DIMENSIONAL CALCULATIONS FOR RELIEF SYSTEMS AND VENT LINES OF THE NPDGAMMA LIQUID HYDROGEN TARGET

Prepared: H. Nann, Indiana UniversityChecked : S. Penttila, ORNLApproved: M. Snow, Indiana University

SCOPE

In this document is summarized the calculations of the sizing of the relief system and vent stack of the NPDGamma liquid hydrogen target. Calculations were performed to determine the size of the relief piping such that the hydrogen mass flow (mass boil-off rate) due to catastrophic vaporization of the liquid hydrogen in the target vessel or isolation vacuum chamber remains subsonic at all times – Sonic flow represents the maximum possible flow in a piping system – and that the maximum pressure in each component remains well below its bursting point. Also the two worst case incidents are discussed and shown that the safety system is correctly dimensioned.

FORMALISM

Calculations are based on the Bates Internal Report # 90-02 [1] and the Crane Technical Paper No. 410 [2]. Using the formulae and algorithms from these two reports, computer programs was written to calculate the maximum pressure occurring during the discharge through the relief system

MODEL

The hydrogen pressure relief system, shown in Figures 1 and 2, consists of:1. The 1.5” nominal size hydrogen vent line from the target vessel to the relief

valve RV104 which is parallel with a rupture disk RD101 inside the vent isolation box. The inner diameter of this line is 1.37 inch.

2. The target isolation vacuum chamber is connected with a 6.0” nominal size commercial steel pipe to the small throughput relief valve RV201, which is parallel with two rupture disks RD201 and RD202. These two rupture disks are inside the vent isolation chamber. The inner diameter of this line is 5.75 inch. The 1.5” OD hydrogen fill/vent line runs coaxially inside the 6.0” OD pipe.

3. All these relief devices are connected to the same volume of the vent isolation chamber. The vent isolation chamber is described in section 4.

Fig. 1. Conceptual schematic of the LH2 target system, cryostat, vacuum/fill/vent line, and vent isolation box.

Fig. 2. The model view of the vent isolation chamber inside the ventilated vent isolation cabinet when the cabinet cover has been removed

CALCULATIONS

The calculations of the maximum pressure in the LH2 target vessel and the isolation vacuum chamber during the catastrophic failure takes into consideration all the pipes and bends up to the end of the vent stack outside of the Target Building, including the pressure relief valves in the vent isolation box. The friction factors for each component in the relief system were taken from the Crane Technical Paper No. 410 [2].

Hydrogen gas is much lighter (M=2 g/mole) than NTP air (average molecular M=29 g/mole) or argon (molecular M=40 g/mole) and will rise in air at temperatures above 23 K (normal boiling point temperature: 20.3 K). Buoyant velocities are related to the difference in air and H2 gas (GH2) densities. The buoyant velocity of hydrogen in NTP air is 3.9 to 29.5 ft/s.

Section 1 presents the formula for the gas flow rate in terms of the gas flow

resistance coefficient and the mass flow rate from the target. Sections 2 and 3

show the calculations for K from the target and cryostat vacuum to the vent

isolation chamber. Section 4 describes the vent isolation chamber in enough

details to under stand the calculations. Section 5 shows the calculation of K from

the vent isolation chamber to the exit of the vent stack. Section 6 gives the basis

Vent isolation chamber

Hydrogen line

Coxial fill/vent line

From isolation vacuum

for the estimate of the heat flux which sets the mass flow rate. Sections 7 and 8

presents the results for the pressure in the target vessel and the vacuum chamber

respectively. Section 9 states the conclusions.

1 Formulae for Flow Rates and Pressure Drop in the Relief Line in the Event of a Catastrophic Vacuum or Target Failure

The following describes calculations based on the formulae and procedures of the Bates Internal Report # 90–02 [1] and the Crane Technical Report No. 410 [2] for various mass flow rates and nominal size diameters of the vent pipe. The rate of mass flow through pipes, valves and fittings is given by the Darcy formula

where w = mass flow rate [lb/s]p1 = inlet (upstream) pressure [psia]p2 = outlet (downstream) pressure [psia]d = inner diameter of vent pipe [inch]Y = net expansion factor for compressible flow through orifices,

nozzles, or pipe (see Table F.1)K = total resistance coefficient for the vent systemT = absolute temperature of the flowing gas [K]M = molecular mass of the gas [g/mol]L = length of the pipe [inch]

The functional dependence of Y versus (p1 – p2)/p1 is linear and can be written in the form

Y = 1 – mxwhere m = absolute value of slope

x = (p1 – p2)/p1

0 x xmax (The value xmax corresponds to sonic flow)

Values for m and xmax for different resistance coefficients K are given in Table 1.

Table 1: Net expansion factor Y for compressible flow through pipe to a larger flow area; ratio of specific heat at constant pressure to specific heat at constant volume for hydrogen is = 1.4.

K m xmax2.0 0.618 0.6124.0 0.504 0.6976.0 0.446 0.7378.0 0.413 0.76210.0 0.389 0.78415.0 0.364 0.81820.0 0.346 0.83925.0 0.339 0.85530.0 0.334 0.86840.0 0.328 0.88360.0 0.321 0.904100.0 0.313 0.926

Substituting the linear form for Y into the Darcy equation yields

Squaring both sides of this equation leads to a cubic equation of the form

x3 + ax2 + bx + c = 0where

This cubic equation was numerically solved for x. For subsonic flow, at least one root must lie in the range 0 < x < xmax. If not, then the flow is sonic. The steady-state pressure is then given by

To determine x we therefore must know the resistance coefficient K and the mass

flow rate.

2 Total Resistance Coefficient for the Vent Line from the LH2 Target Vessel to the Vent Isolation Chamber

The 1.5” vent line from the target to the vent isolation box contains all pipes, bends, and pressure relief valves from the target vessel up to the vent isolation box, see drawing series 312644 in the target website. Individual resistance coefficients for the various components in the vent line, including the relief valve RV104 are listed in Table 2. A friction factor of f = 0.021 for clean commercial steel pipe of nominal 1.5 inch diameter is used. The K-value for the relief valve RV104 was assumed to be the same as that for a globe and angle type stop-check valve [2], K = 55f.

Table 2: Individual and total resistance coefficients K for the vent line from the target vessel to the vent isolation box; reference diameter 1.5 inch.

Component Resistance Coefficient K

365 inch pipe 5.114 - 90° pipe bends; r/d = 1.5

1.18

2 - 45° elbows 0.674 - bellows; 1.5 ID, 2.0 OD, 10 ribs

16.20

1 - 6” flex line, 24 ribs 9.72

1-standard tee (flow through run)

0.42

1 – gate valve 0.17

1 – relief valve 1.16

1 – pipe exit 1.00

TOTAL 35.63

The Crane Technical Paper No. 410 [2] does not contain a resistance coefficient (K) for bellows. Thus the following model was used. A bellow consists of a series of sudden enlargements and contractions, as shown in the Fig. 3.

Fig. 3. Model of bellows consisting of a series of sudden enlargements and contractions.

The actual resistance coefficient will be smaller since the edges are rounded and the cells are small so that vortices cannot develop completely as in a single sudden enlargement or a single sudden contraction. This overestimate of the resistance coefficient will be an error on the side of safety. The resistance to flow due to a sudden enlargement is given by [Ref. 2]

,

and the resistance due to a sudden contraction is

,

where . The subscripts 1 and 2 define the internal diameters of the small and large pipes, respectively (see Fig. 3). Thus we have for one bellow cell (one sudden enlargement plus one sudden contraction)

Example: d1 = 1.50 inchd2 = 2.00 inch

For 10 bellow cells we have K = 4.05.

3 Total Resistance Coefficient for the Vent Line from the Target Isolation Vacuum Chamber to the Vent Isolation Chamber

The 6” vent line from the target isolation vacuum chamber to the vent isolation chamber contains all pipes, bends, and pressure relief valves from the vacuum chamber up to the vent isolation box, see drawing series 312644 in target web site. Individual resistance coefficients for the various components in the relief line, including the relief valve RD201 are given in table 3. The actual size of this relief line is 6.0 inch; however, in order to take into account that the target relief line and gas pre-cooling system run coaxially inside the 6.0 inch pipe, a reference diameter of 4.0 inch was chosen. A friction factor of f = 0.017 for clean commercial steel pipe of nominal 4.0 inch diameter was used.

Table 3: Individual and total resistance coefficients K for the relief line from the target isolation vacuum chamber to the vent isolation box; reference diameter 4.0 inch. The flow is calculated through one 4 inch bellows followed by one rupture disk (RD201).

Component Resistance Coefficient K

335 inch pipe 1.42

1 – 6” bellow; 10 ribs 2.03

1 – standard tee; flow through run

0.34

2 – standard tees; flow through branch

2.04

1 – 4” bellows; 10 ribs 2.46

1 – rupture disk RD201* 1.88

1 – pipe entrance 0.5

1 – pipe exit 1.0

TOTAL 11.67

* according to manufacturer (Fike) for SR-H rupture disks

4 The Vent Isolation Chamber

The vent isolation chamber (see drawing series 315337) is a cylindrical vessel, constructed of 10-inch, Schedule 10 NPS stainless steel pipe of thickness 0.165 inch, with CF flanged, flat heads on either end. It is 28 inches long. It is located inside a ventilated vent isolation cabinet (see Fig. 2). The inlet to the vent isolation chamber is the 1.5-inch pipe from the LH2 target through a flanged head. The CF-flanged outlet at the other end of the chamber is a 6.0-inch pipe of the vent stack going outside of the Target Building. The thickness of the two end flanges is 1.120 inch. Additionally, there are two 10-inch full inlet joints to the side of the cylindrical shell, which are connected to the target isolation vacuum chamber.

Inside the vent isolation chamber (see Fig. 4) are the pressure relief devices for the target vessel, RV104 (set point: 20 psid) and in parallel RD101 (set point: 30 psid), and for the target isolation vacuum chamber, RD101 (set point: 7 psid) and in parallel RD102 (set point: 7 psid).

Fig. 4 Vent isolation chamber with assembly of the relief valve, RV104, and rupture disks, RD101, RD201, and RD202. See drawing series 315337

5 Total Resistance Coefficient for the Vent Stack from the Vent Isolation Chamber to the Outside of the Target Building

The vent stack from the vent isolation chamber contains all pipe, bends, and pressure relief valves from the vent isolation chamber to the outside of the experimental hall. Individual resistance coefficients for the various components in the relief line are given in Table 4. A friction factor of f = 0.015 for clean commercial steel pipe of nominal 6.0 inch diameter is used.

Table 4: Individual and total resistance coefficients K for the relief line from the vent isolation chamber to the outside of the experimental hall; reference diameter 6.0 inch.

Component Resistance Coefficient K

70 feet pipe 2.10

3 – 90° elbows 1.35

2 - 45 elbows 0.48

1 – standard tee, 6 ID(flow through branch)

0.84

1 – pipe entrance 0.50

1 – pipe exit 1.00

1.5inch vent line vent stack

CF flange

TOTAL 6.27

Conversion to 1.5 inch reference diameter pipe:

Conversion to 4.0 inch reference diameter pipe:

To update this, we need to find out what the real vent stack will be. Since we have to convert to the 1.5 and 4.0 inch reference pipes, this will not change the conclusion below.

6 TWO WORST ACCIDENT SCENARIOS AND RESULTING HEAT FLUXES TO LH2

A sketch of the cross section of the LH2 target vessel and the isolation vacuum chamber (cryostat) is show in Fig. 5. In order to reduce the heat flux into the LH2

target vessel, vacuum and approximately 10 layers of superinsulation are wrapped around the LH2 target vessel. Around this, a copper radiation shield, continuously kept to temperatures at below 100 K, is mounted to protect the LH2 target vessel from radiative heating. An additional 1 – 2 cm thick layer of superinsulation is wrapped around the copper radiation shield.

Fig. 5. Sketch of the cryostat cross section and the LH2 target vessel. Around the LH2 target vessel is vacuum and are several layers of superinsulation, also around the copper radiation shielding is 1 – 2 cm thick superinsulation layer. The function of the superinsulation is to prevent radiative and convection heating and to reduce the heat transfer to the LH2 target. The continuously cooled copper radiation shield establishes an intermediate temperature boundary at 100 K.

There are two maximum credible accident scenarios possible which determine the size of the pressure relief system:

(A) A loss of the cryostat isolation vacuum through a large air leak causing the pressure in the target vessel and target lines to rise.

The heat transfer from the warm outer walls of the cryostat into the LH2 is difficult to calculate reliably. However, the literature gives several reports where the heat transfer rates are measured between two surfaces at different temperatures. Most measurements have been performed using liquid helium as the cryogenic fluid. However, the differences between liquid helium and liquid hydrogen are small.

Ref. [3] gives a maximum heat transfer rate = 4.4 103 W/m2 for the case where the cryogenic fluid is liquid helium at 4 K. The cryostat isolation vacuum is let up to 1 atm of air. The thickness of the superinsulation around the target vessel

is only 3 mm which is very thin compared to the 1 – 2 cm thick superinsulation layers of the NPDGamma target.

The enthalpy of vaporization for hydrogen is = 445.6 kJ/kg, the density of LH2 at the normal boiling point (20.4 K) is = 70.78 kg/m3, the mass of 16 liter of LH2 is m = 1.14 kg, and the surface area of the target vessel is A = 0.4 m2. Thus the amount of energy required to boil off the 16 liter of LH2 is

and the boil-off rate (mass evolution rate) is

The mean velocity of flow in a nominal 1.5 inch diameter pipe at this boil-off rate is

Note: The speed of sound in hydrogen at NTP is

Ref. [4] estimates the heat transfer rate in the NPDGamma LH2 target due to a cryostat isolation vacuum failure to air to be 2000 W/m2. It was assumed that the target vessel was surrounded by 1 cm thick superinsulation (about 30 layers). This gives a much smaller (30 times smaller) boil-off rate of

Here the mean velocity of flow in a nominal 1.5 inch diameter pipe is . Nevertheless, to be on the safe side, we will use the much higher flow rate estimate, 31.3 lb/h, from the calculation above in our flow calculations below.

(B) A rupture of the target flask or piping inside the vacuum chamber will release the LH2 into the isolation vacuum chamber and hydrogen will boil off quickly. Here the LH2 is in contact with a larger warm surface area causing a larger boil-off rate. Assuming a heat flux of 1.0 105 W/m2 into the vacuum vessel which has a surface area of about 1 m2 in contact with the liquid hydrogen we obtain a mass flow rate of w = 0.5 lb/s

7 Steady State Pressure in the Target Vessel during Catastrophic Discharge

The total resistance coefficient from the target vessel to the outside atmosphere is K = 35.63 + 0.02 = 35.65 (reference diameter: 1.5 inch; actual inner diameter: 1.375 inch, which was used in the calculations below) from section 2. The steady-state target pressure was calculated with the following assumptions:

Flow temperature: T = 293 K, taken at the warmest point in the relief system. This will overestimate the inlet pressure p1, but this will be an error on the side of safety.

Outlet pressure: p2 = 14.7 psia, venting to air at the normal atmospheric pressure. Assume: Mass flow rate: w = 0.009 lb/s

Total resistance coefficient: K = 40.0 from sections 2 and 5

Results: Sonic flow rate: wsonic = 0.29 lb/sTarget pressure (according to Table 5): p1 = 21.7 psia

Table 5: Maximum discharge pressures for various mass flow rates w and resistance coefficients K. The inner diameter of the relief pipe is 1.370 inch. For comparison, results of calculations for a 10 times larger mass flow rate as above described are included.

ResistanceCoefficient

w = 0.09 lb/sp1 (psia)

w = 0.009 lb/sp1 (psia)

w = 0.004 lb/sp1 (psia)

K = 20 35.5 15.7

K = 25 38.9 17.1

K = 30 42.0 18.6 15.3

K = 40 47.7 21.7 16.2

K = 60 57.2 30.2 17.7

8 Steady State Pressure in the Target Isolation Vacuum Chamber during Catastrophic Discharge

Reference diameter: 4.0 inch: (This takes into account that the target relief line and gas pre-cooling system runs inside the 6.0 diameter target isolation vacuum chamber vent line.)

The total resistance coefficient from the insulating vacuum vessel to the outside atmosphere is K = 11.67 + 1.24 = 12.91

The steady-state pressure in the target isolation vacuum chamber was calculated with the following assumptions:

Mass flow rate: w = 0.5 lb/sFlow temperature: T = 293 K, taken at the warmest point in the relief system. This will overestimate the inlet pressure p1, but this will be an error on the side of safety.Outlet pressure: p2 = 14.7 psia, venting to air at the normal atmospheric pressure.

Assume a total resistance coefficient: K = 15.0 from sections 3 and 5

Results:Sonic flow rate wsonic = 3.28 lb/sVacuum vessel pressure p 1 = 18.6 psia.

9. SUMMARY

The results show that, in the case of a catastrophic cryostat vacuum failure to air, the LH2 target vessel is subjected during the discharge to a pressure of no more than 21.7 (16.2) psia if the boil-off rate is assumed to be 0.009 (0.004) lb/s and the fill/vent piping is a nominal 1.5-inch OD pipe. The maximum pressure during discharge in the target isolation vacuum chamber for the case of a rupture of the target flask is 18.6 psia for a 4.0-inch diameter nominal pipe if a boil off rate of 0.50 lb/s is assumed.

In summary, the results of the above calculations show that the proposed relief piping is properly sized to prevent excessive pressures in the LH2 target vessel and isolation vacuum chamber after catastrophic failures. The calculated discharge pressures are below the pressures at which the relief valves and rupture disks open (p = 14.7 psia + 20 psid = 34.7 psia for the LH2 target vessel and p = 14.7 psia + 7 psid = 21.7 psia for the isolation vacuum chamber). This means that, once the relief devices open, the pressures in the LH2 target vessel and in the isolation vacuum chamber will not increase beyond the set points of the relief devices of 34.7 psia and 21.7 psia, respectively.

References:[1] W.M. Schmitt and C.F. Williamson, Boil-off rates of cryogenic targets subject to catastrophic vacuum failure, Bates Internal Report 90-02 (1990).[2] Flow of Fluids through Valves, Fittings, and Pipe, CRANE Technical Paper No. 410 (1988).[3] S.M. Harrison, IEEE Trans. Appl. Superconduct. 12, 1343 (2002).[4]

S.I. Penttila and S. Covrig, Hydrogen release rate from the NPDGamma

liquid hydrogen target into the BL-13 shielding in a failure of target vacuum and hydrogen boundaries, ORNL-SNS Document FUND13NPDG-24-ES0001-R00 Details (2008).