The mass-flux fraction (or Hirschfelder-Curtiss variable or Kármán-Penner variable) is the ratio of mass-flux of a particular chemical species to the total mass flux of a gaseous mixture. It includes both the convectional mass flux and the diffusional mass flux. It was introduced by
Joseph O. Hirschfelder and
Charles F. Curtiss
Charles is a masculine given name predominantly found in English language, English and French language, French speaking countries. It is from the French form ''Charles'' of the Proto-Germanic, Proto-Germanic name (in runic alphabet) or ''*k ...
in 1948 and later by
Theodore von Kármán
Theodore von Kármán ( hu, ( szőllőskislaki) Kármán Tódor ; born Tivadar Mihály Kármán; 11 May 18816 May 1963) was a Hungarian-American mathematician, aerospace engineer, and physicist who was active primarily in the fields of aeronaut ...
and
Sol Penner
Stanford Solomon Penner (5 July 1921 – 15 July 2016) also known as Sol Penner, was a German-American scientist and engineer, a major figure in combustion physics, especially in rocket engines, and a founder of the Engineering program at Universit ...
in 1954. The mass-flux fraction of a species i is defined as
:
where
*
is the
mass fraction
*
is the mass average velocity of the gaseous mixture
*
is the average velocity with which the species i diffuse relative to
*
is the density of species i
*
is the gas density.
It satisfies the identity
:
similar to mass fraction, but, the mass-flux fraction can take both positive and negative values. This variable is used in steady, one-dimensional
combustion
Combustion, or burning, is a high-temperature exothermic redox chemical reaction between a fuel (the reductant) and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combusti ...
problems in place of mass fraction.
[Penner, S. S. (1957). Chemistry problems in jet propulsion (Vol. 1). Pergamon Press.] For one-dimensional (
direction) steady flows, the conservation equation for the mass-flux fraction reduces to
:
where
is the mass production rate of species i.
References
{{reflist, 30em
Chemical properties
Dimensionless numbers of chemistry
Combustion