Relief Valve Sizing Analysis of SHMS HB, Q1, Q2, Q3 and Dipole

Author: Eric Sun, Date: May 18, 2009

Reviewer: Dave Meekins, Date:

Reviewer: George Biallas, Date:

Reviewer: Steve Lassiter, Date:

Updated on March 30, 2016 (The “J” orifices of the pilot relief valves were increased to “K” orifices per Charles Monroe’s recommendation.)

1. Calculation Basis and Assumptions Unless noted all references are to the ASME 2007 Section VIII, Division 1. Oxford’s Safety Analysis for the HMS Q2/3 Cold Iron Quadruples (Q-UM-DN 64/2, 1993) was used as a basis for this report.

1. SHMS HB, Q1, Q2, and Q3 use the same relief valve, rupture disc, and piping for both the helium and nitrogen vessels. SHMS Dipole uses the same relief valves as others but with a large rupture disc and a long chimney.

2. The design pressure is defined as the most severe condition of coincident pressure and temperature expected in normal operation. For this condition and test conditions, the maximum difference in pressure between the inside and outside of the vessel shall be considered (see UG-21). The set pressure of the relief valves is 4 atm gauge for both helium and nitrogen; the rupture disk, 5 atm gauge. These match the set pressures of the HMS Q1.

3. The maximum allowable working pressure (MAWP) is set at 6 atm (pressure differential) for the temperature ranges of 4 K to 300 K (UG98c). The design pressure and the MAWP are the same for the pressure vessels.

4. A single pressure relieving device, direct spring loaded type, will be used for normal and upset conditions. The set pressure of this pressure relieving device shall prevent the pressure from rising more than 10% of the MWAP as per UG-125(c).

5. A supplemental pressure relieving device (rupture disk) capable of preventing the pressure from rising more than 21% of the MWAP (UG-125(c)(2) ) shall be employed to handle abnormal fault conditions as described in section 4 of this paper (External heat

1 loads). The supplemental rupture device is also required by JLAB due to the primary relieving device operating in a cryogenic environment and its possible freezing during discharge of the cryogens.

6. The compressibility factor: (Charles Monroe, Sigmaphi’s consultant)

7. The nozzle coefficient of the relief valve:

8. The nozzle coefficient of the rupture disk based on ASME code:

9. The nozzle coefficient of the parallel plate is conservatively assumed:

10. The exit helium gas temperature is 6.94 K (per Charles Monroe’s numerical calculation).

11. The exit nitrogen gas temperature is 100 K, and the temperature in the nitrogen shield is 80 K.

12. No credit is taken from other pressure relieving devices employed on adjacent magnets in the closed circuit.

13. For calculating the capacity of the primary relief valve (ASME Section VIII appendix 11),

14. For calculating the capacity of the supplemental rupture disk (ASME Section VIII appendix 11),

2. Magnet Quench with and without Energy Dump (A) Film Boiling Method

When a quench happens, the temperature of the coil will increase. A stable film boiling is therefore assumed on the surface of the coil. The average temperature of the coil can be obtained from QUENCH analysis. According to Fig 6.15, p223, Helium Cryogenics (Steven W. Van Sciver, 1986), the rate of heat flux can be estimated based on the average temperature of the coil. Therefore, the maximum helium flow rate can be calculated. This method is conservative because the average temperature of the coil, which determines the rate of heat flux, is higher than reality since quench calculation ignores stainless steel keys and the existence of the liquid helium. For the HB and the Q1, the average temperature of the coil is obtained when the temperature reaches its maximum. For the Q2/3 and the Dipole, the average temperature is obtained after 25 seconds in the case of having no external dump resistance and after 15 seconds in the case of having an external dump resistance. It is possible that all of the helium is gone already after quench happens 25 seconds later without dump resistance. Table 1 and Table 2 list the flow rate due to quench using the film boiling method. The results from this method were used to size the relief valve and the rupture disk. Table 1 Mass Flow Rate Due to Quench with Loss of Active Protection (Film Boiling Method)

Average Film Effective Mass Flow Rate due to Temperature of Boiling Surface Area Quench with No Dump coil Heat Flux of coil Resistance SHMS HB 100 K 5.1 1.45E4 12.74E3 kg/hr SHMS Q1 90 K 4.5 2.05E4 15.89E3 kg/hr SHMS Q2/3 65 K 2.9 2.731E4 13.64E3 kg/hr SHMS Dipole 45 K 1.8 5.019E4 15.56E3 kg/hr Table 2 Mass Flow Rate Due to Quench with Active Protection (Film Boiling Method)

Average Film Boiling Effective Mass Flow Rate due to Temperature of Heat Flux Surface Area Quench with Dump coil Resistance SHMS HB 60 K 2.6 1.45E4 6.495E3 kg/hr SHMS Q1 50 K 2.0 2.05E4 7.062E3 kg/hr SHMS Q2/3 30 K 1.1 2.731E4 5.175E3 kg/hr SHMS 28 K 1.0 5.019E4 8.646E3 kg/hr Dipole

(B) Quench Method

This method is mainly used to cross check the film boiling method because of wild assumptions in the film boiling method. The quench method is not used to calculate the flow rate of HB and Q1 since their time constants are too small for the method to make sense.

The maximum stored energy of the magnets is 9.09 MJ for Q2/3, and 16.3 MJ for the dipole at their maximum design currents. The rate of energy transferred to the helium has been computed based on transient quench analysis with and without an active dump resistor inline. It was assumed that there were four hotspots with the quench analysis. The four-hotspot situation is more severe than just one hotspot. Vector Fields Opera 13 was used to conduct the quench analysis.

Table 3 Average Mass Flow Rate Due to Quench with Loss of Active Protection (Quench Method) Liquid Liquid Total He Time to Generate Average Mass Flow He He Mass Latent the Latent Energy Rate due to Quench Volume Energy of Helium Inventory based on OPERA/QUENCH SHMS Q2/3 229.4 L 28.67 kg 0.5992 MJ 11.9 s SHMS 384.5 L 47.9 kg 1.00 MJ 18.7 s Dipole with chimney

3 Table 4 Average Mass Flow Rate Due to Quench with Active Protection (Quench Method) Ohmic Heat Generated in Time to Generate the Average Mass Flow the Coil after Quench Ohmic Heat in the Coil Rate due to Quench within 15.0 s after Quench SHMS Q2/3 0.0331 MJ 15.0 s SHMS 0.0877 MJ 15.0 s Dipole

For relief sizing calculations using Quench Method, it was conservatively assumed that initially, all of the generated heat energy would be absorbed by the liquid helium. For the case of loss of active protection, the average helium mass flow was calculated based on the total latent energy of the helium inventory, and the time to generate the latent energy minus 5 seconds because OPERA/QUENCH simulation showed almost no heat generated was generated at the first 5 seconds. For the case of active protection, the average helium mass flow was calculated based on the ohmic heat generated in the coil after the quench within 15 seconds. Warming of the cold force collar mass and the coil was assumed to occur after the helium inventory has boiled off. If the magnets lose their active energy dump protection, it is assumed that the magnet energy is dumped into the helium within the time constant of the magnet. Table 3 lists the average mass flow rate due to quench without active protection (Appendix 1). Table 4 lists the average mass flow rate due to quench with active protection (Appendix 1).

3. JT Valves Failing in the Most Open Position

In the event of the fill JT valves failing in their most open position while the return valves are closed, the capacity of the relief valves shall be enough to vent the gases. The maximum supply rate is from the Oxford Safety Analysis for the HMS Q2/3 Cold Iron Quadruples (Q-UM-DN 64/2, 1993). The maximum instantaneous flow rate is 127 g/s for helium; the maximum sustainable rate, 75 g/s.

Table 5 Failure of the JT Valves

Maximum Supply Rate Helium (127 g/s) Nitrogen (127 g/s)

4.0 Major Fault Loss of insulating vacuum Supplemental relieving devices to cover major fault conditions that lead to external heating of the helium and nitrogen volumes are covered under UG-125-a-(2). The expected mass flow rates for different scenarios are listed below. 4.1 Helium Mass Flow Rate Due to Loss of Vacuum (air) The rupture of the outer vacuum can, allowing rapid inrush of air into the outer vessel chamber is considered to be an abnormal fault condition. The heat flux associated with loss of insulating vacuum resulting in forced air convection, conduction and liquefaction of the air on the surface of the helium vessel is assumed to be . This is based on a JLab internal memo by Schneider (6/1/1999). The temperature of the helium at the exit is assumed to be approximately 7 K (Appendix 2). This is the most severe scenario. In the event of nitrogen leaking into the outer vessel chamber and causing loss of vacuum, the heat flux is assumed to be the same as that of the air leak because air contains 78% of nitrogen by volume.

Table 6 Mass Flow Rate at Loss of Vacuum due to Air Leak

Helium Insulated Surface Area Mass Flow Rate SHMS HB 4.797 SHMS Q1 12.77 SHMS Q2/3 17.86 SHMS Dipole 32.97

4.2 Helium Mass Flow Rate Due to Helium leak (Natural Convection) The fracture of a helium pipe internal to the OVC resulting in helium, spoiling the insulating vacuum is examined next. The heat flux associated with loss of vacuum due to helium gas given rise to natural convection and conduction is This number comes from the Oxford’s Safety Analysis for the HMS Q2/Q3 Cold Iron Quadrupoles (Q-UM-DN 64/2, 1993).

Table 7 Mass Flow Rate at Loss of Vacuum due to Helium Leak

Helium Insulated Surface Area Mass Flow Rate SHMS HB 4.797 SHMS Q1 12.77 SHMS Q2/3 17.86 SHMS Dipole 32.97

5. Capacity of the Relief Valve and the Rupture Disk for the Helium Vessel The capacity (5 atm gauge) of the relief valve and the rupture disk may be calculated according to ASME Section VIII, Division 1, Appendix 11 (Appendix 4). The relief valve is sized so that it is capable of handling the flow rate in the event of quench without active dump protection. The capacity of the relief valve is 13.96 kg/hr when the pressure is 4 atm gauge.

5 The same size of relief valve will be used to take care of the normal quench case with the active protection of the dump resistance for HB, Q1, Q2, Q3, and dipole. In the case of loss of vacuum and loss of active protection of the dump resistance, the rupture disk will kick in. Since HB is small, its relief valve is adequate to vent the helium in the case of loss vacuum and loss of active protection of the dump resistance. The rupture disk of the HB is to provide extra protection. Table 8 Capacity of the Relief Valves

Model Discharge Discharg Maximum Actual Capacity Diameter e Area Possible including Capacity plumbing Relief valve for Anderson 38.86 mm 1186 HB, Q1, Q2, Q3, Greenwood Pilot and Dipole Operated Relief [4 atm gauge] Valve Model No. 25905K34/S Rupture Disk for Fike 3’’ AXIUS 76.2 mm (3 9.121E3 HB, Q1, Q2, Q3 in) [5 atm gauge] Rupture Disk Fike 3’’ AXIUS 82.55 mm 5.352E3 and Relief Valve and Anderson (equivalent) for HB, Q1, Q2, Greenwood Q3 [5 atm gauge] Rupture Disk for Fike 101.6 mm 8.107E3 Dipole 4’’ AXIUS (4 in) [5 atm gauge] Rupture Disk Fike 4’’ AXIUS 108.2 mm 9.195E3 and Relief Valve and Anderson (equivalent) for Dipole Greenwood [5 atm gauge]

When taking into account the restrictions of the piping before the rupture disk, the maximum mass flow rate may be calculated based on the modified Darcy equation. The tube diameter is 101.6 mm (schedule 40, nominal pipe size 4’’) for the Dipole. The combined capacity of the rupture disk and relief valve is for the set pressure of 5 atm (see appendix 4) based on Darcy formula. Per UG-127, the calculated relieving capacity shall be multiplied by a factor of 0.9 since the rupture disk is assumed to be the sole relief device if the relief valve is frozen. The capacity of the rupture disk system for the Dipole with the set pressure of 5 atm is limited by the piping and is given by

Since only 3’’ rupture disk is used for HB, Q1, Q2, and Q3, 3’’ venting pipes shall be used.

Thus, the relief valve is capable of handling the normal event of quenching, and the rupture disk can handle the abnormal fault condition of loss of insulating vacuum, and loss of active protection of the dump resistance.

7 Table 9 Calculated Velocity of He Gas Flow

Velocity of Gas Flow at Exit Ratio between Actual Velocity and Sonic Velocity SHMS HB 70.0 m/s 0.45 SHMS Q1 118 m/s 0.76 SHMS Q2/3 114 m/s 0.74 SHMS Dipole 110 m/s 0.71

The velocity of gas flow at exit is below the helium sonic velocity of 185.7 m/s (Appendix 3). Choking will not happen since the calculated velocity is below the sonic velocity (Table 9).

Table 10 Minimum Required Tube Diameter

Minimum Required Diameter Nominal Diameter of Chosen Pipe SHMS HB 46.3 mm 76.2 mm SHMS Q1 60.0 mm 76.2 mm SHMS Q2/3 59.5 mm 76.2 mm SHMS Dipole 74.7 mm 101.6 mm

The minimum required diameters can be computed based on Oxford Safety Analysis (Q-UM-DN 64/2) (Table 10). The tube diameter of rupture disk is larger than the minimum requirement (Table 10).

It needs 12.4 seconds for the relief valve, and 2.9 seconds for the rupture disk, to vent all of the helium in the Dipole (Table 11).

Table 11 Venting Time of Helium with Relief Valve and Rupture Disk

Fully Open Relief Valve Fully Open Rupture Disk SHMS Q2/3 7.4 s 2.9 s SHMS Dipole 12.4 s 2.9 s

6. Nitrogen Mass Flow Rate Due to Loss of Vacuum In the event of loss of vacuum due to air, helium, or nitrogen leak, the heat flux is assumed to be and the temperature of the nitrogen at the exit is assumed to be approximately 100 K (Appendix 7). Table 12 Nitrogen Mass Flow Rate due to Loss of Vacuum

Surface Area Mass Flow Rate SHMS HB 3.068 SHMS Q1 11.67 SHMS Q2/3 15.38 SHMS Dipole 27.77

7. Capacity of the Relief Valve and Rupture Disk for the Nitrogen Vessel The nitrogen venting capacity of the relief valve and the rupture disk is calculated according to ASME Section VIII, Division 1, Appendix 11 (Appendix 7).

Table 13 Capacity of the Relief Valve and the Rupture Disk for HB, Q1, Q2/3, and Dipole

Model Discharge Discharge Maximum Actual Capacity Diameter Area Capacity Relief Flowsafe 14.64 mm 168.4 Valve F84-8 3/4M X (0.576’’) (0.261 ) 1F SS 0.261 Rupture Fike 25.4 mm 506.7 Disk 1'' AXIUS BT (1’’)

When taking into account the restrictions of the piping before the rupture disk, the maximum mass flow rate is calculated based on the modified Darcy equation. The tube diameter is 25.4 mm (316 schedule 40, nominal size 1''), giving a calculated mass flow capacity of with the set pressure of 5 atm. Per ASME 2007 VIII, Division 1, UG-127, the calculated relieving capacity shall be multiplied by a factor of 0.9 since the rupture disk is assumed to be the sole relief device if the relief valve is frozen. Thus the actual calculated capacity of the rupture disk with the set pressure of 5 atm is:

The mass flows generated due to loss of vacuum are less than the calculated capacity of the relief valve for the Q2/3, and dipole. Therefore, the rupture disk does not open to vent the nitrogen gas for these magnets. However, the rupture disk provides extra protection of nitrogen overpressure.

The velocity of gas flow at exit is below the nitrogen sonic velocity of 203.8 m/s. The actual velocity of the flow is below the sonic (Table 14).

9 Table 14 Velocity of N2 Flow

Actual Velocity of Gas Ratio between Actual Velocity and Flow at Exit (D=25.4 mm) Sonic Velocity SHMS HB 9.3 m/s 0.046 SHMS Q1 35 m/s 0.17 SHMS Q2/3 47 m/s 0.23 SHMS Dipole 84 m/s 0.41

The minimum required diameters are computed based on Oxford Safety Analysis (Q-UM-DN 64/2). The tube diameter of rupture disk is larger than the minimum requirement (Table 15).

Table 15 Minimum Required Tube Diameter

Minimum Required Diameter Chosen Pipe Diameter SHMS HB 4.54 mm 25.4 mm SHMS Q1 8.86 mm 25.4 mm SHMS Q2/3 10.2 mm 25.4 mm SHMS Dipole 13.7 mm 25.4 mm

8. Helium and Nitrogen Leak into Outer Vessel In the event of helium leaking into the outer vessel without rupture of the helium or nitrogen vessels, these cases are essentially the same as the loss of vacuum discussed in Section 4.

(1) Helium Leak

The worst case scenario for a helium leak onto the outer vacuum vessel is a rupture of a helium tube, which causes liquid to spill out onto the surface of the outer vessel. For a 1’’ tube with a 0.035’’ wall thickness, when it fully opens, the mass flow rate is 8071 kg/hr (2.5 atm absolute, 4.2 K). The assumption is conservative since the actual pressure of the liquid helium is only about 1.3 atm absolute. Table 16 shows that two parallel plates, each with a diameter of 4'' (101.6 mm), are good to vent the mass flow at the set pressure of 0.5 atm.

Table 16 Helium Mass Flow Rates

Required Mass Flow Rate Calculated Capacity of two 4’’ Parallel Plates SHMS HB SHMS Q1 SHMS Q2/3 SHMS Dipole (2) Nitrogen Leak

It is assumed that the heat flux is . The contact areas were computed based on the volume of the liquid. Table 17 illustrates that two parallel plates are more than enough.

Table 17 Nitrogen Mass Flow Rates and the Minimum Required Diameter

Contact Mass Flow Rate Calculated Capacity of Two Surface Area Parallel Plates SHMS HB 1.66 SHMS Q1 1.95 SHMS Q2/3 1.74 SHMS Dipole 2.51

9. Summary of the Safety Analysis Table 18 Summary of the Safety Analysis for the SHMS HB Helium Vessel

Number Fault Condition Required Flow Rate Venting Device 1 JT valves fail with input open and (127 g/s) Relief valve exits closed 2 Quench with dump resistance Relief valve 3 Quench without dump resistance Relief valve 4 Loss of vacuum due to helium leak Relief valve 5 Loss of vacuum due to air or Relief valve nitrogen leak 5 Loss of vacuum due to air and 3’’ rupture disc and quench without dump resistor relief valve

Table 19 Summary of the Safety Analysis for the SHMS Q1 Helium Vessel

Number Fault Condition Required Flow Rate Venting Device 1 JT valves fail with input open and (127 g/s) Relief valve exits closed 2 Quench with dump resistance Relief valve 3 Quench without dump resistance Relief Valve 4 Loss of vacuum due to helium leak Relief valve 5 Loss of vacuum due to air or Relief valve nitrogen leak

11 6 Loss of vacuum due to air leak and 3’’ rupture disc and quench without dump resistor relief valve Table 20 Summary of the Safety Analysis for the SHMS Q2/3 Helium Vessel

Number Fault Condition Required Flow Rate Venting Device 1 JT valves fail with input open and (127 g/s) Relief valve exits closed 2 Quench with dump resistance Relief valve 3 Quench without dump resistance Relief valve 4 Loss of vacuum due to helium leak Relief valve 5 Loss of vacuum due to air or 3’’ rupture Disk and nitrogen leak relief valve 6 Loss of vacuum due air leak and 3’’ rupture Disk and quench without dump resistor relief valve

Table 21 Summary of the Safety Analysis for the SHMS Dipole Helium Vessel

Number Fault Condition Required Flow Rate Venting Device 1 JT valves fail with input open and (127 g/s) Relief valve exits closed 2 Quench with dump resistor Relief valve 3 Quench without dump resistor Relief valve 4 Loss of vacuum due to helium leak 4’’ rupture Disc and relief valve 5 Loss of vacuum due to air or 4’’ rupture Disc and nitrogen leak relief valve 6 Loss of vacuum due to air leak and 4’’ rupture Disc and quench without dump resistor relief valve

Table 22 Summary of the Safety Analysis for the Nitrogen Vessel

Number Fault Condition Required Flow Rate Venting Device 1 JT valves fail with input open and (127 g/s) Relief valve exits closed 2 Loss of vacuum due to air, helium, Relief valve and nitrogen leak

13 Table 23 Summary of the Safety Analysis for the Outer Vessel

Number Fault Condition Required Flow Rate Venting Device 1 Helium Leak Parallel plate 2 Nitrogen leak Parallel plate

References Oxford Instruments, Ltd Safety Analysis for Q2/3 Cold Iron Quadrupoles (Q-UM-DN 64/2), 1993

Oxford Instruments, Ltd Quench Protection Design Report (Q-UM-DN 37/2), 1992

Fike Corporation Rupture Disk Sizing, Technical Bulletin TB8102, 2000

ASME ASME Section VIII, Division 1, 2007

Ed Daly SNS Cryomodule Pressure Drop Estimates and LOV Calculations, JLab internal memo, 4/19/2000

W. Schneider Upgraded Cryomodule Loss of Vacuum Calculations, JLab internal memo, 6/1/1999

S. Sciver Helium Cryogenics, 1986 Appendix 1– Magnet Quench

HB (Film Boiling Method) (1) Mass Flow Rate due to Quench with Dump Resistance

Averaged temperature of the coil: Heat flux of film boiling: Effective surface area: Helium latent heat of vaporization:

Mass flow rate due to quench with active protection

(2) Mass Flow Rate due to Quench without Dump Resistance Failed

Averaged temperature of the coil: Heat flux of film boiling:

Q1 (Film Boiling Method) (1) Mass Flow Rate due to Quench with Dump Resistance

Averaged temperature of the coil: Heat flux of film boiling: Effective surface area:

(2) Mass Flow Rate due to Quench without Dump Resistance Protection

15 Q2/3 (Film Boiling Method) (1) Mass Flow Rate due to Quench with Dump Resistance

(2) Mass Flow Rate due to Quench without Dump Resistance Failed

Dipole (Film Boiling Method) (1) Mass Flow Rate due to Quench with Dump Resistance

(2) Mass Flow Rate due to Quench without Dump Resistance Protection

Mass flow rate due to quench with active protection Q2/3 (Quench Method) (1) Mass Flow Rate due to Quench with Active Protection

Ohmic heat generated in the coil after 20 s with quench: Time to generate the ohmic heat: Helium latent heat of vaporization:

(2) Mass Flow Rate due to Quench without Active Protection

Latent energy of the liquid helium: Time to generate the He latent energy: Mass flow rate due to quench with no active protection

Dipole (Quench method) (1) Mass Flow Rate due to Quench with Active Protection

Ohmic heat generated in the coil after 20 s with quench: Time to generate the ohmic heat: Mass flow rate due to quench with active protection

(2) Mass Flow Rate due to Quench without Active Protection

Latent energy of the liquid helium: Time to generate the He latent energy: Mass flow rate due to quench with no active protection

17 Appendix 2 – Helium Mass Flow Due to Loss of Vacuum

(1) Loss of Vacuum due to Air Leak

HB Heat flux of air leak: Surface area of the helium vessel: Mass flow due to loss of vacuum

Q1 Surface area of the helium vessel: Mass flow due to loss of vacuum

Q2/3 Surface area of the helium vessel: Mass flow due to loss of vacuum

Dipole Surface area of the helium vessel: Mass flow due to loss of vacuum

(2) Loss of Vacuum due to Helium Leak

HB Heat flux of helium leak: Mass flow due to loss of vacuum

Q1 Mass flow due to loss of vacuum Q2/3 Mass flow due to loss of vacuum

Dipole Mass flow due to loss of vacuum

19 Appendix 3 - Minimum Required Diameters for Helium Vessel relief Devices

HB Gas constant: Pressure: Temperature: Diameter: Pressure ratio: Pressure at exit:

Density at exit:

Volume rate:

is the maximum flow rate due to the quench or loss of vacuum. Actual velocity:

The minimum cross sectional area before the valve seat may be computed using AD-Merkblatt A2 Section 9.4.1.

Pressure in the helium vessel: Isentropic exponent: Temperature of gas at exit: Outflow coefficient allotted in context with type test: Compressibility factor: Molar gas of mass:

Outflow function for supercritical flow

Minimum area before the valve seat

Minimum diameter of opening Q1 Gas constant: Pressure: Temperature: Diameter: Pressure ratio: Pressure at exit:

Density at exit:

Volume rate:

Minimum diameter of opening

21 Q2/3 Gas constant: Pressure: Temperature: Diameter: Pressure ratio: Pressure at exit:

Density at exit:

Volume rate:

Dipole Volume rate: Actual velocity:

The maximum velocity of gas at temperature T

Specific heat ratio: Maximum velocity:

23 Appendix 4 – Capacity of the Relief Valve and the Rupture Disk for the Helium Vessel

Relief Valve Applied Code: API RP 520, Part 1 Model: Anderson Greenwood Pilot Operated Relief Valve Model No. 25905K34/S Constant for gas: Effective Nozzle coefficient for 90% of Actual Capacity: Molar mass of helium: Temperature of gas at exit: Pressure: Compressibility factor: Discharge area: (Valve Model No. 25905K34/S) Backpressure correction factor: No rupture disk upstream of relief valve:

Maximum discharge capacity of the relief valve:

3’’ Rupture Disk The capacity of the rupture disk may be computed according to ASME Section VIII Division 1 Appendix 11.

Constant for gas: Nozzle coefficient: Discharge diameter: Molar mass of helium: Temperature of gas at exit: Pressure: Compressibility factor: Discharge area: Maximum discharge capacity of the rupture disk:

Modified Darcy Formula for 3’’ Pipe (Actual Size is 3.25’’) The maximum mass flow rate for sonic flow at the exit from the rupture disk may be calculated using the modified Darcy formula (CRANE 1-9).

Pressure in the helium vessel (bar): Pressure in the helium vessel (Pa): Gas temperature in the vessel: Diameter of pipe: Gas constant: Friction factor: (3’’ inch pipe, A-26, CRANE)

Resistance coefficient (from CRANE 2-11, A-28, A-29)

Pipe (:

Elbow 1: = 0.22 Elbow 2: = 0.22 Entrance: Exit:

Check valve (reference pipe is 3''): = 1.35

4'' to 3'' reducer:

Standard tee (flow through run) = 0.36

Total resistance coefficient:

Based on CRANE A-22,

Specific volume at temperature T and pressure p:

Maximum mass flow rate considering the restrictions of the piping:

Per ASME VIII, Division 1, the actual calculated flow rate is

4’’ Rupture Disk Discharge diameter: Maximum discharge capacity of the rupture disk:

25 Modified Darcy Formula for 4’’ pipe (Actual size is 4.26’’) Diameter of pipe: Equivalent diameter of combined rupture disk and relief valve: Diameter: d = min(d1, d2) = 108.2 mm

Friction factor: (4’’ inch pipe, A-26, CRANE)

Resistance coefficient (from CRANE 2-11, A-28, A-29)

Pipe (:

Elbow 1: = 0.204 Entrance: Exit:

The internal diameter of the pipe is 4.26’’. The check valve was designed such that the net effective diameters are 4’’ in the areas of the support brackets and the opening area of the lifting valve. The check valve thus provides little resistance to the flow.

Check valve: = 1.7 Standard tee (flow through run): = 0.34 chimney:

Total resistance coefficient:

Per ASME VIII, Division 1, the actual calculated flow rate is

Flow coefficient of the check valve (A-10, CRANE) is Appendix 4 - Capacity of the Relief Valve and Rupture Disk for the Nitrogen Vessel The capacity of the relief valve and the rupture disk may be computed from ASME Section VIII Division 1 Appendix 11.

Relief Valve Constant for nitrogen gas: Nozzle coefficient: Molar mass of helium: Temperature of gas at exit: Pressure: Compressibility factor: Discharge area: Maximum discharge capacity of the relief valve:

1’’ Rupture Disk Constant for nitrogen gas: Nozzle coefficient: Discharge diameter: Molar mass of helium: Temperature of gas at exit: Pressure: Compressibility factor: Discharge area: Maximum discharge capacity of the relief valve:

Modified Darcy Formula for 1’’ pipe The maximum mass flow rate for sonic flow at the exit from the rupture disk may be calculated using the modified Darcy formula.

Pressure (bar): Pressure (Pa):

27 Gas temperature in the vessel: Diameter of pipe: Gas constant: Friction factor: (Flow in zone of complete turbulence)

Resistance coefficient (from CRANE A-29) Pipe (: Entrance: Elbow 1: Elbow 2: Exit: Total resistance coefficient: Based on CRANE A-22, , Specific volume at temperature T and pressure p:

Per ASME VIII, Division 1, the actual calculated flow rate is: Appendix 5 – Nitrogen Mass Flow Due to Loss of Vacuum

HB Heat flux: Nitrogen latent heat of vaporization: Surface area of the nitrogen shield: Mass flow due to loss of vacuum

Q1 Surface area of the nitrogen shield: Mass flow due to loss of vacuum

Q2/3 Surface area of the nitrogen shield: Mass flow due to loss of vacuum

Dipole Surface area of the helium vessel: Mass flow due to loss of vacuum

29 Appendix 6 Minimum Required Diameters for Nitrogen Vessel

HB Gas constant: Pressure: Temperature: Diameter: Pressure at exit: Density at exit:

Volume rate:

Actual velocity:

Pressure in the nitrogen vessel: Isentropic exponent: Temperature of gas at exit: Outflow coefficient allotted in context with type test: Compressibility factor: Molar gas of mass:

Q1 Volume rate:

Actual velocity: Minimum area before the valve seat

Q2/3 Actual velocity:

Dipole Volume rate: Actual velocity:

The maximum velocity of gas at temperature T

Specific heat ratio: Maximum velocity: