Heat Flux Gradient Limits for LiquidProtected Divertors S' I' AbdelKhalik, S' Shin, and M' Yoda - PowerPoint PPT Presentation

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Heat Flux Gradient Limits for LiquidProtected Divertors S' I' AbdelKhalik, S' Shin, and M' Yoda

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Mechanical Engineering. Atlanta, GA 30332 0405 USA. 2. Work on Liquid Surface Plasma Facing Components and Plasma Surface Interactions ... – PowerPoint PPT presentation

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Title: Heat Flux Gradient Limits for LiquidProtected Divertors S' I' AbdelKhalik, S' Shin, and M' Yoda


1
Heat Flux Gradient Limits for Liquid-Protected
DivertorsS. I. Abdel-Khalik, S. Shin, and M.
Yoda
ARIES Meeting, San Diego (Nov 4-5, 2004)
G. W. Woodruff School of Mechanical
Engineering Atlanta, GA 303320405 USA
2
Problem Definition
  • Work on Liquid Surface Plasma Facing Components
    and Plasma Surface Interactions has been
    performed by the ALPS and APEX Programs
  • Operating Temperature Windows have been
    established for different liquids based on
    allowable limits for Plasma impurities and Power
    Cycle efficiency requirements
  • This work is aimed at establishing limits for the
    maximum allowable heat flux gradients (i.e.
    temperature gradients) to prevent film rupture
    due to thermocapillary effects

3
Problem Definition
  • Maximum Temperature gradients to prevent film
    rupture were previously established -- Analysis
    was extended to determine the maximum allowable
    heat flux gradients (based on comment made by Don
    Steiner)
  • Spatial Variations in the wall and Liquid Surface
    Temperatures are expected due to variations in
    the wall loading
  • Thermocapillary forces created by such
    temperature gradients can lead to film rupture
    and dry spot formation in regions of elevated
    local temperatures
  • Initial Attention focused on Plasma Facing
    Components protected by a non-flowing thin
    liquid film (e.g. porous wetted wall)

4
Problem Definition
open B.C. at top,
L
L
periodic B.C. in x direction
Non-uniform heat flux
ylgtgtho
Gas
Gas
?o initial film thickness
?o initial film thickness
Liquid
Liquid
y
y
Wall
Wall
x
x
Non-uniform wall temperature
Initially, quiescent liquid and gas (u0, v0,
TTm at t0)
Convective cooling
Specified Non-uniform Wall Temperature
Specified Non-uniform Surface Heat flux
  • Two Dimensional Cartesian (x-y) Model (assume no
    variations in toroidal direction)
  • Two Dimensional Cylindrical (r-z) Model has also
    been developed (local hot spot modeling)

5
Variables definition
  • Non-dimensional variables

Specified Non-uniform Surface Heat flux
Specified Non-uniform Wall Temperature
6
Governing Equations
  • Conservation of Mass
  • Momentum
  • Energy

7
Asymptotic Solution
  • Long wave theory with surface tension effect
    (altlt1). Governing Equations reduce to

Specified Non-uniform Wall Temperature
Specified Non-uniform Surface Heat flux
Bankoff, et al. Phys. Fluids (1990)
  • Asymptotic solution used to analyze cases for
    Lithium, Lithium-lead, Flibe, Tin, and Gallium
    with different mean temperature and film
    thickness
  • Asymptotic solution produces conservative (i.e.
    low) temperature gradient limits
  • Limits for High Aspect Ratio cases analyzed by
    numerically solving the full set of conservation
    equations using Level Contour Reconstruction
    Method

8
Asymptotic Solution
Maximum Non-dimensional Temperature Gradient
(?Ts/L)/(?L2/?L?o?o2)
a0.02
Maximum Non-dimensional Heat Flux Gradient
(Q/L)/(a?Lgk/?o)
1/We107 1/We106 1/We105 1/We104 1/We103 1/We
102
?o/?LgL2
1/Fr
Specified Non-uniform Surface Heat flux
Specified Non-uniform Wall Temperature
  • Similar Plots have been obtained for other aspect
    ratios
  • In the limit of zero aspect ratio

9
Results -- Asymptotic Solution Specified
Non-uniform Wall Temp (?o1mm)
  • Property ranges

1/We ? ?o, 1/Fr ? ?o3
10
Results -- Asymptotic Solution Specified
Non-uniform surface heat flux
  • ?o10 mm, a0.02
  • ?o1 mm, aNu1.0

11
Conclusions
  • Limiting values for the heat flux gradients (i.e.
    temperature gradients) to prevent film rupture
    can be determined
  • Generalized charts have been developed to
    determine the heat flux gradient limits for
    different fluids, operating temperatures (i.e.
    properties), and film thickness values
  • For thin liquid films, limits may be more
    restrictive than surface temperature limits based
    on Plasma impurities limit
  • Experimental Validation of Theoretical Model has
    been initiated

12
Extra Slides

13
Results -- Asymptotic Solution (?o10 mm, a0.02)
14
Results -- Asymptotic Solution (?o1 mm, a0.02)
15
Results -- Asymptotic Solution (?o0.1 mm, a0.02)
16
Results -- Asymptotic Solution (?o1 mm, aNu1.0)
17
Results -- Asymptotic Solution (?o1 mm, aNu0.1)
18
Results -- Asymptotic Solution (?o1 mm, aNu0.01)
19
Results -- Asymptotic Solution (L5 cm, aNu1.0)
20
Results -- Asymptotic Solution (L5 cm, aNu0.1)
21
Results -- Asymptotic Solution (L5 cm, aNu0.01)
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