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

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

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

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] 3.3 kJ/pulse @ 12.5 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

Beryllium Material Properties 5 Peter Loveridge, January 2011

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

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

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

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

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

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

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

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

General Conclusions and Future Work 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 Beam High pressure helium gas 14 Peter Loveridge, January 2011