AlllDE S777TM

NATL INST OF STANDARDS & TECH R.I.C.

A1 11 02577794

Gelst, Jon/A water bath black body for fh QC100 .U5753 N0.1228 1986 C.2 NBS-PUB-C PUBLICATIONS

NBS Technical Note 1228

L Water Bath Blackbody for the

5 to 60°C Temperature Range:

Performance Goal, Design Concept,

and Test Results

n Geist and Joel B. Fowler

'BS NBS NBS NBS NBS NBS NBS NBS NBS NBS /

NBS NBS NBS NBS NBS NBS NBS NBS NBS NB.

'BS NBS NBS NBS NBS NBS NBS NBS NBS NBS I

NBS NBS NBS NBS NBS NBS NBS NBS NBS NB.

'BS NBS NBS NBS NBS NBS NBS NBS NBS NBS ' : NBS NBS NBS NBS NBS NBS NBS NBS NBS NB.

NBS NBS NBS NBS NBS NBS NBS NBS NBSNB

BS NBS NBS NBS NBS NBi: 'NB.

'

?5 NBS NBS NBS NBS NBS NBS NBS NBS NBS NB

NBS NBS NBS National Bureau ofStandards \

NBS NBS NBS iVz^5 NBS NBS NB:^ NBS NBS NB,

' ¥RS NBS NBS NBS NBS NBS.NBS NBS l E NBS NBS NBS NBS NBS NBS NBS NBSNB.

QC

ion

115753

#1228

1986

C. 2

^^K9mHa^s\

NBS NBS NBS NBS NBS NBS NBS NBS NB,
M he National Bureau of Standards' was established by an act of Congress on March 3, 1901. The

JP 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 research and provides: (1) a

basis for the nation's physical measurement system, (2) scientific and technological services for industry and

government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety.

The Bureau's technical work is performed by the National Measurement Laboratory, the National

Engineering Laboratory, the Institute for Computer Sciences and Technology, and the Institute for Materials

Science and Engineering

.

The National Measurement Laboratory

Provides the national system of physical and chemical measurement;

coordinates the system with measurement systems of other nations and

furnishes essential services leading to accurate and uniform physical and

chemical measurement throughout the Nation's scientific community, in- dustry, and commerce; provides advisory and research services to other Government agencies; conducts physical and chemical research; develops,

produces, and distributes Standard Reference Materials; and provides

calibration services. The Laboratory consists of the following centers:

Basic Standards^

Radiation Research

Chemical Physics

Analytical Chemistry

TTte National Engineering Laboratory

Provides technology and technical services to the public and private sectors to address national needs and to solve national problems; conducts research in engineering and applied science in support of these efforts; builds and maintains competence in the necessary disciplines required to carry out this research and technical service; develops engineering data and measurement

capabilities; provides engineering measurement traceability services; develops

test methods and proposes engineering standards and code changes; develops

and proposes new engineering practices; and develops and improves

mechanisms to transfer results of its research to the ultimate user. The

Laboratory consists of the following centers:

Applied Mathematics

Electronics and Electrical Engineering'^

Manufacturing Engineering

Building Technology

Fire Research

Chemical Engineering^

The Institute for Computer Sciences and Technology

Conducts research and provides scientific and technical services to aid Federal agencies in the selection, acquisition, application, and use of computer technology to improve effectiveness and economy in Government

operations in accordance with Public Law 89-306 (40 U.S.C. 759), relevant Executive Orders, and other directives; carries out this mission by managing

the Federal Information Processing Standards Prograim, developing Federal ADP standards guidelines, and managing Federal participation in ADP

voluntary standardization activities; provides scientific and technological advisory services and assistance to Federal agencies; and provides the technical foundation for computer-related policies of the Federal Government. The Institute consists of the following centers:

Programming Science and

Technology

Computer Systems

Engineering

The Institute for Materials Science and Engineering

Conducts research and provides measurements, data, standards, reference

materials, quantitative understanding and other technical information fundamental to the processing, structure, properties and performance of materials; addresses the scientific basis for new advanced materials technologies; plans

research around cross-country scientific themes such as nondestructive

evaluation and phase diagram development; oversees Bureau-wide technical programs in nuclear reactor radiation research and nondestructive evaluation; and broadly disseminates generic technical information resulting from

its programs. The Institute consists of the following Divisions:

Ceramics

Fracture and Deformation ^ Polymers

Metallurgy

Reactor Radiation

'Headquarters and Laboratories at Gaithersburg, MD, unless otherwise noted; mailing address Gaithersburg, MD 20899. 'Some divisions within the center are located at Boulder, CO 80303. 'Located at Boulder, CO, with some elements at Gaithersburg, MD.
NBS

RESEARCH

INFORMATION CENTER

Ctdoo

NBS Technical Note 1228

A Water Bath Blackbody for the

5 to 60''C Temperature Range:

Performance Goal, Design Concept,

and Test Results

Jon Geist and Joel B. Fowler

National Bureau of Standards

Gaithersburg, Maryland 20899

Sponsored by:

Newark Air Force Station Newark, OH 43057-5475

Issued October 1986

M^

U.S. Dqiaitmait of Commerce

Malcolm Baldrige, Secretary National Bureau of Standards

Ernest Ambler, Director
National Bureau of Standards U.S. Government Printing Office For sale by the Superintendent

Technical Note 1228 Washington: 1986 of Documents,

Natl. Bur. Stand. (U.S.), U.S. Government Printing Office,

Tech. Note 1228, Washington, DC 20402

21 pages (Oct. 1986)

CODEN: NBTNAE
Table of Contents

Page

1. Introduction 1

2. Design Concept 3

2.1 Mechanical design 3

2.2 Control and measurement 4

2.3 Temperature measurement uncertainties 5

3. Blackbody Quality 6

3.1 Cavity emissivity 7

3.2 Temperature distribution over interior of cavity 8

3.2.1 Temperature uniformity in water surrounding cavity 9

3.2.2 Temperature drop at lip of cavity 11

3.2.3 Temperature drop across cavity wall and paint 12

3.3 Overall estimate of blackbody quality 14

Acknowledgment 16

References 16

List of Figures

Figure 1. Cut-away view of water bath emphasizing changes made to use it as a

near ambient blackbody standard 3

Figure 2. Block diagram of control and measurement subsystems of water bath

blackbody 4

Figure 3. Details of cavity design affecting blackbody quality 7

Figure 4. Configuration of water bath cover specially made for measuring the

variation in temperature in the water surrounding the cavity 10

Figure 5. Temperature differences measured at different locations in cavity

chamber in water bath blackbody 10

Figure 6. Configuration of water bath blackbody for measurement of temperature

drop at lip of cavity 11

Figure 7. The uncertainty in the quality of the water bath blackbody 15

111
Page

List of Tables

Table 1. Uncertainty in the measured temperature of the water in the water bath

as a function of temperature over the operating range of the water bath

blackbody 6

Table 2. Test thermistor corrections at 5, 30, and 60° C 9

Table 3. Values of parameters used to calculate AT from eq (6) 13

Table 4. The calculated variation in the temperature drop AT across the wall of

the cavity and the black paint on the conical section of the cavity where

it intersects the cylindrical section, as a function of water bath

temperature To 13

Table 5. Parameters for use in calculating the quality and the uncertainty in the

quality of the water bath blackbody from eq (l) 14

IV
A WATER BATH BLACKBODY FOR THE 5 TO 60°C TEMPERATURE RANGE:

PERFORMANCE GOAL, DESIGN CONCEPT, AND TEST RESULTS

Jon Geist and Joel B. Fowler

National Bureau of Standards

Gaithersburg, Maryland 20899

Abstract

A water bath blackbody has been built under contract for the Electromagnetic Metrology Engineering Branch at Newark Air Force Station. The performance goal Wcis a large-area, self-calibrating, high-accuracy blackbody

covering the majority of the liquid water temperature range. With the ex- ception of self-calibration, these goals were met. This report describes both

the conceptual design of the water bath blackbody and the results of the

tests that were carried out to characterize the performance of the actual water bath blackbody that was built for Newark Air Force Station. The details

of the construction and operation of that water bath blackbody are described

in a companion report.

Key words: blackbody; blackbody standard; high-accuracy blackbody; large- area blackbody; room-temperature blackbody; water bath blackbody.

1. Litroduction

Since the early 1970s, there has been a need within DOD for a low-temperature blackbody

calibration source accurate to within a few tens of mK in the ambient temperature range.

As a first step in this direction, NBS designed and built a low-temperature reference

blackbody standard and infrared broad band radiometer with an effective wavelength of

about 10 fim. for near ambient radiation. The original design goal required a temperature

range from -40° C to 300° C at whatever accuracy could be achieved by applying the existing

NBS high-temperature blackbody technology to this lower temperature range. The original

approach consisted of a thin walled graphite cavity in intimate contact with a massive

copper cylinder that surrounded the cavity to minimize temperature gradients over the

cavity interior. The cylinder was provided with a number of thermocouples measuring

its temperature at different locations, and was mounted in a multiple winding furnace to

allow better control of any gradients that might be detected.

The first blackbody was constructed in 1975, and estimated to be accurate to ±500 mK

on the basis of the characterization studies performed at that time. In 1982, construction

of a duplicate was initiated, but problems with eissuring the intimate contact between

the graphite crucible and the surrounding copper cylinder were encountered, and it was

not completed until 1984. The second blackbody was compared with the first blackbody

over the temperature range from 0°C to 40° C. At room temperature, the two blackbodies

produced the same radiance at a wavelength of 10 /zm when set to the same temperature,
but at 40° C, they had to be set at temperatures that differed by 200 mK in order to

produce the same radiance. While this result is much better than the initial accuracy

estimate, it is much worse than the few tens of mK required by some DOD programs.

In attempting to find a solution to this problem, it was noted that neither of these blackbodies was ever calibrated by NBS outside the range from 0°C to 40° C. Therefore, it was

proposed that NBS develop a new high-accuracy standard for this limited range based

upon a temperature-controlled water bath.

Such a device promised other advantages besides improved temperature accuracy. A large- area aperture (for example, a few inches) would not significantly degrade the accuracy of

such a device, provided that the interior of the cavity was coated with a specular black

paint. The latter appeared to be feasible with a cavity that would never be used above

100° C. So the water bath blackbody could have a much larger aperture than the copper

blackbodies.

The advantage of a large aperture is that it allows direct measurement and correction of

size of source errors affecting the radiometer, if such exist. Once these are determined or found to be negligible, then the large aperture allows self-calibration of the radiometric

errors affecting the blackbody itself.

Also, measurements of the variation in radiance as a function of position over the interior

of the blackbody cavity would provide the data needed to determine corrections and limits

of error associated with temperature gradients in the cavity. Similarly, measurements of

the variation in radiance with aperture size for a set of infrared reflecting cavity covers with various size apertures would provide the data needed to determine corrections and

limits of error associated with the reflectance of the cavity walls.

It was also proposed to enhance the self-calibration capability of the water bath blackbody

by adding temperature self-calibration based on the ice, the gallium, and the succinonitrile

freezing points, since calibration cells containing the latter materials in very pure form are

available from NBS as Standard Reference Materials. The use of these freezing point standards was found to be more complicated than originally anticipated, and implementation

of this aspect of self-calibration was postponed as a possible future project.

The water bath blackbody constructed on this project has an aperture of about 4 in. in

diameter. Nonradiometric measurements indicate that it is uniform in temperature to

better than ±15 mK over at least the bottom half of its aperture. The thermistor used to

measure the water bath temperature is accurate to within a few mK provided that it is recalibrated periodically. The measurement instrumentation and software for calculating

the temperature as a function of resistance that are provided with the blackbody are accurate to within 10 mK. Radiometric testing will most likely show that the cavity is uniform in temperature over all of its aperture to a much tighter tolerance than listed

above.

The remainder of this report describes the design principles for converting a water bath

into a blackbody, the results of tests and analyses that verify the radiometric quality of
the blackbody, and the nature of the modifications made to the water bath to use it as a high-accuracy blackbody near ambient temperature.

2. Design Concept

2.1 Mechanical design

The design concept for the water bath blackbody is illustrated in figure 1, which shows a cut-away view of a temperature-controlled water bath with a blackbody cavity mounted

in its front wall.

Flow

Nozzle

Cavity

Chamber

Black

Body

Cavity

Baffle

Cooling

Coils

Hose

Figure 1. Cut-away view of water bath emphasizing changes made to use it as a near ambient blackbody standard.

Note the baffle that divides the water bath into a rear chamber and a cavity chamber.

The rear chamber houses the heating and cooling coils. Only the cooling coils are shown

in the figure. The front chamber houses the cavity and isolates it from the heat sources and sinks within the heating/cooling chamber. Also note that the pump outlet is directed

into the chamber that houses the cavity.

Ideally, heating and cooling would occur at the same coils, and the flow rate of the pump

would be infinite. In this ceise, separate chambers would not be needed. However, in a real
system, the chamber walls isolate the cavity from any flow vortices that might carry water

from the heating or cooling coils directly to the cavity wall without sufficient mixing. Under

unfavorable conditions, such vortices can cause temperature nonuniformities as large as a few 100 mK.

The pump outlet is directed through the flow nozzle into the cavity chamber to reduce

the time lag between the temperature in that chamber and the temperature in the heating/cooling chamber to the minimum value consistent with good mixing. The location of

the flow nozzle in the cavity chamber wall is chosen to direct the well-mixed water from

the pump to flow over the cavity surface as a final attempt to assure an isothermal cavity.

The nature of the modifications to a commercial water bath in order to realize this design

concept is described in more detail in reference [l].

2.2 Control and measurement

Figure 2 is a block diagram of the temperature control aspects of the system. The cur- rent source drives a constant current through the four-wire thermistor Rl that is located

in the cavity chamber of the water. The temperature-dependent voltage drop across Rl

is measured by the computer using the digital voltmeter (DVM), which it is controlling

through the IEEE BUS. The computer calculates the water temperature that corresponds

to Rl, and compares this with the operating point temperature input by the operator. If the water temperature diff'ers from the operating point temperature by more than a (programmable) tolerance, then the computer uses an internally mounted Digital-to-Analog

(DAC) converter to change the set point of the time proportional, analog controller that is built into the water bath. This controller regulates the current fiowing in heater R3 based

on the resistance of the platinum resistance thermometer R2.

Water Bath

Unit

Cooling

Coil

Figure 2. Block diagram of control and measurement subsystems of water bath blackbody.
This control scheme is necessary because the bath's set point circuitry has a large temperature coefficient, and as a result, is not capable of holding the bath at a constant

temperature until the circuitry has warmed up for quite a few hours.

2.3 Temperature measurement uncertainties

The sources of error that have a bearing on the quality of the blackbody can be divided into

two types. The first type consists of the sources of errors associated with the measurement

of the temperature of the water surrounding the blackbody cavity, and the second consists

of the sources of error associated with the radiative transfer in the blackbody cavity. Errors

of the first type are briefly described in the following paragraphs, while errors of the second

type are discussed in more detail in the next section.

The constant current source that drives the four-wire thermistor that is used to measure

the temperature in the cavity chamber delivers 10 /zA with an uncertainty of considerably

less than ±100 parts per miillion and a precision of better than ±10 parts per million. This

uncertainty corresponds to ±2.4 mK at 0°C and ±3.2 mK at 60°C. The constant current source was designed and built at NBS, and is described in more detail in reference [l]. The resistance of the thermistor decreases from about 10000 f] at 5°C to about 1000 U at

60° C. The uncertainty in the calibration of the thermistor is less than ±1.5 mK over the

to 60° C temperature range, while its temperature as a function of resistance is accurate

to within 1.2 mK over the same range when calculated from a three-parameter equation

whose parameters have been adjusted to agree with measured values at three points spaced

approximately uniformly over this range. More infornaation on the thermistor can be found

in reference [l]. The DVM reads the voltage drop across the thermistor caused by the lO-fiA current with an uncertainty of ±(0.0039 mV plus 0.0025% of reading). This corresponds to ±2.6 mK

at 5°C and 11.6 mK at 60° C. More information on the digital voltmeter can be found in

reference [l]. The DAC is based upon a commercial device that mounts in one of the expansion slots

on an IBM PC [2] or compatible computer. It has been modified to provide an output

from to 1 V with a resolution of 15 ^V. This corresponds to a temperature resolution of

1.5 mK in setting the water bath operating temperature, which is better than the actual

temperature accuracy and stability limits that are imposed by other components of the

overall system. A little more information on the DAC can be found in reference [l].

The computer used to control the system is an IBM PC-compatible that is better suited

to laboratory automation applications than the IBM PC itself. This computer is no longer

manufactured commercially, but a company with a nationwide network of service facilities

continues to support these machines. A little more information on the computer can be

found in reference [l]. The uncertainties associated with the measurement of the water bath temperature are summarized in Table 1.
TABLE 1. Uncertainty in the measured temperature of the water in the water bath as a

function of temperature over the operating range of the water bath blackbody.

Measured temperature Uncertainty in temperature

0°C 3.4 mK

10°

C

4.9 mK

20°C 5.2 mK

30°C 5.5 mK

40°C 6.5 mK

50°

C

8.6 mK

60° 12.2 mK

In order to maintain the uncertainties listed in Table 1, the constant current source, the

thermistor, and the digital voltmeter all require periodic recalibration. For applications re- quiring the highest accuracy, recalibration of these subsystems before use of the blackbody

is recommended.

3. Blackbody Quality

The quality of the water-bath-mounted cavity as a blackbody when a particular portion

of its cavity walls is viewed during a measurement or calibration is given by

Q - e . [exp(c2/A • To) - l]/[exp(c2/A • T) - 1] « € . [1 + {AT/To) ' {c2/XTo)/{l - exp(-C2/A • To)], ^

^

where e is the cavity emissivity for the viewing geometry, C2 = 1.43879 • lO^fim • K, X \s

the wavelength of interest. To is a convenient (that is, subject to measurement) reference

temperature, and T is the suitably averaged effective temperature of the portion of the

cavity walls that is actually viewed by the radiometer. The approximation shown on the

second line, where AT = T — To, can be used whenever the second term in the square

brackets is small compared to unity.

A truly rigorous, general analysis of the quality of a blackbody cavity is surprisingly complicated, and not particularly useful. The problem is that the thermal radiation transfer

properties of the interior surface of the cavity wall are never known with sufficient accuracy

to allow an uncertainty to be applied to the result of the calculation.

The solution to this problem is to overdesign the cavity so that a relatively simple worst case estimate can be used to determine the maximum deviation from ideal blackbody behavior.

This is the approach that was taken for the water bath blackbody under discussion here.

Thus, one half of the worst case estimate will be used both as the correction factor and as the uncertainty.

The details of the cavity that are needed for a worst case analysis of its use as a ±20-mK

blackbody near ambient are shown in figure 3. Region 3 is the opening of the cavity.

6
Region 2 is the portion of the cavity wall that is not in direct contact with the water in

the bath. Region 1 is the interior surface of the portion of the cavity wall that is in direct

contact with the water. And Region is the exterior surface of the portion of the cavity

wall that is in direct contact with the water. The worst case analysis will apply only to

meeisureinents in which the viewed portion of the cavity is restricted to Region 1.

L 8.0 cm W4—3.1 cm—U—9.4 cm—

W

Region 2 Region 1

I

10.8 cm

1

Figure 3. Details of cavity design affecting blackbody quality.

3.1 Cavity emissivity

Because the walls of the cavity are in local thermodynamic equilibrium, the emissivity e of

the cavity is given by one minus the cavity reflectance. This fact can be used to calculate a very simple approximation for e based upon the assumption that the reflectance of the

interior wall of the cavity is the sum of a perfectly specular contribution p« and a perfectly

diffuse contribution pd, where p, and pd are assumed to be independent of the incidence

angle of the incident radiation. A simple ray trace using the geometry of figure 3 shows

that for radiation entering the cavity at near normal incidence

€ = 1-pI- dFi3 • Pd, (2)

where dFis is the differential configuration factor from the point of interest in Region 1 to

all of Region 3. (A configuration factor from one region to another is the fraction of the
diffusely emitted or reflected flux that originates in the first region and is incident on the

second.) Equation (2) is not a worst case approximation, but conservative choices for pa,

Pdt and dFiz allow eq (2) to be used as the basis for a worst case analysis.

Measurements were carried out to characterize the reflectance of the gloss enamel paint

used to coat the interior of the cavity. These showed that the specular component of

reflectance for near normal incidence is less than 5% from 1 /Ltm to 19 /lim, and that the

nonspecular component of reflectance for near normal incidence is less than 0.2% from 800

nm to 2.5 /zm. No data are available for the diffuse reflectance of the glossy enamel beyond

2.5 /xm, but the general trend is well established. The enamel will become more specular

and less diffuse with increasing wavelength. Similarly, no data are available on the specular

reflectance at other than normal incidence. Again, the general trend is well established.

The average reflectance for both polarizations of the incident radiation is approximately

constant with angle of incidence below Brewster's angle, but increases rapidly with angle

above Brewster's angle, reaching a maximum value of 1 at 90 deg. Thus, 10% and 0.2%

were chosen as conservative upper bounds for p« and pd, respectively.

The value of F13 was calculated from the nominal cavity dimensions. It varied from 0.03 near the tip of the cavity to 0.07 on the conical portion of the cavity near the intersection

with the cylindrical portion, the maximum occurring for points on the conical portion of the

cavity where it intersects the cylindrical section. Thus, 0.07 was chosen as a conservative

estimate for dFizWith the above values for Pa, pd, and dF\z^ eq (2) gives 0.9988 jls a lower bound for e, and

€ = 0.9994 ± 0.0006 as a conservative estimate for the emissivity of the cavity.

If a baffle with a 2-in. aperture and a high infrared reflectance were mounted on the front

of the cavity, then the conservative estimate of e for off-axis viewing of Region 1 would be

increased to 0.99993 ± 0.00007. It is, however, important to note that the increase in e applies only to off-axis viewing. Little improvement in € is predicted for on-axis viewing.

So careful alignment of the measurement geometry based on ray tracing is necessary before

this sort of improvement in cavity emissivity can be obtained.

3.2 Temperature distribution over interior of cavity

The following worst case approximations can be used to obtain a simple equation for the

temperature drop across the wall between Regions and 1 in the cavity:

1) Region 3 is at a uniform temperature represented by Ta.

2) Region 2 is at a uniform temperature represented by T2.

3) The worst case value for 72, which is the temperature at the lip of the cavity, will

be used.

4) Region is at a uniform temperature represented by Tq.

5) To is the temperature of the water in the bath as measured by the thermistor.

8
6) The worst czise emissivity for the interior cavity wall, which is unity, will be used.

For high accuracy, these approximations require that the temperature of Region be

accurately known. This is the role of the water bath and the high-accuracy thermistor.

However, worst c£Lse approximations based on measurements of very modest accuracy are

sufficient for the remainder of the cavity wall. This is similar to the way that this particular

choice of cavity geometry in conjunction with a specular black paint permits the use of

crude estimates of the reflectance of the cavity wall.

Two sets of measurements were carried out in order to characterize the temperature gradients existing in the blackbody cavity. The uniformity of the water in the chamber

surrounding the cavity was carefully measured with the highest accuracy possible, while

the temperature of the outer lip of the cavity was measured to no better than ±50 mK.

3.2.1 Temperature uniformity in water surrounding cavity

In order to measure the variation in the temperature of the water surrounding the cavity to the highest accuracy possible, it was necessary to monitor the temperature in the

cavity chamber during the time that a test thermistor was moved to different locations

in the chamber. The only test thermistor readily available for these measurements was

out of calibration. A special Plexiglas jig was constructed to hold the test and reference

thermistors in close proximity while they were immersed in the cavity chamber, and the

bath was run first at 5°C, then 30° C, and finally at 60° C, while 20 simultaneous readings

from the two thermistors were recorded. The results are listed in Table 2. TABLE 2. Test thermistor corrections at 5, 30, and 60° C.

Nominal Temperature (Test Temperature) - (Standard Temperature)

5°C -20.1 ±1.2 mK

30°C -15.0 ±0.7 mK

60°C + 2.5 ±0.8 mK

The uncertainties listed in Table 2 are single standard deviations of the means of the 20

differences. These corrections were applied in the measurements to be described next.

A special Plexiglas cover for the water bath was made to support the two thermistors

during the measurement of the temperature variations in the cavity chamber. It had a continuous slot connecting eleven short slots used to locate the test thermistor, and a

separate hole for the reference thermistor as shown in figure 4. The location of the cavity

relative to the test slots with the cover in place on the water bath is also indicated with a dotted line in that figure.

For these measurements, the water bath was allowed to stabilize at one of the temperatures,

5, 30, or 60°C. The reference thermistor was located in the reference hole, and the test thermistor was moved from short slot to short slot without changing its immersion depth

in the water, pausing in each slot long enough to allow 20 simultaneous readings of both
Reference ^ ^

/p.

Hole / /O A ^\\ / / / \ ^ \ / /^ ^ \ ^'Xx / / / \ ^ \ / f^ / \Cy\\.

/ V. / \ /^ \

A

/'"^ / \^^\

ri \

Test Slot Figure 4. Configuration of water bath cover specially made for measuring the variation in

temperature in the water surrounding the cavity.

thermistor voltages. This procedure was repeated at each of the three temperatures with

two, one, or no styrofoam spacers controlling the immersion depth of the test thermistor.

The immersion depth with the two spacers supporting the test thermistor was less than

an inch, and the data at this depth were subject to a very noisy immersion error of the

order of 1°C. The data obtained at the two lower depths are shown in figure 5.

20

E.

0)u

c

0>

k.0> 3=O

Vw

3

aw

0)a

E

0)

10 -

-10 -

-20

1 I 1 1 1 1

—A ^ ,^ tv/ -

•^^=S=^=i^ —ff^-

=::«—•———T^^^-^^^*^

L M

^^

--0 —

60 »C ^^s

A

30 "C • O

1 T

1 V

1 1 1 1 1 1 1 1

1 2 3 4 5 6 7 8 9 10 11

Position

Figure 5. Temperature differences measured at different locations in cavity chamber in

water bath blackbody.

Notice that the deep immersion values all fall within a range of ±5 mK. Also notice that

the test thermistor measures closer to ambient at the medium inmaersion depth than at

the low immersion depth. This is probably caused by an immersion error associated with

the test thermistor rather than an indication of a true vertical temperature gradient in the

10
cavity chamber. Radiometric data will be necessary to decide between these two alternate

interpretations of the data in figure 5.

Even without knowing the correct interpretations of the data in figure 5, it is possible

to make some fairly strong statements about the temperature uniformity in the cavity

chamber, namely: The bottom half of the outside walls of the cavity that are actually

in contact with the water are uniform in temperature to well within ±15 mK. Since the

bottom half contains 2 in. of vertical distance, this region is accessible for most calibration

applications.

3.2.2 Temperature drop at lip of cavity

A differential thermocouple was made from a commercially available, glass-insulated,

Chromel/Alumel duplex thermocouple wire, and each junction was insulated with enamel

insulating paint. The reference junction was inmiersed in the cavity chamber of the water

bath. The test junction was pressed flat between the outside surface of the cavity and

the foam surrounding the cavity for one turn around the cavity lip. The free ends were

connected across the input to a DVM, and the voltage recorded when the bath was running

at 60°C. The test junction was then immersed in a dewar containing 11° C tap water, and

the output voltage was again recorded. The general configuration for these measurements

is shown in figure 6. The voltage difference between the test and reference junctions with the test junction at

the lip of the cavity was 0.17 mV ± 0.01 mV. The voltage difference with the test junction

in the 11°C water was 2.02 mV. The uncertainties in the temperatures of the 11°C tap

water and the 60° C cavity chamber water were both well within ±1°C. Thus, when the

water bath temperature is about 60°C, the temperature of the lip of the cavity is 4.12°C

± 0.12°C lower than the temperature of the water in the cavity chamber. This is a worst

case, because 60° C is as far as the water bath will ever get from ambient according to the

performance specification for the entire system.

Differential Thermocouple

DVM

Foam

Insulation

Figure 6. Configuration of water bath blackbody for measurement of temperature drop at

lip of cavity.

11
For the analysis in the next section, the temperature drop at the cavity lip is assumed to

scale with the temperature difference between the water bath and ambient temperatures.

3.2.3 Temperature drop across cavity wall and paint

Subject to the worst case assumptions described at the beginning of this section (3,2),

the equilibrium between the heat radiated out the cavity opening and the heat conducted

across the cavity walls satisfies the following equations:

The differential power conducted through the wall and black paint per unit area at any

point in Region 1 is given by

dP = [To - Ti)/{dal • Kal + dac ' Kac), (3)

where dai and Kai are the respective thickness and conductivity of the aluminum cavity

wall, and dac and Kqc are the same quantities for the acrylic black paint on the interior

of the cavity wall. The above quantity must be balanced by the net differential radiant

power leaving the surface of the paint at the same point in Region 1. Thus,

dP = dFis • o . [T^ - T^) + {dFi2 - dFis) • tr • [T^ - T}), (4)

where a is the Stefan-Boltzmann constant, and dFij is the differential configuration factor

from the point in question in Region i to all of Region j.

Because the temperature difference between Ti and To will be quite small, negligible error

is introduced by approximating Ti by

T^ =T^+4' T^ ' AT, (5)

where AT = Ti — To is the temperature drop across the wall and black paint. With this

approximation, eqs (3) and (4) can be solved simultaneously for AT in closed form. The

result is

^j, ^ P'Tq- jdFis [1 - [Ts/Toy] + [dFi2 - dF.s] [1 - (r2/ro)-'])

l + 4'dFi2-/3 ^

^

where

/? = a . T^idal • Kal + dac ' Kac). (7)

Table 3 lists the nominal values of the cavity parameters that were used to evaluate AT.

The temperature of Region 3 was chosen to be 293.16 K = 20°C.

12
TABLE 3. Values of parameters used to calculate AT from eq (6).

Paxameter Value

inside diameter of cavity 10.8 cm

length of cylindrical portion of cavity 11.1 cm

full angle at tip of cone 60 deg

thickness of cavity wall in Region 1 0.340 cm

thickness of black paint on cavity wall 0.005 cm

thermal conductivity of cavity wall 1.4538 W/cm* K

thermal conductivity of black paint 0.0018 W/cm« K

The effect of the uncertainty in the thickness of the black paint on AT is much larger than

the effect of the uncertainty in all of the other parameters in Table 3 combined. Therefore,

the uncertainties are not listed in the table. The black paint was applied to the cavity

by introducing a few drops into the cavity tip with a medicine dropper, and inverting

the cavity so that the paint could run down the cone. A sample of the paint on a first surface aluminum mirror was prepared in the same way for the reflectance measurements

described in Section 3.1 of this report. After drying, the paint was removed from a corner

of the mirror, and the thickness of the mirror was mieasured in this corner, and in the

adjacent painted area. The difference in thickness was 0.0010 ± 0.0002 in. This number is not necessarily a good value for the thickness of the coating on the interior of the cavity.

The mirror is smoother than the interior of the cavity, and the geometry of the surfaces

is different. Therefore, dac = 0.005 cm ± 0.005 cm (0.0020 ± 0.0020 in.) was chosen as a

conservative estimate of the paint thickness.

For the values shown in Table 3, dFi2 and dFis varied from 0.079 and 0.032, respectively,

at the tip of the cone, to 0.180 and 0.070, respectively, on the conical portion of the

cavity wall where it intersects the cylindrical portion of the cavity wall. Table 4 shows the

calculated variation of AT with the water temperature To for points at the latter location

on the conical portion of the cavity wall. The stated uncertainty is less than 10% larger

than that associated with the uncertainty in the thickness of the paint.

TABLE 4. The calculated variation in the temperature drop AT across the wall of the

cavity and the black paint on the conical section of the cavity where it intersects the

cylindrical section, as a function of water bath temperature Tq.

Operating temperature Temp

0°C

10° C

20° C

30° C

40° C

50° C

60° C

13

rature drop Uncertainty

2.5 mK ±2.5 mK

1.4 mK ±1.4 mK

0.0 mK ±0.0 mK

1.5 mK ±1.5 mK

3.2 mK ±3.2 mK

5.0 mK ±5.0 mK

7.1 mK ±7.1 mK
If a baffle with a 2-in. aperture, a high infrared reflectance, and thermal insulation on

its exterior surface, were mounted on the front of the cavity, then the calculated values

of AT would be reduced by a factor of 4. A carefully conducted experiment comparing

the cavity radiance with and without a baffle of this nature in place could be used as a

self-calibration procedure to determine AT directly. However, because e might also vary

in this experiment, meeisurements at two widely separated wavelengths would be necessary

to assign independent values to e and AT.

3.3 Overall estimate of blackbody quality

We now have all of the information needed to use eq (l) to calculate the quality of the water

bath blackbody at any wavelength. The values of the parameters needed to evaluate eq (1) are summiarized in Table 5. The uncertainty for AT consists of the sum in quadrature of

the uncertainty associated with the calculation of AT, the variation in water temperature

around the cavity, and the uncertainty in the measurement of the water temperature. The

values only apply when viewing is restricted to the bottom half of the cavity.

TABLE 5. Parameters for use in calculating the quality and the uncertainty in the quality

of the water bath blackbody from eq (1).

Parameter Value Uncertainty Restriction

AT -2.5 mK ±15.6 mK To = 0*^0

AT -1.4 mK ±15.8 mK To = 10°C

AT -0.0 mK ±15.9 mK To = 20°C

AT +1.5 mK ±16.0 mK To = 30°C

AT +3.2 mK ±16.7 mK To = 40°C

AT +5.0 mK ±18.0 mK To = 50°C

AT +7.1 mK ±20.6 mK To = 60°C

£ 0.9994 ±0.0006 full aperture

c 0.9999 ±0.0001 half aperture

A simple equation for the uncertainty in the quality of the blackbody can be derived from

eq (l). It states that

dQ = Q* {[de/e]' + [F{c2/XTo) • {dT/To)]'y/\ (8)

where

F{u) = u/{l - exp{-u)). (9)

14
The uncertainty dQ in the quality of the water bath blackbody is plotted as the upper curve

in figure 7 for an unbaffled cavity operated at 0°C. This curve is based on the conservative

estimates of the thermometric properties of the water bath, and the radiometric properties

of the cavity that were derived earlier in this report. The curves at the other temperatures

between 0°C and 60° C fall a little below this curve, the minimum occurring at 40° C.

The differences are so small that the 0°C curve is applicable at all temperatures. At the

long wavelengths, the uncertainty is dominated by the ±0.0006 uncertainty in the cavity

emissivity. At the shortest wavelengths, the uncertainty is dominated by the uncertainty

in the cavity wall temperature, due primarily to the uncertainty in the uniformity of the

water temperature surrounding the cavity.

0.3 - \

»5> 0.2 - \

H

Z

<H

QC

UJ

*J ^ . z 0. — \ ^v. 3

n __l l_l 1 1 1 1 1 L.J,„l 1 1 1 1 ,.1..-J 1 1—

5 10 WAVELENGTH {fim)15 20

Figure 7. The uncertainty in the quality of the water bath blackbody. Case 1, upper curve:

Full aperture, viewing conGned to bottom half of cavity, uncertainties as determined in

this report. Case 2, lower curve: Aperture limited by insulated, reBective baffle with 2-in.

diameter aperture, and uniformity of cavity walls no worse than ±5 mK.

If the level of accuracy shown by the upper curve in figure 7 is not satisfactory for some

applications, then careful measurements of the relative radiance over the conical portion of

the cavity should be made. Most likely, these will show that the cavity bottom is uniform in

temperature to ±5 mK. If this is the case, then there would be a considerable improvement

in accuracy at the long wavelengths if the cavity were equipped with an insulated, reflective

baffle having a 2-in. diameter aperture. The lower curve in figure 7 shows the uncertainty

that would apply in this hypothetical case. Obviously, considerable improvement would be

achieved to the extent that the relative radiance measurements showed considerably less

than ±15-mK variation over the cavity bottom.

15
Acknowledgment

The authors would like to acknowledge Patrick Tobin and Kenneth Angle of NBS for

measuring the temperature variations throughout the water bath at various times during

this project, Victor Weidner and Patricia Barnes of NBS for measuring the reflectance of a sample of the black paint used on the cavity interior, and Jeffery Tapping of Australia's

CSIRO Division of Applied Physics for advice and encouragement during the planning

stages of this project.

References

1. J. B. Fowler and B.J. Belzer, Water Bath Bl&ckbody Operating Instructions, to be

published £ls an NBS Tech. Note.

2. Certain commercial equipment, instruments, or materials are identified in this paper

in order to adequately specify the experimental procedure. Such identification does

not imply recommendation or endorsement by the National Bureau of Standards, nor does it imply that the materials or equipment identified are necessarily the best

available for the purpose.

16
NBS.114A (REV. 2-BC) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO. NBS/TN-1228

2. Performing Organ. Report No. 3. Publ ication Date

October 198 6

4. TITLE AND SUBTITLE

A Water Bath Blackbody for the 5 to 60°C Temperature Range: Performance Goal,

Design Concept, and Test Results

5. AUTHOR(S)

Jon Geist and Joel B. Fowler

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions)

NATIONAL BUREAU OF STANDARDS

U.S. DEPARTMB^T OF COMMERCE

GAITHERSBURG, MD 20899

7. Contract/Grant No.

8. Type of Report & Period Covered

Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State, ZIP)

Newark Air Force Station

Newark, OH 43057-5475

10. SUPPLEMENTARY NOTES

\2^ Document describes a computer program; SF-185, FIPS Software Summary, is attached.

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

bibliography or literature survey, mention it here) A water bath blackbody has been built under contract for the Electromagnetic

Metrology Engineering Branch at Newark Air Force Station. The performance goal was

a large-area, self -calibrating, high-accuracy blackbody covering the majority of

the liquid water temperature range. With the exception of self-calibration, these

goals were met. This report describes both the conceptual design of the water bath

blackbody and the results of the tests that were carried out to characterize the

performance of the actual water bath blackbody that was built for Newark Air Force

Station. The details of the construction and operation of that water bath

blackbody are described in a companion report.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

blackbody; blackbody standard; high-accuracy blackbody; large-area blackbody;

room-temperature blackbody; water bath blackbody

13. AVAILABILITY

|X] Unlimited

I I For Official Distribution. Do Not Release to NTIS

[X] Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

[^_\ Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGtS

21

15. Price

USCOMM-DC 6043-P80



ERRATA SHEET, changes on p. 12

dP = [To - Ti)/{dal/Kal + daclKac), (3)

where dai and Kai are the respective thickness and conductivity of the aluminum cavity

wall, ajid dac and Kac are the same quantities for the acrylic black paint on the interior

of the cavity wall. The above quantity must be balanced by the net differential radiant

power leaving the surface of the paint at the same point in Region 1. Thus,

dP = dFi3 . a . [T^ - T^) + [dF,2 - dF,s) • a • [T^ - T^), (4)

where a is the Stefan-Boltzmiann constant, and dFij is the differential configuration factor

from the point in question in Region i to all of Region j.

Because the temperature difference between Ti and To will be quite small, negligible error

is introduced by approximiating T^ by

T^ = To^ - 4 . T^ AT, (5)

where AT = To — Ti is the temperature drop across the wall and black paint. With this

approxim.ation, eqs (3) ajid (4) caji be solved sim.ultaneously for AT in closed form.. The

result is

.J, ^ ^ • To . {dF,s • [1 - (Ts/To)-^] + [dF,2 - dF,s] • [l - (r2/To)^])

1 + 4 . dFi2 -13 ^ ^

where

13 = a- Ti{dai/Kai + dac/Kac). (7)

ERRATA SHEET for NBS Technical Note 1228

NBS_ Technical Publications

Periodical

Journal of Research—The Journal of Research of the National Bureau of Standards reports NBS research ana development in those disciplines of the physical and engineering sciences in which the Bureau is active. These include physics, chemistry, engineering, mathematics, and computer sciences. Papers cover a broad

range of subjects, with major emphasis on measurement methodology and the basic technology underlying

standardization. Also included from time to time are survey articles on topics closely related to the Bureau's

technical and scientific programs. Issued six times a year.

Nonperiodicals

Monographs—Major contributions to the technical literature on various subjects related to the Bureau's scientific and technical activities. Handbooks—Recommended codes of engineering and industrial practice (including safety codes) developed in cooperation with interested industries, professional organizations, and regulatory bodies.

Special Publications—Include proceedings of conferences sponsored by NBS, NBS annual reports, and other

special publications appropriate to this grouping such as wall charts, p)ocket cards, and bibliographies.

Applied Matiiematics Series—Mathematical tables, manuals, and studies of special interest to physicists,

engineers, chemists, biologists, mathematicians, computer programmers, and others engaged in scientific and

technical work.

National Standard Reference Data Series—Provides quantitative data on the physical and chemical properties

of materials, compiled from the world's literature and critically evaluated. Developed under a worldwide pro- gram coordinated by NBS under the authority of the National Standard Data Act (Public Law 90-396).

NOTE: The Journal of Physical and Chemical Reference Data (JPCRD) is published quarterly for NBS by

the American Chemical Society (ACS) and the American Institute of Physics (AIP). Subscriptions, reprints,

and supplements are available from ACS, 1155 Sixteenth St., NW, Washington, I)C 20056.

Building Science Series—Disseminates technical information developed at the Bureau on building materials,

components, systems, and whole structures. The series presents research results, test methods, and perfor- mance criteria related to the structural and environmental functions and the durability and safety

characteristics of building elements and systems.

Technical Notes—Studies or reports which are complete in themselves but restrictive in their treatment of a

subject. Analogous to monographs but not so comprehensive in scope or definitive in treatment of the subject

area. Often serve as a vehicle for final reports of work performed at NBS under the sponsorship of other government agencies.

Voluntary Product Standards—Developed under procedures published by the Department of Commerce in Part 10, Title 15, of the Code of Federal Regulations. The standards establish nationally recognized re- quirements for products, and provide all concerned interests with a basis for common understanding of the

characteristics of the products. NBS administers this program as a supplement to the activities of the private

sector standardizing organizations.

Consumer Information Series—Practical information, based on NBS research and experience, covering areas of interest to the consumer. Easily understandable language and illustrations provide useful background

knowledge for shopping in today's technological marketplace.

Order the above NBS publications from: Superintendent of Documents, Government Printing Office,

Washington, DC 20402. Order the following NBS publications—FIPS and NBSIR 's^rom the National Technical Information Service, Springfield, VA 22161.

Federal Information Processing Standards Publications (FIPS PUB)—Publications in this series collectively constitute the Federal Information Processing Standards Register. The Register serves as the official source of

information in the Federal Government regarding standards issued by NBS pursuant to the Federal Property

and Administrative Services Act of 1949 as amended. Public Law 89-306 (79 Stat. 1127), and as implemented

by Executive Order 11717 (38 FR 12315, dated May 11, 1973) and Part 6 of Title 15 CFR (Code of Federal

Regulations).

NBS Interagency Reports (NBSIR)—A special series of interim or final reports on work performed by NBS

for outside sponsors (both government and non-government). In general, initial distribution is handled by the sponsor; public distribution is by the National Technical Information Service, Springfield, VA 22161, in paper copy or microfiche form.
U.S. Department of Commerce

National Bureau of Standards

Gaithersburg, MD 20899

Official Business

Penalty for Private Use $300