October 2015 

NASA/TM2015-218810

NESC-RP-15-01017 

 

Simplified Methodology to Estimate the 

Maximum Liquid Helium (LHe) Cryostat 

Pressure from a Vacuum Jacket Failure 

Eugene K. Ungar 

Johnson Space Center, Houston, Texas 

W. Lance Richards/NESC 

Langley Research Center, Hampton, Virginia 
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October 2015 

NASA/TM2015-218810

NESC-RP-15-01017 

 

Simplified Methodology to Estimate the 

Maximum Liquid Helium (LHe) Cryostat 

Pressure from a Vacuum Jacket Failure 

Eugene K. Ungar 

Johnson Space Center, Houston, Texas 

W. Lance Richards/NESC 

Langley Research Center, Hampton, Virginia 
Available from: 

NASA STI Program / Mail Stop 148 

NASA Langley Research Center 

Hampton, VA 23681-2199

Fax: 757-864-6500

Acknowledgments 

The author wishes to thank Mr. Andrew Hong (JSC) for performing the numerical 

analysis for the present work. 

The use of trademarks or names of manufacturers in the report is for accurate reporting and does not 

constitute an official endorsement, either expressed or implied, of such products or manufacturers by the 

National Aeronautics and Space Administration.
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NESC-RP15-01017

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Title:

Simplified Methodology to Estimate the Maximum LHe 

Cryostat Pressure from a Vacuum Jacket Failure

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NESC Request No.: TI-15-01017

Simplified Methodology to Estimate the Maximum Liquid Helium 

(LHe) Cryostat Pressure from a Vacuum Jacket Failure

September 24, 2015
NASA Engineering and Safety Center 

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Cryostat Pressure from a Vacuum Jacket Failure

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NESC Request No.: TI-15-01017

Report Approval and Revision History

NOTE: This document was approved at the September 24, 2015, NRB. This document was 

submitted to the NESC Director on September 25, 2015, for configuration control.

Approved: Original Signature on File 9/28/15

NESC Director Date

Version Description of Revision Office of Primary 

Responsibility Effective Date

1.0 Initial Release W. Lance Richards, 

NESC Chief Engineer, 

AFRC

09/24/2015
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Table of Contents

Technical Assessment Report ....................................................................................................................4

1.0 Notification and Authorization.....................................................................................................4

2.0 Signature Page................................................................................................................................5

3.0 Team List........................................................................................................................................6

3.1 Acknowledgements.............................................................................................................6

4.0 Executive Summary.......................................................................................................................7

5.0 Problem Description......................................................................................................................8

5.1 Simplified Methodology .....................................................................................................8

6.0 Findings, Observations, and NESC Recommendations............................................................18

6.1 Findings ............................................................................................................................18

6.2 Observations.....................................................................................................................18

6.3 NESC Recommendations .................................................................................................18

7.0 Lessons Learned...........................................................................................................................18

8.0 Recommendations for NASA Standards and Specifications....................................................18

9.0 Definition of Terms......................................................................................................................19

10.0 Acronyms List ..............................................................................................................................20

11.0 References.....................................................................................................................................20

12.0 Appendices....................................................................................................................................21

Appendix A. Derivation of Pseudo-Latent Heat....................................................................................22

Appendix B. Simplified Methodology Roadmap...................................................................................25

List of Figures

Figure 5.1-1. Loss and Contraction Coefficients for Entrances and Transitions - All Contraction 

Coefficients Are Based on Incompressible Flow Values..................................................11

Figure 5.1-2. Diameter Ratio Limits ......................................................................................................15

Figure 5.1-3. Limit of Simple Methodology ..........................................................................................15

Figure A-1. Control Volume for Venting Supercritical Tank ..............................................................22

Figure B-1. CGA Assessment Temperature.........................................................................................26

Figure B-2. Pseudo Latent Heat ...........................................................................................................27

Figure B-3. Calculation Flow Chart.....................................................................................................28

List of Tables

Table 5.1-1. Results of SINDA/FLUINT Supercritical Analyses.........................................................10

Table 5.1-2. Range of SINDA/FLUINT Runs......................................................................................12

Table 5.1-3. l/d Ratio Points of Equivalence between Detailed SINDA/FLUINT Model and the 

Simple Methodology.........................................................................................................14

Table 5.1-4. Limiting Section in the SOFIA Dewars............................................................................16

Table 5-1.5. Comparison of Simplified Methodology and SINDA/FLUINT Results ..........................17
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Technical Assessment Report

1.0 Notification and Authorization

Mr. Edward J. Ingraham, the Safety and Mission Assurance Lead for the Stratospheric 

Observatory for Infrared Astronomy (SOFIA) Program at the Ames Research Center, requested 

that the NASA Engineering and Safety Center (NESC) develop a simplified method of 

predicting the maximum pressure in a cryogenic liquid helium (LHe) dewar after a sudden loss 

of vacuum jacket thermal insulation.

Dr. Eugene Ungar, Discipline Deputy for the Life Support/Active Thermal Technical Discipline 

Team at Johnson Space Center (JSC), was selected as the technical lead for this assessment.

The key stakeholder for this assessment is Mr. Edward J. Ingraham. 
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2.0 Signature Page

Submitted by: 

Team Signature Page on File – 9/30/15

Dr. W. Lance Richards Date

Significant Contributors: 

Dr. Eugene K. Ungar Date

Signatories declare the findings, observations, and NESC recommendations compiled in the 

report are factually based from data extracted from program/project documents, contractor 

reports, and open literature, and/or generated from independently conducted tests, analyses, and 

inspections.
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3.0 Team List

Name Discipline Organization

Core Team

W. Lance Richards NESC Lead AFRC

Eugene K. Ungar NESC Technical Lead, Discipline Deputy 

for the Life Support/Active Thermal 

Technical Discipline Team

JSC

John LaNeave MTSO Program Analyst LaRC

Administrative Support

Linda Burgess Planning and Control Analyst LaRC/AMA

Dee Bullock Technical Writer LaRC/AMA

3.1 Acknowledgements

The author wishes to thank Mr. Andrew Hong (JSC) for performing the numerical analysis for 

the present work.
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4.0 Executive Summary

The aircraft-based Stratospheric Observatory for Infrared Astronomy (SOFIA) is a platform for 

multiple infrared astronomical observation experiments. These experiments carry sensors cooled 

to liquid helium (LHe) temperatures. The LHe supply is contained in large (i.e., 10 liters or 

more) vacuum-insulated dewars. Should the dewar vacuum insulation fail, the inrushing air will 

condense and freeze on the dewar wall, resulting in a large heat flux on the dewar’s contents. 

The heat flux results in a rise in pressure and the actuation of the dewar pressure relief system. 

A previous NASA Engineering and Safety Center (NESC) assessment [ref. 1] provided 

recommendations for the wall heat flux that would be expected from a loss of vacuum and 

detailed an appropriate method to use in calculating the maximum pressure that would occur in a 

loss of vacuum event. This method involved building a detailed supercritical helium 

compressible flow thermal/fluid model of the vent stack and exercising the model over the 

appropriate range of parameters. 

The experimenters designing science instruments for SOFIA are not experts in compressible 

supercritical flows and do not generally have access to the thermal/fluid modeling packages that 

are required to build detailed models of the vent stacks. Therefore, the SOFIA Program engaged 

the NESC to develop a simplified methodology to estimate the maximum pressure in a LHe 

dewar after the loss of vacuum insulation. The method would allow the university-based science 

instrument development teams to conservatively determine the cryostat’s vent neck sizing during 

preliminary design of new SOFIA Science Instruments.

This report details the development of the simplified method, the method itself, and the limits of 

its applicability. The simplified methodology provides an estimate of the dewar pressure after a 

loss of vacuum insulation that can be used for the initial design of the LHe dewar vent stacks. 

However, since it is not an exact tool, final verification of the dewar pressure vessel design 

requires a complete, detailed real fluid compressible flow model of the vent stack. 
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5.0 Problem Description

Accurately predicting the maximum pressure of a LHe dewar after a loss of vacuum insulation 

requires a detailed real fluid compressible flow model of the vent stack. Owing to the cost and 

complexity of the applicable codes, developing and executing such a model would typically be 

beyond the capability of the SOFIA researchers who are planning new experiments. Therefore, a 

simpler method of predicting the peak pressure is desired for preliminary dewar and vent stack 

design. 

5.1 Simplified Methodology

Predicting the Pressure in a Loss of Vacuum Insulation Condition

The NESC’s previous work for the SOFIA Program [ref. 1] recommended using 4 W/cm2as the 

loss of vacuum insulation dewar wall heat flux. The pressure inside the dewar at this condition 

must be calculated during the design phase to ensure that the dewar is sufficiently strong to 

withstand a vacuum insulation failure. 

The peak pressure during a loss of vacuum insulation event must be calculated through iteration. 

First, the peak pressure state inside the dewar is assumed and the vent stack mass flow rate is 

calculated. The wall heating that would create this mass flow rate is then calculated. The dewar 

pressure is iterated until the result converges to a wall heat flux of 4 W/cm2. 

In the explanation and calculations of the present work, it is implicitly assumed that the dewar 

pressure is known, since the pressure is required for the iterating calculation that returns the 

dewar wall heat flux at each step.

The Dewar State during Loss of Vacuum Insulation

The Compressed Gas Association (CGA) Standards [ref. 2] require that the loss of vacuum 

insulation condition be analyzed at a particular combination of pressure and temperature for a 

supercritical fluid. At a given pressure, the dewar stack is analyzed at the temperature where

(1⁄√v)hfg

∗ Eq. (1)

is at a minimum. Here, v is the fluid specific volume and hfg

∗

is the pseudo latent heat1. The 

pseudo latent heat includes the effect of the internal energy change in the dewar and allows the 

energy balance on the dewar to be written simply as 

ṁ =

Q

hfg

∗ Eq. (2)

 

1 The derivation of the pseudo latent heat for a supercritical fluid is contained in Appendix A.
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where ṁ is the venting mass flow rate and Q is the dewar heat load. The pseudo latent heat for a 

supercritical fluid is defined as:

hfg

∗ = v

dh

dv

|

p

Eq. (3)

where p is the fluid pressure and h is its enthalpy. 

The NESC’s previous analytical work [ref. 1] confirmed that evaluating the dewar vent stack at 

the CGA recommended temperature yielded the lower limit of wall heat flux that was required to 

obtain the defined pressure. Thus, choosing the CGA-recommended combination of temperature 

and pressure yields conservative results.

The Origin of the Simplified Methodology 

The wall heat flux resulting from a loss of vacuum insulation increases the dewar pressure, 

which actuates the pressure relief mechanism and results in high-speed flow through the dewar 

vent stack. At high pressures, the flow can be choked at the vent stack inlet, at the exit, or at an 

intermediate transition or restriction. 

During previous SOFIA analyses, it was observed that there was generally a readily identifiable 

section of the vent stack that would limit the flow – e.g., a small diameter entrance or an orifice. 

It was also found that when the supercritical helium was approximated as an ideal gas at the 

dewar condition, the calculated mass flow rate based on choking at the limiting entrance or 

transition was less than the mass flow rate calculated using the detailed real fluid model2. Using 

this lower mass flow rate would yield a conservative prediction of the dewar’s wall heat flux 

capability. The simplified method of the current work was developed by building on this 

observation.

Results of Prior Work

As a follow-on to the work performed for ref. 1, NASA/Johnson Space Center Engineering 

performed detailed analyses for a number of already designed, built, and accepted dewars that 

were flown by SOFIA in 2014 and 2015 (refs. 38). The supercritical helium compressible flow 

in the dewar vent stacks was analyzed using SINDA/FLUINT at specified dewar pressures 

ranging from 228 to 998 kPa (absolute). The vent stack was taken as adiabatic owing to the very 

short duration of the venting transient. The limiting conditions found in these analyses are 

summarized in Table 5.1-1. 

 

2 Because the helium at relief conditions is a near-critical supercritical fluid, an ideal gas representation is not an 

accurate representation of the venting physics. However, it was found that an ideal gas assumption resulted in a 

conservative value of the venting mass flow rate and the concomitant wall heat flux. 
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Table 5.1-1. Results of SINDA/FLUINT Supercritical Analyses

At dewar pressures greater than 500 kPa, the analyses were performed at the CGA-recommended 

temperature condition. At lower pressures, the lowest temperature where the SINDA/FLUINT 

model was stable and yielded accurate, thermodynamically consistent results was used. At these 

pressures, the limit of the model stability was within 0.3 K of the CGA recommendation. 

The list of limiting conditions shows that the flow was limited by choking at the stack entrance 

in fewer than half of the cases. In the majority of the cases, the flow was limited by choking at 

the exit of the vent stack. Because of this behavior, it is not sufficient to develop a simplified 

real gas method that only considers choking at the vent stack entrance. The effect of the vent 

stack length must also be accounted for3. 

Simplified Method

In the simplified methodology, the supercritical helium is analyzed as an ideal gas. Choking is 

assumed to occur at the entrance of the smallest effective flow area in the stack. Neither 

assumption is physically correct, but the analysis yields a conservative result over a wide range 

of applications when compared to a physically correct real fluid analysis. 

 

3

If the analyzed vent stacks had always choked at the stack entrance, developing a simplified model would have 

been quite direct. Stack length, intermediate transitions, and other vent design details could have been ignored. 

Experiment Acronym Reference entrance p max (kPa abs) T (K) model T CGA (K) limiting condition

502.5 7.08 7.08 choked at inlet and exit

528.8 7.22 7.22 choked at inlet and exit

445.0 6.83 6.83 choked at exit

471.3 7.01 7.01 choked at exit

399.0 6.75 6.56 choked at inlet

425.3 6.75 6.66 choked at exit of large tube

998.0 9.00 9.00 choked at exit

783.0 8.17 8.17 choked at exit

745.0 8.04 8.04 choked at exit

998.0 9.00 9.00 choked at exit

783.0 8.17 8.17 choked at exit

745.0 8.04 8.04 choked at exit

227.0 5.28 5.24 no choking except at exit orifice

253.3 5.50 5.50 no choking except at exit orifice

334.1 6.40 6.11 choked at inlet and exit

360.4 6.48 6.24 choked at inlet and exit

380.0 6.55 6.40 choked at inlet and exit

385.0 6.65 6.46 choked at inlet and exit

334.1 6.40 6.11 choked at inlet and exit of main path and orifice

360.4 6.48 6.24 choked at inlet and exit of main path and orifice

380.0 6.55 6.40 choked at inlet and exit of main path and orifice

385.0 6.65 6.46 choked at inlet and exit of main path and orifice

398.9 6.75 6.52 choked at exits to cabin

425.2 6.85 6.67 choked at exits to cabin

598.7 7.48 7.48 choked at exits to cabin

625.0 7.58 7.58 choked at exits to cabin

695.2 7.84 7.84 choked at exit

721.5 7.93 7.93 choked at exit

876.3 8.51 8.51 choked at inlet and exit

Field-Imaging Far-Infrared Line 

Spectrometer (FIFI-LS) FIFI LS LHe re-entrant

Field-Imaging Far-Infrared Line 

Spectrometer (FIFI-LS) LHeII FIFI LS Lhe II re-entrant

Faint Object Infrared Camera for 

the SOFIA Telescope

FORCAST flush

ground test performed by Savage 

et al. [ref. 9]

re-entrant

flush

6 re-entrant

German REceiver for Astronomy 

at Terahertz Frequencies

GREAT re-entrant

Echelon-Cross- Echelle 

Spectrograph

EXES without 

parallel flow 

path

re-entrant

7 High-resolution Airborne Wideband CameraHAWC+ re-entrant

1

1

2

1

3

4

5

Echelon-Cross- Echelle 

Spectrograph

EXES with 

parallel path re-entrant

First Light Infrared TEst CAMera FLITECAM
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For a supercritical tank with a vent stack of zero length (a limiting case), the ideal gas analysis 

yields a mass flow rate ~40% lower4than does a detailed SINDA/FLUINT model using real gas 

behavior. If the vent stack length grows, eventually the stack exit will also choke. Still longer 

vent stacks will choke at the stack exit only. Once this occurs, the venting mass flow rate will 

decrease with increasing stack length. 

The ~40% margin provided by using the ideal gas relations is traded for vent stack length in the 

simplified methodology. That is, by calculating the mass flow rate based on ideal gas choking at 

the vent stack entrance, the simplified method yields conservative results for a range of vent 

stack lengths. 

The work in this assessment consisted of comparing the mass flow rate calculated using the ideal 

gas method with that calculated from a full SINDA/FLUINT model for representative adiabatic 

vent geometries. The comparative calculations were performed for circular tubes. They were 

performed for a number of diameters, for a number of entrances and transition types, and over a 

range of supercritical pressures from slightly above the critical pressure of 227 kPa to a 

maximum of 1,000 kPa. This allowed the limits of the simplified method to be explored and 

defined.

The entrances and transitions included in the study are shown in Figure 5.1-1. The figure 

includes the head losses associated with the entrances and transitions and the associated vena 

contracta contraction coefficients5. 

Figure 5.1-1. Loss and Contraction Coefficients for Entrances and Transitions - All Contraction 

Coefficients Are Based on Incompressible Flow Values 

 

4 This translates to an allowable wall heat flux 40% lower than for the real fluid case. Therefore, the allowable heat 

flux is conservatively underpredicted.

5 These are the vena contracta coefficients for incompressible flow. Although the flow at the dewar stack entrance is 

compressible, the incompressible flow values are used.
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A total of 337 comparative cases were run. Table 5.1-2 lists the pressure, temperature, diameter, 

tube length, and entrance/transition type for each case. The table includes the CGA 

recommended temperature for comparison. 

Table 5.1-2. Range of SINDA/FLUINT Runs

In addition to the SINDA/FLUINT analysis, simplified ideal gas calculations were performed for 

each case in Table 5.1-2 at the CGA recommended temperature. The supercritical helium was 

treated as an ideal gas and the flow at the entrance choking limit was found. The calculations 

were performed as follows:

The ideal gas density and acoustic velocity were calculated at the dewar conditions 

(pressure and CGA temperature in Table 5.1-2). 

The density, , is

ρ =

p

RT

(Eq. 4)

where p is the pressure, R is the ideal gas constant for helium (2077 J/kg K), and T is 

the absolute temperature.

The acoustic velocity is

a = √γRT (Eq. 5)

where  is the ratio of specific heats (1.67 for helium).

The acoustically limited mass flow rate, ṁ , was calculated from

ṁ = ρ a CC FC ACS (Eq. 6)

p (kPa) T (K) d (mm) entrance/transition l/d T (K) CGA

228 5.3 10,20,30 re-entrant, smooth, and annular 20 to 200 5.26

250 5.5 10,20,30 re-entrant, smooth, and annular 20 to 200 5.45

300 6.1 10,20,30 re-entrant, smooth, and annular 20 to 200 5.86

400 6.75 10,20,30 re-entrant, smooth, and annular 20 to 200 6.52

500 7.04 10,20,30 re-entrant, smooth, and annular 20 to 200 7.04

600 7.47 10,20,30 re-entrant, smooth, and annular 20 to 200 7.47

700 7.85 10,20,30 re-entrant, smooth, and annular 20 to 200 7.85

800 8.23 10,20,30 re-entrant, smooth, and annular 20 to 200 8.23

900 8.6 10,20,30 re-entrant, smooth, and annular 20 to 200 8.6

1000 8.95 10,20,30 re-entrant, smooth, and annular 20 to 200 8.95
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where CC is the contraction coefficient (Figure 5.1-1), ACS is the cross-sectional area 

at the entrance or transition, and FC is the compressible flow coefficient that accounts 

for choking at the vena contracta

FC = (

2

γ+1

)

γ+1

2 ( γ−1)

(Eq. 7)

which is 0.562 for helium.

The mass flow rates calculated by the simple ideal gas method and those calculated from the 

SINDA/FLUINT model were compared to find the dimensionless length for each case where the 

two were equivalent. This defines the limit of applicability for the simplified methodology. 

These limits are listed in Table 5.1-3. For shorter lengths, the ideal gas calculation is 

conservative – for longer lengths, it is not. 
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Table 5.1-3. l/d Ratio Points of Equivalence between Detailed SINDA/FLUINT Model and the 

Simple Methodology

p (kPa) T (K) d (mm)

reentrant 

l/d limit

flush 

entrance 

l/d limit

annular 

entrance 

l/d limit

228 5.3 10 159 119 81

228 5.3 20 178 136 91

228 5.3 30 190 139 92

250 5.5 10 >200 177 127

250 5.5 20 >200 194 140

250 5.5 30 >200 >200 148

300 6.1 10 >200 183 132

300 6.1 20 >200 196 145

300 6.1 30 >200 >200 150

400 6.75 10 >200 193 146

400 6.75 20 >200 >200 160

400 6.75 30 >200 >200 164

500 7.04 10 >200 >200 189

500 7.04 20 >200 >200 >200

500 7.04 30 >200 >200 >200

600 7.47 10 >200 >200 185

600 7.47 20 >200 >200 >200

600 7.47 30 >200 >200 >200

700 7.85 10 >200 >200 176

700 7.85 20 >200 >200 191

700 7.85 30 >200 >200 199

800 8.23 10 >200 >200 163

800 8.23 20 >200 >200 177

800 8.23 30 >200 >200 185

900 8.6 10 >200 200 153

900 8.6 20 >200 >200 167

900 8.6 30 >200 >200 174

1000 8.95 10 >200 185 145

1000 8.95 20 >200 >200 160

1000 8.95 30 >200 >200 166

The limits of applicability are plotted in Figure 5.1-2. The figure and Table 5.1-3 show that the 

annular entrance is the limiting case for all pressures. 
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Figure 5.1-2. Diameter Ratio Limits

The lowest values in Figure 5.1-2 define the limits of the simplified methodology. These limits 

are enveloped by the red area in Figure 5.1-3. For pressures between 228 and 1,000 kPa at 

diameter ratios below the red area, the simple method yields a conservative prediction of the 

mass flow rate. 

Figure 5.1-3. Limit of Simple Methodology

Comparison with the Detailed Model

The SOFIA dewar vents that were analyzed in refs. 1 and 38 contained one section whose 

entrance had a smaller effective flow area than the remainder of the stack and would thus limit 
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the flow. The effective flow area is the product of the flow area and the contraction coefficient 

(Figure 5.1-1). The vent stack limiting features for these dewars are listed in Table 5.1-4.

Table 5.1-4. Limiting Section in the SOFIA Dewars

Instrument Acronym Limiting section

Diameter  Length

Entrance to 

limiting 

section

Other sections

Field-Imaging Far-Infrared 

Line Spectrometer (FIFI-LS) FIFI-LS 24 mm 438 mm re-entrant none

Field-Imaging Far-Infrared 

Line Spectrometer (FIFI-LS) 

LHeII

FIFI-LS 

LHeII 11.8 mm 442 mm re-entrant none

Faint Object Infrared Camera 

for the SOFIA Telescope FORCAST 18.2 mm 246 flush downstream larger diameter section with similar length

Echelon-Cross-Echelle 

Spectrograph EXES 18.5 mm 495 mm re-entrant none

German REceiver for 

Astronomy at Terahertz 

Frequencies

GREAT 13 mm 255 mm re-entrant

downstream larger diameter 

section with similar length 

plus parallel restrictive path 

to relief valve

High-resolution Airborne 

Wideband Camera HAWC+ 23.6 mm 606 mm re-entrant none

First Light Infrared TEst 

CAMera FLITECAM 11.7 mm 204 mm re-entrant

downstream annular section 

with 94% of the flow area 

and similar length6

The diameter ratio (l/d) for the limiting section of the SOFIA dewars listed in Table 5.1-4 range 

from 13.5 to 37.5. All are well below the limits shown in Figure 5.1-3. Therefore, the simple 

method is applicable. 

Table 5.1-5 lists the heat fluxes calculated for the SOFIA experiments using the detailed 

SINDA/FLUINT model and the simplified ideal gas methodology. The simplified method 

results are conservative for all the cases investigated. The margin on the heat flux ranges from 

12 to 45%.

 

6 The limiting section is set by the product of flow area and entrance/transition contraction coefficient.
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Table 5-1.5. Comparison of Simplified Methodology and SINDA/FLUINT Results

The table shows that the simplified ideal gas method yields conservative results for all the 

SOFIA dewars assessed thus far. By using the simplified ideal gas method within its defined 

limits, conservative predictions of the allowable wall heat flux on a LHe dewar can be obtained.

To use the simplified methodology to calculate the dewar pressure with 4 W/cm2of external 

heating (the loss of vacuum heat flux), an iterative method is used. The method is detailed in 

Appendix B.

The simplified method can be used to provide an estimate of the dewar pressure after a loss of 

vacuum insulation. This result can be used for the initial design of the LHe dewar vent stacks. 

However, since the simplified method is not an exact tool, final verification of the dewar 

pressure vessel design requires a complete detailed real fluid compressible flow model of the 

vent stack. 
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6.0 Findings, Observations, and NESC Recommendations

6.1 Findings

The following findings were identified:

F-1. A simplified ideal gas method can be used to conservatively predict the dewar pressure 

under a loss of vacuum insulation if the following conditions are met. 

a. The dewar pressure is between 228 and 1,000 kPa.

b. The sections of the stack are short enough that the simplified method is 

conservative.

c. There is an identifiable limiting entrance or transition.

F-2. The ideal gas method predicts the dewar heat load with margins of 12 to 45% for the 

SOFIA dewars that have been assessed to date using detailed real fluid SINDA/FLUINT 

models. 

F-3. The simplified method can be used for initial sizing. The dewar maximum pressure for 

verification must be determined using a detailed compressible real fluid flow analysis.

6.2 Observations

No observations were made in the present work.

6.3 NESC Recommendations

The following NESC recommendations are directed toward the SOFIA Program:

R-1. Use the simplified method to provide an initial estimate of the dewar pressure after a loss 

of vacuum insulation. (F-1, F-2)

R-2. Use the simplified method only for initial vent stack sizing. A detailed real fluid 

compressible flow model is required for final design verification. (F-3)

7.0 Lessons Learned

No applicable lessons learned were identified for entry into the NASA Lessons Learned 

Information System (LLIS) as a result of this assessment.

8.0 Recommendations for NASA Standards and Specifications

No recommendations for NASA standards and specifications were identified as a result of this 

assessment.
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9.0 Definition of Terms

Corrective Actions Changes to design processes, work instructions, workmanship practices, 

training, inspections, tests, procedures, specifications, drawings, tools, 

equipment, facilities, resources, or material that result in preventing, 

minimizing, or limiting the potential for recurrence of a problem. 

Finding A relevant factual conclusion and/or issue that is within the assessment 

scope and that the team has rigorously based on data from their 

independent analyses, tests, inspections, and/or reviews of technical 

documentation.

Lessons Learned Knowledge, understanding, or conclusive insight gained by experience 

that may benefit other current or future NASA programs and projects. 

The experience may be positive, as in a successful test or mission, or 

negative, as in a mishap or failure.

Observation A noteworthy fact, issue, and/or risk, which may not be directly within the 

assessment scope, but could generate a separate issue or concern if not 

addressed. Alternatively, an observation can be a positive 

acknowledgement of a Center/Program/Project/Organization’s operational 

structure, tools, and/or support provided.

Problem The subject of the independent technical assessment.

Proximate Cause The event(s) that occurred, including any condition(s) that existed 

immediately before the undesired outcome, directly resulted in its 

occurrence and, if eliminated or modified, would have prevented the 

undesired outcome.

Recommendation A proposed measurable stakeholder action directly supported by specific 

Finding(s) and/or Observation(s) that will correct or mitigate an identified 

issue or risk.

Root Cause One of multiple factors (events, conditions, or organizational factors) that 

contributed to or created the proximate cause and subsequent undesired 

outcome and, if eliminated or modified, would have prevented the 

undesired outcome. Typically, multiple root causes contribute to an 

undesired outcome.

Supporting Narrative A paragraph, or section, in an NESC final report that provides the detailed 

explanation of a succinctly worded finding or observation. For example, 

the logical deduction that led to a finding or observation; descriptions of 

assumptions, exceptions, clarifications, and boundary conditions. Avoid 

squeezing all of this information into a finding or observation
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10.0 Acronyms List

AFRC Armstrong Flight Research Center

AMA Analytical Mechanics Associates

CGA Compressed Gas Association

cm Centimeter

EXES Echelon-Cross- Echelle Spectrograph

FIFI-LS Field-Imaging Far-Infrared Line Spectrometer

FIFI-LS LHeII Field-Imaging Far-Infrared Line Spectrometer LHeII (total surface of LHe)

FLITECAM First Light Infrared TEst CAMera

FORCAST Faint Object Infrared Camera for the SOFIA Telescope

GREAT German REceiver for Astronomy at Terahertz Frequencies

HAWC+ High-resolution Airborne Wideband Camera

He Helium

JSC Johnson Space Center

K Kelvin

kPa Peak Pressure

l/d Diameter Ratio

LaRC Langley Research Center

LHe Liquid Helium 

mm Millimeter

MTSO Management and Technical Support Office

NASA National Aeronautics and Space Administration

NESC NASA Engineering and Safety Center

SOFIA Stratospheric Observatory for Infrared Astronomy

W/cm2 Watt Per Square Centimeter

11.0 References

1. Ungar, E. K.: SOFIA Cryogenic Helium Dewar Heat Flux Evaluation, Maximum Expected 

Wall Heat Flux and Maximum Pressure after Sudden Loss of Vacuum Insulation on the 

Stratospheric Observatory for Infrared Astronomy (SOFIA) Liquid Helium (LHe) Dewars. 

NESC-RP-13-00911, August 2014; NASA/TM2014-218540, October 2014.

2. Compressed Gas Association, Pressure Relief Device Standards – Part 3 – Stationary Storage 

Containers for Compressed Gases, CGA S-1.3-2008.

3. “FORCAST Results,” e-mail from Eugene Ungar to William Condzella (NASA Safety and 

Mission Assurance for SOFIA at the Armstrong (nee Dryden) Flight Research Center),

September 10, 2014.

4. “GREAT Results,” e-mail from Eugene Ungar to William Condzella, March 10, 2015.

5. “EXES Results,” e-mail from Eugene Ungar to William Condzella, January 20, 2015.
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6. “Updated EXES Results,” e-mail from Eugene Ungar to William Condzella, January 30, 

2015.

7. “FLITECAM Results,” e-mail from Eugene Ungar to William Condzella, March 10, 2015.

8. “HAWC+ Results,” e-mail from Eugene Ungar to William Condzella, May 18, 2015.

9. Savage, M. L.; Limmongkol, S.; Bacher, R. E.; Brown, T. M.; Koerber, C. T.; Smith, E.; and 

Waddell, P.: “He Cryostat Vent Sizing for SOFIA Science Instruments.” Ground Based 

Instrumentation for Astronomy, Proc. of the SPIE, Vol. 5492, 2004, pp. 16891698.

10. Lemmon, E. W.; Huber, M. L.; and McLinden, M. O.: NIST Standard Reference Database 

23: Reference Fluid Thermodynamic and Transport Properties-REFPROP. Version 9.1, 

National Institute of Standards and Technology, Standard Reference Data Program, 

Gaithersburg, 2013.

12.0 Appendices

Appendix A. Derivation of Pseudo-Latent Heat

Appendix B. Simplified Methodology Roadmap
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Appendix A. Derivation of Pseudo-Latent Heat

Supercritical Venting Tank with dp

dt = 0

Consider the venting tank shown in Figure A-1. The tank contains a homogeneous supercritical 

fluid at pressure, p. The tank vents through a relief stack. The mass of the fluid in the tank is m, 

its density is , and its specific internal energy is u. The mass flow rate of the fluid leaving the 

tank is ṁ and its specific enthalpy is h.

Figure A-1. Control Volume for Venting Supercritical Tank

The control volume for the system is taken as shown in the diagram. Taking part of the control 

volume border inside the tank creates a negligible error in the representation of the fluid mass, 

but minimizes the fluid kinetic energy at the exit and allows it to be neglected.

Mass Balance  The mass balance on the control volume is 

ṁ = −

dm

dt

where t is time.
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Energy Balance – The energy balance on the control volume is: 

Q =

dU

dt + ṁ h

U = mu = m(h − pv)

The energy balance can be expressed as:

Q =

d

dt

[mh − mpv] −

dm

dt h

Expanding the energy balance

Q = h

dm

dt + m

dh

dt − mp

dv

dt − mv

dp

dt − pv

dm

dt − h

dm

dt

Because

−mv

dp

dt = 0 since

dp

dt = 0

this allows the energy balance to be simplified to: 

Q = m

dh

dt − mp

dv

dt − pv

dm

dt

Specific volume, v, is defined as:

v =

V

m

where V is the tank volume, so

dv

dt = −

V

m2

dm

dt

and

dv

dt = −v

1

m

dm

dt

This allows the energy balance to be recast as: 

Q = m

dh

dt + mpv

1

m

dm

dt − pv

dm

dt

or

Q = m

dh

dt
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dh

dt =

dh

dv

dv

dt =

dh

dv

(−

v

m

dm

dt )

Recall

ṁ = −

dm

dt

so

dh

dt =

dh

dv

(

v

m

ṁ )

Q = m (

dh

dv

v

m

ṁ )

Q = ṁ v

dh

dv

so

ṁ =

Q

v

dh

dv

Define the pseudo-latent heat, hfg

∗

, as:

hfg

∗ =

Q

ṁ

ṁ =

Q

hfg

∗

The pseudo-latent heat for a supercritical fluid is:

hfg

∗ = v

dh

dv

|

p
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Appendix B. Simplified Methodology Roadmap

Use of Simplified Methodology

To use the simplified method to predict the maximum pressure in a LHe dewar after loss of 

vacuum insulation, the following iterative procedure is used:

1. Choose a supercritical pressure to start the iteration.

2. Ensure that the proposed vent stack geometry meets the limits of the simplified 

method at the chosen pressure.

3. Find the temperature recommended by the CGA for assessment at the chosen 

pressure.

4. Identify the limiting entrance or transition.

5. Assess the throughput of the vent stack at the pressure of interest using a simplified 

compressible ideal gas flow technique.

6. Calculate the dewar heat load required to produce the calculated mass flow rate and, 

by extension, the assumed pressure. 

7. Calculate the dewar wall heat flux.

8. Compare the dewar heat flux to the recommended loss of vacuum insulation heat 

flux, 4 W/cm2. If another iteration is necessary, adjust the assumed dewar pressure 

and repeat.

Detailed explanations for the steps follow.

Detailed Roadmap

1. Choose a pressure.

The simplified method can be used for supercritical pressures ranging from 228 to 1,000 kPa. 

Any pressure in that range can be chosen as the initial pressure.

2. Verify that the vent stack geometry meets the simplified methodology limits.

Use Figure 5.1-3 to verify that all sections of the vent stack are short enough that the simplified 

method is accurate. For non-circular vent sections, use the hydraulic diameter to calculate the 

length to diameter ratio.

3. Find the CGA-recommended temperature.

The CGA-recommended temperature can be calculated using the third-order polynomial shown 

in Figure B-1. This polynomial was developed from numerical differencing of NIST RefProp 

[ref. 10] helium properties.
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Figure B-1. CGA Assessment Temperature

4. Identify the limiting entrance or transition.

Calculate the product of the flow area and the entrance or transition contraction coefficient 

(Figure 5.1-1) for each section of the vent stack. The limiting entrance or transition is the one 

with the smallest product of flow area and contraction coefficient.

5. Calculate the vent stack throughput.

Use Equations 47 to calculate the mass flow rate, ṁ .

ṁ = ρ a CC FC ACS Eq. (6)

is the helium density calculated using an ideal gas assumption

ρ =

p

RT

Eq. (4)

where p is the pressure, R is the ideal gas constant for helium (2,077 J/kg K), and T is 

the absolute temperature.

The acoustic velocity, a, is also calculated using an ideal gas assumption

a = √γRT Eq. (5)

where is the ratio of specific heats (1.67 for helium).

CC is the entrance contraction coefficient (Figure 5.1-1) at the limiting entrance or 

transition. 

FC is the compressible flow coefficient that accounts for choking at the vena contracta

FC = (

2

γ+1

)

γ+1

2 ( γ−1)

Eq. (7)
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which is 0.562 for helium. 

ACS is the cross-sectional area at the limiting entrance or transition.

6. Calculate the dewar heat load.

The dewar heat load, Q, is calculated using Equation 2: 

ṁ =

Q

hfg

∗ Eq. (2)

where hfg

∗

is the pseudo latent heat. The pseudo latent heat is calculated using the third-order 

polynomial shown in Figure B-2. This polynomial was developed from numerical differencing 

of NIST RefProp [ref. 10] helium properties.

Figure B-2. Pseudo Latent Heat

7. Calculate the dewar wall heat flux.

The wall heat flux is the ratio of the dewar heat load and dewar surface area.

8. Update dewar pressure if required.

If the calculated heat flux is below 4 W/cm2, the assumed dewar pressure must be increased. If it 

is higher than 4 W/cm2, the assumed dewar pressure must be decreased. Using a linear 

correction to find the new pressure will lead to rapid convergence

pnew = pold

q"

4 W/cm2

where pnew and pold are the new and previously assumed dewar pressures, respectively.

The procedure is shown in flowchart form in Figure B-3.
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Figure B-3. Calculation Flow Chart
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Simplified Methodology to Estimate the Maximum Liquid Helium (LHe) 

Cryostat Pressure from a Vacuum Jacket Failure

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Ungar, Eugene K.; Richards, W. Lance

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14. ABSTRACT

The Safety and Mission Assurance Lead for the Stratospheric Observatory for Infrared Astronomy (SOFIA) Program at the 

Ames Research Center, requested that the NASA Engineering and Safety Center (NESC) develop a simplified method of 

predicting the maximum pressure in a cryogenic liquid helium (LHe) dewar after a sudden loss of vacuum jacket thermal 

insulation. The outcome of the NESC assessment is contained in this document.

15. SUBJECT TERMS

Liquid Helium; NASA Engineering and Safety Center; Stratospheric Observatory for Infrared Astronomy;SOFIA; Vacuum

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