Shock Waves in Solid Targets

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Shock Waves in Solid Targets

• Preliminary Calculations

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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

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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.
  SFma
• Should be similar to Fluid Gravity code (older
  but material models the same?)

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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.
  SFma
• Should be similar to Fluid Gravity code (older
  but material models the same?)
• ANSYS
• Uses Implicit Time Integration
• Suitable for Quasi static problems ie SF0

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Implicit vs Explicit Time Integration

• Explicit Time Integration (used by LS Dyna)
• Central Difference method used
• Accelerations (and stresses) evaluated at time t
• Accelerations -gt velocities -gt displacements
• Small time steps required to maintain stability
• Can solve non-linear problems for non-linear
  materials
• Best for dynamic problems (SFma)

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Implicit vs Explicit Time Integration

• Implicit Time Integration (used by ANSYS) -
• Finite Element method used
• Average acceleration calculated
• Displacements evaluated at time t?t
• 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 (SF0)

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Study by Alec Milne Fluid Gravity Engineering
Limited

• Cylindrical bar 1cm in radius is heated
  instantaneously from 300K to 2300K and left to
  expand

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Study by Alec Milne, Fluid Gravity Engineering
Limited
The y axis is radius (metres)
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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.

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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 ar?T 65 microns
• 2. The calculation is for ?T 1000 K, whereas
• for a Nufact target ?T 100 K

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Can ANSYS be used to study proton beam induced
shockwaves?

• Equation of state giving shockwave velocity

For tantalum c0 3414 m/s
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Can ANSYS be used to study proton beam induced
shockwaves?

• Equation of state giving shockwave velocity

For tantalum c0 3414 m/s Cf ANSYS implicit
wave propagation velocity
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ANSYS benchmark study same conditions as Alec
Milne/FGES study i.e.?T 1000 K
The y axis is radial deflection (metres)
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Comparison between Alec Milne/FGES and ANSYS
results
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ANSYS benchmark study same conditions as Alec
Milne/FGES study - EXCEPT ?T 100 K (not 1000 K)
Surface deflections in 1 cm radius Ta rod over 20
µs after instantaneous uniform temperature jump
of 100 K
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ANSYS benchmark study same conditions as Alec
Milne/FGES study - EXCEPT ?T 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
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ANSYS benchmark study same conditions as Alec
Milne/FGES study - EXCEPT ?T 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 Cf static case
400 x 106 Pa
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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

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Elastic shock waves in a candidate solid Ta
neutrino factory target
Temperature jump after 1 ns pulse (Initial
temperature 2000K )
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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)
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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?)

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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

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Elastic shock wave studies for draft ISOLDE
proposal
Temperature jump after 2.4 µs pulse (Initial
temperature 2000K )
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Elastic shock wave studies for draft ISOLDE
proposal
Temperature profile at centre of cylinder over 4
x 250 ns bunches
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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
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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)
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Comparison between Nufact target and ISOLDE test
Peak power density 300 J/cc in both cases
Temperature jump after 2.4 µs pulse (Initial
temperature 2000K )
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Effect of pulse length on shockwave magnitude