DNS assessment of relation between mean reaction and scalar dissipation rates in the flamelet regime of premixed turbulent combustion

Abstract

The linear relation between the mean rate of product creation and the mean scalar dissipation rate, derived in the seminal paper by K.N.C. Bray [‘The interaction between turbulence and combustion’, Proceedings of the Combustion Institute, Vol. 17 (1979), pp. 223–233], is the cornerstone for models of premixed turbulent combustion that deal with the dissipation rate in order to close the reaction rate. In the present work, this linear relation is straightforwardly validated by analysing data computed earlier in the 3D Direct Numerical Simulation (DNS) of three statistically stationary, 1D, planar turbulent flames associated with the flamelet regime of premixed combustion. Although the linear relation does not hold at the leading and trailing edges of the mean flame brush, such a result is expected within the framework of Bray's theory. However, the present DNS yields substantially larger (smaller) values of an input parameter c_m (or K₂ = 1/(2c_m − 1)), involved by the studied linear relation, when compared to the commonly used value of c_m = 0.7 (or K₂ = 2.5). To gain further insight into the issue and into the eventual dependence of c_m on mixture composition, the DNS data are combined with the results of numerical simulations of stationary, 1D, planar laminar methane–air flames with complex chemistry, with the results being reported in terms of differently defined combustion progress variables c, i.e. the normalised temperature, density, or mole fraction of CH₄, O₂, CO₂ or H₂O. Such a study indicates the dependence of c_m both on the definition of c and on the equivalence ratio. Nevertheless, K₂ and c_m can be estimated by processing the results of simulations of counterpart laminar premixed flames. Similar conclusions were also drawn by skipping the DNS data, but invoking a presumed beta probability density function in order to evaluate c_m for the differently defined c's and various equivalence ratios.

Keywords:

• premixed turbulent flame
• scalar dissipation rate
• DNS
• modelling

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Here, a test is called straightforward provided that it addresses solely Equations (1(1) )–(4(4) ), but not a model that invokes not only these equations, but also other equations and assumptions.

2. The curve W_ρ(c_ρ), shown as a dot–dashed line, is localised to a narrow range of c_ρ when compared to the curve W_T(c_T), shown as a double-dot–dashed line, because c_ρ = c_TT_b/T, i.e. c_T = 0.42 and c_ρ = 0.84 if T = 0.5T_b = 3.5T_u.

Additional information

Funding

The first author (AL) was supported by the Chalmers E-Science Centre; the Swedish Energy Agency; the Chalmers Combustion Engine Research Center (CERC).