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






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






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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• 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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• 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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• 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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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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Liquid velocity Vapor velocity

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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






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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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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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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




– Multiphase reaction• Example 5 Ozone decomposition in fluidized bed



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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







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







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


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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


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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


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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

Modeling Multiphase Flows with Heat and Mass Transfer · Modeling Multiphase Flows with Heat and...

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