Assessment of the Eulerian Two-Fluid Model for disperse ... · 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1 K e =...

UNIVERSIDA

DFED

ERAL DE MINAS GERAIS

DEPARTAM

ENTO DE ENGENHARIANUCLE

AR

Nuclear New Horizons: Fueling or FutureOctober 21-25, 2019 - Santos, SP, Brazil

Assessment of the Eulerian Two-Fluid Model fordisperse and sharp interface flow simulation with

application in steam generators

Godino Darioa, Santiago F. Corzoa, Norberto M. Nigroa, Damian E.Ramajoa

a Research Center for Computational MethodsCIMEC-UNL/CONICET, Santa Fé, Argentina

23-10-2019

INAC 2019 - R10-010 Eulerian model - Steam generators 23-10-2019 1 / 22

Motivation Motivation

Motivation

In the nuclear industry the multiphase flows play a preponderant role. To understandthese flows is of great importance for the design, and particularly to ensure the safe

operation of the plants

Primary side

Feedercoolant

Pressurizer

Pump

Secondary side

Steam generator (sec. side)

Primary sideSteam line

CollectorTurbine

Pressurizer

Pump

The computational simulation has been mostly from system codes, which are widely used forthe design and verification of nuclear power plants due to their ability to solve the overallthermal-hydraulics, neutronic and plant control in a simplified way.


Motivation General objective

Motivation and general objective

MOTIVATION

CFD models can be used in scale steam generators simulation, but not in real-scaleinstallations.

Flujo ensecador de vapor

Flujo enseparador ciclonico

Flujo en orificio by-pass

Flujo enbafflesoporte

Flujo enhaz detubos

0 00

To improve thetwo-phase flow

simulation, somebenchmark tests

must be performed

Corzo,Godino,Nigro,Ramajo, Thermal hydraulics simulation of the RD-14M steam generator facility, Annals of Nuclear Energy, 2017

Godino,Corzo,Nigro,Ramajo, CFD simulation of the pre-heater of a nuclear facility steam generator using a thermal coupled model, Nuclear

Engineering and Design, 2018


Motivation Objective

Objectives of the present work

Interfacial momentum exchange

Evaluate the effect of drag, lift, walllubrication, turbulent dispersion and virtualmass forces on the different regime flows tofind a unique set of models able for the all ofthem.

Turbulence

Assess the more widely used turbulencemodels for industrial (real-scale) applications.

Blending

Evaluate the use of blending strategy forrepresenting the rheology changes.

Precalentador

BafflesSoporte

Tubosen U

SeparadorCiclónico

Secador

Downcomer

Agua de alimentación

Raiser

Salidade Vapor

Gotas finas de líquido en vapor

Gotas de líquido en vapor

Líquido con burbujas de vapor

Mezcla de vapor y líquido


Motivation Objective

Governing equations

Continuity equation for α (ϕ1 : Continuous phase, ϕ2:Disperse phase):

∂(αϕρϕ)

∂t+∇ · (αϕρϕUϕ) = Γϕ

Conservation momentum equation:∂(αϕρϕUϕ)

∂t+∇·(αϕρϕUϕUϕ) = −∇·(αϕ(τϕ+Rϕ))

−αϕ∇p + αϕρϕg + Mϕ + (Γ2,1Uϕ − Γ1,2Uϕ)

Disperse flowFlow analysis

Volume averaging

Modelabstraction

Energy conservation equation (in terms of total energy)

∂[αϕρϕ(hϕ + 12 UϕUϕ)]

∂t+∇ · [αϕρϕUϕ(hϕ +

12

UϕUϕ)]− αϕ

(∂p∂t

+ Uϕ · ∇p)

=

−∇ · (αϕqϕ) + αϕ∇ · (Uϕτϕ) + (Γϕ,ϕ′hϕ − Γϕ′,ϕhϕ) + αϕUϕMϕ

In the momentum equations the coupling between the two phases is through the interfacialforce terms Mϕ and the moment exchanged during the mass transfer (evaporation).


Motivation Blending

Blending methodology

Blending methodology is used to locally and run-time switch between three flow regime:

1-Bubbly flow (αs < 0,3): Steam bubblesmoves in a slow liquid continuous flow (riser).Due to the lower bubble density, the higherbubble deformation, and the higher liquidviscosity, the drag, lift, wall lubrication,turbulent dispersion and virtual mass forces arereally significant.

2-Segregated flow (0,3 < αs < 0,7): Is atransition regime.

ffs = f1d - f2d

αG

f2d= 1- f1d

f1d

1

0.0

0.2

0.4

0.6

0.8

0.2 0.4 0.6 0.8 1

Keff = K1d.f1d + K2d.f2d + Ksf.fsf

K1d.f1d

1-Bubbly flow 3-Drop flow2-Segregated flow

K2d.f2dKeff

f

3-Drop flow (αs > 0,7): Liquid drops are dragged by a fast steam flow (separators and dryers).Due to the larger liquid density and the lower steam viscosity, the lift, wall lubrication,turbulent dispersion and virtual mass forces of minor impact. Drag and inertial forces compete.


Motivation Blending

Blending

Blending

Fluid: water and air

Bubble/drop size: 3 mm

Air inlet velocity: 0.4 m/s

Interfacial models: Drag(Grace/Tomiyama/Marschall),lift(Tomiyama),WLF(Frank),TDF (Burn),VMF (Constant)

Air/liquid vertical column

Video blending


./Video/blending.avi

Motivation Blending

Interfacial moment exchange

Interfacial forces:

M1,2 = −M2,1 = MD+ML+MWL+MVM +MTD

1 Drag force

FD = −34

CDα2ρ1

d2|UR|UR

2 Lift forceFL = CLα2ρ1UR ×∇× UR

3 Wall lubrication forceFWL = −CWLα2ρ1|UR|2n

4 Turbulent dispersion forceFTD = −CTDρ1k1∇α2

5 Virtual mass force

FVM = CVMα2ρ1

(DU2

dt− DU1

dt

)

Bubble concentration

Drag force

Liftforce

Turbulentdispersionforce

Rotation

Bubbles

Walllubricationforce

Liquid

VirtualMassforce

Relativeacceleration

UR

UR

UR

Drag models:Grace for bubbles in waterTomiyama for drops in airMarschall for continuous-continuousfluid


Motivation Blending


Interfacial forces:


1 Drag force

FD = −34

CDα2ρ1

d2|UR|UR





FVM = CVMα2ρ1

(DU2

dt− DU1

dt

)


Drag force

Liftforce


Rotation

Bubbles


Liquid

VirtualMassforce


UR

UR

UR

Lift models: Constant, Moraga,Tomiyama


Motivation Blending


Interfacial forces:


1 Drag force

FD = −34

CDα2ρ1

d2|UR|UR





FVM = CVMα2ρ1

(DU2

dt− DU1

dt

)


Drag force

Liftforce


Rotation

Bubbles


Liquid

VirtualMassforce


UR

UR

UR

Wall lubrication models: Antal, Frank


Motivation Blending


Interfacial forces:


1 Drag force

FD = −34

CDα2ρ1

d2|UR|UR





FVM = CVMα2ρ1

(DU2

dt− DU1

dt

)


Drag force

Liftforce


Rotation

Bubbles


Liquid

VirtualMassforce


UR

UR

UR

Turbulent dispersion models: Lopez deBertodano, Gosman, Burn


Motivation Blending


Interfacial forces:


1 Drag force

FD = −34

CDα2ρ1

d2|UR|UR





FVM = CVMα2ρ1

(DU2

dt− DU1

dt

)


Drag force

Liftforce


Rotation

Bubbles


Liquid

VirtualMassforce


UR

UR

UR

Virtual mass models: Constant, Lamb


Motivation Multiphase benchmarks

Multiphase benchmarks

Four two-phase benchmarks were considered:

Case 1. Bubble plume: Ascending bubble plume in a vertical rectangularcolumn of water

Case 2. TOPFlOW: Gas-Liquid Flow around an Obstacle in a Vertical Pipe (TOPFLOWexperiments)

Case 3. Horizontal gas/liquid flow: Counter-current flow of water and air(HAWAC experiments)

Case 4. Horizontal fluid/fluid flow: Co-current flow


Results Multiphase benchmarks

Case 1. Bubble plume

Case 1. Bubble plumeThe test was carried out and simulatedby Krepper et al. in 2007[1].Air is injected from a sparger at thebottom side of a rectangular watercolumn of 100 mm wide, 20 mm depthand 1448 mm height.Small bubbles (1 mm < φb < 5 mm)ascend swelling the column.The void fraction distribution and theaverage void fraction for several gasvelocities are measured.In this test the effect of all theinterfacial forces becomes significant.

20 [mm]

100 [mm]

824

[mm

]52

4 [m

m]

Detail A

20 [mm]

20 [mm]

Detail A

[1] Krepper, Vanga, Zaruba, Prasser, and Lopez de Bertodano. Experimental and numerical studies of void fraction distribution in rectangularbubble columns. Nuclear eng. and design, 237(4), 2007.



Case 1. Bubble plume

Mesh convergence (Vg = 10 mm/s)

Krepper (2006)ExperimentalCFD - Mesh 1CFD - Mesh 2CFD - Mesh 3

0.10

0.08

0.06

0.04

0.02

0.00 0.02 0.06 0.10Position in x[m]

Position in x[m]

0.08

0.06

0.04

0.02

0.000.02 0.06 0.10

Gas

Vol

ume

fract

ion

[-]G

as V

olum

e fra

ctio

n [-]

Turbulence modeling (Vg = 6, 10 mm/s)

Turbulence model -κ-εTurbulence model κ-ωSSTTurbulence model: κ-ωSato

ExperimentalKrepper (2006)

0.00 0.02 0.06 0.10Position in x[m]

Gas

Vol

ume

fract

ion

[-]

0.00 0.02 0.06 0.10Position in x[m]

0.08

0.06

0.04

0.02

0.08

0.06

0.04

0.02

Vg = 10 [mm/s] Vg = 10 [mm/s]

Vg = 6 [mm/s] Vg = 6 [mm/s]

0.06 0.10Position in x[m]

0.00 0.02 0.06 0.10Position in x[m]

0.00 0.02

Gas

Vol

ume

fract

ion

[-]

0.01

0.02

0.03

0.04

0.05

0.01

0.03

0.04

0.06



Case 1. Bubble plume (Cont.)

Swelling effect

Aver

aged

void

frac

tion

[-]

0.01

0.02

0.03

0.04

0.05

4.0 6.0 8.0 10.0 12.0Vg [mm/s]

Turbulence model -κ-εTurbulence model κ-ωSSTTurbulence model: κ-ωSato

Krepper (2006)

Kreeper[1] overestimated the averagedvoid fraction. The error increased

with Vg up to 26 %.κ− ω SST model showed the best

agreement.

Void fraction and velocity patterns

Vg: 10 [mm/s] Vg: 6 [mm/s]

0.150.110.00 0.037 0.075Fracción de α



Case 2. Flow around an obstacle

Case 2. TOPFlOW:The test was carried out and simulated byPrasser et al. in 2008[2].Air is injected from a perforated injectortubes introducing small bubbles (2 mm < φb

< 12 mm) at the bottom side of a circularwater column of 195 mm of diameter and 9m of height.A constant water flow is circulated and theair-water mixture pass through an obstacle.The void fraction and the phases velocitiespatterns for several gas/liquid velocities aremeasured downstream of the obstacle.Air accumulation over the obstacle ismeasured.

Baffle

Inletair/steam

Inletwater

[2] Prasser, Beyer, Frank, Al Issa, Carl, Pietruske, and Schütz. Gas–liquid flow around an obstacle in a vertical pipe. Nuclear eng. anddesign, 238(7), 2008.



Case 2. Flow around an obstacle

Void fraction - Water Velocity

0.110.080.00 0.04 0.060.02

ExperimentFrank (2007)

CFD Frank (2007)

OpenFOAM

Void fraction


CFD Frank (2007)OpenFOAM

21.60.0 0.8 1.20.4

Water velocitya) b)

Void fraction

Z=+160 [mm]


CFD - Frank (2007)OpenFOAM

Z=+80 [mm]

Experiment - Frank (2007) CFD - Frank (2007)OpenFOAM

Void fraction0.25

1.250.001.875

0.6250.100.050.00

0.0750.025

Void fraction

Comparison between Experiments, OpenFOAM and Prasser[2].



Case 2. Flow around an obstacle (Cont)

Normalized void fraction and axial water velocity axial in symmetry planes. Upstream ofthe obstacle (z = -20 and -520 mm)

-20 [mm] -20 [mm]

-100 -50 0 50 100x [mm] x [mm]

-100 -50 0 50 100

2.4

2.0

1.6

1.2

0.8

0.4

0.0

Norm

alize

d vo

id fr

actio

n [-]

Abso

lute

velo

city

of w

ater

[m/s] 2.0

1.6

1.2

0.8

0.4

0.0

OpenFoam CFDCFF - Frank (2007)Experiment - Frank (2007)

2.4

2.0

1.6

1.2

0.8

0.4

0.0-100 -50 0 50 100

Norm

alize

d vo

id fr

actio

n [-]

x [mm] x [mm]-100 -50 0 50 100

Abso

lute

velo

city

of w

ater

[m/s]

1.5

1.2

0.9

0.6

0.4

0.0

-520 [mm]OpenFoam CFDCFF - Frank (2007)Experiment - Frank (2007)

-520 [mm]

Comparison between Experiments, OpenFOAM and Prasser[2].INAC 2019 - R10-010 Eulerian model - Steam generators 23-10-2019 15 / 22


Case 2. Flow around an obstacle (Cont)

Normalized void fraction and axial water velocity axial in symmetry planes.Downstreamof the obstacle (z = 80 and 20 mm)

80 [mm] 80 [mm]

-100 -50 0 50 100x [mm] x [mm]

-100 -50 0 50 100

Abso

lute

velo

city

of w

ater

[m/s] 2.4

2.0

1.6

1.2

0.8

0.4

0.0

3.6

3.0

2.4

1.8

1.2

0.6

0.0

OpenFoam CFDCFF - Frank (2007)Experiment - Frank (2007)

Norm

alize

d vo

id fr

actio

n [-]

20 [mm] 20 [mm]

-100 -50 0 50 100x [mm] x [mm]

-100 -50 0 50 100

2.4

2.0

1.6

1.2

0.8

0.4

0.0

Norm

alize

d vo

id fr

actio

n [-]

2.4

2.0

1.6

1.2

0.8

0.4

0.0Abso

lute

velo

city

of w

ater

[m/s]OpenFoam CFD

CFF - Frank (2007)Experiment - Frank (2007)

Comparison between Experiments, OpenFOAM and Prasser[2].INAC 2019 - R10-010 Eulerian model - Steam generators 23-10-2019 16 / 22


Case 3. Counter-current flow

Case 3. Horizontalcounter-current gas/liquid flow:The test was performed byStäbler[3], and numericallyreproduced by Wintterle et al.[4],Porombka and Höhne [5]. Thisconsists on a rectangular channelof 583 mm in wide, 110 mm indepth, and 138 mm in height. Thewater enters at 0.7 m/s from the leftside through a 9 mm height sectionwhereas the air flows at 4.44 m/s incounter-current direction.

Inlet water

Inletair

Outletair Outlet

water

yx

z

Depth=110 [mm]

pa

ULin

y0

90 [m

m]

95 [mm]

235 [mm]

UGin

pa

paMP1

MP2

380 [mm]

90 -y0

300 [mm]

dp

[3] Stäbler. Experimentelle untersuchung und physikalische beschreibung der schichtenströmung in horizontalen kanälen. 2007.[4] Wintterle, Laurien, Stäbler, Meyer, and Schulenberg. Experimental and numerical investigation of counter-current stratified flows inhorizontal channels. Nuclear eng. and design, 238, 2008.[5] Porombka and Höhne. Drag and turbulence modelling for free surface flows within the two-fluid euler–euler framework. ChemicalEngineering Science, 134, 2015.



Case 3. Counter-current flow

Air velocity - Water velocity

Höhne - with dampeningHöhne - without dampeningCFD Mesh 3

ExperimentCFD Mesh 1

MP1 MP2Air velocity [m/s]

6.304.750.00 1.60 3.15

0.09

0.07

0.05

0.03

0.01

y [m

]

0.09

0.07

0.05

0.03

0.01

Velocity [m/s]-8 -6 -4 -2 -7 -5

Velocity [m/s]-3 -1

0.012

0.008

0.004

0.00

0.012

0.008

0.004

0.00

Void fraction along two verticallines located at the MP1 and

MP2 axial positions

MP2 - Mesh 3MP2 - Mesh 1MP1 - Mesh 3

MP1 - Mesh 1

MP1 - ExperimentMP2 - Experiment

0.008

0.010

0.012

0.014

y [m

]

Void fraction [-]0 0.2 0.4 0.6 0.8 1

Comparison between OpenFOAM, experiments [3] and simulations [4,5].



Case 4. Co-current flow

Case 4. Horizontal co-currentflow liquid/liquid: The testconsists of a 2D rectangularchannel of 40 mm in wide and 20mm in height, where two misciblefluids with the same density of 1kg/m (non-buoyant) and viscositiesof 1,85 × 10−5 Pa.s and 5 × 10−5

flows co-current driven by aimposed pressure difference of 2.1mPa. This is an academic test withanalytic and numeric solutionsproposed by Marschall[6].

L

dH

xy

fluid 1

fluid 2

[6] Marschall. H. Marschall. Towards the numerical simulation of multi-scale two-phase flows. PhD thesis, Technische Universität München,2011.



Case 4. Co-current flow

Fluid velocities

A very good agreementwas found. Only drag issignificant for this test.

The segregated model isthe only one able to

correctly capture theinterfacial efforts

Comparison between OpenFOAM and analytic results [6].



Conclusions

1- The two-fluid model was assessed against four benchmarksrepresenting flow regime commonly found in steam generators and manyindustrial processes.

2- The four cases were solved with the same computational model andcompared with experimental and analytic results founding goodagreement for all cases.

3- The linear blending model was suitable for switching betweendisperse and segregated flow

4- The segregated model proposed by Marschall for simple co-currentflows was also suitable for capturing the interfacial drag in morecomplex counter-current flows.

5- The κ - ω SST model showed to be a little better than the k-epsilonrealizable and the κ− ω-Sato models.



Thank you for your attention!

The authors would like to thank:

Universidad Nacional del Litoral (CAI+D 2016 PIC50420150100067LI).

Agencia Nacional de Promoción Científica y Tecnológica (PICT2016-2908)

Consejo Nacional de Investigaciones Científicas y TecnológicasCONICET.


Assessment of the Eulerian Two-Fluid Model for disperse ... · 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1 K e =...

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