Army Research Laboratory 

Aberdeen Proving Ground, MD 21005-5066 

ARL-TR-2420 April 200 1 

a 

A Video Thermography Technique for 

Temperature Measurements of PulseHeated Metallic Rods 

Clinton E. Hollandsworth 

Charles R. Stumpfel 

John D. Powell 

Charles R. Hummer 

Weapons & Materials Research Directorate, ART, 

c 

Approved for public release; distribution is unlimited. 

i 
Abstract 

A video thermography technique for measuring the surface 

temperature of metallic rods is described in this report. The technique 

employs a video camera with charge-coupled devices as the detection 

elements; it is applicable to materials that can be preheated to form 

an oxide layer with a stable emissivity. The procedure is illustrated by 

the measurement of the surface temperature of molybdenum rods that 

have been rapidly heated to about 800 K by an electrical discharge. 

The thermal emission profile of the sample is observed with the video 

camera, and the final surface temperature is inferred from previously 

obtained calibration data. The time-dependent current through the 

rod is also measured and used as input in theoretical calculations that 

describe the coupled transport of electromagnetic fields and heat 

through the sample. The temperatures predicted by the model 

calculations are in excellent agreement with the values inferred from 

the experiments. 

i 

. 
ACKNOWLEDGMENTS 

The authors would like to thank the following individuals: Keith Mahan of the U.S. 

Army Research Laboratory (ARL) for assistance with sample preparation and 

characterization and for valuable support throughout the experimental phase of the 

work; Joe Correri and Wayne Gardner of ARL for assistance in setting up the pulsed 

power configuration; Paul Beming of ARL for useful technical consultation and a 

critical review of this report. Nancy Nicholas, ARL technical editor, identified errors 

in the initial report draft, made improvements, and significantly improved the 

quality level of the communications in the final report. 

_._ 

111 
LNTENTI~NALLYLEFT BLANK 

iv 
Contents 

1. Introduction ...................................... 1 

2. Temperature Measurement Technique .................. 

2.1 TheCamera.............................*..* .... 

2.2 Sample Preparation and Emission Considerations .......... 

2.3 Procedure for Preparing the Sample Surface ............... 

2.4 Calibration Procedures ............................. 

3. 

4. 

5. 

Experimental Arrangement and Procedures. ............. 9 

3.1 ElectricalSetup .................................. 9 

3-2 Temperature Measurement Procedure ................... 10 

Theoretical Analysis ................................ 11 

Results.....................................* ..... 13 

6. Discussion and Future Work. . . . . . . . . . . . . . . . . . . . . . . . . . 16 

References . . . .._......................*................ 19 

Appendix 

A. Calculation of Uncertainty in Temperature Measurement 

Attributable to Uncertainty in Emissivity . . . . . . . . . . . . . . . . 2 1 

B. Summary of Procedures for Calibration of Flashcam System 

and Temperature Measurement . . . . . . . . . . . . . . . . . . . . . . . 2 7 

Distribution List . . . . . . . . . . . , . . . . . . . , . . . , . . . . . . . . . . . . . . . . 31 

Report Documentation Page . . . . . . . . . . . . . . . . . . e . . , . . . . . . e . . . 

33 

Figures 

1. Flashcam Image of Heated Rod and Blackbody Simulator. . . . . . . . . 7 

2. Digitized Scans of Images of Heated Rod and Blackbody 

Simulator . . e . . . . . . . . . . . . . e . . . . . . . . e . . . . . . . . 8 

3. Flashcam Response to Simulated Blackbody Radiation _ . . . . . . . 8 

4. Experimental Arrangement . . . . . . . . . . . . . . . . . . . . . , . . . 10 

5. Current Trace for Shot S2: Charge Voltage = 7.51 kV . , . . . . . . . 13 

6. Surface Temperature Versus Time for Shot S2 . . . . . . . . . . . . . e 14 

7. Flashcam Image of Molybdenum Rod . e . . . e . . . . . . . . . . . . . 14 

8. Profiles of Surface Temperature of Heated Rods Versus 

Calibration Curves I . . e . . . . . . . . . . . . . . . . . . . . . . . . . . 15 

V 
Tables 

1. Coefficients for Thermophysical Properties of Molybdenum . . . . . 12 

2. Comparison of Theoretically Ckulated and Experimentally Measured 

Temperatures . I e . . . . . . . . . . . . . . . e . . . . . . . . . . . . . . 15 

h 

vi 
, 

A VIDEO THERMOGRAPHY TECHNIQUE FOR TEMPERATURE 

MEASUREMENTS OF PULSE-HEATED METALLIC RODS 

1. Introduction 

Much of the database pertaining to the thermophysical properties of metals have 

been accumulated in static, direct current (DC) conditions or dynamic conditions 

at heating times in the millisecond range. Although a number of very accurate 

measurements of thermophysical properties have been made for heating times in 

the microsecond and even the sub-microsecond range, the samples employed 

typically are very small diameter wires or thin foils. The goal in many of these 

experiments was to obtain data at very high temperatures. The procedure 

followed generally uses a current pulse whose time dependence, in conjunction 

with the small physical dimensions of the sample, is such that both skin depth 

effects and heat transport within the sample may be neglected. 

Some Army applications of pulsed power and electromagnetic technology 

involve heating times in the microsecond range. In these applications, the 

conductors are too large to ignore diffusion processes and size-related effects. 

For this reason, an exploratory effort to study the behavior of particular metals 

and alloys that are heated electrically in times on the order of 100 microseconds 

is under way at the US. Army Research Laboratory (ARL). In these experiments, 

a capacitor bank supplies electrical currents that reverse direction in a few tens 

of microseconds. The purpose of this work is twofold. First, data are not 

available for some materials of special interest to the Army, and it is desired to 

provide these data. Second, there is a requirement to provide data to validate 

numerical computer codes developed to support Army applications. 

The period of heating in these experiments is so short that thermal conduction in 

the sample does not play a significant role. Sample geometry, specific heat, and 

resistivity largely determine both the sample temperature and the voltage 

produced across the sample. Thus, measurement of the voltage across a portion 

of the sample and the current through it provides information about the validity 

of these parameters. Theoretical calculations that couple the diffusion of current 

with heat transport in the sample [l] are then required in order to properly 

interpret the measured voltage. In some recent ARL experiments with 

substances whose properties are well known, excellent agreement between 

theory and experiment was obtained for the time-dependent voltage drop across 

the heated rod. Known values t2] for the relevant thermophysical properties 

were employed in the theoretical calculations. This agreement has lent credence 

to our use of similar techniques to determine properties of relevant materials 

that are not well characterized. 
In order to complete the validation of our codes, it is also desirable to measure 

the temperature of the samples subjected to pulsed heating. Since the current 

pulse in our experiment has the functional form of a damped sine wave that 

persists for about 200 microseconds, a continuous measurement of the 

temperature during this period would be difficult and would require specialized 

instrumentation. However, the final temperature of a heated rod, with 

appropriate precautions and sample preparation, can be measured by a 

thermography technique that employs standard video cameras. In this report, 

we describe a technique for surface temperature measurement that relies on the 

response of an electronically shuttered camera that is sensitive to visible and 

near infrared (IR) radiation. The radiation is detected in an array of chargecoupled devices (CCDs). 

The method is applied to the measurement of the final temperature of the 

surface of a molybdenum rod heated to approximately 800 K, and the results are 

compared with the value predicted by theoretical calculation. Although 

measurements were performed on a variety of materials, molybdenum was 

chosen as an element to illustrate the technique because it has been studied 

intensively by the National Institute of Standards and Technology (NET) 131. Its 

thermophysical properties, resistivity, and specific heat are known to 

approximately 3% accuracy for the temperature range of interest to us. In our 

experiments, an oscillatory current was used which produced peak heating rates 

greater than 10 million degrees Kelvin per second (K/s). 

The voltage measurements discussed previously will be presented in another 

report. Our purpose here is to describe the technique for measuring the final 

surface temperature of a heated rod. 

2. Temperature Measurement Technique 

Several proven thermography techniques exist, which are based on the 

measurement of spectral radiance over a narrow spectral band, at two or more 

narrow spectral bands, over a broad spectral band, or integrated over all 

wavelengths 141. In this work, measurements were made over a broad spectral 

band extending to wavelengths below the shortest wavelength emitted by the 

heated sample. Video thermography, wherein a thermal emission image of the 

source is acquired and the video levels are calibrated to provide a direct reading 

of temperature, is the technique used in our measurements. Stumpfel 151 

discussed some of the underlying theory that relates thermal emissions from an 

emitting metallic surface to the response of a detector. 
The response characteristics of systems that are particularly sensitive to the 

shorter wavelength portion of a given emission spectrum can be illustrated by 

simple application of Planck’s distribution law for blackbody emission. This 

distribution shows that for wavelengths much shorter than the value at which 

peak spectral radiance occurs, there is an extremely strong dependence of 

spectral radiance on temperature. For example, for temperatures around 800 K, 

the peak spectral radiance occurs at 3622 run. For this same temperature, the 

spectral radiance at 1000 run increases with temperature as T”. Thus, a 

temperature increase from 800 K to 900 K would increase the spectral radiance at 

1000 run by a factor of about eight. 

Any system that responds across this short wavelength band (as our system 

does) will therefore exhibit extremely strong temperature dependence. This 

sensitivity to temperature change increases the accuracy of temperature 

measurements, but the saturation level of the CCDs limits the temperature range 

observed with a given setup of the camera. For example, with the lens aperture 

and exposure time used in the present measurement at 800 K, the range of 

observable temperatures was only about 100 K. 

A major difficulty in making temperature measurements in the present 

experiment is the high level of light produced at early times by the electrical arcs 

that normally accompany current initiation when high voltages and large 

currents are involved. These arcs can complicate the measurement by producing 

(a) extraneous light that is reflected from the sample, (b) saturation in the 

detectors, OK (c) both. These problems suggest that a detector with some form of 

electronic shuttering is desirable. The availability of a silicon CCD-video camera, 

the “Flashcam’,” which has a fast electronic shutter and external triggering 

capability, appears to offer a good choice for the present experiment. A 

preliminary study of heated rods with the Flashcam camera indicated that this 

system has adequate sensitivity to observe blackbody radiators at temperatures 

above -670 K. 

2.1 The Camera 

The Flashcam is a programmable, fast shutter, multiple exposure camera that 

responds to radiant flux in the wavelength range from 350 to 1040 run. The 

camera can be operated with the following properties: (a) 1 to 10 exposures per 

frame; (b) exposure times of 1 to 1000 p; and (c) time between exposures is 

selectable from 1 to 1000 us. In the triggered mode, an external pulse triggers the 

camera, which begins an exposure sequence after a pre-set delay. The Flashcam 

can be triggered at any time or with repeated triggers, and imaging frequencies 

as fast as 60 frames per second are attainable. 

‘The Cooke Corporation, Flashcam serial no. 335NG0041. 

3 
The camera can be operated in one of two output modes, capturing a single 

digital image or recording images continuously on videotape. The analog output 

from the CCD array is digitized by an &bit analog-to-digital converter, stored as 

a digital image, and made available for transfer to a personal computer via a 

standard printer cable. In the triggered mode, a single digital image that may 

contain the summation of as many as 10 exposures is retained in a buffer. In 

addition, an S-bit digital-to-analog converter transforms the digitized image to a 

standard RS-170 video signal that is provided at a video output jack. When 

operated in a free-run mode (no trigger), the camera resembles a normal video 

camera except that the video signal is obtained by re-conversion from the digital 

signal. In this mode, the re-converted signal is normally stored continuously on 

videotape. In the course of our calibrations and experiments, we have used the 

camera in both triggered and free-run modes. 

2.2 Sample Preparation and Emissivity Considerations 

Before any temperature measurements can be attempted, it is necessary to 

prepare samples with stable thermal emission characteristics. In general, metal 

surfaces oxidize when heated in air. The oxidization rates accelerate rapidly for 

most metals as the temperature rises above 600 K. For a given metal and 

temperature, the resultant layer of oxidized metal may tend to flake off or 

remain on the surface. For some metals (e.g., copper and iron) at higher 

temperatures (e.g., above 1000 K), a very porous oxide layer forms and 

continually scales off, revealing new metal. In this case, the bulk metal may be 

completely oxidized and may crumble in a short time. Such metals are not good 

candidates for ~ these experiments. Fortunately, there are elements whose surfaces 

at certain temperatures will form a dense oxide layer that prevents additional 

oxygen atoms from reaching the underlying metal atoms. These metals can often 

maintain a quasi-stable surface over a considerable range of high temperatures. 

Metals that oxidize in this manner are the best candidates for these experiments; 

molybdenum is such a metal. 

All molybdenum samples were 99.97% pure and in the form of cylindrical rods, 

150 mm in length by 5 mm in diameter. The samples were received from the 

supplier with freshly machined surfaces. In pulsed heating experiments with 

freshly machined molybdenum, the un-oxidized surface of the rod begins to 

oxidize at a high rate when the rod is rapidly heated in air to temperatures 

around 800 K. Because the current pulse in our experiments is so brief, most of 

the oxidization will occur after the pulse ends, i.e., as the sample cools over a 

period of many seconds. To minimize changes in the surface during the 

’ experiment and also during repeated heating for calibration, it is necessary to 

work with samples that have been oxidized previously in a controlled manner. 

Several factors must be considered to achieve the proper preparation. 

The emissivity, E, of the sample is an important quantity for the temperature 

measurement as the observed radiation is directly proportional to its value. 

4 
Because a freshly machined metallic surface originally has a very low ernissivity, 

estimated to be less than E - 0.1, the emissivity will begin to increase in an 

unknown manner as soon as the rod is heated by the current pulse. For some 

metals, the emissivity continues to rise as the thickness of the oxide layer 

increases until a quasi-equilibrium value is reached, Ernissivity is determined by 

the composition and morphology of both the oxide layer and the underlying 

oxide-to-metal interface. Because a thin oxide layer may partially transmit IR 

radiation, the composition and morphology of the underlying oxide-to-metal 

interface may have a significant effect on the overall emissivity.. There are 

examples of materials, which on the basis of the high transmittance of the oxide 

layer and the high reflectance of the metal, might be expected to have low 

emissivities; however, those materials actually have quite high emissivity 

values’. Such high values may result from an irregular morphology in the 

interface region, particularly at the interface between the metal oxide layer and 

the metal. 

The general description of oxide layer formation just given would probably 

apply to the oxide layers formed on molybdenum rods heated in these 

experiments. Oxide layers 0.2 pm thick on molybdenum are observed to transmit 

visible and near IR [61. Knowledge of the details of the surface and its emissivity 

is not critical to the temperature measurement technique described herein, but 

any variations in emissivity (e.g., between calibration and the experimental 

measurement) will increase uncertainty in the temperature measurements. 

Appendix A of this report shows that even a fairly large uncertainty in the value 

of emissivity leads to only a small uncertainty in the measured temperature for 

these experiments. Therefore, reasonable care in stabilizing the emissivity results 

in only small uncertainties in temperature measurements. 

2.3 Procedure for Preparing the Sample Surface 

When a freshly machined molybdenum rod with low emissivity is heated, it will 

oxidize, and its emissivity will increase considerably. To avoid this large 

emissivity increase, an approach of pre-oxidizing the surfaces to form a stable 

oxide layer was used. This approach minimizes the uncertainty in the 

temperature measurement attributable to uncertainty in the sample emissivity. 

The sample was pre-heated in air to form a stable black oxide layer with 

emissivity much increased over that of the freshly machined surface. The 

treatment for molybdenum consisted of placing the sample, initially at room 

temperature, in an oven at 770 K for 10 minutes. The appearance of the surface 

changed from specularly reflective to diffusely black as a result of this treatment. 

In addition to the initial surface oxidization treatment (heating at 770 K for 

10 minutes), one sample was also repeatedly heated to selected temperatures in 

order to calibrate the Flashcam camera. This procedure consists of heating the 

2A well-known example is transmissive sapphire, J’$O,, “hard-coated” onto reflective aluminum. 

5 
sample for a few minutes to achieve thermal equilibrium and then quickly 

removing it and viewing it with the camera. This process was repeated for a 

series of temperatures from 750 to 850 K. After these additional heating cycles, 

the sample was observed to lose its small remaining specular reflectance and 

appear more diffusely black. This change in appearance probably was 

accompanied by a slight increase in the emissivity, estimated to be within the 

range between 0.8 and 0.9. In future tests, the oven oxidization treatment for 

molybdenum could be performed at a temperature higher than 770 K or 

extended to times longer than 10 minutes in order to further stabilize the 

ernissivity of the sample. Considerable uncertainties in the emissivity are shown 

in Appendix A to cause only small uncertainties in the temperature 

measurement for these experiments. The authors estimated the emissivity of the 

sample after treatment by comparing it to that of a blackbody by the procedure 

described in the next section. 

The thicknesses of the oxide layers for the pre-oxidized molybdenum samples 

are not well known at present. It is estimated from prior experience and existing 

literature, however, that the thicknesses of these layers probably lie in the 5- to 

SO-pm range. After the samples are removed from the oven and allowed to cool, 

the oxide layers at both ends of the rods are removed, and the resistances of the 

oxidized molybdenum rods are re-measured. No change in resistance from the 

original room temperature value (410 @) could be detected to within the lo-@2 

accuracy of our resistance bridge for any of the samples. 

2.4 Calibration Procedures 

In the following discussion, calibration procedure refers to the process of 

establishing the relationship between rod temperature and Flashcam signal 

level. Although a blackbody simulator (BBS) was used to assist in choosing the 

proper settings for the camera and to verify some assumptions about sample 

emissivity, it was not an integral part of the calibration procedure. Because 

several steps are involved in both calibration of the camera and the assignment 

of a temperature to an experimental result, the procedure is summarized in 

Appendix B. A more detailed description is presented in the remainder of this 

section of the report. 

After the desired oxide layer was achieved, the sample was assumed to have a 

stable average spectral emissivity, estimated to be about 0.9 in the band detected 

by the Flashcam camera (350 to 1040 nm). To check this assumption, the sample 

was compared to a BBS by heating it to the same temperature as the BBS and 

then viewing the sample in front of or alongside the BBS. The Flashcam signals 

for the sample and BBS were compared and showed only small differences, thus 

indicating that the sample had very high emissivity in the response band of the 

Flashcam. The small difference in signal could be attributed both to the slightly 

lower emissivity of the sample and to experimental uncertainties associated with 

knowing the true temperature of the BBS and the true temperature of the sample 

6 
after its removal from the oven. For this comparison, the uncertainties in the true 

temperatures are estimated to be +lO K for the BBS and +20 K for the 

molybdenum sample. 

Because the sample cools during transfer from the oven to the viewing position, 

it was heated to a somewhat higher temperature than the desired calibration 

value. An example of the comparisons is given in Figure 1, which shows the 

Flashcam images of a heated molybdenum sample and the BBS. In this case, the 

sample was heated initially to a temperature of 779 K, removed from the oven, 

and placed in “vee-block” supports just in front of the BBS, held at a temperature 

of 773 K. A computer program was written to tabulate the CCD detector values 

along a row selected by positioning a cursor in the Flashcam image. Figure 2 

shows the results of horizontal scans taken across the diameter of the BBS and 

along the sample. The camera was triggered manually just after placement of the 

rod in the blocks, and therefore, a delay of about 2 seconds occurs in obtaining 

the first image. Some cooling occurs during the transfer of the rod from the oven 

to the vee-blocks. The reduced amplitudes of video signals near the ends of the 

rod relative to the center are a result of subsequent cooling attributable to 

conduction through the supports. 

In order to characterize the Flashcam’s response to blackbody radiation over a 

range of temperatures, calibration data were acquired for various camera 

~ly~~tuurcs; aMl ~,\yosnrr integration times. Typical rcsponsc curves are r;hown in 

Figure 3. 
50 

0 

Blackbody 

Sample 

Figure 2. Digitized Scans of Images of Heated Rod and Blackbody Simulator. 

300 _ .- --_ --l-.-l_ ---------___--._ 

l-----Y I 

--- ------- ---- I 

-1-numbekO.85 I 

l-number=2 

f-number=8 

250 , 

0 

700 750 800 850 900 

Temperature (K) 

950 1000 1050 

Figure 3. Flashcam Response to Simulated Blackbody Radiation. 
The rate at which the heated rod cools may possibly affect the accuracy of the 

temperature measurement and must be considered during the c,llibrLltions imnd 

for the experiment. The rod cools by three mechanisms: (a) radiation, 

(b) convection to air, and (c) by conduction to the rod supports or electrical 

clamps. During calibration, cooling is readily observed by recording the 

Flashcam images at a standard video rate of 30 frames per second. Over many 

separate runs, the center of the rod sample was observed to cool at a rate of 

about 10 K/s from initial temperatures of around 800 K. 

The distance between the support points for the rod was the same for both the 

experiment and the calibration. Not surprisingly, the cooling rates observed 

during the experiment (discussed in Section 3 of this report) were about the same 

as those recorded during the calibration runs. Because of the short delay, 50 ms, 

between heating and image capture in the experiment, no corrections for sample 

cooling were necessary. 

3. Experimental Arrangement and Procedures 

3.1 Electrical Setup 

The heating source is a 1600~PF capacitor bank consisting of eight 200+F 

capacitors. A 40-mCI resistor attached directly to the terminal of each capacitor 

limits the output current of the capacitor. Two RG-217 coaxial cables carry the 

current from each capacitor to the input terminals of a triggered vacuum flashover switch 171. The output of the switch is coupled through 16 coaxial cables to 

the electrode plates shown in Figure 4. This arrangement produces a nearly 

axisymmetrical current into the conducting wire or rod. The outer copper braids 

of the coaxial cables are clamped to brass fittings threaded into the ground plate. 

Tht, c~lyy~ cer~t~ CLMIJ UC tur, surruunded by a pJy&+~ core, is cacti& 

through the gap to the second plate where the conductor makes electrical contact 

with the second or “hot” plate. The electrode assembly and capacitors are 

housed in a limited access range, whereas the charging unit and recording 

instruments are situated in a remote control room. The vacuum flash-over switch 

is triggered remotely after the capacitor bank is charged to the desired voltage. 

Both current and voltage measurements are required in order to compare theory 

and experiment in the work described in the introduction. To avoid errors 

associated with either the differentiation or integration of recorded signals, the 

current and the derivative of the current are measured separately. Four Pearson 

coils are used to measure the total current from the capacitor bank. The center 

conductors of the two cables attached to each capacitor are routed through the 

center of a Pearson coil. The connections become coaxial again at the periphery 

9 
of the capacitor container where the center conductors are routed through the 

outer braids of the cables. A Rogowski belt embedded in the ground plate (see 

Figure 4) measures the derivative of the current. 

Figure 4. Experimental Arrangement. 

3.2 Temperature Measurement Procedure 

The electrode plates are spaced 76 mm apart, and the voltage probes are attached 

across the central 50 mm of the rod. Initiation of current flow in the sample is 

accompanied by the production of electrical arcs between the plates, particularly 

at contact points. Copious quantities of visible light, to which the Flashcam is 

particularly sensitive, are produced. This light is troublesome for two reasons. 

First, arc emissions may reflect directly from the sample surface or indirectly 

from the surfaces of the aluminum electrodes. Such reflections, if added to the 

thermal emissions of the rod, will produce significant errors in the temperature 

measurement. Second, detectors in the CCD array may be saturated by arc 

emissions, a situation that could produce errors because of uncertainties in the 

recovery time of the detectors. Thus, it is necessary to avoid data accumulation 

until the initial illumination has decayed and the detectors have recovered. By 

observing a series of images of decaying arcs and molybdenum rods heated 

electrically, the authors determined that a 50~11s delay was more than adequate 

to ensure that the arc light did not affect the images of the thermal emission from 

the rod. For all the experiments involving the capture of a single image, the 

camera was triggered 50 ms after the pulse and the integration time was 10 rns 

(ten l-ms exposures). The measured cooling rate of 10 K/s implies that sample 

temperature drops only 0.5 K during the 50-ms delay. Thus, no correction for 

cooling is necessary. 
The limited range of temperatures that can be measured with the Flashcam 

(about 100 K) makes it necessary to have a good estimate of the final temperature 

before measurement in order to properly set the f-stop and exposure time for the 

camera. To this end, a series of computer calculations [I], based on a model 

described in Section 5, was undertaken to estimate the final temperature of the 

rod as a function of capacitor-bank charge voltage. The timeldependent current 

used in the calculations was taken from a circuit theory model via the 

parameters (i.e., resistance, inductance, and capacitance) known from experience 

to represent average values for the experiment. The computations were 

continued until the charge voltage required (about 7.5 kV) to produce an 

approximate final temperature of 800 K was identified. 

For all temperature measurements with the capacitor bank, the camera was 

positioned with a lens-to-sample distance of 65 cm, the same distance employed 

for the calibration runs. Temperature measurements were made by both 

recording methods discussed previously. 

4. Theoretical Analysis 

Calculations of the temperature and electromagnetic fields as a function of both 

space and time within the sample are undertaken with a simplified version of a 

model previously developed. The model calculations serve two purposes: first, 

as previously discussed, they predict the approximate charging voltage needed 

to produce a given temperature at the surface of the sample. Second, they also 

provide detailed results that can be compared to the experimental data, e.g., the 

final temperature of the sample surface. The data that are required as input into 

the model consist of the total current as a function of time as well the 

thermophysical properties of the sample undergoing study. 

The simplified model is one-dimensional in the radial direction. This 

approximation should be valid, provided the current input is nearly 

axisymmetrical and provided the region of interest is not too close to the 

electrode plates. The pertinent equations to be solved consist of the coupled heat 

transport and Maxwell equations. These equations have been derived, presented, 

and discussed for a reasonably general two-dimensional case 111. For the onedimensional limit and for a situation in which the sample is motionless and 

melting is ignored, the simplified equations reduce to 

and 

11 
(2) 

In these equations, B represents the magnetic induction field, T represents the 

temperature, and p represents the magnetic permeability. The variables o, p, C, 

and K represent the electrical conductivity, the density, the specific heat, and the 

thermal conductivity of the sample, respectively. The last three of these 

properties and the resistivity q (=1/a) are obtained from curve fits to data in 

references 2 and 3 and approximated as a power series in T. For any such 

property F, 

(3) 

The coefficients for any particular property, in appropriate SI units, are listed in 

Table 1 for molybdenum. 

Table 1. Coefficients for Thermophysical Properties of Molybdenum 

Coefficient C (J&K) rl (Q-4 K (W/mw P (kg/m3) 

d-3) 

4-2) 

d-1) 

40) 

41) 

42) 

a(3) 

44) 

0 

0 

0 

2.22624~10~ 

1.12844 x 10-l 

-5.87392 x10" 

2.08333~10" 

0 

0 

0 

0 

-1.95022~10‘~ 

2.41338x 10-lo 

1.89567x 10”’ 

1.54632 x 10-” 

-5.0 x lo" 

3.16906 x 10’ 0 

-2.67950x 10’ 0 

7.85718 x lo4 0 

5.564x10' 1.023 x 10” 

0 0 

0 0 

0 0 

0 0 

Equation (1) describes the transport of the magnetic induction field within the 

sample, and Equation (2) describes both the transportation and generation of 

heat. Ordinary heat conduction is accounted for, although it is usually negligible 

on the time scales of interest. The last two terms on the right-hand side of 

Equation (2) can be recognized as the energy dissipated per unit volume and 

time by ohmic heating. No other source terms or transportation mechanisms are 

considered. Clearly, the two equations are coupled since the electrical 

conductivity depends upon temperature, and the source term in the energy 

equation depends on the magnetic induction. 

12 
Equations (1) and (2) must be solved, subject to the boundary conditions that the 

temperature gradient be zero both at r = 0 and at r = rO, where r, is the radius of 

the sample. From Ampere’s law, it also follows that B(r = 0) = 0 and 

B(r=r,)=$ 

0 

(4) 

where i is the total pulsed current at time t. The value of i as a function of time is 

input directly from the experimental data or from the circuit fits described 

earlier. The equations are then represented in standard finite difference form and 

solved numerically by an iterative procedure as described in reference 1. 

5. Results 

Three runs were made with pre-oxidized samples at a charge voltage of 

approximately 7.5 kV. A plot of the circuit current used to heat the sample in 

Shot S2 is shown in Figure 5. The calculated surface temperature of the sample as 

a function function of time for this shot is shown in Figure 6. 

400 - 

350 

300 

250 

200 

z-- 

5. 150. 

E 

s!! 2 100 loo0 

50 - 

0 -I 

0 250 3 

-50 - 

-100 - 

Time (ps) 

Figure 5. Current Trace for Shot S2: Charge Voltage = 7.51 kV. 
As noted previously, the camera was calibrated in both the triggered and freerun mode of operation, and both were used in the experiments. The Flashcam 

image of a molybdenum rod heated to approximately 800 K is shown in Figure 7; 

the digitized Flashcam output for all three shots is shown in Figure 8. Also 

shown in Figure 8 are three calibration curves that indicate the temperature to be 

associated with a given signal amplitude. The horizontal position of the 

calibration curves in this graph has been arbitrarily shifted for clarity of 

presentation. All data, both calibration and experiment, were obtained for the 

following conditions: (a) f-number of 0.85, (b) 10 successive l-ms exposures, and 

(c) a lens-to-sample distance of 65 cm. 

goo i 

0 50 100 150 200 250 

Time (ps) 

Figure 6. Predicted Surface Temperature Versus Time for Shot S2. 
0 

0 20 

Pixel Number 

40 60 

Figure 8. Profiles of Surface Temperature of Heated Rods Versus Calibration Curves. 

The three separate temperature measurements and corresponding theoretical 

predictions are compared in Table 2. The predictions were obtained with the 

model discussed previously and with the experimentally measured current used 

as input. The differences between the theoretical and experimental results are 

well within the experimental uncertainty, but they do not reflect the normal 

spread of differences because the number of experiments was limited. 

Table 2. Comparison of Theoretically Calculated and Experimentally 

Measured Temperatures (all results are in K.) 

Theory Experiment Difference 

Sl 774 770 -4 

s2 776 772 -4 

s3 777 774 -3 

This result provides an important and necessary confirmation of our approach. It 

;11c;t) .prt)viJtls the iml~~+us to cclntinrrc, 1_7ffmts to dwrlop ;I yrnrcdnrP fm thr 
evaluation of some of the thermophysical properties for new alloys and 

materials in electrical heating experiments with a capacitor bank. 

6. Discussion and Future Work 

In recent years, data pertaining to the thermophysical properties of several 

elements and alloys, which are important for various Army applications of 

pulsed power, have been accumulated in ARL experiments. Emphasis has 

centered on three elements, molybdenum, tantalum, and tungsten, because the 

thermophysical properties of all three materials are known to very high 

accuracy-an essential requirement for validating the experiments. In this 

report, we have shown that the temperature predicted by the preferred 

thermophysical parameters for molybdenum is in agreement with the 

experimentally measured temperature at 800 K. 

For future work, the experimental uncertainties in the temperature measurement 

by our video thermography technique could be reduced. The largest uncertainty 

is associated with establishing a value for the temperatures of the rods during 

calibration. This uncertainty consists of two components: ascertaining the true 

temperature of the rod within the oven and knowing how much the rod cools 

during removal from the oven and positioning for calibration. A more direct, 

automated way of transfer of the heated rod from the oven to a position near the 

BBS could be devised. The present manual procedure used to remove the sample 

from the oven and position it for calibration requires that a correction for cooling 

be applied. This correction was estimated to be -15 K. The overall uncertainty 

associated with our temperature measurement is estimated to be +20 K. 

Many options and alternate techniques, not exercised in the present experiment, 

could be used to extend the range of temperature measurements with video 

thermography. Broad band spectral techniques, such as those used in the present 

experiment, will always offer more potential for high speed imaging than will 

narrow band techniques because more photons are collected. However, the use 

of narrow spectral band filters, possible at the radiances associated with higher 

temperatures, could also be a useful tool in some situations, e.g., as a means of 

reducing extraneous arc light or to improve accuracy. A two-color thermometry 

technique, based on the ratio of spectral radiance in two bands [Bl, may offer 

advantages for very high temperature measurements. 

Moreover, the spatial resolution capability of the camera was hardly exploited in 

the present experiment because, at the time of measurement, the entire rod was 

at the same temperature. It could be useful in future studies employing high 
evaluation of some of the thermophysical properties for new alloys and 

materials in electrical heating experiments with a capacitor bank. 

6. Discussign and Future Work 

In recent years, data pertaining to the thermophysical properties of several 

elements and alloys, which are important for various Army applications of 

pulsed power, have been accumulated in ARL experiments. Emphasis has 

centered on three elements, molybdenum, tantalum, and tungsten, because the 

thermophysical properties of all three materials are known to very high 

accuracy-an essential requirement for validating the experiments. In this 

report, we have shown that the temperature predicted by the preferred 

thermophysical parameters for molybdenum is in agreement with the 

experimentally measured temperature at 800 K. 

For future work, the experimental uncertainties in the temperature measurement 

by our video thermography technique could be reduced. The largest uncertainty 

is associated with establishing a value for the temperatures of the rods during 

calibration. This uncertainty consists of two components: ascertaining the true 

temperature of the rod within the oven and knowing how much the rod cools 

during removal from the oven and positioning for calibration. A more direct, 

automated way of transfer of the heated rod from the oven to a position near the 

BBS could be devised. The present manual procedure used to remove the sample 

from the oven and position it for calibration requires that a correction for cooli.ng 

be applied. This correction was estimated to be -15 K. The overall uncertainty 

associated with our temperature measurement is estimated to be 420 K. 

Many options and alternate techniques, not exercised in the present experiment, 

could be used to extend the range of temperature measurements with video 

thermography. Broad band spectral techniques, such as those used in the present 

experiment, will always offer more potential for high speed imaging than will 

narrow band techniques because more photons are collected. However, th.e use 

of narrow spectral band filters, possible at the radiances associated with higher 

temperatures, could also be a useful tool in some situations, e.g., as a means of 

reducing extraneous arc light or to improve accuracy. A two-color thermometry 

technique, based on the ratio of spectral radiance in two bands [81, may offer 

advantages for very high temperature measurements. 

Moreover, the spatial resolution capability of the camera was hardly exploited in 

the present experiment because, at the time of measurement, the entire rod was 

at the same temperature, It could be useful in future studies employing high 

16 
speed imaging techniques to observe the changing temperature distributions on 

rapidly heated rods. 

Finally, the earliest time when .measurement of the surface temperature occurs 

could be reduced by the redesigning of the fixtures used to mount the sample. 

These fixtures were not designed with temperature measurements in mind. 

Redesign could significantly reduce the arc light output during heating. 

17 
i 

18 
References 

1. 

2. 

3. 

4. 

5. 

4. 

7. 

8. 

Powell, J.D., “Current and Heat Transport in Axisymmetric Conductors,” 

ARL-TR-2066, US. Army Research Laboratory, Aberdeen Proving Ground, 

MD, 1999. 

Desai, P-D, T.K. Chu, H.M. James, and C.Y. Ho, “Electrical Resistivity of 

Selected Elements,” Journal of Physical and Chemical Reference Data, Vol. 

13, No. 4, pp 1069-1096,1984. 

Cezairliyan, A., M.S. Morse, H.A. Berman, and C.W. Beckett, “High-Speed 

(Subsecond) Measurement of Heat Capacity, Electrical Resistivity, and 

Thermal Radiation Properties of Molybdenum in the Range 1900 to 2800 K,” 

Journal of Research of National Bureau of Standards-A, Phvsics and 

Chernistrv, Vol. 74A, No. 1, pp. 65-92, January-February 1970. 

Dewitt, D.P., and G.D. Nutter (Editors), Theorv and Practice of Radiation 

Thermometrv, John Wiley and Sons, Inc., New York, 1988. 

Stumpfel, C.R., “In-Flight Projectile Imaging by Infrared Emission/Rotating 

Mirror Technique With Temperature Calibration,” ARL Report ARL-TR1148, AD A313428, U.S. Army Research Laboratory, Aberdeen Proving 

Ground, MD, July 1996. 

Di Giulio, M., G. Manno, G. Micocci, A, Serra, and A. Tepore, “Physical 

Properties of Molybdenum Oxide Thin Films for NO Gas Detection,” Physica 

Status Solidi (a), Vol. 168, pp. 249-259,1998. 

Ford, R.D., G., Dorr, R., Reams, and A. J. Toepfer, “High-Coulomb Triggered 

Vacuum Flashover Switch,” 11th IEEE International Pulsed Power 

Conference, Baltimore, Maryland (1997), IEEE catalog No. 97CH36127, Vol. 

II, p. 893,1999. 

Zielinski, A.E., S. Niles, and J.D. Powell, “Current and Heat Transport 

During a Pulsed Electrical Discharge,” Journal of Applied Phvsics, Vol. 86, p. 

4933,1999. 

19 
20 
APPENDIX A 

CALCULATION OF UNCERTAINTY IN TEMPERATURE 

MEASUREMENT ATTRrBUTABLE TO UNCERTAINTY IN EMISSMTY 

21 
22 
‘A graybody is defined as an emitter with spectral emissivity that is less than one and independent 

of wavelength. 

23 

CALCULATION OF UNCERTAINTY IN TEMPERATURE MEASUREMENT 

ATTRIBUTABLE TO UNCERTAINTY IN EMISSIVITY 

In this appendix, we evaluate the uncertainty in temperature measurement 

attributable to uncertainty in emissivity of the sample. The area of concern 

involves possible differences between the emissivity during calibration and the 

emissivity during the experiment. For example, if the calibration were performed 

with a rod having an emissivity of 0.8 but the experiment were performed with a 

rod having 0.6, what error would be introduced in the temperature 

measurement? A more complete analysis of these kinds of uncertainties is given 

by Stumpfel151. 

The contribution to the signal generated by the Flashcam system at any 

wavelength is proportional to the spectral emissivity; the total signal produced 

results from integration over a range of wavelengths. To calculate the signal 

expected for a given temperature and emissivity, the following procedure was 

used. 

For each of several selected spectral emissivities, the spectral radiance was 

calculated from Plan&s Distribution Law. This calculation consisted of an 

integration of the distribution function over wavelength with the limits 

determined by the “cut-off” wavelengths of the Flashcam, 350 and 1040 run, 

respectively. Finally, the response of the Flashcam to various wavelengths, i.e., 

data supplied by the manufacturer, was folded into the results of the integration. 

As an example of these calculations, the relative response curves versus 

temperature over a temperature range of 780 to 820 K and for an emissivity of 1.0 

and graybody emissivities of 0.6 and 0.8 are plotted in Figure A-l. 

The effect of uncertainty in the emissivity on the temperature measurements can 

be quickly evaluated for a range of emissivities via this computational 

procedure. The values in Table A-l were obtained from plots of signal versus 

temperature such as those of Figure A-l. 

Let Tm represent the measured temperature and T, the true temperature. Then, 

the difference or error, AT, is defined as 

AT=Tm-T,. 
12 --"-.--."- -----_-----_-_ _-.....- 

-emissivity=l 

-. _. . emlsslvity&8 

- - I emlssivity=0.6 

10 

O775 780 785 790 795 800 805 810 815 820 825 

Temperature (K) 

Figure A-l. Relative Response of Camera for Selected Emissivities. 

At measured temperature, T,, around 800 K, the following temperature errors, 

AT, result when the emissivities for the calibration and experiment are as 

indicated in Table A-1. 

Table A-l. Temperature Error, AT (K), at 800 K Resulting From Different 

Emissivities, E, During Calibration and During the Exper*iment 

I 

E, Experiment 

E, Calibration 0.4 0.6 0.8 1.0 

0.4 0 +14 +28 +38 

0.6 -16 0 +10 +20 

0.8 -30 -12 0 +10 

1.0 -40 -22 -8 0 

With the particular surface preparation of the rod used in the experiment, we 

estimate that the probable emissivity for both calibration and experiment is 

around 0.8. Let us assume that the emissivity uncertainty is +0.2. Then from the 

table, if the emissivity during the calibration were 0.8 and the emissivity during 

24 

i 
the experiment were 0.6, then the error, AT, would be -12 K with the measured 

temperature lower than the true temperature. Likewise, for an emissivity of 1.0 

during the experiment, the error would be +lO K with the measured temperature 

higher than the true temperature. The errors in this example are about 1.5% of 

the absolute temperature of 800 K. However, when the pre-oxidization surface 

technique is used (including the blackbody comparison), we believe the 

emissivity variations are much less than 20.2, We conclude that the uncertainties 

in our measured temperatures attributable to uncertainties in the emissivity of 

the samples are small. This insensitivity is a general characteristic of systems that 

sense the shortest effective wavelengths emitted by a thermal source. A 

discussion of this principle is given by Dewitt 141. 

25 
26 
APPENDIX B 

SUMMARY OF PROCEDURES FOR CALIBRATION OF FLASHCAM 

SYSTEM AND TEMPERATURE MEASUREMENT 

27 
28 
STJMMARY OF PROCEDURES FOR CALIBRATION OF FLASHCAM SYSTEM 

AND TEMPERATURE MEASUREMENT 

Calibration: 

1. Pre-oxidize molybdenum sample using oven treatment so that surface is 

stable and has a high emissivity. 

2. Place molybdenum sample in pre-heated oven and heat to desired calibration 

temperature. 

3. Remove sample rapidly from oven and record digital image or series of 

images on videotape. 

4. Repeat Steps 2 and 3 using temperature steps appropriate for complete 

coverage of the desired temperature range. 

5. Measure output video signal levels versus temperature and save in 

appropriate form for later comparison to corresponding data from experiment. 

Experiment: 

1. Pre-oxidize molybdenum sample using oven treatment so that the surface has 

a stable, high emissivity similar to that used in the calibration. The same rod 

used for calibration may also be used in the measurement. 

2. Place rod between electrode plates and discharge current through rod. 

3. Record, with selected delay time, either a single digitized image or a series of 

images on videotape. 

4. Use signal level versus temperature results from the calibration to assign 

temperatures based on the signal levels recorded in the experiment. 

29 
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1. TITLE AND SUBTITLE 5. FUNDING NUMBERS 

A Video Thermography Technique for Temperature Measurements of Pulse-Heated Metallic Rods 

_ PR: lL161102AH43 

j. AUTHOR(S) 

Hollandsworth, C.E.; Stumpfel, CR.; Powell, J.D.; Hummer, CR. 

‘. PERFORMING ORGANIZATION NAME(S) AND ADDRESS a. PERFORMING ORGANIZATION 

REPORT NUMBER 

U.S. Army Research Laboratory 

Weapons & Materials Research Directorate 

Aberdeen Proving Ground, MD 21005-5066 

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Weapons & Materials Research Directorate ARL-TR-2420 

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I. SUPPLEMENTARY NOTES 

2a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE 

Approved for public release; distribution is unlimited. 

3. ABSTRACT (M&mum 200 words) 

A video thermography technique for measuring the surface temperature of metallic rods is described in this report. The 

technique employs a video camera with charge-coupled devices as the detection elements; it is applicable to materials that can 

be preheated to form an oxide layer with a stable emissivity. The procedure is illustrated by the measurement of the surface 

temperature of molybdenum rods that have been rapidly heated to about 800 K by an electrical discharge. The thermal emission 

profile of the sample is observed with the video camera, and the final surface temperature is inferred from previously obtained 

calibration data. The time-dependent current through the rod is also measured and used as input in theoretical calculations that 

describe the coupled transport of electromagnetic fields and heat through the sample. The temperatures predicted by the model 

calculations are in excellent agreement with the values inferred from the experiments. 

4. SUBJECT TERMS 15. NUMBER OF PAGES 

molybdenum temperature measurement 40 

pulse heating thermography 16. PRICE CODE 

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