Hongjie Zhang

Purge gas flow impact on tritium permeation

 Integrated simulation on tritium permeation in the solid breeder unit

FNST, August 18-20, 2009

FNST 2009

Issues Tritium behavior in blanket is a complicated phenomenon which

consist of tritium generation, tritium permeation, purge gas thermo-fluid and nuclear heating

No single integrated program of theory, computer modeling to simulate tritium behavior in blanket units.

Handling of 3D complicated large scale geometry Objective

Develop a predictive capability of tritium and hydrogen permeation from breeding zones to the coolant in the helium cooled pebble-bed blanket.

Construct 3-D convection-diffusion models Integrated with thermal-fluid analysis in TBM unit

Take into account the tritium generation rate distribution and nuclear heating rate distribution.

Provide predictive capabilities, and Assist solid breeder design

Motivations and Objectives

FNST 2009

COMSOL model Set-up Convection-diffusion model with imported velocity and

temperature profiles Apply Law-boundary conditions at gas-metal interface. Works on 2-D or 3-D small scale geometry Memory issue for large-scale geometry

Sctetra model Extend CFD code for tritium permeation assessment in TBM unit Add multi-species permeation / Isotope permeation Support Law-dependent boundary condition or Rate-dependent

boundary condition at gas-metal interface Support 3-D complex geometry at large scale

Previous work and Recent advancement

Two multi-physics models based on different codes were developed

FNST 2009

Ωbreeder

Model Domain Ωstructure

Ωcoolant

Methodology Develop a 3-D multi-species convection-diffusion permeation model Integrated with

thermal-fluid analysis in porous media to account for the effects of purge stream convection and the accompanying velocity and temperature profile

Model domain: 1.the purge flow region 2.the structure3.the coolant.

•H2, T2, and HT are transported by diffusion and convection in the two fluid phase•diffusion is the only transport mechanism in the structure phase

c1t

uc1 D12c1Qc

c2

tD2

2c2

c3

t Uc3 D3

2c3

B.C.s at the gas-structure interface should ensure • The flux continuity• The concentration discontinuities

c2 SP11/2

2211 cDcD

C1

C3

Solid

c2 c2

T2

Diffusion across a film

T

T2

FNST 2009

Reflects the variations of porosity and transport in the bed near the wall regions

Governing equations

**11

121

11 Kp

t

uuuu

u

]}/)2/(exp[1{* 111*

pdywNC

*K

qTTCt

TCp

p

1

21111

111

u

To obtain the convective part of the flux, velocity distributions can be introduced by solving the N-S equation based on Brinkman model of a flow in a packed bed. Considering the wall effect, which reflects the variations of porosity and tritium transport in the bed near the wall regions, the calculation uses the following governing equations:

Momentum conservation equation

Energy conservation equation

*

]}/)2/(exp[1{* 122*

pdywNCKK

2Cp2

T2

t2

2T2

3Cp3

T3

t3Cp3UT3 3

2T3

c1t

uc1 D12c1Qc

c2

tD2

2c2

c3

t Uc3 D3

2c3

Diffusive species conservation equation

FNST 2009 Experiments: Permeation of deuterium through a palladium membrane, which was accompanied by co-permeation of hydrogen were performed.

Two cases were compared: Permeation of D2 only through Pd membrane (0.025mm, 825K, 865K) Co-permeation of H2 D2 through Pd membrane(0.025mm, 825K)

Calculated permeation flux agree well with the experimental results for both cases

Modal Validation - Co-permeation of deuterium and hydrogen

through Pd, K. Kizu, A. Pisarev, T. Tanabe, J. of Nuclear Materials, 289(2001) 291-302

1E-4 1E-3 0.01 0.1 1 101E-8

1E-7

1E-6

1E-5

1E-4

1E-3

J(D2

)/m

ol m-2

s-1

P(D2) (Pa)

Calculated 825K Measured 825K Calculated 865K Measured 865K

1E-3 0.01 0.1 11E-8

1E-7

1E-6

1E-5

1E-4

1E-3

Su

rfa

ce f

lux

/ m

ol m

-2

s-1

Effective deuterium pressure (Pa)

Calculated H2 flux

Calculated D2 flux

Calculated HD flux Measured H

2 flux

Measured D2 flux

Measured HD flux

Case 1

D2 permeation flux as a function of upstream deuterium pressure

HD H2 D2 permeation flux in co-permeation measurements as a function of effective deuterium pressure PD=P(D2)+P(HD)/2 and at a fixed value of effective H2 pressure PH=P(H2)+P(HD)/2=0.063Pa.

Case 2

H2 D2 partial pressures from

P_H2 : 0.06 ~ 0.0035

P_D2 : 0.0001 ~ 1

FNST 2009

Model Application - multi-physics simulation in a TBM unit As a part of integrated multi-physics

modeling capability, able to Evaluate temperature profile, velocity profile,

chemical composition Calculate Tritium Concentration, Tritium

permeation flux, and other parameters of interest

Handle any 3-D large scale geometry Multi-physics simulation in a TBM unit

-0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

0

1x106

2x106

3x106

4x106

5x106

6x106

7x106

8x106

He

at r

ate

dis

trib

utio

n (

W/m

3 )

Distance from FW(m)

-0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

0.0

2.0x10-6

4.0x10-6

6.0x10-6

8.0x10-6

1.0x10-5

1.2x10-5

1.4x10-5

1.6x10-5

1.8x10-5

2.0x10-5

Tri

tium

pro

duct

ion

rat

e d

istr

ibu

tion

(m

ol/m

3 s)

Distance from FW(m)

Tritium production rate distribution in the radial direction

Heating rate distribution in the radial direction

TBM unit

Purge gas inlet

Purge gas outlet

Coolant channels

FNST 2009

0.00 0.02 0.04 0.06 0.08 0.100.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

Per

me

atio

n f

lux

to c

oo

lan

t/P

rod

uct

ion

Average purge flow velocity (m/s)

Model Application - multi-physics simulation in a TBM unit

Purge gas streamline

Tritium concentration in breeder

Temperature

Low velocity field will appear in the Left-Bottom corner and Right-Top corner, which will affect tritium concentration slightly.

Tritium permeation over the production decreases quickly as the average purge gas velocity increases

Tritium concentration is impacted by production rate, Velocity and Temperature profiles

FNST 2009

Conclusion

3-D multi-species convection-diffusion permeation model Integrated with thermal-fluid analysis in porous media are assessed to provide predictive capabilities and assist solid breeder design

Benchmark cases agree well with experimental results, and more benchmark with available data can be done

As a part of integrated multi-physics modeling capability, able to Evaluate temperature profile, velocity profile, chemical composition Calculate Tritium Concentration, Tritium permeation flux, and other parameters of interest Handle 3-D large scale geometry

Simulation in a TBM unit show that parameters such as temperature distribution and purge gas flow can strongly affect tritium transport. Under reasonable purge velocity profile, increasing the inlet velocity is an effective method to reduce tritium permeation to the coolant.

FNST 2009

Thank you