Post on 23-Dec-2015
Packed Bed Target for Euronu
DAVENNE, 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, 2012
APC, Paris
ContentsBackground – Will a T2K style target work for EuronuWhy consider a packed bed target for Euronu
Simple model of a packed bed –Sphere TemperatureSphere StressPressure DropResults Summary for EUROnu
Packed Bed Target Concept –CFD Model results
Packed Bed Target testing
Conclusions
Will a T2K style target work for Euronu?
48 (°C) 255 (°C) 0 (MPa) 220 (MPa)
Steady-State Temperature Steady-State Stress
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/m2 K
HTC = 10kW/m2 K
T2K target - helium cooled graphite cylinder designed for 750kW beam power. Has operated successfully up to
200kW
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.
Steady-State AnalysisBeryllium Target
Surface HTC = 10,000 W/m2K
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“Pencil Shaped” Solid Target
– Shorter conduction path to coolant– Thermal stress is reduced but off
centre beam case and Inertial stress still a concern (+50MPa)
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
Simple packed bed target model
W
Assume parabolic energy deposition profile
Obtain gas temperature as a function of transverse position
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.
Sphere Stress Inertial dynamic component
Inertial stress is negligible if expansion time << spill timeInertial stress is important if expansion time >> 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
Euronu spill time ~10 microseconds
Sphere Stress Steady state thermal component
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R TcTs
Determine stress from temperature
gradient
Compare stress to temperature
dependant material yield strength for
safety factor
Youngs Modulus, E reduces with increasing
temperature
Pressure Drop
W
Use Ergun equation or similar correlation (e.g. Achenbach) to determine pressure drop through packed bed
Results Summary for EUROnu24mm wide cannister packed with 3mm diameter Ti6Al4V spheres.
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Beam Energy
Beam Sigma
Target Width
Beam Power
Sphere material
Sphere diameter
Helium pressure
Maximum Power
Deposition
Maximum Helium
TemperatureSphere Core Temperature
Max Sphere VM Stress
Minimum Yield Stress /
VM StressPressure
Drop4.5 GeV 4mm 24mm 1MW Ti6Al4V 3mm 10bar 2.2e9W/m3 133°C 296°C 49MPa 11.7 0.45bar4.5 GeV 4mm 24mm 1.3MW Ti6Al4V 3mm 10bar 2.9e9W/m3 133°C 331°C 65MPa 8.7 0.73bar4.5 GeV 4mm 24mm 4MW Ti6Al4V 3mm 10bar 8.8e9W/m3 200°C 650°C 116MPa 3.8 2.8bar4.5 GeV 4mm 24mm 4MW Ti6Al4V 3mm 20bar 8.8e9W/m3 133°C 557°C 140MPa 3.2 3.4bar4.5 GeV 4mm 24mm 4MW Ti6Al4V 3mm 20bar 8.8e9W/m3 200°C 650°C 116MPa 3.8 1.4bar
INPUTS LIMITING FACTORS
1.3MW looks relatively easy4MW more challenging but does not look impossible
Packed Bed Target Concept
Packed bed cannister in transverse flow configuration
Model ParametersProton Beam Energy = 4.5GeVBeam Power = 1MWBeam sigma = 4mmPacked Bed radius = 12mmPacked Bed Length = 780mmPacked Bed sphere diameter = 3mmPacked Bed sphere material : TitaniumCoolant = Helium at 10 bar pressure
Titanium alloy cannister containing packed bed of titanium or beryllium spheres
Cannister perforated with elipitical holes graded in size along length
Packed Bed Model (FLUKA + CFX v13)
Streamlines in packed bedPacked bed modelled as a porous domainPermeability 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
Helium Flow
Helium Gas TemperatureTotal helium mass flow = 93 grams/sMaximum Helium temperature = 857K
=584°CHelium average outlet Temperature
= 109°C
Helium VelocityMaximum flow velocity = 202m/sMaximum Mach Number < 0.2
Titanium spheres
Titanium temperature contoursMaximum titanium temperature = 946K
=673°C (N.B. Melting temp =1668°C)
High Temperature regionHighest temperature Spheres occur near outlet
holes due to the gas leaving the cannister being at its hottest
Pressure DropPressure contours on a section midway through targetHelium outlet pressure = 10bar Helium inlet pressure = 11.2barMajority of pressure drop across holes and not across packed bed
• 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
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Frequency [Hz]
Ie=100Amps, N=25 turns
Ie=100Amps, N=50 turns
Ie=100Amps, N=75 turns
Packed Bed Testing
Packed bed induction heating theory
Duquenne 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.
Induction heater testGraydon et al.
Conclusions for EUROnu
• A packed bed target has been adopted as the baseline target design for the EUROnu superbeam. 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.
Solid Peripherally cooled Target
Packed Bed or segmented Target
Flowing Target - powder jet, mercury jet
Beam Power ≈1MW 4MW+? ?
Limiting factors
Heat Transfer AreaThermal and Inertial
StressOff axis beam
Helium PressureRadiation damage
Window components
ReliabilityComplexity
Development Time
Where does a Packed Bed Target fit?
Simple, well proven A bit more complex, less experience Much harder, very complex
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
Neutrino Factory IDS report – target section requires reviewExtract from International Design Study for the Neutrino Factory Interim Design ReportThe IDS-NF collaboration19 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.
Figure 4 Variation of Youngs Modulus with Temperature for Ti6Al4V ref: Iter Material Properties Handbook
Figure 5 Variation of thermal conductivity with Temperature for Ti6Al4V ref: Iter Material Properties Handbook
Figure 6 Variation of specific heat capacity with Temperature for Ti6Al4V ref: Iter Material Properties Handbook
Figure 7 Variation of yield strength with Temperature for Ti6Al4V ref: Iter Material Properties Handbook
Figure 8 Variation of thermal expansion coefficient with Temperature for Ti6Al4V ref: ASM material data sheet
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Temperature and stress in a uniformly heated sphere
Packed Bed Notes
The Ergun equation, relates the friction factor in a packed column as a function to the Reynolds number:
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), and
is the void fraction of the bed ε (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.
where fp and Grp are defined as
Energy Deposition calculated from FLUKA
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FLUKA compound model used to determine energy deposited
in target material
Temperature profile a function of energy deposition, Q, radius
and thermal conductivity, k
R TcTs
Sphere Temperature
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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