RADIO FREQUENCY LIQUID LEVEL GAUGING IN

PROPANE TANK CAR SAFETY TESTS - A FEASIBILITY STUDY

J. D. Siegwarth

Thermophysical Properties Division

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

January 1979

GC

100

.056

79-1600

atisnal Bureao of Standards MAY 1 5 1979

NBSIR 79-1600

4 '

RADIO FREQUENCY LIQUID LEVEL GAUGING IN

PROPANE TANK CAR SAFETY TESTS - A FEASIBILITY STUDY

J. D. Siegwarth

Thermophysical Properties Division

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

January 1979

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

CONTENTS

ABSTRACT iv

1. INTRODUCTION 1

2. TANK CAR RESONANCE MEASUREMENTS 2

3. LIQUID LEVEL MEASUREMENTS IN A SMALL HORIZONTAL CYLINDRICAL TANK 4

4. CONCLUSIONS 7

5. ACKNOWLEDGMENTS 8

6. REFERENCES 8 APPENDIX 1. Resonance Frequency Measurements of Model Tank Car 9

ill
RADIO FREQUENCY LIQUID LEVEL GAUGING IN PROPANE TANK CAR SAFETY TESTSA FEASIBILITY STUDY

J. Dc Siegwarth

Thermophysical Properties Division

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

Selected

(8000 gallon)

used to gauge

The change of

a function of

sion to which

technique is

radio frequency (rf) resonances of an empty 30,300 liter

tank car have been measured to determine whether rf can be

the propane liquid levels during tank car fire safety tests,

resonant frequencies of a small horizontal cylindrical tank as liquid volume has been tested in order to estimate the precithe amount of propane in a tank car can be measured . The

applicable to routine tank car gauging.

Key words: Level gauging, propane, radio frequency

Iv
1 . INTRODUCTION

On July 28, 1973 and again on December 5, 1973 full sized propane tank cars containing 1.25 x 10^ L (33,000 gal) of liquid propane were subject

to an all enveloping fire. These tests were part of an RPI-AAR Tank Car

Safety Research and Test Program [1] ultimately aimed at reducing the probability of tank car rupture in accidents with associated fires.

The tank cars tested were instrumented so that pressure, various temperatures, safety valve performance and quantity of liquid remaining in the

tank could be measured while the car is subjected to a fire. Much of this

instrumentation failed early in the test. For instance, none of the level

measuring devices developed for these tests gave any usable information in

either test. The level devices are described in the report only as a resistance gauge, a hot wire gauge and a thermistor gauge.

An rf (radio frequency) resonance type level system should function

more reliably in the extreme environment of these fire tests since the gauge

is not dependent on the thermal or any other property of the sensor. The

tank size and shape and the dielectric constant of the fluid within are the

relevant physical parameters. The shape and size of the small antenna re- quired is unimportant and only a single coaxial lead (probably cooled) is

sufficient.

Details of rf gauging have been presented in an earlier report [2]

Briefly, closed conducting cavities of any shape resonate at discrete

frequencies above some cutoff frequency dictated by the cavity size and

shape. These resonant frequencies correspond to standing magnetic and

electric field patterns inside the tank generated by current patterns in the

walls [3]. These patterns remain in fixed positions in the walls but vary

in magnitude at the resonant frequency. The actual number of resonant

frequencies is infinite. Only the frequencies immediately above the cutoff

are well separated. The electric fields associated with these modes are sensitive to the dielectric constant, e, of the vessel volume such that

f

n where fj^ is the frequency of the nth mode. If the vessel is only partly

filled with a fluid of higher e , resonant modes still exist though the field

patterns are altered from the case of uniform e . Whereas the mode

frequencies of a geometric vessel such as a sphere or a cylinder can be

calculated analytically for uniform dielectric constant, this is no longer

true for a tank only partially filled. For a partially filled tank however,

the resonant frequency of a mode changes monotonically between the two

frequencies dictated by the completely empty e and the completely full e.

One of the methods for measuring the rf resonances of a tank consists

of inserting a small loop antenna into the tank and driving the antenna with

an rf generator while monitoring the power reflected from the antenna. The

reflected power decreases at the frequency of a resonance. This frequency

can be converted to a tank level reading of the tank contents with an accuracy dependent upon the resonant line width, the accuracy with which the

resonant frequency can be measured, and the accuracy of the calibration of

the tank gauge in terms of frequency as a function of level height.

Some preliminary measurements have been made to obtain information on the resonance line width or "Q" of a tank car and to estimate the resolution in

a measurement of liquid volume. The ratios of the resonant frequencies are independent of the size of vessels of the same shape. This fact is used in

this work to model the tank car for some of the tests.
2 . TANK CAR RESONANCE MEASUREMENTS

A 3 X 10^ L (8000 gal) tank car used to transport diesel oil was se- lected for a study of the line widths of the rf resonance modes of a tank

car. This tank car has a diameter of 2.979 m (78 in.) for a length of

9.72 m (31.94 ft). The tank is longer because the ends approximate spherical sections. The radius of curvature of the ends is so large that each add

only about 20 cm maximum to the tank length at the centerline. A cylindrical dome approximately one meter in diameter and 1/2 meter high is located

on the top center of the tank. This dome communicates with the interior of

the tank through a hole cut through the top of the tank. A 2.5 cm diameter

valve stem extends vertically along a diameter of the tank up into the dome

about 30 cm from the center of the tank. There is access into the dome

through a hatch in the top center.

A loop antenna was mounted on a curved rectangular aluminum plate clamped across the approximately 55.9 cm (22 in) diameter hole in the tank shell inside the dome. The plate was mounted with its length perpendicular to the

centerline of the tank. The loop antenna was mounted in a plane perpendicular to the tank centerline. Three different loops were used. The first was 12.7 cm square, the second was 28 cm diameter circle and the last was a 21.5 cm diameter circle. The antennas were formed by bending a 1.5 mm diameter copper wire to the desired shape.

The resonant frequencies were measured by placing the frequency marker

of an rf sweep unit near the line to be measured, then switching the sweep

unit to the continuous wave mode. The position of the scope trace could be

easily placed at the minimum vertical position corresponding to maximum rf

power absorption. The frequency was measured with a frequency counter.

The Q (resonant frequency divided by the resonant line width) was estimated by measuring the half power point frequencies which were determined by

observing the rf power absorption level on a scope trace. A lower limit on

the estimated Q is 1600. The longest antenna was employed for this measurement and saturation effects broaden the line. The frequency of the absorption peak (i.e. center of the line) could be easily measured to one part in

10 ^.

The rf power input to the tank at a resonant frequency is increased

when the antenna size is increased. A large antenna can become part of the

resonant structure of the tank thereby shifting the resonant frequencies.

The largest antenna used in this tank produced a small but detectable shift

in the resonant frequencies so the results of the smaller circular antenna

are used to compare with calculated resonant frequencies.

The tank resonances were calculated from the solution to Maxwells equations for a cylindrical vessel. The tank car was assumed to be a perfect

cylinder 1.979 m diameter by 10.09 m long. The resonant frequencies calculated are shown in table I and the modes are identified^. The outside

length of the tank was reduced by 3.6 cm to account for end thickness and

shape to arrive at the inside length. The mode frequencies are not strongly

dependent on the length of the tank. The measured resonant frequencies are shown in the last column. No attempt has been made to identify the experimental modes though for a few resonances identification can be inferred.

Modes are identified as TM or TE followed by three digits. Reference 3 describes this notation in detail and includes diagrams of the electric field

configurations associated with some lower modes.

2
4 Table I. Resonant frequencies of a 3 x 10 L (8000 gal) tank car using

a 21.5 cm diameter loop antenna perpendicular to the tank centerline.

Calculated Measured

Mode Frequency Frequencies

TE 111 90.06 MHz 89.87 MHz

TE 112 93.67 91.87

TE 113 99.39 99.35

TE 115 115.81

TM 010 116.04 116.05

TM Oil 117 .118.60

TM 012 li9 . 79

TE 116 125.87 125.87

TE 117 136 .137.31

TM 015 137.8 138 . 24

TM 016 146.35 147.63 TE 211 148 .

TE 118 148.2 148.39

148 . 77 TE 212 150.3

TE 213 153.94 154.19

154.98

TM 017 155.85 157.71

159.24

161.26

161.41

TE 214 158.91

TE 119 160.58

TE 215 165.03 165.28

TM 018 166.14 168.4

TE 216 172.24 176.45 TE 111 173.15

TM 109 177.09 179.11

TE 217 180.38 180.85

The modes are identified in the first column and the frequencies calculated

for a 1.979 m diameter by 10.09 meter long cylindrical cavity are given in

the second column. Measured frequencies for the actual tank car are listed

in the third column. The mode identifications are tentative.

3
The experimental and calculated values of the resonant frequencies

differ slightly. This is expected since resonance measurements on a small

scale model of a tank (Appendix 1) show that the valve stem, running on a diameter through the center of the tank, does shift the resonant frequencies

slightly. The shifts in frequency of the various TE modes from the values

calculated for the tank car are generally in the same direction as observed

in the model tank though some of the shifts are relatively larger. No

measurements were made to determine whether any TM modes were present or whether the extra experimental lines in the vicinity of the calculated mode

lines result from removal of TE mode degeneracies. Though only one TM at

most appeared to be present in the model tank, several features of the tank

car differed from the model which could lead either to degeneracy removal or

to coupling to the TM modes. For instance, the hole in the tank shell is

relatively larger than the hole in the model and was not covered completely

by the plate on which the antenna was mounted. The valve rod extends

through the shell of the tank, without touching, up into the dome so that

the dome is electrically coupled to the tank. Effects due to the curved

ends of the tank were not investigated but are assumed small.

The experimental frequencies agree quite well with the calculated

values for an ideal cylindrical vessel 1.979 m I.D. by 10.09 m long. Small

shifts in resonant frequencies can probably be accounted for by the presence

of the valve stem (Appendix I). Protrusions such as the valve stem do not

significantly alter the resonant frequencies and the Q is large.

3. LIQUID LEVEL MEASUREMENTS IN A SMALL HORIZONTAL CYLINDRICAL TANK

As noted above, the frequency to liquid level relationship, if ex- pressed as a ratio of any mode frequency to either the full or empty mode

frequency, is independent of tank size. To estimate how precisely propane

levels, i.e., the amount of propane, can be gauged using rf, resonant frequencies as a function of liquid level were measured in a 28.5 cm diamter x 32.7 cm long cylindrical tank. For safety, kerosene, with a dielectric con- stant of about 2.1, was used as the dielectric fluid. Since the dielectric

constant of propane is around 1.6, level measurements with kerosene should

be more precise. Values of the frequency as a function of liquid volume are listed in table II for frequencies below 1000 MHz. Three of the mode frequencies are shown as a function of liquid volume per unit length in figure

1. The modes with electric fields vertical are much more strongly perturbed

by the ullage space. The cutoff frequency identified in Table II as TE 111

is doubly degenerate. The resonant line splits because of the differing

sensitivity of the two polarizations. The horizontal E field TE 111 mode is

much less sensitive to level changes in a nearly full or empty tank than the

vertical E field TE 111. The mode identified as the TM Oil also shows good

sensitivity near full and empty whereas the TM 010 does not. The TM 011 and

TE 111 mode frequencies are shown as a function of liquid volume in figure

1. The volume is shown as volume per unit length since the precision of the

measurement in % is independent of tank length provided the tank is horizontal.

The limiting slope of the TE 111 and TM

approaches full and empty are given in Table

Oil modes as the tank

III

4
Table II. Frequency as a function of kerosene volume in a horizontal

28.5 cm diameter by 32. 7 cm long cylindrical tank.

Volume TE 111 TE 111

per cm E field E field TM 010 TM Oil

length Vertical Horizontal

0 768.3 MHz 771.2 804.7 927.3

8.13 765.3 771.1 804.8 926.1

14.98 762.6 770.5 804 .

925.0

28.07 758.2 7 6*9.

803.85 922.0

53.97 747.8 764.1 799.9 913.6

83.07 731.5 749.5 788.4 895.75

129.27 709.0 722.5 763.6 864.4 998.0

170.19 686.1 690.9 730.8 836.1 977.4 982.0

227.29 657.5 650.2 685.6 794.0 938.8 963.1

284.52 633.3 617.4 649.0 758.6 909.0 941.8

334 . 19 614.4 594 .

621.3 730.0 890.0 915.1

383.95 598.9 574.7 601.0 706.3 873.75 887.5

445.59 580.0 557.0 682.2 851.9 853.8

491.97 569.05 547.5 569.05 669.8 841.1

523.65 560.9 540.9 563.2 660.8 828 .

880.1

564.41 551.2 535.2 560.0 652.8 796.1 812.0

590.69 541.1 533.1 558.5 648.9 787.1 799.2

615.23 536.3 531.9 557.9 645.9 775.7 785.0

625.33 533.6 531.7 557.8 644 .

779 .

633.20 531.1 531.1 557.9 643.8 774.4

641.53 530.0 530.0 557.6 643.4 772 .

The volume in the first column is given per unit length of the tank. Only

frequencies belcw 1000 MHz for the lowest six resonances were measured.

The upper two are not identified. Note that only the TE 111 mode with a vertical E field and the TM Oil mode show significant level dependence near

full and empty. The two TE 111 modes merge as the tank is approaches

full.

5
FREQUENCY,

MHz

% FULL

Resonant frequencies of selected modes as a function of liquid level in a horizontal

cylindrical tank.

Figure 1.
Table III

Mode Af per % change in kerosene volume

approaching full approaching empty

TE 111 1.8 MHZ/% 2.4 MHz/%

TM Oil .77 MHZ/% 1.0 MHz/%

If this model were sealed up to the diameter of the tank car discussed

above the slopes in table III are reduced by the ratio of the diameters

which is 0.144. Assuming Q is still 1600 and the uncertainty in the resonant line frequency measurement is no more than l/5th the line width, then

the line frequency can be measured to one part in 8000. vSince propane is

the fluid of interest, the change in frequency between empty and full, hence

the slopes in table III, are reduced by the factor: (e / \l/2

^ f j V propane' kerosene

or 0.873. The volume resolution of an rf gauage as this scaled up tank

approaches empty is given by

AV(%) = (0.873 X 0 . 144S ( f/5Q) = (.001)f/S

where S is the slope given in table III and f is the resonant frequency.

For the TE 111 vertical mode near empty AV = 0.04%. As the propane level

approaches full, f decreases by lAfe which compensates for the decrease of S

in table III and the resolution, AV, remains 0.04%. This resolution is

equivalent to + 50 1 (+ 13 gal) uncertainty in a measurement of the contents

of a 1.2510^L (33,000 gal.) propane tank car. The resolution attainable

with the TM Oil mode near full and empty is somewhat less than half that of

the TE 111 mode. An antenna configuration that does not excite the horizontal TE 111 mode is desirable if the TE 111 mode is used for gauging.

How well this resolution can be translated into gauging accuracy depends on how accurately the gauge is calibrated and how well temperature

changes are taken into account. Temperature changes effect the resonant

frequency both through changes in tank size and change in liquid dielectric

constant due to density changes. If the dielectric constant varies from

carload to carload, this variation must be included also.

4. CONCLUSIONS

Measurements of the rf resonant modes of an empty tank car along with

some measurements of resonant frequencies as a function of liquid levels

indicate that tank car contents could be measured to a AV/V, of better than

0.1% if the fluid dielectric constant is known, the tank is isothermal and

the size is known. When the temperature varies during the course of the

flame test measurement, errors are introduced. First, the tank expands,

thereby decreasing the resonant frequencies of the empty tank. This error amounts to about 1% at the very high temperatures found on the shell above

the liquid but might be corrected if tank wall temperatures are recorded.

An additional error is introduced by heating the fluid. the dielectric

constant, e , changes approximately according to (e -])/(£ + 2) =pCn, where

p is the density and Cj^ is a constant. This equation is linear to about

1% over the density range encountered in the tests. A correction can again

be applied by using temperature data.

The magnitude of the uncertainty of the mass of liquid remaining in the.

tank has been estimated to be about 5% for the case of a spherical tank

containing two phase fluids [2]. Temperature data might again be used to

reduce this uncertainty. However, further study of density change effects

and correction methods are required to determine what gauging accuracy is

obtainable under conditions existing during fire tests.

7
5. ACKNOWLEDGMENTS

The author wishes to thank R. S. Collier for suggesting the rf measurements in a tank car and the Denver and Rio Grande Western Railroad Company

for making their tank car Number AX 5230 available for rf measurements. The

author wishes to thank especially Frank Robinson and Robert Guerrieri of

that company for making the necessary arrangements.

6. REFERENCES

[1] Railroad Tank Car Safety Research and Test Project, Report RA-11-6-31

(AAA R-201) and RPI/AAR Technical Progress Report (Dec. 12, 1975).

[2] Collier, R.S., Ellerbruch, D. , Cruz, J.E., Stokes, R. W. , Luft, P.E.,

Peterson, R. G. , and Hiester, A.E., Mass Quantity Gauging by RF Mode

Analysis, NBSIR 73-318 (June 1973).

[3] Barrow, W.L. and Mieher, W.W., Natural Oscillations of Electrical Cavity

Resonators, Proc . IRE 28, 184 (1940).

8
APPENDIX 1 Resonance Frequency Measurements of Model Tank Car

A cylindrical stainless steel tank 1.65 cm long by 30.094 cm ID v/as

used to model a tank car. This would model a tank 2.44 m (8 ft) in diameter

by 13.41 m (44 ft) long. A 3.8 cm diameter hole was cut in the tank about

4 cm from the half way point between the ends. The hole was shifted slightly

from the center because a welded seam interferred. An open end of the tank

was closed by bolting an aluminum plate over it. This cover made relatively

poor electrical contact apparently, because pressing against the plate would

slightly shift some mode frequencies.

The coupling to the cavity -was achieved with a loop antenna of about

3 cm^ placed through the hole so the plane of the loop was perpendicular to

the centerline of the cylinder. Some mode degeneracies were apparently re- moved, i.e., resonance lines separated, by placing the plane of the loop

parallel to the centerline because six additional resonances were observed,

all near lines measured with a perpendicular antenna placement.

The experimental resonance frequencies are compared to calculated frequencies in the first 3 columns of table III. The experimental results are about 0.2% high at lower frequencies, essentially agree at the intermediate frequencies and lower or higher by as much as 0.4% at high frequencies.

Some of the disagreement could be due to the poorly contacting flange cover. Most tank cars have an approximately 2.5 cm diameter valve stem running

vertically across the tank diameter from a point inside the dome. This was modeled in this tank by a 10-32 threaded rod on a diameter pressing against

the top and bottom of the tank about one cm from the antenna hole. The pre- sence of this rod reduced the TE 111 mode frequency by about 1/2% and added

a trace of the TE 112 and strong lines at 667.5 and 763.8 MHz. The other

mode lines were present and sometimes shifted by a few tenths of a percent.

These results are shown in the fourth column of table III.

If a tank car should be measured while being filled with diesel oil,

then the fill pipe would be inserted through the top with the end near the

bottom of the car. This was modeled with an aluminum strip about 1 cm wide

extending about 23 cm into the tank but grounded at the edge of the hole.

The identified modes, with a couple of exceptions, were not significantly

altered as shown in column 5, table III. The unidentified lines in column

4 have all been shifted.

For the most part, no TM modes were observed with the coupling used,

though there was a little of the TM 011 mode observable after the valve stem

was added. The other unidentified modes could also be shifted TM modes.

9
Table IV. Resonant frequencies of a model tank car in MHz.

Tank Frequencies With Valve Stem

Mode (calc) Tank (exp) Valve Stem + Fill Tube

257 fill

517 514 stem

TE 111 591.2 592.5 589.0 589.1

TE 112 611.8 609.0 609.0

612.7 612.7

TE 113 644.6 645.5 643.1 643.2

667.5 670.2

TE 114 688.0 688.8 689.9 685.5

732.0

TE 115 740.1 740.7 738.7 738.7

TM Oil 768.5 763.8 783.9

TE 116 799.2 799.1 799.4 806.3

TE 117 863.8 861.5 862.2 862.1

863.8

883.0 897.4

TE 118 932.8 930.1 933.3

940.0

TE 211 969.03 970.3

971.1

970.6 971.6

TE 212 985.9 983.0 983.2

984.4 984.5

TE 119 1005.2 1003.8 1004.3 1005.1

TE 213 1006.7 1004.5 1007.0 1006.2

TE 214 1035.0 1031.5 1031.5

1032.3 1032.3

TE 215 1063.1 1067.0 1067.7

tube

The modes and the calculated frequencies for an ideal cylinder of the model

dimensions are given in the first two columns. The experimental mode

frequencies are given in the third column. The TM Oil was not excited in

the simple tank, but some line-splitting occurs in the higher modes. The

experimental resonance lines measured in the tank car model show effects of

the value stem and the value stem plus a fill tube in the 4th and 5th

columns respectively. The simulated valve stem and fill tubes did shift resonances slightly and introduce or delete a few other resonances.

10
NBS-1 14A (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUHLlCiATION OR REPORT NO.

NBSIR 79-1600

2. Gov’t Accession

No.

3. Recipient’s Accession No.

4. TITLE AND SUBTITLE

RADIO FREQUENCY LIQUID LEVEL GAUGING IN PROPANE TANK

CAR SAFETY TESTS - A FEASIBILITY STUDY

5. Publication Date January 1979

6. Performing Organization Code

736

7. AUTHOR(S)

J. D. Siegwarth

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 7360460

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP) 13. Type of Report & Period Covered

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

Selected radio frequency (rf) resonances of an empty 30,300 liter

(S,000 gallon) tank car have been measured to determine whether rf can

be used to gauge the propane liquid levels during tank car fire safety

tests. The change of resonant frequencies of a small horizontal cylindrical tank as a function of liquid volume has been tested in order

to estimate the precision to which the amount of propane in a tank car

can be measured,

gauging.

The technique is applicable to routine tank car

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons)

Level gauging; propane; radio frequency

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