ARIES Meeting, UCSD (March 2004)

Preliminary Assessment of Porous Gas-Cooled and Thin-Liquid-Protected DivertorsS. I. Abdel-Khalik, S. Shin, and M. Yoda

ARIES Meeting, UCSD (March 2004)

G. W. Woodruff School ofMechanical Engineering

Atlanta, GA 30332–0405 USA

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Outline

•Porous Gas Cooled Divertors

•Thin-Liquid-Protected Divertors

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•Compare predictions of the MERLOT code against FLUENT (6.1.22) predictions Assess impact of using the incompressible fluid

continuity equation on MERLOT’s Predictions

Porous Gas Cooled DivertorsObjective

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Porous Gas Cooled Divertors Test Problem Definition

• FLUENT has been used to solve the conservation equations (mass, momentum, and energy)

• Assumptions Laminar flow Isotropic porosity Either incompressible or

compressible flow Local thermodynamic equilibrium

between the gas and solid matrix Two-dimensional (r, )

• 60754 grid for r and directional resolution

surface heat flux

flow inlet to porous channel

flow outlet from porous channel

rori r

ro=12 mm, ri=9 mm

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Porous Gas Cooled Divertors Effective Heat Transfer Coeffcient

Eff

ecti

ve h

eat t

rans

fer

coef

fici

ent [

W/m

2K

]

[radian]

Tin=823K, Tout=1423K

Heat input : Q=30 MW/m2,

Porous medium characteristic dimension : dp=0.1 mm,

Porosity : =0.8

Coolant: Helium at 823K & 4.0 MPa

cpg=5191 J/kg K, kg=0.3 W/m K,

g=3.9610-5 kg/m s,

g=2.327 kg/m3 (for incompressible)

Solid Structure :

ks=100W/m K,

s=19300 kg/m3, cps=132 J/kg K

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Tem

pera

ture

[K

]

[radian]

helium gas bulk temperature

wall temperature

Incompressible

Compressible

Porous Gas Cooled Divertors Temperature Distribution

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Pre

ssur

e dr

op [

MP

a]

Velocity [m/s]

Pre

ssur

e dr

op [

MP

a]

Velocity [m/s]

p

og

p

og

d

V

d

V

ds

dP2

323

2 )1(75.1

)1(150

Ergun equation

Pressure drop P =

0rd

ds

dP

Tin=823K, Q=5 MW/m2, dp=0.1 mm

Porosity : =0.5 Porosity : =0.8

Porous Gas Cooled Divertors Pressure Drop

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Porous Gas-Cooled DivertorsPreliminary Conclusions

• Heat transfer coefficients predicted by MERLOT and FLUENT appear to be consistent

• Pressure drop predicted by MERLOT is significantly lower than that predicted by FLUENT for either compressible or incompressible assumption

• Acceleration pressure drop due to gas compressibility effects can not be ignored

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• This work is aimed at establishing limits for the maximum allowable temperature gradients (i.e. heat flux gradients) to prevent film rupture due to thermocapillary effects

Thin-Liquid-Protected DivertorsObjective

A maximum allowable surface temperature has been established to limit liquid evaporation and plasma contamination (~380 oC for Li)

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)

2-(

2cos)( l

lsms

xx

xTTxT

Thin-Liquid-Protected Divertors Problem Definition

Non-uniform wall temperature

Wall

Thin Film

ho initial film thickness

xl

yl

• Initially, quiescent liquid and gas (u=0, v=0, T=Tm at t=0)

Liquid (Lithium)

Gas (Air)periodic B.C. in x direction

open B.C. at top, 0

y

T

y

v

y

u

x

y

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• Evolution of the free surface is modeled using the Level Contour Reconstruction Method

• Two Grid Structures Volume - entire computational domain

(both phases) discretized by a standard, uniform, stationary, finite difference grid.

Phase Interface - discretized by Lagrangian points or elements whose motions are explicitly tracked.

Phase 2

Phase 1

F

Thin-Liquid-Protected Divertors Numerical Method

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A single field formulation

Constant but unequal material properties

Surface tension included as local surface delta function sources

0 u

)(

T )dδ()(t

f sσκμρPt

ρ xxnuuguuu

TkcTt

cTρ

)()(

u• Energy

• Momentum

• Conservation of Mass

Thin-Liquid-Protected Divertors Governing Equations

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)(d)(

d AABB

B

As

e ss

sF ttt

n

Force on a line element

NUMERICAL METHOD

tnttt

ssss

)(

thermocapillary force

normal surface tension force

o=6.6210-2 N/m

o=1.7410-4 N/moC

Tm=573 K

)( moo TT

Thin-Liquid-Protected Divertors Variable Surface Tension Source Term

Variable surface tension :

BtBAtA

n

n : unit vector in normal direction

t : unit vecotr in tangential direction

: curvature

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),()(),( tIt GLG xx

),()(),( tIt GLG xx

• Material property field (Liquid=>Lithium, Gas=>Air*)

),()(),( tIccctcc GLG xx

),()(),( tIkkktkk GLG xx

(L=504.8 kg/m3, G=1.046 kg/m3)

(L=4.5110-4 kg/ms, G=2.010-5 kg/ms)

(cL=4287 J/kgoC, cG=1008 J/kgoC)

(kL=46.6 W/moC, kG=0.029 W/moC)

Thin-Liquid-Protected Divertors Material Properties

* Effect of Liquid/Gas density ratio becomes insignificant for values 100

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• Two-dimensional simulation with 0.01[m]0.001[m] box size and 25050 resolution

• ho=0.2 mm, Ts=10 K

Thin-Liquid-Protected Divertors Steady State Results, very thin films

x [m]

y [m

]

time [sec]

y [m

]

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• Two-dimensional simulation with 0.01[m]0.001[m] box size and 25050 resolution

• ho=0.2 mm, Ts=10 K

Thin-Liquid-Protected Divertors Steady State Results, very thin films

velocity vector plot

temperature plot

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• Two-dimensional simulation with 0.01[m]0.001[m] box size, 25050 resolution, and ho=0.2 mm

Thin-Liquid-Protected Divertors Steady State Results, very thin films

x [m]

y [m

]

time [sec]

y [m

]

black : Ts=10 K blue : Ts=20 K red : Ts=30 K

maximum y location

minimum y location

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Thin-Liquid-Protected Divertors Steady State Results, moderate film thickness

x [m]

y [m

]

• Two-dimensional simulation with 0.1[m]0.01[m] box size and 25050 resolution

• ho=2 mm, Ts=100 K

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• Two-dimensional simulation with 0.1[m]0.01[m] box size and 25050 resolution

• ho=2 mm, Ts=100 K

Thin-Liquid-Protected Divertors Steady State Results, moderate film thickness

velocity vector plot

temperature plot

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• Two-dimensional simulation with 0.1[m]0.01[m] box size, 25050 resolution, and ho=2 mm

Thin-Liquid-Protected Divertors Steady State Results, moderate film thickness

y [m

]

time [sec]

maximum y location

minimum y location

black : Ts=100 K blue : Ts=250 K

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Thin Liquid-Protected DivertorsPreliminary Conclusions

• Methodology can be used to determine the Limiting values for temperature gradients (i.e. heat flux gradients) necessary to prevent film rupture

• In some cases (very thin films), limits may be more restrictive than surface temperature limits

• Path Forward:

Generalized charts will be developed to determine the temperature gradient limits for different fluids and film thickness values