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

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Assume parabolic energy deposition profile

Obtain gas temperature as a function of transverse position

Sphere Temperature

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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

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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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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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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