Peter Struk and Daniel Dietrich

Glenn Research Center, Cleveland, Ohio

Russell Valentine and Ioan Feier

Case Western Reserve University, Cleveland, Ohio

Comparisons of Gas-Phase Temperature

Measurements in a Flame Using

Thin-Filament Pyrometry

and Thermocouples

NASA/TM—2003-212096

February 2003

AIAA–2003–853

https://ntrs.nasa.gov/search.jsp?R=20030055631 2018-05-15T16:37:58+00:00Z
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Peter Struk and Daniel Dietrich

Glenn Research Center, Cleveland, Ohio

Russell Valentine and Ioan Feier

Case Western Reserve University, Cleveland, Ohio

Comparisons of Gas-Phase Temperature

Measurements in a Flame Using

Thin-Filament Pyrometry

and Thermocouples

NASA/TM—2003-212096

February 2003

National Aeronautics and

Space Administration

Glenn Research Center

Prepared for the

41st Aerospace Sciences Meeting and Exhibit

sponsored by the American Institute of Aeronautics and Astronautics

Reno, Nevada, January 6–9, 2003

AIAA–2003–853
Acknowledgments

The authors acknowledge the NASA Office of Biological and Physical Research (OBPR), the Graduate Student

Researchers Program (GSRP), the Ohio Aerospace Institute (OAI), and the National Center for Microgravity

Research (NCMR) for their support of this research.

Available from

NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22100

Available electronically at http://gltrs.grc.nasa.gov
NASA/TMó2003-212096 1 

COMPARISONS OF GAS-PHASE TEMPERATURE MEASUREMENTS 

IN A FLAME USING THIN-FILAMENT PYROMETRY AND THERMOCOUPLES 

Peter Struk and Daniel Dietrich 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Russell Valentine and Ioan Feier* 

Case Western Reserve University 

Cleveland, Ohio 44106

Abstract

Less-intrusive, fast-responding, and full-field 

temperature measurements have long been a desired 

tool for the research community. Recently, the emission 

of a silicon-carbide (SiC) fiber placed in a flowing hot 

(or reacting) gas has been used to measure the 

temperature profile along the length of the fiber. The 

relationship between the gas and fiber temperature 

comes from an energy balance on the fiber. In the 

present work, we compared single point flame 

temperature measurements using thin-filament 

pyrometry (TFP) and thermocouples. The data was 

from vertically traversing a thermocouple and a SiC 

fiber through a methanol/air diffusion flame of a 

porous-metal wick burner. The results showed that the 

gas temperature using the TFP technique agreed with 

the thermocouple measurements (25.4 μm diameter 

wire) within 3.5% for temperatures above 1200 K. 

Additionally, we imaged the entire SiC fiber (with a 

spatial resolution of 0.14 mm) while it was in the flame 

using a high resolution CCD camera. The intensity 

level along the fiber length is a function of the 

temperature. This results in a one-dimensional 

temperature profiles at various heights above the burner 

wick. This temperature measurement technique, while 

having a precision of less than 1 K, showed data scatter 

as high as ±38 K. Finally, we discuss the major sources 

of uncertainty in gas temperature measurement using 

TFP. 

Introduction

The ideal gas-phase temperature measurement is a 

full-field measurement with good spatial resolution, is 

accurate, has a fast response time, is non-intrusive, has 

wide dynamic range, and is easy to apply. Thinfilament pyrometry (TFP) is a technique that meets 

several of the above characteristics especially for higher 

temperature applications like combustion. TFP uses a 

*NASA Resident Research Associate at Glenn Research Center. 

thin-filament that is typically on the order of 

10 to 100 microns in diameter. Silicon-Carbide, or SiC, 

has emerged as a material with suitable properties for 

TFP: good strength even at flame temperatures, 

relatively constant emissivity, resistant to oxidation and 

catalytic effects, and widely available. When used for 

temperature measurements, the SiC fiber is placed in a 

thermal environment which heats the SiC. 

Subsequently, the SiC emits thermal gray body 

radiation, which is then detected, quantified, and related 

to the temperature of the fiber. Finally, the fiber 

temperature is related to the surrounding gas 

temperature through an energy balance on the fiber. 

Vilimpoc and Goss1

 first reported results using the 

TFP technique. They measured a line temperature 

profile at various heights above a H2-N2 jet diffusion 

flame. A rotating mirror traced the image of the fiber 

onto an InGaAs detector that was sensitive to radiation 

from 900 to 1600 nm. The measurable filament

temperature ranged from 1000 to 2370 K with a 

reported precision varying from ±80 K at low 

temperatures to ±8 K at high temperatures. The gas 

temperature profiles came from balancing convective 

and radiant energy (neglecting axial conduction along 

the fiber). Bedat et al.2

 used an InSb (2.5 to 6.0 μm 

sensitivity) detector to extend the low temperature 

range of TFP to approximately 550 K. They used a 

narrow band filter at 3.9 μm to limit the interference 

from flame radiation. 

Pitts3

 used a cooled 16-bit camera (spectral 

response was not reported) to image a 15 micron SiC 

fiber in an acoustically phase-locked flickering (i.e. 

transient) laminar methane/air diffusion flame. He 

reported a measurement precision of 1.4 ±1 K for the 

filament temperature. The author, however, did not 

correct for radiative and conductive losses. Pitts 

acknowledged that the accuracy of the gas temperature 

measurement is considerably less than the precision 

without detailed knowledge of the flow velocities and 

chemical composition of the gas surrounding the SiC 

fiber. 
NASA/TMó2003-212096 2 

Ji et al.4

 reported calibrating a SiC fiber 

temperature over a McKenna burner using an InSb 

detector in the wavelength range of 3300 to 4000 nm. 

This work compared measured temperatures to values 

of the calculated adiabatic flame temperature. These 

values agreed to within 25 K. This work also compared 

measured thermocouple temperatures at similar 

locations, which differed from the adiabatic 

temperature by as much as 150 K. No account of 

radiative or conductive losses was reported in this 

paper. 

The emphasis of this work was to apply the TFP 

technique to measure the gas temperature of a practical 

diffusion flame and compare these results to more 

traditional thermocouple measurements. The flame was 

a small (1.3 cm height), axisymmetric, steady diffusion 

flame from a porous-metal wick burner. The fuel was 

methanol, burned in room air, and the resulting flame 

was very dim blue (nearly invisible to the eye). The 

dim, soot-free flame was necessary to eliminate broadband radiant emission from soot which greatly 

complicates temperature measurement using the TFP 

technique. The specific measurement techniques at 

different heights above the burner wick include: 

1. A single-point fine-wire thermocouple 

(25.4 μm diameter wire with a 63.5 μm bead 

diameter) measurement along the centerline of 

the flame. 

1. A single point measurement using a 15μm 

diameter SiC fiber mounted horizontally 

across the flame. A spectrometer (sensitivity 

585 to 1160 nmÜ

) detected emission from a 

small SiC portion intersecting along the 

centerline (i.e. the same location where the 

thermocouple bead was located previously). 

2. The entire SiC fiber using a CCD camera

sensitive between 200 and 1100 nm. 

We present comparisons of the resulting 

measurements from the above techniques. Additionally, 

emphasis is placed on estimating the uncertainty of the 

gas temperature when accounting for radiative and 

conductive losses in the measurements. 

Experiment

The test apparatus consisted of a burner mounted 

on a vertical translation stage, a thermocouple, a 

silicon-carbide fiber (SiC), and various optical 

diagnostic/camera equipment (Figure 1). The 

thermocouple was parallel to and 3 mm below the SiC 

 

Ü

The actual spectral sensitivity was narrower than the detector 

capability due to the optics used in the experiment (discussed later). 

fiber, with both perpendicular to the burner centerline. 

The thermocouple bead was on the burner centerline. 

Both the thermocouple and SiC fiber were under slight 

tension to prevent sagging when in the flame. The 

custom built burner consisted of a fuel reservoir 

penetrated by a cylindrical porous bronze metal wick. 

The bronze wick had a diameter of 3.25 mm and a 

wetted length of 6.2 mm. The fuel was methanol, and 

the resulting diffusion flame, burning in room air, was 

very dim blue (nearly invisible to the eye). Figure 2 

shows typical flame images taken with the CCD. 

The test procedure was to traverse the flame 

vertically through the fixed thermocouple and SiC fiber 

arrangement. With the thermocouple initially at the 

wick surface and the SiC fiber 3 mm above the wick 

surface, the burner translated 15 mm downwards in 

0.5 mm increments. At each increment, there were three 

separate but near simultaneous measurements: 

(1) a high-resolution, CCD camera image of the 

glowing SiC fiber; (2) a type-S thermocouple 

measurement of flame temperature, and (3) a 

spectrometer (sensitive from 585 to 1160 nm) 

measurement of a point along the SiC fiber at the 

centerline of the flame. At each location, at least 

1 minute passed prior to taking the measurements to 

ensure that the flame was steady. 

Figure 1. Schematic of experimental setup. 

CCD Controller 

CCD Camera 

Macro Lens 

BG-25 Filter 

L1BC Filter 

SiC Fiber 

Thermocouple 

Lens 

Burner 

Spectrometer

Fiber 

Optic 

Cable
NASA/TMó2003-212096 3 

Figure 2. CCD camera images of a methanol/air 

diffusion flame. The upper image was taken just 

prior to testing (with image enhancement to bring 

out the flame) and the lower image was taken during 

testing with a SiC fiber and thermocouple placed in 

the flame. The SiC fiber emission and glowing 

thermocouple dominate the emission detected by the 

camera; hence, no flame is visible in the lower 

image.

Experimental Apparatus

SiC

The SiC fiber used in these tests was manufactured 

by a polymer pyrolysis process. The fiber is 

homogeneously composed of ultra fine beta-SiC 

crystallites and an amorphous mixture of silicon (58%), 

carbon (21%), and oxygen (11%). The fiber diameter 

was nominally 15 μm but may vary from 12 to 18 μm 

according to the manufacturer. 

Thermocouple

The thermocouples were bare wire, type-S (Pt ñ 

Pt/10% Rh), with the bead of the thermocouple located 

on the centerline of the burner. We choose two 

thermocouple wire diameters, 76.2 μm (0.003î) and 

25.4 μm (0.001î), to show the effect of conductive 

losses along the fiber. The spherical thermocouple bead 

was 2.5 times the wire diameter as reported by the 

manufacturer. 

A thermocouple signal conditioner (amplifier) and 

a data acquisition system measured the thermocouple 

voltage. The relationship between the thermocouple 

voltage and temperature is via a polynomial curve fit 

provided by the manufacturer. 

Spectrometer

The spectrometer is sensitive to light in the 

wavelength range from 585 nm to 1160 nm. The 

spectrometer has a 2048 element linear-detector array 

with each pixel digitized to 12 bits of resolution. The 

integration time (duration during which the light 

emission from the SiC was allowed to accumulate on 

the detector) varied between 60 to 200 msec. 

The spectrometer measured the spectrum of light at 

a point on the SiC fiber directly above the 

thermocouple bead (i.e. along the flame centerline). 

A lens was in front of the open end of the fiber optic 

cable in order to focus the emission from a single point 

of the SiC fiber onto the end of the fiber optic cable 

(Figure 1). 

CCD camera

The camera uses a high-resolution (16 bit), thermoelectrically cooled, back-illuminated, charge-coupled 

device (CCD) array with a rectangular 330 by 

1100 pixel array. The CCD has a spectral response from 

200 to 1100 nm. A 60 mm macro lens was in the front 

of the camera to image the fiber. The exposure time on 

the camera was 5 msec, the cameraís shortest duration. 

An additional blue-glass filter (BG-25) reduced the 

intensity of the emission to prevent saturation of the 

CCD. A UV filter (L1BC) was part of the lens and thus 

accounted for in the analysis. A thermoelectric cooler 

kept the CCD array at 233 K to limit detector noise. 

Analysis

Thermocouple

The temperature of the thermocouple bead and 

actual temperature of the local gas are different and are 

related by a steady-state energy balance on the surface 

of the thermocouple bead (equation 1).5,6 Heat is added 

to the thermocouple bead through convection from the 

hot gases of the flame. Heat is lost from the 

thermocouple bead by radiation. Either a loss or gain of 

heat can occur by axial conduction along the 

thermocouple wire. In equation 1, we assume the 

conduction term to be symmetric about the bead (i.e. on 

the burner centerline). Catalytic effects are neglected. 

1 cm 

3 mm 

Thermocouple wire 

Silicon-carbide fiber 
NASA/TMó2003-212096 4 

2 0

( ) ( ) 4 4

= 



 





 −

− − − ∞

b

w

w w

b g b b b

dx

dT k A

hA T T εσA T T

 (1) 

Equation 1 can be rearranged to solve for the gas 

temperature (equation 2). 















 



 



















 = + − ∞ +

b

w

b

w w g b b dx

dT

hA

k A T T

h

T T 2 ( ) εσ 4 4 (2) 

To compute the heat transfer coefficient, h, in 

equation 2, we used a Nusselt number for forced 

convection over a sphere at low Reynolds number 

(equation 3).7

 The characteristic length for the Reynolds 

number is the thermocouple bead diameter (190 or 

63 μm). 

( )

g

b

k

h D

Nu × = + × = 0.82 2 0.2 Re (3) 

( ) 













 × = ≤ ≤ =

g

U Db

ν

Pr 0.71, 0.07 Re 20 Re

The velocity used in the Reynolds number is from 

a scaling analysis for a candle flame which is 

appropriate for Grashof numbers >1 (equation 4).8

avg

g gH U

ρ

(ρ − ρ ) = ∞ (4) 

U is the maximum characteristic velocity for a 

flame of height H, the local density is ρH, and the mean 

density, ρmean, is the average value between the ρH and 

the ambient density ρ∞. For our flame, the estimated 

characteristic velocity was 40 cm/s which yielded Re ~ 

0.1 (using properties of air at the final film, or average, 

temperature). 

The conductive term along the thermocouple wires 

(last term in equation 2) is difficult to calculate because 

it requires knowledge of the temperature gradient at the 

interface of the thermocouple bead and wire. This 

correction can be significant depending on the 

temperature gradient and thermocouple wire diameter. 

In many practical flame configurations, temperature 

gradients are steep. Thus, the only recourse to minimize 

conductive loss is to use small diameter thermocouples. 

We used two thermocouple wire diameters, 76.2 and 

25.4 μm, during separate tests. Our results show that 

the gas temperature measured using the smaller 

diameter wire agreed better with the spectrometer data 

(presented later) compared to the tests with the larger 

diameter wire. We attribute this difference to the 

importance of conductive loss at larger thermocouple 

wire diameters and non-negligible temperature 

gradients; the latter due to slight variations in the 

position of the thermocouple bead with the centerline of 

the flame. 

To evaluate the thermophysical properties in 

equations 2, 3, and 4, the composition and temperature 

of the gas must be known. Since we did not make 

measurements of the gas constituents surrounding the 

thermocouple, we must make an assumption regarding 

the gas composition. In this analysis, we assumed that 

the surrounding gas is air and values for thermophysical 

properties were from Incropera & DeWitt (1990).9

 The 

thermophysical properties are evaluated at the film 

temperature, that is the average value between the 

thermocouple and gas temperature. Since the gas 

temperature is unknown, the gas temperature must be 

deduced in an iterative fashion. The total emissivity of 

the bare wire thermocouple is a function of temperature 

(and oxidation level of the surface) and ranged between 

0.18 < ε < 0.24.10 Although oxidation effects may 

change the emissivity of the thermocouple especially 

during exposure to flame conditions, we neglect the 

effect of thermocouple oxidation in the analysis. Figure 

3 shows the results of the thermocouple measurement 

(25.4 μm diameter wire) and the calculated gas 

temperature around the thermocouple along the 

centerline of the flame. 

2000

1800

1600

1400

1200

1000

800

600

400

Temperature (K)

0 5 10 15 20

Height above burner wick (mm)

 Thermocouple

 Gas Surrounding Thermocouple

 SiC Fiber

 Gas Surround SiC Fiber

Figure 3. Temperature measurements along the 

centerline of the burner as a function of height using 

a thermocouple and spectrometer / SiC fiber TFP 

technique. 
NASA/TMó2003-212096 5 

Spectrometer

The spectrometer measured the spectral emission 

from a point on the SiC fiber located on the centerline 

of the flame. Equations 5 and 6 show the total spectral 

emission, ITotal, where the SiC emission is equal to the 

emission of a black body at the fiber temperature, 

IBB(λ,T), times the emissivity of the fiber. Taking 

measurements of just the blue flame produced no 

appreciable signal on the spectrometer, consequently 

we were able to neglect the emission of the flame in our 

analysis. The spectrometer does produce, however, a 

signal even when no ambient radiation is allowed to 

reach the detector (e.g. covered detector). This ìdark 

signalî is measured prior to each test and subtracted 

from the SiC signal. 

I ( ,T) [ ( ) I ( ,T) I ( ,T)] Total λ = ε λ × BB λ + flame λ (5) 





 



  −



 



 =

exp 1

( , )

4 2

1

T

C

C I BB T

λ

πλ

λ

14387.69( )

1.884 10

2

2

3

27

1

C m K

m s

photons m C

= ×

















×

× = ×

μ

μ

 (6) 

The emission measured by the spectrometer is 

different than the total emission leaving the SiC fiber 

(and flame). The difference results from attenuation of 

the light signal through the atmosphere, various optics 

in the system prior to reaching the detector, and the 

quantum efficiency of the detector. The final signal on 

the detector is converted to a voltage which is then 

converted to counts in the A/D converter. The detector 

signal, R(λ), can be expressed mathematically as in 

equation 7 where λ is the wavelength of light, T is the 

temperature of the SiC, G corresponds to the detected 

photons to voltage conversion, QE(λ) is the spectral 

quantum efficiency of the detector, and Loss(λ) is the 

spectral attenuation of the light due to the optics. 

Following the procedure of Miller11, a function, S(λ), 

relates the spectral sensitivity of the detector and optics 

to the incoming radiation (equation 8). Thus, a 

blackbody intensity profile (equation 9) comes from 

rearranging equations 7 and 8. 

R( ,T) G [ ] QE( ) Loss( ) ( ) I ( ,T) λ = × λ × λ ×ε λ × BB λ (7) 

[ ] ( ) ( )

1 ( ) λ λ

λ

QE Loss

S × = (8) 

( )

( , ) ( ) ( , )

ε λ

λ λ λ ⋅

⋅ = GR T S I BB T (9) 

The data show that the emissivity of SiC is 

relatively uniform in the wavelength range of the 

spectrometer and the temperature range of the flame.12

Also, the conversion from detected photons to voltage 

is linear, hence, the variable G is constant. Since the 

emissivity and G are independent of λ and T, they can 

be eliminated from the equation by normalizing 

equation 7 by values at a normalization wavelength, λ0 

(equation 10). The normalized functions (denoted by a 

bar) can be rearranged to solve for the blackbody 

intensity as shown in equation 11. 

































⋅

⋅ = ( , )

( , )

( ) ( )

( ) ( )

( , )

( , )

0

0 0

0 I T

I T

QE Loss

QE Loss

R T

R T

BB

BB

λ

λ

λ λ

λ λ

λ

λ (10) 

IBB (λ,T) = S(λ) × R(λ,T) (11) 

A custom computer program calculated the 

temperature of a blackbody that best matches (in a 

least-squares sense) the measured spectral distribution 

according to equation 11. To do this calculation, the 

sensitivity function of our spectrometer / optical system 

was determined using a blackbody calibration source at 

three temperatures (800, 900, and 1000 °C). The 

sensitivity function was the same (within the 

uncertainty of the detector) at each temperature (as 

expected since it should only be a function of 

wavelength). Although the spectrometer is sensitive to 

light between 585 and 1160 nm, we used data only in 

the range from 766 to 940 nm. Outside this range, the 

signal to noise ratio was quite high (particularly near 

the extremes of the detector sensitivity). The 

normalization wavelength was 894 nm which 

corresponds to the most intense signal on the 

spectrometer. The selection of the normalization 

wavelength does not affect the results so long as there is 

a large signal to noise ratio at the wavelength of choice. 

Figure 4 shows the sensitivity function as a function of 

wavelength, normalized by the signal at 894 nm. 

3.0

2.5

2.0

1.5

1.0

0.5

0.0

Normalized Sensitivity Function

0.70 0.75 0.80 0.85 0.90 0.95 1.00

Wavelength (μm)

Figure 4. Sensitivity function (normalized at 894 nm) 

for the spectrometer as a function of wavelength from 

blackbody calibration. 
NASA/TMó2003-212096 6 

The gas temperature surrounding the SiC is 

obtained in a similar fashion to the calculation 

presented for the thermocouple . Performing an energy 

balance on a differential axial element of the SiC fiber 

yields equation 12. As with the thermocouple, the SiC 

absorbs heat from convection, loses heat from radiation, 

and loses or gains heat by axial conduction along the 

fiber. 

0

4

( ) ( ) 4 4

=













 −

− − − ∞

dx

dT

k

dx

D d

h T T T T

f

f

f

g f f εσ

 (12) 

Based on temperature profiles obtained from the 

CCD camera (see for example, Figure 7, which will be 

discussed later), we were able to estimate the 

temperature gradients along the SiC fiber. Based on the 

maximum temperature gradients and the small fiber 

diameter, we calculated the conductive correction to be 

on the order of ±1 K. Thus we neglect axial conduction 

in equation 12 and rearrange the equation to solve for 

the gas temperature just using a radiation correction 

(equation 13). 

( ) 4 4 = + T − T∞ hTg T f f

εσ (13) 

 The heat transfer coefficient, h, comes from a 

Nusselt number correlation for forced convection over a 

cylinder (equation 14).13,14 A typical Reynolds number 

for our problem based on the SiC fiber diameter, Df, 

was ~ 0.01. 

g

f

k

h D

Nu

× =

= (0.42×Pr ) + (0.57×Re × Pr ) 0.2 0.5 0.33

 (14) 

( ) 













 × = ≤ ≤ =

g

U D f

ν

Pr 0.71, 0.01 Re 10,000 Re

Figure 3 (shown previously) displays the results of 

the temperature calculation of the SiC fiber using the 

spectrometer and the estimate of the surrounding gas 

temperature along the centerline of the flame. 

CCD camera

The CCD imaged the entire burner, flame, 

thermocouple, and SiC fiber. The light from the SiC 

and thermocouple dominated the image (Figure 2) 

although the flame radiation was detectable and 

produced a small signal near the flame (not apparent in 

the right hand side of Figure 2). Additionally, the CCD 

camera produced a signal (ìdark currentî) even when 

no light was incident on the detector (e.g. covered) 

although this effect was minimized by the 

thermoelectric cooler of the detector. Both the flame 

signal and dark signal were subtracted from the 

measured intensities of the camera on a pixel by pixel 

basis. 

We relate the measured intensity at each pixel 

location along the length of the fiber (with a resolution 

of approximately 0.14 millimeters per pixel) to the fiber 

temperature. The SiC fiber diameter (~0.015 mm) is 

smaller than the resolution of a single pixel in the image 

plane by an order of magnitude. The image of the 

glowing SiC fiber, however, produced an apparent fiber 

diameter that was almost 5 pixels wide (~ 0.7 mm). 

This ìbloomingî phenomenon is visually apparent to 

the naked eye when observing the glowing SiC fiber. 

Although the physical mechanism, whether optical or in 

the electronics of the detector (or both), is not clear, the 

blooming effect must be accounted for in the analysis. 

This was done using two methods, a column sum 

method and a maximum intensity method. For the 

column sum method, all the intensities in each vertical 

column (y-direction) of a region surrounding the fiber 

were summed to get a intensity profile (x-direction) 

along the fiber. The region around the fiber consisted of 

10 pixels above and below the centerline of the SiC 

fiber. The maximum method used the maximum 

intensity of each column in the same region to find a 

horizontal intensity profile along the fiber. These two 

techniques produced almost identical results; therefore, 

we present only the results of the maximum method. 

The measured intensity at each pixel corresponds 

to the integrated effect of all incident radiation to which 

the detector (pixel) is sensitive. The incident radiation 

comes from a gray body emitter (the SiC fiber) and is 

attenuated by various optical components before 

reaching the detector. The detector responds differently 

to various wavelengths of light (i.e. quantum efficiency, 

which is the fraction of detected photons per incident 

photons on the detector). 

Mathematically, the detected signal is proportional 

to the integral across the detector spectral sensitivity of 

the product of the emission of the SiC fiber, 

ε(λ)⋅IBB(λ,T); the attenuation, Loss (λ); and the 

quantum efficiency, QE(λ). Multiplying the integral by 

the exposure time, ∆t; the pixel area, A; and a 

conversion factor from charge to counts, G, yields the 

detected signal per pixel in units of counts, P(T) as 

shown in equation 15. For this analysis, ε, G, A, and ∆t

are assumed to be constant. 
NASA/TMó2003-212096 7 

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

LOSS (transmission)

200 300 400 500 600 700 800 900 1000 1100

Wavelength(nm)

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

QE (fraction of photons converted to charge)

 LOSS • QE

 QE of detector

 L1BC Filter (LOSS)

 BG25 Filter (LOSS)

 Lens (LOSS)

Figure 5. The optical transmissive properties of the components used to image the SiC fiber, the quantum 

efficiency of the detector, and their product as a function of wavelength. 

[ ] () () () ( ) ∫ ⋅∆ ⋅ ⋅ ⋅ ⋅

=

2

1

,

( )

λ

λ

G T A Loss λ QE λ ε λ I λ T dλ

P T

BB

(15) 

The CCD camera is sensitive to light between 

λ1=200 nm and λ2=1100 nm. The loss function is the 

product of the transmission efficiencies of the optical 

elements in the system (filters and lenses, see 

Figure 1). Figure 5 shows the manufacturerís 

transmission efficiencies for all of the optical 

elements in the system and the calculated overall loss 

function versus λ. The unknown quantity, G (as well 

as ε, A, and ∆t), drops out of equation 15 by taking 

the ratio of the CCD counts at any arbitrary 

temperature, P(T), to the counts at a known 

temperature, P(T0) (equation 16). 

[ ] () () ( )

[ ] () () ( ) ∫

∫

× ×

× ×

= 2

1

2

1

0

0

,

,

( )

( )

λ

λ

λ

λ

λ λ λ λ

λ λ λ λ

Loss QE I T d

Loss QE I T d

P T

P T

BB

BB

 (16) 

For this analysis, the unknown reference 

temperature, T0, was obtained from the spectrometer 

temperature measurement taken simultaneously with 

the CCD of a point on the SiC fiber at the centerline 

of the flame. Using the maximum method described 

earlier, the CCD counts at the pixel location 

corresponding to the intersection of the SiC with the 

flame centerline was used to obtain P(T0). Knowing 

T0 and P(T0), we generate a curve relating P(T) to T

by numerically integrating equation 16. Figure 6 

shows the various curves generated by the numerical 

integration over several tests (each curve 

corresponding to a different height above the burner). 

While the camera precision is less than 1 K (20000 

discretization levels over an 800 K temperature 

range), the calculated fiber temperature varies as high 

as ±38 K from the mean value for a given count value 

(Figure 6). The uncertainty in the measurement 

accuracy arises from variations in pixel response, 

optical transmission properties, fiber emissivity, and 

the reference temperature, T0. 

For each image from the CCD, we converted all 

the pixel count (maximum) values to temperatures 

using the calibration curve generated for that 

particular height above the burner yielding a one 

dimensional temperature profile along the SiC fiber. 

Figure 7 shows the temperature profile of the SiC 

fiber at 5.5 mm above the burner surface. The gas 

temperature profile along the SiC fiber is found using 

the same energy-balance technique as for the 

spectrometer measurement. Using the data from the 

various heights above the burner, we generated a 2D 

contour map of the temperature profiles of the gas 

above the wick of the burner (Figure 8). For the gas 

temperature calculation, we neglect a conductive 

losses based on estimates that the maximum 

conduction correction is roughly ±1 K as discussed 
NASA/TMó2003-212096 8 

previously. The characteristic velocity of the flame 

was the velocity for the entire length of the fiber. 

This approximation is justifiable since the gas 

temperature shows only small changes with large 

variations of velocity. The uncertainty in the gas 

temperature calculation are the topic of the next 

section. 

1800

1700

1600

1500

1400

1300

1200

1100

1000

Temperature (K)

0 5 10 15 20

CCD Counts x103 , P(T), Using Maximum Method

Figure 6. Temperature vs. count values for the 

CCD camera. Each curve represents the data 

obtained for each height above the burner. The 

variation in the curves shows the uncertainty in 

this method can be as high as ±38K. 

2000

1800

1600

1400

1200

1000

Temperature (K)

-10 -5 0 5 10

Position from Burner Center (mm)

 Fiber

 Gas Phase

Figure 7. SiC fiber and surrounding gas 

temperature at a height of 5.5 mm above the 

burner wick computed from CCD camera images 

of the SiC fiber placed in the flame. 

18

15

12

9

6

3

Height above Burner Wick (mm)

-6 -4 -2 0 2 4 6

Position from Burner Centerline (mm)

1700

 1600 

 1600 

 1600 1500 

 1500 

 1500 

 1400 

 1400 

 1400 

 1300 

 1300 

 1300 

 1300 

 1200 

 1200 

 1100 

 1100 

Figure 8. 2D gas temperature contours for a 

methanol/air diffusion flame. The plot is 

generated from the 1D temperature profiles 

obtained using TFP (CCD camera) at 0.5 mm 

increments above the wick surface. 

Uncertainty in Gas Temperature Calculation

The relationship between the fiber temperature 

(obtained using TFP) and the gas temperature comes 

from an energy balance on the fiber. This relationship 

includes the convective heat transfer between the 

fiber and the gas, radiative loss from the fiber to the 

ambient, and conductive energy transport along the 

fiber. The SiC is not catalytically active, so we 

neglect catalytic effects. Further, we neglect 

conductive energy loss along the fiber, which we 

estimate to be small (~ 1 K). Equation 13 shows the 

resulting relationship between the gas and fiber 

temperatures. Because we do not directly measure the 

gas temperature it is important to consider the 

sources of potential error and their influence on the 

accuracy of the gas temperature measurement. 

The major sources of uncertainty in gas 

temperature (Tg) are in the determination of the fiber 

temperature (Tf), the emissivity (ε) of the fiber, and 

the convective heat transfer coefficient (h). The heat 

transfer coefficient comes from Nusselt number (Nu) 

correlations for heat transfer which is related to the 

fiber diameter (Df) as shown in equation 14. There 

exist several sources of uncertainty in the 

determination of Nu. First, these correlations may not 

be valid at the scale (fiber diameter and potentially 

large temperature gradients along the fiber) we are 

using them; they are bulk correlations for heat 

∆T = 75K 
NASA/TMó2003-212096 9 

transfer. Second, the correlation requires knowledge 

of the Reynolds Number (Re), which in turn requires 

knowledge of the velocity perpendicular to the fiber. 

In the present paper, we use an estimate of this 

velocity from buoyant scaling arguments. Finally, 

both Re and Nu require the thermo-physical 

properties of the convecting gas. These properties are 

functions of both temperature and gas composition, 

both of which are estimates. 

As for the other variables, Df can vary 

considerably (the manufacturer quotes 12 to 18 μm), 

and ε depends on the oxidative coating that forms on 

the fiber (and therefore the age of the fiber). Finally, 

there is obviously uncertainty in the determination of 

the actual fiber temperature. Figure 9 shows how 

variations in each of these parameters effects the gas 

temperature. This figure uses a fiber temperature of 

1800 K measured near the tip of the flame for 

reference, which results in a gas temperature of 

1914 K. The figure shows the absolute change in gas 

temperature (referenced to 1914 K) as a function of 

the percent change in Tfiber, Nu, Df, and ε from their 

measured or assumed values. 

Figure 9 shows, as one would expect, that there 

is a nearly one to one correlation between 

uncertainties in fiber temperature and errors in the 

assumed gas temperature (the slight deviation from 

one-to-one results from the radiation correction). 

Fortunately, as Figure 9 shows, there is a far smaller 

dependence on the values of Nu, Df, and ε. In fact, 

variations as much as 30 percent in these variables 

results in errors in gas temperatures of less than 50 K 

-300

-200

-100

0

100

200

300

Gas Temperature Change ( K )

-30 -20 -10 0 10 20 30

Percent Change in Variable ( % )

-15

-10

-5

0

5

10

15

Percent Change in Gas Temperature (%)

Tgas = 1914 K

 Df, Df base = 15 μm

ε, εβασε = 0.87

 Νυ, Νυβασε = 0.5

 Τφ , Τφ βασε = 1800 Κ

Figure 9. Variation in gas temperature calculation 

with changes in fiber diameter, fiber emissivity, 

Nusselt number, and fiber temperature. 

(2.6%). Therefore, while there is a large uncertainty 

regarding the exact and appropriate values of Df, Nu

and ε, the resulting errors in gas temperature are 

relatively small. 

Conclusions

In the present work, we compared single point 

flame temperature measurements using thin-filament 

pyrometry (TFP) and thermocouples. The data was 

from vertically traversing a thermocouple and a 

silicon-carbide (SiC) fiber through a methanol/air 

diffusion flame of a porous-metal wick burner. One 

TFP technique used a spectrometer which measured 

the radiative emission at a point on the SiC along the 

burner centerline. The relationship between the 

emission and fiber temperature was from gray body 

theory and the measured response of the spectrometer 

based on blackbody calibration. The relationship 

between the gas temperature and the SiC fiber (or 

thermocouple) temperature comes from an energy 

balance on the fiber. The results showed that the gas 

temperature using the TFP technique agreed with the 

thermocouple measurements (25.4 μm diameter wire) 

within 3.5% for temperatures above 1200 K. The 

agreement was not as good with larger diameter 

thermocouples indicating the increased importance of 

conductive losses with larger thermocouple wires. 

Additionally, we imaged the entire SiC fiber 

while it was embedded in the flame using a high 

resolution CCD camera which is sensitive to UV and 

visible light. The light emission from the heated SiC 

fiber dominated the image. We related the maximum 

intensity level along the fiber length (with a spatial 

resolution of 0.14 mm) to the temperature. This 

relationship comes from an integration across the 

detector’s spectral response of the incident radiation. 

The calculation required a single-point temperature 

calibration which we obtained from the single-point 

spectrometer measurement which were done 

simultaneously. We made estimates of the gas 

temperature surrounding the fiber using an energybalance and appropriate heat-transfer correlations. 

From the data, we generated 1D temperature profiles 

at various heights above the burner wick. This 

temperature measurement technique, while having a 

precision of less than 1 K, showed data scatter as 

high as ±38K. 

Finally, we discuss the major sources of 

uncertainty in gas temperature. The largest 

uncertainty in gas temperature comes from the fiber 

temperature itself showing almost a one to one 

variation. There is a far smaller dependence on the 

values of heat transfer coefficient (Nusselt number), 

fiber diameter, and emissivity. In fact, variations as 

much as 30 percent in these variables results in errors 

in gas temperatures of less than 50 K (2.6%). 
NASA/TMó2003-212096 10 

Nomenclature

h heat transfer coefficient 

H flame characteristic length (1.3 cm) 

A pixel area 

Ab thermocouple bead surface area 

Aw thermocouple wire cross-sectional area 

D diameter 

R spectrometer signal 

G linear conversion of detected photons to volts 

Loss spectral attenuation by optical elements 

S detector spectral sensitivity function 

QE detector quantum efficiency 

T temperature 

I radiant intensity 

k thermal conductivity 

x axial coordinate along fiber and thermocouple 

Nu Nusselt number 

Re Reynolds number 

Pr Prandtl number 

P detected pixel counts 

g gravitational acceleration 

ρ density 

U characteristic buoyant velocity (~ 44cm/s) 

ε emissivity 

σ Stefan-Boltzmann Constant 

λ wavelength 

ν kinematic viscosity of the gas 

subscripts

w thermocouple wire 

BB black body 

b thermocouple bead 

g local gas 

f silicon-carbide fiber 

0 normalization value 

∞ ambient or surrounding conditions 

avg average or mean value 

References

1. Vilimpoc, V. and Goss, L.P. (1988). SiC-Based 

Thin-Filament Pyrometry: Theory and Thermal 

Properties. Twenty-second Symposium 

(International) on Combustion / The Combustion 

Institute, Pittsburgh, PA, 907. 

2. Bedat B., Giovanninni, A., and Pauzin, S. 

(1994). Thin filament infrared pyrometry: 

instantaneous temperature profile measurements 

in a weakly turbulent hydrocarbon premixed 

flame. Experiments in Fluids, 17, 397. 

3. Pitts, W.M. Thin-Filament Pyrometry in 

Flickering Laminar Diffusion Flames. (1996). 

Twenty-sixth Symposium (International) on 

Combustion / The Combustion Institute, 

Pittsburgh, PA, 1171. 

4. Ji, J., Sivathanu, Y.R., and Gore, J.P. (1999). 

Thin Filament Spectral Pyrometry for Flame 

Temperature Measurements. First Joint Meeting 

of the U.S. Sections of the Combustion Institute: 

Western States, Central States, Eastern States, 

Washington, D.C., 184. 

5. Bradley, D. and Matthews, K.J. (1968). 

Measurement of High Temperatures with Fine 

Wire Thermocouples. Journal of Mechanical 

Engineering Science, 10, 299. 

6. Govatzidakis, G.J. (1993). Thermocouple 

Thermometry in Soot Bearing Flames, M.S. 

Thesis, Brown University. 

7. Yelistratov, S.L. (1984). Experimental 

investigation of forced-convection heat transfer 

to a sphere at low Reynolds numbers. Heat 

Transfer ñ Soviet Research, 16(6), 71. 

8. Ross, H.D., Dietrich, D.L., and Tíien, J.S. 

(1990). Observations of Candle Flames in Low 

Gravity and Low Pressure. Fall Technical 

Meeting of the Eastern States Section of the 

Combustion Institute, Orlando, FL. 

9. Incropera, F.P. and De Witt, D.P. (1990). 

Fundamentals of Heat and Mass Transfer (3rd

Ed.). John Wiley and Sons, Inc. New York, NY. 

10. Bradley, D. and Entwistle, A.G. (1968). 

Determination of the emissivity, for total 

radiation, of small diameter platinum-10% 

rhodium wires in the temperature range 600-

1450°C. British Journal of Applied Physics, 12, 

708. 

11. Miller, F.J. (2000). Multi-wavelength Optical 

Pyrometry for Solid-Phase Temperature 

Measurements. Spring Technical Meeting of the 

Western States Section of the Combustion 

Institute. 

12. Touloukian, Y.S. and Makita, T. (1970). 

Thermal Radiative Properties: Non-Metallic 

Solids. Thermophysical Properties of Matter, 8, 

IFI / Plenum, New York, NY. 

13. Kramers, H. (1946). Physica, 12, 61. 

14. Hinze, J. (1975). Turbulence (2nd Ed). McGrawHill Series in Mechanical Engineering, New 

York, NY. 88. 

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February 2003

NASA TM—2003-212096

AIAA–2003–853

E–13749

WBS–22–101–32–06

16

Comparisons of Gas-Phase Temperature Measurements in a Flame Using

Thin-Filament Pyrometry and Thermocouples

Peter Struk, Daniel Dietrich, Russell Valentine, and Ioan Feier

Temperature measurement; Gas temperature; Radiation pyrometers; Thermocouples;

Silicon carbides; CCD cameras

Unclassified -Unlimited

Subject Category: 70 Distribution: Nonstandard

Prepared for the 41st Aerospace Sciences Meeting and Exhibit sponsored by the American Institute of Aeronautics and

Astronautics, Reno, Nevada, January 6–9, 2003. Peter Struk and Daniel Dietrich, NASA Glenn Research Center; Russell

Valentine, Case Western Reserve University, Cleveland, Ohio 44106; and Ioan Feier, Case Western Reserve University,

Cleveland, Ohio 44106, and NASA Resident Research Associate at Glenn Research Center. Responsible person, Peter

Struk, organization code 6711, 216–433–5948.

Less-intrusive, fast-responding, and full-field temperature measurements have long been a desired tool for the research

community. Recently, the emission of a silicon-carbide (SiC) fiber placed in a flowing hot (or reacting) gas has been used

to measure the temperature profile along the length of the fiber. The relationship between the gas and fiber temperature

comes from an energy balance on the fiber. In the present work, we compared single point flame temperature measurements using thin-filament pyrometry (TFP) and thermocouples. The data was from vertically traversing a thermocouple

and a SiC fiber through a methanol/air diffusion flame of a porous-metal wick burner. The results showed that the gas

temperature using the TFP technique agreed with the thermocouple measurements (25.4 mm diameter wire) within

3.5 percent for temperatures above 1200 K. Additionally, we imaged the entire SiC fiber (with a spatial resolution of

0.14 mm) while it was in the flame using a high resolution CCD camera. The intensity level along the fiber length is a

function of the temperature. This results in a one-dimensional temperature profiles at various heights above the burner

wick. This temperature measurement technique, while having a precision of less than 1 K, showed data scatter as high as

±38 K. Finally, we discuss the major sources of uncertainty in gas temperature measurement using TFP.