NBSIR 75-756

ULTRASONIC INTERFEROMETER MANOMETER

Peter L.M. Heydemann

National Bureau of Standards

Department of Commerce

Washington, D.C. 20234

July 1975

Annual Report

Prepared for

CCG-Army/Navy

US Army Missile Command

US Army Metro! ogv and Calibration Center

Redstone Arsenal", AL 35809

Naval Plant Representative

Metrology Engineering Center

1675 W. Mission Blvd.

Pomona, CA 91766

ABSTRACT

This report describes the design and construction of a 15 kPa -

Ultrasonic Interferometer Manometer "ULTIMA II". The manometer consists

of three mercury columns of 75 mm diameter with a maximum height difference

of 110 mm. The column lengths are measured with ultrasonic interferometers

in terms of the known wavelength of a 10 MHz sound wave in the mercury.

. Construction of the manometer has been completed and the instrument is

now being evaluated.

LIST OF FIGURES

Fig. 1 Vector representation of interferometer output signal

2 Front view of ULTIMA II manometer

3 Bottom closure

4 Ancillary equipment used with ULTIMA II

5 Interferometer components, schematic

6 Signals from phase sensitive detectors

7 Data print-out

8 Column lengths

9 Indicated pressure

INTRODUCTION

To measure pressure with a manometer requires the completion of four

major steps:

1) The surfaces of the liquid columns must be located,

2) the location of the surfaces must be transferred to a scale,

3) the distance between the locations must be measured

and 4) the average temperature of the columns of liquid must be

determined.

For accurate manometer measurements none of these tasks is trivial. In

the ultrasonic interferometer manometer described in this report the first

three steps are performed by ultrasonic interferometry; the fourth step is

facilitated by the fact that the ultrasonic interferometer manometer is fully

automatic. It can therefore be enclosed in a thermally lagged or thermostated

enclosure, thus reducing temperature gradients and fluctuations.

The prototype described here, ULTIMA II, is designed for pressures up

to 15 kPa, about 110 mmHg, with a resolution of about 5 Pa or better. Earlier

experiments have shown that column length can be extended to one meter with a

resolution of 10 Pa or better.

-2~

THE BASIC THEORY

Suppose a wave train of carrier frequency f traverses the length L of a

liquid column several times undergoing multiple reflections at the top and

bottom end faces. The p-th echo is finally picked up, amplified, and then

demodulated in two phase sensitive detectors with continuous reference signals

V\ = cos wt and r2 = sin wt. The output signals from the detectors are

Ui = cos (wt - 2p$L) cos wt

(1) u 2 = cos (wt - 2paL) sin wt

with p the number of the echo , 3 = 2n/x, and x the wavelength in the liquid.

We will assume that no phase change occurs in reflection and that the frequency

f is constant enough not to change X or effect phase changes in the amplifiers

and detectors, which would interfere with the measurement. After some

arithmetic we obtain from equ.(l)

Ui = j [cos 2psL + cos (2wt - 2p3L)j

(2) . u 2

= j [sin 2p3L + sin (2wt - 2p3L)] .

The first terms in equ. (2) represent sinusoidal functions of sample

length L. The second terms are high frequency signals to be suppressed with

low pass filters. The first terms go through a full cycle whenever 2p3L changes

by 2tt. The change of L, the liquid column length, for a full cycle or fringe is

(3) AL = X/2p .

The two electrical output signals of equ. (2) are our of phase by 90°.

They contain the quadrature information necessary to discriminate between

increasing or decreasing length of the sample. The vector defined by these two

signals can be in one of four quadrants and the change of length per quadrant is

(4) AL/quadrant = X/8p.

This is illustrated by Fig. 1. Here the horizontal vector represents uj and

the vertical vector represents u 2

. The phase angle between them is 90°.

These two component vectors determine the position of a third vector, which rotates

left or right as the column moves. Note that for a given AL/At, where t is

time, the vector rotates faster the higher the echo number p is. Each time

the vector moves into another quadrant a count signal is generated.

With 3 = 2-tt/x and X = c/f we have

(5) AL/count = gj=j .

The speed of sound c in mercury was previously determined as

c = 1449.57 m/s

at 23°C with a precision of 0.03 m/s, an estimated systematic uncertainty of

0.05 m/s and a temperature coefficient of -3.2 x 10 _1+ °C*" 1

. With a frequency

of 10.5 MHz the resolution per count using the second echo is

(6) AL = 8.62 ym at 23°C

This resolution can be improved by determining the instantaneous angle a

= 2p$L from the component vectors Uj and u 2

. If a can be resolved to, for

example, 10°, the resolution is improved to

(7) AL = 0.96 ym.

Examples of the achievable resolution are given in a later paragraph.





GLASS 1 UBE

TEFLON WASHER

Fig, 3





THE MANOMETER

Fig. 2 is a front view of ULTIMA II with part of the enclosure removed.

It shows the three mercury columns mounted on a stainless steel mounting plate.

The bottom closures with ultrasonic transducers are mounted underneath the mounting

plate and are not visible in the photo. A typical bottom closure is shown

schematically in Fig. 3. The three mercury columns are connected at the bottom

through the stainless steel tubes and fittings protruding from the mounting plate.

There is a provision for draining the mercury. The space above the top of the

outer mercury columns is connected on the outside to the pressure port. The

center column is connected to a reference vacuum pumping system. The bellows on

top of the tubes are needed to adjust for slight misalignment of the plumbing.

The glass tubes have an internal diameter of about 75 mm and are 100 mm

# and 140 mm long respectively. They are sealed with polytetrafl uoroethyl ene washers.

A thin layer of chromium is vacuum deposited on the inside of the tubes to

neutralize electrostatic charges on the glass, which may cause discontinuous

variations of the surface tension.

Fig. 4 shows some of the ancillary equipment. In front of the manometer

box are the three circulators used to feed electrical signals into and out of the

transducers. Behind the manometer are the control panel and the pumping systems.

The reference pumping system consists of an oil pump and a mercury diffusion pump.

The test pressure system uses helium. Helium can be bled into the system through

suitable valves and a screw pump, or it can be withdrawn with the help of a

separate fore pump.

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THE INTERFEROMETER

Fig. 5 is a schematic of the RF part of the electronics. The RF-oscil lator

is a crystal controlled oscillator that supplies a 10 MHz signal to the gated

amplifier (RF switch followed by power amplifier) and to the detectors. From

the gated amplifier the signal is routed to the mercury column (sample) through

a circulator (not shown). The output signal from the mercury column is fed to

the amplifier - a high-gain, turn receiver - and then to the phase sensitive

detectors. The resulting signal is given in Fig. 6, where the echo train is

shown after phase sensitive detection in the two detectors.

The amplifier (receiver) performs an additional function: It demodulates

the RF pulse echo train and generates a logic level pulse for each echo. The

process controller uses these pulses to count down to the desired echo. The

amplitudes of the phase sensitive detected signals for a given echo determine the

size and polarity of the component vectors discussed in the section on "Basic

Theory" in connection with Fig. 1. The amplitudes of the selected p-th echo

are sampled, held, measured, converted to digital code and stored for further use.

This process of transmitting a pulse, receiving and processing the echo, and

storing the information is successively applied to each of the three columns.

One such scan is made every ten milliseconds and each time the stored data

is updated. If the sign of one of the component vectors changes from one scan

to the next, the respective up/down counter is updated. The stored data can be

printed out on a teletype for further processing.

THE PROCESS CONTROLLER

The timing and signal processing functions of the instrument are under

the control of an Intel 4040 microcomputer. In addition to interfacing with

a MIDAS data acquisition system the microprocessor also monitors the system

performance to detect and compensate for the effect of external disturbances,

that would lower the reliability of the system.

In detail the microprocessor performs the following functions:

Start

Set multiplexer to column 1 Trigger the gated amplifier

Count down to preset echo

Sample and hold component vectors

Measure time of flight and compare with previous

reading. If within tolerance, proceed; if out

of tolerance, wait 2 ms and return to "Trigger"

Meaure component vectors, convert and store result

Update up/down counters

Repeat for columns 2 and 3

Test for MIDAS command; if no MIDAS command is present,

go back to "Set", if present, stop system and move data

taken during last scan from storage to the MIDAS system's

teletype; then go back to "Set".

It is conceivable in the future to use the microprocessor also to compute

the instantaneous pressure from the raw data. At the present time all further

data processing is done on a UNIVAC 1108 digital computer.

-7-

OUTPUT DATA

An example of the data printed out on the teletype is reproduced in Fig. 7.

The first six columns contain from left to right: the two component vectors for

mercury column 1, those for mercury column 2 and those for mercury column 3; the

next three columns contain the fringe counts for the three mercury columns. The

next to last column contains the temperature of the manometer in 10" 2 °C and

the last column gives the time of day.

When these data were taken all three mercury columns were in equilibrium

position, the interferometer operated on the second echo, and data were read

out once every 30 seconds. From these data the actual differential height of the

mercury columns was calculated. In the present case the average differential

height was about zero. The data listed in Figs. 8 and 9 are therefore indicative

of the stability of the system under equilibrium conditions. Listed in Fig. 8 are

the time and the calculated lengths of the three .columns in micrometers. The

slight differences in the initial lengths drop out of all further calculations,

since only changes in column lengths need to be considered. The fluctuation of

the three lengths listed in Fig. 8 is of the order of a few tenths of a micrometer.

From these three column lengths the indicated pressure is calculated. Listed in

Fig. 9 are the time, the temperature of the manometer and the pressure in micrometers

of mercury and in Pascal. The standard deviation of the third column is about

0.25 micrometer of mercury. This is presently the limit of resolution. It appears

that the fluctuation of the indicated pressure is caused by vibrations of the

surface of the mercury columns, which is turn are due to structure borne sound

from the pumping system and from the building.

UL T-l MA II TRIAL RUNS

EQUILIBRIUM POSITION

PUMPED

THERMALLY LAGGED' WITH BOX 1 ONLY

3 0 S INTERVAL

COLUMN LENGTHS IN MICROMETERS : TIME COL. 1 COL. 2 COL

1 62 541

1 62 61 0

1 6271 1

1 62741

00

00

1 62645.00

00

00

59992.997

59992 .997

59993.063

59993.083

59993.063

59994.609

59994.895

59995. 0 67

59994. 609

59994 . 636

59996. 534

59996.966

59996.275

59996. 362

59996.275

00

00

1 6281 1

1 62841

162912.00

1 62939 .00

1 630 1 0 . 0 0

59993.083

59992 .697

59992.81 1 59992 .997

59993. 1 70

59994.695

59994.881

59994 . 623

5999^. 722

59994.961

59997.396

59996. 52

1

59996.435

59996.966

59997. 0 52

Fig. 8

ULTIMA II TRIAL RUNS

EQUILIBRIUM POSITION

PUMPED

THERMALLY LAGGED WITH BOX 1 ONLY

30 S INTERVAL

FLUCTUATION OF INDICATED PRESSURE

TIME TEMP. CO ? ( UMHG ) P (PA)

1 62 541 . 00

1 62 61 0 . 00

1 62645. 00

1 6271 1 .00

1 62741 . 0 0

23 .460 0 0 0 23-460000

23.460000

23.460000

23 .460 0 0 0

.042966750

- . 0 66425761

.3861 6359

. 0 6593750 0 - .042966750

.0 0 570 12635

-.01 146731

4

. 0 51 50 5733

.0 11 402527

- . 0 0 570 1 2635

1 6261 1.00

1 62641 . 0 0 162912.00

1 62939 . 0 0

1 630 10.00

23 .460 0 00

23 . 470 0 0 0 23 .470 0 0 0 23.460000

23.460000

- . 34472 656

. 1 7236328

0 . - .25927734

- . 1 2939453

- .045739662

. 02266980 0

0 . - . 0 3440 1 942

-.0171 68576

* (UMHG) = MICROMETER OF MERCURY COLUMN

Fig, 9

ERRORS AND UNCERTAINTIES

Several sources of error have been discussed in past reports, but we shall

review only the uncertainty caused by temperature as the main source of error

The pressure indicated by the manometer is calculated from

(8) P = g§H

where p is the pressure in [Pa], g is the acceleration due to gravity in [m/s 2

]

is the density of mercury at the appropriate temperature in [kg/m 3

] and H

is the difference in meniscus heights in [m]

.

The error in p caused by the temperature measurement can be expressed as

follows, if the temperature is uniform throughout the entire manometer:

(9) dp = g H d§ + g§ dH

(10) d§ = 8

Q

ct£ dT

(11) • dH =' ftdm + m 3 )-m 2 } dT

where aa , a

c are the thermal coefficients of density and of

"* speed of sound,

c0

is the speed of sound in mercury,

m1 ,m2,m 3 are the fringe counts including the fractional values,

dT is the uncertainty in the temperature determination.

With an indicated pressure of 15 kPa (about 110 mmHg) an uncertainty of

dT = 0.01 °C causes an uncertainty in the pressure of

(12) dp = 2.7 x 10~ 2 + 4.6 x 10 -2 [Pa], dp/p = 4.2 ppm

the first term deriving from the temperature effect on density, the second

from that on the speed of sound.

Generally the temperature is not uniform throughout the manometer and

a more realistic uncertainty statement is

3

(13) dp =

g 1=1

0

a + (m0 + m^) dT,

which, for the same column lengths as above, renders

(14) dp = 4.3 x 10" 2 + 7.6 x 10" 2 [Pa]

dp/p = 7.9 ppm

for dT = 0.01°C.

The absolute uncertainty given in equs. (12) and (14) is independent of pressure.

Consequently the relative uncertainty v/ill increase rapidly at lower pressures.

Trial runs have only just been started and it is therefore difficult to

predict problems that might show up. The manometer has responded very well

to pressure changes and has returned to the equilibrium position to within

a fraction of a fringe.

When the manometer is left in the equilibrium position under vacuum there

appear to be disturbances about once every 8 to 12 hours. These may be caused

by a very slow leak or by the diffusion of helium from the seals, walls or even

the mercury. This is the first problem under study now.

PROBLEMS

ULTIMA II TRIAL RUNS

EQUILIBRIUM POSITION

PUMPED

THERMALLY LAGGED WITH BOX 1 ONLY

30 S INTERVAL

DATA FROM MIDAS SYSTEM

VECTOR 1 VECTOR 2 VECTO R 3 COUNT 1 COUNT 2 COUNT 3 CO T I ME

0 69 020 035 -0 50 -0 51 038 0000000 -0000000 0 0 0 0 0 0 0 2346 l 62541

068 020 036 -0 50 -0 53 0 34 0 0 G 0 G 0 0 - 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2346 l 6261 0 069 021 036 -047 -049 040 0000000 - 0 0 0 0 0 G 0 0 0 0 0 0 0 0 2346 l 62645

0 69 021 035 -0 50 - G 50 0 40 0000000 -0000000 000000 0 2346 l 627 1 1 069 02 1 034 -0 51 -049 G40 G 0 0 0 0 0 0 -0 G 0 0 0 0 0 0 0 0 0 0 G 0 2346 l 62 741

0 68 021 036 -049 -0 55 029 0000000 -ocooooo 000000 0 2346 l 628 i 1 0 68 02 1 037 -047 -0 52 0 36 G0000GG - 0 0 0 G 0 0 0 0 C 0 0 0 0 0 2347 l 62 84 1 0 69 020 0 34 -049 -0 51 037 0 0 0 0 0 0 0 - 0 0 0 0 0 0 0 000000 0 2347 l 629 1 2

068 020 034 -0 50 -0 53 034 0000000 -0000000 000000 0 2346 l 62939

0 68 022 037 -049 -0 54 033 ocooooo -0000000 0000000 2346 l 630 1 0

Fig, 7