1. UKNFWG 12 January 2005Chris Densham Shock Waves in Solid Targets Preliminary Calculations

2. UKNFWG 12 January 2005Chris Densham 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

3. UKNFWG 12 January 2005Chris Densham 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?)

4. UKNFWG 12 January 2005Chris Densham 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

5. UKNFWG 12 January 2005Chris Densham 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)

6. UKNFWG 12 January 2005Chris Densham 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)

7. UKNFWG 12 January 2005Chris Densham Study by Alec Milne Fluid Gravity Engineering Limited “Cylindrical bar 1cm in radius is heated instantaneously from 300K to 2300K and left to expand”

8. UKNFWG 12 January 2005Chris Densham The y axis is radius (metres) Study by Alec Milne, Fluid Gravity Engineering Limited

9. UKNFWG 12 January 2005Chris Densham 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.”

10. UKNFWG 12 January 2005Chris Densham 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 microns 2.The calculation is for ΔT = 1000 K, whereas for a Nufact target ΔT ≈ 100 K

11. UKNFWG 12 January 2005Chris Densham Can ANSYS be used to study proton beam induced shockwaves? Equation of state giving shockwave velocity: For tantalum c 0 = 3414 m/s

12. UKNFWG 12 January 2005Chris Densham Can ANSYS be used to study proton beam induced shockwaves? Equation of state giving shockwave velocity: For tantalum c 0 = 3414 m/s Cf: ANSYS implicit wave propagation velocity :

13. UKNFWG 12 January 2005Chris Densham ANSYS benchmark study: same conditions as Alec Milne/FGES study i.e.ΔT = 1000 K The y axis is radial deflection (metres)

14. UKNFWG 12 January 2005Chris Densham Comparison between Alec Milne/FGES and ANSYS results Alec Milne/ FGES ANSYS Amplitude of initial radial oscillation 100 μm120 μm Radial oscillation period 7.5 μs8.3 μs Mean expansion/ deformation 150 μm plastic deformation 160 μm elastic deformation

15. UKNFWG 12 January 2005Chris Densham 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

16. UKNFWG 12 January 2005Chris Densham 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

17. UKNFWG 12 January 2005Chris Densham ANSYS benchmark study: same conditions as Alec Milne/FGES study - EXCEPT ΔT = 100 K (not 1000 K) = 400 x 10 6 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:

18. UKNFWG 12 January 2005Chris Densham 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

19. UKNFWG 12 January 2005Chris Densham Elastic shock waves in a candidate solid Ta neutrino factory target Temperature jump after 1 ns pulse (Initial temperature = 2000K )

20. UKNFWG 12 January 2005Chris Densham 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)

21. UKNFWG 12 January 2005Chris Densham 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?)

22. UKNFWG 12 January 2005Chris Densham

23. UKNFWG 12 January 2005Chris Densham 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

24. UKNFWG 12 January 2005Chris Densham Elastic shock wave studies for draft ISOLDE proposal Temperature jump after 2.4 μs pulse (Initial temperature = 2000K )

25. UKNFWG 12 January 2005Chris Densham Elastic shock wave studies for draft ISOLDE proposal Temperature profile at centre of cylinder over 4 x 250 ns bunches

26. UKNFWG 12 January 2005Chris Densham 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

27. UKNFWG 12 January 2005Chris Densham 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)

28. UKNFWG 12 January 2005Chris Densham Comparison between Nufact target and ISOLDE test Temperature jump after 2.4 μs pulse (Initial temperature = 2000K ) Peak power density = 300 J/cc in both cases

29. UKNFWG 12 January 2005Chris Densham Effect of pulse length on shockwave magnitude