Mixture fraction (
) is a quantity used in
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 ...
studies that measures the
mass fraction of one stream (usually the fuel stream) of a mixture formed by two feed streams, one the fuel stream and the other the oxidizer stream. Both the feed streams are allowed to have inert gases. The mixture fraction definition is usually normalized such that it approaches unity in the fuel stream and zero in the oxidizer stream. The mixture-fraction variable is commonly used as a replacement for the physical coordinate normal to the flame surface, in nonpremixed combustion.
Definition
Assume a two-stream problem having one portion of the boundary the fuel stream with fuel mass fraction
and another portion of the boundary the oxidizer stream with oxidizer mass fraction
. For example, if the oxidizer stream is air and the fuel stream contains only the fuel, then
and
. In addition, assume there is no oxygen in the fuel stream and there is no fuel in the oxidizer stream. Let
be the mass of oxygen required to burn unit mass of fuel (for
hydrogen
Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic, an ...
gas,
and for
alkanes
In organic chemistry, an alkane, or paraffin (a historical trivial name that also has other meanings), is an acyclic saturated hydrocarbon. In other words, an alkane consists of hydrogen and carbon atoms arranged in a tree structure in which ...
,
). Introduce the scaled mass fractions as
and
. Then the mixture fraction is defined as
:
where
:
is the stoichiometry parameter, also known as the overall
equivalence ratio
Equivalence or Equivalent may refer to:
Arts and entertainment
*Album-equivalent unit, a measurement unit in the music industry
*Equivalence class (music)
*''Equivalent VIII'', or ''The Bricks'', a minimalist sculpture by Carl Andre
*'' Equival ...
. On the fuel-stream boundary,
and
since there is no oxygen in the fuel stream, and hence
. Similarly, on the oxidizer-stream boundary,
and
so that
. Anywhere else in the mixing domain,