Pressure Vessel Safety Calculation

Takeyasu ItoLos Alamos National Laboratory

EDM Collaboration MeetingDurham, NC

May 20-21, 2008

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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.

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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).

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Dual Use Cryostat

HV electrodes

HV Heat Shields

3He Atomic Beam Source

3He Injection Test Apparatus

HV Test Apparatus

HV LHe Volume

Parameter Value

Outer vacuum vessel volume

2.58 m2

Outer vacuum vessel surface area

11.35 m2

Outer vacuum vessel material

6061 aluminum

Outer vacuum vessel MAWP

15 psid

Liquid helium vessel volume

0.272 m3

Liquid helium vessel surface area

2.6 m2

Liquid helium vessel material

SS304

Liquid helium vessel MAWP

30 psid

Selected parameters

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Credible Accident Scenarios

• Loss of isolation vacuum to air or helium

• Failure of liquid helium containing vessels

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Loss of isolation vacuum to air

Outer Vacuum Vessel

Liquid Helium Vessel

Relief valve

AIR

AIR FREEZES

Q Q Q

Q

Q

He gas

P

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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

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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

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Rate of heat transfer to liquid helium: some measured values

dq/dt (W/m2) Condition Reference

(1-6) x 104 No superinsulation H.M.Long and P.E.Loveday in Technology of Liquid Helium, (NBS Monograph 111, 1968)

1.4 x 104 No superinsulation ANL Physics Division Cryogenic Safety Manual (2001) [ATLAS]

3.1 x 105 No superinsulation, superfluid S. M. Harrison, IEEE Trans. Appl. Superconduct. 12, 1343 (2002) [AMS].

1.25 x 103 1 in. thick superinsulation H.M.Long and P.E.Loveday in Technology of Liquid Helium, NBS Monograph 111 (1968)

7.5 x 102 24 layers of superinsulation M. Wiseman, R. Bundy, J. P. Kelley, and W. Schneider, in Application of Cryogenic Technology (Plenum Press, 1989) [CEBAF]

4.4 x 103 3 mm superinsulation “Cryocoat Ultralight”, superfluid

S. M. Harrison, IEEE Trans. Appl. Superconduct. 12, 1343 (2002) [AMS].

We adopt: with superinsulation

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˙ q = 2000 W/m2

Note: thermal conductivity of gas filled superinsulation is 7x104W/m/K, which gives a heat flux of 2000 W/m2 when subject to a 300 K temperature difference.

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Boiloff Rate

• Helium latent heat:

• Total heat flow into LHe vessel:

• Helium mass flow:

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˙ M =5200 W

82.9 J/mol× (4.00 g/mol) = 0.251 kg/s

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hV = 82.9 J/mol

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˙ Q = 2.6 m2 × 2000 W/m2 = 5200 W

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Pressure Buildup

• Darcy’s formula:

• Resistance coefficient– Straight pipe

– For turbulent flow in a smooth pipe

– “Minor corrections”: correction for entrance, exit, bend, etc.

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P =8

π 2 K˙ M 2

ρY 2D4

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˙ M : mass flow (kg/s) 0.251 kg/s

ρ : density (kg/m3) 0.179 kg/m3 (STP)

Y : expantion correction coefficient 0.8

D : diameter of the pipe (m) 0.0729 m (2.87 in.)

K : resistance coefficient 6.3

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K = f L /D( )f = friction factorL = length of the pipe

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f =0.316

Re0.25Re= Reynolds number

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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.

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Strength Calculation Using ANSYS (By John Ramsey)

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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)

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Pressure Buildup in Dual Use Cryostat

• Darcy’s formula:

• Resistance coefficient

• Pressure drop

€

P =8

π 2 K˙ M 2

ρY 2D4

€

˙ M : mass flow (kg/s) 0.251 kg/s

ρ : density (kg/m3) 0.179 kg/m3 (STP)

Y : expantion correction coefficient 0.8

D : diameter of the pipe (m) 0.0729 m (2.87 in.)

K : resistance coefficient 6.3

Component K Component K

Entrance 0.5 90 degree bend 0.4

Shaped Curve 1.0 Rupture disk 2.0

Bellows 0.2 Exit 1.0

Dividing T 1.0 2.89” 40” long pipe 0.2

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K tot = 6.3

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P =14.5 psi

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Reality Check

Dual Use Cryostat CEBAF SRF Cavity

LHe vessel volume (m3) 0.272 0.445

LHe vessel surface area (m2) 2.6 3.48

LHe vessel MAWP (psi) 30 60

Rapture disk burst pressure (psi) 12 45

Rapture disk size (in.) 3 2

Vent line ID (in.) 2.87 2.4

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Comment by Bob Bourque (head of the LANL Pressure vessel committee)

Our value Bob Bourque’s recommendation

Heat flux into liquid helium with superinsulation

2000 W/m2 6000 W/m2

Temperature of helium gas coming out of the vent

300 K 50 K

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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.

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cf . hV = 82.9 J/mol

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c p =5

2R = 21 J/K/mol