1. Pressure Vessel Safety Calculation Takeyasu Ito Los Alamos National Laboratory EDM Collaboration Meeting Durham, NC May 20-21, 2008

2. 2 Introduction Cryostat needs to meet the safety requirements of the facility Recent examples – Liquid hydrogen target for the SAMPLE experiment at MIT-Bates – Liquid hydrogen target for the G0 experiment at JLAB – Superconducting magnet for the G0 Experiment at JLAB – Liquid hydrogen target for the NPDGamma Experiment at LANL and ORNL/SNS The nEDM apparatus needs to meet the safety requirements of ORNL/SNS. In addition, the portion of the nEDM apparatus to be first tested at LANL needs to meet the LANL safety requirements. This is a summary of what we did for the Dual Use Cryostat. – More details can be found in the Design Document posted on the Twiki site.

3. 3 Some useful references W.M.Schmitt and C.F.Williamson, “Boiloff rates of cryogenic targets subject to catastrophic vacuum failure”, Batess Internal Report #90- 02 (1990) NPDGamma liquid hydrogen target engineering document (2007) G.Cavallari, I.Gorine, D.Guesewell, R. Stierilin, “Safety tests with the LEP superconducting cavity”, CERN/ER/RF (1989) Physics division cryogenic safety manual, Argonne National Laboratory Physics Division Cryogenic Safety Committee (2001).

4. 4 Dual Use Cryostat HV electrodes HV Heat Shields 3 He Atomic Beam Source 3 He Injection Test Apparatus HV Test Apparatus HV LHe Volume ParameterValue Outer vacuum vessel volume 2.58 m 2 Outer vacuum vessel surface area 11.35 m 2 Outer vacuum vessel material 6061 aluminum Outer vacuum vessel MAWP 15 psid Liquid helium vessel volume 0.272 m 3 Liquid helium vessel surface area 2.6 m 2 Liquid helium vessel material SS304 Liquid helium vessel MAWP 30 psid Selected parameters

5. 5 Credible Accident Scenarios Loss of isolation vacuum to air or helium Failure of liquid helium containing vessels

6. 6 Loss of isolation vacuum to air Outer Vacuum Vessel Liquid Helium Vessel Relief valve AIR AIR FREEZES QQQ Q Q He gas PP

7. 7 Sizing the relief system: things to do Estimate the rate of heat transfer to liquid helium Determine the boiloff rate Calculate the pressure drop Calculate the strength of the vessel

8. 8 Rate of heat transfer to liquid helium due to loss of vacuum LHe Frozen air Vessel wall Film boiling The rate of heat transfer depends on: Rate of air flow Heat resistance due to Vessel wall Helium gas film Frozen air layer

9. 9 Rate of heat transfer to liquid helium: some measured values dq/dt (W/m 2 ) ConditionReference (1-6) x 10 4 No superinsulationH.M.Long and P.E.Loveday in Technology of Liquid Helium, (NBS Monograph 111, 1968) 1.4 x 10 4 No superinsulationANL Physics Division Cryogenic Safety Manual (2001) [ATLAS] 3.1 x 10 5 No superinsulation, superfluidS. M. Harrison, IEEE Trans. Appl. Superconduct. 12, 1343 (2002) [AMS]. 1.25 x 10 3 1 in. thick superinsulationH.M.Long and P.E.Loveday in Technology of Liquid Helium, NBS Monograph 111 (1968) 7.5 x 10 2 24 layers of superinsulationM. Wiseman, R. Bundy, J. P. Kelley, and W. Schneider, in Application of Cryogenic Technology (Plenum Press, 1989) [CEBAF] 4.4 x 10 3 3 mm superinsulation “Cryocoat Ultralight”, superfluid S. M. Harrison, IEEE Trans. Appl. Superconduct. 12, 1343 (2002) [AMS]. We adopt: with superinsulation Note: thermal conductivity of gas filled superinsulation is 7x10 4  W/m/K, which gives a heat flux of 2000 W/m 2 when subject to a 300 K temperature difference.

10. 10 Boiloff Rate Helium latent heat: Total heat flow into LHe vessel: Helium mass flow:

11. 11 Pressure Buildup Darcy’s formula: Resistance coefficient – Straight pipe – For turbulent flow in a smooth pipe – “Minor corrections”: correction for entrance, exit, bend, etc. f = friction factor L = length of the pipe Re= Reynolds number

12. 12 MAWP (Maximum Allowable Working Pressure) Definition given by ASME Boiler and Pressure Vessel Code Section II Part D In general, MAWP is a pressure which raises the membrane stress in the metal to the lesser of the following two value: – the tensile strength/3.5 – the 0.2% yield strength/1.5.

13. 13 Strength Calculation Using ANSYS (By John Ramsey)

14. 14 Outer Vacuum Vessel Liquid Helium Vessel 26” 27” 20” 12” 3.0” OD pipe Rupture disk (3”, 12 psi) Emergency vent stack Primary vent stack Relief valve Parallel plate (3”, 6 psi)

15. 15 Pressure Buildup in Dual Use Cryostat Darcy’s formula: Resistance coefficient Pressure drop ComponentK K Entrance0.590 degree bend0.4 Shaped Curve1.0Rupture disk2.0 Bellows0.2Exit1.0 Dividing T1.02.89” 40” long pipe0.2

16. 16 Reality Check Dual Use CryostatCEBAF SRF Cavity LHe vessel volume (m 3 )0.2720.445 LHe vessel surface area (m 2 )2.63.48 LHe vessel MAWP (psi)3060 Rapture disk burst pressure (psi)1245 Rapture disk size (in.)32 Vent line ID (in.)2.872.4

17. 17 Comment by Bob Bourque (head of the LANL Pressure vessel committee) Our valueBob Bourque’s recommendation Heat flux into liquid helium with superinsulation 2000 W/m 2 6000 W/m 2 Temperature of helium gas coming out of the vent 300 K50 K

18. 18 Remarks Heat capacity of gas not taken into account – Taking the gas heat capacity into account might reduce the estimated boil off rate. – However, estimating how much heat goes into heating the gas is very difficult. There are many approximations and they are on the side of safety, costing in heat load. If a more accurate estimate is necessary, we might need to use CFD calculation, such as FLUENCE.