1. ANALYSIS OF THE HORN UNDER THERMAL SHOCK – FIRST RESULTS
Cracow University of Technology
Institute of Applied Mechanics
P. Cupiał
EUROnu Project

2. Outline of the talk
15.04.
2010
Benchmark test of the response of a 2D structure under transient heat loading – step of heat flux applied to a plate surface
Impulse of a heat flux on a plate
First results of the dynamic response of the horn due to an impulse of heat flux coming from the target
Other activieties underway in Krakow now

3. Benchmark – a plate with a step of heat flux applied to one surface
15.04.
2010
A simply-supported plate made of aluminium under a step of heat flux applied to the top surface.
A constant value of heat flux of magnitude 107 W/m2 is applied at time zero. Adiabatic conditions are assumed on all surfaces except the top one where heat is applied.
Plate dimensions: sides: a=0.1 m, b=0.15 m, h=0.001 m.

4. Temperature and displacement vs. time
under heat step – analytical solution
15.04.
2010
The temperature field T(z,t) is found as a solution of the transient one-dimensional heat conduction equation:
with boundary conditions:
The plate deforms in bending under the applied heat flux; the displacements are the solution of the dynamic plate bending problem:
 - coefficient of linear thermal expansion

5. Temperature and displacement vs. time
under heat step – analytical solution
15.04.
2010
The results are shown for a point on the top surface, with in-plane coordinates: x=a/2, y=b/2
Due to the constant heat supply and no heat removal the temperature increases infinitly with time.
The z-displacement due to bending is a sum of a quasi-static- and a dynamic oscillating term.

6. FEM analysis – temperature vs. time
15.04.
2010

7. FEM analysis – displacement vs. time
15.04.
2010

8. FEM analysis – temperature vs. time
(due to heat pulse)
15.04.
2010
The plate as above is subjected to a rectangular pulse of amplitude 4.5*108 W/m2, of duration 100 s.
The results are for the same point on the plate as before.

9. FEM analysis – displacement vs. time
(due to heat pulse)
15.04.
2010

10. Response of the horn due to a pulse of heat
flux from the target – axisymmetric analysis
15.04.
2010

11. Response of the horn due to a pulse of heat
flux from the target – axisymmetric analysis
15.04.
2010
The aim is to estimate the possible stress levels under a conservative assumptions that all power dissipated in a one-horn configuration is transmitted to the cylindrical section of the horn in the direct vicinity of the target.
The calculation of the heat pulse:
Avarage power of Q=200 kW is dissipated over the cylindrical surface with radius 3.5 cm and length 40cm (the area S=0.093 m2)
The average heat flux is thus equal to qav=2.2*106 W/m2
The pulse length being 100 s in the time interval 0.02 s (corresponding to 50 Hz frequency between the pulses) the maximum amplitude of a rectangular heat flux pulse is qmax=200qav=4.4*108 W/m2.
The value of 4.5*108 W/m2 has been used in calculations.

12. Response of the horn due to a single pulse
of heat flux from the target
15.04.
2010
The results at a selected point that lies on the section of the horn when the heat flux is applied

13. Response of the horn due to a pulse of heat
flux from the target
15.04.
2010
The transient stress results are important, e.g., in the estimation of the horn fatigue life in the target-horn system

14. Fatigue analysis – S-N Curve
15.04.
2010
ALUMINUM ALLOY 6082
„INFINITE LARGE” NUMBER OF CYCLES, N < 108

15. EQUIVALENT COMPLETELY REVERSED UNIAXIAL STRESS
Fatigue analysis – formulas
15.04
2010
EQUIVALENT COMPLETELY REVERSED UNIAXIAL STRESS
EFFECTIVE STRESS AMPLITUDE
EFFECTIVE MEAN STRESS
ULTIMATE STRESS

16. Response of the horn due to a pulse of heat
flux from the target – 3D analysis
15.04.
2010
3D analysis is much more time consuming, but it alows for the modelling of asymmetry effects in the system. Preliminary results have been obtained for the 3D model. Further comparison is still under way.

17. Other activities - 4-horn support – first concept (A.Wroblewski)
15.04.
2010
The horns with reflectors are shown. An important issue now is that space is very limited to accommodate the horns and services in a tunnel 3m in diameter.

18. Other activities – heat exchange – first concept (A.Wroblewski)
15.04.
2010
The possibility of heat exchange in the horn region around the target is being studied using an analytical and the FEM models. This concerns heat removal in the long time scale.

19. Summary
15.04.
2010
An analytical benchmark has been used to test coupled thermomechanical ANSYS analysis accuracy of a surgace structure (a plate) with heat fluxes specified on the face. Very good agreement has been obtained between analytical and FE solutions.
First 2D and 3D calculations have been done of the horn under the excitation by a pulse coming from heat deposition in the solid graphite target.
The stress levels together with other stresses (including those due to magnetic forces) will be used to estimate the integrity and fatigue life of the integrated horn-target system and in the assesment of the feasibility of integration of target inside the horn and its design.
The horn support system has to be considered in collaboration with Strasburg (details about possible tunel diameter is important as well as information about the services and e.g. electric connecting blocks, etc.).