CFD modelling of liquid pressurized water and phase change through leaks in micro … · 2012. 3....

64th IUVSTA Workshop

CFD modelling of liquid pressurized water and phase change through leaks in micro-cracks

Quantitative estimates - comparison with analytical solutions

A. Kumar, C. Souprayen, M. Levett FLUIDYNL. Worth, R. Pearce ITER Organization

Presenter : A. Tripathi FLUIDYN


Vapour leak in the vacuum vessel of ITER

Detection of leaks and determination of the fastest method to pinpoint the leak location

FLUIDYN mandated for 2 tasks : • Model the spatial distribution of water vapour from a leak in the

BSM according to the leak type, operational state and location• Model the liquid water behaviour flowing through a crevice

into the vacuum according to the type of crevice

Introduction (1)


Preliminary studies : • Analytical tool based on Sharipov (99) and Sharipov et al (2010)• CFD modeling of He flowing into crevice (pure gas+ heat

exchange)

CFD modeling for water leaks (with phase change)• Use of Homogeneous Equation Model (HEM)• 4 cases :

1. Isothermal fluid : all heat needed is available2. Isothermal wall boundary : maximum heat from the wall3. Adiabatic wall boundary : no heat from the wall4. Conjugated Heat Transfer (1D) in the wall : more realistic

Introduction (2)


Geometry and case definition

Length of 3 mm or 1cm depending on case H/w = 2Inlet pressure of 4.5E+05 PaOutlet pressure of 1.0E+05 PaRarefaction parameter at outlet ~80Temperature of fluid (or wall) = 420 KComputational domain : ¼ of the cross-section 16000 hexahedral elements.

Brief description of the analytical tool

Sharipov model :• Isothermal flow• Total evaporation• Laminar liquid flow• Sharp interface between liquid and steam• Whole range of rarefied gas ( slip to free molecular regime)

Methodology :• Initialization : First guess of the mass flow rate• Based on rarefied gas solution, pressure profile upstream

reconstructed up to the saturated pressure. Gaseous and liquidlengths estimated.

• Liquid mass flow rate from Poiseuille solution estimated with liquidlength.

• Convergence criteria: balance between liquid and gas flow rate.

Wat

er

Ste

am

P3P1P0 P2=Psaturation

Interface: Total phase change

Dense gas Rarefied gas


Fluidyn-MP-NSNT

Boundary Conditions: • Inlet: Liquid+ 10-8 mass fraction of gas• Outlet: Open at pressure 1bar• Structure: Adiabatic or isothermal or solution 1D conduction heat

transfer in steel

Equation for mixture EOS

Transport equation for the gas phase

Source term for evaporation

0ρtρ

U

CFD model : HEM & 1D conduction model

UUUU Spρtρ

T

p

Sptp

TlnρlnTρ

tTρCp

UqU

ρρ S

t

JU

olhi

iii

olhi

iii XRTRT

p

22

2 ,2

sat h og gash og

pcS t


Results for isothermal fluid for 3mm tube


Results for isothermal fluid for 1cm tube


Isothermal fluid case

•CFD-HEM and analytical solution are matching.•Differences may be due to:

• non-slip conditions for this case (rarefaction order of 100).• different EOS laws for both Psat(T) and viscosities(T) liq and gas.

Mass flow rate (kg/s) Distance to Psat (m)

Sharipov HEM Sharipov HEM

3mm 1.2E-08 1.13E-08 2.21E-03 1.97E-03

1cm 3.7E-09 2.55E-09 7.37E-03 5.51E-03


A Posteriori analysis of energy requirement:•Mass flow rate Qm=1.2 10-8 kg/s•Heat for evaporation Lv = 2.1 106 J/kg•Qw= 0.0256 W to be distributed on a equivalent surface (of wall)•S= 42x10-6 m x 0.003m = 0.126 10-6 m2

Average surface heat flux to be injected= 203kW/m2

Analysis with 3D CFD HEM and heat transfer in fluid andstructure•Isothermal wall boundary (maximum heat flux from wall)•Adiabatic wall boundary (no heat flux from wall)•Conjugated Heat Transfer (1D-CHT) in the wall (conduction limited heat flux from wall = most realistic)

Thermal budget

Can the Wall provide such heat flux (even worse on a sharp interface) ????


Pressure Profile

0,E+001,E+052,E+053,E+054,E+055,E+05

0,000 0,001 0,002 0,003 0,004

Distance from the inlet (m)

Pres

sure

(pa)

Vapor Mass Fraction Profile

0,00,10,20,30,40,50,60,7

0,000 0,001 0,002 0,003 0,004


Vapo

r Mas

s Fr

actio

n

Vapor Volume Fraction Profile

0,0

0,2

0,4

0,6

0,8

1,0

1,2

0,000 0,001 0,001 0,002 0,002 0,003 0,003 0,004


Vapo

r Vo

lum

e Fr

actio

n

Velocity Profile

050

100150200250

0,000 0,001 0,002 0,003 0,004


Velo

city

(m/s

)

Results for isothermal wall (1/2)

•Sharp Interface lost, pressure drop smoother, 30% mass fraction ofliquid at outlet•In relation with temperature drop (not maintained by heat flux fromwall)


Temperature Profile

406408410412414416418420422

0,000 0,001 0,002 0,003 0,004


Tem

pera

ture

(K)

Evaporation rate profile

0,0E+005,0E-131,0E-121,5E-122,0E-122,5E-123,0E-123,5E-12

0,000 0,001 0,001 0,002 0,002 0,003 0,003 0,004


Rat

e of

Ev

apor

atio

n (k

g/s)

Results for isothermal wall (2/2)


Velocity Profile

0

20

40

60

80

100

0,000 0,001 0,001 0,002 0,002 0,003 0,003 0,004Distance from the inlet (m)

Velo

city

(m/s

)

Pressure Profile

0,E+001,E+052,E+053,E+054,E+055,E+05

0,000 0,001 0,002 0,003 0,004Distance from the inlet (m)

Pres

sure

(pa)


0,000,010,020,030,040,050,060,070,08

0,000 0,001 0,001 0,002 0,002 0,003 0,003 0,004

Distance From the Inlet (m)

Vapo

r M

ass

Frac

tion


0,0

0,2

0,4

0,6

0,8

1,0

1,2

0,000 0,001 0,001 0,002 0,002 0,003 0,003 0,004


Vapo

r Vol

ume

Frac

tion

Results for adiabatic wall (1/2)

•Sharp Interface lost, pressure drop smoother, 93% mass fraction of liquidat outlet•In relation with strong temperature drop (latent heat pumping and noheat at all from the wall)


Temperature Profile

375380385390395400405410415420425

0,000 0,001 0,002 0,003 0,004


Tem

pera

ture

(K)

Evaporation Rate Profile

0,0E+005,0E-131,0E-121,5E-122,0E-122,5E-123,0E-123,5E-124,0E-124,5E-12

0,000 0,001 0,002 0,003 0,004


Rat

e of

Eva

pora

tion

(kg/

s)

Results for adiabatic wall (2/2)


Pressure Profile

0,E+00

1,E+05

2,E+05

3,E+05

4,E+05

5,E+05


Pres

sure

(pa)

Velocity Profile

020406080

100120140


Velo

city

(m/s

)


0,00

0,05

0,10

0,15

0,20

0,25


Vapo

r mas

s fra

ctio

n


0,000,100,200,300,400,500,600,700,800,901,00

0,000 0,001 0,002 0,003 0,004


Vapo

r Vo

lum

e Fr

actio

n

Results for conducting wall (1/2)

•Sharp Interface lost, pressure drop smoother, 80% mass fraction of liquidat outlet•In relation with strong temperature drop (limited heat from wallconduction)•Results at 70ms transient: wall keeps on cooling


Temperature Profile

380385390395400405410415420425

0,000 0,001 0,002 0,003 0,004


Tem

pera

ture

(K)

Wall

Fluid

Evaporation Rate Profile

0

1E-12

2E-12

3E-12

4E-12

5E-12

6E-12

0,000 0,001 0,002 0,003 0,004


Evap

orat

ion

Rat

e (k

g/s)

Results for conducting wall (2/2)


Comparison of all non-isothermal cases

Temperature Profile for different wall condition

375380385390395400405410415420425

0,000 0,001 0,002 0,003 0,004


1D Heat conductionfrom the wall

Adiabatic wall

Isothermal Wall

Vapor mass fraction profile for different wall conditions

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7


1D heat conductionthrough wallAdiabatic wall

Isothermal wall

Pressure Profiles for all cases

0,E+005,E+041,E+052,E+052,E+053,E+053,E+054,E+054,E+055,E+055,E+05

0,000 0,001 0,002 0,003 0,004


Pres

sure

(pa) Isothermal

Sharipov's Model

Isothermal wall

Adiabatic wall

Wall with 1D heatconduction model

CFD-HEM adiabatic (kg/s)

CFD-HEM 1D heat conduction (kg/s)

CFD-HEM isothermal wall (kg/s)

CFD-HEM isothermal flow (kg/s)

Sharipov’s model (kg/s)

8.0E-08 4.96E-08 1.98E-08 1.13E-08 1.2E-08


Conclusions

In similar conditions, fair agreement of CFD-HEM with Sharipov’s model.For non-isothermal flows : • mass flow rate higher than isothermal flow. • only partial evaporation

1D heat conduction between that of the isothermal wall and adiabatic case.Area of phase change ?

ITER cases

CFD modelling of liquid pressurized water and phase change through leaks in micro … · 2012. 3....

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