application of multiphase flow modeling techniques to the...

Application of multiphase flowmodeling techniques to the

transport of submerged mineralwool fibers

Gregory Cartland-Glover and Eckhard Krepper

Institut fur Sicherheitsforschung

Soren Alt and Wolfgang Kastner

Institut fur Proßtechnik, Prozessautomatisierung und Meßtechnik

11th July 2007

Institut fur SicherheitsforschungMitglied der Leibniz-Gemeinschaft

Cartland-Glover, Alt, Kastner &Krepper

Introduction Numerical Models Results Conclusions Future Work

Debris generation and transport in BWR and PWR

I Typical particles include paint chips, metal casings, lost tools andmineral wool fibres

I Generated by LOCA steam jets destroying insulation material onlocal infrastructure

I Transported to the wetwell pool in the containment sump

I Fine particles can remain suspended for several days, whilstheavier particles descend to the base of the sump

I Water jets and recirculation pumps cause wetted fibres andagglomerated particles to be transported to strainers and pumps

I Increases in pressure drop across the strainers can exceed pumpspecifications

I Can quickly compromise the defense-in-depth concept

Cartland-Glover, Alt, Kastner &Krepper 1 / 16

I Transported to the wetwell pool in the containment sumpI Fine particles can remain suspended for several days, whilst

heavier particles descend to the base of the sumpI Water jets and recirculation pumps cause wetted fibres and

agglomerated particles to be transported to strainers and pumpsI Increases in pressure drop across the strainers can exceed pump

specificationsI Can quickly compromise the defense-in-depth concept

I Transported to the wetwell pool in the containment sump

I Fine particles can remain suspended for several days, whilstheavier particles descend to the base of the sump

heavier particles descend to the base of the sump

agglomerated particles to be transported to strainers and pumps

specifications

specificationsI Can quickly compromise the defense-in-depth concept

Project Scope

I Particle debris generation by steamblasting

I Terminal velocity and sinkingcharacteristics in a vertical column

I Sedimentation and resuspension ofsubmerged particles in a horizontal flow

I Pressure drop analysis with theaccumulation of particles infilters/strainers

I Multiphase water jet injection

I Scale-up to containment sump scale

+ typical geometries+ multiphase interactions and

phenomena+ equipment (pumps, filters, etc)

Project Scope

Study of sedimentation and resuspension of submergedparticles in a horizontal flow

I Experimental study uses

+ Laser PIV+ High-speed video+ Ultrasound velocity+ Turbidity+ Pertinent concentrations

I Numerical study can

examine

+ Whole channel+ Channel section upstream

of the impeller+ Flow disruption by baffles

I To determine the impact

of+ Local velocity field+ Local concentration

profiles+ Viscosity+ Buoyancy, drag and

turbulence dispersionforces

I Experimental study uses+ Laser PIV+ High-speed video

+ Ultrasound velocity+ Turbidity+ Pertinent concentrations

examine

I Experimental study uses+ Laser PIV+ High-speed video+ Ultrasound velocity+ Turbidity

+ Pertinent concentrations

examine

I Experimental study uses+ Laser PIV+ High-speed video+ Ultrasound velocity+ Turbidity+ Pertinent concentrations

examine

examine+ Whole channel

+ Channel section upstreamof the impeller

+ Flow disruption by baffles

examine+ Whole channel+ Channel section upstream

of the impeller

+ Flow disruption by baffles

Overview of numerical models used

I Eulerian-Eulerian multiphase flow

I SST turbulence

I Virtual particle (1)I Viscosity closure models (2) to (7)

+ Relative and mixture (2) and (3)+ Dispersed phase eddy viscosity (4)+ Continuous phase eddy viscosity (5) and (6)

I Interphase forces (7) to (12)+ Buoyancy (7)+ Drag (8)+ Turbulent Dispersion (9)

I Boundary and initial conditions+ Low velocity, sedimenting conditions+ Medium velocity, sedimenting and resuspending conditions+ High velocity, transport of solids with little sedimentation

I SST turbulence

I Virtual particle (1)

I Viscosity closure models (2) to (7)+ Relative and mixture (2) and (3)+ Dispersed phase eddy viscosity (4)+ Continuous phase eddy viscosity (5) and (6)

I SST turbulence

The virtual particle

I Particles can be

classified by

+ sphericity+ compactness+ convexity

Class Particles

I Measured distribution ofagglomerate velocities

I Mean terminal velocity of particles0.05 m s−1

I Assumed spherical agglomerate offibres

I Drag = Buoyancy

I Iteratively resolve CD

I Terminal velocity ≡ measured

mean velocities was obtained

+ dp = 5 mm

+ ρc = 997 kg m−3

+ ρf = 2800 kg m−3

+ ρp = 1030 kg m−3

I This also gives a particle share of0.018

αp =ρp − ρcρf − ρc

d = diameter; α = particle share; ρ = density; Subscripts: c = continuous; p = dispersed; f = fibre;

I Particles can be

classified by

Class Particles

I Drag = Buoyancy

+ dp = 5 mm

+ ρc = 997 kg m−3

+ ρf = 2800 kg m−3

+ ρp = 1030 kg m−3

I Particles can be

classified by

Class Particles

I Drag = Buoyancy

+ dp = 5 mm

+ ρc = 997 kg m−3

+ ρf = 2800 kg m−3

+ ρp = 1030 kg m−3

I Particles can be

classified by

Class Particles

I Drag = Buoyancy

+ dp = 5 mm

+ ρc = 997 kg m−3

+ ρf = 2800 kg m−3

+ ρp = 1030 kg m−3

I Particles can be

classified by

Class Particles

I Drag = Buoyancy

+ dp = 5 mm

+ ρc = 997 kg m−3

+ ρf = 2800 kg m−3

+ ρp = 1030 kg m−3

I Particles can be

classified by

Class Particles

I Drag = Buoyancy

+ dp = 5 mm

+ ρc = 997 kg m−3

+ ρf = 2800 kg m−3

+ ρp = 1030 kg m−3

I Particles can be

classified by

Class Particles

I Drag = Buoyancy

+ dp = 5 mm

+ ρc = 997 kg m−3

+ ρf = 2800 kg m−3

+ ρp = 1030 kg m−3

I Particles can be

classified by

Class Particles

I Drag = Buoyancy

+ dp = 5 mm

+ ρc = 997 kg m−3

+ ρf = 2800 kg m−3

+ ρp = 1030 kg m−3

Molecular Viscosities

I Mixture viscosityµcp = µcµr (2)

I Relative viscosity

µr1 = 1 +

{0 rp < 0.6

r3p104 rp ≥ 0.6

µr2 =

)−µinrpmax

µr3 = 1 + µinrp + Chydr2p (3c)

Chyd = hydrodynamic constant = 6.2; r = volume fraction; µ = dynamic viscosity; µin = intrinsic viscosity = 2.5; Subscripts: c =continuous; cp = mixture; r = relative; p = dispersed; pmax = maximum dispersed phase fraction;

Molecular Viscosities

I Mixture viscosityµcp = µcµr (2)

I Relative viscosity

µr1 = 1 +

{0 rp < 0.6

r3p104 rp ≥ 0.6

µr2 =

)−µinrpmax

µr3 = 1 + µinrp + Chydr2p (3c)

Chyd = hydrodynamic constant = 6.2; r = volume fraction; µ = dynamic viscosity; µin = intrinsic viscosity = 2.5; Subscripts: c =continuous; cp = mixture; r = relative; p = dispersed; pmax = maximum dispersed phase fraction;

Eddy Viscosities

I Dispersed phase eddy viscosity, where ν = µ/ρ

νtp =νtc

σtc(4)

I Continuous phase eddy viscosity

νtc = cµk2c

εc(5a)

νtc =c0.5µ kc

(c0.5µ ωc, 2τij tanh

(2k0.5c

cµωcy, 500νcy2ωc

)2]) (5b)

τij =1

(∂Ui

∂xj+∂Uj

Cµ = turbulence constant = 0.09; fmax = maximum function; k = turbulent kinetic energy; U = mean velocity vector component; x= position vector component; y = distance to nearest wall; ε = eddy dissipation rate; ν = kinematic viscosity; σ = turbulent Prandtl

number; τ = shear rate tensor; ω = eddy frequency; Subscripts: c = continuous; i = ith direction vector component; j = jth directionvector component; p = dispersed; t = turbulent eddy;

Eddy Viscosities

I Dispersed phase eddy viscosity, where ν = µ/ρ

νtp =νtc

σtc(4)

I Continuous phase eddy viscosity

νtc = cµk2c

εc(5a)

νtc =c0.5µ kc

(c0.5µ ωc, 2τij tanh

(2k0.5c

cµωcy, 500νcy2ωc

)2]) (5b)

τij =1

(∂Ui

∂xj+∂Uj

Cµ = turbulence constant = 0.09; fmax = maximum function; k = turbulent kinetic energy; U = mean velocity vector component; x= position vector component; y = distance to nearest wall; ε = eddy dissipation rate; ν = kinematic viscosity; σ = turbulent Prandtl

number; τ = shear rate tensor; ω = eddy frequency; Subscripts: c = continuous; i = ith direction vector component; j = jth directionvector component; p = dispersed; t = turbulent eddy;

Interphase forces

I Buoyancy force characterises the motion of the particles

SBcp = grp (ρp − ρc) (7)

I Drag Force characterises the resistance of the particles to fluidflow

MDcp = CD

cp (Up −Uc) (8)

I Turbulent dispersion force characterises the response and spreadof particles due to turbulent eddies

MTDcp = CTDC

(∇rprp−∇rcrc

CDcp = momentum exchange coefficient; CTD = turbulence dispersion coefficient; g = gravitational acceleration; M = interfacial

force; r = volume fraction; S = body or external force; U = mean velocity vector; ν = kinematic viscosity; ρ = density; σ = turbulentPrandtl number; Subscripts: c = continuous; cp = mixture; p = dispersed; t = turbulent eddy; Superscripts: B = buoyancy; D = drag;TD = turbulence dispersion

Interphase forces

MDcp = CD

cp (Up −Uc) (8)

MTDcp = CTDC

(∇rprp−∇rcrc

Interphase forces

MDcp = CD

cp (Up −Uc) (8)

MTDcp = CTDC

(∇rprp−∇rcrc

Key terms in drag and turbulent dispersion forces

I Eddy diffusivity hypothesis resolves the spread of volume fraction by velocityfluctuations

r′ku′k =

σtk∇rk (10)

I Analogous to eddy viscosity hypothesis

u′ku′k = νtk∇uk (11)

I CDcp = momentum exchange coefficient

CDcp =3

dprpρc |Up −Uc| (12a)

Rep � 124Rep

(1 + 0.15Re0.687p

)1 < Rep < 103

0.44 103 < Rep < 2 ∗ 105

Rep =dpUnp

νc(12c)

3gρp − ρcρc

CD(12d)

CD = drag coefficient; d = particle diameter; Re = Reynolds number; r = volume fraction; r′ = fluctuating volume fraction; U =

mean velocity vector; u′ = fluctuating velocity vector; ν = kinematic viscosity; ρ = density; σ = turbulent Prandtl number; Subscripts:c = continuous; cp = mixture; p = dispersed; t = turbulent eddy; T = terminal settling velocity

r′ku′k =

σtk∇rk (10)

CDcp =3

Rep � 124Rep

(1 + 0.15Re0.687p

)1 < Rep < 103

0.44 103 < Rep < 2 ∗ 105

Rep =dpUnp

νc(12c)

3gρp − ρcρc

CD(12d)

r′ku′k =

σtk∇rk (10)

CDcp =3

Rep � 124Rep

(1 + 0.15Re0.687p

)1 < Rep < 103

0.44 103 < Rep < 2 ∗ 105

Rep =dpUnp

νc(12c)

3gρp − ρcρc

CD(12d)

Effect of relative viscosity

Horizontal velocity of continuous phase

0.00 0.01 0.02 0.03 0.04 0.05

Horizontal Component of Uc (m s−1)

TDF = 0; ReA = 4 ∗ 103

0.00 0.02 0.04 0.06 0.08 0.10 0.12

TDF = 0; ReB = 2 ∗ 104

0.30 0.35 0.40 0.45 0.50 0.55 0.60

TDF = 0; ReC = 1 ∗ 105

Dispersed phase volume fraction

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

rp (-)

TDF = 0; ReA = 4 ∗ 103

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

rp (-)

TDF = 0; ReB = 2 ∗ 104

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

rp (-)

TDF = 0; ReC = 1 ∗ 105

I SST Turbulence: thick solid lines; Laminar: thin solid lines;

I Relative viscosities:

Red :µr1 = 1 +

{0 rp < 0.6

r3p104 rp ≥ 0.6

; Blue : µr2 =

(1− rp

)−µinrpmax; Black: µr3 = 1 + µinrp + Chydr

Effect of coefficient of turbulence dispersion (1)

Horizontal velocity of continuous phase

0.00 0.01 0.02 0.03 0.04 0.05

ReA = 4 ∗ 103

0.00 0.02 0.04 0.06 0.08 0.10 0.12

ReB = 2 ∗ 104

0.30 0.35 0.40 0.45 0.50 0.55 0.60

ReC = 1 ∗ 105

Dispersed phase volume fraction

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

rp (-)

ReA = 4 ∗ 103

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

rp (-)

ReB = 2 ∗ 104

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

rp (-)

ReC = 1 ∗ 105

I Coefficient of turbulent dispersion: TDF = 0: thick black solid lines; TDF = 1: thick red lines; TDF = 50: thick blue solid lines;TDF = 100: thick cyan solid lines; Laminar: thin black solid lines;

I Relative viscosity: µr2 =

(1− rp

)−µinrpmax;

Product of eddy diffusivity and volume fraction gradient

10−12 10−6 100 106 1012

)(m s−1)

ReA = 4 ∗ 103

10−12 10−6 100 106 1012

)(m s−1)

ReB = 2 ∗ 104

10−12 10−6 100 106 1012

)(m s−1)

ReC = 1 ∗ 105

Momentum exchange coefficient

10−12 10−6 100 106

CDcp (kg m−3 s−1)

ReA = 4 ∗ 103

10−12 10−6 100 106

ReB = 2 ∗ 104

10−12 10−6 100 106

ReC = 1 ∗ 105

(1− rp

)−µinrpmax;

Turbulence dispersion force

10−4 10−2 100 102 104

MTDcp (kg m−2 s−2)

ReA = 4 ∗ 103

10−4 10−2 100 102 104

ReB = 2 ∗ 104

0 20 40 60 80 100 120

ReC = 1 ∗ 105

Buoyancy force

−400 −300 −200 −100 0

SBcp (kg m−2 s−2)

ReA = 4 ∗ 103

−400 −300 −200 −100 0

ReB = 2 ∗ 104

−400 −300 −200 −100 0

ReC = 1 ∗ 105

(1− rp

)−µinrpmax;

Conclusions

I Qualitatively correct phenomena observed at different velocityconditions

I Selected relative viscosity correlations show no significant effects

I Requires a modified turbulent dispersion force to give qualitativephenomena

I Modification made through CTD

I Influence of momentum exchange on the turbulence dispersionforce is shown at higher velocities

I Influence of viscosity is strongest in the particulate layer at lowervelocities

I Direct experiments to gain further information on the transportproperties of the particles

Conclusions

Future Work

I Acquire experimental data to select and validate applied closure andinterfacial force models

I Use higher velocities to measure turbulence dispersion force

I To resolve the momentum exchange term+ Particle description+ Particle drag coefficient+ Particle contact area

I Relative viscosity has an influence at lower velocities and higher volume

fractions+ Particle shape and orientation+ Intrinsic viscosity+ Volume fraction dependency

I Modify flow by introducing baffles

I Scale-up to containment vessel size

I Increase complexity+ Particle size and shape distributions+ Agglomeration and fragmentation models+ Multiphase interactions (gas-liquid-solid) with descending hot water jets

Future Work

Acknowledgments

I Project partners:+ IPM Zittau

Thoralf Gocht, Rainer Hampel, Alexander Kratzsch, StefanRenger, Andre Seeliger and Frank Zacharias

+ FZDAlexander Grahn

I German Federal Ministry of Economy and Labor Contracts No.1501270 and 1501307

application of multiphase flow modeling techniques to the...

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