Will a T2K style target work for Euronu?

1. Packed Bed Target for EuronuDAVENNE, Tristan (RAL) ; LOVERIDGE, Peter (RAL) ; CARETTA, Ottone (RAL) ; DENSHAM, Chris (RAL) ; ZITO, Marco (CEA Saclay) ; LONGHIN, Andrea (CEA Saclay) ; LEPERS, Benjamin (Universite de Strasbourg) ; DRACOS, Marcos (Universite de Strasbourg) ; BOBETH, Christophe (Universite de Strasbourg)Fourth EUROnu Annual MeetingJune 12-15, 2012APC, Paris

2. ContentsBackground – Will a T2K style target work for EuronuWhy consider a packed bed target for EuronuSimple model of a packed bed –Sphere TemperatureSphere StressPressure DropResults Summary for EUROnuPacked Bed Target Concept –CFD Model resultsPacked Bed Target testingConclusions

3. Will a T2K style target work for Euronu? Steady-State Temperature Steady-State Stress T2K target - helium cooled graphite cylinder designed for 750kW beam power. Has operated successfully up to 200kW • Consider 4 x 1MW beryllium target (36kW deposited in target, beryllium preferred over graphite due to better resistance to radiation damage) • ‘low’ energy beam results in majority of heating at front of target • The large ΔT between the target surface and core leads to an excessive steady-state thermal stress • This ΔT depends on the material thermal conductivity and cannot be overcome by more aggressive surface cooling HTC = 10kW/m2K HTC = 10kW/m2K

4. “Pencil Shaped” Solid Target σy Steady-State Stress • Shorter conduction path to coolant • Thermal stress is reduced but off centre beam case and Inertial stress still a concern (+50MPa) 0 (MPa) 110 (MPa) 8 targets 6 targets 4 targets 3 targets 2 targets 1MW beam power produces peak steady state stress equivalent to yield stress of beryllium. Need more than 4 targets to have a viable solution for 4MW.

5. Why consider a packed bed target for Euronu? Small target segments result in low thermal stress and also low inertial stress (stress waves and excited natural frequencies) Not sensitive to off centre beam Structural integrity not dependant on target material Surface to volume ratio through out target enables significant heat removal while maintaining reasonable target temperature, (particularly suited to ‘low’ energy beam and high energy density) Points to note Lends itself to gas cooling High power designs require pressurised gas Bulk density lower than material density (approx factor of 2) may result in a reduction in yield compared to a solid target made of the same material. Suitable alternative materials with higher density may be available Some relevant papers: A helium gas cooled stationary granular target (Pugnat & Sievers) 2002 Conceptual Designs for a Spallation Neutron Target Constructed of a Helium-Cooled, Packed Bed of Tungsten Particles (Ammerman et al.) The “Sphere Dump” – A new low-cost high-power beam dump concept (Walz & Lucas) 1969

6. Simple packed bed target model W Assume parabolic energy deposition profile Obtain gas temperature as a function of transverse position

7. Sphere Temperature W Sphere core temperature is seen to depend on gas temperature and energy deposition, variation in thermal conductivity with temperature is also accounted for.

8. Sphere Stress Inertial dynamic component Peak dynamic stress in a 3mm Ti6Al4V sphere as a result of varying spill time (beam pulse length) calculated with FLUKA + Autodyn Oscillation period Ideally spill time > oscillation period Euronu spill time ~10 microseconds Inertial stress is negligible if expansion time << spill time Inertial stress is important if expansion time >> spill time

9. Sphere Stress Steady state thermal component W Determine stress from temperature gradient Youngs Modulus, E reduces with increasing temperature Compare stress to temperature dependant material yield strength for safety factor R Tc Ts

10. Pressure Drop W Use Ergun equation or similar correlation (e.g. Achenbach) to determine pressure drop through packed bed

11. Results Summary for EUROnu24mm wide cannister packed with 3mm diameter Ti6Al4V spheres. W 1.3MW looks relatively easy 4MW more challenging but does not look impossible

12. Packed Bed Target Concept Titanium alloy cannister containing packed bed of titanium or beryllium spheres Cannister perforated with elipitical holes graded in size along length Packed bed cannister in transverse flow configuration Model Parameters Proton Beam Energy = 4.5GeV Beam Power = 1MW Beam sigma = 4mm Packed Bed radius = 12mm Packed Bed Length = 780mm Packed Bed sphere diameter = 3mm Packed Bed sphere material : Titanium Coolant = Helium at 10 bar pressure

13. Packed Bed Model (FLUKA + CFX v13) Streamlines in packed bed Packed bed modelled as a porous domain Permeability and loss coefficients calculated from Ergun equation (dependant on sphere size) Overall heat transfer coefficient accounts for sphere size, material thermal conductivity and forced convection with helium Interfacial surface area depends on sphere size Acts as a natural diffuser flow spreads through target easily Velocity vectors showing inlet and outlet channels and entry and exit from packed bed

14. Helium Flow Helium Velocity Maximum flow velocity = 202m/s Maximum Mach Number < 0.2 Helium Gas Temperature Total helium mass flow = 93 grams/s Maximum Helium temperature = 857K =584°C Helium average outlet Temperature = 109°C

15. Titanium spheres High Temperature region Highest temperature Spheres occur near outlet holes due to the gas leaving the cannister being at its hottest Titanium temperature contours Maximum titanium temperature = 946K =673°C (N.B. Melting temp =1668°C)

16. Pressure Drop Pressure contours on a section midway through target Helium outlet pressure = 10bar Helium inlet pressure = 11.2bar Majority of pressure drop across holes and not across packed bed

17. Beam enters the target cannister through a beam window which separates target coolant from target station helium • Beryllium is a candidate material for the window • Peripheral or surface cooling look to be feasible options • Static and inertial stresses result from beam heating are manageable • Pressure stresses can be dealt with by having a hemispherical window design

18. Packed Bed Testing Induction heater test Graydon et al. Induction Heating Packed bed placed in an alternating magnetic field. Eddy currents induced in conductive spheres. Resultant Joule heating provides internal heating of spheres. Packed bed induction heating theory Duquenne et al.

19. Conclusions for EUROnu • A packed bed target has been adopted as the baseline target design for the EUROnusuperbeam. It offers • Inherently low steady state and inertial stress as well as tolerance to off-centre beams. • A potential design up to 4MW beam power while the more conventional solid target is limited to less than 1MW beam power. • A CFD model of a packed bed target concept for 1MW beam power indicates the feasibility of such a target. • Stress in window components, containment vessel, required operating pressure and radiation damage may be the limiting factors for a packed bed target, however heat dissipation is less of a problem. • Vibration levels and relative motion and wear between spheres is as yet an unknown and so an in-beam test would be useful. • Induction heating offers potential for an offline test of the heat transfer and pressure drop characteristics of a packed bed design.

20. Where does a Packed Bed Target fit? Beam Power ≈1MW 4MW+? ? Flowing Target - powder jet, mercury jet Solid Peripherally cooled Target Packed Bed or segmented Target Simple, well proven A bit more complex, less experience Much harder, very complex

21. Packed Bed Target for a neutrino factory? • A titanium packed bed offers a potential design to dissipate the heat load from a 4MW 4.5GeV proton beam. • The neutrino factory baseline beam pulse has a challenging 2ns pulse length. • Some evidence to suggest a low density neutrino factory target would offer comparable physics performance. J.Back

22. Neutrino Factory IDS report – target section requires review • Extract from International Design Study for the Neutrino Factory Interim Design Report • The IDS-NF collaboration • 19 October • “According to a MARS15 simulation [209, 251], 11% of the beam energy is deposited in the target, corresponding to 9 kJ/pulse at 50 Hz. This energy is deposited over two nuclear interaction lengths along the jet (30 cm, 15 cm3), so, noting that the specic heat of mercury is 4.7 J/cm3/K, the temperature rise of the mercury during a beam pulse is about 130 K. The boiling point of mercury is 357 C, so the mercury jet, which enters the target volume at room temperature, is not vaporised at 50-Hz operation. Although the mercury jet is not vaporised, it will be disrupted and dispersed by the pressure waves induced by the pulsed energy deposition.” • Notable errors • Peak energy deposition is calculated based on the assumption that the deposited energy is uniformly deposited throughout the target! • Value used for the heat capacity of mercury is incorrect (should be 140J/kgK) (4.7J/cc/K /13.7g/cc = 0.343J/g/K =343J/kgK) • Temperature jump is calculated as 130K and conclusion states that there will be no boiling of the mercury • Actual peak energy deposition in mercury with baseline parameters (8GeV, 1.2mm, 50Hz, 4MW) is in the order of 100J/g or 1000K temperature jump.

25. Temperature and stress in a uniformly heated sphere

26. Packed Bed Notes The Ergun equation, relates the friction factor in a packed column as a function to the Reynolds number: where fp and Grp are defined as where: Δp is the pressure drop across the bed,L is the length of the bed (not the column),Dp is the equivalent spherical diameter of the packing,ρ is the density of fluid,μ is the dynamic viscosity of the fluid,Vs is the superficial velocity(i.e. the velocity that the fluid would have through the empty tube at the same volumetric flow rate), andε is the void fraction of the bed (Bed porosity at any time). CFX v13 uses two Energy Equations, one for fluid and one for solid with interfacial heat transfer applied as an equivalent source/sink term in each equation. Overall heat transfer coefficient and interfacial area defined to account for thermal conductivity through solid components of packed bed as well as forced convection between gas and solid.

27. Energy Deposition calculated from FLUKA W FLUKA compound model used to determine energy deposited in target material R Tc Ts Temperature profile a function of energy deposition, Q, radius and thermal conductivity, k

28. Sphere Temperature W Heat conducting out of sphere = heat removed by forced convection Empirical Nusselt number correlation for heat transfer in packed bed (Achenbach et al.) Sphere core temperature can be determined