An active particle diffusion theory of flame quenching for laminar flames Page: 3 of 26
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NACA RM E51L18
The process of quenching is important to the behavior of flames
because this process may control flame stabilization, pressure limits
of flammability, concentration limits of flammability, and the effi-
ciency of combustion in the region of cold surfaces. The experimental
approach to the study of quenching usually involves the measurement of
a quenching distance which is considered to be (1) the minimum diameter
of a tube or the distance between parallel plates through which a flame
will flash back; (2) the minimum distance between parallel plates for
which a flame will propagate from a spark of minimum energy; or (3) the
length of the dead space between a burner rim and a stable flame. The
magnitude of the quenching distance varies with fuel type, fuel-oxidant
ratio, pressure, temperature, and quenching-surface geometry. The
quenching distance is related to the other combustion properties of the
mixture such as flame speed, minimum ignition energy, and limits of
flammability. Any complete theory of the combustion wave should show
the relations between all the combustible mixture properties and make
possible the estimation of the magnitude of one from a knowledge of
the others. Also the relation of each combustion property to the true
fundamental properties of the gas mixture should be clear,..
One relation has been derived by Lewis and von Elbe (reference 1,
pp. 211 to 480) who consider the transport of enthalpy in the combus-
tion wave to be governed by heat transport only. Diffusion is
neglected. Use of this approximation makes it possible to relate min-
imum ignition energy, burning velocity, and quenching distance by one
equation. From this equation, Lewis and von Elbe (references 1 and 2)
have calculated quenching distances for some methane-oxygen-nitrogen
mixtures and propane-air mixtures at atmospheric pressure and room
temperature. The average deviation of the calculated quenching distance
from the measured is 23 percent for hydrocarbon-lean mixtures and is
somewhat greater for hydrocarbon-rich mixtures. Because burning-
velocity measurements are uncertain at low pressures, quenching-distance
calculations could be made for atmospheric pressure only.
A second type of approximate theoretical treatment of the combus-
tion wave results from considering the diffusion of atoms and free
radicals as the governing process. Such an approximate treatment has
been used for the study of burning velocities (flame speeds) by Lewis
and von Elbe (reference 3) and later Tanford and Pease (references 4
As part of a flame propagation investigation at the NACA Lewis
laboratory, the maximum flame velocities for hydrocarbon-air mixtures
for paraffin, olefin, diolefin, and acetylene hydrocarbons have been
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Simon, Dorothy M. & Belles, Frank E. An active particle diffusion theory of flame quenching for laminar flames, report, March 4, 1952; (digital.library.unt.edu/ark:/67531/metadc59077/m1/3/: accessed February 17, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.