Window Design

1. Muon Collider Collaboration MeetingBerkeley, Oct 2002 Window Design Wing Lau & Stephanie Yang Oxford University

2. This presentation reports on the progress and results of two areas of work: • The thickness optimisation of the bellow window at the flange end; • The temperature distribution of liquid hydrogen inside the window at various flow speeds

3. A quick re-cap on where we are on Window design The design of the bellow window is such that it is possible to scale the standard design linearly to suit any window dimension and still keeping the same pressure rating, i.e. burst pressure at 120 psi. Here is the design table that we have devised to provide the Window designer with a set of concave and convex radii and centre coordinates that will guarantee the required pressure rating.

4. Thickness optimisation The previous bellow window gave an average 45% reduction in thickness at the centre area compared with the torispherical design; However, the same design required a much thicker section at the junction near to the ring flange; This exercise examines how this thicker section could be optimised further without compromising on its pressure rating performance

5. Thk. = 5mm Thk.=0.9mm Previous Window design Optimised Window design

6. The 22cm Absorber Window Deflection of the optimised Window at burst pressure (125 psi) Deflection of previous window at burst pressure (121psi)

7. The 34cm Vacuum Window -- internal pressure Deflection of the optimised Window at burst pressure (83 psi) Deflection of previous window at burst pressure (79psi)

8. The 34cm Vacuum Window -- incremental external load No buckling at 52 psi Local buckling detected at 54 psi The 0.13mm thick window General buckling developed at about 55 psi

9. The 34cm Vacuum Window -- incremental external load Shape of Window at first yield ( P= 34.5psi )

10. Deflection of the previous window under external pressure 29psi 45psi 52psi @ 54 psi @ 55 psi

11. Deflection of the optimised window under external pressure No obvious buckling occurs when external pressure reaches 34psi (when material reaches yield)

12. Is this design acceptable?

13. Stresses are well below yield in this region Stresses at this junction are as high as 300 MPa Stress distribution at burst pressure

14. Let us examine what happens to the two window designs during burst pressure The previous window geometry: Ultimate tensile stresses are concentrated very local to the window centre. This high stress reduces significantly at a short distance away from the centre. The failure mode is such that material tearing occurs only at the window centre. It is not envisaged that this will lead to fragments detaching from the rest of the window. The latest window geometry: High stresses, approaching UTS values, are detected at the outer perimeter of the Window. These stresses could well expand beyond the UTS value, should there be any slight over machining or under cutting (about 15 microns) in this area. Under this assumption, it is possible for the whole window to come away from the main flange when it reaches the burst pressure. The detached fragment would further impinge on the adjoining components, e.g. the Vacuum window which is itself also very thin. From a safety point of view, the consequence of this knock-on effect may need further discussion.

15. An Observation • So far, we have looked at the Window safety from a single source of loading only, i.e. the pressure load. • There are other loads which may or may not be significant to the Window safety, but have not yet been included in the analysis. These include: • Thermal load caused, possibly, by the uneven temperature distribution of the liquid hydrogen during operation; • Differential thermal load at the Window anchor points; • Eddy current effect; • Magnet quench effect, if applicable • Although not all these loads will occur simultaneously and concurrently with the burst pressure event, it is worth summarising all the possible load events and scenarios to ensure that the Window meets all the safety requirements

16. Conclusion As for the Window thickness optimisation, we believe sufficient work has been done to make the Window “leaner and fitter”. This latest geometry is as far as we could go in optimising its thickness against the required pressure rating; Further work is still needed to understand how the Window behaves under different load events and other load combination scenarios; The use of the Aluminium Lithium Alloy would reduce its overall thickness by yet another 40 - 45%. It remains to be seen whether the manufacturing of such thin structure would pose any unforeseen problem. Don Summers would be in the best position to confirm; We have briefly looked at the flat window design which seems to offer a good alternative to the “curved” window if internal pressure is the only load seen by it. For the flat window to work, it requires an accurate prediction of the pre-tensioned load. Its advantage over the “curved” window fades somewhat when the magnitude of thermal loads can not be established, as this would greatly alter the level of the pre-tensioning upon which the flat window is so heavily relied. We suggest postponing this development work until the thermal loads are better understood.

17. The thermal / fluid analysis

18. Progress on the fluid-thermal simulation • We have revised the nozzle sizes and flow speeds in line with the suggestions made by the Fermi Cryogenic group. This changes were required to ensure that the flow can develop an acceptable pressure head delivered by the refrigerating pumps. • To comply with this requirement, we have • Taken cognises of the increased the total number of inlet and outlet nozzles; • Reduced the flow inlet speed from 5m/s to 0.56m/s, or less. This is an extremely slow speed, but would reduce the pressure head to a level that is acceptable to the cryogenic group; • The nozzle diameter was also reduced from a nominal 15mm to 11mm. • For this reason, we have carried out a series of steady state thermal analyses based on the flow distribution and speeds developed inside the window.

19. A summary of the fluid and thermal runs • To help understand the fluid flow and thermal interaction of the coolant, we have used a series of 2-D models. The actual flow pattern in a 3 dimensional flow will be somewhat different, but such analysis is extremely time consuming and the construction of the grid models is very complex. It could only be used once the 2 dimensional flow characters are fully understood. • Two 2-D models were set up:- • One with a symmetrical pair of single inlet and outlet nozzles. The nozzles are positioned at 20 degree towards one of the window surfaces for the best cooling effect. The following flow speeds were looked at:- • 0.36 m/s • 0.54 m/s • 1 m/s • The other with a set of two inlet and two outlet nozzles, each pointing at 20 degree to the upper and lower window surfaces respectively, again for the best cooling effect. Only flow speed at 1m/s was studied to see if the addition of another set of nozzles would have any noticeable effect on the cooling performance. • Here are the results

20. Flow Speed at 0.36ms-1

21. Flow Seed 0.36ms-1 Local hot spot Beam Width 15mm Beam Width 45mm Beam Width 100mm Beam Width 155mm

22. Flow Speed 0.56ms-1

23. Flow Speed 0.56ms-1 Beam Width 15mm Beam Width 45mm Beam Width 100mm Beam Width 155mm

24. Flow Speed 1ms-1

25. Flow Speed 1ms-1 Beam Width 15mm Beam Width 45mm Beam Width 100mm Beam Width 155mm

26. 2 Nozzle – 1ms-1

27. Flow Speed 1ms-1

28. 2 Nozzle – 2ms-1

29. Flow Speed 2ms-1

31. Conclusion The above results suggest that while it is important to actively encourage the fluid to flow from one side of the Window to the other with sufficient speed so that it can remove as much heat as possible, but high speed flow does not guarantee a complete heat removal; The presence of any vortex will promote stagnant pools of swirling liquid which could easily be heated up to and beyond the boiling point. This is undesirable and will lead to the expansion of the liquid hydrogen inside the Window with serious consequences. The CFX results will give us a better idea on how this develops; The results suggest that rather than keep increasing the flow speed as a mechanism for improving heat removal and which could lead to the formation of turbulence and vortex, our aim is to come up with an optimal flow speed which is free of local turbulence and vortex but is just enough to remove the given amount of heat.