september 24-25, 2003 hapl program meeting, uw, madison 1 report on target action items a.r. raffray...

September 24-25, 2003HAPL Program Meeting, UW, Madison

1

Report on Target Action Items

A.R. Raffray and B. Christensen

University of California, San Diego

Target Survival Workshop

HAPL Program Meeting

University of Wisconsin, Madison

September 24-25, 2003


2

Action Items from Last Target Survival Workshop(see http://aries.ucsd.edu/HAPL/MEETINGS/0212-HAPL/program.html)

4. Evaluate how much temperature drop there is to keep the insulated target cold (with beta decay heat) and determine how beneficial this temperature drop is with respect to survival estimates.

5(a). Evaluate the effect of asymmetric heating in particular on local phase change behavior.

5(b). Summarize phase change results from new model for the thermo-mechanical behavior of the target.

I

II

III


3

Coupled Thermo-Mechanical Model of Target

• 1-D heat conduction equation with variable properties

• DT vapor (if present)is modeled as a thermal resistance (neglect capacitance)

• DT solid assumed rigid initially• Evaporation/sublimation increase the

pressure of the vapor but latent heat effects are negligible

• Plastic shell deformation behavior modeled (limiting cases: fully rigid and membrane behavior)

Plastic Shell Vapor Gap

Rigid DT Solid

Simplified Target Cross Section

DT Vapor Core

• Phase change analysis assumes a pre-existing vapor micro-gap- Vapor bubbles/gap insulate the DT

- Vapor growth could result in the destruction of the target

- Pre-existing “small” vapor bubbles/defects could be eliminated through density change


4

Deflection of the Plastic Shell due to DT Vapor Pressure Two Possible Cases:

• Membrane theory (valid for r/t > 10) for a sphere with a uniform internal pressure

• From bending theory, max. deflection under the center of the load*

Uniform Internal Pressure, P

r

t

- Where A is a numerical coefficient =f (ro , R, t, )

- This equation is valid for any edge support positioned 3 degrees or more from the center of the load

€

δ =Pr2(1− μ )

2Et

€

δ =APR (1− μ 2 )

Et2

*Roark’s Formulas for Stress & Strain, 6th Edition, p. 546

t

ro

RP


5

Comparison of the Calculated Deflection of the Plastic Shell by Membrane and Bending Theory for a Pressure of 104 Pa for Several

Vapor Bubble Sizes , ro

0.0E+00

5.0E-07

1.0E-06

1.5E-06

2.0E-06

2.5E-06

0.0E+00 5.0E-06 1.0E-05 1.5E-05 2.0E-05 2.5E-05 3.0E-05 3.5E-05 4.0E-05

Vapor Bubble Size, r o (m)

Deflection (m)

Membrane Theory

Bending Theory (Roark)

ro

R

• Bubble size for which bending theory approaches membrane theory is independent of pressure, ~ 37 m in this case

• Would need much smaller bubble size in target to avoid large “membrane-like” deflections


6

Model Results Show Unacceptable High Vapor Region Thickness Based on Membrane Theory Even for Heat Fluxes ~ 1 W/cm2

0.00E+00

5.00E-05

1.00E-04

1.50E-04

2.00E-04

2.50E-04

3.00E-04

0 1 2 3 4 5 6 7 8 9 10

Heat Flux (W/cm2)

Vapor Gap (m)

Membrane Theory, tv_o = 1e-6 m

Bending Theory, tv_o = 1e-6 m, ro = 37e-6 m

Membrane Theory, tv_o = 3e-6 m

• The Model Correctly Predicts that for Large Bubble Radius (37m), the Maximum Deflection Using Bending Theory is Equal to the Deflection Predicted by Membrane Theory

tv_o=pre-existing vapor gap thickness


7

Pre-existing Vapor Bubbles Could Close if the Bubble Size is Below a Critical Size and the Heat Flux is Above a Critical Value

0.00E+00

5.00E-06

1.00E-05

1.50E-05

2.00E-05

2.50E-05

3.00E-05

0 1 2 3 4 5 6 7 8 9 10

Heat Flux (W/cm2)

Vapor Gap (m)

Rigid, tv_o = 1e-6 m

Rigid, tv_o = 3e-6 m

Bending, tv_o = 1e-6 m, ro = 5e-6 m

Bending, tv_o = 3e-6 m, ro= 5e-6m




time = 0.015 s

Tinit = 18 K

• e.g. for bubble size, ro =5 m, vapor gap will close for initial thicknesses, tv,o, of 3 m and minimum heat

fluxes of ~1.7 W/cm2

Plastic Shell

Local Vapor Bubble

Rigid DT Solid

tv,o

ro


8

The Critical Bubble Size, ro,crit Depends on Initial Vapor Region Thickness and Initial Bubble Size

0.00E+00

2.00E-03

4.00E-03

6.00E-03

8.00E-03

1.00E-02

1.20E-02

1.40E-02

1.60E-02

0.00E+00

1.00E-06

2.00E-06

3.00E-06

4.00E-06

5.00E-06

6.00E-06

7.00E-06

8.00E-06

9.00E-06

1.00E-05

Bubble Size, r o (m)

Time to Bubble Closure (s)

tv = 1e-7 m

tv = 5e-7 mtv = 1e-6 mtv = 5e-6 m tv = 3e-6 m

q’’ = 5.5 W/cm2, Plastic Thickness = 2 m


9

The Heat Flux Into the Target is Limited by Homogeneous Nucleation (0.8Tc ~ 32 K)

18

23

28

33

38

43

0 1 2 3 4 5 6 7 8 9 10

Heat Flux (W/cm 2)

Temperature (K)

Rigid

Bending, ro = 5 microns




DT temperature as a function of heat flux for original target


10

Example Case with Insulating Foam Showing the Combined Effect of Including an Insulating Foam and Allowing for Phase Change

0.0E+00

2.0E-09

4.0E-09

6.0E-09

8.0E-09

1.0E-08

1.2E-08

1.4E-08

1.6E-08

1.8E-08

8 9 10 11 12 13 14 15 16 17 18

Heat Flux (W/cm 2)

Vapor Gap (m)

20.5

21

21.5

22

22.5

23

23.5

24

8 9 10 11 12 13 14 15 16 17 18

Heat Flux (W/cm 2)

Temperature (K)

100 microns of 10% Dense Insulating Foam

ro = 5e-6 m, tv_o = 1e-6 m

Low heat fluxes may not be self healing

• The heat flux can be increased substantially• For this example, the gap closes and the heat flux

is limited by TDT for homogeneous nucleation (q’’>>20 W/cm2)

Max. DT temperature as a f(q’’)(<0.8Tc for q’’ considered)


11

Temperature Drop through Foam due to Beta Decay Heat

• 0.0186 MeV decay with half life of 12.32 yr- q’’’ from beta decay in DT small ~ 1.3 x 105 W/m3

- q’’ through outer insulating layer ~ 50 W/m2

- T through 100 m 10% dense insulating layer(k~0.01 W/m-K) ~ 0.5 K

- T though DT ice even lower ~ 1 K

DT Vapor Core

Foam

Plastic Shell

DT Ice

DT/Foam

• Would need to maintain target surface at a lower temperature (~1 K) than DT bulk


12

Effect of 2-D Heat Flux Distribution to Account for Relative Velocity Effect on Flux on Xe Atoms Impacting the Target Perimeter from Front to

Back During Flight

• 1-D ANSYS results very close to 2-D ANSYS results for typical cases considered- Reasonably conservative to use 1-D analysis

Maximum DT Temperature for Different Cases (K)Xe Conditions Maximum Heat Flux t=0.005 second t=0.015 second t=0.025 second t=0.06 second

Uniform Heat Flux Cases (1-D) 1mtorr&1000K 770 W/m2 18.13 18.23 18.3 18.471mtorr&2000K 1350 18.22 18.4 18.52 18.821mtorr&3000K 2000 18.33 18.6 18.78 19.251mtorr&4000K 2400 18.4 18.72 18.95 19.51

10mtorr&1000K 6600 19.13 19.83 19.86 20.0410mtorr&2000K 11700 19.85 19.97 20.13 23.5910mtorr&3000K 17250 19.87 20.22 22.1 27.4810mtorr&4000K 22100 20.04 20.55 25.53? 31.13100mtorr&1000K 39000 20.58 23.8? 32.24 47.8

Varying Heat Flux Cases, from Max. Heat Flux at Leading Edge to ~20% of this value at Trailing Edge, 180° (2-D) 1mtorr&1000K 770 W/m2 18.12 18.22 18.29 18.461mtorr&2000K 1350 18.21 18.39 18.51 18.811mtorr&3000K 2000 18.32 18.59 18.77 19.221mtorr&4000K 2400 18.39 18.71 18.93 19.46

10mtorr&1000K 6600 19.07 19.69 19.73 20.1210mtorr&2000K 11700 19.74 19.88 20.05 23.2310mtorr&3000K 17250 19.78 20.11 20.49 27.5110mtorr&4000K 22100 19.9 20.39 21.43 30.29100mtorr&1000K 39000 20.26 23.63 31.99 46.03

V


13

2-D ANSYS Model Used to Study the Effects of Local Vapor Bubble Formation on Heat Transfer

• 3 m thick vapor bubble

• Bubble arc length varied and results compared to 1-D case

Plastic Shell

Local Vapor Bubble

Rigid DT

DT Vapor Core

3 m


14

Comparison of the Results For a Small Bubble to those Obtained for a Continuous Vapor Gap Show that a 2-D

Heat Transfer Model may be Important for Small Bubbles

Entire arc length

Time (s)

15 m arc length

Time (s)

Outer Surface of the Plastic Shell Vapor-Plastic Interface Vapor-DT Interface


15

Comparison of the Results For a Bubble to those Obtained for a Continuous Vapor Gap Show that a 1-D Heat Transfer

Model is Sufficient for Large Bubbles (15-50 m arc length for 3 m gap)

Entire arc length

Time (s)

50 m arc length

Time (s)

Outer Surface of the Plastic Shell Vapor-Plastic Interface Vapor-DT Interface

september 24-25, 2003 hapl program meeting, uw, madison 1 report on target action items a.r. raffray...

Documents