investigation of a “pencil shaped” solid target peter loveridge, mike fitton, ottone caretta...
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Investigation of a “Pencil Shaped” Solid Target
Peter Loveridge, Mike Fitton, Ottone Caretta
High Power Targets Group
Rutherford Appleton Laboratory, UK
January 2011
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Introduction
EUROnu Annual Meeting, January 2011
• EUROnu target-station scheme has 4 targets and 4 horns– Each target exposed to ¼ of the total beam power (1.11e14 protons/pulse, 4.5 GeV, 12.5
Hz repetition rate)– Reduced Beam induced heating in target by a factor of 4
• Baseline target technology is a solid beryllium rod, peripherally cooled
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protonsprotons
protonsprotons
2.5 m
2.5 m
protonsprotons
protonsprotons
Beam Separator4 MW Proton
beam from accumulator
at 50 Hz
4 x 1MW Proton beam each at
12.5 Hz
Decay Volume
Target Station (4 targets, 4 horns)
Beryllium Material PropertiesElastic Modulus
0
50
100
150
200
250
300
350
0 100 200 300 400 500 600
Temperature [C]
[GP
a]
Poisson Ratio
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0 100 200 300 400 500 600
Temperature [C]
[ -
]
Heat Capacity
0
500
1000
1500
2000
2500
3000
3500
0 100 200 300 400 500 600
Temperature [C]
[J/k
g.K
]
Linear Expansion Coefficient
0
5
10
15
20
25
0 100 200 300 400 500 600
Temperature [C]
[x10
-6 /K
]
Thermal Conductivity
0
25
50
75
100
125
150
175
200
0 100 200 300 400 500 600
Temperature [C]
[W/m
.K]
Electrical Resistivity
0
5
10
15
20
25
30
0 100 200 300 400 500 600
Temperature [C]
[µΩ
.cm
]
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Beryllium Material PropertiesElastic Modulus
0
50
100
150
200
250
300
350
0 100 200 300 400 500 600
Temperature [C]
[GP
a]
Poisson Ratio
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0 100 200 300 400 500 600
Temperature [C]
[ -
]
Heat Capacity
0
500
1000
1500
2000
2500
3000
3500
0 100 200 300 400 500 600
Temperature [C]
[J/k
g.K
]
Linear Expansion Coefficient
0
5
10
15
20
25
0 100 200 300 400 500 600
Temperature [C]
[x10
-6 /K
]
Thermal Conductivity
0
25
50
75
100
125
150
175
200
0 100 200 300 400 500 600
Temperature [C]
[W/m
.K]
Electrical Resistivity
0
5
10
15
20
25
30
0 100 200 300 400 500 600
Temperature [C]
[µΩ
.cm
]
Note degradation in strength at elevated temperature
Suggest to limit Tmax to, say ~300°C ?
Need to define a design stress limit as some fraction of σy say, ~160 MPa ?
Strength of BerylliumRef: ITER Material Properties Handbook,
minimum fit to data
0
50
100
150
200
250
300
350
400
0 100 200 300 400 500 600 700 800
Temperature [°C]
[MP
a]
Yield Strength
UTS
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Motivation for a “Pencil shaped” target
• Need to find a way to reduce the high steady-state thermal stress present in the case of a solid cylindrical beryllium target
– Stress driven by large radial temperature variation at thermal equilibrium
• A potential solution – place the cooling fluid closer to the region peak energy deposition in the target
– Shorter conduction path– Reduced ΔT between surface and location of Tmax– Tmax is reduced – more favourable material properties– Lower thermal stress
• Engineering solutions being considered:– “Pencil shaped” solid target - PL– Packed pebble bed target - TD
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“Pencil” Target Concept Design
• Pencil shaped Beryllium target contained within a Titanium “can”• Pressurised Helium gas cooling, outlet at 10 bar• Supported as a cantilever from the upstream end
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BEAM
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Drawing not to scale!
He In
He
Out
Titanium “Can” Beryllium Target
Beam Window Intermediate tube
Geometry Parameterisation
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Length 800 mm
Ø2
4 m
m
(r =
3σ
)
A
B C
Beam
Deposited beam energy in three example beryllium targets
Cylinder “Pencil” Cone
EUROnu Annual Meeting, January 2011
Deposited Energy (FLUKA)
• Benefits of a cone shape (compared to a cylinder):– Integrated heat load is reduced (less material in front of the beam?)– Coolant fluid in close proximity to the region of maximum heat deposition
Cylinder: Ø24 mm, 800 mm long
Integrated Heat Load 2.9 kJ/pulsei.e. 36 kW heating from 1 MW beam
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Cone: 1 mm < Ø < 24 mm, 800 mm longIntegrated Heat Load 2.0 kJ/pulse
i.e. 24 kW heating from 1 MW beam
EUROnu Annual Meeting, January 2011
Well Centred Beam (Standard Operating Case)
• Results from steady-state thermo-mechanical analysis:– Need surface HTC of the order 4kW/m2K in order to limit Tmax to ~300°C– Gives max stress = 83 MPa
Temperature (left) and Von-Mises thermal stress (right) corresponding to a steady state operation with a surface HTC = 4kW/m2K, bulk fluid temp = 30°C
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Uniform HTC = 4kW/m2 K
72°C 318°C 0MPa 83MPa
Off Centre Beam (Accident Case)
• Results from steady-state thermo-mechanical analysis:– Total heat load is reduced in the case of the beam being mis-steered– Location of Tmax moves downstream
Energy deposition (left) and temperature corresponding to a steady state operation with a surface HTC = 4kW/m2K, bulk fluid temp = 30°C (right)
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Lateral beam position offset = 2 x beam sigma: Integrated Heat Load 21.2 kJ/pulsei.e. 14 kW heating from 1 MW beam
34°C 201°C
Uniform HTC = 4kW/m2 K
Off Centre Beam (Accident Case)
• Lateral deflection due to steady-state off-centre heating:– 13 mm lateral deflection if cantilevered from downstream end– Max stress increased to 120 MPa (recall 83 MPa in well centred beam case)
Deflection (left) and Von-Mises thermal stress (right) corresponding to a laterally mis-steered beam
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0 mm 13 mm 0MPa 120MPa
CFX conjugate heat transfer model
• Cooling fluid = Helium• Turbulence model = Shear Stress Transport (SST)• Inlet mass flow rate = 60g/s• Inlet temperature = 300K• Outlet Pressure = 10bar• Heat deposition in target = 24kW steady state from Fluka simulation• Model of 36° slice (1/10th of target) with symmetry boundary conditions
• Cooling channel outer surface defined by 3 radii and connected with spline
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TargetHeliumInlet
Outlet
Radius 1 Radius 2 Radius 30.4m 0.4m
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Mesh at downstream end of target
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Boundary layer inflation
Fluid Domain
Solid Domain
EUROnu Annual Meeting, January 2011
Linear cooling channel (Equal area at both ends)
Cooling channel
R1 = 7.2mm
R2 = 10.6mm
R3 = 14mm
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4kW/m2.K
Helium velocity minimum at peak heat
Design 1
EUROnu Annual Meeting, January 2011
Constant area (at R1, R2 & R3) cooling channel
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Cooling channel
R1 = 7.2mm
R2 = 9.5mm
R3 = 14mm
4kW/m2.K
Helium velocity maximum here due to gas heating
Design 2
EUROnu Annual Meeting, January 2011
Cooling channel area reduced at centre & increased at ends (2)
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Cooling channel
R1 = 9mm
R2 = 9mm
R3 = 14.4mm
4kW/m2.K
Design 3
Helium velocity maximum at peak heat
EUROnu Annual Meeting, January 2011
Helium Cooling Summary
• Beryllium target can be cooled with 60g/s helium at 10bar and maintain a steady-state temperature of approximately 300°C
• Mass flow rate is double that of the T2K target cooling but the volume flow rate is a factor of 3 less due to the target operating at high pressure
• 60g/s @ 10bar & 300K = 135m3/hr (Design 3 volumetric flow rate)• For comparison 30g/s @ 1.6bar & 300K = 421m3/hr (T2K volumetric flow rate)
• Guess total P (Target + Heat Exchangers + Pipe work) is 5bar • Ideal compressor work is then approximately 8kW (T2K = 20kW)
• Seems reasonable
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Maximum Temperature [°C]
Pressure Drop[bar]
Linear cooling channel 530 0.55
Uniform area channel 389 0.93
“Optimised” channel 314 1.27
EUROnu Annual Meeting, January 2011
General Conclusions and further work
• Pencil target geometry merits further investigation– Steady-state thermal stress within acceptable range– Initial investigation into pressurised helium cooling appears feasible– Off centre beam effects could be problematic..?
• Need to study pion production for “pencil” target geometry – Andrea??– Look for any “show-stoppers”
• Carry out further thermo-mechanical studies including:– Input CFX heat transfer result into ANSYS mechanical model– Profile the target instead of the “can” for ease of manufacture– Helium return flow
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