A description is given of an instrument to determine the temperatures of rapidly varying flames. This instrument uses a photoelectric modification of the line‐reversal method, wherein the light beam from a temperature‐variable incandescent source is split into two monochromatic beams by means of mirrors and filters to impinge upon 931A multiplier phototubes. The phototube signals are sent to a mu‐bridge null detector, whose output is fed to an oscilloscope for photography of results. The instrument can detect 25°K temperature differences between about 1540° and 3100°K and three millisecond time differences. Typical time‐temperature results are given, along with the analytical procedures used.

1.
Ch.
Féry
,
Compt. Rend.
137
,
909
–
912
(
1903
).
Google Scholar
 
2.
B. Lewis and G. von Elbe, Temperature, Its Measurement and Control in Science and Industry (Reinhold Publishing Corporation, New York, 1941), pp. 710–714.
3.
H. F. Mulliken, reference 2, pp. 780–781.
4.
J. T. Agnew, “Line reversal techniques in the determination of gun flash or other rapid transient phenomena,” Paper No. 51—F‐6, presented at the Fall Meeting, Minneapolis, Minnesota (September 26–28, 1951), of the American Society of Mechanical Engineers.
5.
D. H. Jacobs and S. Scholnick, North American Aviation, Inc., Reports Nos. AL‐100, AL‐160, and AL‐248.
6.
F. C. Kracek and W. S. Benedict, “An experimental study of powder gas radiation and temperature,” National Defense Research Committee, Armor and Ordnance Report No. A‐252 (OSRD No. 3291), Division 1.
7.
El Wakil, Myers, and Uyehara, “An instantaneous and continuous sodium‐line reversal pyrometer,” Paper No. 50—A‐94, presented at the Annual Meeting, New York, New York (November 26‐December 1, 1950) of the American Society of Mechanical Engineers.
8.
Limit of light scattering by flame for light intensity ratio to be unchanged. Let A = Light absorbed by the flame in any given wavelength. E = Light emitted by the flame in any given wavelength. IB = Light intensity from blackbody source in any given wavelength. Ir = Light intensity at the receiver in any given wavelength. R = Ratio of light intensities in two wavelengths. S = Amount of light scattered by flame. α = Flame absorptivity in any given wavelength. β = Ratio of light scattered to that incident on the flame. ε = Emissivity of flame in any given wavelength. λ = Wavelength. Take the case when the flame and blackbody source are at the same temperature. In transparent flames (no scattering), assuming that the energy absorbed by the flame does not affect the flame temperature history, and that flame absorption and emission are independent phenomena, the following conditions hold for the flame in any wavelength:
A = IBα (1)
 
E = IBε. (2)
The total light to the receiver is equal to the light from the source minus the light absorbed by the flame, plus the light emitted by the flame, i.e.,
Ir = IB−A+E, (3)
 
 = IB−IBα+IBε, (4)
 
 = IB(1−α+ε); (5)
but, by Kirchoff’s law,
α = ε, (6)
therefore, Ir = IB, (7) and
R = (IB)λ1/(IB)λ2. (8)
In the case of semitransparent flames, Eqs. (1) and (2) will still hold, and also,
S = IBβ∶(β1 = β2 because λ1 and λ2 are adjacent wavelengths). (9)
Providing IB(1−α)λ1⩾S⩽IB(1−α)λ2, the light to the receiver is equal to the light from the source minus the light scattered by the flame minus the light absorbed by the flame plus the light emitted by the flame, i.e.,
Ir = IB−S−A+E, (10)
 
 = IB−IBβ−IBα+IBε, (11)
 
 = IB(1−β−α+ε), (12)
 
 = IB(1−β), (13)
and
R = (IB)λ1(1−β)(IB)λ2(1−β); (14)
which reduces to
R = (IB)λ1/(IB)λ2, (15)
which is the same as Eq. (8). However, if IB(1−α)λ1⩾S>IB(1−α)λ2, although Eqs. (10) through (13) hold in λ1, now (A)λ2≠(IBα)λ2 but becomes:
(A)λ2 = (IB)λ2−S (16)
 
 = (IB−IBβ)λ2 (17)
and Eq. (10) becomes:
(Ir)λ2 = (IB)λ2−(IBβ)λ2−(IB−IBβ)λ2+(IBε)λ2 (18)
 
 = (IBε)λ2, (19)
and
R = (IB)λ1(1−β)(IBε)λ2. (20)
Equation (20) is not the same as Eq. (15), showing that when the scattering exceeds the quantity one minus the absorptivity (or emissivity) of either wavelength, the ratio of the light intensities in two wavelengths is changed and cannot be used to detect the line‐reversal point. Therefore, the light scattering by the flame must not be greater than this quantity in either wavelength of light received by the phototubes; that is, the flame must transmit a reasonable portion of the incident light from the background source in the wavelengths in which measurement is being made.
9.
An alternative circuit to detect one‐to‐one ratios has been designed and is under development, wherein each phototube signal is used to amplitude modulate a radio‐frequency carrier. Rectified opposite phases of the respective modulated signals are placed across a resistor bridge, and the output from the center of the bridge to ground is placed on the Y‐input terminals of the oscilloscope. Another alternative would be to place the two phototube signals directly on differential Y amplifiers of a properly designed oscilloscope.
This content is only available via PDF.
© 1954 American Institute of Physics.
1954
American Institute of Physics
You do not currently have access to this content.