By S. Saeidi

Contribution from: S. Smolentsev, S. Malang

University of Los AngelesAugust, 2009

IntroductionMotivation/GoalsProblem DefinitionMathematical modelNumerical CodeTest ResultsConclusion and Future Investigation

Liquid metal, such as PbLi has so many advantages using as heat transfer fluid

Corrosion behavior of ferritic steel exposed to PbLi is not well understood

Maintaining acceptable limits for material loss is an important goal in blanket development

For ferritic steel/PbLi, corrosion is controlled by convection, diffusion and dissolution at the solid-liquid interface

Mass, heat and momentum transfer are coupledThe main purpose is to develop a numerical code

to access corrosion of ferritic steel in PbLi under either experimental or real blanket conditions

There are no commercial codes available for corrosion analysis under fusion blanket conditions

Experimental data are available on ferritic steel/PbLi corrosion, but no good interpretation exists

We need a code, which would help us to perform some initial corrosion analysis under blanket conditions

We want to help experimentalists to understand the data, and to understand the corrosion phenomenon itself

Use of code for benchmarking with more sophisticated software, which is planned to be developed in future (HIMAG)

Corrosion is a result of dissolution of wall material, which is then transported by the flow

Transport mechanism are convection and diffusionFlow is either laminar or turbulent. MHD effects should

be includedWe consider only one component (Fe) diffusing into PbLiWe also consider deposition phenomenon, which occurs in

the cold part of the loopHeat, mass and momentum transfer are coupled. The

mathematical model should include energy equation, flow equations (including MHD effects), and mass transfer equation

The boundary condition at the solid-liquid interface assumes saturation concentration at given wall temperature

Flow

Heat Transfer:

Mass Transfer:

)(111

Bj

y

Uy

yyx

P

y

UV

x

UU

t

Ut

mm

0)(1

Vyyyx

U mm

'''1

qy

Tkky

yyy

TV

x

TU

t

TC t

mmp

y

CtDDmy

ymyy

CV

x

CU

t

C 1

m=0 – plane geometrym=1 – pipe t, kt, Dt=0 – laminar t, kt, Dt>0 – turbulent Turbulence closures are used to calculate t, kt, Dt

 MHD effects are included through jxB, P/x, t, kt, Dt

 

More equationsare used to introduce MHD effects

•Saturation concentration equation expressed in mole fraction (percentage)

Borgstedt, H.U and Rohrig, H.D:1991, Journal of Nuclear Materials 181-197

Mass diffusion coefficient plotted as a function of the wall temperature

Saturation concentration Csat of iron atoms in PbLi as function of temperature

MODULE DESCRIPTION STATUS

MAIN Switches between the modules Included

INPUT Reads input data Included

VELO Calculates velocity profile Included

TEMP Solves the energy equation Included

CONC Solves the admixture transport equation Included

OUTPUT Prepares and organizes data output Included

• Velocity distribution can be calculated for both laminar and turbulent flow regimes for simple geometries (pipe, rectangular duct, parallel channel) with or without a magnetic field•Finite-difference computer code•Non-uniform meshes with clustering points near the walls•Implicit method for solving equations (Tri-diagonal solver)

Flow BC type

Nu (calc.) Nu (theory)

Plane channel, slug flow

Const. T (C)

4.94 4.94

Plane channel, parabolic velocity profile

Const. T (C)

3.77 3.77

Plane channel, parabolic velocity profile

Const. Q 4.12 4.12

Pipe, slug flow Const. T (C)

5.78 5.78

Pipe, parabolic velocity profile

Const. Q 3.66 3.66

Pipe, parabolic velocity profile

Const. Q 4.36 4.36

The comparisons have been made for a laminar flow

Plot of Nusselt number along x direction in Plane channel with parabolic velocity profile

Flow Length: 2mChannel Width: 20cmTwall= 500 CLaminar flow= U=3 cm/sCwall=0.01 Kg/m3

Concentration profileTemperature profile

Plot of Sherwood number along the X direction:

Rate of mass transfer along the X direction:

•Sh decreases along the x until the flow become fully developed

Initials steps towards a mathematical model and numerical code for modeling of corrosion/deposition processes have been performed

We will keep working on the code and use it to analyze the effect of the flow regime, MHD, flow geometry, inlet conditions, etc. on corrosion/deposition of ferritic steel in PbLi under either experimental or real blanket conditions

We will look for experimental data and run the code trying to reproduce the experimental data

In the future, the code will be used for benchmarking with more sophisticated software (HIMAG)