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
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. Time averaged heat input load
ANSYS Model Setup
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] Hz
well centred beam, sigma = 4mm
Uniform heat transfer coefficient applied at the outer surface
Beam
Time averaged heat input load 4
Peter Loveridge, January 2011

5. Beryllium Material Properties5
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
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
Elastic stress waves propagate at the speed of sound in the target material
They act in addition to the “quasi-static” thermal stress
Single beam spill
Gauge-point 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
The combined stress-magnitude generated by a combination of
1. the “quasi-static” steady-state stress ( 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
Beam
High pressure helium gas 14
Peter Loveridge, January 2011