(2-10) Towards Evaluation of Turbulent Flame Speed((SI-4)S. I. Engine Combustion 4-Flame Propagation)

Abstract

During the last decade, a new approach to multi-dimensional computations of premixed turbulent combustion has been developed. It consists of the use of an analytical expression for the local turbulent flame speed in order to close the averaged balance equations describing the combustion process. Several models have been suggested utilizing this approach and a number of successful applications to 3D computations of combustion in S. I. engines was reported at COMODIA 98. Although a submodel of turbulent flame speed, S_t, is at the core of this approach, a consensus has not been reached on this issue. The choice of the most reliable submodel is strongly impeded by the wide scatter of the published experimental data on S_t. Moreover, this scatter questions the physical correctness and practical usefulness of the concept of turbulent flame speed. The main goal of this work is to support the concept by discussing certain physical sources of the scatter and by outlining methods of reducing it. Three physical mechanisms are discussed in the paper. First, numerous experimental data indicate that typical premixed turbulent flames are developing flames, rather than fully developed ones, i. e., the mean turbulent flame brush thickness, δ_t, is not constant but grows permanently either with time in expanding flames or with the distance from the flame-holder in stationary flames. Due to the growth of δ_t, the speeds associated with different reference surfaces inside the flame brush can be substantially different, e. g., the difference can be as large as u'. A new method of unambigouosly defining the reference surface, the speed of which straightforwardly characterizes the mass burning rate, is developed by theoretically analyzing self-similar (i. e., spatial profiles of the mean progress variable, measured at different flame development times and presented in the dimensionless form by using δ_t(t), are collapsed to a universal curve) premixed turbulent flames in the statistically planar, one-dimensional case. This reference surface is characterized by the following reference value of the Favre-averaged progress variable [numerical formula] ; [numerical formula] ; [numerical formula], where ρ(ε)≡ρ^^-((x-x_f)/δ_t)/p_u is a universal dimensionless profile of the mean density (ρ(-∞)=1) and x_f(t) s the flame position. Numerical simulations indicate that the speed of this reference surface is equal to the mass burning rate divided by p_u and, thus, support the proposed method. Second, the mass burning rate in expanding spherical flames is well known to develop as the flame kernel grows, because, in particular, it experiences a wider range of the turbulence spectrum. Simple estimates discussed in the paper show that such transient effects can change the dependence of flame speed on turbulence characteristics not only quantitatively but even qualitatively. To suppress these effects, flame development time should be sufficiently large (e. g., larger than the turbulence time scale). Third, the speed of a statistically spherical flame differs from the speed of the planar one, other things being equal, due to (1) the mean flame curvature effects, and (2) the reduction in the maximum gas flow velocity induced by hot combustion product expansion, due to a wide flame thickness. In laminar flames, such effects are well known but weak. In turbulent flames, the effects can be substantial, because δ_t, is much larger than the laminar flame thickness. By analogy with the laminar combustion, the following equation [numerical formula], is proposed to be used in order to evaluate a fully developed turbulent flame speed, S^o_t, by processing the dependencies of the mean flame radius, r_f, on time, t, measured in expanding spherical flames. Here, Ma_t is a turbulent analog of the Markstein number used widely in laminar flame studies. This processing has been applied to the published experimental data. The