Neil T. Van Dresar and Gregory A. Zimmerli

Glenn Research Center, Cleveland, Ohio

Pressure-Volume-Temperature (PVT) Gauging of an 

Isothermal Cryogenic Propellant Tank Pressurized 

With Gaseous Helium

NASA/TP—2014-218083

February 2014
NASA STI Program . . . in Profi le

Since its founding, NASA has been dedicated to the 

advancement of aeronautics and space science. The 

NASA Scientifi c and Technical Information (STI) 

program plays a key part in helping NASA maintain 

this important role.

The NASA STI Program operates under the auspices 

of the Agency Chief Information Offi cer. It collects, 

organizes, provides for archiving, and disseminates 

NASA’s STI. The NASA STI program provides access 

to the NASA Aeronautics and Space Database and 

its public interface, the NASA Technical Reports 

Server, thus providing one of the largest collections 

of aeronautical and space science STI in the world. 

Results are published in both non-NASA channels 

and by NASA in the NASA STI Report Series, which 

includes the following report types:

• TECHNICAL PUBLICATION. Reports of 

completed research or a major signifi cant phase 

of research that present the results of NASA 

programs and include extensive data or theoretical 

analysis. Includes compilations of signifi cant 

scientifi c and technical data and information 

deemed to be of continuing reference value. 

NASA counterpart of peer-reviewed formal 

professional papers but has less stringent 

limitations on manuscript length and extent of 

graphic presentations.

• TECHNICAL MEMORANDUM. Scientifi c 

and technical fi ndings that are preliminary or 

of specialized interest, e.g., quick release 

reports, working papers, and bibliographies that 

contain minimal annotation. Does not contain 

extensive analysis.

• CONTRACTOR REPORT. Scientifi c and 

technical fi ndings by NASA-sponsored 

contractors and grantees.

• CONFERENCE PUBLICATION. Collected 

papers from scientifi c and technical 

conferences, symposia, seminars, or other 

meetings sponsored or cosponsored by NASA.

• SPECIAL PUBLICATION. Scientifi c, 

technical, or historical information from 

NASA programs, projects, and missions, often 

concerned with subjects having substantial 

public interest.

• TECHNICAL TRANSLATION. Englishlanguage translations of foreign scientifi c and 

technical material pertinent to NASA’s mission.

Specialized services also include creating custom 

thesauri, building customized databases, organizing 

and publishing research results.

For more information about the NASA STI 

program, see the following:

• Access the NASA STI program home page at 

http://www.sti.nasa.gov

• E-mail your question to help@sti.nasa.gov

• Fax your question to the NASA STI 

Information Desk at 443–757–5803

• Phone the NASA STI Information Desk at

 443–757–5802

• Write to:

 STI Information Desk

 NASA Center for AeroSpace Information

 7115 Standard Drive

 Hanover, MD 21076–1320
Neil T. Van Dresar and Gregory A. Zimmerli

Glenn Research Center, Cleveland, Ohio

Pressure-Volume-Temperature (PVT) Gauging of an 

Isothermal Cryogenic Propellant Tank Pressurized 

With Gaseous Helium

NASA/TP—2014-218083

February 2014

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Acknowledgments

This work was supported by NASA through the Exploration Technology Development Program Offi ce, Cryogenic Fluid Management 

Project. The authors recognize the outstanding support provided by the entire test facility team of operations engineers and 

technicians at the Creek Road Cryogenic Complex, the test hardware design engineers, and the data system programmers at the 

NASA Glenn Research Center.

Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5301 Shawnee Road

Alexandria, VA 22312

Available electronically at http://www.sti.nasa.gov

Level of Review: This material has been technically reviewed by expert reviewer(s). 
NASA/TP—2014-218083 1 

Pressure-Volume-Temperature (PVT) Gauging of an Isothermal Cryogenic 

Propellant Tank Pressurized With Gaseous Helium 

Neil T. Van Dresar and Gregory A. Zimmerli 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Summary 

Results are presented for pressure-volume-temperature 

(PVT) gauging of a liquid oxygen/liquid nitrogen tank 

pressurized with gaseous helium that was supplied by a highpressure cryogenic tank simulating a cold helium supply bottle 

on a spacecraft. The fluid inside the test tank was kept 

isothermal by frequent operation of a liquid circulation pump 

and spray system, and the propellant tank was suspended from 

load cells to obtain a high-accuracy reference standard for the 

gauging measurements. 

Liquid quantity gauging errors of less than 2 percent of the 

tank volume were obtained when quasi-steady-state conditions 

existed in the propellant and helium supply tanks. Accurate 

gauging required careful attention to, and corrections for, 

second-order effects of helium solubility in the liquid 

propellant plus differences in the propellant/helium 

composition and temperature in the various plumbing lines 

attached to the tanks. 

On the basis of results from a helium solubility test, a model 

was developed to predict the amount of helium dissolved in 

the liquid as a function of cumulative pump operation time. 

Use of this model allowed correction of the basic PVT 

gauging calculations and attainment of the reported gauging 

accuracy. This helium solubility model is system specific, but 

it may be adaptable to other hardware systems. 

Symbols 

C1, C2, C3 calibration coefficients for reference gauging 

system (RGS) 

LCR load cell reading 

LVI liquid-vapor interface 

MAWP maximum allowable working pressure 

m mass 

P pressure 

T temperature 

U uncertainty 

V volume 

xHe mole fraction of helium 

 liquid fill fraction by volume 

ξ stretch coefficient for volume expansion due to 

pressurization 

 density 

Subscripts 

adj adjusted for different sensed volumes 

b bottle 

e external 

f fluid 

He helium 

i initial condition 

j load cell index number 

l liquid 

PVT pressure-volume-temperature gauging method 

RGS reference gauging system (tank-weighing 

system) 

sat saturation 

sol soluble or dissolved in liquid 

t tank 

u ullage 

v saturated vapor 

0 reference condition at zero internal-to-external 

pressure difference 

Superscripts 

* corrected for effect of external volumes 

Overview of Pressure-VolumeTemperature Gauging 

If a spacecraft’s cryogenic propellant tank is pressurized 

with gaseous helium (GHe), the pressure-volume-temperature 

(PVT) liquid quantity gauging method may be an attractive 

low-gravity gauging option because it requires little, if any, 

additional hardware. PVT gauging has been utilized 

successfully in communications satellites with storable 

propellants (Refs. 1 and 2). For cryogens, PVT gauging has 

been examined analytically (Ref. 3) and experimentally 

(Ref. 4). In the earlier study (Ref. 4), a liquid nitrogen (LN2) 

tank was pressurized with GHe from the test facility supply 

system. The interest at that time was to determine if PVT 

gauging was suitable for cryogenic propellant tanks, with the 

focus on behavior within the LN2 test tank. In the present 

study, a larger liquid oxygen (LO2)/LN2 tank was pressurized 
NASA/TP—2014-218083 2 

Figure 1.—Simplified pressure-volume-temperature 

schematic showing locations of pressure, P, and 

temperature, T, gauges. 

with GHe stored at cryogenic temperature and high pressure in 

a dedicated supply tank somewhat representative of a supply 

system used on flight systems. 

The PVT method is based on conservation of pressurant 

mass. Therefore, the key operational requirement is that no 

venting or leakage of the pressurant gas is allowed. Helium is 

most commonly used. Other gases could be considered, but 

only if they are noncondensable in the liquid propellant of 

choice. Gauging is most accurate when the propellant tank and 

the supply bottle are isothermal and at steady-state or quasisteady-state thermal conditions. The test results presented here 

are for the isothermal case and demonstrate the achievable 

accuracy of the PVT technique under ideal conditions. 

Accurate gauging may be possible for conditions deviating 

from these ideal conditions, but this will require further study. 

The hardware and required instrumentation are represented 

in Figure 1. Both the GHe supply bottle and the propellant 

tank must have accurately known volumes, and both must be 

equipped with suitable pressure and temperature sensors. In 

the isothermal model that follows, line effects are neglected, 

meaning either that the volumes of the transfer line on both 

sides of the valve are negligibly small or that the temperatures 

and fluid compositions in the lines are considered identical to 

those of the tank volumes connected to the lines. The primary 

PVT calculations steps follow: 

(1) Determine the total GHe mass from initial conditions. 

Assume that all GHe mass initially resides in the GHe 

supply bottle, with no GHe initially present in the 

propellant tank: 

mbi = biVb where bi = f(Tbi, Pbi) (1) 

Here  is density, T is temperature, P is pressure, and 

the subscripts b and i refer to bottle and initial 

condition. 

(2) At a later time, after the propellant tank is pressurized 

with GHe, determine how much GHe remains in the 

supply bottle mb and how much has been transferred to 

the propellant tank: 

mb = bVb where b = f(Tb, Pb) (2) 

 m = mbi – mb

 (3) 

(3) Assume that the GHe transferred to the propellant tank 

uniformly occupies the entire ullage volume at a partial 

pressure PHe equal to the total tank pressure Pt minus 

the propellant’s vapor pressure Psat: 

PHe = Pt – Psat where Psat = f(Tt) (4) 

(4) Obtain the density of GHe in the ullage using the GHe 

partial pressure and tank temperature. Combine this 

with the mass of GHe transferred to the ullage to 

calculate the ullage volume Vu: 

Vu = m/He where He = f(PHe, Tt) (5) 

(5) This can be converted to a volumetric liquid fill fraction : 

  = 1 – (Vu/Vt) (6) 

where the subscript u refers to ullage. 

(6) If the quantity of interest is the amount of liquid 

propellant mass ml

, then the PVT result must be 

converted: 

ml

 = lVt where l = f(Pt, Tl) (7) 

This last step will add additional uncertainty to the gauging 

measurement, especially if the liquid cryogen is not isothermal. This uncertainty arises from uncertainties in both the 

pressure and temperature measurements, which lead to 

uncertainty in the computed liquid density. 
NASA/TP—2014-218083 3 

Test Apparatus and Instrumentation 

Tests were conducted using a tank inside a 1.8-m-diameter 

by 3.0-m-high vacuum chamber (Fig. 2). The propellant tank, 

which was not insulated, had a main diameter of 1.22 m and 

an overall height of 1.91 m (Fig. 3). The propellant tank was 

suspended from the vacuum chamber lid via three load cells 

used to weigh the tank. The load cells served as a reference 

gauging system (RGS) for determining the accuracy of the 

PVT measurements. A fourth load cell connecting the bottom 

of the propellant tank to a pivoting loading beam mounted to 

the facility floor allowed calibration of the RGS. The calibration system was disconnected during tests. A submerged liquid 

pump was located inside the propellant tank, near the bottom 

(Fig. 4). The pump discharge flowed through a vertical pipe to 

two spray hoops in the tank ullage. Then, liquid was discharged through a large number of holes in the spray hoops, 

with a significant portion of the droplets directed upward to 

cool the upper tank wall and lid via direct contact. Two silicon 

diode sensor rakes were located near the tank centerline. One 

was used to measure temperatures from top to bottom inside 

the tank. The other held an array of point sensors used to 

detect the liquid level at 10 percent intervals. The propellant 

tank was equipped with a pair of pressure transducers for lowand high-range measurements. 

Figure 5 shows the high-pressure tank, which was located 

outside the vacuum chamber to serve as a GHe supply bottle. 

The supply tank was wrapped with LN2 cooling coils fed by 

an automated control system and covered with foam insulation. Three silicon diode sensors vertically distributed inside 

the tank were used to measure temperatures inside the supply 

tank. The GHe supply tank also was equipped with a pressure 

transducer for measuring pressures. A 1.2-cm-diameter GHe 

transfer line connected the supply tank to the propellant tank. 

Installed in the transfer line were a Coriolis flowmeter and two 

valves—one for control and the other for hard shutoff. 

Figure 2.—Vacuum chamber, propellant (test) tank, and 

reference gauging system. 

Figure 3.—Propellant tank suspended from vacuum 

chamber lid. 
NASA/TP—2014-218083 4 

Figure 4.—Internal propellant tank components (two orthogonal views). Figure 5.—Gaseous helium supply 

tank prior to installation of liquid 

nitrogen cooling coils and 

insulation.

Table I shows the specifications for the instrumentation. 

TABLE I.—INSTRUMENTATION SPECIFICATIONS 

Instrument/measurement Range Uncertainty 

Propellant tank pressure 0 to 0.7 MPa and 0 to 2.1 MPa 0.11% of full scale 

Gaseous helium supply-tank pressure 0 to 13.8 MPa 0.3% of full scale 

Silicon diodes 2 to 100 K 0.25 K 

Load cells supporting tank 0 to 900 kg 0.03% of full scale 

Calibration load cell 0 to 1800 kg 0.03% of full scale 

Flowmeter 0 to 2180 kg/hr 0.05% of rate 

A multistep process was used to determine the tank 

volumes. First, a small high-pressure gas cylinder was used as 

a source to pressurize the GHe supply tank. The volume of the 

cylinder was determined by weighing the cylinder with a 

laboratory scale when empty and again when filled with water. 

Then, the cylinder was connected to the GHe supply tank with 

a short, small-diameter transfer line equipped with a shutoff 

valve. The cylinder was purged, then pressurized with GHe 

and allowed to reach thermal equilibrium. Similarly, the GHe 

supply tank was purged and allowed to equilibrate, but at an 

initial pressure of approximately one atmosphere after being 

purged with helium. Next, the valve was opened, allowing 

GHe to flow into the supply tank until the pressures equalized 

in the cylinder and the supply tank. The volume of the supply 

tank was calculated using a mass balance (with a correction 

for the volume of the transfer line). Then, a similar process 

was performed to determine the propellant tank volume by 

pressurizing the GHe supply tank and then flowing GHe into 

the propellant tank. The resulting room temperature volumes 

were 0.4055 m3

 for the supply tank and 1.623 m3 for the 

propellant tank. The volumes were measured after all internal 

hardware was in place; therefore, no corrections were 

necessary for displaced volumes. At test conditions, both tanks 

were at approximately 90 K. Correcting the measured volumes 

for thermal contraction involves a 0.8-percent reduction; thus, 

the adjusted cold volumes for the GHe supply tank and 

propellant tanks were 0.4024 m3

0.0025 and 1.610 m30.016, 

respectively. Uncertainty estimates were calculated using the 

methods of Coleman and Steele (Ref. 5) and the manufacturers’ accuracy specifications for the laboratory scale, 
NASA/TP—2014-218083 5 

pressure sensors, and temperature sensors. Both tanks had 

additional plumbing lines attached to them for filling, venting, 

and other purposes. These lines contain volumes external to 

the primary tank compartments, and the fluid in these volumes 

was generally not at the same temperatures as measured in the 

GHe supply and propellant tanks. These external volumes 

were estimated by measuring the lengths and diameters of the 

various lines connected to each tank and summing the 

calculated segment volumes. The external volume for the GHe 

supply tank was equal to 10 percent of the tank’s volume 

uncertainty, whereas the external volume for the propellant 

tank was equal to 50 percent of the tank’s volume uncertainty. 

In an ideal tank-weighing system, the tank would have no 

connections to the surroundings other than the load cells that it 

was suspended from. However, the tank for these gauging 

measurements was necessarily equipped with fill, vent, and 

drain lines plus electrical leads for power and instrumentation. 

The RGS was calibrated by applying measured loads from 0 to 

100 percent of the liquid full-scale weight; this was done at 

tank pressures of 0.34 and 1.65 MPa (the minimum and 

maximum test pressures) and was performed both before and 

after the gauging tests. Furthermore, the calibration data were 

collected with the test tank at both ambient and subambient 

temperatures. The tank was pressurized with nitrogen gas. 

Then, the mass of nitrogen was evaluated from the product of 

the tank volume and gas density, which was obtained from 

temperature and pressure data. The RGS had a slight, but 

noticeable, sensitivity to pressure: the flex hoses used in the 

fill and vent lines were thought to stiffen when pressurized 

and thus exert external forces on the tank. A calibration 

equation of the following form was used: 

    

3

1 1 LCR 2 3 j

m f C j C Pt C (8) 

with coefficients of C1 = 1.006, C2 = –6.879 kg/MPa, and 

C3 = –766.3 kg, where mf is the mass of the fluid, LCRj is the 

load cell reading, and Pt is the total pressure in the tank. The 

resulting correlation fit the data (warm and cool conditions) to 

within 0.25 percent of the full-scale LO2 weight (4.1 kg). 

The first coefficient is very close to the tank’s dry mass. The 

second term is quite small, equal to 0.1 percent of the liquid 

full-scale mass at 0.34 MPa and 0.6 percent at 1.65 MPa. 

So that the PVT results could be compared with those of the 

RGS, the RGS calculations from Equation (8) were converted 

to a liquid volumetric fill fraction: 

He

He

RGS

    

     

 





 

v

v t

f

V

m

l

 (9) 

where v refers to saturated vapor. 

The liquid and ullage were assumed to be isothermal. The 

vapor density in Equation (9), which is for pure saturated 

propellant vapor, was determined as a function of the propellant 

tank temperature, and the GHe density was determined as a 

function of the GHe partial pressure and propellant tank 

temperature. The propellant tank volume sensed by the load 

cells was slightly less than that sensed by the PVT method 

because of the fill line, vent line, and other attached volumes 

that extended outside of the vacuum chamber. This corresponded to a 0.1-percent difference in the sensed volumes. For a 

proper comparison of the PVT results to the RGS, the RGS 

result was adjusted (multiplied) by the ratio of sensed tank 

volumes (equal to 0.9986) for the two methods as follows: 

RGS

,PVT

,RGS RGS,adj = 

t

t

V

V

 (10) 

The propellant tank was equipped with hardware to extract 

fluid samples for the chemical composition analysis. Three 

small-diameter tubes were positioned in the tank to extract 

samples at heights corresponding to the 20-, 50-, and 80-percent 

fill locations. Each sampling line was connected to an isolation 

valve outside of the vacuum chamber. On the opposite side of 

the isolation valves, each sampling line was connected to a 

500-cm3

 accumulator volume plus a 75-cm3 gas sample bottle 

that could be swapped out during testing. Additional valves 

allowed evacuation and venting of the lines. 

Sensitivity Analysis 

The various pressures, temperatures, and volumes input to 

the fundamental PVT measurement will inevitably have measurement errors associated with them. In this section, two 

example PVT measurements, at propellant tank pressures of 

0.34 and 1.65 MPa, and over a liquid fill fraction range from 

0.05 to 0.95, are used to illustrate the effect of measurement 

errors. The calculations are based on an LO2 temperature of 

92 K, a GHe supply temperature of 89 K, and a propellantTABLE II.—INPUT MEASUREMENT OFFSET TO PRODUCE A 1-PERCENT PRESSURE-VOLUMETEMPERATURE GAUGING ERROR AT 5-PERCENT LIQUID FILL AND TWO TANK PRESSURES 

Input Offset 

direction 

Propellant tank pressure 

0.34 MPa 1.65 MPa 

Supply tank volume, Vb Negative 1.05 percent of Vb 1.05 percent of Vb

Propellant-tank to supply-tank volume ratio, Vt/Vb, 

 or propellant-tank volume, Vt

Positive 1.04 percent of Vt 1.06 percent of Vt

Propellant tank temperature, Tt Negative 0.18 percent of Tt 0.65 percent of Tt

Supply tank temperature, Tb Positive 1.11 percent of Tb 1.23 percent of Tb

Propellant tank pressure, Pt Positive 0.69 percent of Pt 1.02 percent of Pt

Supply tank pressure, Pb Negative 1.10 percent of Pb 1.26 percent of Pb
NASA/TP—2014-218083 6 

tank to GHe-supply-tank volume ratio of 4.0. These values are 

representative of the experimental data to be presented later. 

The analysis assumed that the final pressure in the GHe supply 

tank would be 0.69 MPa greater than the propellant tank 

pressure. Therefore, an initial pressure in the supply tank was 

found that satisfied this requirement and was used in the 

analysis. Each PVT input was independently iterated to find 

the value that would produce a worst-case 1-percent gauging 

error (of full-scale propellant tank volume). In all cases, the 

1-percent gauging error occurred at the minimum fill fraction 

(0.05). Table II shows the results. 

Generally, the first five input items in Table II were 

constant or approximately constant, whereas the last item, 

supply-tank pressure, decreased with liquid fill. The offset 

direction shown in the table indicates whether a positive or 

negative offset will produce a positive error in the PVT 

gauging result, where a positive error is defined as a gauging 

result that is greater than the actual value. The absolute value 

of the PVT gauging error for a fixed input offset increased as 

the fill fraction decreased. This occurred with all of the input 

measurements listed in Table II. Figure 6 shows an example 

for the propellant tank temperature input. 

As seen in Table II, supply-tank volume, propellant tank 

volume, supply-tank temperature, and supply-tank pressure 

measurement errors had a similar effect at both low and high 

propellant tank pressures. The case with a low propellant tank 

pressure was substantially more sensitive to errors in propellant tank temperature, and to a lesser extent, propellant tank 

pressure. Obtaining accurate gauging results was more difficult at a lower propellant tank pressure than at a higher 

propellant tank pressure. 

A similar analysis was performed to determine the effect of 

a GHe leak in the two-tank system. If a constant GHe leak rate 

(mass/time) is assumed, the error increases with time, which in 

the present work roughly equated to decreasing fill fraction. 

A GHe leak always resulted in a negative PVT gauging error; 

that is, the PVT measurement was less than the actual fill 

fraction. The location of the leak (supply tank, propellant tank, 

or transfer line) was irrelevant. Increasing the propellant tank 

Figure 6.—Pressure-volume-temperature (PVT) gauging 

error with propellant tank temperature offset (error) equal 

to 0.65 percent of the propellant tank temperature at a 

pressure of 1.65 MPa. (See Sensivitiy Analysis section 

for other specifications.) 

pressure caused a slight reduction in sensitivity to GHe 

leakage: at 0.34 MPa, a 1-percent gauging error (at 5-percent 

fill) resulted from a loss of 0.47 percent of the initial GHe 

mass in the supply tank, whereas at 1.65 MPa the same error 

would require a 0.75-percent loss. 

Test Matrix and Procedures 

The tests reported herein, and listed in Table III, were all 

run in August 2007. These include nine PVT tests conducted 

at nominal propellant tank pressures of 0.34, 1.03, and 

1.65 MPa. Six were LO2 tests, and three were LN2 tests. The 

PVT tests were conducted at starting fill fractions of 0.92 to 

0.98, followed by approximate decrements of 0.1, to final fill 

fractions of 0.05 to 0.10. A test was typically conducted within 

4 to 5 hr. A special test (test 25), discussed later, was conducted to collect data to characterize the rate and degree that 

GHe was dissolved into LO2 for the specific test hardware and 

operations used in this study. 

For all tests, the GHe supply tank was charged with the 

required amount of GHe and cooled to 90 K. The initial GHe 

mass was predetermined such that the supply tank pressure at 

the end of a gauging test run would exceed the propellant tank 

pressure by at least 0.7 MPa. For each test run, the propellant 

tank was filled to the starting fill level and allowed to reach 

quasi-steady-state tank wall and lid temperatures while the 

tank was vented to the atmosphere. The pump/spray system 

was operated intermittently to cool the unwetted tank lid. 

When the propellant tank and GHe supply tank were both 

filled and at near-isothermal conditions, a test run was started 

by closing the propellant tank vent and recording the initial 

conditions in the GHe supply tank. 

The first PVT measurement was initiated by pressurizing 

the propellant tank to the desired pressure. This involved 

transferring GHe from the supply to the propellant tank and 

operating the pump to create isothermal conditions in the 

propellant tank. Pump/spray operation would cause a pressure 

reduction in the propellant tank. Therefore, multiple pressurization and mixing steps were performed to reach quasisteady-state, isothermal conditions at the desired pressure. As 

TABLE III.—COMPLETED TESTS 

Test 

number 

Propellant Nominal propellant 

tank pressure, 

MPa 

18 LO2 1.03 

19 LO2 1.65 

20 LO2 0.34 

22 LO2 0.34 

23 LO2 1.03 

24 LO2 1.65 

25 LO2 1.08a

28 LN2 1.65 

29 LN2 1.03 

30 LN2 0.34 a

Initial condition. 
NASA/TP—2014-218083 7 

will be discussed in the results section, true steady-state 

conditions cannot be attained if GHe is being dissolved in the 

liquid during active mixing of the propellant tank. Meanwhile, 

the pressure and temperature in the GHe supply tank were 

monitored to determine when the tank reached steady state. 

Conditions for a steady-state measurement were considered to 

exist if the computed value of GHe density in the supply tank 

was steady and if all liquid and ullage temperatures in the 

propellant tank were approximately equal. Real-time plotting 

of the data allowed monitoring of both tanks. After quasisteady-state and isothermal conditions prevailed in both tanks, 

the propellant tank was drained to the next targeted liquid fill 

fraction and the procedures just described were repeated. The 

data system operated continuously, recording steady and 

unsteady data from both tanks as well as the RGS. 

Liquid and ullage samples were collected during the tests 

conducted at nominal propellant tank pressures of 1.03 and 

1.65 MPa. Samples were taken at 65- to 70-percent fill (one 

ullage sample and two liquid samples) and again at 30- to 

35-percent fill (two ullage samples and one liquid sample). 

Then, the samples were sent to an independent laboratory for 

gas chromatography analysis (according to ASTM D1946) to 

determine the GHe concentrations. 

Effect of Helium Solubility 

GHe has a slow diffusion rate and low equilibrium 

solubility in LO2 and LN2 within the temperature and pressure 

ranges for typical spacecraft propulsion systems (Refs. 6 

and 7). However, the amount of GHe in solution may become 

significant for PVT gauging when the tank contents are 

actively mixed for extended periods of time such as in the 

present experiment. Consequently, when high-accuracy PVT 

gauging results are desired, it may be necessary to account for 

the loss of GHe from the ullage to the liquid. 

An estimate of GHe solubility in the liquid propellant under 

the test conditions showed that, under worst-case assumptions, 

dissolved GHe is significant and could affect PVT measurement accuracy. Test 25 was conducted and analyzed to provide more insight into the degree and rate of GHe infusion into 

LO2 for this test program’s specific test hardware and mixing 

operations. A simple mechanistic model was developed and 

used to determine the mass of soluble GHe as a function of the 

elapsed mixing pump operation time during the PVT tests. 

The GHe solubility correction to the PVT gauging measurement was on the order of 2 percent for LO2 and 3 percent 

for LN2. The reader is referred to Appendix A for a discussion 

of the worst-case estimate, an analysis of test 25 results, and 

model development for predicting the dissolved GHe mole 

fraction as a function of mixing time in the present PVT tests. 

Corrections to the Calculated PressureVolume-Temperature Gauging 

Measurements Due to External Volumes 

A number of external volumes were connected to the GHe 

supply and propellant tanks that could introduce errors if they 

were not appropriately accounted for in the gauging 

calculations. These external volumes were various plumbing 

lines that were dead-ended at shutoff valves outside of the 

vacuum chamber. The errors result from local thermodynamic 

conditions in these volumes that differ from the assumed 

isothermal states in the two tanks and from the assumed 

uniform mixture of GHe and vapor in the propellant tank. The 

net correction to the calculated PVT gauging measurements 

for external volume effects was about 0.5 percent for this 

work. Appendix B presents the details of this analysis. 

Tank Volume Expansion Due to Pressure 

The effect of tank stretch (or volume change due to 

pressurization) should be carefully evaluated in a PVT 

measurement system. For the present work, a structural 

analysis of the GHe supply tank was conducted to determine 

the tank’s volume change as a function of pressure; the tank’s 

known geometry, wall thickness, and construction material. At 

the supply tank’s maximum allowable working pressure 

(MAWP), the volume increased by 0.13 percent at room 

temperature. The volume change was 7 percent less at LO2

temperature. The percent volume change was assumed to be 

similar for the propellant test tank and the small high-pressure 

gas cylinder used in the GHe supply tank volume measurement at the respective MAWPs of these vessels. The stretch 

coefficient ξ defined as 

MAWP

V0

V

  (11) 

was used to calculate the appropriate tank volumes as a 

function of pressure: 

V V0  1 P (12) 

where the subscript zero refers to conditions at a zero internalto-external pressure difference. Tank stretch can have an 

impact in several ways. First, the tank stretch can alter the 

measured volumes of the GHe supply tank and the propellant 

tank. This was investigated and found to be negligible in 

 
NASA/TP—2014-218083 8 

comparison to the other sources of tank volume measurement 

error. Second, the effect of tank stretch could change the 

calibration of the RGS. The most significant change to the 

calibration coefficients for the RGS was in the tank pressure 

coefficient C2 of Equation (8) (because of the slight change in 

propellant tank volume from the low to high calibration 

pressures), but the resulting difference in calculated fluid mass 

was negligible. Third, the fill level determined from the RGS 

using Equation (9) can change because of the small increase in 

the propellant tank volume. This effect was negligible at low 

tank pressures, but a small discernible change resulted at high 

tank pressures and varied with fill fraction. For the present 

work, the maximum effect was a 0.1-percent difference at 

99-percent fill and a propellant tank pressure of 1.65 MPa. 

This effect reduced the value of the propellant tank liquid fill 

fraction computed from the RGS measurements. The fourth 

effect of stretch is on the PVT measurement itself. Stretch of 

the GHe supply tank caused a small reduction in the measured 

fill fraction, whereas stretch of the propellant tank caused the 

opposite effect. For the present work, these two effects very 

nearly canceled each other. Each of the effects caused an 

approximate 0.1-percent change in fill fraction as the fill 

fraction approached zero at the 1.65-MPa test pressure. The 

changes became negligible at higher fill fractions and at all fill 

fractions at lower pressures. The combined effects of stretch 

on the GHe supply and propellant tanks on the PVT 

measurements for the present work are negligible in all cases. 

Because all of the effects of tank stretch in the present work 

were minor in comparison to other sources of error and 

uncertainty, tank stretch effects were omitted from further 

analysis in the present results. 

Experimental Gauging Results 

The quasi-steady-state PVT results obtained at a nominal 

propellant tank pressure of 1.65 MPa are plotted in Figure 7 as 

a function of fill fraction. Similarly, the results for 1.03 and 

0.34 MPa are shown in Figures 8 and 9. The results are 

presented as the percent difference between the PVT result 

and the RGS based on the total tank volume. The PVT results 

were corrected for the effects of GHe solubility and external 

volumes, as discussed previously in this report; and the RGS 

results were adjusted to the sensed tank volume of the PVT 

method using Equation (10). In each figure, estimated error 

bars—which represent only the error for the PVT measurement, are shown for one of the tests. There is also a smaller, 

but significant, error associated with the RGS. The reader is 

referred to Appendix C for a discussion of the analysis used to 

estimate the error bars, details regarding the percentage 

contributions of the various uncertainty terms to the overall 

estimate of the PVT measurement error, and the RGS 

uncertainty estimate. 

In Figure 7, the results for high propellant tank pressure 

have an orderly, repeatable trend with minimal scatter. There 

Figure 7.—Pressure-volume-temperature (PVT) gauging 

results for nominal 1.65-MPa propellant tank pressure; RGS, 

reference gauging system. 

Figure 8.—Pressure-volume-temperature (PVT) gauging 

results for nominal 1.03-MPa propellant tank pressure; RGS, 

reference gauging system. 

Figure 9.—Pressure-volume-temperature (PVT) gauging 

results for nominal 0.34-MPa propellant tank pressure; RGS, 

reference gauging system. 
NASA/TP—2014-218083 9 

is no significant difference between the two LO2 tests (tests 19 

and 24) or the LN2 test (test 28). The measurement error is 

very near zero at high fill fraction and increases to maximum 

values of less than 2 percent at fill fractions of 0.05 to 0.1. 

This behavior is consistent with the earlier discussion of input 

errors and could be due to offsets of any of the values input 

(tank volumes, pressures, or temperatures) to the PVT measurement or some combination thereof. The GHe solubility 

correction for LN2 was greater than for LO2 (see App. A). The 

good agreement of the PVT results for both propellants 

indicates that the solubility correction has high fidelity. 

The results for the intermediate propellant tank pressure 

shown in Figure 8 are quite similar to the results in Figure 7. 

The same overall trend is seen but with slightly more data 

scatter at high fill fractions. The overall dataset is somewhat 

more centered about 0-percent error, and all the data points are 

within a 1.5-percent error band. The instrumentation used for 

the results at the intermediate and high propellant tank 

pressure tests was identical, and the increased scatter at the 

intermediate pressure may be due to various input measurement errors/offsets being a greater percentage of the input 

values at this pressure. 

At the lowest propellant tank pressure (0.34 MPa), a lower 

range pressure transducer was utilized in the propellant tank 

(LO2 tests 20 and 22). Figure 9 shows the results. During the 

LN2 test (test 30), the lower pressure range transducer 

produced readings that grew progressively different from the 

readings of the higher range transducer (which remained in 

service). The authors’ best judgment is that this anomalous 

behavior indicated a gradual failure of the low-range pressure 

transducer during the LN2 test. For the analysis of the LN2

data, the offset between the two pressure transducers from the 

LO2 data were subtracted from the high-range transducer 

readings and used as the input propellant tank pressure. 

Therefore, the results in Figure 9 for test 30 were not obtained 

in the exact manner as the other data and should be viewed 

with caution. Figure 9 again shows good PVT gauging 

accuracy with errors within 1.5 percent. There is more scatter, 

and although the two LO2 test series show similar behavior, 

repeatability is not as good as at the intermediate and high 

propellant tank pressures. This result is not unexpected 

because prior analysis has shown that PVT gauging will have 

more uncertainty at low propellant tank pressures. Figure 9 

does not exhibit the same trend of increasing error as fill 

fraction decreases that is observed in Figures 7 and 8. One 

could thus speculate that the high-range pressure transducer 

used in the higher pressure tests had a more positive error or 

offset (percent of input, as discussed in the sensitivity 

analysis) than the low-range transducer. 

Figure 10 shows an example of the effects of the corrections 

for external volumes and GHe solubility for test 24 (LO2 at 

1.65 MPa). The effects are typical of the other tests. The 

correction for the external volumes was relatively small and 

reduced the gauging result by a nearly constant value for all 

fill fractions. The correction for solubility was significantly 

greater and increased the PVT result by as much as 2 percent 

at the lower fill fractions. (The maximum correction is about 

3 percent for the LN2 tests.) Note that the solubility correction 

removed the kink in the fill fraction dependence exhibited by 

the basic PVT results. The kink occurs at the fill fraction 

where the propellant tank mixing turnover time (as discussed 

in App. A) was reached. The solubility model takes this into 

account, removes the kink, and results in a linear trend of 

gauging error versus fill fraction. 

Overall, all of the quasi-steady-state PVT data agreed with 

the RGS to within 1.5 percent of full scale (tank volume). This 

agreement gives us confidence that the tank volume, temperature, and pressure measurements were free from substantial 

errors, that the GHe solubility model used to correct the basic 

calculation is valid, and that no significant GHe leaks existed 

in the test hardware. 

Thus far, PVT gauging results have been shown for quasisteady-state conditions. To obtain steady-state conditions, a 

sufficient hold time is necessary to allow the GHe supply tank 

to attain a steady pressure and temperature after GHe has been 

transferred to the propellant tank. The tests at the nominal 

1.65-MPa propellant tank pressure had the largest temperature 

drop during GHe transfer and required about 15 min to attain a 

new steady-state condition. The calculated supply tank GHe 

density would reach a steady-state value more quickly than 

15 min (i.e., although pressure and temperature could both be 

increasing, the pressure-to-temperature ratio had become 

constant), so a shorter wait (~10 min) for equilibrium conditions in the supply tank was acceptable. The time required to 

return to steady-state supply-tank conditions was less for the 

lower-pressure tests. 

Steady-state thermodynamic conditions could never be truly 

attained in the propellant tank because heat leak into the tank 

caused the liquid temperature to rise continually. Running the 

mixing pump and spray system would produce isothermal 

conditions in the propellant tank while adding additional heat 

Figure 10.—Example of typical effects of external volume 

and helium solubility corrections to basic pressure-volumetemperature (PVT) result; test 24—liquid oxygen at 

1.65 MPa; RGS, reference gauging system. 
NASA/TP—2014-218083 10 

to the tank. Longer pump operating times were necessary for 

the higher pressure tests because more warm GHe was 

transferred to the propellant tank in these tests and had to be 

mixed with the tank contents. (The transferred GHe warmed 

up because the transfer line was not well insulated.) 

Intermittent pump operation, chosen for this work, produced a 

sawtooth response in tank pressure—the pressure dropped 

when the pump was operating and rose when the pump was 

off. At the higher fill fractions, GHe was driven into solution 

in the liquid when the pump was operating. Therefore, at high 

fill fractions (after GHe flow was completed), the sawtooth 

pressure response had a decreasing overall trend with time, but 

at lower fill fractions, the sawtooth pattern had more 

consistent maximums and minimums. 

Although PVT is not considered to be an accurate real-time 

measurement technique, examination of real-time gauging 

results may be of interest. In Figures 11 and 12, the real-time 

PVT gauging results are shown for two example tests. These 

figures also show the times corresponding to steady-state 

results, the timeline for pump operation, and the timeline for 

GHe transfer to the propellant tank. Figure 11 shows the 

results for test 24 (LO2) at a propellant tank pressure of 

1.65 MPa. In this test, the test procedure was to operate the 

pump while GHe was transferred to the propellant tank. This 

procedure kept the propellant tank close to isothermal 

conditions at all times. The real-time gauging results are 

surprisingly good and are typically within 0.5 percent of the 

steady-state results. The occasional negative spikes occur 

when the pump was started. The positive error trends in the 

real-time gauging occur when GHe was transferred to the 

propellant tank, and the negative trends occur after GHe flow 

was stopped. The transient conditions in the supply tank, 

discussed earlier, existed during these positive-negative error 

trends. The second example, shown in Figure 12, is for test 20 

(LO2) at a propellant tank pressure of 0.34 MPa. In this case, 

the real-time errors were much larger (up to –6 percent) 

because the pump was operated less frequently; thus, more 

substantial thermal stratification was present in the ullage. 

Operating the pump would return the tank to isothermal 

conditions (within minutes), and accurate quasi-steady-state 

results were then obtained. Rigorous mixer control logic was 

not implemented for the tests. The examples in Figures 11 and 

12 show the effect of the mixer operation history on real-time 

results. 

Sample extraction had a very small effect on the gauging 

results. The liquid sample extraction caused a minor drop in 

fill fraction with a corresponding removal of dissolved GHe 

from the propellant tank. The change in fill fraction itself did 

not alter the accuracy of the PVT or RGS measurements. The 

mass of dissolved GHe in the liquid samples was essentially 

negligible, but nevertheless, it was included in the calculation 

of expelled mass. The removal of ullage samples had an effect 

on the order of 0.1 percent of the total mass of GHe in the tank 

at the time of sample withdrawal. This percentage was 

insensitive to propellant tank pressure and was about the same 

Figure 11.—Real-time pressure-volume-temperature (PVT) 

gauging results for nominal 1.65-MPa propellant tank 

pressure (liquid oxygen test 24); RGS, reference gauging 

system; GHe, gaseous helium. 

Figure 12.—Real-time pressure-volume-temperature (PVT) 

gauging results for nominal 0.34-MPa propellant tank 

pressure (liquid oxygen test 20); RGS, reference gauging 

system; GHe, gaseous helium. 

at both the high and low fill fractions where samples were 

collected because a single ullage sample was extracted at the 

high fill level, whereas two ullage samples were withdrawn at 

the lower level where the ullage volume was approximately 

twice as large. The PVT gauging result had no effect prior to 

sampling when fill fractions were greater than 0.7, had a 

negative shift of about 0.03 to 0.04 percent after the first 

sample collection event when fill fractions were from 0.7 to 

0.4, and had a negative shift of about 0.06 to 0.07 percent 

when fill fractions were less than 0.4. The negative shift was 

similar to the effect of a GHe leak as discussed earlier. These 

effects were considered to be negligible and were not factored 

into the PVT gauging results presented herein. 

The results of the gas species concentration analyses of the 

extracted samples can be compared with the assumptions used 

to model the PVT method. The ullage sample compositions 

 
NASA/TP—2014-218083 11 

can be compared with the Dalton model (which for a mixture, 

assumes that the mole fraction of each component equals the 

partial pressure of that component divided by the total 

pressure). Figure 13 compares the GHe mole fraction in the 

ullage from the Dalton model with the experimental values 

(gas chromatograph analysis of the samples). The GHe mole 

fractions from the sample analysis are about 3 percent lower 

than what the Dalton model predicted. The results for LO2 and 

LN2 are similar. 

Figure 14 compares the GHe mole fractions from the 

analyzed liquid samples with the predicted values from the 

GHe solubility model. The higher solubility of GHe in LN2 in 

comparison to LO2 is readily evident. The sampled and 

solubility-model-predicted values compare quite well, considering that these values were near the reported detection limit 

of 0.1 mol% for the gas chromatography method used to 

analyze the samples. The results shown in Figures 13 and 14 

are for samples collected from the 1.03- and 1.65-MPa tests, 

excluding test 18. The results from test 18 were deemed 

unreliable because they were inconsistent with all other data. 

The earlier sections in this document address only PVT 

gauging applied to an isothermal propellant tank. During the 

test program, a special test was conducted to obtain data under 

conditions where the propellant tank was intentionally allowed 

to thermally stratify as GHe was added to the tank and liquid 

was expelled. For this test only, the mixer pump in the 

propellant test was never operated. A single test point from 

this test, at an approximate 10-percent liquid fill level, is 

thoroughly analyzed in Appendix D. An accurate gauging 

result—within 2 percent of tank volume—is shown to be 

possible by accounting for the temperature and GHe 

concentration profiles in the tank. Implementation of the 

stratified PVT gauging method in a low-gravity environment 

will require an extensive development effort in the areas of 

liquid versus vapor phase determination, multidimensional 

Figure 13.—Comparison of helium mole fractions, xHe, in 

ullage from Dalton model and analyzed samples. 

Figure 14.—Comparison of helium mole fractions, xHe, in 

liquid from solubility model and analyzed samples. 

numerical integration of the fluid volume and density, and 

real-time measurement or modeling of local GHe 

concentration. 

Summary of Results 

Pressure-volume-temperature (PVT) gauging experiments 

were successfully completed for liquid oxygen (LO2) and 

liquid nitrogen (LN2) tests using gaseous helium (GHe) 

pressurization. Helium was supplied by a cryogenic highpressure supply tank that simulated a cold GHe supply bottle 

on a flight system. Gauging errors of less than 2 percent of 

propellant tank volume were demonstrated at nominal tank 

pressures of 0.34, 1.03, and 1.65 MPa. The measured PVT 

errors are relative to reference gauging measurements from a 

calibrated, high-accuracy system composed of calibrationstandard load cells, which weighed the tank. 

The reported results were obtained for quasi-steady-state 

conditions in an isothermal propellant tank. Isothermal 

conditions were obtained by frequent operation of an ullage 

spray system fed by a submerged liquid circulation pump. Use 

of the PVT method when a thermally stratified ullage exists in 

the propellant tank requires further study. 

Obtaining accurate PVT measurements required careful 

attention to second-order effects, including the solubility of 

GHe in the liquid propellant and corrections for small external 

volumes attached to the propellant tank, such as the vent and fill 

lines—where the thermodynamic conditions differ from the 

isothermal and well-mixed conditions in the tank’s ullage. Tank 

stretch, or volume change due to pressure, was not significant in 

the present work, but it should be carefully evaluated in flight 

systems with thin-walled, lightweight tankage. 

A special GHe solubility test was performed, and the data 

were used to develop and validate a model to predict the 

amount of GHe dissolved in the liquid propellant as a function 

of pump operation time. This simple solubility model allowed 

the basic PVT calculations to be adjusted for GHe lost from 

the ullage when GHe was dissolved in the liquid. The 
NASA/TP—2014-218083 12 

solubility model is considered to be specific to the test 

hardware of the present experiments, but it can be adapted to 

other PVT gauging applications. 

During the tests at intermediate and high propellant tank 

pressure, samples were extracted from both the ullage and the 

liquid regions of the propellant tank. Helium mole fractions 

obtained from chemical analysis of these samples were in 

reasonably good agreement with values predicted from the 

solubility model for the liquid and from the partial pressure 

(Dalton) model for the ullage. 

Data also were obtained for real-time PVT gauging as the 

propellant tank fill fraction was reduced. If the ullage was 

allowed to stratify thermally, gauging accuracy was 

substantially degraded. When the ullage was kept in a near 

isothermal state by operation of the pump/spray system as 

GHe was transferred to the propellant tank, PVT gauging 

accuracy was only slightly degraded, by 0.5 percent. 

 
NASA/TP—2014-218083 13 

Appendix A.—Helium Solubility Analysis and Correction 

An upper bound of the amount of GHe in solution for the 

PVT gauging method can be estimated when the propellant 

tank is at the maximum expected temperature, pressure, and 

liquid fill fraction. Then, a published correlation derived from 

experimental solubility data (Ref. 6) can be used to predict the 

equilibrium mole fraction of GHe in LO2. For the range of 

temperature, pressure, and initial fill fraction of interest in the 

present work, the worst-case scenario resulted in an LO2 PVT 

measurement error of 3.8 percent of full scale (resulting in a 

PVT measured fill level lower than the true value). This upper 

bound estimate assumes that the entire liquid volume is 

infused with GHe at the initial fill level (95 percent) prior to 

any expulsion of liquid. At this high initial fill level, the 

amount of GHe in solution is about 75 percent of the amount 

initially present in the ullage. There would be no further 

change in the amount of soluble GHe if the temperature and 

pressure remained the same: the dissolved GHe would be 

expelled with the liquid as the tank was drained. Under this 

scenario, the PVT measurement error is a constant offset at all 

fill levels. The total soluble GHe is about 4 percent of the GHe 

required to expel liquid and maintain tank pressure to a fill 

level of 5 percent. The values given apply to tank pressures 

from 0.4 to 1.8 MPa. 

A similar correlation for equilibrium mole fractions in 

helium-nitrogen systems (Ref. 7) also was used. The worstcase PVT measurement error was 4.8 to 4.9 percent for LN2, 

similar to the helium-oxygen behavior discussed earlier, but 

slightly larger. 

Because the magnitude of the worst-case GHe solubility 

effect was greater than the desired gauging measurement 

accuracy, further study was warranted. The rate due to 

diffusion only under quiescent tank conditions is known to be 

very slow (the entire liquid mass would take weeks to reach 

equilibrium solubility), but the forced convection of the liquid 

due to pumping through the spray hoops could greatly increase 

the solubility rate. 

A special test (test 25) was conducted to experimentally 

evaluate the rate and degree of GHe solubility in LO2. In this 

test, the propellant tank was filled to 91 percent and quickly 

pressurized with GHe to an initial pressure of 1.08 MPa. The 

liquid pump was operated continuously for several hours, 

spraying liquid into the ullage and circulating the tank 

contents by ingesting liquid from the bottom of the tank. 

Figure 15 shows the pressure and average fluid temperature 

history. The start time (0 min) was defined as the start of GHe 

flow into the tank. Helium flow was stopped at 2.27 min. 

After the initial spike, tank pressure collapse was seen when 

the pressure dropped quickly as the GHe (which was warm 

because of heating as it flowed through the transfer line) 

cooled to the average tank fluid temperature. There was a 

small but significant increase in temperature coinciding with 

Figure 15.—Pressure and temperature histories for special 

solubility test 25. 

GHe inflow. The otherwise steady increase in temperature was 

attributed to the combined energy input from heat transfer 

through the tank wall and energy dissipation from the pump. 

After the initial pressure collapse, the pressure continued to 

decrease for approximately 40 min. This pressure decrease 

was attributed to GHe leaving the ullage (and reducing the 

GHe partial pressure) as it was dissolved into the liquid. The 

dissolution process was thought to take place primarily within 

the small liquid droplets exiting the spray hoops and falling 

through the ullage or within the thin liquid films flowing down 

the tank sidewall. The free surface of the liquid may also have 

been agitated because of the droplets impinging on the free 

surface, thus promoting additional dissolution. When the 

pressure reached a minimum, the liquid was thought to have 

reached a state of substantial GHe infusion throughout its 

entire volume. After this, the pressure slowly increased, 

primarily as a result of the energy input from wall heating and 

pump operation. The minimum pressure occurred at a time 

approximately equal to the mixing turnover time for the tank. 

The mixing turnover time is the time it takes for the entire 

liquid volume to pass through the pump and is calculated as 

the liquid volume divided by the pump’s volumetric flowrate. 

Figure 16 shows the temperature profile near the tank’s 

central axis at various times. The addition of warm GHe 

caused an increase in temperature in the ullage as seen at 

2.1 min. At 4, 10, 15, and 20 min, a slightly warmer liquid 

layer propagated toward the tank bottom. From 30 min on, the 

fluid temperature was uniform. This temperature profile is 

consistent with a slightly warmer layer forming at the liquid 

surface and spreading downward until it extends completely to 

the tank bottom. A similar process is thought to have occurred 

with the GHe-infused layer. 

 
NASA/TP—2014-218083 14 

Figure 16.—Tank temperature profiles for special solubility 

test 25 at various times. 

A computational model was developed to predict the 

dissolved GHe mass in the PVT tests using the results of 

test 25 as a starting point. The model is based on conservation 

of GHe mass (sum of GHe in ullage and in solution) and 

propellant mass. It uses the helium-oxygen solubility correlation of Zimmerli et al. (Ref. 6) to calculate the equilibrium 

value of dissolved GHe. Key points and assumptions of the 

model follow: 

(1) The initial conditions for fill fraction, pressure, and 

temperature were matched to the experimental data. 

The initial infused GHe mass was zero. 

(2) The temperature history was specified with two linear 

curve fits to the experimental data—one for the period 

of GHe addition and the other for the remainder of the 

test duration. (The step up in temperature increase was 

fitted, but the spike was not.) This was done to remove 

the influence of noise in the temperature data, which is 

evident in Figure 15. Using the temperature history 

simplified the problem, so it was not necessary to solve 

for an energy balance. 

(3) Vapor properties were at the saturated state for the 

given temperature. 

(4) The mass of GHe added to the tank was found by 

numerical integration of readings from the flowmeter 

placed in the GHe transfer line. At 2.27 min, the GHe 

flow was shut off and the mass of GHe in the tank 

remained constant for the remainder of the test. 

(5) For each time step, the incremental liquid mass pumped 

through the spray hoops was infused with the equilibrium quantity of soluble GHe at the current tank 

average temperature and pressure. 

(6) A layer of GHe-infused liquid formed at the liquidullage interface. Its thickness and volume increased 

with time until the entire liquid volume was infused 

with GHe. 

(7) The average mass fraction of GHe in the infused liquid 

volume was updated at each time step. The average 

mass fraction of the infused volume was allowed to be 

less than or greater than the value based on the current 

tank temperature and pressure. The latter situation 

generally occurred when pressure was decreasing. 

(8) The total tank pressure was iterated at each time step to 

satisfy the GHe mass balance. When the solution was 

obtained, the partial pressure of the GHe was determined and the masses of GHe in the ullage and in 

solution were found. 

Figure 17 compares the predicted tank pressure history with 

the experimental results. The model matched the pressure data 

reasonably well. However, it did not match the spike (which is 

not thought to be important), and it predicted a slower rate of 

pressure drop while the GHe-infused liquid volume was growing. The faster rate of pressure drop of the experimental data 

indicates that the amount of GHe dissolved in the infused GHe 

layer during this phase actually exceeded the equilibrium 

value. The model also predicted a more prominent minimum 

pressure (when the turnover time was reached), whereas the 

actual data have a broader minimum pressure, indicating that 

the actual transition from pumping pure propellant to GHeinfused propellant was not an abrupt process. 

Figure 18 shows the predicted GHe mass fraction in the 

infused liquid volume. The “instantaneous response model” 

mass fraction, obtained by assuming that the entire infused 

volume had a GHe mole fraction based on the current tank 

pressure and average temperature, is included for comparison. 

After a sufficiently long time, when the liquid had circulated 

through the pump several times and the pressure and 

temperature were slowly rising because of heat input, the 

infused liquid model and instantaneous response model were 

in good agreement. When pressure was changing more 

rapidly, the infused liquid model predicted a GHe mass fraction that lagged behind the instantaneous response calculation, 

as expected. Differences between the two models were relatively minor and unimportant to the resulting correction to the 

PVT gauging results. 

Figure 17.—Comparison of predicted and experimental 

pressure histories for special solubility test 25. 

 
NASA/TP—2014-218083 15 

Figure 18.—Comparison of infused liquid model’s 

predicted soluble helium mass fraction for special 

solubility test to instantaneous response model’s value 

based on measured pressure and spatially averaged 

temperature. 

Figure 19.—Comparison of predicted and experimental 

soluble helium mass histories for special solubility 

test 25. 

Figure 20.—Soluble helium mass histories for pressurevolume-temperature test 19. 

Figure 19 compares the time-dependent predicted soluble 

GHe mass from the model with experimentally derived values. 

The experimentally derived values were obtained by integrating the GHe flowrate into the tank and then subtracting the 

GHe mass in the ullage (found by using pressure and 

temperature to obtain the oxygen partial pressure, the GHe 

partial pressure, the GHe density, and the fill fraction based on 

the load cell readings). The uncertainty for this calculation 

was high during the initial phase when the temperature and 

pressure spikes occurred (most likely creating nonuniform 

ullage conditions), but otherwise, this calculation is thought to 

be reasonably accurate. Figure 19 shows that the experimentally derived curve is steeper initially and then more 

rounded. The sharp bend in the model’s prediction occurred 

when the tank turnover time was reached. The predicted and 

experimentally derived values for soluble GHe mass are in 

good agreement when the elapsed time is large. The final 

predicted mass fraction of 810–5, corresponding to a mole 

percent of 0.07 percent, is below the sample analysis detection 

limit and, therefore, could not be compared with a sample 

analysis. Overall, we think that the agreement is reasonably 

good for a simple model and that the model is useful and 

sufficient for a more refined analysis of the PVT test data. 

This model required a few additional features for predicting 

the mass of soluble GHe in the PVT tests: 

(1) During PVT gauging, the pump was operated intermittently. Therefore, the GHe-infused liquid volume 

grew only when the pump was on. 

(2) If liquid was expelled before the turnover time was 

reached (pumped volume was less than the liquid 

volume), the expelled liquid was free of infused GHe. 

(3) If liquid was expelled after the turnover time was 

reached, the infused volume decreased and the expelled 

liquid had the same GHe mass fraction as the infused 

volume. 

(4) The mass of expelled soluble GHe was integrated over 

time and accounted for in the overall PVT GHe mass 

balance. 

Figure 20 shows an example of the predicted GHe solubility 

for test 19 (LO2 at 1.65 MPa). Similar trends were obtained for 

the other tests with lesser amounts of GHe going into solution 

at the lower test pressures. There was no expelled GHe 

(soluble GHe in the expelled liquid) until the fill fraction 

dropped to about 0.6 (at approximately 110 min in the 

example). The total soluble GHe was the sum of GHe infused 

in the liquid inside the tank plus GHe infused in the expelled 

liquid. The rate at which GHe was lost to solubility was 

greatest early in the tests because initially there was no soluble 

GHe in the liquid being pumped through the spray hoops. 

Later, when all the liquid was infused with GHe and liquid 

was expelled, the slow increase in total soluble GHe was due 

to the increasing propellant tank temperature. 

 
NASA/TP—2014-218083 16 

Generally, the amount of GHe in solution, as a percentage 

of total GHe transferred to the propellant tank, decreased with 

fill fraction for all tests. At the minimum fill fraction (0.05 to 

0.10), the soluble GHe as a percent of total transferred GHe 

was about 2 percent for LO2 and 3 percent for LN2. These 

values are less than the worst-case estimates because some of 

the liquid was removed from the propellant tank before the 

entire liquid volume had become infused with GHe at the 

equilibrium mole fraction.
NASA/TP—2014-218083 17 

Appendix B.—Correction for Effects of External Volumes 

The analysis was simplified by grouping the fluid 

temperatures into three classifications: the known GHe supply 

and propellant tank temperatures were defined as “cold,” the 

“warm” ambient temperature was assumed to be 290 K, and 

the “cool” temperature was the average of the warm and cold 

temperatures. The fluids in the external volumes of the GHe 

supply tank and in the portion of the lines attached to the 

propellant tank, but outside the vacuum chamber, were 

assumed to be at the warm temperature; most of these lines 

were not insulated and were exposed to outdoor ambient 

conditions. The fluids in the remaining portions of volumes 

attached to the propellant tank but inside the vacuum chamber 

were assumed to be at the cool temperature; these lines also 

were uninsulated but were within a vacuum environment. The 

assumption of cool temperatures was partially verified by 

temperature measurements inside the fill and vent lines. 

Further assumptions (discussed shortly) were made regarding 

the fluid composition inside the various external volumes. The 

revised equations that include these corrections follow: 

Mass of GHe transferred from the GHe supply tank: 

 m* = (bi – b)(Vb – Vbe) + (bei – be)Vbe (B1) 

where b, e, and i refer to bottle, external, and initial. 

Mass of GHe in the propellant tank ullage excluding the 

extended tank volumes: 

 (B2) 

Total propellant tank ullage volume including the extended 

propellant tank volumes: 

 (B3) 

Details of individual corrections follow: 

(1) All of the various lines attached to the GHe supply tank 

contained warm, pure GHe. The total volume of these 

lines was 0.08 percent of the GHe supply tank volume. 

The result was about a 0.05-percent reduction in the 

calculated ∆m. The resulting PVT fill level measurement correction increased from 0 percent at 100-percent 

fill to 0.05 percent at 0-percent fill. 

(2) The GHe transfer line attached to the propellant tank 

was assumed to contain pure GHe. There were warm 

and cool segments. The total volume of this line was 

0.09 percent of the propellant tank volume. This 

adjustment caused a 0.05-percent reduction in the 

measured fill level. 

(3) The propellant tank vent line initially contained vapor, 

but GHe entered the vent line during the initial propellant 

tank pressurization, so the vent line was assumed to 

contain the same mixture composition as the ullage. The 

total volume of this line was 0.26 percent of the tank 

volume. It also had warm and cool segments. This 

correction reduced the PVT result by 0.15 percent. 

(4) The fill and drain lines, plus a set of liquid extraction 

lines used for a separate test series of Joule-Thomson 

devices, would not ingest GHe unless the tank was 

either empty or almost empty and could, therefore, be 

assumed to contain pure vaporized propellant. The 

temperature of these line volumes was not important 

because there was no impact on the GHe mass balance. 

However, the volumes were part of the overall propellant tank volume. The total volume of these lines was 

0.13 percent of the tank volume. Correcting for these 

external volumes reduced the calculated fill level by 

0.13 percent. 

(5) Sampling lines used to extract both ullage and liquid 

samples for the chemical composition analysis had the 

smallest volume of all the external volumes considered 

and could be neglected in this regard. However, when 

samples were withdrawn, the GHe mass balance could 

be affected. This is discussed in the Experimental 

Gauging Results section. 

m u  m me * * He,

  te u u V

m

V

He

* * He,
 
NASA/TP—2014-218083 19 

Appendix C.—Uncertainty of Pressure-Volume-Temperature Measurements 

An uncertainty analysis was performed on a few 

representative PVT tests (tests 20, 24, and 29) to obtain 

rigorous estimates of the PVT gauging measurement error for 

the tests reported herein. The methodology used was based on 

the work of Coleman and Steele (Ref. 5). The analysis was 

applied to Equations (1) to (6), where Equation (5) was 

revised to include the mass of GHe dissolved in the liquid msol

as follows: 

 (C1) 

Interested readers are referred to a similar analysis by Van 

Dresar (Ref. 3) for further details. A key result of this earlier 

work was the development of a relationship expressing the 

uncertainty of the GHe density in the propellant tank’s ullage 

as the sum of the effects of temperature and pressure 

measurement uncertainty: 

 (C2) 

Note that there is an indirect effect of ullage temperature 

measurement uncertainty (the dPsat/dT term) on the uncertainty 

of the GHe density in the propellant tank’s ullage. This arises 

from the use of Equation (4) where the propellant’s vapor 

pressure is used to determine the partial pressure of GHe in the 

ullage. The expression dPsat/dT was calculated using the 

Clausius-Clapeyron Equation. 

Table IV shows the uncertainty values input to the analyses. 

Most of the values were previously discussed in the main body 

of this report. There was one addition: the uncertainty of the 

dissolved GHe mass was taken to be 20 percent on the basis of 

the data plotted in Figure 19. As will be seen shortly, the GHe 

solubility uncertainty played a small part in the overall PVT 

uncertainty result. 

Figure 7 shows error bars based on the uncertainty calculations for test 24 (LO2 at 1.65 MPa). The uncertainty ranges 

from 0.6 to 1.4 percent of the full-scale propellant tank 

volume, with the largest uncertainty occurring at the lowest 

fill fraction. Results for the other tests at this propellant tank 

pressure should be similar. Uncertainties also were calculated 

for test 29 (LN2 at 1.03 MPa), with identical uncertainty value 

input as for the analysis of test 24. As shown in Figure 8, the 

uncertainty ranged from 0.7 to 1.7 percent of full-scale 

volume—slightly greater than, but otherwise very similar to, 

the higher propellant tank pressure case shown in Figure 7. 

The differences in the error bar ranges between the LO2 and 

LN2 cases are minor for Figures 7 and 8. Figure 9 shows the 

error bars for test 20 at the lowest propellant tank pressure. 

The PVT gauging uncertainty for this test ranged from 1.9 to 

3.8 percent, with the uncertainty increasing as the liquid fill 

fraction decreased. The low-range pressure transducer for the 

GHe supply tank was over ranged (and was valved off) at the 

start of all 0.34-MPa tests (e.g., test 20), and it could not be 

used as planned. The higher uncertainty of the lowest propellant tank pressure tests is partly due to the greater uncertainty 

of the GHe supply pressure measurement (because of less than 

optimal sizing of the pressure transducer) and, in the case of 

test 30, the likely failure of the low-range propellant tank 

pressure transducer (which was not addressed in the uncertainty analysis). 

There is another source of uncertainty or error not included 

in the error bars of Figures 7 to 9. This is the possible error of 

the RGS. Earlier, in the discussion of the calibration of the 

RGS as a function of applied load (simulated liquid fill 

fraction) and propellant tank pressure and temperature, the 

goodness of fit of the correlation was 0.25 percent of the fullscale LO2 weight. There is no apparent trend of the error with 

any of the listed parameters. This uncertainty source is small, 

but not negligible, especially at the higher fill fractions and 

higher propellant tank pressures where the PVT uncertainty 

is lowest.

TABLE IV.—UNCERTAINTY VALUES USED IN UNCERTAINTY ANALYSES 

Uncertainty terms Test 24 (LO2 at 1.65 MPa) 

Test 29 (LN2 at 1.03 MPa) 

Test 20 (LO2 at 

0.34 MPa) 

Propellant tank volume 1.0 percent Same 

Helium supply tank volume 0.6 percent Same 

Propellant tank pressure 0.11 percent of full scale (±2.27 kPa) Same (0.76 Pa) 

Helium supply tank pressurea 0.10 percent of full scale (±13.8 kPa) Same 

Propellant tank ullage temperature 0.25 K Same 

Helium supply tank temperaturea 0.25 K Same 

Helium mass dissolved in liquid propellant 20 percent Same a

Both initial condition and time of gauging measurement. 

 

He

sol



   m m Vu

2

2

He

2 He

2

He sat

He

2 He

d

d

He Tt Pt t

U

P

U

T

P

T

P

P

U 













  































    
NASA/TP—2014-218083 20 

Figures 21 and 22 show the uncertainty percentage contributions for the highest (1.65 MPa) and lowest (0.34) propellant tank pressure tests. The sources of uncertainty are the nine 

terms listed in the leftmost column of Table IV. A comparison 

of Figures 21 and 22 shows that the two cases are very 

different. For the high-pressure case, the GHe supply-tank 

temperature measurement was the major contributor of 

uncertainty at high propellant tank fill fractions. As the fill 

fraction dropped, the GHe supply-tank temperature contribution diminished, and the largest source of uncertainty 

became the propellant tank volume uncertainty. For the low 

propellant tank pressure example, the GHe supply tank 

pressure measurement dominated the uncertainty at high 

propellant tank liquid fill fractions and remained a major 

source of uncertainty as the fill fraction was reduced. At the 

lower fill fractions, the propellant tank temperature uncertainty became a major source of uncertainty. If the full-scale 

range of GHe supply tank pressure transducer had been better 

matched to the initial conditions for this test, its contribution 

would have been reduced and the other terms would have been 

more significant, especially the uncertainty of the propellant 

tank temperature. 

Figure 21.—Uncertainty percentage contributions for test 24—liquid oxygen at 1.65 MPa. 

Figure 22.—Uncertainty percentage contributions for test 20—liquid oxygen at 0.34 MPa.
NASA/TP—2014-218083 21 

Appendix D.—Pressure-Volume-Temperature Gauging of a 

Thermally Stratified Propellant Tank 

A thermally stratified PVT gauging test was conducted to 

investigate the applicability of the PVT method to a case with 

substantial thermal stratification within the propellant tank. 

The test apparatus was the same as used for the isothermal 

PVT tests. For the thermally stratified PVT test, the propellant 

tank’s liquid pump was not operated, thus allowing thermal 

gradients to develop in the propellant tank because of heat 

input from the external environment, warm tank lid, and GHe 

pressurant. The GHe supply tank was kept at room temperature, about 290 K, compared with the 90 K supply 

temperature used for the isothermal PVT tests. The single test 

point analyzed in this appendix was from an LO2 test at a 

liquid fill level of approximately 10 percent. The propellant 

tank pressure was 1.28 MPa, and the temperature profile is 

shown in Figure 23, where the symbols denote test data. The 

solid line is a fitted profile generated by a piecewise cubic 

Hermite interpolating polynomial, which preserves the shape 

of the data and respects monotonicity. Figure 23 shows that 

that the propellant tank condition was far from isothermal. 

Determining an average propellant tank temperature that will 

result in an accurate PVT gauging measurement may not 

be realistic. 

One can start by noting that the previously presented 

analysis for the mass transferred from the GHe supply tank to 

the propellant tank (i.e., Eqs. (1) to (3)) is still valid. The only 

difference is that the supply tank temperature was at room 

temperature and consequently, there was no need to treat the 

external supply tank volumes separately because they were 

also at room temperature. 

Proceeding with the isothermal analysis on the propellant 

tank (the subject of the main body of this report), a gauging 

result can be obtained for an assumed “averaged” propellant 

tank temperature. One can infer from Figure 23 that this 

temperature must fall between the minimum and maximum 

temperatures (94 and 172 K). Figure 24 shows the results of 

this approach. As the temperature was increased, the computed fill level dropped substantially from 33 percent to 0. 

Above 107 K, it was not possible for oxygen and GHe to 

coexist at the test pressure of 1.28 MPa. Lower temperatures, 

as low as the oxygen triple point, were possible if the 

propellant tank was actively cooled, as partially indicated by 

the dashed line. Clearly, applying the isothermal PVT 

calculation method to this thermally stratified example 

involves unacceptably high uncertainty in the gauging result. 

As expected, the RGS was much less sensitive to the 

“average” propellant tank temperature. If Equations (8) 

and (9) are employed for this example, the resulting RGS 

gauging measurements are obtained as shown in Figure 25. The 

RGS calculation gave a liquid fill level ranging from 9.1 to 

8.9 percent for the range of temperatures shown in Figure 24. 

A detailed analysis is shown to demonstrate that an accurate 

PVT gauging result is possible if sufficient data are available 

 

Figure 23.—Propellant tank temperature profile for 

thermally stratified example. 

Figure 24.—Resulting pressure-volume-temperature (PVT) 

measurement when isothermal conditions were assumed 

for thermally stratified test example. 

Figure 25.—Resulting reference gauging system (RGS) measurement when isothermal conditions were assumed for 

thermally stratified test example. 

to quantify the thermal stratification, and to a lesser extent, the 

GHe concentration gradient. An increased level of complexity 

is required to produce a more accurate PVT gauging result. 

The additional complexity involves nonuniform temperature 

and GHe concentration profiles in the propellant tank’s ullage. 

The available data were one dimensional; therefore, it was 

assumed that the temperature and GHe concentration profiles 
NASA/TP—2014-218083 22 

were functions of the vertical position only. The temperature 

data were frequently measured and recorded over the entire 

duration of the test at distributed locations from the top to 

bottom of the propellant tank, but the GHe concentration was 

sampled only at a small number of locations at a limited 

number of times during the test. At the nominal 10-percent fill 

level, GHe concentration samples were available for three 

locations in the ullage corresponding to fill level locations of 

20, 50, and 80 percent. This allowed us to estimate the GHe 

concentration profile as accurately as possible. The availability of GHe concentration data was the reason that this 

specific test point was chosen for the detailed analysis of a 

stratified PVT gauging measurement. 

To make the fitted temperature distribution usable, a 

software function was developed to calculate the tank segment 

volumes as a function of height from the base of the tank. The 

tank consisted of five segments stacked as shown in Figure 26: 

bottom head, lower cylinder, truncated transitional head, upper 

cylinder, and top head. Each head had a 2:1 ellipsoidal 

geometry. For the detailed PVT analysis, the tank was further 

segmented into thin horizontal volume slices. The slice 

thicknesses were approximately 13 mm or less, with 

adjustments for thermal contraction. The slice containing the 

liquid-vapor interface (LVI) was divided into two parts, one 

for each phase. The temperature of each slice was obtained 

Figure 26.—Cross-sectional view of propellant tank. 

from the fitted temperature distribution. Volumes of each slice 

were computed by the software function. GHe densities were 

found for each slice by inputting the local temperature and 

GHe partial pressure to a fluid properties software program 

(Ref. 8). 

The first slice-method analysis assumed a constant GHe 

partial pressure throughout the ullage. The method iterated the 

location of the LVI until the mass of GHe in the propellant 

tank ullage equaled the GHe mass transferred from the GHe 

supply tank. The partial pressure was obtained from 

Equation (4) using the temperature at the LVI location. The 

GHe mass in the propellant tank was obtained by numerically 

integrating over all the ullage slices. A similar slice-method 

analysis was used to calculate the gauging result from the 

RGS. In the RGS analysis, the masses of the liquid, propellant 

vapor, and GHe were each determined for all slices of the tank 

volume and numerically integrated. The analysis iterated the 

location of the LVI until the calculated total mass equaled the 

result from Equation (8). Table V shows the results of the slice 

analyses. Equation (10) was again used to convert the RGS 

results to the same tank volume basis used for the PVT 

measurements. The PVT result was in much better agreement 

with the RGS measurement (a difference of 3.2 percent of tank 

volume) when the thermal stratification data were included in 

the analysis. 

Both the PVT and RGS slice analyses account for the 

propellant tank external volumes and the different temperatures and GHe concentrations in these external volumes. 

(See App. B for more details about the external volumes.) 

There is no correction for the external volume of the GHe 

supply tank because this tank was at room temperature for the 

stratified PVT test. The propellant tank volume calculated 

from the tank geometry was slightly larger than the measured 

volume reported earlier in this report, primarily because of the 

displaced volume from internal hardware such as the pump, 

instrumentation rakes and leads, and the spray bar system. The 

difference was about 0.025 m3

, or 1.6 percent of the tank 

volume, so the slice volumes were reduced by this amount to 

adjust for the displaced volume. 

TABLE V.—GAUGING RESULTS FOR STRATIFIED 

PRESSURE-VOLUME-TEMPERATURE (PVT) EXAMPLE 

Modeling approach PVT fill 

fraction 

RGSa

 fill 

fraction 

Isothermal 0 to 0.33 

(unreliable) 

0.089 to 

0.091 

Fitted temperature profile with 

 constant GHe concentration in 

 ullage (first slice method) 

0.063 0.095 

Fitted temperature profile and 

 fitted GHe concentration (second 

 slice method) 

0.096 0.097 

a

Reference gauging system. 

 
NASA/TP—2014-218083 23 

Figure 27.—Helium concentration for stratified pressurevolume-temperature test at fill fraction of 0.1. 

Figure 27 shows the GHe concentration profile in the 

propellant tank. The experimental results (sample analysis) 

were obtained from gas chromatography of the extracted 

samples. The calculated and fitted results were generated by a 

second, more complex, slice analysis for the PVT and RGS 

measurement methods that accounted for nonuniform distributions of both temperature and GHe concentration. This 

analysis was identical to the first slice method discussed 

earlier except that it used a fitted linear GHe mole fraction 

distribution. It was assumed that the GHe mole fraction at the 

liquid-vapor interface (LVI) should equal the ratio of the GHe 

partial pressure to the total tank pressure, as is the case for the 

isothermal PVT measurement methodology. The curve-fit was 

constrained by the conditions that the GHe mole fraction could 

not exceed unity and that the fitted line should intercept the 

computed value at the LVI. In the numerical procedure, the 

unknown height of the LVI (in essence, the PVT gauging 

objective) was iterated until the GHe mass balance was satisfied. The corresponding temperature at this height (obtained 

from the piecewise polynomial fit shown in Figure 23) was 

used to find the propellant’s vapor pressure. The GHe partial 

pressure was obtained using Equation (4), and the GHe mole 

fraction was calculated by dividing the GHe partial pressure 

by the total tank pressure. The linear fit of the GHe concentration profile was recalculated during each iteration because 

the LVI location and GHe mole fraction at the LVI were 

updated every iteration. 

Results from the second analysis are also shown in Table V. 

The difference between the PVT and RGS measurements was 

reduced further, to within 0.1 percent of the tank volume. 

Again, the change in the RGS result was much smaller than 

the change in the PVT result, but it was still significant. 

These results show that an accurate PVT result can be 

obtained given sufficient information about the temperature 

and GHe concentration profiles within the propellant tank. For 

the example shown, with a settled normal gravity liquid 

orientation in the tank, a relatively simple one-dimensional 

analysis could be successfully used because of several reasons. 

First, the liquid and ullage regions were separated by a simple 

well-characterized interface that was perpendicular to the 

tank’s axis of symmetry. Second, posttest GHe concentration 

data were available from chemical analysis of the extracted 

samples. Clearly, further development of this method will be 

required to perform stratified PVT measurements in real time. 

Application of the second method is not considered to be 

practical in spaceflight systems because of the difficulty of 

obtaining real-time GHe concentration data. Use of the first 

method will be possible if distributed temperature sensors are 

available to capture the temperature distribution within the 

propellant tank. As the example in this appendix shows, the 

stratified PVT measurement error will likely be greater than an 

isothermal PVT measurement. 

Glenn Research Center 

National Aeronautics and Space Administration 

Cleveland, Ohio, February, 2014 

References 

1. Chobotov, M.V.; and Purohit, G.P.: Low-Gravity Propellant 

Gauging System for Accurate Predictions of Spacecraft End-ofLife. J. Spacecr. Rockets, vol. 30, no. 1, 1993, pp. 92–101. 

2. Paros, J.M.; Purohit, G.P.; and Clark, R.W.: Satellite Propellant 

Gauging System Using High Resolution Quartz Pressure 

Transducers. ISA Paper #93–099, 1993. 

3. Van Dresar, N.T.: An Uncertainty Analysis of the PVT Gauging 

Method Applied to Sub-Critical Cryogenic Propellant Tanks. 

Cryogenics, vol. 44, 2004, pp. 515–523. 

4. Van Dresar, N.T.: PVT Gauging With Liquid Nitrogen. 

Cryogenics, vol. 46, 2006, pp. 118–125. 

5. Coleman, H.W.; and Steele, W.G.: Experimentation and 

Uncertainty Analysis for Engineers. 2nd ed., Wiley and Sons, 

New York, NY, 1999. 

6. Zimmerli, G.A.; Asipauskas, M.; and Van Dresar, N.T.: 

Empirical Correlations for the Solubility of Pressurant Gases in 

Cryogenic Propellants. Cryogenics, vol. 50, 2010, pp. 556–560. 

7. Van Dresar, N.T.; and Zimmerli, G.A.: Correlation of Helium 

Solubility in Liquid Nitrogen. NASA/TM—2012-217716, 2012. 

http://ntrs.nasa.gov 

8. Lemmon, E.W.; Huber, M.L.; and McLinden, M.O.: NIST 

Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, Version 8.0. 

National Institute of Standards and Technology, Standard 

Reference Data Program, Gaithersburg, 2007. 
REPORT DOCUMENTATION PAGE Form Approved 

OMB No. 0704-0188 

The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the 

data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this 

burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. 

Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB 

control number. 

PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 

1. REPORT DATE (DD-MM-YYYY)

01-02-2014 

2. REPORT TYPE

Technical Publication 

3. DATES COVERED (From - To)

4. TITLE AND SUBTITLE

Pressure-Volume-Temperature (PVT) Gauging of an Isothermal Cryogenic Propellant Tank 

Pressurized With Gaseous Helium 

5a. CONTRACT NUMBER

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Van Dresar, Neil, T.; Zimmerli, Gregory, A. 

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

WBS 645454.01.04.04.02 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration 

John H. Glenn Research Center at Lewis Field 

Cleveland, Ohio 44135-3191 

8. PERFORMING ORGANIZATION

 REPORT NUMBER

E-18769 

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration 

Washington, DC 20546-0001 

10. SPONSORING/MONITOR'S

 ACRONYM(S)

NASA 

11. SPONSORING/MONITORING

 REPORT NUMBER

NASA/TP-2014-218083 

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified-Unlimited 

Subject Category: 28 

Available electronically at http://www.sti.nasa.gov 

This publication is available from the NASA Center for AeroSpace Information, 443-757-5802

13. SUPPLEMENTARY NOTES

14. ABSTRACT

Results are presented for pressure-volume-temperature (PVT) gauging of a liquid oxygen/liquid nitrogen tank pressurized with gaseous 

helium that was supplied by a high-pressure cryogenic tank simulating a cold helium supply bottle on a spacecraft. The fluid inside the test 

tank was kept isothermal by frequent operation of a liquid circulation pump and spray system, and the propellant tank was suspended from 

load cells to obtain a high-accuracy reference standard for the gauging measurements. Liquid quantity gauging errors of less than 2 percent 

of the tank volume were obtained when quasi-steady-state conditions existed in the propellant and helium supply tanks. Accurate gauging 

required careful attention to, and corrections for, second-order effects of helium solubility in the liquid propellant plus differences in the 

propellant/helium composition and temperature in the various plumbing lines attached to the tanks. On the basis of results from a helium 

solubility test, a model was developed to predict the amount of helium dissolved in the liquid as a function of cumulative pump operation 

time. Use of this model allowed correction of the basic PVT gauging calculations and attainment of the reported gauging accuracy. This 

helium solubility model is system specific, but it may be adaptable to other hardware systems.

15. SUBJECT TERMS

Liquid oxygen; Liquid nitrogen; Helium; Cryogenic fluids; Microgravity; Measuring instruments 

16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF

 ABSTRACT

UU 

18. NUMBER

 OF 

 PAGES

30 

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email:help@sti.nasa.gov) 

a. REPORT

U 

b. ABSTRACT

U 

c. THIS 

PAGE

U 

19b. TELEPHONE NUMBER (include area code)

443-757-5802 

Standard Form 298 (Rev. 8-98)

Prescribed by ANSI Std. Z39-18