Update on calculations

1. Vacuum barrier stability: CERN to comment on the shape/force calculations presented last week

2. Tube sizes: not constrained by pressure requirements (see Wendell’s email)

3. Global model with pressure scenarios and mechanical conditions: SOTON presentation shared earlier in the week and in the following. CERN to advice how to proceed: modelling and design

4. Other calculations: CERN to advise

DFX Helium Vessel Global Model: pressure scenarios

Required by BS EN 13445-3 for cat3 pressure vessel using DBA

Cold vessel at PHe <= 3.5bar

DFX vacuum at 0<= PvDFX <= 1.5bar

SC-Link vacuum at 0<= PvLink <= 1.5bar

Cases PHe (bara) PvDFX (bara) PvLink (bara)

A1 3.5 0 0

A2 3.5 1.5 0

A3 3.5 0 1.5

Relevant scenarios of pressure combinations (A4-A6 uncessary due to lower loads)

DFX Helium Vessel Global Model: whole length and mechanical constraints

The model shall include the whole length to account for the bending of the L-shapeby 3.5bar inside the vessel

The stress distribution determined by the mechanical supports/constraints:

Vertical supportby the vacuum break

Cases Vertical Support Longitudinal Support Centring

B1 Fixed Yes (No?) No

B2 Fixed Yes (No?) Yes

B3 Roller Yes (No?) Yes

B4 Roller Yes (No?) No

Longitudinalsupport

Centring support

Longitudinalsupport

DFX Helium Vessel Global Model: longitudinal is necessary

With out the longitudinal support:1. When the warm flange of the vacuum break is fixed, the stress on

the vacuum break braces is too high

2. The longitudinal support is a must if the warm flange is only fixed in the vertical direction (horizontal roller). Otherwise the bellows will extend too much under the 3.5bar insider the vessel

A1+B1(No Longitudinal)+Warm

Fixed

DFX Helium Vessel Global Model: Mechanical support options

B1 (CERN): Fixed vertical support on the warm flange of the vacuum break

Cases Vertical Support Longitudinal Support Centring

B1 Fixed Yes No

B2 Fixed Yes Yes

B3 Roller Yes Yes

B4 Roller Yes No

B3 (SOTON): Vertical support on the warm flange of the vacuum break can slide horizontally

FEM Modelling

Materials using linearized elastoplastic constitutive relations for direct DBA as specified by BS EN 13445-3.

Thermal deformation coupled for combined thermal stress

DFX Helium Vessel Global Model: A1+B1 Cold

DFX Helium Vessel Global Model: A1+B3 at 3.5bar

A1+B1 has more stress on the vacuum break braces than A1+B3, where the warm flange on the roller slides by 2mm to ease the tension

DFX Helium Vessel Global Model: A2+B1 Cold

DFX Helium Vessel Global Model: A2+B3 Cold

A2 has abnormal pressure of 1.5bara in the DFX vacuum, resulting in a upwards force on the DFX cold vessel. Stress is lower for both A2+B1 and A2+B3, although the latter is still better.

DFX Helium Vessel Global Model: A3+B1 Cold: not converged

Missing colours exceeds 150MPa

DFX Helium Vessel Global Model: A3+B3 Cold

A3 has abnormal pressure of 1.5bara in the SC-Link vacuum resulting in a downwards force on the DFX cold vessel. Stress is higher for both A3+B1 and A3+B3, the former does not converge in the solution and the latter is within stress and plastic deformation limits.

Conclusion:

Global model analysis shows mechanical support configuration B3 is necessary for the pressure vessel tests/operation requirements

Configuration B1 suffers more stress and potentially unstable under A3 condition

DFX Helium Vessel Global Model: A4(1.5bar)+B1 Cold

DFX Helium Vessel Global Model: A4(1.5bar)+B3 Cold

Smaller Horizontal Section

Orthotropic equivalent bellows so far

Smaller bellows need strengthening

Similar behaviour to large horizontal section

Cold at 3.5bar: Fixed (A1+B1)

Cold at 3.5bar: Roller (A1+B3)

Cold at 1.5bar: Fixed A4+B1 (not converged)

Cold at 1.5bar: Roller (A4+B3)