1. Packed Bed Target Design Concept (for EURONu) Tristan Davenne, Ottone Caretta, Peter Loveridge, Chris Densham (RAL); Andrea Longhin, Marco Zito (CEA Saclay) ; Benjamin Lepers, Christophe Bobeth, Marcos Dracos (Universite de Strasbourg) 4th High Power Targetry Workshop May 2 nd to May 6 th 2011 Malmö, Sweden Organized by the European Spallation Source, Lund

2. Introduction Relevant papers: A helium gas cooled stationary granular target (Pugnat & Sievers) 2002 [considered for a neutrino factory target with 4MW beam] Conceptual Designs for a Spallation Neutron Target Constructed of a Helium-Cooled, Packed Bed of Tungsten Particles (Ammerman et al.) [ATW, 15MW power deposited, 36cm diameter] Sievers 2001

3. Why consider a packed bed target? Large surface to volume ratio, large surface area for heat transfer Coolant can pass close to maximum energy deposition High heat transfer coefficients Low quasi static thermal stress Low inertial stress If stress levels in a simpler ‘T2K style’ solid target are unacceptable.

4. EURONu Example Beam KE: 4.5GeV 1.11e14 protons/bunch Frequency: 12.5Hz Beam Sigma: 4mm Beam Power: 1-1.3MW (x4) Consider peripherally cooled Beryllium or Graphite cylinder

5. Stress in a EURONu solid peripherally cooled beryllium target Peter Loveridge, January 2011 Reached limit for a solid peripherally cooled target What is heat dissipation capability of a packed bed target? 2 targets3 targets4 targets6 targets8 targets σyσy σyσy

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

7. Energy Deposition calculated with FLUKA Half Density material model does not give peak energy density in a sphere

8. Sphere Temperature ‘Steady State’ 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 Temperature profile a function of uniform energy deposition, Q, radius and thermal conductivity, k

9. Sphere Temperature ‘Steady State’ Sphere core temperature is seen to depend on gas temperature and energy deposition, variation in thermal conductivity with temperature is also accounted for.

10. Sphere Stress - Quasi static thermal component R Tc Ts Determine stress from temperature gradient Compare stress to temperature dependant material yield strength for safety factor Youngs Modulus, E reduces with increasing temperature

11. Sphere Stress - Inertial dynamic component Inertial stress is negligible if oscillation period << spill time Inertial stress is important if oscillation period >> spill time 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

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

13. Example Case for EURONu 24mm diameter cannister packed with 3mm diameter Ti6Al4V spheres.

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

15. 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

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

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

18. Cannister components Internal Temperatures Outer Can Surface Temp Almost Symmetric Temperature contours Maximum surface Temperature = 426K = 153°C

19. 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

20. Packed Bed Testing References of interest: “Particle to fluid heat transfer in water fluidized systems” Holman et al. Used 30kW induction heater to investigate heat transfer from steel and lead spheres down to 1/16 inch diameter “Fluid-particle heat transfer in packed beds” Baumeister et al. Induction heating of air cooled 3/8 inch steel spheres “Development of a Forced-Convection Liquid-Fluoride-Salt Test Loop” Graydon et al. ORNL Induction heating of 3cm diameter graphite spheres and rods, 30kHz supply providing 200kW to the spheres (1.2kW per sphere) Graphite pebble bed Graydon et al. 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.

21. Packed Bed Testing Packed bed induction heating theory Duquenne et al.

22. Work required to develop this target concept Detailed design consideration of window and containment, thermal and stress analysis. Consideration of damage to packed spheres due to relative movement and abrasion between spheres. Testing to validate CFD models. Testing to evaluate induced vibrations and movements within the packed bed.