1. The structural and Fluid flow analyses of the Hydrogen Absorber Window for the Muon Cooling collaboration project Presented at the MICE meeting at IIT 5 –8 Feb 2002 By Wing Lau, Oxford University, UK

2. The FEA work reported herewith has two purposes:- to look at the structural response of the Window undergoing a pressure increment to the burst pressure level; and to understand the flow pattern of the fluid inside the Window compartment The pressure test – 2 Window geometries have been analysed: Window 1 -- with a thickness of 127  m at the centre of the crown Window 2 -- with a thickness of 330  m at the centre of the crown Aim of the FEA analyses is to predict the deflection of the Window under various pressure load up to the first material UTS value at which the burst of the Window is anticipated. It is hope that the results, which were computed from the non-linear FEA calculations, could be used to compare with the photogrammetry results

3. The FE models include a 2-D axisymmetrical model on Windows 1 & 2, and a 3-D solid model for Window 2 only. The 2-D axisymmetrical model on Window 1 & Window 2 (same profile but slightly different crown thickness): The 3-D Solid model for Window 2

4. Stress-Strain relationship for the 6061-T6 material ( actual stress-strain relationship may vary slightly ) Rate of the applied pressure in FEA

5. The FEA results:- Window 1 – 2D axisymmetrical model: The deflection of the Window under various pressure First yield at 0.14 MPa

6. Window 1 – 2-D axisymmetrical model ( continue ): Deflection curve of particular points at the crown area Pressure at which first yield was detected

7. Window 1 – 2-D axisymmetric model Establishing the pressure at first yield. The centre of the crown yielded at as early as 21 psi. It soon spreaded to cover a patch of 2-3mm radius at about 34 psi. UTS was detected at (centre of crown ) about 47-48 psi First yield at crown centre General yield

8. Window 1 – 2-D axisymmetrical model The animated display of the Window deformation at various internal pressure

9. Photogrammetry results & FEA results by NIU FEA results by Oxford Comparison of results on Window 1at 0.18 Mpa test pressure: Comparing the Oxford FEA results with the NIU photogrammetry and FEA results

10. Comparison of results on Window 1at 0.24 Mpa test pressure: Comparing the Oxford FEA results with the NIU photogrammetry and FEA results

11. Comparison of results on Window 1 Graph summarizing the shape of the Window at the two preceding pressures, and the final pressure before it bursts.

12. Window 2 - 2D axisymmetric model Window 2 has the same basic profile of Window 1 except it is nearly 3 times thicker at the centre of the crown

13. At 100 psi test pressure Window 2 - 2D axisymmetric model

14. At 109 psi test pressure (first UTS value) Window 2 - 2D axisymmetric model

15. Modified format ( linear curve added ) of the photogrammetry results First yield at approx. 79psi Window 2 - 2D axisymmetric model

16. Animated stress development of the Window

17. Window 2 – 3-D solid FEA model The animated display of the Window deformation at various internal pressure. They confirm that there is no spurious harmonic variations around the Window.

18. Comparison of results on Window 3 Graph summarizing the shape of the Window at the various pressures before it bursts.

19. Window 3 – 2-D axisymmetrical model The animated display of the Window deformation at various internal pressure

20. Fluid Flow analysis – to establish the relationship between the flow pattern, the inlet velocity, the fluid viscosity and the nozzle arrangements 2 models were set up: 1)A back to back Window arrangement with inlet and outlet nozzles perpendicular to the flange seating; 2)A back to back Window arrangement with inlet and outlet nozzles at an oblique angle to flange seating inlet and outlet nozzles perpendicular to the flange seating inlet and outlet nozzles at an oblique angle to flange seating Plane of symmetry Fluid boundary Fluid

21. The Fluid model 2 different fluid medium were used for the run: One using air at room temperature, and one using water ( to see the viscosity effect) For the air flow model, 2 inlet velocities were run on each model:- 1)At 5 m/s (relatively lamina flow); 2)At 100 m/s ( turbulent flow ) Line of symmetry Model 1 – parallel nozzle arrangement Model 2 – oblique nozzle arrangement

22. Results of the fluid flow analysis:- Parallel nozzle arrangement with air flow at room temperature Inlet velocity = 5m/s Velocity profile in Y direction Air inlet

23. Results of the fluid flow analysis:- Parallel nozzle arrangement with air flow at room temperature Inlet velocity = 100 m/s Velocity profile in Y-direction Air inlet

24. Results of the fluid flow analysis:- Parallel nozzle arrangement with air flow at room temperature Inlet velocity = 5 m/s Vorticity profile Air inlet

25. Results of the fluid flow analysis:- Oblique nozzle arrangement with air flow at room temperature Inlet velocity = 5 m/s Velocity profile in Y-direction Air inlet

26. Results of the fluid flow analysis:- Oblique nozzle arrangement with air flow at room temperature Inlet velocity = 100 m/s Velocity profile in Y-direction Air inlet

27. Results of the fluid flow analysis:- Oblique nozzle arrangement with water flow at room temperature Water inlet velocity = 5 m/s Velocity profile in Y-direction Water inlet

28. Results of the fluid flow analysis:- Oblique nozzle arrangement with water flow at room temperature Water inlet velocity = 5 m/s Velocity profile in Z-direction Water inlet

29. Results of the fluid flow analysis:- Oblique nozzle arrangement with LH 2 flow at room temperature LH 2 inlet velocity = 5 m/s Velocity profile in Z-direction

30. 3-D Fluid Flow model A simple 3-D cylindrical model with a parallel inlet and out nozzle was set up to investigate the 3-D effect of the flow. The flow medium is air at room temperature with an inlet velocity of 100m/s. The 3-D model is:- Air out Air in

31. Preliminary results of the 3-D flow:- A cut out view showing half of the cylindrical section as the outside boundary will have zero velocity imposed throughout Air in