Correlation of flame speed with stretch in turbulent premixed methane/air flames

Abstract

IntroductionIn the flamelet approach of turbulent premixed combustion, the flames are modeled as a wrinkled surface whose propagation speed, termed the "displacement speed," is prescribed in terms of the local flow field and flame geometry [l]. Theoretical studies [2] suggest a linear relation between the flame speed and stretch for small values of stretch, where 5' : is the laminar flame speed, l i a = m 5~/ S i is the nondimensional stretch or the Karlovitz number, and M a = L/SF is the Markstein number. The nominal flame thickness, S F , is determined as the ratio of the mass diffusivity of the unburnt mixture to the laminar flame speed. Thus, the turbulent flame model relies on an accurate estimate of the Markstein number in specific flame configurations. Experimental measurement of flame speed and stretch in turbulent flames, however, is extremely difficult. As a result, measurement of flame speeds under strained flow fields has been made in simpler geometries [3,4], in which the effect of flame curvature is often omitted.In this study we present results of direct numerical simulations of unsteady turbulent flames with detaiIed methane/air chemistry, thereby providing an alternative method of obtaining flame structure and propagation statistics. The objective is t o determine the correlation between the displacement speed and stretch over a broad range of Karlovitz numbers. The observed response of the displacement speed is then interpreted in terms of local tangential strain rate and curvature effects. Numerical MethodThe numerical scheme is based on the solution of the Navier-Stokes, species and energy equations for a compressible gas mixture with temperature dependent properties. The explicit finite difference algorithm uses a fourth-order low storage Runge-Kutta scheme for time advancement and an eighth-order explicit spatial differencing scheme [5]. The chemical mechanism is based on a detailed C1 mechanism by Warnatz [6] with 17 species and 68 reversible reactions. The species mass diffusion is determined by prescribing the Lewis numbers of each species [7]. The molecular viscosity of the mixture is temperature dependent, while the thermodynamic properties (enthalpy, specific heat) are temperature and composition dependent. The Prandtl number is taken to be 0.708.The computations are initialized with a one-dimensional steady laminar flame profile. A fuel-lean mixture (equivalence ratio of 0.7) of methane/air is preheated to 800 K in the reactant freestream. The profiles are obtained from a one-dimensional steady code PREMIX [SI, and the solntion is allowed to adjust t o the simplified transport in a one-dimensional DNS.The turbulence is prescribed by an initial two-dimensional turbulent kinetic energy spectrum function [9] which is superimposed on the laminar flame. The ratio of the turbulence intensity, u', to S i is taken to be 10, and the ratio of the integral eddy scale, L11, to SF is 2.77. The turbulence Reynolds number based LI1 and the unburned gas properties at 800 K is 181. The computationa...

Effects of Turbulent Reynolds Number on the Displacement Speed Statistics in the Thin Reaction Zones Regime of Turbulent Premixed Combustion

“…However, such simulations remain extremely expensive and are not yet feasible for parametric studies. Previous work has indicated that displacement speed statistics obtained from three-dimensional DNS with simplified chemistry [14][15][16][17][18][19][20][21][22] are in agreement with those obtained from two-dimensional DNS with complex chemistry [3][4][5][6][7][8][9][10][11][12][13]. In the present study, three-dimensional DNS with simplified chemistry is adopted in order to allow for an extensive parametric study without excessive computational cost.…”

“…The displacement speed is defined as the speed at which the flame surface moves normal to itself with respect to an initially coincident material surface. Statistics of displacement speed for turbulent premixed flames have been studied extensively in previous work based on two-dimensional direct numerical simulations (DNS) with detailed chemistry [3][4][5][6][7][8][9][10][11][12][13] and on three-dimensional DNS with simplified chemistry [14][15][16][17][18][19][20][21][22]. These studies have looked at the effects of local strain rate and curvature effect on S d [13][14][15][16][17][18][19][20][21][22][23][24] and have included the influence of root-mean-square (rms) turbulent velocity fluctuation magnitude u and Lewis number Le [9,15,17,22] on these effects.…”

Three-dimensional direct numerical simulation of turbulent lean premixed methane combustion with detailed kinetics

“…The earliest work in this area investigated two-dimensional configurations using a detailed C1 mechanism [1,2,3,4]. Bell et al [5] produced the first simulation of a turbulent methane flame in three dimensions with moderate-fidelity kinetics using DRM-19, which 20 is a simplified mechanism derived from GRIMech 1.2.…”

Investigation of Flame Stretch in Turbulent Lifted Jet Flame

“…In general, the instantaneous flame stretch is both positive and negative as has been noted in many earlier studies (Rutland and Trouvé, 1993;Bray and Cant, 1991;Chen and Im, 1998;Nye et al, 1996;Renou et al, 1998;Kostiuk and Bray, 1993). However, these studies suggested that there is 50% or less probability for the flame stretch to be negative and this probability can be calculated by integrating the pdf shown in Fig. 14 from −∞ to 0.…”

“…The instantaneous flame stretch can be positive or negative; a positive value implies that the flame surface area increases due to the combined effects of turbulence and flame propagation and negative stretch suggests that the flame surface is compressed resulting in the loss of flame area per unit volume. Earlier numerical (Rutland and Trouvé, 1993;Bray and Cant, 1991;Chen and Im, 1998), experimental (Nye et al, 1996;Renou et al, 1998) and modelling (Kostiuk and Bray, 1993) studies have demonstrated that there is 20-50% probability for the flame stretch to be negative. In the view of RANS methodology the average value of the flame stretch, Φ s , is expected to be predominantly positive and many modelling methods have been proposed in the past with this view.…”