l6(

REPORT CCG 71-57, NBS 2210471

NBSIR 74-531-5^6'^

ULTRASONIC INTERFEROMETER MANOMETER

P. Heydemann

Pressure and Vacuxim Section

Heat Division, NBS

Washington, D.C. 20234

July 1974

Annual report for period July 1, 1973 - June 30, 1974

Prepared for CCG - Army/Navy

OBJECTIVE

It is the objective of this project to develop, design and construct a

mercury manometer covering the range from 2 to 2300 mmHg with an accuracy of

± 10 ym for 2 to 1000"~^S^,^± 30 lim for 1500 to 2300 mmHg. The ultrasonic

fringe counting interferometer shall be adapted to this application.

Such a manometer would be useful as a standard manometer in calibration

laboratories. It would be capable of automatic operation. Its analog or

digital output could be used as input to a very stable pressure controller in

an automatic calibration stand. Even over long periods of use only the thermometers and a crystal oscillator need to be recalibrated, a task that can readily

be performed in most laboratories.

The principle of the ultrasonic fringe counting interferometer is as

•follows: A short wavetrain (50 ys) with a very well known carrier frequency

(10 MHz) is launched from a transducer at the bottom of the mercury column

into the mercury. The pulse is reflected at the surface and received and converted

into an electrical signal again by the transducer. Part of the pulse energy is

reflected into the column again and again. Each time an echo impinges upon

the transducer an analog electrical signal is generated. The received signals are

phase sensitive detected in two detectors with a 90° phase shift between the

reference signals. The resulting output signal is a vector. Its amplitude depends

on the amplitude of the received echo. Its phase depends on the length L of the

mercury column. A change of column length equal to X/2, where X is the sound

wavelength, causes the output vector to rotate by 27r. An electronic counter circuit

can be designed that recognizes the direction of rotation and generates one count

for each tt/A rotation. If echos other than the first are used, one count per

I

TrMp rotation is generated, where p is the order of the echo.

With a carrier frequency of 9 MHz and a speed of sound in mercury of about

1500 m/s the following resolution per count is expected:

1st echo : 20 ym

2nd echo : 10 ym

4th echo : 5 ym

10th echo : 2 ym .

Instead of using echos of very high order ntimber it may be more expedient to

interpolate between counts with a direct phase measurement.

The accuracy of the measurement depends to a large extent upon the accuracy

with which the speed of sound in mercury is known. The best presently available

data indicate a precision of about 1 part in 10,000, but no estimate of systematic

uncertainty is available and it is therefore imperative to perform speed of sound

measurements of the highest possible accuracy.

The laser interferometer manometer now under construction at NBS will be used

to perform such measurements and an accuracy approaching a few parts per million

is expected.

1

Abstract

The developments during this report period led to the design of a

W-tube manometer with a maximum column length of 115cm. Two different

ways of measuring the acoustical length of the columns were tested and precise

measurements of the speed of sound in mercury were made.

INTRODUCTION

In this report we shall describe the W-tube manometer and the measurements

made with it without going into great detail about individual problems encountered

and solved. These have been dealt with in two quarterly reports.

The effort described in this report was supported in part by funds from the

CCG. Substantial funding was obtained through regular STRS allocation from NBS.

DESIGN OF THE W-TUBE MANOMETER

Fig. 1 shows a schematic of the W-tube manomfeter. The manometer is mounted

on a truncated-triangular stainless steel baseplate with three adjustable

supports. Large holes are provided for the bottom closure flanges. A rectangular

mounting plate, ground plane and parallel, serves as reference plane for the

bottom closure. It also carries the three manometer tubes. The three manometer

tubes are connected through lateral holes with welded-in tubulations, appropiriate

fittings and tubes all made of stainless steel.

The three manometer tubes are sealed against the mounting plate and the top

closures with polytetrafuoroethylene washers. Each tube is tightened down with

four screw rods anchored in the mounting plate. The glass tubes have an outer

diameter of -5^ mm and an inner diameter of 50 mm. Their length is 600 mm for the

outer columns and 1150 mm for the long center column.

Fig. 2 shows a cut through a bottom closure. The closure plates are 65 mm

in diameter, 6mm thick and consist of titanium. The titanium disks are sealed

against the mounting plate with 0-rings. Flange rings are used to press the

titanium disks flush against the mounting plate to ensure that all three closure

disks are parallel to each other. The single-crystal quartz transducers are

bonded to the closure plates with epoxy bonds.

Immediately before assembly all parts must be carefully cleaned and

degreased. Particular attention must be paid to the closure plates. After

degreasing they are etched with a solution of 25 to 30% HND3 and 2% HF in

water followed by thorough rinsing with distilled water. Carefully and recently

cleaned mercury must be used. The acoustic coupling between the closure plates

and the mercury will improve for several days after filling the manometer with

mercury. ^

The manometer is placed on a 60 mm thick plywood plate resting

on top of a stone foundation. For additional isolation from structure-borne

sound square foam-rubber pads 12 mm thick and 35 mm on edge were placed under

the dishes carrying the adjustable supports. This provides sufficient vibration

isolation to work even with the longest columns.

Horizontal adjustment of the mounting plate is achieved with a sensitive

spirit level placed on the plate and appropriate adjustment of the support

screws. Final adjustment is made by watching the undetected echo sequence on an

oscilloscope and adjusting for uniform and small decay of the echos. Fig. 3

gives examples for a well adjusted plate and for one tilted about 0.04 degrees.

PNEUMATIC CONNECTIONS

To conveniently operate the manometer for experimental purposes the

manometer was connected as shown in Fig. 4. The system of valves allows

one to pressurize or release either side of the manometer relative to the

other keeping it under helium pressure at all times. Thus the contamination

of the mercury is kept to a minimum and smooth travel of the menisci is maintained.

A motor-driven valve in the mercury line to the center column can be used

to arrest the manometer at any column length without disturbing the surfaces. This

is particularly useful for the more time-consuming excess fringe measurements.

The burst pressure of the glass tubes is 180 psi or more as determined from

3

experiments with five annealed and unannealed tubes.

ACOUSTIC PERFORMANCE

Of great concern in the development of a long column manometer is the

attenuation of the acoustic signal through the length of the mercury column.

Measurements of the apparent attenuation, including the effects of beam

spread and diffraction were made and the results are shown in Fig. 5. Here

we have plotted the amplitude of the first echo as a function of column length

in arbitrary units. Also plotted is the decrement, that is the amplitude ratio of

successive echos, versus the length of the column. As the column length changes

from 100 to 1100 mm the amplitude decreases from 1 to about .3 and the decrement

rises ':^rm 1.6 to 5.7. At column lengths above about 300 mm it is not practical

to work with echos other than the first.

Fig. 6. a to 6.1 shows CRT photographs of the echo sequences at various column

lengths. Note that the sweep rates have been adjusted to show three echos. The

vertical sensitivity settings have been left undisturbed. The variation of the echo

amplitudes is small enough to be compressed to a near constant amplitude by a

hard-limiting, tuned amplifier.

The tubes used in this manometer have not been coated with chromium or other

conductive layers on the inside as an anti-static measure. Nevertheless the surface^

are quiet enough even when moving to maintain a running fringe count. The maximum

rate of change of pressure applied was 4.5 mm Hg/s. For practical purposes half trii o

•rate- should not be exceeded.

It was found that the long column is easily excited to oscillations by

structure-borne sound causing large enough ripples on the surface to make the

interferometer fail. Placing the manometer on foam rubber pads improved the

4

ACOUSTIC LENGTH MEASUREMENT

The ultrasonic interferometric length measurement is based on the

following principles: a short (50 ys) acoustical wavetraia with constant carrier

frequency (10 MHz) is radiated into the column, reflected at the surface,

received, converted into an electrical signal and amplified. The phase of the

received echo is compared with the carrier. This phase changes by 2-n whenever

the column length changes by half the wavelength of the acoustic wave. By deriving

analog signals for the phase a count of half wavelength can be obtained. Two

4 analog signals tn quadrature can be used to discriminate between upwards and downwards movements.

It is obvious from the foregoing that the count begins with zero at some

arbitrary length, which could, for example, be the equilibrium position of all

columns with no differential pressure applied. If for any reason the acoustic

signal is interrupted during the operation of the manometer, the continuous count is

not maintained, the columns must be returned to equilibrium and the counter must be

reset to zero. If this happens frequently and even at reasonably low rates of

change of pressure, it will make the use of this manometer quite impractical.

While we found that in the present set-up loss of continuous count is not a problem

we nevertheless investigated ways of acoustically determining the length without

reliance on an accumulated count.

There are two other methods which at least in principle can be applied here.

The first is an interferometer method making use of the fact that the wavelength

of the acoustic wave can be adjusted so that

> = 2L, Xn = c/f^

where n is an integer, X is the wavelength, L is the length of the column, c is

the speed of sound in mercury and f^^ is a frequency. The f^^ can be recognized in

a system employing phase sensitive detection by the fact that all detected echos

go through zero at this frequency provided that phase shifts in the electronic

apparatus are properly compensated.

5

To solve the above equation for L we must determine n, which is always an

Integer, obtain c with sufficient accuracy from other measurements, and measure

f for at least one n. n

The f can be set to about 4 Hz. The f are about 10 MHz. The speed of

n n

sound c is known to about .01%. This must be improved by about two orders of

magnitude, n, which for a one meter column is about 15,000, must be determined

and herein lies the difficulty.

We have

f = B£

^ = f

n 2L ' 2L 1

f = nf, . n 1

If measurements are made at f and f , we have

n n+m

and

- f = mf,

n+m n 1

This permits one to calculate f^ provided m is known, m can be counted by going

from one critical frequency adjustment to either the next, or the tenth, or the

hundredth. With f^ known we can calculate n from

f

n

Written in closed form we have then

T cm ^ _ cn ^ " 2(f - f ) ^ "

2f

n+m n n

There are several ways to determine m accurately and several of these are

presently being explored. In any case m is an integer and no uncertainty will

be assigned to it. The frequency difference in the denominator of the left equation

is limited by the usable bandwidth of the apparatus to about 150 kHz. Since the

frequencies f , and f can be determined to about 4 Hz , the uncertainty of the

n+m n difference will be about 8 Hz/150 kHz or 50 ppm. This is clearly too large.

6

The second equation has an uncertainty - neglecting that due to the speed of

sound and of n - of only 4 Hz/10 MHz or .4 ppm, but it requires the determination

of n. How this can be done is illustrated in Appendix A with data taken recently

with the long column.

A second interferometer method operates on the fractional fringes method.

Here one operates with several fixed and well-known wavelengths sent out sequentially

into the column of unknown length L. When the reflected signals are picked up at

the receiver their phase shifts relative to the transmitted signal will be

0 = n X 27r + g . The column length can be calculated from

One assumes now that a small number of wavelengths can be foxmd, which produce

a unique set of fringe fractions g^ for each length L up to a maximum length.

From model experiments on the computer we conclude that five wavelengths are

sufficient to produce such unique sets for lengths up to one meter. The wavelengths

must be chosen judiciously for best performance. Errors in the fractional fringe

data reduce the usable column lengths. We have set up a computer program v/hich

accepts five frequencies f^ and the corresponding values of sin g-^ and cos g^,

generates a table of nX^ + g^X^/2ir and compares it with the input data. A

tolerance for the comparison can be set. The lowest n for -which a matching set can

be found is printed out. With the knowledge of n the length L can then easily

be calculated. An example is given in Appendix B.

TEMPERATURE EFFECTS

The ultrasonic transit time t through the column (path length 2L) is

'n

2L

t =

c

its dependence on temperature T is given by

dt

t a dT B dT

1 + aT 1 + 3T

7

where a is the thermal expansivity and 3 is the temperature coefficient of

the speed of sound. With a = 1.8/ x 10"'^ K~l and 3 = - 3.18 x 10"^ K"^

= 5 X 10-"^ X dT.

A temperature change of dT = IK causes a change in the transit time of

5 X lO"'* or 0.05%. Generally not the transit time but a harmonic of the

resonance frequency near 10 MHz is measured. This measurement can be made to

about 4 X 10"'^ (4 Hz in 10 MHz) . Since the above temperature coefficient applies

also to the frequency, except for a sign change, a temperature stability of .8 mK

is required to fully exploit the sensitive frequency measurement.

To illustrate the effect of the diurnal temperature cycle asstime that the

temperature drops by IK over an 8 hour period. This then causes a frequency drift

of about -10 Hz/min. Measurements are presently taken manually and therefore

slowly. Each time measurements are taken one must also determine the frequency drift

with time and correct the measured frequencies for the temperature drift effect.

In the future we expect to control the data aquisition with a MIDAS process

controller. This should accelerate the collection of data and reduce the

temperature drift effect. However, a very tight temperature control will always

be necessary for accurate column length measurements. For an uncertainty in the

length determination of 1 ppm the temperature must be stable and known to better

than 2 mK.

THE SPEED OF SOUND IN MERCURY

Preliminary measurements of the speed of sound in mercury were made.

The ultrasonic transit time was measured with the fringe counting interferometers.

The column length was measured by detecting the position of the mercury meniscus

with a telescope and reading the position from a vertical scale by rotating the

telescope about its vertical axis. The scale had previously been calibrated with

a laser to better than .01 mm. Great care was taken to reduce all errors connected

8

with the rotation of the telescope. It was found that the mercury meniscus

could be located reproducibly by using a properly lit white backdrop with black

marks behind the column. The temperature of the manometer* was measured with two

platinum thermometers , one on the reference plate and one on the upper part of the

column

The speed of sound was calculated from

^

- 8 f o (ni-n^) + a[no(ATi-AT2) + niATi-n2AT2]

where n^ is the length of the mercury column below the lowest reading position

measured in X/8, and L2 are the corrected scale readings, f frequency of

carrier, nj and n2 counter readings at li and I2 respectively, a is the temperature

coefficient of velocity, AT = T- T -,T . = 23''C.

vet ref

In the present set-up Iq = 48 mm and therefore ng = 2648 with X = .145 mm.

Two series of measurements were made. Sufficient data to illustrate them is given

in Appendix C. The results are summarized in Table I. To obtain an estimate of

the systematic uncertainty we form the total differential of the equation for the

speed of sound Cq

dc

= ^^ + ^^^^ [2dn + ni ATid^ + ni^dAT + ATij^dnJ .

Our estimate for the variances of the parameters is

dJl = .03 mm d& = 3 x 10"^ K'^

^

df = 2 Hz dAT = .05 K ,

dn = 1 count

Tic

The root sum square (RSS) of th^^erms of dcQ is

RSS = 7.5 A 10"1

<X-b - Id'

and the resultant estimate of the uncertainty of Cq is

S(c ) = .-Hr m/s.

o

We have then for the speed of sound in mercury contained in a glass tube

with an internal diameter D=350X and at 23 °C

c = 1449.57 m/s

with a random uncertainty of 0.04 m/s and a systematic uncertainty of -rii m/s.

Several measurements of the speed of sound in mercury have been reported in the

literature, but all of them lack an indication of the uncertainty of measurement.

They are listed nevertheless in Table II.

ELECTRONIC APPAEATUS

Fig. 8 shows a block diagram of the elctronic apparatus currently in use.

Most of the components have been described in the preceding annual report.

Only the limiter, the counter and the failure detector shall be discussed here.

The limiter is used to compress the variable amplitude signal (Fig. 6. a to

6.JI) sufficiently to render the input signal to the phase sensitive detectors

constant. This ensures that the output from the filter is standardized regardles

of the column length. Consequently either one of the filter output signals can

be used for interpolation and also a failure signal can 6asily be derived.

Fig, 9 shows the output from the limiters for three column lengths. The

amplitude of the first echo is independent of column length up to the maximum

length of 1100 mm. cuvu«yivvL C l ai~eY^

A failure indicator was designed to actuate an alarm or ^^un(j/cjiaitovwhenever the magnitude of the vector (uj ,U2) falls below a certain level. The

level was selected to allow trouble free operation of the counter. The failure

indicator consists essentially of two squarerjand an adder plus some additional

logic circuitry. The failure indicator is very helpful in avoiding erroneous

counts when the interferometer runs unattended.

.10

With the help of the failure detector we could show that the up/down

counter used until recently generated occasional, erroneous counts from

noise and from jitter in the input signals. A new counter employing a novel

anti-jitter circuit and quadrature detector was therefore designed and breadboarded. The counter contains memory elements and can -therefore

operate without the sample and hold amplifier and filters. The read-out

design has not been completed yet.

FUTURE WORK

We plan to complete the design of the new up/down counter including

printed circuit board layout and will assemble several counters for use with

the manometer.

We will complete the electronics for operation of all three columns and for

control and data aquisition by means of a process controller.

We plan a more accurate measurement of the speed of sound using a laser

interferometer instead of the scale.

We will make measurements of the speed of sound in glass tubes with different

diameters.

We expect to begin operating the instrument as a standard manometer

with an accuracy essentially limited by our current knowledge of the speed of

sound in mercury.

Longer range plans include a consolidation of the electronic circuitry

into one single-purpose package and the design and construction of an air

thermostat of sufficient stability. Also we plan to extend the column length

to a total of 2.5m.

LIST OF FIGURES

Fig. 1 W-tube ultrasonic manometer.

Fig. 2 Bottom closure.

Fig. 3 Dependence of apparent attenuation on tilt;

(a) horizontal, (b) tilted .04**.

Fig. 4 Pneumatic connections.

Fig. 5 First echo amplitude (a) and decrement (b) as function of column length.

Fig. 6 Echo sequences for various column lengths; sweep rate adjusted to show

three echos; amplification constant.

(a) 100 mm (g) 700 mm

(b) 200 mm (h) 800 mm

(c) 300 mm (i) 900 mm

(d) 400 mm (k) 1000 mm

(e) 500 mm (1) 1100 nmi

(f) 600 mm

Fig. 7 Interpolation

Fig. 8 Block digram of electronic apparatus

Fig. 9 Limiter output for three column lengths;

(A) 1100 mm, (B) 550 mm,. (C) 60 mm.

Table I Results of speed of sound measurements

Table II Speed of sound in mercury at 23°C

Appendix A Determination of L with critical frequencies

Appendix B Fractional fringes

Appendix C Data taken for the determination of the speed of sound

in mercury. ,

3

E

eo

lO

o o

Fig. 1 W-tube ultrasonic manometer.

1-^

I I

I I

! I

MOUNTING PLATE

BASE PLATE

0-RIN

DSL

GLASS 1

TEFLON WASHER

SEAL

TITANIUM DISK

UBE

QUARTZ TRANSDUCER

Fig. 2 Bottom closure

IJ r fi

I it I

1^

1

1

f 1

\ I

^ -2

i 1^

I:

......

ti^agisaiS iiMta.?rafiitifiii jgfiMWMi.'iaa'gji'a iw^g'iiBti^xii'tiSii Fig. 3 Dependence of apparent attenuation on tilt; ||

(a) horizontal, (b) tilted .04°. r|





11

a.

j(a) 100 mm

b.

I (b) 200 mm

c.

Fig. 6 Echo sequences for various column lengths; sweep rate adjusted to show

three echos; amplification constant.

1 »>JI^*l»i;iB4»H5 J*«W tis^t^fi

f (e)^^JOOjnm

g.

n

1

' I (g) 700 mm

[I ii^-rifVirtl^TlW<iliBiW

h.

I.

(i) 900 wm

k.

QkriOOO Tm



SAMPLE

RF OSC. SWITCH RF - AMP

i

CIRCULATOR

i

DETECTOR PHASE

I

PREAMP.

I

LIMITER

DET.

COUNTER

Fig. 8 Block digram of electronic apparatus

< CD O

TABLE I. Results of speed of sound

measurements in mercury

First set of data:

c V v2

2/3 1449.66 m/s +9 81

5/6 1449.68 m/s +11 121

6/7 1449.51 m/s -6 36

7/8 1449.49 m/s -8 64

8/9 1449.53 mls -4 16

mean 1449.57 m/s S = 318

standard deviation of the mean d = .04 m/s

Second set of data:

c V v2

11/12 1449.73 m/s 16 256

13/14 1449.64 m/ s 7 49

14/15 1449.50 m/s -7 49

15/16 1449.52 m/

-5 25

16/17

mean

1449.47

1449.57

m/

m/ s -10 100

S= 479

standard deviation of the mean d = .05 m/s.

Standard deviation of the mean of ten measurements d = .03 m/s

TABLE II. Speed of Sound in Mercury at 23°C

Experimentor c [tn/s]

this report 1449.57

Coppens et al 1449.69

Freyer et al 1449.6

Hill et al 1450.7

Hunter et al 1452

A.B. Coppens, R.T. Beyer, J. Ballou

E.B. Freyer, J.C. Hubbard, D.W. Andrews

J. Am. Chem. Soc. 51, 759 (1929)

J.E. Hill, A.L. Ruoff

J. Chem. Phys. 43. 2150 (1965)

J.L. Hunter, T.J. Welch, C.J. Montrose

JASA 35, 1568 (1963)

all values were reduced to 23*'C using the temperature coefficient a =

-3.20 X 10"^ *C"1 reported by J.C. Hubbard and A.L. Loomis in Phil. Mag. _5» 1177

(1928).

JASA 41, 1443 (1967)

APPENDIX A

DETEEMINATION OF L WITH CRITICAL FREQUENCIES

DATA:

1

2

3

A

5

6

7

. 8

9

10

11

12

13

time

18.23

18.24

18.25

18.26

18.27

18.28

18.29

18.30

18.31

18.32

18.33

18.34

18.35

fringe ct,

0

0

0

0

41

92

0

33

97

frequency

9900520

9900509

9900502

9900498

9927196

9960398

9900475

9900469

9921958

9963619

9901759

9900445

frequency

corrected for

dT

9900509

9900508

9900510

9927214

9960422

9900511

9900511

9922006

9963673

9901819

9900511

COMPUTATION:

Points 2, 3, 4, 8, 9 and 13 taken at the same fringe

Af^ 6 Hz/min (temperature drift)

^n+41 " ^n

41

^n+92 " ^n

92

= fl,l = 651.317 Hz

fl,2 = 651.217 Hz

APPENDIX A (Cont'd)

f f

"33 ^

= fi.3 = 651.364 Hz

^ = fl,if = 651.155 Hz

average fi = 651.263 Hz

f /fi = 15202.01 : 15202 n

^

f 1 = — = 651.2636

^ n

L - |j = 1.11322 m
>.
APPENDIX B

DATA:

sin g

.999

.999

.999

.999

.999

L = 1.110216 m

FRACTIONAL FRINGES

cos g

.000

.000

.000

.000

.000

f

9956680.0

9954076.0

9951474.7

9950820.7

9949517.4

u

s>oMgonoo

0)

0)

(0

(U poo

4-> at I0) 4J

0) •OJ4J

>4OC

QJ 4J

(d

0)

W

COO

(0

V4

0)oooo - H

i*

(U

CO

CO MPS

m CM o m o iH CO o>

iH es es

m CN m in CM M

CX3 00 00 00

00 CM CM o m CM m CM o CO m

CM CM in 1^

m

CN

m in CNI si- CN -sT 00 00 00 00

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p

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m ON CO CO in

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m vO

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CM in tn CM •<r CM CM in

m CN Cvl sf

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CO 00 00 CO 00 o CO VO <r o tH o

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r-i rH tH iH rH iH 1 iH iH iH tH rH tH iH

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m CO CJN o Cvl • • • • CJN r>. VO CTN CJN CJN VO H CM Csl CM CM

CN CM CM CM CM CM CM CN CM CM CM

CM CM CM CM CN CM CN CM CN 1

0) CO 00 CN VO CM 00 00 CM vO CN

iH 1—1 C3N C3N o\ CJN cr> 00 ON ON CT. CJN 00

cS

H

u CM CM CN CM CM CM CN CN CN CM CM CM CM

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00 vO 00 o 1 00 vO 00 in

O o o o O o CJN o 1 o o O O o ON O

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