STUDIES TOWARDS TARGET-HORN
INTEGRATION
Cracow University of Technology
Institute of Applied Mechanics
P. Cupial, A. Wroblewski
EUROnu Project
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
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
Horn geometry used
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.
18.11.
2009
Prototype available at CERN
18.11.
2009
Finite-element model of the horn
1
ELEMENTS
MAT
NUM
Y
Z
X
1
ELEMENTS
MAT NUM
Superbeam horn FE model
Superbeam horn FE model
18.11.
2009
Approximate modelling of magnetic forces
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:
B  0 r  RI
 0  (r )
B
r
r
RI  r  RII ,  (r )   J (u )udu
RI
0 I
B
RII  r  RI
2r
r
 0 I  0 (r )
B

RI  r  RII , (r )   J (u )udu
2r
r
RI
B  0 r  RII
18.11.
2009
Approximate modelling of magnetic forces
Lorentz force:
F   J  B dV
V
Definition of the pressure:
dF  pRd dz
Assuming uniform current density over thickness:
0 I 2

RI  RII
t
p  2 2 (1  ), R 
, 
8 R
6
2
R
0 I 2

RI  RII
t
p  2 2 (1  ), R 
,  
8 R
6
2
R
In the case of thin cylindrical shells:
0 I 2
p 2 2
8 R
18.11.
2009
Horn response to magnetic field – FE
harmonic analysis
Response at a selected point to a harmonic current with amplitude
300 kA
18.11.
2009
Horn response to a single current pulse
Response at a selected point to a current pulse of amplitude 300 kA
of 100 s duration
18.11.
2009
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
Comments on response under pulse
excitation
Impulse resonance
The case with no damping
The effect of damping
18.11.
2009
Coupled magneto-structural analysis –
static benchmark solution
z
Infinite solenoid with a circumferential current
density (per area):
J  J 0e
18.11.
2009
J
Analytical solution:
r
Magnetic field vector inside the cylinder:
B   0 J 0 (b  r )e z
a
Lorentz force:
b
J  B   0 J 02 (b  r )e r
Mechanical equations of equilibrium:
dtrr t rr  t 

  0 J 02 (b  r )  0
dr
r
Coupled magneto-structural analysis –
static benchmark solution
Constitutive equations:
dur 1
u
1
 [t rr  (t  t zz )],    r  [t  (t rr  t zz )]
dr Y
r Y
1
 zz  [t zz  (t  t rr )]
Y
 rr 
Mechanical boundary conditions:
t rr  0,
r  a, b
18.11.
2009
Coupled magneto-structural analysis –
static benchmark solution
Stresses in the solenoid (F.C. Moon „Magneto-solid
Mechanics”, 1984):
2 2
1
3


r
2
t    0 J 02 b 2 [ A  B 2  (1  )]
 (1  )r
r
4
2
3
1


t rr   0 J 02 b 2 [ A  B 2  (1  )] 2 r 2  (1  )r
r
4
3
where:
a
1  2
, 
b
1 
1


2
A  (1  )(1   )  (1  )( 2    1)(1  ) 1
2
4
3
1


B   (1  )  (1  )(1  ) 1
2
4
3

18.11.
2009
FEM vs. Analytical solution
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 = 0.003770 T
Bz= 003750 T
t =62.44 N/m2
t =61.34 N/m2
18.11.
2009
Thermomechanical analysis under Jule
heating
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
18.11.
2009
Temperature distribution
1
18.11.
2009
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
TEMP
(AVG)
RSYS=0
SMN =25
SMX =79.838
Z
Y
MN X
1
MX
25
37.186
49.372
61.559
73.745
31.093
43.279
55.466
67.652
79.838
Current dissipation 18kW
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
TEMP
(AVG)
RSYS=0
SMN =25
SMX =131.287
Z
Y
MN X
MX
25
48.619
72.239
95.858
119.478
36.81
60.429
84.049
107.668
131.287
Current dissipation 40kW
Thermal stresses
1
18.11.
2009
1
NODAL SOLUTION
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
SEQV
(AVG)
DMX =.001215
SMN =6627
SMX =.288E+09
STEP=1
SUB =1
TIME=1
SEQV
(AVG)
DMX =.001183
SMN =22610
SMX =.282E+09
Y
Z
X
Z Y
X
MN
MN
MX
MX
1
NODAL SOLUTION
22610
New HORN
.628E+08
STEP=1 .314E+08
SUB =1
03/2009, thermal
TIME=1
SEQV
(AVG)
DMX =.001215
SMN =6627
SMX =.288E+09
.941E+08
.125E+09
.157E+09
.188E+09
static analysis
.220E+09
.251E+09
NOV 13 2009
14:48:07
6627
.282E+09
.639E+08
.128E+09
.192E+09
.256E+09
.320E+08
.959E+08
.160E+09
.224E+09
.288E+09
Current dissipation 40kW
Stresses of the order of 95 MPa for the
more intensive of the two heat sources.
Locally high stresses due to numerical
singularities.
MX
6627
.320E+08
.639E+08
Current dissipation 40kW
.959E+08
.128E+09
.160E+09
.192E+09
.224E+09
.256E+09
.288E+09
Integration of the target inside the horn
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)
18.11.
2009
Horn temperature distribution under Jule
heating and radiation from the target
Conservative assumption that all
power dissipated in the target
goes to the horn.
1
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
TEMP
(AVG)
RSYS=0
SMN =25
SMX =131.287
1
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
TEMP
(AVG)
RSYS=0
SMN =24.964
SMX =131.287
Y
Z
18.11.
2009
MN X
Y
Z
MX
X
MN
MX
25
36.81
48.619
60.429
72.239
84.049
95.858
107.668
119.478
131.287
+200kW
24.964
48.591
36.777
Additional heating causes a local
temperature increase of 30 to 50 deg.
72.219
60.405
95.846
84.032
119.474
107.66
+600kW
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.
131.287
Plans for the near future
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
18.11.
2009