APPLICATION OF THE EDDY DAMPED QUASI-NORMAL MARKOVIAN SPECTRAL TRANSPORT-THEORY TO PREMIXED TURBULENT FLAME PROPAGATION

The eddy damped quasi-normal Markovian (EDQNM) turbulence theory was a pplied to a modified Kuramoto-Sivashinsky field equation to develop a spectral model for investigating the single and two-point scalar stati stics associated with a flame front (treated as a passive scalar inter face) propagating through isotropic turbulence. As a result of the pre sence of a uniform mean gradient in the scalar field, all correlations involving the scalar were found to be functions of both the wave numb er, k, and mu, the cosine of the angle between the ik vector and the m ean gradient vector. An infinite Legendre expansion separated out the wave number and angle dependencies, where the first term in each serie s accounted for the isotropic contribution to the correlations and the higher order terms accounted for the anisotropy introduced as a resul t of the mean gradient. It was found that while strong anisotropy exis ted in the scalar field at short times, at steady state the scalar fie ld became nearly isotropic. A parameter study was then conducted to as certain the effect of independently varying u'/s(L) and Re-lambda (whe re u' is the rms velocity, s(L) is the laminar burning velocity, and R e-lambda is the Reynolds number based on the Taylor microscale). The t urbulent burning velocity increased with increases in either u'/s(L) o r Re-lambda, however, the model predicted a finite turbulent burning v elocity as u'/s(L) --> infinity, even though flame quenching was not a ccounted for. This finite asymptote for the burning velocity was trace d to tile constitutive relationship used for the flame thickness and t he ratio of the Markstein length to the flame thickness. It was also s hown that the dominant wrinkling of the flame surface and subsequent c ontribution to the turbulent burning velocity occurred at smaller and smaller length scales as the inertial range of the scalar spectrum inc reased. Single point models will therefore have great difficulty repro ducing this significant result. Scalar spectra exhibited changes over all wave numbers as either u'/s(L) or Re-lambda, was modified. Transfe r spectra, which arose in the form of convolution integrals as a resul t of the advection and propagation processes, were also analyzed and s eparated into their pairwise spectral interactions to determine which nonlinear terms in each integral were dominant. (C) 1997 American Inst itute of Physics.