NSTX CSUPreliminary Assessment of PFCs

Art Brooks

December 8, 2010

1

Overview

• Project has chosen to use isotropic graphite (ie ATJ or equivalent) based on cost savings over CFCs

• Structural response of PFC tiles and supports analyzed subject to Surface Heat flux and EM loading (eddy and halo currents interacting with background fields)

• Goal is to determine operating limits for existing design and investigate alternative geometries that can increase performance

2

GRD Requirements – Heat Flux

Heat Flux applied to Plasma Facing Surface of TilesFor IBDhs this includes vertical surface

3

Requirements – EM Loads Eddy Currents

SPARK Scan of above disruptions yieldedMax dB/dt = 520 T/s Radial, 460 T/s Verticalat diverter 4

dB/dt scan from Plasma at Horizontal Inboard Diverter During Disruptions

Based on 2 MA for NSTX CSU 5

Max Radial dB/dt 520 T/s

Max Vertical dB/dt

460 T/s

Requirements - HaloAnalysis Priority [1=high]

Scenario index and analysis

sequence

Scenario category

Disruption scenario descriptionInitial Ip

[MA]

Initial position

index

Final position

index

Drift time [s]

Quench time [s]

Ip quench rate

[GA/s]

Halo fraction

fh

1 1 1 Centered disruption, fast quench 2 1 1 0.01 0.001 2 0

1 2 2 Initiated shifted to CS, fast quench, no halo 2 2 2 0.01 0.001 2 0

1 6 2 Inward drift to CS, very slow quench, halo 2 1 2 0.01 0.1 0.02 0.2

1 3 3 Initiated shifted down to inboard, fast quench, no halo 2 3 3 0.01 0.001 2 0

1 7 3 Vertical drift to inboard, very slow quench, halo 2 1 3 0.01 0.1 0.02 0.35

1 4 4 Initiated shifted down to middle, fast quench, no halo 2 4 4 0.01 0.001 2 0

1 8 4 Vertical drift to middle, very slow quench, halo 2 1 4 0.01 0.1 0.02 0.35

1 5 5 Initiated shifted down to outboard, fast quench, no halo 2 5 5 0.01 0.001 2 0

1 9 5 Vertical drift to outboard, very slow quench, halo 2 1 5 0.01 0.1 0.02 0.35

Excepted fromDisruption_scenario_currents_v2.xlsx

For IBDhs, Halo = 35 kA per 15 deg Tile( 2MA/24Tiles*.35HCF*1.2TPF)

Halo current assumed to take longest pathacross TF for worse case loading unless justification can be made not to.6

Requirements – Peak Background Fields

Coil R (center) dR Z (center) dZ nR nZ Turns Fill (cm) (cm) (cm) (cm) 0.0000

OH (half-plane) 24.2083 6.9340 106.0400 212.0800 4.0 110 442 0.7013PF1a 31.9300 5.9268 159.0600 46.3533 4.0 16 64 0.8594PF1b 40.0380 3.3600 180.4200 18.1167 2.0 16 32 0.7938PF1c 55.0520 3.7258 181.3600 16.6379 2.0 10 20 0.8560PF2a 79.9998 16.2712 193.3473 6.7970 7.0 2 14 0.7409PF2b 79.9998 16.2712 185.2600 6.7970 7.0 2 14 0.7409PF3a 149.4460 18.6436 163.3474 6.7970 7.5 2 15 0.6928PF3b 149.4460 18.6436 155.2600 6.7970 7.5 2 15 0.6928PF4b 179.4612 9.1542 80.7212 6.7970 2.0 4 8 0.7525PF4c 180.6473 11.5265 88.8086 6.7970 4.5 2 9 0.6723PF5a 201.2798 13.5331 65.2069 6.8580 6.0 2 12 0.7733PF5b 201.2798 13.5331 57.8002 6.8580 6.0 2 12 0.7733

PF Configuration from NSTX_CS_Upgrade_100504.xlsScan of 96 scenarios in same spreadsheet used to establish max fields:

Max Br = 0.5 TMax Bz = -0.57 T

Avg Btf ~ 2 T at IBDhs Max Btf ~ 3 T at CS

Btf = 1T at 0.9344m

7

ATJ Graphite Properties

ATJ very brittle – Yield strength close to Ultimate

Representative Tensile Stress-Strain Curve fromGRAPHITE DESIGN HANDBOOK GA 1988 (for 2020 graphite)

8

Structural Design Criteria

• Per NSTX Structural Design Criteria

– Design Tresca Stress Values (Sm) = 2/3 Sy or ½ Su• General primary membrane 1.0 KSm

• Local primary membrane 1.5 KSm

• Primary membrane plus bending stresses 1.5 KSm

• Total primary plus secondary stress 3.0 KSm

• For ATJ

– Sm (tensile) = 13 MPa

– Sm (compression) = 33 MPa• Criteria if applied to ATJ (questionable for brittle material with poor

ductility) would allow Tensile stresses of 39 MPa for thermal plus EM loading

• Performance herein assumes peak tensile stress < Su = 26 MPa

9

Heat up of IBDhs Tile subjected to 5 MW/m2 for 5 s

10

11

1st Pulse Heat Flux/Pulse Length Capability

Surface Temperature of 5 cm Graphite Tile Subject to Uniform Heat Flux

Re-Radiating from Surface, adiabatic back

0

500

1000

1500

2000

2500

3000

3500

0 1 2 3 4 5 6

Time, s

Te

mp

era

ture

, C

15 MW/m2, e=.3

15 MW/m2, e=.7

10 MW/m2, e=.3

10 MW/m2, e=.7

5 MW/m2, e=.3

5 MW/m2, e=.7

Single pulse without ratcheting with ATJ Graphite

~DNavg

1D analysis in good agreement with 3D away from corner

Eddy Current Distribution

12

Eddy current loop~ 3 kA

Net Moments on Tileare small:

Mr = 50 N-mMth = 14 N-mMr = 3 N-m

Halo Current Distribution

13

35 kA flowing from inner to outer radius,crossing TF Field produces forces of

Fr =-223 NFth = 3160 NFz = 10500 N

Compressive Stress on Tile Surface

14

-33.6 MPaCompressionWhere Temp = 1435C

15

Peak ATJ Stress 85.4 MPa>> Su (26 MPA)

Supports restricting free expansion

Tensile Stress at Support too high

High Z Stress Reduced Modestly by deleting contact in region

Sz=43 MPa

Sz=56 MPaNote: Results for previous analysis with vertical halo

2D Study of T-Bar Size

17Includes Thermal, Eddy & Halo Loading

Alternate Geometry – Single, Larger T-Bar

18

Peak Tensile Stress27.7 MPa in slot

2D Estimate of Split Tile (ie 48 vs 24 Tiles Toroidally)

19

Peak Tensile Stress in slot Drops from 27.7 MPa to 9.5 MPa

General Observations• A tile free to expand thermally will perform better than one

rigidly clamped– Grafoil is very compliant if not fully compressed– Eliminating cross T-bar also allows freer expansion

• A free tile must still resist EM loading (moments about T-bar and launching forces)– Eddy current forces are modest due to low electrical conductivity of

graphite but Halo forces are significant

• Slot size has large impact on tensile stresses– Slot radius can increase with size reducing peak stress

• Tile width impacts not just thermal stress thru thickness but mitigates effect of EM forces

• Cross T-bar does not appear to be effective or desired

20

Ongoing work• Following Slides are a first pass thru thermal and structural

response for the other tile types on the CS– Center Stack Angled Section (CSAS)

– Inboard Diverter Vertical Section (IBDvs)

• EM Loading from Eddy and Halo Currents not yet included

• T-Bars assumed bonded to Tile– As shown leads to high thermal stresses in tile

– Need to redo assuming unbonded – found to help for IBDhs

• Mounting Hardware still needs to be assessed for all tiles

• CSAS and IBDvs tiles are thinner and may not permit (or need) larger slots– CSAS will benefit from splitting in half vertically - TBD

21

Center Stack Angled Section (CSAS)Temperature Response – Single Pulse

Heating much lower on CSAS and IBDvs

Center Stack Angled Section (CSAS)Structural Response

Max Peak Stress Intensity at slots and sharp corners 246 MPa

Tensile Stress 101 MPaFor assumed bonded(needs to be rerun)

Assumes bonded along red section above

Inboard Diverter Vertical Section (IBDvs) Temperature Response – Single Pulse

Heating much lower on CSAS and IBDvs (than IBDhs)

Inboard Diverter Vertical Section (IBDvs)

Structural Response

IBDvs

Max Peak Stress Intensity at Slots 46MPa

Max Tensile StressAt slots 14 MPa

(not shown) Assumes bonded along red section above

Inboard Diverter Vertical Section (IBDvs) Structural Response – T-Bar

IBDvs

T Bar Stresses fairly low for inconel or SS – 56.8 MPa (8.1 ksi)(without EM loads)