V-05N-TAC（ October 29,2002）

Mechanical Structure Analysisand Code Validation

JAERI

Shuichi ISHIKURA　

Technical issues in target designTechnical issues in target design

■ Pressure wave.(Especially, EOS of mercury and FSI*)* Fluid-Structure-Interaction.

■ Thermal stress.(Presented by Dr. Hino)

■ Generation of negative pressure in mercury and cavitation.　　■ Damage of target container by cavitation erosion.

■ Material damage because of proton irradiation.

Structural design of target container under pressure wave

( cavitation is not considered )

Structural concept of liquid Structural concept of liquid mercury targetmercury target

Herium

D2O

Mercury

Beam window

Proton beam

Brade

Beam dump

外側 容器重 水水銀 ビ ームダ ンプ 外側 容器重 水水銀 ビ ームダ ンプ

3GeV_0.91MW_25Hz

Target Vessel

80.5cm

160cm

8.5cm

Triple-wallVessel

Distribution of heat deposition in mercury target

Z

3GeV0.91MW25Hz

Analytical code:NMTC/JAM

0

100

200

300

400

500

600

700

0 10 20 30 40 50 60 70

Y=0cm1cm2cm3cm4cm

Hea

t gen

erat

ion

dens

ity: Q

[W/c

c/M

W]

Distance from window: Z(cm)

y = m1*(1-m2*exp(m3*(m0+m4))...エラー値

1.3143e+081444.2m1 2.467e+061.4101m2 0.03412-0.23581m3

7.4226e+066.9087m4 0.00098013-0.068969m5 1.3197e+066.6026m6

NA2758.9カイ２乗NA0.99948R

Gausian distribution

-15 -10 -5 0 5 10 15

-6

-4

-2

0

2

4

6

0

100

200

300

400

500

600

700

-15 -10 -5 0 5 10 15

Q(x),W/ccQ(y),W/ccQ(x)-fit,W/ccQ(y)-fit,W/cc

Q(x

),W/c

c/M

W

X-Horizontal, cmY-Vertical, cm

Max=668W/cc

Temperature rise distribution by heat generation Temperature rise distribution by heat generation and formation of compression fieldand formation of compression field

Generation of pressure wave in mercury and load on target container.（ 0.91MW/25Hz）

Injection of pulsed proton beam(1µs) :36.4 kJ/pulse.

Heat generation by nuclear spallation : Q ～ 20 kJ/pulse.

Max. heat density : q　～ 26.7 J/cc/pulse.

Max. temperature rise : ΔT　=q

　/ρ CV ～ 17 ℃/pulse

Max. compressed press. : P　= α ΔT

　KS ～ 68MPa

Sound velocity in mercury : V ～ 1400 m/s

Load on target container.

Structural integrity of the target container?

ΔTmax=17℃Beam

Stress evaluation of beam windowStress evaluation of beam windowAnalytical modelAnalytical model（1/4model）

・Code LS-DYNA（Vr．950）・Number of elements

・Vessel: Shell element　5.16×104

・Hg: Solid element 　66.3×104

Proton beam

50.47cmt10mm

160c

m

1/4model

t2.5mmt5mm

Bradet10mm

t7.5mm

8.5cm

Effect of beam window type on Effect of beam window type on mechanical strengthmechanical strength

Hg

Inner container

Outer container

PHg

Pout

Flat-plate typeLiquid or gas

Pout > PHg

Hg

Inner container

Outer container

Pout

Semi-cylindrical type

Liquid or gas

Dynamic responses of stress at center of window

Window thickness : 2.5mm

-150

-100

-50

0

50

100

150

0 500 1000 1500

Stre

ss ,

MPa

Time , µs

93.6MPa(Center)

-46.6MPa

100.6MPa (Outer surface)

-80.6MPa

-113.4MPa (Inner surface)

88.7MPa

202MPa

-150

-100

-50

0

50

100

150

0 500 1000 1500

Stre

ss, M

Pa

Time , µs

103.4MPa (Outer surface)

-50.7MPa

-103.6MPa (Inner surface)

47.3MPa

28.6MPa (Center)

-12.6MPa

154MPa

Semi-cylindrical type Flat-plate-type

Stress amplitude generated in Flat-plate-type is smalleradvantageous for fatigue strength.

Membrane stress intensity generated in Flat-plate-type is smalleradvantageous for instantaneous brake.

Comparison of changes in stress/pressure/displacement at window and upper plate.

Dip. in center of window Press. in mercury Stresses in corner of window

-200

-150

-100

-50

0

50

100

150

200

0 500 1000 1500

Stre

ss, M

Pa

Time , µs

Inner surface

Outer surface

Middle surface

-40

-20

0

20

40

60

80

0 100 200 300 400 500

Pres

sure

, MPa

Time , µs

Max. 75MPa

-200

-150

-100

-50

0

50

100

150

200

0 500 1000 1500St

ress

, MP

aTime , µs

Inner surface

Outer surface

Middle surface

-200

-150

-100

-50

0

50

100

150

200

0 500 1000 1500

Stre

ss, M

Pa

Time , µs

Inner surface

Outer surface

Middle surface

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0 500 1000 1500 2000 2500 3000

Dis

plac

emen

t, m

m

Time, µs

Stresses in center of window Stresses in upper plate

Normal Service Stress Intensity Limits (SNS)

Stress Category [Note (1)]

Primary

General Membrane Pm

Local Membrane PL

Bending Pb

Description Average stress across wall to maintain equilibrum with mechanical loads including pressure and gravity. Excludes discontinuities and stress concentrations.

Average stress across wall from pressure and gravity. Considers discontinuities but not stress concentrations.

Linear bending stress caused by pressure and gravity. Excludes discontinuities and stress concentrations.

Pm

PL

1.1S m

1.65S m

PL + P b

Secondary Membrane + Bending

Q

Self-equilibrating stress caused by mechanical loads at structural discontinuities or equivalent linear bending stress due to differential expansion. Excludes local stress concentrations.

Peak F

(1) Local stress concentration (notch). (2) Non-linear portion of thermal stress. (3) Stress due to shock produced by proton pulses

PL + P b+ Pd + Q

PL + P b+ Pd + Q + F

3Sm

Sa1.65S m

Dynamic Pd

Reversing dynamic stress produced by proton pulses

[Note (2)]

[Note (4)] [Note (3)]

Legend

Allowable Value

Calculated Value

Stress category and allowable stressesSame as SNS

Maximum stress ranges(2Salt) at main parts of target container by pressure wave

271Upper/Under plate

207Corner of window 330345

232Center of window

Fatigue stress range, 2Salt

Secondary stress range, 3Sm

Max. stress intensity range

Evaluation part

100

120

140

160

180

200

106 107 108 109 1010 1011Alte

rnat

ing

stre

ss in

tens

ity; S

alt (

MPa

)

Number of Cycles ( N )

For N>109

Salt<165MPa

Analytical value

13621 =×

2Salt

Design fatigue curve of SUS316(LN)

Conclusions by pressure wave analyses

• Structural integrity of the flat-plate type beam window of 316(LN)SS is secured against the pressure wave load which generated 1MW proton beam condition.

Analytical evaluation of cavitation erosion

1. Single bubble behavior under pressure change in mercury.

2. Evaluation of shock wave and micro-jet when bubble collapses.

3. Evaluation of the damage of the window wall by Liquid-Solidinteraction analyses.

Generation mechanism of cavitation erosion1. Due to Shock wave

The shock wave generated by rebound following gas bubble shrinkage collides with the solid surface (Pmax ~Gpa).

2. Due to micro-jetBubble collapses toward the wall, and liquid collide with the solid wall as a micro-jet（~200m/s, Pmax~GPa）

Concept of micro-jet generationConcept of shock wave generation

Micro-jet Solid wall

Solid wallSolid wall

V=130m/s　 　193MPa(Water)

Single bubble behavior in mercurySingle bubble behavior in mercury

0.01

0.1

1

10

100

1000

104

105

-20

-10

0

10

20

30

40

50

0 0.5 1 1.5 2 2.5 3 3.5 4

Ro=1mmRo=100µmRo=10µmRo=1µmRo=0.1µm

Ps(MPa)=Pm*sin wt

Rel

ativ

e ra

dius

, R

(t)/R

o

Transient of pressure field ; Ps(t)=Pm*sin ω

tTime ,ms

Hg-bubbleRo=0.1µ～1mmPo=1barPm=10MPaPs=Pm*sinωtω=2πff=9000Hz

0.1

1

10

100

1000

104

105

-150

-100

-50

0

50

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35R

elat

ive

radi

us ,

R(t)

/Ro

Bubble collapse velocity , m/s

Time , ms

Hg-bubbleRo=0.1µmPo=1barPm=10MPaPs=Pm*sinωtω=2πff=9000Hz

Growth and collapse behavior of tiny bubble (R0=0.1µm).Bubble radius response which is

dependent on initial bubble radius. (Bubbles were excited by sine-wave of 10MPa-9kHz. ) The collapse speed of the

bubble influences the micro-jet velocity in mercury.

Relationship between collision speed and impact pressure when Relationship between collision speed and impact pressure when micromicro-- jet collides with solid walljet collides with solid wall

velocitycollisionvvelocitySoundcdensityLiquid

vc

L

L

LL

:::

PsPs vspeedat body wall rigid with collides liquid power whenImpact

L

L

ρρ ××=

；

1

10

100

1000

104

0 50 100 150 200

P-impact(Water-SS316)P-impact(mercury-SS316)P-impact(mercury-Rigid)

Impa

ct p

ress

ure

, MPa

Impact velocity , m/s

Yield strength(SS316(LN))

Mercury

Water

Vcc

ccPFluidFluidSolidSolid

FluidFluidSsolidSolidpact ρρ

ρρ+

=Im

Impact pressure to elastic wall

Impact velocity

DL

D

Hg

SUS316(LN)

Pit depth～4µm

0

5

10

15

20

25

30

50 100 150 200 250 300 350

Water(σy=200MPa),D0.1*L0.2Mercury(σy=200MPa)Mercury(σy=400MPa)Mercury(σy=200MPa),D0.2*L0.4Mercury(σy=400MPa)

Max

imum

pit

dept

h , m

icro

-m

Impact velocity, m/s

Range of forecast collision speed of water

Range of forecast collision speed of mercury

Plastic strain　　　　～0.6

Hg

Preliminary analyses of pit formation Preliminary analyses of pit formation by collision of mercury microby collision of mercury micro--jet with jet with solid wallsolid wall（by AUTODYN）

Category to evaluate damage by cavitation erosion. *　LEFM: Linear Elastic Fracture Mechanics

Generation of Pit

Local progress（Pit diam./Depth）

Progress

Estimation of fatigue life

Evaluation by LEFM*Crack growth rate

Steady state Transient by beam trip

Low thermal stressHigh compressive thermal stress

Stress evaluation for decreased window thickness

Uniform progress（Window thickness decreases）

Acceleration examination

No crack propagation

Evaluation of structural integrity

Concept of crack generated around pit

•The bottom of pit is V-notch shape, so it was assumed initial crack. The crack is considered propagating due to alternative pressure wave load. However, structural integrity is secured if the crack does not propagate to the limit crack length.

•High compressive stress field is generated on the inner surface of the flat-plate-type beam window due to the steady state thermal stress. Therefore, inner surface of the beam window does not become tensile stress field even if the stress by the pressure wave load. The crack generated around pit does not propagate.

•Although the tensile stress would be generated due to beam trip (because the thermal stress decreases), a frequency of this tensile stress generation is too low to affect the cavitation erosion damage.

Future work1. Experiment work

It is necessary to repeat experiment more than 108 cycles under practical operation condition as possible (purity of mercury, stress field, and flow condition).

- to measure the profile of damage, especially depth of pit- to clarify the damage growth behavior (does it stop or progress?) .

2. Analytical workIt is necessary for pressure wave analyses to consider the EOS of the mercury when

the cavitation occurs, because mercury would become the bubbly-liquid state.The bubble-dynamics code is being developed.

It is necessary to analyze the shock wave and the micro-jet behavior near the structure wall which cause erosion

- to clarify the mechanism of cavitation erosion - to supplement the experimental result.

The analyses is being carried out by an existing Euler-Lagrange impact code (preliminary).

Analytical item necessary for target impact analysis and evaluating cavitation damage.

Irradiation effect at crack growth rate

There is a necessity for developing the code.

Fatigue damage evaluation by which irradiation hardening to load cycles in target operation life.Fracture mechanics evaluation by which “Pit+Crack” is assumed.

Evaluation of fatigue life.

・Process of pit progress

・Pit profile.

There is a necessity for developing the code.

The pit progress is evaluated by the condition of the design analysis result (negative pressure) based on the experimental data.

Evaluation of pit progress.

DittoDittoElasto-Plastic interaction with solid wall by shock wave when bubble collapses in mercury.

When bubble collapses・Formation of shock wave.

・Nonlinear EOS of bubbly-Hg.

・Strain rate hardening.

dε/dt = ～107

AUTODYNDYTRANRADIOSS

Elasto-Plastic interaction with solid wall by micro jet when bubble collapses in mercury.

・Is it possible because of the potential flow?

FLUENTFormation of micro jet when bubble collapses in mercury.FROW-3DEtc.（Stagnant and flowing condition）

When bubble collapses・Formation of micro jet

・Nonlinear EOS of bubbly-Hg.

・Direct coupling of bubbly-liquid equations.

AUTODYNDYTRANRADIOSSEtc.

Fluid-Structure interaction analysis which uses nonlinear EOS of Hg which considers dynamic response of bubbly-liquid. The macro behavior of the bubbly-liquid is simulated.

Interaction of bubbly-liquid and container

Note and necessary dataAnalytical codeAnalytical contentAnalytical item

END