1. STUDIES TOWARDS TARGET-HORN INTEGRATION Institute of Applied Mechanics
Cracow University of Technology
Institute of Applied Mechanics
P. Cupial, A. Wroblewski
EUROnu Project

2. Outline of the talk
18.11.
2009
1. Dynamic response of the horn to excitation by current pulses (P.Cupial)
the horn geometry – new finite-element model
approximate modelling of magnetic forces
response of the horn to harmonic and pulse excitation
response of structures under a single pulse and a sequence of pulses – important points
coupled-field approach to response under magnetic-field excitation

3. Outline of the talk
18.11.
2009
2. First estimates of heat transfer in the target-horn system (A.Wroblewski)
horn temperature and stress distribution due to current heating
early estimates of the effect of heat radiated from the target on the temperature and stresses in the horn

4. Horn geometry used
18.11.
2009
The advantage of studying this geometry is that the prototype is available at CERN and experimental verification is possible. Present Superbeam horn dimensions are comparable to the NF ones.

5. Prototype available at CERN
18.11.
2009

6. Finite-element model of the horn
18.11.
2009 1 X Y Z
Superbeam horn FE model
ELEMENTS
MAT NUM 1
Superbeam horn FE model
ELEMENTS
MAT NUM

7. Approximate modelling of magnetic forces
18.11.
2009
The analsis assumes cylindrical geometry
Inner cylinder with radia RI, RII and thickness t=RII-RI
Outer cylinder with radia R’I, R’II and the same thickness
Magnetic field distribution:

8. Approximate modelling of magnetic forces
18.11.
2009
Lorentz force:
Definition of the pressure:
Assuming uniform current density over thickness:
In the case of thin cylindrical shells:

9. Horn response to magnetic field – FE
harmonic analysis
18.11.
2009
Response at a selected point to a harmonic current with amplitude 300 kA

10. Horn response to a single current pulse
18.11.
2009
Response at a selected point to a current pulse of amplitude 300 kA of 100 s duration

11. Comments on the response under pulse
excitation
18.11.
2009
Displacement and stress in the beam middle-point excited by a half-sine pulse applied at the middle point, pulse duration/period of the lowest mode = 3
The corresponding plots when pulse duration/period over lowest mode = 0.01

12. Comments on response under pulse
excitation
18.11.
2009
Impulse resonance
The case with no damping
The effect of damping

13. Coupled magneto-structural analysis – static benchmark solution
18.11.
2009
Infinite solenoid with a circumferential current density (per area):
Analytical solution:
Magnetic field vector inside the cylinder:
Lorentz force:
Mechanical equations of equilibrium:

14. Coupled magneto-structural analysis – static benchmark solution
18.11.
2009
Constitutive equations:
Mechanical boundary conditions:

15. Coupled magneto-structural analysis – static benchmark solution
18.11.
2009
Stresses in the solenoid (F.C. Moon „Magneto-solid Mechanics”, 1984):
where:

16. FEM vs. Analytical solution
18.11.
2009
Material properties: E=10.76*1011 N/m2, =0.35, =0
Geometric properties: a=0.01 m, b=0.02 m
Loading: J=106 A/m2
Results for r=0.017 m
Analytical Ansys
Bz = T Bz= T
t =62.44 N/m t =61.34 N/m2

17. Thermomechanical analysis under Jule
heating
18.11.
2009
Parameters used:
Max. current: 300 kA
Pulse repetition rate : 50 Hz
Pulse length: 100 s
Jule losses calculated for the NF horn at CERN by J.M. Maugain, S.Rangod, F. Voelker: 18 or 40 kW. These have been applied as uniform heat sources over the part of horn carrying the current
Water flow: 82 l/min
Water inlet temperature: 25 oC
Water outlet temperature: 40 oC

18. Temperature distribution
18.11.
2009 1 MN MX X Y Z
Current dissipation 18kW 25
31.093
37.186
43.279
49.372
55.466
61.559
67.652
73.745
79.838
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
TEMP (AVG)
RSYS=0
SMN =25
SMX =79.838 1 MN MX X Y Z
Current dissipation 40kW 25
36.81
48.619
60.429
72.239
84.049
95.858
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
TEMP (AVG)
RSYS=0
SMN =25
SMX =

19. Thermal stresses
18.11.
2009 1 MN MX X Y Z
New HORN 03/2009, thermal static analysis
22610
.314E+08
.628E+08
.941E+08
.125E+09
.157E+09
.188E+09
.220E+09
.251E+09
.282E+09
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
SEQV (AVG)
DMX =
SMN =22610
SMX =.282E+09 1 MN MX X Y Z
Current dissipation 40kW
6627
.320E+08
.639E+08
.959E+08
.128E+09
.160E+09
.192E+09
.224E+09
.256E+09
.288E+09
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
SEQV (AVG)
DMX =
SMN =6627
SMX =.288E+09
Stresses of the order of 95 MPa for the more intensive of the two heat sources.
Locally high stresses due to numerical singularities.

20. Integration of the target inside the horn
18.11.
2009
Concept of integration of a pebble-bed target inside a horm (P. Sievers)
For a 4 MW beam power dissipated in the target amounts to:
600 kW (estimated by P. Sievers)
200 kW (from the report by A.Longhin)

21. Horn temperature distribution under Jule
heating and radiation from the target
18.11.
2009
Conservative assumption that all power dissipated in the target goes to the horn. 1 MN MX X Y Z
+200kW 25
36.81
48.619
60.429
72.239
84.049
95.858
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
TEMP (AVG)
RSYS=0
SMN =25
SMX = 1 MN MX X Y Z
+600kW
24.964
36.777
48.591
60.405
72.219
84.032
95.846
107.66
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
TEMP (AVG)
RSYS=0
SMN =24.964
SMX =
Additional heating causes a local temperature increase of 30 to 50 deg.
These are preliminary results, assuming that the temperature of the cooling water is not influenced by the additional heat source (higher water flow). A FLOTRAN analysis has just started.

22. Plans for the near future
18.11.
2009
Continuation of the dynamic analysis of the horn under a sequence of pulses (calculation of stresses, coupled-field dynamic analysis)
Transient thermomechanical analysis
More detailed analysis of the thermomechanical phenomena accounting for the water flow using FLOTRAN
Horn fatigue life estimate, based on the combined calculated dynamic and thermomechanical stress levels.(The present CERN estimate is only 6 weeks!)
Modelling of the present superbeam geometry