Transport equations for (i) the rate
of product creation and (ii) its Favre-averaged value
are derived from the first principles by assuming that
depends solely on the temperature and mass fraction of a deficient reactant in a premixed turbulent flame characterized by the Lewis number
different from unity. The right hand side of the transport equation for
involves seven unclosed terms, with some of them having opposite signs and approximately equal large magnitudes when compared to the left-hand-side terms. Accordingly, separately closing each term does not seem to be a promising approach, but a joint closure relation for the sum
of the seven terms is sought. For this purpose, theoretical and numerical investigations of variously stretched laminar premixed flames characterized by
are performed and the linear relation between
integrated along the normal to a laminar flame and a product of (i) the consumption velocity
and (ii) the stretch rate
evaluated in the flame reaction zone is obtained. Based on this finding and simple physical reasoning, a joint closure relation of
is hypothesized, where
is the density and
is the stretch rate. The joint closure relation is tested against 3D DNS data obtained from three statistically 1D, planar, adiabatic, premixed turbulent flames in the case of a single-step chemistry and
, 0.6, or 0.8. In all three cases, the agreement between
and
extracted from the DNS is good with exception of large (
) values of the mean combustion progress variable
in the case of
. The developed linear relation between
and
helps to understand why the leading edge of a premixed turbulent flame brush can control its speed.
相似文献