Sizing of the Shield-Line Safety Valves on the SVBs in B180 at CERN related to the Super-FRS Magnet Testing

Authors: Felix Wamers, Marion Kauschke, Alexander Täschner, Yu Xiang (CSCY, GSI)

Checked by:

EDMS ID:

Abstract This document presents the reasoning and calculations for the sizing of safety valves on the Satellite

Valve Boxes (SVBs) in B180 at CERN, which are needed to protect the thermal-shield circuits (50-80 K)

between the SVBs and the SuperFRS magnets against overpressure caused by hazardous events, such as

Loss of Insulation Vacuum (LOIV).

Table of Contents Abstract ......................................................................................................................................................... 1

Table of Contents .......................................................................................................................................... 1

1. Introduction ........................................................................................................................................... 2

2. Safety Scenario – Geometrical, Thermal, & Hydraulic Aspects ............................................................. 3

3. Safety Valve Sizing - “Static” Approach ................................................................................................. 5

3.1 Relief Mass-Flow Rate and Temperature ...................................................................................... 5

3.2 Calculation of the SV minimum discharge area ............................................................................ 7

3.3 Pressure Drop Calculation ............................................................................................................. 8

4. Safety Valve Sizing - “Dynamic” Approach Using EcosimPro .............................................................. 10

4.1 Model Description ....................................................................................................................... 10

4.2 Relief Mass-Flow Rate ................................................................................................................. 12

4.3 Pressure Evolution and Pressure Drop ........................................................................................ 13

4.4 Switching off the Heat Transfer between Helium and Pipes ...................................................... 15

5. Summary & Conclusions ...................................................................................................................... 15

References ................................................................................................................................................... 17

1. Introduction

The superconducting magnets of the SuperFRS fragment separator of FAIR will be cold-tested at CERN

[1]. These tests will be performed using the cryogenic infrastructure in Building 180 (B180) at CERN. Parts

of this infrastructure are currently being designed, tendered, and/or constructed.

The facilities in B180 will host three cryogenic test stands for SuperFRS magnets to be operated in

parallel; that is, being either a) cooled down, b) cold and undergoing tests, or c) warmed up.

The SuperFRS testing will (including pre-series models) comprise 24 dipole magnets, and 33 multiplet

magnets, each of which are going to be cryogenically supplied with cold/liquid helium via the same cryo

interface at any of the three test stands. All SuperFRS magnet types are bath-cooled magnets with an

additional thermal shield. Correspondingly, the cryo connections towards and within the cryostats

consist of in total 5 pipes: The thermal shield supply and return at 50 to 80 K, the LHe filling line hosting a

JT-expansion valve, the cold GHe return from the bath boil-off, and a dedicated line for flushing the

cryostat from the bottom in order to realize the cool-down / warm-up.

In B180, a cryoplant including a LN2-based precooler distributes the helium coolant towards a so-called

Satellite Valve Box (SVB) at each of the three test stands. From each SVB, the cryogenic supply to and

from the individual magnet cryostats are then realized using knee-like jumper connections.

In any case of malfunctioning (such as power failure, quenching, structural damage to equipment, etc.),

the cryogenic/hydraulic connection between the magnets/cryostats and the cryogenic infrastructure in

B180 will be blocked via Normally-Closed-like valves in the process-line connections in the SVBs.

- The process-lines and other pressure vessels on the cryo-plant side in B180 will be protected by

safety devices in the responsibility of the CERN cryo group.

- The LHe bath vessels (together with the connected 4.5 K piping, also including the ones in the

jumper connection) of the SuperFRS magnets will be protected by dedicated safety valves on

(top of) the respective magnet cryostats, in responsibility of GSI and/or the magnet designer

- MISSING until recently, had been the safety valve for the shield lines, between the closing valves

in the SVBs, and the magnet cryostat, including the jumper connections. CERN have meanwhile

implemented a P&ID change of their SVBs in order to include such a safety valve.

The present document shall provide:

1. A description of the accident SCENARIO (loss of insulation vacuum to air – LOIV)

2. The SIZING of the corresponding Safety Valve

3. The PRESSURE DROP calculation for this scenario

2. Safety Scenario – Geometrical, Thermal, & Hydraulic Aspects

We start by describing the physical situation in a normal, cold-operation, scenario, at which a LOIV

accident sets in. Figure 1 depicts the geometrical setting of a shield-line connection between magnet and

SVB.

Figure 1: Sketch of the Shield Lines connected between SVB, via Jumper, to Magnet, and back towards to Safety Valve. The helium-carrying shield lines are shown as green, the yet missing safety valve red.

During normal operation, the shield lines are carrying helium at 58 K and 16.7 bar(a) in the supply, and

helium at 61 K and 16.2 bar (a) in the return [2].

In case of a hazardous event, such as a loss of insulation vacuum towards air in the jumper or magnet

cryostat, the control valves for the shield supply and return circuits in the SVB will be closed, and the

helium in the shield lines will heat up and be pressurized. The design pressure of the systems (magnet

cryostats, jumper) is PS = 19 bar(g), so that the SV needs to be sized and designed in order to guarantee

and allow this design pressure.

In order to determine, for example, the total mass of helium, the relevant geometrical and

thermodynamical parameters of the considered system, subdivided into sections of SVB, Jumper, and

Magnet, are summarized in the following Table 1:

Table 1: (Conservative) Geometrical Description of the Shield-Line System in terms of the Feedbox (SVB), Jumper, and Dipole Sections

Line within Feedbox

Material Steel

Length / m 2.5 x2 (supply and return)

D_out / mm 33.7 DN25

D_in / mm 28.5

Outer Surface / m2 0.45 Surface of Fluid

Volume / m3 0.0032 Volume of Fluid

Line between Feedbox and Cryostat (Jumper) Steel

Length / m 6 x2 (supply & return)

D_out / mm 33.7

D_in / mm 28.5

Outer Surface / m2 1.07 Surface of Fluid

Volume / m3 0.0077 Volume of Fluid

Line within Dipole Cryostat Copper

Length / m 30 x2 (two parallel channels)

D_out / mm 8

D_in / mm 6

Outer Surface / m2 1.13 Surface of Fluid

Volume / m3 0.0017 Volume of Fluid

Line within Long-Multiplet Cryostat

Length / m 30 x2 (two parallel channels)

D_out / mm 10

D_in / mm 8

Outer Surface / m2 1.51 Surface of Fluid

Volume / m3 0.0030 Volume of Fluid

One should note, that the current preliminary design of both dipole and (long) multiplet foresees two-

channel piping around the shield (one inner, and one outer) of around 30 m each at 6 mm or 8mm inner

diameter, respectively [3,4].

For the case of the dipole, the (conservatively calculated) shield line helium volume thus amounts to

about 1.7 l, for the long multiplet to about 3.0 l. Using the more conservative supply operation

parameters of 58 K and 16.7 bar throughout this results in a total helium mass in the considered shield-

line system of

(10.6 + 1.7) liters 167 g for the SVB-Jumper-Dipole system, and

(10.6 + 3.0) liters 185 g, for the SVB-Jumper-Long-Multiplet system.

Summarizing the relevant parameters in Table 2:

Table 2: Parameters of the helium within the thermal-shield circuit relevant for the heat-up due to the LOIV.

SVB-Jumper + Dipole SVB-Jumper + Long Multiplet

Helium Volume / l 12.5 13.9

Helium Mass / g 167 185

Helium Surface / m2 2.65 3.03

Total Heat Power / kW 13.3 15.2

For the here considered hazardous event of a Loss of Insulation Vacuum to Air (LOIV), we are considering

a very conservative value of 5 kW/m2 as the corresponding heat load onto the shield-line helium itself.

This value corresponds to the value of heat flux onto not-MLI-insulated vessels carrying LN2 by

Lehmann&Zahn, a value which is proposed as a GHe carrying vessels in the 50-80 K temperature regime

within the Kryolize User Guide [5].

3. Safety Valve Sizing - “Static” Approach

The relevant physical quantities entering the sizing of a safety device protecting against overpressure,

such as in the European Standard EN 4126-1 are

Fluid Relief Pressure, atmospheric Back Pressure - PR , PB / bar(a),

Fluid Relief Temperature - TR / K,

Fluid peak Mass-Flow Rate to be relieved - MR / kg/s.

With the Design Pressure of the SFRS shield circuits fixed at PS = 20 bar(a) = 19 bar(g), the relieving

pressure for the safety valves is defined to be within the range of 100% to max. 110% of that value, being

the maximum allowable working pressure Pmax [7]:

𝑃𝑆 = 19 𝑏𝑎𝑟(𝑔) ≤ 𝑃𝑅 ≤ 20.9 𝑏𝑎𝑟(𝑔) = 110% ∙ 𝑃𝑆 ≡ 𝑃𝑚𝑎𝑥 = 21.9 𝑏𝑎𝑟(𝑎).

Usually, for safety devices protecting pressure vessels filled with cryogenic liquids, dedicated Standards

such as EN 13648-3 [8] are used to calculate/determine the applicable relief mass-flow rate MR and

temperature TR entering the safety-device sizing.

3.1 Relief Mass-Flow Rate and Temperature

For the above presented safety scenario however – Loss Of Insulation Vacuum to air (LOIV) onto GHe

thermal-shield piping circuit at supercritical temperatures between 50 K and 80 K – no norm or standard

is applicable that would determine the rules for calculating MR and/or TR. Instead, a dedicated physics

calculation based on the respective present system needs to be performed.

Such calculations, for the SFRS dipole and long-multiplet systems, shall be presented in the following

paragraph.

In order to estimate the order of magnitude of the mass flow to be relieved via the thermal-shield safety

valve on top of the B180 SVBs, the LOIV is approximated by the following state-change scenario:

𝑆𝑇𝐴𝑅𝑇 (𝑆𝑉 𝑐𝑙𝑜𝑠𝑒𝑑, 16.7 𝑏𝑎𝑟, 58 𝐾)

𝐿𝑂𝐼𝑉 (5

𝑘𝑊

𝑚2),𝑖𝑠𝑜𝑐ℎ𝑜𝑟𝑖𝑐

→

𝑅𝐸𝐿𝐼𝐸𝐹 (𝑆𝑉 𝑜𝑝𝑒𝑛, 20 𝑏𝑎𝑟, ~70𝐾)

𝐿𝑂𝐼𝑉(5𝑘𝑊

𝑚2),𝑖𝑠𝑜𝑏𝑎𝑟𝑖𝑐

→

𝐹𝐼𝑁𝐴𝐿 (𝑆𝑉 𝑠𝑡𝑖𝑙𝑙 𝑜𝑝𝑒𝑛, 20𝑏𝑎𝑟, 300𝐾)

The assumption of a continuous 5kW/m2 heat influx, beyond the ~77 K temperature for air/nitrogen

condensation, is very conservative here.

a) Super-FRS Dipole

Table 3 shows the calculation for the case of the Dipole circuit.

Table 3: Calculation for the Dipole: Isochoric Heat-up until Relief, then isobaric heat up of total mass to 300 K at 20 bar(a).

Start Relief Final (SV still open)

T / K 58.00 69.32 300.00

P / bar(a) 16.70 20.00 20.00

rho / kg/m3 13.36 13.36 3.18

V /m3 0.013 0.013 0.013

m / kg 0.167 0.167 0.040

∆m (A->B) / kg 0.128

Enthalphy H / J/kg 319339.08 379645.60 1579652.28

∆H (A->B) / J/kg 60306.53 1200006.68

E_input = ∆H * m / J 10101.19 200998.12

LOIV Heat Flux / W/m2 5000.00 5000.00 5000.00

Surface Area Piping / m2 2.65 2.65 2.65

LOIV Heat Power / W 13265.37 13265.37 13265.37

Time (A->B) / s 0.76 15.15

Averaged Mass Flow kg/s 0.0084

From the START state at operation conditions it takes about the 0.75 s until the relieving pressure of 20

bar(a) is reached and the safety valve opens.

The total helium mass in the system is 167 g. The enthalpy difference between RELIEF and FINAL states

are about 1.2 MJ/kg, equivalent to an energy difference of about 201 kJ for the 167 g.

As soon as the SV opens, assuming a continuous conservative value of 5kW/m2 heat influx, it takes about

15 s to reach the FINAL state, isobarically. In total about 128 g of helium are relieved via the valve, so

that the time-averaged relief mass flow results in close to 8.4 g/s.

b) Super-FRS long Multiplet

Table 4 shows the corresponding long-multiplet calculation.

Table 4: Calculation for the long Multiplet: Isochoric heat-up until relief, then heat up of total mass to 300 K at 20 bar(a)

Start Relief Final (SV still open)

T / K 58.00 69.32 300.00

P / bar(a) 16.70 20.00 20.00

rho / kg/m3 13.36 13.36 3.18

V /m3 0.014 0.014 0.014

m / kg 0.185 0.185 0.044

∆m (A->B) / kg 0.141

Enthalphy H / J/kg 319339.08 379645.60 1579652.28

∆H (A->B) / J/kg 60306.53 1200006.68

E_input = ∆H * m / J 11163.93 222144.89

LOIV Heat Flux / W/m2 5000.00 5000.00 5000.00

Surface Area Piping / m2 3.03 3.03 3.03

LOIV Heat Power / W 15150.33 15150.33 15150.33

Time (A->B) / s 0.74 14.66

Averaged Mass Flow kg/s 0.0096

The equivalent calculation for the long-multiplet system yields a helium relieving time of about 14.7 s, a

mass to be relieved of about 141 g, and a time-averaged mass-flow rate of about 9.6 g/s.

3.2 Calculation of the SV minimum discharge area

The minimum discharge area of the considered safety valve may at this point be determined using the

rules summarized, e.g., in EN ISO 4126-1 [8], based on the above calculated values for mass-flow rate,

relief pressure, back pressure, and relief temperature, according to these formulae:

𝐴 =𝑀𝑅

0.2883 ∙ 𝐶 ∙ 𝐾𝑑𝑟∙√𝑃𝑅 ∙ 𝜌,

𝐶 = 3.948 ∙ √𝑘 (2

𝑘 + 1)

𝑘+1𝑘−1

Where MR stands for the mass flow, PR the absolute relief pressure, ρ the relief density, C a function of

the isentropic coefficient k (= 5/3 for helium). The discharge area to be chosen depends on the discharge

coefficient Kdr, specified by the respective SV producer and/or supplier.

For example, if we assume a typical discharge coefficient of Kdr = 0.6, we obtain the following minimum

discharge areas and diameters, shown in Table 5.

Table 5: SV discharge dimensions according to EN ISO 4126-1, assuming a typical discharge coefficient of Kdr = 0.6.

Dipole Circuit Long-Multiplet Circuit

Relief Mass Flow / g/s 8.4 9.6

Isentropic Coefficient k / 1 5/3 5/3

Function “C” / 1 2.87 2.87

Min. Discharge Area / mm2 3.34 3.82

Min. Discharge Diameter / mm 2.06 2.21

Since the Safety valve needs to be able to serve both configurations, the larger area/diameter of the two

cases is the one to be chosen.

3.3 Pressure Drop Calculation

Assuming the constant averaged relief mass flows calculated above, as of 8.4 g/s for the Dipole and 9.6

g/s for the long-Multiplet circuits, we iterate the pressure evolution along the piping sections, each

subdivided in 10 elements of equal length, and solve the system in order to be exhausting at 20 bar(a) at

the safety valve. The helium flow is calculated to be as indicated by the green lines in Figure 1. The

geometrical parameters of the piping, dipole and multiplet, have been shown above.

Here we have assumed the helium temperature to stay constant at the initial relief temperature of about

69 K. The inner-wall rugosity of the pipes has been assumed to be 10-6 m.

The pressure drop as such has been calculated using the Colebrook equations [9].

a) Pressure Drop along the Dipole circuit

Table 6 shows that a pressure drop of 755 mbar is to be expected. This value, added to the set pressure

of 20 bar(a), is safely within the maximum allowable pressure, Pmax, of 21.9 bar(a).

However, it is larger than the 3% of PS (= 0.57 bar) that are allowed as pressure drop along the safety-

valve exhaust line, which is practically the entire system.

Table 6: Iterative pressure drop calculation along Dipole circuit assuming a mass-flow rate of 8.4 g/s

Helium Channel

P / bar T / K Mdot / kg/s

Length / m

rho / kg/m3

v / m/s dP / bar P_out / bar

(FB, supply)

1 20.75 69.32 0.0084 0.25 13.84 9.54E-01 0.000012 20.755

2 20.75 69.32 0.0084 0.25 13.84 9.54E-01 0.000012 20.755

9 20.75 69.32 0.0084 0.25 13.84 9.54E-01 0.000012 20.755

10 20.75 69.32 0.0084 0.25 13.84 9.54E-01 0.000012 20.755

(Jumper, supply)

1 20.75 69.32 0.0084 0.58 13.84 9.54E-01 0.000027 20.755

2 20.75 69.32 0.0084 0.58 13.84 9.54E-01 0.000027 20.754

9 20.75 69.32 0.0084 0.58 13.84 9.54E-01 0.000027 20.754

10 20.75 69.32 0.0084 0.58 13.84 9.54E-01 0.000027 20.754

Dipole 1 20.75 69.32 0.0042 3.00 13.84 1.08E+01 0.074209 20.680

(2 parallel channels)

2 20.68 69.32 0.0042 3.00 13.79 1.08E+01 0.074463 20.606

Furthest away from SV

6 20.38 69.32 0.0042 3.00 13.60 1.10E+01 0.075507 20.305

9 20.15 69.32 0.0042 3.00 13.45 1.11E+01 0.076320 20.077

10 20.08 69.32 0.0042 3.00 13.40 1.11E+01 0.076597 20.000

(Jumper, return)

1 20.00 69.32 0.0084 0.58 13.36 9.88E-01 0.000028 20.000

2 20.00 69.32 0.0084 0.58 13.36 9.88E-01 0.000028 20.000

9 20.00 69.32 0.0084 0.58 13.36 9.88E-01 0.000028 20.000

10 20.00 69.32 0.0084 0.58 13.36 9.88E-01 0.000028 20.000

(FB, return)

1 20.00 69.32 0.0084 0.25 13.36 9.88E-01 0.000012 20.000

2 20.00 69.32 0.0084 0.25 13.36 9.88E-01 0.000012 20.000

9 20.00 69.32 0.0084 0.25 13.36 9.89E-01 0.000012 20.000

10 20.00 69.32 0.0084 0.25 13.36 9.89E-01 0.000012 20.000

b) Pressure Drop along longMultiplet system

Table 7 shows that a pressure drop of 240 mbar is to be expected. This value, added to the set pressure

of 20 bar(a), is safely within the maximum allowable pressure, Pmax, of 21.9 bar(a).

Table 7: Iterative pressure drop calculation along the long-Multiplet circuit assuming a mass-flow rate of 9.6 g/s.

Helium Channel

P / bar T / K Mdot / kg/s

Length / m

rho / kg/m3

v / m/s dP / bar P_out / bar

(FB, supply)

1 20.24 69.32 0.0096 0.25 13.51 1.12E+00 0.000015 20.241

2 20.24 69.32 0.0096 0.25 13.51 1.12E+00 0.000015 20.241

9 20.24 69.32 0.0096 0.25 13.51 1.12E+00 0.000015 20.241

10 20.24 69.32 0.0096 0.25 13.51 1.12E+00 0.000015 20.241

(Jumper, supply)

1 20.24 69.32 0.0096 0.58 13.51 1.12E+00 0.000036 20.241

2 20.24 69.32 0.0096 0.58 13.51 1.12E+00 0.000036 20.241

9 20.24 69.32 0.0096 0.58 13.51 1.12E+00 0.000036 20.241

10 20.24 69.32 0.0096 0.58 13.51 1.12E+00 0.000036 20.241

long Multiplet

1 20.24 69.32 0.0048 3.00 13.51 7.08E+00 0.023914 20.217

(2 parallel channels)

2 20.22 69.32 0.0048 3.00 13.49 7.09E+00 0.023941 20.193

Furthest away from SV

6 20.12 69.32 0.0048 3.00 13.43 7.12E+00 0.024050 20.097

9 20.05 69.32 0.0048 3.00 13.39 7.15E+00 0.024133 20.025

10 20.02 69.32 0.0048 3.00 13.37 7.16E+00 0.024160 20.001

(Jumper, return)

1 20.00 69.32 0.0096 0.58 13.36 1.13E+00 0.000036 20.000

2 20.00 69.32 0.0096 0.58 13.36 1.13E+00 0.000036 20.000

9 20.00 69.32 0.0096 0.58 13.36 1.13E+00 0.000036 20.000

10 20.00 69.32 0.0096 0.58 13.36 1.13E+00 0.000036 20.000

(FB, return)

1 20.00 69.32 0.0096 0.25 13.36 1.13E+00 0.000015 20.000

2 20.00 69.32 0.0096 0.25 13.36 1.13E+00 0.000015 20.000

9 20.00 69.32 0.0096 0.25 13.36 1.13E+00 0.000015 20.000

10 20.00 69.32 0.0096 0.25 13.36 1.13E+00 0.000015 20.000

4. Safety Valve Sizing - “Dynamic” Approach Using EcosimPro

4.1 Model Description

We have modelled the system depicted in Figure 1 using the modelling and simulation tool “EcosimPro

5.4.14” using the “Cryolib 1.1” library for cryogenic media and components.

Figure 2: Logical scheme of the thermal-shield circuit as modelled using EcosimPro and the Cryolib.

Figure 2 shows the scheme of the thermo-hydraulic system created to model the thermal-shield circuit

described above. EcosimPro is a program that solves complex systems of coupled differential and/or

algebraic equations [10]. The Cryolib is a collection of models for components used in connection with

cryoplants and cryogenic engineering in general [11].

The components in the scheme shown in Figure 2 are explained in the following Table 8:

Table 8: Details on the components in the EcosimPro scheme.

Pictogram/Name Component Comment

Green Lines Hydraulical (helium-flow) connections

Source_B180 Logical source of the helium circuit Mass Flow set to zero here Closed valve imitation

Helium Working fluid Definition of the working fluid to be helium

Pipe_SVB_supply The supply pipe within the SVB Steel

DV1, DV2, DV3, DV4 Dummy valves, needed logically for the connection of pipes

All set Normally Open, with Cv = 1000, to be unresistive

Pipe_SVB_supply The supply pipe within the SVB Steel

Pipe_Jumper_supply The supply pipe within the Jumper Steel

Pipe_Magnet The piping around the shield within the magnet cryostat

Two parallel channels, Copper

Pipe_Jumper_Return The return pipe within the Jumper Steel

Pipe_SVB_Return The return pipe within the SVB Steel

SafetyValve_SVB The Safety Valve Realised as proportional valve opening linearly between 20 and 22 bar(a), with Cv=1

Sink_SV Logical sink of the helium circuit 1 bar, 300K (atmosphere)

Generally, each component has been set up identically to the geometrical and/or other specifications

shown in the various tables above.

Equally as in the scenario described above, the model system is exposed to a constant 5 kW/m2 of heat

flux, being ‘injected’ directly into the helium fluid. The helium is in thermal contact with the wall of the

piping, which thus works as a heat buffer. The walls, however, are not in any thermal contact with the

‘outside world’, i.e., not in contact with any atmospheric air as they would be in reality.

4.2 Relief Mass-Flow Rate

Figure 3 and Figure 4 show the temporal mass-flow evolution through the safety valve as calculated

using the presented EcosimPro model. One sees peak values of around 9.5 g/s about 2s after opening of

the SV, both for the Dipole and Multiplet systems. The mass flow rate then exponentially decays, to

around 2 g/s at a time of around 30 s. These values are generally comparable with the values obtained

above.

Figure 3: Mass Flow through (red) and opening of (blue) the Safety Valve. Dipole circuit.

Figure 4: Mass Flow through (red) and opening of (blue) the Safety Valve, as a function of time. Long Multiplet circuit.

4.3 Pressure Evolution and Pressure Drop

Figure 5 and Figure 6 show the temporal pressure evolution at two spots within the system: at the safety

valve itself (red), and at the point furthest away from it (blue), representing the location of highest

pressure in the entire system.

For the dipole system that peak pressure reaches close to 21.4 bar(a), at the time of the maximum mass-

flow rate, while for the long-multiplet with the larger cryostat-internal piping diameter it stays lower at

close to 21 bar(a).

The pressure drop can be viewed as the difference between those two pressure values. It amounts to

about 700 mbar in the dipole case, and to about 300 mbar in the multiplet case.

Figure 5: Pressure as a function of time at the Safety valve (red), and at the very end of the relief line, at the supply within the SVB (blue). Dipole Circuit.

Figure 6: Pressure as a function of time at the Safety valve (red), and at the very end of the relief line, at the supply within the SVB (blue). Long-Multiplet Circuit.

Even having chosen a comparatively small safety valve with Cv = 1, the pressure stays below the

maximum allowed pressure of 21.9 bar(a), everywhere in the system, and at any time.

4.4 Switching off the Heat Transfer between Helium and Pipes

The heat transfer coefficient between fluid and piping can be artificially set to zero in the above

presented EcosimPro model. Such, the 5kW/m2 heat flux being assumed due to the LOIV are only

impacting on the helium in the piping system – which is a very safety-conservative assumption.

Doing so and re-running the simulation, we find that the pressure evolution in the case of the Dipole

circuit (6 mm inner diameter piping) reaches values close to 23 bar(a).

However, for the long-multiplet circuit (8 mm internal diameter) the pressure evolution stays within legal

margins, below 21.9 bar(a), see Figure 7:

Figure 7: Pressure as a function of time at the Safety valve (red), and at the very end of the relief line, at the supply within the SVB (blue). Long-Multiplet Circuit, with any heat transfer between helium and piping switched off.

5. Summary & Conclusions

Table 9 summarises the “static” calculation results presented above.

Table 9: Summary of the results concerning the mass flow rate, pressure drop, and SV minimum discharge diameter for the Dipole and long-Multiplett thermal-shield circuits.

Dipole Circuit Long Multiplet Circuit

Relief Pressure / bar(a) 20 20

Back Pressure / bar(a) 1 1

Relief Temperature / K 69.3 69.3

Relief Duration / s 15.0 14.6

Avg. Mass-Flow Rate / g/s 8.3 9.5

Pressure Drop Along Whole Discharge Line / bar(a)

0.736 0.236

Given the set pressure of PS = 19 bar(g), the maximum allowable working pressure of 1.1*PS = 20.9 bar(g)

= 21.9 bar(a) is not exceeded – thus the considered single SV on the shield return line on the SVB is

sufficient and safe.

However, the pressure drop of 736 mbar along the entire (SVB-Jumper-Dipole-Jumper-SVB-SV) dipole

shield line is larger than the allowed 3% PS. It is left how to interpret the definition of the ‘discharge

pipe’, and whether it extends along the whole system or not. If yes, then strictly speaking the pressure

drop is exceeding the legal bounds, and in order to solve the situation, for example, a second Safety

Valve on the supply line of the thermal-shield circuit on top of the SVBs needs to be installed.

Table 10 summarizes the EcosimPro calculation. Its results generally agree with the simpler calculation

done before, in particular in the statement that the maximum allowed working pressure of 21.9 bar(a) is

nowhere and never exceeded, and in also in the sense that the previously calculated average mass flow

rates have the same order of magnitude.

Table 10: Summary of the EcosimPro-model results on mass-flow rate, peak pressure, and peak pressure drop for the Dipole and Multiplet systems, given a Safety Valve of the size Cv = 1.

Dipole Circuit Long-Multiplet Circuit

Peak Mass-Flow Rate / g/s 9.4 9.8

Peak Pressure / bar(a) 21.35 20.95

Pressure Drop / bar(a) 0.7 0.3

As a conclusion we see the solution of one Safety Valve on the return shield line on the SVBs as sufficient

and safe, and we suggest to size them according to EN ISO 4126-1, for a relief temperature of 70 K, a

relief pressure of 20 bar(a), and for a mass-flow rate of 10 g/s.

As a second conclusion, from the observation of the pressure-drop result shown in Figure 7 on the

conservative consideration of no heat transfer back from helium to the piping walls, we recommend to

increase the internal diameter of also the dipole shield piping from 6 mm to at least 8 mm like for the

long multiplet. Preferably, both would be increased to 10 mm.

References

[1] CERN GSI collaboration contract on SFRS Magnet Testing

[2] A. Perin (CERN), private communication

[3] L. Quettier (CEA), private communication

[4] H. Mueller (GSI), private communication

[5] A. Henriques (CERN), Kryolize User Guide, CERN, 2014

[6] EN ISO 4126-1, Safety devices for protection against excessive pressure – Part 1: Safety valves, 2004

[7] Directive 97/23/EC of the European Parliament and of the Council of 29 May 1997 on the

approximation of the laws of the Member States concerning pressure equipment

[8] EN ISO 13648-3, Safety devices for protection against excessive pressure – Part 3: Determination of

required discharge – Capacity and sizing, 2002.

[9] Colebrook, C.F., Turbulent flow in pipes, with particular reference to the transition region between

smooth and rough pipe laws. Journal of the Institution of Civil Engineers, London, February 1939.

[10] F. Vazquez et al., Introduction to Modelling and Simulation with EcosimPro, Pearson, Madrid, 2010.

[11] Cryolib 1.1 Reference Manual, Empresarios Agrupados, 2014.