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
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