Transcript LS-Dyna and ANSYS Calculations of Shocks in Solids

Shock simulations in solid targets
Chris Densham
Rutherford Appleton Laboratory
Contents
•
Introduction
•
ANSYS results for NF Ta target
•
Effect of multiple bunches on shock wave magnitude
•
LS-Dyna results for NF Ta target
•
- G.Skoro, Sheffield
Shock heating of a thin wire – target lifetime experiment at
RAL
•
LS-Dyna calculations for wire test
•
Graphite target for T2K experiment
- G.Skoro, Sheffield
Elastic shock waves in a candidate solid Ta
neutrino factory target
• 10 mm diameter tantalum cylinder
• 10 mm diameter proton beam (parabolic distribution
for simplicity)
• 300 J/cc/pulse peak power (Typ. for 4 MW proton
beam depositing 1 MW in target)
• Pulse length = 1 ns
Elastic shock waves in a candidate solid Ta
neutrino factory target
Temperature jump
after 1 ns pulse
(Initial temperature =
2000K )
Elastic shock waves in a candidate solid Ta
neutrino factory target
Elastic stress waves in 1 cm diameter Ta
cylinder over 10 μs after ‘instantaneous’
(1ns) pulse
Stress (Pa) at : centre (purple) and
outer radius (blue)
Effect of multiple bunches
Elastic stress waves after 10x1ns bunches/
1 μs spill
Effect of multiple bunches
Elastic stress waves after 10x1ns bunches/
1 μs spill
1 μs (end of
beam spill)
10 μs
Shock wave magnitude at centre of target as function of spill time for multiple 1ns bunches
6.00E+08
Stress (Pa) along centreline of target
5.00E+08
1 x 1 ns bunch/spill radial/hoop
stress
1 x 1 ns bunch/spill radial/hoop stress
10x1ns bunches/spill, max radial/hoop stress
at centre
140 bunches (radial/hoop)
4.00E+08
3.00E+08
2.00E+08
1.00E+08
140 bunches (radial/hoop stress)
0.00E+00
0.00E+00
1.00E-06
2.00E-06
3.00E-06
Spill length (s)
4.00E-06
5.00E-06
6.00E-06
Shock wave magnitude at centre of target as function of spill time for multiple 1ns bunches
6.00E+08
1 x 1 ns bunch/spill radial/hoop stress
5.00E+08
1 x 1 ns bunch/spill radial/hoop
stress
10x1ns bunches/spill, max radial/hoop stress
at centre
Stress (Pa) along centreline of target
10x1ns bunches/spill, max Von Mises stress at
centre
140 bunches (Von Mises stress)
4.00E+08
140 bunches (radial/hoop)
3.00E+08
2.00E+08
140 bunches (Von Mises)
1.00E+08
140 bunches (hoop stress)
0.00E+00
0.00E+00
1.00E-06
2.00E-06
3.00E-06
Spill length (s)
4.00E-06
5.00E-06
6.00E-06
Effect of multiple bunches
Elastic stress waves in 1 cm diameter Ta
cylinder over 5 μs after 10x1ns bunches/
3 μs spill
NB time for shock wave to travel from
centre to surface and back to centre = 3 μs
LS-Dyna calculations –
Goran Skoro, Sheffield University
LS-Dyna calculations –
Goran Skoro, Sheffield University
• Material model:
Temperature Dependent Bilinear Isotropic

'Classical' inelastic model

Nonlinear
– Uses 2 slopes (elastic, plastic) for representing of the stress-strain
curve
– Inputs: density, Young's modulus, CTE, Poisson's ratio,
temperature dependent yield stress, ...
• Element type: LS-Dyna Explicit Solid
• Material: TANTALUM
Geometry: NF target
Tinitial = 2000K
Boundary conditions: free
20cm
Uniform thermal load of 100K
2cm
(equivalent energy density of ~ 300 J/cc)
G. Skoro (Sheffield)
G. Skoro (Sheffield)
Literature data on fatigue life of tantalum…
Literature data on fatigue life of tantalum…
… fortunately this data is for low cycle (ie
slow) fatigue
The need for experiments
- Calculations are only as good as material data used
- Material data is sparse…
- Hence, need for experiments to determine material model
data
- Experiment at RAL: Current pulse through wire (equivalent to ~
300 J/cc);
- Use VISAR to measure surface velocity;
- Ideally, use results to 'extract' material properties at high
temperatures...
- Predict lifetime of a future neutrino target
Shock wave experiment at RAL
Pulsed ohmic-heating of wires may be able to replicate pulsed
proton beam induced shock.
current
pulse
tantalum (or graphite) wire
Energy density in the Ta wire needs to be ε0 = 300 J cm-3 to
correspond to 1 MW dissipated in a target of 1 cm radius and
20 cm in length at 50 Hz.
JRJ Bennett (NuFACT05)
Transient Conditions
•Assume an electric field E is instantaneously applied across a
conducting wire.
•Apply Maxwell’s equations.
•This produces a diffusion equation:
j
1   2 j z 1 j z
 2 

t  0  r
r r



In cylindrical coordinates, where j is the current density.
•The solution is:
 2   n 2t J 0 r n  
j z  j z 0 1   e



a

J
a

n 1
n 1
n 

 = 1/0
JRJ Bennett (NuFACT05)
Characteristic
time for the
shock to travel
across the
radius
I 
a
s 
v
Need:
a2

Characteristic
Time for the
current to
penetrate the wire
s I
10000
τs
τI
ns1000
100
10
0.1
a, mm
1
JRJ Bennett (NuFACT05)
Doing the Test
The ISIS Extraction Kicker Pulsed Power Supply
8 kA
Voltage
waveform
Time, 100 ns intervals
Rise time: ~50 ns
Voltage peak: ~40 kV
Repetition rate up to 50 Hz.
+ There is a spare power supply available for use.
1
1 e 
0.8
t
j/j0
0.6
0.1 mm
0.2 mm
0.3 mm
0.4 mm
0.4
0.6 mm
0.2
0
0
2 10
8
4 10
8
6 10
t,
8
8 10
8
1 10
7
s
Current density at r = 0 versus time (t, s), for different wire
radii (a, mm).
JRJ Bennett (NuFACT05)
LS-Dyna
calculations for
shock-heating
of different
wire radii using
ISIS kicker
magnet power
supply
G. Skoro (Sheffield)
Comparison of
stresses
expected in
neutrino
factory target
(top) with
stresses
generated in
wire test
(bottom)
G. Skoro (Sheffield)
Comparison of
stresses
expected in
neutrino
factory target
(top) with
stresses
generated in
wire test
(bottom)
NB Peter
Sievers:
Need to add
radial pinch due
to magnetic
field in wire
G. Skoro (Sheffield)
Schematic section of the wire shock-wave test assembly
ISO 63 cross
Penning
gauge
window
ct
Co-axial
cables
2 copper
bars
Wire
support
plate
window
tantalum
wire
Electrical return
copper strip
ISO 63 tee
bulkhead high voltage
feed-throughs
turbopump
JRJ Bennett (RAL)
Temperature
measurement
(Transient optical spectroscopy)
– see R. Brownsword talk last
UKNF meeting
tantalum
wire
JRJ Bennett (RAL)
Temperature
measurement
tantalum
wire
VISAR (see Richard
Brownsword’s talk next)
JRJ Bennett (RAL)
T2K experiment
Long baseline neutrino oscillation experiment
from Tokai to Kamioka.
Dm132 (eV2)
Sensitivity on
ne appearance
10-1
Super-K: 50 kton
Water Cherenkov
~1GeV n beam
(100 of K2K)
10
sin22q13
>0.006(90%)
-2
~20
10-3
J-PARC
0.75MW 50GeV PS
10-4 -3
10
Physics motivations
Discovery of nne appearance
Precise meas. of disappearance nnx
Discovery of CP violation (Phase2)
10-2
CHOO
Z
exclu
ded
10-1
1
Neutrino Beam Line for T2K Experiment
Components
Primary proton beam line

Normal conducting magnets

Superconducting arc

Proton beam monitors
Target
Station
Target/Horn system
130m
Decay pipe (130m)
Beam dump
decay volume
Near neutrino detector
280m
muon monitors
Beam dump/-pit
Special Features
Superconducting combined function magnets
Off-axis beam
Near detector
To Super-Kamiokande
Decay Volume
(excavated)
Jan.28, 2005
50 GeV (40 at T=0)
Primary Beam
single turn fast extraction
3.3x1014proton/pulse
Default acceleration cycle for 50GeV
3.53 sec cycle
750kW (~2.6MJ/pulse)
0.7s
8 (15) bunches
e=6p (7.5p)mm.mr @ 50 (40) GeV
0.12s
injection
598ns
58ns
4.2s
0.7s
idling
Total ~3.53s (from TDR)
Idling time is to adjust total power.
If beam loss, power consumption allow,
this can be reduced.
T2K target conceptual design
• Graphite Bar Target : r=15mm, L=900mm (2 interaction length)
– Energy deposit … Total: 58kJ/spill, Max:186J/g  DT  200K
MARS
Distribution of the energy deposit in the target (w/ 1 spill)
J/gK degree
cm
• Co-axial 2 layer cooling pipe.
– Cooling pipe: Graphite / Ti alloy (Ti-6Al-4V), Refrigerant: Helium (Water)
T2K Target outline assy.
into horn
Helium
supply
channel
Helium
return
Streamlines showing velocity in the helium.
Calc. by John Butterworth
T2K graphite target temperature distribution
immediately after first spill, beam 1 cm off-axis
John Butterworth
T2K graphite target temperature progression
during first 80 seconds
80 s
T2K graphite target shock-wave progression
over 50 µs after 5 µs beam spill (beam on axis).
7 MPa
(~OK?)
5 μs (end of
beam spill)
Irradiation Effect of Graphite
Expected radiation damage of the target
•
•
The approximation formula used by NuMI target group : 0.25dpa/year
MARS simulation
: 0.15~0.20 dpa/year
Dimension change … shrinkage by ~5mm in length in 5 years at maximum. ~75m in radius
Degradation of thermal conductivity … decreased by 97%
@ 200 C
70~80% @ 400 C
Magnitude of the damage strongly depends on the irradiation temperature.
•
It is better to keep the temperature of target around 400 ~ 800 C
400
600
800 1000
Irradiation
JAERI report (1991)
Temperature(℃)
-0.5%
2dpa
1dpa
800oC
400oC
Dimension change
Toyo-Tanso Co Ltd. IG-11
Thermal conductivity (After/Before)
1
2
3
(dpa)
A PSI pyrolytic graphite target after
c.1.2 x 1022 protons/cm2…
LS-Dyna
calculations for
shock-heating
of different
graphite wire
radii using
ISIS kicker
magnet power
supply
G. Skoro (Sheffield)
Summary of results so far:
•
Neutrino Factory:
• Shock waves in Ta characterised within limitations of
materials knowledge
• Effects of beam pulse length and multiple bunches/pulse
understood
•
Shock test of wire:
•
Power supply available which can supply necessary
current (8kA) within short enough time to generate
shocks of similar magnitude to those in NF
•
Method of remote temperature measurement of wire
fully tested – transient optical spectroscopy
•
VISAR to be purchased with sufficient time resolution
and velocity sensitivity to measure surface velocity of
wire and compare results with LS-Dyna calculations
Still to do:
Shock test of Ta wire:
•
•
•
•
•
Perform experiment
Work out how to extract material data from experiment
From lifetime test, predict lifetime of tantalum NF target
Repeat experiment with graphite:
•
Graphite is target material of choice for CNGS and T2K
(JPARC facility)
•
Serious candidate material for a NF