Thermo-mechanical Stress in a Beryllium Superbeam Target for EUROnu (Separate target and horn)

1. Thermo-mechanical Stress in a Beryllium Superbeam Target for EUROnu(Separate target and horn) Peter Loveridge High Power Targets Group Rutherford Appleton Laboratory, UK P.Loveridge@rl.ac.uk January 2011 1

2. Introduction • Analysed the thermal stresses induced in a cylindrical beryllium superbeam target for EUROnu using FLUKA and ANSYS simulations • “Quasi-static” thermal stress • Driven by non-uniform heating • Acoustic stress waves • Arise due to “short” duration of the applied heating 2 Peter Loveridge, January 2011

3. Analysis Procedure (ANSYS) • Multi-stage process involving linked FLUKA and ANSYS simulations • Can choose which physical timescales to investigate: • “Quasi-static” thermal stress[thermal conduction timescales of the order ~seconds] • Inertial stress due to bulk oscillations (“violin modes”)[1st mode period typically of the order ~milliseconds] • Elastic (acoustic) stress wave propagation[characteristic time period of the order ~microseconds] A typical process flow diagram for beam induced heating analysis 3 Peter Loveridge, January 2011

4. ANSYS Model Setup Beam • Beryllium cylinder Ø30mm L780mm, cantilevered from the upstream end • 1 MW beam power on target (concept is 4 targets in 4 horns) • 1.11e14 protons/pulse, 4.5 GeV, 12.5 Hz repetition rate • 41 kW time averaged power in target [FLUKA] • 3.3 kJ/pulse @ 12.5 Hz • well centred beam, sigma = 4mm • Uniform heat transfer coefficient applied at the outer surface Time averaged heat input load 4 Peter Loveridge, January 2011

5. Beryllium Material Properties 5 Peter Loveridge, January 2011

6. Beryllium Material Properties Note degradation in strength at elevated temperature Suggest to limit Tmax to, say ~250°C ? Need to define a design stress limit as some fraction of σy 6 Peter Loveridge, January 2011

7. Single Spill Effects (Quasi-Static stress) • Q. What is the effect of a single beam spill? • At room temperature a single spill generates a ΔT of 19°C and a Von-Mises stress of 28 MPa • At elevated temperatures the ΔT is somewhat reduced (see temperature dependent material properties) 0°C 19°C 0MPa 28MPa Temperature increase (left) and Von-Mises thermal stress (right) corresponding to a single beam spill at room temperature • i.e. the effect of each individual beam spill is quite modest 7 Peter Loveridge, January 2011

8. Steady State Operation (Quasi-Static stress) • Q. What is the cumulative effect of a large number of beam pulses? • Radial ΔT depends on average power and thermal conductivity • This drives the “quasi-static” thermal stress magnitude • Surface temperature depends on heat transfer coefficient • To limit the max steady-state core temperature to say ~ 250°C we need HTC = 10 kW/m2K, Tbulk = 30°C • Seems reasonable for direct water cooling Temperature (left) and and Von-Mises thermal stress (right) corresponding to a steady state operation with a surface HTC = 10kW/m2K, bulk fluid temp = 30°C 8 Peter Loveridge, January 2011

9. Steady State Operation Results Summary σy σy Results summary for steady-state analysis 8 targets 6 targets 4 targets 3 targets 2 targets 9 Peter Loveridge, January 2011

10. Quasi-Static Stress: Conclusions • The high beam repetition rate (12.5 Hz) means that each individual pulse generates only a modest ΔT (19°C) and thermal stress (28MPa) • However, the large average power on target (~40kW) leads to a significant thermal stress at steady-state operation • 1 MW beam power per target looks challenging in terms of safety factor on yield stress 10 Peter Loveridge, January 2011

11. Elastic Stress-Waves Single beam spill Gauge-point • Elastic stress waves propagate at the speed of sound in the target material • They act in addition to the “quasi-static” thermal stress 11 Peter Loveridge, January 2011

12. Effect Of Spill Time • Stress-waves are only generated where the spill time is short with respect to the characteristic dimensions and speed of sound in the target. ~50 MPa 12 Peter Loveridge, January 2011

13. Elastic Stress-Waves: Conclusions • EUROnu spill time is likely to be short enough to generate acoustic stress waves in a beryllium target • Need to allow for ~50 MPa in addition to the “quasi-static” thermal stress 13 Peter Loveridge, January 2011

14. General Conclusions and Future Work High pressure helium gas Beam • The combined stress-magnitude generated by a combination of 1. the “quasi-static” steady-state stress (220 - 240 MPa) 2. the acoustic stress waves (50 MPa) 3. off centre beam induced “violin modes” ( ?? MPa) appear too large for a solid beryllium target operating at 1 MW average beam power. (recall Beryllium σy ~225 MPa) • Suggest to investigate the following: • “Sharp pencil” geometry 14 Peter Loveridge, January 2011