uknfwg 12 january 2005chris densham shock waves in solid targets preliminary calculations
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Shock Waves in Solid Targets
Preliminary Calculations
Codes used for study of shock waves
• Specialist codes eg used by Fluid Gravity Engineering Limited – Arbitrary Lagrangian-Eulerian (ALE) codes (developed for military)
Developed for dynamic e.g. impact problems ALE not relevant? – Useful for large deformations where mesh would
become highly distorted Expensive and specialised
Codes used for study of shock waves
• Specialist codes eg used by Fluid Gravity Engineering Limited – Arbitrary Lagrangian-Eulerian (ALE) codes (developed for military)
Developed for dynamic e.g. impact problems ALE not relevant? – Useful for large deformations where mesh would
become highly distorted
Expensive and specialised
• LS-Dyna
Uses Explicit Time Integration (ALE method is included)
– suitable for dynamic e.g. Impact problems i.e. ΣF=ma Should be similar to Fluid Gravity code (older but material models the
same?)
Codes used for study of shock waves
• Specialist codes eg used by Fluid Gravity Engineering Limited – Arbitrary Lagrangian-Eulerian (ALE) codes (developed for military)
Developed for dynamic e.g. impact problems ALE not relevant? – Useful for large deformations where mesh would
become highly distorted Expensive and specialised
• LS-Dyna
Uses Explicit Time Integration (ALE method is included)
– suitable for dynamic e.g. Impact problems i.e. ΣF=ma Should be similar to Fluid Gravity code (older but material models the
same?)
• ANSYS
Uses Implicit Time Integration Suitable for ‘Quasi static’ problems ie ΣF≈0
Implicit vs Explicit Time Integration
Explicit Time Integration (used by LS Dyna)
• Central Difference method used
• Accelerations (and stresses) evaluated at time t
• Accelerations -> velocities -> displacements
• Small time steps required to maintain stability
• Can solve non-linear problems for non-linear materials
• Best for dynamic problems (ΣF=ma)
Implicit vs Explicit Time Integration
Implicit Time Integration (used by ANSYS) -
• Finite Element method used
• Average acceleration calculated
• Displacements evaluated at time t+Δt
• Always stable – but small time steps needed to capture transient response
• Non-linear materials can be used to solve static problems
• Can solve non-linear (transient) problems…
• …but only for linear material properties
• Best for static or ‘quasi’ static problems (ΣF≈0)
Study by Alec Milne Fluid Gravity Engineering Limited
“Cylindrical bar 1cm in radius is heated instantaneously from 300K to 2300K and left to expand”
The y axis is radius (metres)
Study by Alec Milne, Fluid Gravity Engineering Limited
Study by Alec Milne Fluid Gravity Engineering Limited
Alec Milne:“We find that these models predict there is the potential
for a problem […]. These results use 4 different material models. All of these show that the material expands and then oscillates about an equilibrium position. The oscillations damp down but the new equilibrium radius is 1.015cm. i.e. an irreversible expansion of 150 microns has taken place. The damping differs from model to model. The key point is all predict damage.”
Study by Alec Milne Fluid Gravity Engineering Limited
Alec Milne:“We find that these models predict there is the potential for
a problem […]. These results use 4 different material models. All of these show that the material expands and then oscillates about an equilibrium position. The oscillations damp down but the new equilibrium radius is 1.015cm. i.e. an irreversible expansion of 150 microns has taken place. The damping differs from model to model. The key point is all predict damage.”
NB:1. Thermal expansion αrΔT = 65 microns2. The calculation is for ΔT = 1000 K, whereas
for a Nufact target ΔT ≈ 100 K
Can ANSYS be used to study proton beam induced shockwaves?
Equation of state giving shockwave velocity:
20 pps qusucu
For tantalum c0 = 3414 m/s
Can ANSYS be used to study proton beam induced shockwaves?
Equation of state giving shockwave velocity:
20 pps qusucu
For tantalum c0 = 3414 m/s
Cf: ANSYS implicit wave propagation velocity :
smE
c /334516600
107.185 9
ANSYS benchmark study: same conditions as Alec Milne/FGES study i.e.ΔT = 1000 K
The y axis is radial deflection (metres)
Comparison between Alec Milne/FGES and ANSYS results
Alec Milne/ FGES
ANSYS
Amplitude of initial radial oscillation
100 μm 120 μm
Radial oscillation period
7.5 μs 8.3 μs
Mean expansion/ deformation
150 μm plastic
deformation
160 μm elastic
deformation
ANSYS benchmark study: same conditions as Alec Milne/FGES study - EXCEPT ΔT = 100 K (not 1000 K)
Surface deflections in 1 cm radius Ta rod over 20 μs after ‘instantaneous’ uniform temperature jump of 100 K
ANSYS benchmark study: same conditions as Alec Milne/FGES study - EXCEPT ΔT = 100 K (not 1000 K)
Elastic stress waves in 1 cm radius Ta rod over 20 μs after ‘instantaneous’ (1ns) pulse
Stress (Pa) at : centre (purple) and outer radius (blue)
Surface deflections in 1 cm radius Ta rod over 20 μs after ‘instantaneous’ uniform temperature jump of 100 K
ANSYS benchmark study: same conditions as Alec Milne/FGES study - EXCEPT ΔT = 100 K (not 1000 K)
21
),(,,
TE
trzr
= 400 x 106 Pa
Elastic stress waves in 1 cm radius Ta rod over 20 μs after ‘instantaneous’ (1ns) pulse
Stress (Pa) at : centre (purple) and outer radius (blue)
Surface deflections in 1 cm radius Ta rod over 20 μs after ‘instantaneous’ uniform temperature jump of 100 K
Cf static case:
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)
Material model data
- At high temperatures material data is scarce…
- Hence, need for experiments to determine material model data e.g.
- Standard flyer-plate surface shock wave experiment (difficult at high temperatures and not representative of proton beam loading conditions)
- Scanning electron beam (can achieve stress and thermal cycling ie fatigue but no ‘shock’ wave generated)
- Current pulse through wire (JRJB talk)
- Experiment at ISOLDE (Is it representative? Can we extract useful data?)
Elastic shock wave studies for draft ISOLDE proposal
• 3 mm diameter Ta cylinder
• Beam diameter = 1 mm (parabolic distribution for simplicity)
• Peak power deposited = 300 J/cc
• Pulse length = 4 bunches of 250 ns in 2.4 μs
Elastic shock wave studies for draft ISOLDE proposal
Temperature jump after 2.4 μs pulse
(Initial temperature = 2000K )
Elastic shock wave studies for draft ISOLDE proposal
Temperature profile at centre of cylinder over 4 x 250 ns bunches
Elastic shock wave studies for draft ISOLDE proposal
Temperature profile at centre of cylinder over 4 x 250 ns bunches
Radial displacements of target cylinder surface during and after pulse
Elastic shock wave studies for draft ISOLDE proposal
Temperature profile at centre of cylinder over 4 x 250 ns bunches
Elastic stress waves target rod over 5 μs during and after pulse
Stress (Pa) at : centre (blue) outer radius (purple)beam outer radius
(red)
Comparison between Nufact target and ISOLDE test
Temperature jump after 2.4 μs pulse
(Initial temperature = 2000K )
-1.00E+09 -5.00E+08 0.00E+00 5.00E+08 1.00E+09 1.50E+09
Maximum negative stress(r=0)
Shockwave oscillationamplitude (r=0)
Maximum stress at surface
Shockwave oscillationamplitude at surface
Stress (Pa)
ISOLDE test
Nufact target
Peak power density = 300 J/cc in both cases
Effect of pulse length on shockwave magnitude
-8.00E+08
-6.00E+08
-4.00E+08
-2.00E+08
0.00E+00
2.00E+08
4.00E+08
6.00E+08
8.00E+08
1.00E+09
1.20E+09
1.00E-08 1.00E-07 1.00E-06 1.00E-05Proton beam pulse length (s)
Str
ess
(Pa)
Maximum negative stress(r=0)
Shockwave oscillation amplitude (r=0)
Maximum stress at surface
Shockwave oscillation amplitude at surface
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