqliqpPPbTTam satqsatppq ==−⋅+−⋅= , ,&
• Mass conservation equation
• Mass transfer source due to boiling or condensation
• Functions and describe physical state of the interface (wall, bulk boiling/condensation)
• Mass transfer source may also be caused by heterogeneous reaction
a b
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Equations: momentum of phase q
( )
( ) ( )qvmqliftqqq
n
ppqpqpq
qqqqqqqq
FFFvmR
gpvDtD
,,1
rrrr&
r
rr
+++++
+⋅∇+∇−=
∑=
ρα
ραταρα
qrrqpdpq dvvCR /75.0 rrr⋅⋅⋅⋅⋅= αρ
( )qqqpTDq kCF ρααρ /∇=r
• Momentum conservation equation
• Drag of particle with diameter dq
• Turbulent dispersion force
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Equations: energy of phase q
( ) ( )∑=
+++∇−∇+∂∂
−=n
ppqpqpqqqqqq
qqq hmQSqvtp
DthD
1: &
rrταρα
wwq qAS ′′⋅=
EQlw qqqq ′′+′′+′′=′′
• Energy conservation equation
• Source term due to the wall heat flux at wall cell
• Wall heat flux partition due to boiling
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Equations: UDSI of phase q
( ) ( ) qp
qp
qpq
qpqqq
qpqq Sv
t=∇Γ−⋅∇+
∂∂ φαφραφρα r
qpφ
• Scalar p conservation equation by phase q
• Interpretations of in different examples
– In example 4, is a fraction (weight) a bubbles with diameter transported by gas phase
– In example 5, is a mass fraction of ozone in ozone-oxygen mixture that constitutes gas phase
gasdiam
qp αφ =
gasozone
qp X=φ
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Outline• Underlying equations• Examples
– Nucleate subcooled boiling model• Example 1 Boiling flow in nuclear reactor• Example 2 Pool boiling curve benchmark• Example 3 Pool boiling in cylindrical vessel
– Coalescence and break up model• Example 4 Flow in bio reactor
– Heterogeneous reaction• Example 5 Ozone decomposition in fluidized bed
– Condensation• Example 6 Mist formation in condenser
– Gas assisted molding• Example 7 Molding flow in fridge handle
Euler
Mixture
VOF
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Nucleate boiling model• RPI (Rensselaer Polytechnic Institute) model of wall heat flux
partitioning• Implemented as a source term in energy equation for liquid phase
Tw
Tbulk
Tsat
Wall heat flux =
Single phase heat flux
+ Quenching heat flux
+ Evaporation heat flux
Wall heat flux
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Example 1 Boiling flow in nuclear reactor
• Flow in nuclear fuel assembly– Pressure 50 atm– Reliq=300,000– Heat flux 0.522
MW/m2
– Inlet subcooling 4.5 K
– y+=100
Liquid enters
Liquid vapor mixture exits
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Example 1 Boiling flow in nuclear reactor
• Additional terms are included in r.h.s. of mass, momentum, energy and turbulence equation to account for– Condensation or evaporation at surface of bubbles in free stream
(mass equation for each phase)– Turbulent dispersion of bubbles if liquid flow is turbulent
(momentum equation for each phase)– Additional turbulence created by bubbles (t. k. energy and
dissipation equation)– Modified lift force to account for vortex shedding by bubbles
(momentum equation for each phase)– Latent heat deposition (energy for liquid phase, temperature of
vapor phase is fixed to saturation)
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Example 1 Boiling flow in nuclear reactor
• Wall temperature is defined by bisection method from flux partitioning
• Turbulent dispersion force and bubble induced turbulence stabilize solution
• ~3-4 hours to get converged solution on 2GHz CPU
• 80,000 cells
Comparison with experiment for vapor void fraction
0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Axial distance, mVo
id fr
actio
n
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Example 2 Pool boiling curve benchmark
• RPI model was designed for forced convection situation• Question:
– Can this model be applied to a pool boiling where bulk liquid temperature is at or below saturation?
• Answer:– Preliminary results show that, yes, it can. Heat transfer
mechanism at the pool boiling wall is still governed by single phase heat transfer, quenching and vaporization.
– In the case of pool boiling, single phase heat transfer mechanism is determined by conduction and natural convection.
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Example 2 Pool boiling curve benchmark
• Benchmark experiment by C. Wang and V. Dhir1
• Water was boiled on different copper surfaces corresponding to different contact angles
• RPI model was used with some correlations corresponding to boiling on stainless steel surface
• Density of water varies with temperature so natural convection was accounted for
• Laminar flow was modeled qw’’
water
1 Wang C & Dhir V (1993). ASME J. of Heat Transfer. 115
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Example 2 Pool boiling curve benchmark
qw’’(t)=const
symm
pressure outletw
ater• Boiling curve comparison for water
at normal condition
symm
FLUENT
CHF & Film boiling
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Example 3 Pool boiling is cylindrical vessel
• Experiment by Aszodi1
• Radiation heat flux on side walls of the cylindrical vessel with water
• First, natural convection starts
• Later boiling starts at the side walls
• Water at saturation after boiling develops
• Flow is weakly turbulent based on Ra
0
5000
10000
15000
20000
25000
0 500 1000 1500 2000
time, sec
Heat
flux
, W/m
2
qw’’(t)water
1 Aszodi A et al. (2000). Heat and Mass Transfer, 36
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Example 3: nucleate boiling (3)• RPI model applied with
single phase heat transfer by conduction, density of water varies with temperature
• Special treatment was applied to last cell row at outlet mimicking free surface behavior
– Uliq=0, i.e., degassing free surface
– If flow is reverse, void fraction and liquid temperature are extrapolated from next cell center
qw’’(t) axis
qw’’=0
pressure outletw
atercellT =,αflow
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Example 2: nucleate boiling (4)
Vapor void fraction comparison with experiment1
Heated w
all
Heated w
all
Axis
Axis
FLUENT Experiment
1 Aszodi A et al. (2000). Heat and Mass Transfer, 36
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Example 2: nucleate boiling (5)
Liquid velocity Vapor velocity
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Example 2: nucleate boiling (6)
qw’’(t) axis
qw’’=0
pressure outletw
ater• Liquid temperature history
comparison near the wall
Boiling jump
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Nucleate boiling• Summary on RPI nucleate boiling model
– Applicable for subcooled boiling in nuclear reactors, heated tanks with liquid, electronic chip cooling by boiling
– Bulk liquid must be at or below saturation– Vapor void fraction should not exceed 90%, i.e. full CHF and free
board cannot be modeled– Model was originally developed for highly turbulent flows under
high pressure and validated for channel flows for pressure range 2.7-50 atms, inlet subcooling 4.5-60K, Re= 30,000-300,000 , stainless steel wall material
– Model was preliminary validated for pool boiling
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Outline
Euler
Mixture
VOF
• Underlying equations• Examples
– Nucleate subcooled boiling model• Example 1 Boiling flow in nuclear reactor• Example 2 Pool boiling curve benchmark• Example 3 Pool boiling in cylindrical vessel
– Coalescence and break up model• Example 4 Flow in bio reactor
– Heterogeneous reaction• Example 5 Ozone decomposition in fluidized bed
– Condensation• Example 6 Mist formation in condenser
– Gas assisted molding• Example 7 Molding flow in fridge handle
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Example 4: coalescence/breakup• This model accounts for break up and coalescence of bubbles• It assumes that break up is caused by turbulent eddies• It assumes that coalescence is caused by turbulence, buoyancy and
laminar shear• Bubble size spectrum is split into several bubble size intervals (groups).
Each group is characterized by its share (weight)• Population balance is solved for each size group represented by User
Defined Scalar (UDS) with source and sinks due to coalescence and break up
• Average bubble diameter is calculated as Sauter diameter weighted by group weight, i.e., UDS
• Average bubble diameter is used in the drag law
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Example 4: coalescence/breakup (1)• For each bubble size interval
(group) a UDS equation is solved
• Source is
0
0.05
0.1
0.15
0.2
0.25
0.3
1 2 3 4 5 6 7 8 9 10 11
Bubble diam, mm
Bubb
le s
hare
( ) ididdd
didd Su
t=⋅∇+
∂∂ φραφρα
d1φ
d2φ
diφ
eCoalescenceCoalescenc
BreakupBreakupi
DB
DBS
−+
−=
Bubble size distribution
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Example 4: coalescence/breakup (2)• Airlift reactor geometry and
experimental conditions taken from Kawase and Hashimoto (1996)1
• Full Eulerian Multi-Fluid model is used in conjunction with population balance equations
Gas bubbles
1 Kawase Y & Hashimoto N. (1996). J. Chem. Tech. Biotechnol. 65
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Example 4: coalescence/breakup (3)• Breakup and
coalescence was modeled by considering a discrete distribution of 9 bubble groups
• For comparison purposes, calculations were also performed for single size bubble (d=1mm) based on the sparger diameter
alfag = 0.1 Liquid velocity
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Example 4: coalescence/breakup (4)
Gas void Sauter diameter
Large bubbles
Small bubbles
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Example 4: coalescence/breakup (5)
0.01
0.1
0.01 0.1Superficial gas velocity, Usgr (m/s)
Ris
er g
as h
old-
up (-
-)
Kawase & Hashimoto (1996)FLUENT (Breakup & Coalescence)
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Example 4: coalescence/breakup (6)
0.01
0.1
0.01 0.1Superficial gas velocity, Usgr (m/s)
Mas
s tra
nsfe
r coe
ffici
ent,
kLa
(1/s
)
Kawase and Hashimoto (1996)FLUENT (Breakup & Coalescence)
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Example 4: coalescence/breakup (7)• Summary of coalescence/break up model
– Applicable to bubble column type problems
– Single drag law for averaged bubble size– Breakup function has adjustable constants– It was tested for bubble columns only
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Outline
Euler
Mixture
VOF
• Underlying equations• Examples
– Nucleate subcooled boiling model• Example 1 Boiling flow in nuclear reactor• Example 2 Pool boiling curve benchmark• Example 3 Pool boiling in cylindrical vessel
– Coalescence and break up model• Example 4 Flow in bio reactor
– Multiphase reaction• Example 5 Ozone decomposition in fluidized bed
– Condensation• Example 6 Mist formation in condenser
– Gas assisted molding• Example 7 Molding flow in fridge handle
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Example 5: O3 decomposition• Ozone decomposition is catalyzed by
sand impregnated with iron oxide in fluidized bed
O3 (g) → 1.5 O2 (g)
• The decomposition rate is expressed ask = 1.57 α [O3]
where α is the volume fraction of catalysts, [O3] is the mass fraction of ozone O3
O2
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Example 5: O3 decomposition (1)• Operating conditions
– The fluidized bed– Catalyst particles are of 117 µm diameter
• Physical models– Eulerian granular model– Syamlal/O’Brian drag law– Species transport in multiphase represented by UDS
(mass fraction of O2) carried by gas phase– R.H.S. of transport equation for UDS ([O2]) contains
sink/source terms due to reaction
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Example 5: O3 decomposition (2)• Solid void
fraction
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Example 5: O3 decomposition (3)• Product
(O2) mass fraction
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Example 5: O3 decomposition (4)• Gas phase
velocity
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Example 5: O3 decomposition (5)• Summary on multiphase reactions
– In Fluent 6.1, User Defined Scalars are used to represent species mass fractions and reactions rates are defined through UDF
– Fluent 6.2 will have a multiphase species capability
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Euler
Mixture
VOF
• Underlying equations• Examples
– Nucleate subcooled boiling model• Example 1 Boiling flow in nuclear reactor• Example 2 Pool boiling curve benchmark• Example 3 Pool boiling in cylindrical vessel
– Coalescence and break up model• Example 4 Flow in bio reactor
– Multiphase reaction• Example 5 Ozone decomposition in fluidized bed
– Condensation• Example 6 Mist formation in condenser
– Gas assisted molding• Example 7 Molding flow in fridge handle
Outline
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Example 6: condensation• Steam is passing through a cooling stage
in condenser and condensation mist is formed
• Cooling stage is approximated as liquid zone with sink term in mixture energy equation
• Mist droplet size is prescribed 10-5 m• Mass transfer rate = const*(P-
Psat(Tsteam)) is prescribed as source term in mass conservation equation
• Latent heat is accounted for in mixture energy equation
Steam
Steam and condensate
Cooling stage
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Example 6: condensation (1)• Grid size 9425 cells• Steady state simulation
Mist void
Mixture temperature
Mist velocity
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Example 6: condensation (2)• Summary on condensation model
– Contains adjustable parameters– Does not account for further growth of mist droplets
due to condensation– Does not account for coalescence of mist droplets on
walls and liquid film formation
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Euler
Mixture
VOF
• Underlying equations• Examples
– Nucleate subcooled boiling model• Example 1 Boiling flow in nuclear reactor• Example 2 Pool boiling curve benchmark• Example 3 Pool boiling in cylindrical vessel
– Coalescence and break up model• Example 4 Flow in bio reactor
– Multiphase reaction• Example 5 Ozone decomposition in fluidized bed
– Condensation• Example 6 Mist formation in condenser
– Gas assisted molding• Example 7 Molding flow in fridge handle
Outline
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Example 7: Gas-Assist Injection Molding (GAIM)
• GAIM -industrial process used to produce appliance handles , computer bezels, chasses, covers etc.
• injection of a second fluid into a partially filled tool cavity
• allows to hollow out thick section of a product and/or production of thin-wall product
Refrigerator handle
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• Mesh– simplified geometry– approximately 40k cells
• Boundary conditions– inlet pgauge = 20, 2 bar– outlet pgauge = 0 bar
• Material properties– Air: ideal compressible
gas– Resin: Newtonian, high
viscosity fluid, µ = 1000 Pa s 25 cm
Example 7: Gas-Assist Injection Molding (1)
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• Numerical settings– Solver: PISO scheme for pressure/velocity coupling– PRESTO! scheme for pressure term– Time step of 0.1-0.5 ms
• Recommendations– energy equation was turned off during initial 100 time
steps– viscosity of the air was artificially increased to 1 Pa s– density and momentum under relaxed by 0.5
Example 7: Gas-Assist Injection Molding (2)
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• Resin is injected into a molding form at pgauge=20 bars during 0.5 s
• After the initial 0.5 s, pressure is reduced to 2 bars and air is injected into the molding form
• Observations– resin disintegration after 1 s– negligible compressibility effects, low Mach Number– small temperature rise observed
Example 7: Gas-Assist Injection Molding (3)
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• Summary on gas-assist molding model– Applicable to 3D complex mold flows– Standard model is utilized, i.e., no UDF– Although high viscosity Newtonian mold material
was used here, non-Newtonian liquids can also be modeled
– UDF can be used to apply customized models of liquid viscosity
Example 7: Gas-Assist Injection Molding (4)
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• Multiphase flow equations were reviewed and examples of interphasic exchange models were presented
• Models of boiling, bubbles size evolution, multiphase reactions, condensation and molding flows were presented
• Areas of applicability and limitations of each model were discussed
Summary