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Heat and Mass Transfer

, Volume 44, Issue 3, pp 355–366 | Cite as

Theoretical modeling and numerical simulation of the corrosion and precipitation in non-isothermal liquid lead alloy pipe/loop systems

  • Taide Tan
  • Yitung ChenEmail author
  • Huajun Chen
Original

Abstract

A theoretical kinetic model based on the boundary layer theory was developed to investigate the corrosion/precipitation in non-isothermal lead alloy pipe/loop systems. The analytical expressions of the local corrosion/precipitation rate and the bulk concentration of the corrosion products were obtained by considering a turbulent core region and a laminar sub-layer. Numerical solutions were also obtained together with considering the effect of eddy mass diffusivity in lead alloy systems.

Keywords

Corrosion Rate Corrosion Product Sherwood Number Lead Alloy Accelerator Drive System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

a0

Mean wall concentration

ak

Coefficient constant

Ai

Airy function

A1

Coefficient for solubility

Aρ

Coefficient for density of lead or lead alloy

B1

Coefficient for solubility

Bρ

Coefficient for density of lead or lead alloy

c

Concentration of corrosion product

cb

Bulk concentration of corrosion production

cl

Concentration of corrosion product in laminar sub-layer

cb0

Mean concentration in the turbulent core region

cOxy

Oxygen concentration in LBE liquid

\({\hat{c}_{l}}\)

A part of the Fourier series of c l

cs

Solubility of the corrosion product

cw

Wall concentration of the corrosion product

Dm

Molecular diffusivity

Dt

Eddy mass diffusivity

f

The Fanning friction factor

Jy

Corrosion production flux in y-direction

K

Mass transfer coefficient

L

Reference length (loop/pipe)

L0

Test leg length

\({\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{p}}\)

Effective pressure, p+ρgh

Pr

Prandtl number, Pr =  υ/α

q

Corrosion/precipitate rate at the wall

R

Radius of the pipe/loop

R'

Net rate of production/consumption of the corrosion product

Rg

Gas constant

Re

Reynolds number

Sc

Schmidt number Sc =  υ/D M

Sh

Sherwood number ShKd h /D M

Taverage

Average temperature

Tmax

Maximal temperature

Tmin

Minimal temperature

\(T_{\rm int}\)

middle temperature \({T_{\rm int} = (T_{{\max}} + T_{{\min}})/2}\)

\({\vec{u}}\)

Velocity of the melt flow

u*

The friction velocity

Vl

Velocity in boundary layer

Vb

Bulk velocity

x

Coordinate in longitude direction

x0

Beginning coordinate of the test leg

y+

Limit of laminar sub-layer

Yk

Coefficients of the Fourier series of c l

y

Coordinate in transverse direction of x

Greek symbols

δ

Thickness of laminar sub-layer

ζ

Variable for similarity solution

η

Dimensionless coordinate of transverse direction

ξ

Dimensionless coordinate of longitude direction

μ

Viscosity

ρ

Density of fluid

τw

Wall shear stress

υ

Kinematic viscosity

Γ

Gamma function

Δ

Difference

Gradient operator

∇ ·

Divergence operator

Subscript and superscript

ave

Average value

max

Maximum value

min

Minimum value

ini

Medium value

0

Beginning or initial value

oxy

Properties of oxygen

Notes

Acknowledgments

This research is supported by U.S. Department of Energy (Grant No. DE-FG04-2001AL67358).

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of NevadaLas VegasUSA

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