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U.S. DEPARTMENT OF COMMERCE/National Bureau of Standards

Ultrasonic Calorimeter for

Beam Power Measurements

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NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards 1 was established by an act of Congress March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology

and facilitate their effective application for public benefit. To this end, the Bureau conducts

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the Institute for Computer Sciences and Technology, and the Office for Information Programs.

THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United

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1 Headquarters and Laboratories at Gaithersburg, Maryland, unless otherwise noted; mailing address Washington. D.C. 20234.

- Located at Boulder. Colorado 80302.
>J Bureau ©f Standards

2 6 1976

Ultrasonic Calorimeter for

Beam Power Measurements — -t e-cXW\ Lc\\ <\° \ P3> .(b&k

Thomas L. Zapf

Morris E. Harvey

Neil T. Larsen

Robert E. Stoltenberg

Electromagnetics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

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U.S. DEPARTMENT OF COMMERCE, Elliot L. Richardson, Secretary

Edward 0. Vetter, Under Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

u ,£>.NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

Issued September 1976
NATIONAL BUREAU OF STANDARDS TECHNICAL NOTE 686

Nat. Bur. Stand. (U.S.), Tech Note 686, 36 pages (September 1976)

CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1976

For sale by the Superintendent of Documents, U.S. Government Printing Office , Washington, DC. 20402

(Order by SD Catalog No. C13. 46:686). Price 85 cents (Add 25 percent additional for other than U.S. mailing
CONTENTS

Page

1. INTRODUCTION 1

2 . THEORY 2 2.1 Calorimetric Methods 2 2.2 Flow Calorimetry 3 2.3 Twin Flow Methods 3 3. DESCRIPTION OF CALORIMETER 4 3.1 The Twin Series Flow Comparator 4 3.2 Ultrasonic Absorbers; Vessel Design 4 3.3 Solid Absorber 6 3.4 Heat-absorbing Liquid 7 3.5 Liquid Circulation System 9 3.6 Heat Exchanger 9 3.7 Temperature Sensors 10

3.8 Electrical Heaters 11

4. HEAT LOSSES IN CALORIMETER 12

4.1 Heat Loss in the Coupling Liquid 12

4.2 Heating from Lossy Transducer 13

4.3 Absorption in Membrane 13

4.4 Heat Distribution 14

4.5 Radiant Power Loss 16

5. ELECTRICAL FEEDBACK AND CONTROL 16

5.1 Power Feedback 16

5.2 Temperature Bridge 17

5.3 Bridge Electronics 19

5.4 Metering Circuits 21

6. OPERATIONAL PROCEDURES 21

6.1 Preliminary Procedures 21

6 . 2 Precautions 2 2 6.3 Ultrasonic Power Measurements 22

6.4 Determination of the J, K, and G Factors 23

7. EQUATIONS OF OPERATION 23

8. SUMMARY OF MEASUREMENT UNCERTAINTIES 25

9 . ACKNOWLEDGMENTS 26

10 . REFERENCES 27
LIST OF TABLES

Page

Table 1. Summary of estimated uncertainties 28

LIST OF ILLUSTRATIONS

Figure 1. The NBS ultrasonic calorimeter, showing the electrical control

unit, the twin, series-flow comparator in a water bath, pumps,

and electrical power supply 29

Figure 2. Schematic diagram of the twin, series-flow ultrasonic

comparator 3 Figure 3. Schematic diagram of the electrical control unit 31
ULTRASONIC CALORIMETER FOR BEAM POWER MEASUREMENTS

Thomas L. Zapf, Morris E. Harvey, Neil T. Larsen and Robert E. Stoltenberg

An ultrasonic calorimeter has been designed and constructed at

the National Bureau of Standards for the measurement of beam power

up to a few watts from ultrasonic transducers. The calorimeter,

described as a twin, series flow, ultrasonic calorimetric comparator,

operates in the frequency range from 1 to 15 MHz with uncertainties

less than ± (7% + 0.2 mW) . Twin vessels are provided so that thermal

effects of an ultrasonic sound beam absorbed in one vessel can be

compared rapidly with accurately measured dc electrical power in the

other vessel. Absorbing liquid enters each vessel near the ultrasonic input port. The temperatures of the absorbing liquid at the

input ports are equalized by a heat exchanger, and the mass-flow rates

are the same in both vessels. Twin temperature sensors, located in

the output flow from the vessels, are connected in an electrical bridge

circuit. In automatic operation the bridge is connected to a feedback

circuit. With ultrasonic power introduced into one vessel, the feedback circuit promptly applies power to an electrical heater in the

other vessel to regain bridge balance. The ultrasonic power then

equals the measured dc power corrected for known errors.

Key words: Calorimeter; ultrasonic calorimeter; ultrasonic power

measurements

.

1. INTRODUCTION

The accurate measurement of beam power from ultrasonic transducers has

become increasingly important to manufacturers and users of ultrasonic equipment especially that used for medical diagnostic and therapeutic purposes.

Routine medical applications of ultrasound, and research on the effects of

ultrasound on body tissues, require power levels ranging from less than a milliwatt to several watts. Ultrasonic transducers used for nondestructive

evaluation equipment are often subjected to harsh environments and rough usage

and must be calibrated periodically to correct for deterioration and drift.

Often, this testing and calibration must be done by the users of the equipment.

This usually requires construction of their own measuring instruments based on pnenomena such as radiation force, acousto-optic effects, piezoelectricity,

thermoelectricity, or calorimetry. As part of a program to provide needed mea- surement services for ultrasonic equipment, the National Bureau of Standards has

recently developed calorimetric equipment for measuring ultrasonic beam power.

The calorimetric equipment (shown in figure 1) was designed to measure ultrasonic beam power from 1 mW to 10 W, at frequencies from about 1 to 15 MHz.

Measurements made with this equipment are referenced to accurately-measurable dc

electrical standards. The equipment will accommodate ultrasonic beams having

diameters as large as 26 mm. This is sufficient for a wide variety of medical

diagnostic and therapeutic transducers, and for many transducers used for
nondestructive evaluation. The most important design goal was to minimize the

net error in measurements when the equipment is used within the power and

frequency ranges and beam diameters mentioned above.

The equipment in its present form is not portable. It is normally used

in a water bath. Although relatively trouble free, it must be regarded as a laboratory instrument requiring some protection from abuse, and a few minutes

of daily maintenance.

2 . THEORY

2 . 1 Calorimetric Methods

In a lossy, homogeneous medium in which energy is propagated, absorption

(i.e., conversion to heat) causes an exponential reduction of ultrasonic power

with propagation distance. The attenuation generally increases with frequency

for solids, or with the square of the frequency for liquids. This dependence

on frequency presents a peculiar problem in the design of calorimetric ultrasonic power meters. While calorimetric measuring equipment, in general, is

considered to be "broadband," the range of frequencies that a particular

ultrasonic calorimetric system will accommodate is limited, primarily because

of compromises required for optimization to achieve best accuracy.

In any ultrasonic power measuring device, the pressure waves produced by

the transducer must be conveyed through a low-loss medium to the measuring

region. The commonly-accepted and readily-available coupling medium for

medical transducers is water. Some specifications require or suggest that the

transducer face be kept at a particular temperature during measurements to

simulate conditions of use. This requires that the coupling medium be maintained

at the specified temperature, and that there be a flow system for carrying

away whatever heat is produced in the coupling medium by losses in the transducer. It also requires that the absorber at the entrance port of the calorimetric vessel be kept at the same specified temperature to prevent transfer

of heat to or from the coupling medium. These requirements can be met by

using a heat-exchanger in the flow system.

Calorimetric methods have proven valuable for measurements of power and

energy in various forms, mechanical, electrical, light, sonic, etc. A comprehensive bibliography of calorimetry in nuclear science has been published by

S.R. Gunn [1,2]*, who has also published a review of laser power and energy

measurements by calorimetry [3].

Radio frequency and microwave calorimetry is already well established,

with numerous manufacturers providing equipment.

In ultrasonics, calorimetric methods have been described by various

authors [4,5,6,7,8]. Some of these publications contain references to earlier

literature on calorimetry.

*Numbers in brackets indicate literature references,

2
2 . 2 Flow Calorimetry

In a flow calorimetric system, the applied power, P, is converted to

heat, which causes a rise in temperature, AT, in the liquid flowing at a constant mass-flow rate, m, past a temperature sensor. If heat losses in the

system are negligible, the power is

P = smAT

where s is the specific heat of the heat-absorbing liquid. The term "heatabsorbing liquid" or simply "absorbing liquid" will be used to denote that

there is conversion to heat from some other form of energy, or that heat is

transferred to the liquid from an absorbing solid, or both. The steady-state

temperature rise in the flowing liquid in the calorimeter per unit of absorbed

power is

AT/P = 1/sm.

For the greatest temperature rise per unit power, the specific heat and

the mass-flow rate should be small; however, a small mass flow rate would

cause a long volume displacement time,

t = m/m

where m refers to the mass of liquid in the heat-conversion-and-sensing volume

of the system, i.e., m = pV, where V is the volume and p is the density of the

liquid. It is evident that the sensitivity and response time can be adjusted

by changing the flow rate. The volume, V, must be kept to a minimum so that t will be minimized. Yet the vessel size and shape must be such that the ultrasonic beam energy is, as nearly as possible, completely absorbed (converted to

heat) . Reflections that would allow ultrasonic energy to escape through the

ports of the vessel must be minimized. The specific acoustic impedance of the

absorbing liquid and any solids in the liquid, must be near that of water (the

standard coupling medium) to minimize reflections at interfaces.

2 . 3 Twin Flow Methods

Advantages of twin, series-flow calorimetric methods were recognized by

Gunn [9] and used for measuring the power of alpha-radioactive samples. He

points out the decreased need for accurately controlling the flow rate and

temperature rise. Wholey and Boff [10] described a twin, series-flow system

with feedback for the measurement of microwave power. The features of the

system are desirable and appropriate to an ultrasonic calorimeter, and the

present ultrasonic calorimeter is generally similar to the Wholey and Boff

system.

In a twin, series-flow system, the temperatures of the liquids at the

ports and the mass-flow rates are the same in both vessels, ambient temperature effects are minimized, and insulation requirements are not as stringent

as in single flow systems. However, it is desirable that the temperature
sensors be well matched over the range of temperatures encountered. A heatexchanger is required to keep the temperatures of the absorbing liquid and the

transducer-cooling liquid nearly equal at the inputs to each vessel.

A twin system can be used as a comparator for comparing the powers from

two ultrasonic transducers, or as a standard power meter with the substitution

of (or comparison with) known electrical power.

3. DESCRIPTION OF CALORIMETER

3 . 1 The Twin Series Flow Comparator

The calorimeter may be described as a twin, series-flow, ultrasonic calorimetric comparator for measuring ultrasonic beam power from ultrasonic transducers. Figure 2 shows schematically the calorimetric vessels, sensors, pumps,

and the heat exchanger. The temperatures of the flowing liquids at the ultrasonic ports, and the mass-flow rates, are the same in both calorimetric vessels,

which are of identical design. Twin temperature sensors, located in the output

flow from the vessels, are connected in an electrical bridge circuit. The

bridge is connected to a null indicator or, in the automatic mode, to a feedback circuit. With ultrasonic power introduced into one vessel, the feedback

circuit promptly applies power to an electrical heater in the other vessel to

regain bridge balance.

The calorimeter is normally placed in a temperature-controlled water bath

which may be operated from 2°C above room temperature to 40 °C without use of

a cooling coil. A cooling coil permits use at lower temperatures. The electrical control unit and the pump with three pump heads are placed on the table

beside the water bath.

Each vessel has a port for the introduction of ultrasonic power and each

contains an electrical resistance heater for inserting accurately measurable

electrical power. A thin, non-reflecting membrane at each ultrasonic port

prevents mixing of the absorbing liquid in the vessel and the coupling liquid.

Water is used as a coupling medium. The absorption of ultrasound in water in

the 1 to 15 MHz range is very much smaller than in the absorbing liquid. The

heat conductivity of water is larger, and the specific heat is larger; therefore, water can effectively transfer heat from the ultrasonic transducer and

carry it away with a relatively small increase in water temperature.

3 . 2 Ultrasonic Absorbers; Vessel Design

Among the factors that were considered in choosing suitable ultrasonic

absorbers and heat transfer materials were (1) the specific acoustic impedance,

(2) the absorption per unit distance, (3) the temperature rise per unit energy,

(4) the pressure required to circulate the liquid, (5) long time compatibility

of the liquid with other system materials, and (6) toxicity and hazardous

characteristics of the material.

4
In choosing an assortment of materials as candidates for use as absorbers

the most important requirement was that reflection of power from the first

surface of the absorber be minimized. For the power reflection ratio to be

less than 1% at the interface between the coupling medium (water) and the

absorbing material", it is necessary that the specific acoustic impedance, pc,

at the absorbing material be within the range (1.5 ± 0.3) x 10 kg«m «s This requirement limits the number of liquids and solids that can be considered

as potentially useful.

Other factors include ultrasonic attenuation, which for calorimetry means absorption by conversion to heat without significant scattering effects. A

large value of attenuation per unit distance, a , for all frequencies of

interest is essential. A low value of specific heat, s, is desirable so that

a given value of power causes a large change in temperature. A high value of

heat conductivity, k, is desirable to minimize the size of heat exchanger

required for the system. The viscosity of the liquid should be low to facilitate mixing in the flowing liquid and minimize the pressure needed to obtain a required mass-flow rate, m. A number of more promising liquids were investigated in some detail.

Among the liquids having relatively high attenuation at 1 MHz, carbon disulfide

was ranked very high for its good impedance match with water and its low

viscosity; but, it is highly toxic, flammable, and incompatible -with many

materials. Oils of various kinds, and silicone fluids, although showing high

attenuation and satisfactory specific acoustic impedance, had higher viscosity

than desired for a flow system. A flow system using these liquids in conical

vessels could possibly have been developed, but heat distribution errors would

have been large and the response time was estimated as many times greater than

that obtainable using a combination of a solid as an ultrasonic absorber and a liquid as a vehicle for heat transfer from the solid to the sensor in a flow

system.

By using a solid as the principal absorber and a liquid to transfer the

heat to the sensor, the vessel size, the effective volume of liquid, the

effective volume-displacement time, and the power-feedback response time could

all be reduced. However, the time required to attain heat- transfer equilibrium

between the solid and the liquid can be significant. In the calorimeter, the

equilibrium time is kept small by flowing the liquid over the surfaces of a number of thin wafers of the solid so that the heat transfer distance from the

middle of the solid to the liquid is small.

The absorbing solids and liquids are contained in a cylindrical vessel

of height, h. Reflections of ultrasound from the bottom make the effective

absorbing path length, x, approximately double the height, i.e., x - 2h.

Ideally, the ultrasonic power would be completely absorbed (converted to heat)

in the vessel. Some power is absorbed in the walls and bottom of the vessel

which, if well insulated externally, yields the heat to the liquid. Some

power is returned in the direction of the ultrasonic port. That portion which
is not reflected from the surface of the transducer back into the absorbing

liquid, or the portion which escapes through the water coupling medium over

the upper edge of the vessel, is not measured, and therefore is a loss of

power contributing to the errors in the measurement. At the lowest design

frequency, the depth of the absorbing material must be chosen so that the

absorbing path length, x, is sufficient to make the reflected unabsorbed power

acceptably small. In a homogeneous absorbing material, the power in the

propagating beam at a distance, x, is diminished exponentially,

-2a x

P = P e X

o where P is the power at x = and a is the amplitude attenuation per unit

distance in the material. Then, for each absorbing layer in the vessel,

x = (-l/2ax

) ln(P/P

Q

)

The value of h is obtained from the cumulative value of x for all solid and

liquid absorbing layers. The height, h, should be as small as possible, while

allowing for adequate absorption, to minimize the response time of the system.

Measurements on the completed assembly by a pulse-echo method at 2 MHz showed

a maximum power reflection of less than 0.001, and this source of reflection

was the bottom of the vessel.

3 . 3 Solid Absorber

The absorbing solid consists of four wafers of silicone elastomer and

four wafers of butyl rubber. Each wafer is about 1 mm thick. The silicone

ft — *? —1 elastomer has a specific acoustic impedance of about 1.5 x 10 kg«m *s , which is nearly equal to that of water and the absorbing liquid, so that the

power reflection coefficient is about 0.001. The four layers of the silicone

elastomer provide a power attenuation ratio for two-way travel at 1 MHz of

P/P = 0.36 as measured by pulse transmission techniques. Following these are four wafers of butyl rubber. At the interface between the liquid and the

butyl rubber, the power reflection coefficient is about 0.02. This is acceptable

because the reflected power must pass through the four upper layers of silicone

elastomer with a one-way power attenuation ratio of 0.6. About 75% of this is

re-reflected by the transducer face back into the calorimeter. Then the

actual loss is 0.02 x 0.6 x .25 = 0.003 = 0.3%. The power attenuation ratio

for two-way travel in the butyl rubber at 1 MHz is 0.013. The total power

attenuation ratio for two-way travel at 1 MHz is then 0.36 x 0.013 = 0.005 = 0.5%.

Re-reflection from the transducer face reduces the loss to approximately 1/4

of this, or to about 0.1%. Thus, the net loss of power reflected out of the

vessel determined by summing the losses at the two interfaces is estimated as less than 0.4% at 1 MHz and inversely proportional to the frequency. At
frequencies above 5 MHz, for example, the error is less than 0.1%. This is

obtained using the correction +0.4%/f, where f is the frequency in MHz. The

residual error (i.e., the remaining error of unknown sign after the correction

has been applied) is then believed to be within ± 0.1% at frequencies below

5 MHz and negligible at higher frequencies.

Although reflections in the calorimetric vessel result in only a very

small power loss, they can cause small, but noticeable, variations if the

transducer is moved slightly during a test. To reduce the effect, it is good

practice to rock the transducer slightly during the last minute of each test

run, and average the measurement results of three test runs. This practice

has the effect of randomizing an error that otherwise may occur as a systematic

error.An estimate of the time required for the heat developed in the solid

absorber to attain an equilibrium gradient with the moving liquid can be

obtained by considering the thermal diffusion in the solid. The time constant,

t, for thermal diffusion of heat through a distance, x, of a material having

density, p, specific heat, s, and heat conductivity, k, is

t = x

2 ps/k.

_3 In the butyl rubber dxsks, the half -thickness is x = 0.5 x 10 m,

p = 1.2 x 10~ 3 kg-m~ 3

, s = 2.0 x 10 3 J-kg~ 1 -K~

1

, and k = 0.09 W-m~ 1 -K~

1

. Then t = 7 s. Thermal diffusion is complete within 1% after 5t = 35 s.

3 . 4 Heat-absorbing Liquid

The heat-absorbing liquid is an inert perf luorinated liquid that is

3 -3 commercially-available. It has a density of 1.9 x 10 kg-m , a specific

acoustic impedance of 1.4 x 10 kg*m *s , an ultrasonic attenuation per unit

2 -12 -1 2 distance divided by f of 1.6 x 10 Np-m «s , a specific heat of

3 -1 -1 -3

1.0 x 10 J*kg *K , a viscosity of 7 x 10 Pa-s, and is non-toxic and non- corrosive. The specific acoustic impedance is close to that of water, so that

the power reflection coefficient is less than 0.12%. An estimated 75% of

these losses are reflected from the transducer face and reintroduced into the

vessel, leaving a net loss less than 0.03%.

The use of water as a heat-aborbing liquid was considered, because it has

high heat conductivity, and lower viscosity. Its use would probably result in

smaller thermal time constants in the system, but the mass-flow rate would

have to be reduced to keep the AT/P sensitivity high. However, it was not

used because it is corrosive and could cause electrolysis in the electrical

heater.
1% . At lower frequencies the error becomes less significant because of the

frequency-squared absorption characteristics of the absorbing liquid. Although

this evaluation is subject to considerable error (e.g., from laminar flow

differences in the liquid under the membrane for electrical versus ultrasonic

heating), it is believed desirable to apply a correction factor of (1 + 0.0005 f] where f is the frequency in MHz. The residual error is then believed to be

within ± 0.02% f.

At the bottom of the vessels, absorption of ultrasonic or electrical

energy is essentially complete. Both vessels are of similar construction,

they are in similar, thermally-insulated, environments, and have nearly equal

temperatures at the bottom. Therefore, the heat losses through the bottoms of

both vessels are small and nearly equal; hence, the net error is negligible.

Air convection loss from each vessel were appraised by using a special

test vessel and found to be less than 0.4% when the vessels are insulated by

filling the case with polystyrene beads, and about 0.6% if left unfilled.

Because these losses from each vessel are approximately equal, the net error should be less than 0.1%. Other tests indicate that losses by conduction

through the flange and water well could cause a loss of as much as 1.5% at

high frequencies or when the A' heater is used. This is probably the major

source of the heat-distribution errors that are effectively corrected by

application of the heat-distribution factor, H, to be discussed.

Losses through the cylindrical sidewall and flange depend on the heat

distribution in the vessel. As mentioned, this depends on the frequency of

the ultrasound, or the location of the electrical heater, in each vessel.

Sidewall heat-distribution errors were evaluated repeatedly by using the A

1 and

A" heaters. The A" heater simulated the heat source distribution at ultrasonic frequencies near" 0.8 MHz, and the A

1 heater simulated heating at frequencies higher than 10 MHz. To correct for the heat distribution errors at

all frequencies based on data obtained with the A' and A" heaters, an interpolation formula was developed. Heat-distribution interpolation factors as a function of frequency were calculated based on the known values of the

attenuation-per-unit-distance and thickness of each layer of material in the

vessel. The interpolation formula is

T = T' - N(T' - T") , where T' and T" are the measured heat-loss corrections corresponding to the A

1 and A" heaters, and N is an interpolation factor. The heat-distribution

correction factor is given by

H = 1 + T. Typical values of T' and T" are less than 0.005; thus N need not be known very

accurately to provide adequate interpolation accuracy. Indeed, the average of

a set of 13 determinations of these values over a period of 4 months was

T

1 = 0.003 and T" = 0.000. In practice it is convenient to use these values

to determine T and H rather than to redetermine the values at intervals. The
3 . 5 Liquid Circulation System

A pump is needed in each leg of the system to provide pressure to move liquid through the vessel, the sensor, and the heat exchanger, keeping the

pressure at the input ports to each vessel very near atmospheric pressure. A

third pump head circulates the coupling liquid through the heat exchanger to

the water well above each vessel. The pump heads can be driven by a variable

speed drive motor from about 0.1 to 2 revolutions per second to provide volume

flow for the absorbing liquid from 0.08 x 10~ to 1.7 x 10~ m -s" . The

shortest response time is obtained when the pump is operated at maximum speed.

If the pump speed is too great, the excessive pressure in the system can cause fluid to leak out or air to leak in. As pump speed is reduced to a very low

level, the response time increases and too much heat is lost from the fluid

before it reaches the sensor. A "normal" pump speed equivalent to about

— ft 3 — 1 1.2 x 10 m «s was chosen to avoid these troublesome extremes.

A bypass valve is provided to allow control of the relative pressures at

the membranes in the A and B vessels when the pumps are operating at the

normal flow rate. If there were no bypass circuit, and if one of the pumps

tended to pump more than the other, pressure at one membrane could build up to

a high level tending to stretch and burst it.

The reservoir and clamps provide a ready source of liquid to accommodate

changes in the system volume.

Each pump head introduces heat energy into the system at a rate proportional

to the speed of the pump and the torque. The power dissipated in frictional

losses in pumping is

P = 2ttST

where S is the pump speed, and T is the frictional torque. At typical values

of S = 1.2 revs" and T = 0.14 N«m (measured value), then P = 1.1 W. A

portion ( of this power is carried away by the pump hardware, and a portion is

transferred to the liquid causing a rise in temperature. The heat produced in

the liquid is a load on the heat exchanger. The load is greatest when the

mass-flow rate is greatest. In the twin flow system, twin pump heads tend to

equalize the heating in each leg, thereby minimizing this source of error. Any residual unbalance is eliminated by the initial nulling balance adjustment

required as part of the operational procedures.

3 . 6 Heat Exchanger

A constant-temperature water bath with three tubes functions as a heat

exchanger to insure controlled and nearly equal temperatures for the liquids

at the entrances to the vessels. The temperature of the water bath can be

controlled at a specified temperature between 25 and 40°C. A small, constant,

temperature difference between vessels can be corrected by the initial balance

procedure. However, it is desirable to keep the temperature difference small
(say, less than 5% of the temperature rise created by the ultrasonic and

electrical heating) to avoid large temperature differences at the sensors. A

large temperature difference between vessels could make the heat losses in the

vessels unequal and cause an error.

In the chosen design, all three tubes are 6 m long and the absorbing

liquid and the coupling liquid are thermally-coupled closely to each other.

The tubes are arranged so that the liquids are equally exposed to whatever

temperature differences may exist in the bath.

3 . 7 Temperature Sensors

The temperature sensors are nickel-iron alloy resistance thermometers of

approximately 6 76 ohms at 25 °C, with a temperature coefficient of resistance

of about 3 fi«K , or a fractional change of about 0.004 K . The voltage

across each sensor is about 0.2 V, and the temperature coefficient of output

voltage of the sensor-bridge is e/AT = 0.0008 V*K . When the liquid exhibits

a temperature rise per unit power of AT/P = 0.53 K'W , which corresponds to

the maximum mass-flow rate, the sensor circuit voltage/power ratio is

e/P = (e/AT) (AT/P) = 0.0004 V*W . At lower mass-flow rates, this figure

would be proportionately higher. A more convenient measure of sensitivity can

be defined as the inverse of the above ratio, which is S = P/e = 2.5 x 10 W«V

The calibration procedure, outlined later in this paper, will correct for some mismatching of the sensor sensitivities. To facilitate bridge circuit

design, the sensor elements should be of nearly equal resistance. Also, they

should be matched so that, for a given change of temperature, the fractional

change of resistances will be nearly equal. For a temperature change of 27 K,

which is 5 times as large as expected, the measured values of the fractional

-3 -1 -3 -1 change of resistance per kelvin was 4.576 x 10 K and 4.578 x 10 K , the ratio of these being 0.9996, indicating a mismatch well under 0.1%.

The sensors are each mounted in a thermometer holder and thermometer well

through which flows the absorbing liquid. Because of small differences in the

shapes of the sensors, the holders, and the wells, the sensitivities of the

sensors, as mounted, can be unequal by as much as a few percent. The effect

of the inequality is eliminated by application of the J or K correction factor

determined in the calibration procedure, the uncertainty of the measurements

(electrical) being ± 0.5%, or less.

A mismatch in the self heating effect in the sensors can cause the bridge

balance to be a function of the oscillator voltage. It was found that a 1%

change in oscillator voltage causes a change in bridge balance equivalent to

a power change of 0.17 mW. The specifications for the oscillator list a temperature coefficient of voltage of 0.002 K . After a warmup period of 15

minutes or more, the oscillator should be so stable that changes in the null

balance from this cause should remain well within 0.12 mW during the measurement

period

.

10
Throughout the system the liquid is in laminar flow. The thermal patterns in the flowing liquid can be different for each electrical heater and

ultrasonic transducer. To prevent significant errors, thermal diffusers are inserted in the sensor housing in front of the sensor. The thermal diffusers consist of a copper disk having holes near the periphery, and wads of fine

copper wire. The high heat conductivity of these elements in the line of flow

makes the sensor response less dependent on the particular thermal pattern in

the laminar flow in the output tube from the vessel. Residual errors from

this effect are believed to be less than ± 1%.

3 . 8 Electrical Heaters

The A and B heaters were made from resistance wire (0.0254 mm diameter,

26 ohms per meter) cut to a length to give 10 ohms resistance. The wire was bent to a zig-zag pattern and attached with thread to an aluminum oxide disk.

This design exposes nearly all of the wire to the absorbing liquid. The

heaters can dissipate 10 watts.

In the first calorimeter constructed, two extra heaters were inserted in one of the vessels to evaluate heat distribution errors. The A' heater

(1.7 ohms) was located at the top of the vessel diametrically opposite the

liquid inlet port. It simulated ultrasonic heating at 15 MHz in which ultrasound absorption is more than 95% complete before ultrasound enters the second

layer of rubber.

The A" heater (1.8 ahras) was distributed vertically through the layers

of rubber in a "W" shape. It simulated ultrasonic heating at 0.8 MHz in which

ultrasound absorption is approximately uniform through the vessel. The heaters

2 were attached to copper studs in the flange above each vessel. A loss (I R)

of power could occur through the copper studs and copper wires (AWG No. 24) con- nected thereto. By measuring the temperature difference along a known length

of a potential-lead wire of the same material and size as the current-carrying

wires, this loss was estimated as about 0.08%.

In the use of the A" and A' heaters, another heat loss occurs from con- duction through their copper studs and then through the plastic flange and

water well to the flowing water. The loss, expressed as a fraction of the

heater power, was estimated by using heat transfer formulas as approximately

0.3%. Thus, the total loss through the studs is believed to be less than 0.4%.

This would result in an error in the measurement of ultrasonic power. To

correct for this error of known sign, a correction of -0.3% is applied. The

residual error is then believed to be within ± 0.1%.

11
The heat developed in the current-carrying lead-in wires (I 2 R loss) flows

into the calorimeter vessel and into the case. The part that flows into the

vessel can be significant. The resistance of one current-carrying wire 0.15 m

long is R = 0.013 ohm. When the current I = 0.95 A in the 1.7 ohm heater, the

power developed is P = I

2 R = 0.012 W per wire. There are two current-carrying

wires, and if the assumption is made that the power divides equally between

calorimeter and shield, the power injected into the calorimeter is 0.012 W. This would result in .0.8% heat power injected into the heater that is not

measured electrically. Ginnings and West [11] have suggested a solution to

this problem. To correct for this error at each heater, one of the smalldiameter potential leads was left connected to the junction of the currentcarrying wire and the copper stud at the calorimeter vessel, and the other

potential lead was connected to the other current-carrying wire near a foil

heat sink attached to the inside surface of the case. With these connections,

the heat developed in one current-carrying wire is measured as electrical

power in the heater, and equals the heat introduced into the vessel from the near part of the two current-carrying wires. With this corrective measure

incorporated, the residual error from this source is believed to be less than

± 0.1%.

4 . HEAT LOSSES IN CALORIMETER

4 . 1 Heat Loss in the Coupling Liquid

The fraction of ultrasonic beam power converted to heat in the water

coupling liquid between the transducer and the membrane can be calculated and

a correction applied to the calorimetrically-measured power to yield the total

beam power emitted from the transducer. The coupling-loss correction factor

is defined here in terms of the exponential attenuation formula for power, a being the distance attenuation coefficient,

2 (a /f 2 )f 2 x

C = P /P = e

o' where P is the ultrasonic power entering the water coupling medium of depth

x, P is the ultrasonic beam power emerging from the water and entering the

2 -15 -1 2 calorimeter through the membrane, a /f = 20 x 10 Np*m «s at 28°C, and f

is the ultrasonic frequency in Hz. For example, at f = 15 MHz, if x = 4.6 mm,

the calorimetrically-measured power should be multiplied by C = 1.042. In the

temperature range from 25-40 °C a more accurate correction can be calculated if

the attenuation is determined from

a /f 2 = [20 - 0.417(T - 28°C)] x 10 _15 Np-m

-1

'S

2

. The distance x = 4.6 mm is the distance from the membrane to the shoulder

of the water well upon which a transducer would be placed. If the active

surface of the transducer is above this shoulder, an additional distance

12
should be added to 4.6 mm to obtain the total distance, x, for use in the

formula. If allowance for error of about ± 1 mm in the distance measurement

is assumed (to allow for uncertainty in the position of the membrane as well

as in the distance measurement) , the uncertainty in total beam power at 15 MHz

for 6 mm depth of coupling medium is + 1%.

4 . 2 Heating from Lossy Transducer

For evaluating the effect of heating from a lossy transducer, a special

transducer housing was prepared in which the piezoelectric element was replaced

by a copper disk to which an electrical heater (resistor) was attached. When

this "transducer" was placed in the ultrasonic port of the calorimeter and

energized with known power, the power measured by the calorimeter was a measure

of the heat transfer downward through the membrane. The ratio of power transferred into the calorimeter (at a thermal flow rate) to the power loss in the

"transducer" was measured and found to be 2.2%. Assume that a typical solidbacked ceramic transducer has an efficiency of 50%, i.e., that the ultrasonic

beam power and the power loss in the transducer (and its mount) are equal.

Also assume that less than 1/3 of the heat loss comes through the face of the

transducer, most of it escaping through the backing and sides. Then the error

(assuming no correction is made) from heat transfer downward through the

membrane from the transducer is less than +0.7% for a normal flow rate. For

an air-backed quartz transducer having an efficiency of 95%, the estimated

error is about +0.1%. If a correction is applied based on these estimates,

the residual uncertainty for solid-backed ceramic transducers may be con- sidered as ± 0.3%, and ± 0.1% for air-backed quartz transducers. Based on the

above considerations, the correction factor for a solid-backed ceramic transducer is L = 0.993, and the correction factor for an air-backed quartz

transducer is L = 0.999.

4 . 3 Absorption in Membrane

A thin membrane separates the coupling liquid (water) from the absorbing

liquid. The membrane is not completely acoustically transparent. A membrane

of thickness x = 13 x 10 m (i.e., 0.0005 inch) is thin relative to a wavelength at 1 MHz, and at 15 MHz x is about . IX in polyethylene (A =

-4

1.3 x 10 m) . At 15 MHz the attenuation per unit distance in bulk polyethylene 2—1 — fi —2

is about 8.1 x 10 Np-m , and for x = 13 x 10 m, a = ax = 1.0 x 10 '' Np

,

and P/P = e

' * = 0.98. Thus, about 2% of the incident power would be con- verted to heat in a thickness of bulk material equal to that of the membrane.

In the moving membrane of thickness about 0.1A the loss is probably smaller

than that calculated. Some of this heat is conducted to the absorbing liquid,

and some is carried away by the water coupling liquid. The latter constitutes

13
a source of error, probably less than -0.5% at 15 MHz, and proportionately

smaller at lower frequencies. A correction factor of (1 + 0.00025 f ), where f is the frequency in MHz, is applied. The residual error is then believed to

be within + (0.01 f) %.

4 . 4 Heat Distribution

The heat distribution in the ultrasonically-heated vessel varies with

frequency. At low frequencies, conversion of ultrasonic energy into heat

takes place over somewhat greater depth than at higher frequencies. Ideally,

the heat distribution caused by ultrasonic absorption should be duplicated by

the electrical heater. Because the ultrasonic absorption pattern varies with

frequency, a fixed, distributed electrical heater can provide approximately

equivalent heat distribution at only a single ultrasonic frequency. The

electrically heated liquid then yields heat to the absorbing solid material

downstream from the heat source causing a large time constant. To avoid a long response time in normal operation, the B vessel contains a single electrical heater, B (10 ohms) , at the bottom of the vessel. The A vessel con- tained three heaters, one temporary heater near the top, A', one temporary

heater distributed vertically, A", and one at the bottom, A (10 ohms). The A

and B electrical heaters are under all solid absorbing material. When these

heaters are used, the electrical-heating volume-displacement time is reduced

to a minimum and reflections from the heater and its framework are acceptable.

With this arrangement, heat-distribution errors are to be expected, and require

quantitative evaluation. Heat can be lost from each vessel at its top, bottom,

and sidewall. At the top of the vessel, heat can enter or exit through the

membrane if a temperature difference exists across the membrane. This temperature difference is kept small by the heat exchanger so that the coupling

liquid and absorbing liquid are at very nearly the same temperature as these

liquids move over and under the membrane in a laminar-flow pattern. Ultrasonic absorption in the absorbing liquid just beneath the membrane can cause a rise in temperature with a consequent heat loss through the membrane. A measure of the largest errors to be expected from heat transfer upward through

the membrane was obtained by the use of special heaters. Two electricalresistance heaters were mounted in the upper part of one vessel. One of these was temporarily located at the side of the vessel close to the entrance of the

absorbing liquid so that it would yield heat to the absorbing liquid passing

under the membrane. The other (A 1 , previously described) was located at the

side of the vessel opposite the entrance so that its heat was yielded to the

absorbing liquid just after passing under the membrane. By applying equal

power to each of these heaters in succession, the heat loss upward through the

membrane was evaluated. Roughly half the membrane heat-loss error so obtained

can be considered equivalent to that at 15 MHz and was found to be less than

14
1%. At lower frequencies the error becomes less significant because of the

frequency-squared absorption characteristics of the absorbing liquid. Although

this evaluation is subject to considerable error (e.g., from laminar flow

differences in the liquid under the membrane for electrical versus ultrasonic

heating) , it is believed desirable to apply a correction factor of (1 + 0.0005 f)

,

where f is the frequency in MHz. The residual error is then believed to be

within ± 0.02% f.

At the bottom of the vessels, absorption of ultrasonic or electrical

energy is essentially complete. Both vessels are of similar construction,

they are in similar, thermally-insulated, environments, and have nearly equal

temperatures at the bottom. Therefore, the heat losses through the bottoms of

both vessels are small and nearly equal; hence, the net error is negligible.

Air convection loss from each vessel were appraised by using a special

test vessel and found to be less than 0.4% when the vessels are insulated by

filling the case with polystyrene beads, and about 0.6% if left unfilled.

Because these losses from each vessel are approximately equal, the net error should be less than 0.1%. Other tests indicate that losses by conduction

through the flange and water well could cause a loss of as much as 1.5% at

high frequencies or when the A

1 heater is used. This is probably the major

source of the heat-distribution errors that are effectively corrected by

application of the heat-distribution factor, H, to be discussed.

Losses through the cylindrical sidewall and flange depend on the heat

distribution in the vessel. As mentioned, this depends on the frequency of

the ultrasound, or the location of the electrical heater, in each vessel.

Sidewall heat-distribution errors were evaluated repeatedly by using the A

1 and

A" heaters. The A" heater simulated the heat source distribution at ultrasonic frequencies near 0.8 MHz, and the A

1 heater simulated heating at frequencies higher than 10 MHz. To correct for the heat distribution errors at

all frequencies based on data obtained with the A

1 and A" heaters, an interpolation formula was developed. Heat-distribution interpolation factors as a function of frequency were calculated based on the known values of the

attenuation-per-unit-distance and thickness of each layer of material in the

vessel. The interpolation formula is

T = T' - N(T' - T")

,

where T

1 and T" are the measured heat-loss corrections corresponding to the A' and A" heaters, and N is an interpolation factor. The heat-distribution

correction factor is given by

H = 1 + T. Typical values of T' and T" are less than 0.005; thus N need not be known very

accurately to provide adequate interpolation accuracy. Indeed, the average of

a set of 13 determinations of these values over a period of 4 months was

T' = 0.003 and T" = 0.000. In practice it is convenient to use these values

to determine T and H rather than to redetermine the values at intervals. The

15
A

1 and A" heaters were later removed from the vessels. After the small cor- rection has been made for this heat-distribution error, the uncertainty in the

final results from this source is believed to be less than ± 0.5%.

4 . 5 Radiant Power Loss

From Stefan's law, the radiant power emitted by a body is given by

4 4 P = eoA(T, - T ) b s where e is the emissivity of the surface, the Stef an-Boltzmann constant

-8 -2 -4

a = 5 . 7 x 10 W«m «K , A is the surface area of the body, and T, and T are the absolute temperatures of the body and the surroundings, respectively. For

the emissivity of brass we assume 0.3. The surface area of the brass vessel is

A = 2.6 x 10~ 3 m . If AT = TV - T = 5 K and T = 298 K (25°C) , then b s s P = 0.024 W. This temperature difference corresponds to operation at the 10 W

level with a high flow rate. The loss is only 0.24% of 10 W. At lower power

levels it is best not to reduce the flow rate proportionately, but to use as high a flow rate as possible, consistent with adequate resolution, a rule that

will also minimize the response time. The difference in the radiant power

loss from the two vessels is much less than that calculated above. The net error is estimated to be no greater than ± 0.1%.

5. ELECTRICAL FEEDBACK AND CONTROL

5 . 1 Power Feedback

The difference between the temperatures of the matched sensing elements

in the two vessels produces a voltage which is amplified to develop electrical

power for dissipation in one vessel that is very nearly equal to the power

dissipated in the other vessel. Feedback is relatively prompt, and the system

responds rapidly to reduce the difference in power. Wholey and Boff [10]

discuss the effect of loop gain in. a feedback calorimetric system. If the

effective loop gain is large compared to unity, the powers in both vessels

become nearly equal. In a power feedback system with power-to-voltage sensors

and constant voltage gain in the amplifiers, the voltage feedback ratio and

loop gain under static conditions are not constant, but are proportional to

the voltage developed across the electrical load. To reduce this variation in

the loop gain, the amplifier is modified as noted below.

For a non-inverting feedback amplifier with open-loop gain A and input

voltage e , the voltage fed back to the amplifier inverting input is e

f = 6Vf where 3 is the voltage feedback ratio. The net amplifier input is e = e - e_.

16
and the amplifier output (heater) voltage is Vf = Ae = Ae - AgVf

. The loop

gain is A3, and the closed-loop gain is

V

f /ex

= A/(l + A3) = (l/3)/(l + 1/A3).

For the moment, assume that there are no heat-distribution errors; i.e.,

heat losses in the two vessels are presumed equal, and assume that A is

constant for all power levels. P is the power developed in the test vessel,

2 2 x

P

f = Vf /Rf = If:Rf is the feedback power developed in the feedback resistance

load, R.p, in the other vessel, e and e f are the voltages developed from the

H X I thermal sensors in the streams from the vessels, and the power/voltage

sensitivity factors are defined by S = P /e and S_ = P^/e^. Then

~ X X X I I t e

f = V^/Rf S

f and 3 = e

f /Vf = Pf /Vf S

f = Vf /Rf Sf = /Pf /R

f /Sf = I f/Sf

. The

closed-loop voltage gain can be written

(P

f /BS

f )/(P

x/S

x

) = (l/3)/d + 1/A3)

and from this the power ratio is

P

f/P

x

= (S

f /S

x )/(1 + 1/A3) = 1/GK = 1/J

where G = 1 + 1/A3 is the gain correction factor, K = S /S f is the sensitivity

ratio factor, and J = KG is a correction factor. As the power level is decreased, the gain error 1/A3 , increases.

As constructed, the open-loop gain is modified by a square-rooter circuit

in the amplifier. This has the desirable effect of making the gain error

small and constant for all measurement power levels when operation is within

the functional range of the amplifier and square-root circuit. The square

root function deteriorates only at very low power levels. The small error is

corrected by application of the correction factor J. The response time in automatic operation is about 4 minutes for 99.9%

response.

5 . 2 Temperature Bridge

The temperature measurement and control system used in the calorimeter is

based on a bridge with inductively coupled ratio arms [12]. This approach

provides the best stability and sensitivity by eliminating the effects of

thermal electromotive forces and by relying upon the inherent ratio stability

of an inductive voltage divider.

The electrical circuitry (see figure 3) may be divided into several

functional blocks for easier understanding: (1) the bridge; (2) oscillator;

(3) preamplifier and bandpass filter; (4) post amplifier; (5) power amplifier;

and (6) auxiliary circuits.

17
All controls used in normal measurements are located on the front panel

of the electrical control unit. The exceptions to this are the pump speed and

direction controls located in a separate box and the phase balance variable

capacitor which is accessible on the rear of the chassis. Most connectors are

on the rear of the chassis. Exceptions are the connectors for the voltmeter

and an external detector (optional) which are located on the front panel.

Connectors and adapters forming a coaxial link between the internal oscillator

and the bridge circuit are located on the chassis. The link can be disconnected to permit use of an external oscillator (manual operation only) , or a T-adapter can be inserted to provide access to the internal oscillator voltage

for use as a reference for an external detector, if desired.

The inductive branch of the bridge comprises T2 and T3 ; the two temperature dependent resistance sensors make up the other branch. Excitation is

coupled from the oscillator through Tl , and the unbalanced signal is coupled

out to the preamplifier through T4

.

The 1000 Hz bridge oscillator supplies 7.5 volts to a 18:1 step-down

voltage transformer, Tl , from which 0.4 volts is supplied to the sensor bridge.

The bridge consists of the two sensors, the phase balance capacitors, the

402:2 step-down inductive voltage divider, T2 , and the multi-decade inductive

voltage divider, T3 . T3 has a least count of ratio (1 division on the lowest

dial) of 1 x 10 . T2 and T3 are connected so that the least count on the

inductive voltage divider, T3, which is used as the N (null) BALANCE adjust-

— 8 ment, is equivalent to a change of bridge ratio of 5 x 10 . The sensors are nickel-iron resistance thermometers having a resistance R = 676 ohms at 25°C,

— 1 —8

and AR/AT = 3 fi«K .A change of 5 x 10 in the bridge ratio would occur if one sensor changed resistance by 0.14 x 10 ohm. This is equivalent to

47 x 10

} K. At the normal flow rate, the absorbing liquid exhibits a temperature rise per unit power of AT/P = 0.4 K-W (measured value) hence, the least

count on the N BALANCE inductive voltage divider corresponds to a power of

about 0.12 x 10~ 3 W.

The bridge output signal is amplified and detected by a synchronous

detector to yield a positive or negative voltage to drive the null indicator.

A SENSITIVITY control is provided for changing the gain of the amplifier when

it is used as a null amplifier (e.g., in manual operation). In automatic

operation, when the detector voltage is positive (only) it also controls a d-c

amplifier which drives a follower and the B, or A, heater, as selected by the

MAIN POWER rotary switch. The follower can be controlled manually by the MAIN

LEVEL SET control when the AUTO-MAN switch is in the MAN position. Similarly,

the AUXILIARY LEVEL SET control can drive the B, A, A' , or A" heaters as selected by the AUXILIARY POWER rotary switch. This switch is electrically

interconnected to the MAIN POWER rotary switch so as to prevent the simultaneous application of power to one heater from both power sources. When the
MAIN POWER rotary switch is placed in the N position, both power sources are disconnected from the heaters so that the N BALANCE control can be adjusted to

balance the bridge.

5 . 3 Bridge Electronics

The oscillator module, Yl , simultaneously generates stable, low-distortion

sine and cosine waveforms at 1000 Hz. The cosine output is used as the reference

waveform for the in-phase detector that provides a dc output proportional to the

resistive unbalance of the sensing bridge. The sine output is similarly used as the reference for the phase detector which provides a dc output proportional

to the reactive unbalance. The frequency of the oscillator can be adjusted by

selection of R21 and R22. R23 is selected to provide the proper output amplitude.

The preamplifier is a very low noise integrated circuit optimized for the

amplification of nanovolt signals from the particular source resistance presented by the sensing bridge. Amplifier AR1 provides approximately 60 dB of

gain. The dc output voltage at pin 7 of AR1 is set to 7.5 volts by means of

R3 . Diodes Dl and D2 provide a clamping action for signals large enough to

overload the amplifier. The noise performance of the preamplifier is close to

the theoretical limit; the spot noise figure is 2.0 dB at 1 kHz.

The bandpass assembly, FLl , is a 2-pole state-variable filter with a center frequency of 1 kHz and Q of 10. It provides a voltage gain of 20 dB.

The center frequency of the filter is adjusted by tuning ganged controls R9

and Rll. Tuning is best accomplished by initially adjusting R9 and Rll for zero phase shift through the filter, as indicated by a Lissajous pattern on an oscilloscope. Final trim adjustments can then be made by observing the

indication of the balance meter with switch SI in POWER position while slightly

upsetting the adjustment of CI. The principle here is that small quadrature

signals can be deliberately generated by varying CI while adjusting the tuning

of the bandpass filter such that these signals produce no output from the

power detector, Ul . This insures that residual phase shifts in the transformers, etc., have been properly compensated by equal and opposite phase

shifts introduced by a slight detuning of the bandpass filter. The effect of

the detuning on the gain of the filter is negligible, and the setting is

stable.

A post-amplifier, A3, provides up to an additional 60 dB of AC gain after

the filter and allows for front panel adjustment of the servo sensitivity in

the MANUAL mode. In the AUTO mode, R27A may be adjusted to provide maximum

gain without servo instability (typically 34 dB)

19
The amplified error signal from AR3 is applied to two 4-quadrant analog

multipliers which serve as phase-sensitive detectors for both the in-phase and

quadrature components of the amplified error signal. The in-phase detector,

Ul , is driven by the cosine output of the 2-phase oscillator, Yl . The output

of the multiplier consists of the product of two sinusoids of the same frequency and therefore contains a dc component proportional to the amplitude of

each and to the cosine of the phase difference between them. The dc component

is taken through a lowpass single-pole filter, controlled by the TIME CONSTANT

switch. Finally, buffer amplifier AR4 isolates the lowpass filter from the

following circuitry and provides an additional 16 dB of gain. The detected

error signal from AR4 is clamped by AR6 to permit positive values only.

The error signal from the sensing bridge is proportional to the temperature difference between the two sensors, and the output signal from the phase

detector is a linear function of the temperature difference. However, when

the feedback loop is closed in automatic operation, the power in the heater is

proportional to the square of the voltage across it. Therefore, in order to

make the servo loop gain a constant, independent of the signal level, it is

necessary to extract the square root of the amplified error signal before

applying it to the heater. A small dc offset provided by AR7 prevents the

gain of the square rooter, U3 , from approaching infinity at low signal levels.

The dc offset is then removed by AR8 and the signal is presented to the power

amplifier which drives the heater. The power amplifier comprises AR9 , Q2 , and

Q3.

The second phase detector, U2 , performs in the same manner except that it

is driven by the sine output of oscillator Yl . It provides a dc signal which

is proportional to the reactive unbalance in the sensing bridge. By setting

switch SI to the QUAD position, the signal may be nulled by trimming CI and C2

.

If overloading occurs in the amplifier, the response time may be lengthened

significantly. A circuit to indicate overload was incorporated to notify the

operator to change the time constant control to compensate. The ac signal

from the bandpass filter, FLl , is rectified by D3 and compared with a dc level

set by R20. The comparator AR2 will cause a front panel overload lamp to

light if the amplitude is high enough to cause overload in the servo. A null meter is necessary to permit initial balance of the bridge before

automatic operation, or for full manual operation. The null meter amplifier,

AR5 , drives a front panel zero-center indicator with approximate logarithmic

response provided by diodes D4 and D5 . The input to the meter circuitry is

selected by a front panel switch SI.

20
5 . 4 Metering Circuits

The 1-ohm precision , resistor in the output of the auxiliary power supply

is used with a digital voltmeter to convert the voltage readings to current

readings, in amperes. It is connected to the circuit as a 4-terminal resistance. It can be removed, and measured by ordinary resistance measurement

methods, and the voltmeter can be calibrated by ordinary potentiometric

methods, in an electrical measurements laboratory.

The digital voltmeter (DVM) circuit is arranged so that a digital d-c

voltmeter can be switched to measure the voltage applied to any heater (B, A,

A', or A"), or the current supplied by the auxiliary power supply by measuring

the voltage across a precision 1-ohm resistor which carries the current. This

permits the measurement of both voltage and current for any heater, the resistance of which can then be calculated. The precision 1-ohm resistor has been

adjusted to 1.0000 ohm ± 0.05%. The voltmeter supplied with the system is

accurate within ± 0.05% ± 2 digits. In the worst case, when the reading is

1.000, the full range of the meter is not being used and the 2-digit limits

are equivalent to ± 0.2%. In the measurement of the heater resistance, the

voltage can be adjusted to obtain nearly full-scale voltmeter readings that

minimize the effect of the ± 2 digit uncertainty. Two readings are required,

and the net error in calculated heater resistance is estimated as ± 0.1%.

Electrical power is calculated by squaring the heater voltage and dividing by

the heater resistance; therefore, in the worst case, the measured electrical

power could be in error by ± 0.6%, but in most cases is much less.

6. OPERATIONAL PROCEDURES

6 . 1 Preliminary Procedures

Prior to using the calorimeter, the system should be purged of bubbles.

Bubble traps have been incorporated in the design of the calorimeter to prevent

bubbles from entering the vessels during operation. Bubbles that occur in the

system can be eliminated by manipulation of the rubber tubing and by reverse operation of the pumps whenever necessary, usually about once a day, before

operation.

Next, the normal pressure on the membranes is adjusted by opening the

reservoir clamps and adjusting the height of the reservoir until both membranes

are slightly convex upward, and then closing the clamps.

The transducer to be tested is then mounted over one of the vessels using

simple brackets and an adapter-spacer. The adapter-spacer must be used to

center the transducer in the water well over the vessel, to keep it from being

pushed into the membrane, and to keep water flowing under the transducer to flush

away heat developed at the face of the transducer. The spacer also assures a

21
definite placement of the transducer so that the coupling-loss correction factor

can be determined with adequate accuracy, and so that the beam is aligned with

the axis of the vessel. A set of adapter-spacers with beveled inside edges was constructed to accommodate most circular transducers. A transparent disk is

placed over the other vessel to control the flow of coupling liquid (water)

.

6 . 2 Precautions

At high power levels, the onset of cavitation is a limit to the power that can be measured accurately by the calorimeter. For a transducer near the

surface of water, gaseous cavitation can occur if the acoustical pressure

5 exceeds the ambient (atmospheric) pressure which is about 1.0 x 10 Pa at sea

ft 2—1

level. The intensity in water (p c = 1.5 x 10 kg»m »s ) corresponding to a value of peak pressure equal to that of the ambient pressure is given by

I = p

2 /2p c = 3.3 x 10 3 W-rn"2

With the power evenly distributed over the useful area of the calorimeter port

2 (about 5 cm ) the maximum cw power that can be measured without risking cavitation is about 1.7 W. For transducers having an area smaller than the calorimeter port area, the maximum power without cavitation would be smaller than

this. However, with pulsed waveform, somewhat larger power can be used without

cavitation occurring. If there is any question whether cavitation will occur

in a specific case, a separate test should be made to determine the maximum

excitation to the transducer that can be used without cavitation. The troublesome region for cavitation in the calorimeter is immediately in front of the

transducer. Beyond this region the ultrasound is attenuated, and cavitation is

not so likely to occur. At very low power levels it is necessary to minimize drift in the calorimeter

by placing a plastic sheet or cover over the bath after mounting the transducer.

To avoid errors caused by the small reflections in the vessel, it is good

practice to gently rock the transducer a few degrees during the last minute of

the test.

6 . 3 Ultrasonic Power Measurements

For automatic operation of the calorimeter the system must be balanced

prior to the application of ultrasonic power. This is accomplished by adjusting the null balance control in the electrical control unit. Then, the

ultrasonic transducer can be energized. In automatic operation, the system

will attain equilibrium in 3 to 4 minutes. The voltage across the electrical

heater, V^^ , is then read and recorded. The feedback electrical power is then

2 calculated from the formula P = V„n /R_ , where FL is the resistance of the

22
B heater. The ultrasonic power in vessel A is

P UA = P FBJHCFL

where J = GK, G is the gain correction factor in the feedback circuit, K is the

sensitivity ratio factor, H is the heat-distribution correction factor, C is the

coupling-loss correction factor, F is a frequency dependent correction factor,

and L is a transducer loss correction factor. These factors are discussed below.

6 . 4 Determination of the J, K, and G Factors

It is desirable that the power/voltage sensitivities, S-. and S D , of the a a temperature sensors be matched such that the ratio, K, of these sensitivities

is constant for all power levels and flow rates. However, the sensor sensitivities may vary independently to some extent, especially as a function of flow

rate, because of slight differences in construction. Also, the gain correction

factor, G, is a function of power level. The values of K and G and J = KG at

any flow rate and power level combination, as typically used in a test of a transducer, can be determined by the following procedure. Transparent cover disks are placed in both vessels A and B. After a few minutes, adjust the null

balance control to obtain an initial balance. Increase the electrical power,

P , to obtain the desired feedback power, P , about equal to that used in

the test. After equilibrium is again obtained, the feedback voltage is read

and recorded, and P„_ is calculated. Then, J = P^/P^. r £} ISA r a

7. EQUATIONS OF OPERATION

With ultrasonic power, P , and also some electrical power, P (included

UA FjI\ for generality) in the A vessel, the power sensed by the A sensor is

PA

- PUA/HA

CA

+ P EA

where P is the ultrasonic beam power emitted by the transducer, C is the

coupling-loss correction factor, H is the heat-distribution correction factor.

The A sensor power/voltage sensitivity is

SA

= VeA

where e is the voltage developed by the bridge circuit applied to the feedback

amplifier as a result of power P A (with P = 0)

a a In vessel B, the power sensed by the B sensor is (in general)

PB

= WH

B

CB

+ PEB

The B sensor power/voltage sensitivity is

SB

= W

23
When feedback power, P , is applied to the heater in vessel B,

p = p EB FB

At equilibrium, in normal operation (Prm = 0) UB

eA

= eFBG

where e^ is the bridge voltage developed as a result of the feedback power

alone, and G = 1 + 1/A3 is the gain correction factor for the automatic feedback circuit. Then

VSA

= P FBG/ S B

or

PA

= PFBGK

where K = S A /S D . The equation for automatic operation is

PUA = (P FBGK " P EA )HA

C

A- The equation for manual operation is

P =(P K-P )HC. UA k EB EA; A^A

A correction factor, F, is applied to correct for certain systematic

errors described previously that are either constant or a function of the

ultrasonic frequency (in megahertz)

F = 1 - 0.003 + 0.004/f + 0.0005 f + 0.00025 f

= 1 - 0.003 + 0.004/f + 0.00075 f

The first correction term (F, = -0.003) accounts for the evaluation heater

2 (I R) lead-wire losses. The second correction term (F~ = 0.004/f) accounts for

the reflection loss from solids in the vessel. The third correction term

(F, = 0.0005 f) accounts for heat conduction loss through the membrane. The

fourth correction term (F. = 0.00025 f) accounts for the loss in the membrane

by absorption of ultrasonic energy.

A correction, L, for heat loss from the test transducer can be applied.

For solid-backed ceramic transducers L = 0.993, and for air-backed quartz

transducers L = 0.999.

The full equation for automatic operation is

PUA = (PFBGK " PEA )HA

CA

FL =(P FBJ " P EA )

H

A

CA

FL

where J = GK. For manual operation, the full equation is

PUA= (PEBK " PEA )HA

CA

FL -

24
If the ultrasound is introduced into the B vessel and electrical power is

applied manually to the A vessel, the equations above must be modified by

exchanging the symbols A and B in the subscripts, including the equation for K (thus, K = Sg/S, in this mode of operation) . The corrections H and C are applied in the same manner as for normal operation, because the vessels are essentially identical. If automatic operation is desired, with electrical

feedback into the A vessel, switch the AUTO switch (at the rear of the chassis)

to the A position. This switch reverses the phase of the signal from the

oscillator to the sensor bridge so that the bridge output signal will produce

proper operation of the phase sensitive detector.

Two ultrasonic beams can be compared simultaneously by placing one transducer over the A vessel and the other over the B vessel. First, a null balance

is obtained with the beams off. Then, with both beams on, one of them can be

adjusted to regain equilibrium. If no electrical power is used in either

vessel,

pua = p ubkhacafaVh

b

cb

f

blb

where K = S-/S,,. If electrical power is manually added to the vessel having

the smallest ultrasonic power, the unknown power can be determined by solving

the equation

P UA/HACAFA

LA

+ PEA = K (P UB

/H

B

C BF

BL

B

+ P EB )

8 . SUMMARY OF MEASUREMENT UNCERTAINTIES

Elementary sources of error in the calibration and use of the calorimeter

have been discussed in the foregoing text. A summary of these error sources,

with estimates of the magnitude of the possible errors, is given in table 1.

Only those sources of error that are believed to contribute in excess of 0.1% are listed. These estimates are based on a limited set of experiments. It

must be recognized that such limits are subjective and are not strict bounds.

A component of uncertainty from system noise and drift has been included in the

table to account for changes in the system characteristics during a test and

calibration. Credible limits of systematic error are believed to be ± 2.5%

from 1 to 10 MHz, and ± 3% from 10 MHz to 15 MHz; the standard deviation of

random errors has been found to be about 1.5%. The sum of the limits of

systematic error and 3 times the standard deviation is about ± 8%.

Accuracy of the calorimetric measuremt-tts depends also on the stability of

the beam power from the transducer under test. The uncertainties shown in the

table do not include effects of drifts or random variations during the test

from, or within, the device under test.

25
9 . ACKNOWLEDGMENTS

This project was supported in part by the Acoustics Branch, Division of

Electronics Products, Bureau of Radiological Health, Food and Drug Administration. The authors thank H.F. Stewart and B.A. Herman of that agency for their

advice and support. Within the National Bureau of Standards, the authors thank

P. A. Hudson and M.C. Jones for their technical advice and suggestions,

V. Lecinski for numerous mechanical drawings, W.G. Layne and W.T. Roberts for

fabrication of the mechanical parts

.

26
10. REFERENCES

[I] Gunn, S.R. , Radiometric calorimetry : a review, Nuclear Instruments and

Methods 29, 1-24 (1964) .

[2] Gunn, S.R., Radiometric calorimetry: a review, (1970 supplement),

Nuclear Instruments and Methods 8J3_, 285-312 (1970) .

[3] Gunn, S.R. , Calorimetric measurements of laser energy and power,

J. Phys. E: Sci . Instrum. 6, 105-114 (1973).

[4] Wells, P.N.T. Bullen, M.A. , Follett, D.H., Freundlich, H.F. and

James, J. Angell, The dosimetry of small ultrasonic beams, Ultrasonics,

106-110 (1963)

.

[5] Sokollu, A. , Absolute measurement of total radiated power of ultrasonic

transducers for biomedical use, Bulletin du Laboratoire d'Electroacoustique,

Unlversite de Liege 9, 23-27 (April 1966)

.

[6] Zieniuk, J.K., Ultrasonic thermoprobe , Ultrasonics, 136-137 (July 1966).

[7] Jones, J.B. , A calorimetric method and apparatus for evaluating transducer

assemblies, IEEE Trans, on Sonics and Ultrasonics SU-16 , 76-78 (April 1969).

[8] Zieniuk, J.K. and Evans, B. , The influence of thermal parameters on making

ultrasonic power measurements by a calorimetric method, Acustica 2_5_ 47-52 (1971)

.

[9] Gunn, S.R. High capacity radiometric calorimeters, U.S. Atomic Energy

Commission, UCRL-5375 (1958)

.

[10] Wholey, B. and Boff, F. , Improvements in microwave power measurements

through the use of feedback, IRE Proceedings, Pt. B., Supp. No. 23,

740-743 (1962)

.

[II] Ginnings, D.C. and West, E.D., Heater lead problem in calorimetry, Rev.

Sci. Instruments 3_5, No. 8, 965-967 (August 1964).

[12] Larsen, N.T., 50 Microdegree temperature controller, Review of Scientific

Instruments 39, No. 1, 1-12 (January 1968).

27
Table 1. Summary of estimated uncertainties.

Source of Error

Uncertainty (limits of error)

Ultrasonic Frequency

1 MHz 5 MHz 10 MHz 15 MHz

I. SYSTEMATIC ERROR LIMITS

1. Reflection loss from solids (F2)

2

.

Sensor ratio (J or K) correction

3

.

Sensor element mismatch

4

.

Sensor laminar flow dependency

5. Evaluation heater lead-wire loss (Fl)

6. Evaluation heater lead-wire power

7. Coupling loss (C) correction

8. Lossy transducer heat (L) correction

9. Loss in membrane (F4)

10. Loss through membrane by conduction (F3)

11. Heat-distribution (H) correction

12. Radiant power loss mismatch

13. Electrical power (P^) measurement

± 0.1 ± 0.1 0.0 0.0

+0.5 ±0.5 ±0.5 ±0.5

± 0.1 ± 0.1 ± 0.1 ± 0.1

±1 ±1 ±1 ±1

± 0.1 ± 0.1 ± 0.1 ± 0.1

± 0.1 ± 0.1 ± 0.1 ± 0.1

± 0.0 ± 0.1 ± 0.5 ± 1

± 0.3 ± 0.3 ± 0.3 ± 0.3

0.0 0.0 ± 0.1 + 0.2

0.0 ± 0.1 ± 0.2 ± 0.3

± 0.5 + 0.5 ± 0.5 ± 0.5

± 0.1 ± 0.1 ± 0.1 ± 0.1

±0.6 ±0.6 ±0.6 ±0.6

II. RANDOM ERRORS

Noise and drift (std. dev. - 1.5% + 0.2 mW)

Systematic ± Eu

± /ZTP"

Credible

+ 3.4 ± 3.6 ± 4.1 ± 4.8

±1.4 ±1.4 ±1.5 ±1.8

± 2.5 ± 2.5 ± 2.5 ± 3.0

Random (a = 1.5% + 0.2 mW)
Figure 1. The NBS ultrasonic calorimeter, showing the electrical

control unit, the twin, series-flow comparator in a water bath, pumps, and electrical power supply.

29
ULTRASONIC TRANSDUCER

CALORIMETRIC VESSELS

Figure 2. Schematic diagram of the twin, series-flow

ultrasonic comparator.

30
n il

1.1= H*

2_i afc o ^s 5|S o o S3

«3 3 SSi

3LU

Mil- 5&?

HP ?1>!

31
NBS-114A (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBS Tech Note No. 686

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Ultrasonic Calorimeter for Beam Power Measurements

5. Publication Date September 1976

6. Performing Organization Code

276

7. author(S) Thomas L. Zapf, Morris E. Harvey, Neil T. Larsen

and Robert E. Stoltenberg

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. 2762111

11. Contract/Grant No.

1 2. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP) Sponsored in part by:

Acoustics Branch

Division of Electronic Products

Bureau of Radiological Health

Food and Drug Administration

13. Type of Report & Period

Covered

t4.. Soon soring Agency Code nteragency 6 Agreement

FDA 224-74-6038

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.)

An ultrasonic calorimeter has been designed and constructed at the National

Bureau of Standards for the measurement of beam power up to a few watts from ultrasonic transducers. The calorimeter, described as a twin, series flow, ultrasonic

calorimetric comparator, operates in the frequency range from 1 to 15 MHz with un- certainties less than ± (7% +0.2 mW) . Twin vessels are provided so that thermal

effects of an ultrasonic sound beam absorbed in one vessel can be compared rapidly

with accurately measured dc electrical power in the other vessel. Absorbing liquid

enters each vessel near the ultrasonic input port. The temperatures of the absorbing

liquid at the input ports are equalized by a heat exchanger, and the mass-flow rates are the same in both vessels. Twin temperature sensors, located in the output flow

from the vessels, are connected in an electrical bridge circuit. In automatic operatioi

the bridge is connected to a feedback circuit. With ultrasonic power introduced into

one vessel, the feedback circuit promptly applies power to an electrical heater in the

other vessel to regain bridge balance. The ultrasonic power then equals the measured

dc power corrected for known errors.

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)

Calorimeter; ultrasonic calorimeter; ultrasonic power measurements.

18. AVAILABILITY (x_ Unlimited

2 For Official Distribution. Do Not Release to NTIS

"~

' Order From Sup. of Doc, U.S. Government Printing Office

_ Washington, D.C. 20402, SD Cat. No. C13

| X! Order From National Technical Information Service (NTIS)

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