A DNS Study of Sensitivity of Scaling Exponents for Premixed Turbulent Consumption Velocity to Transient Effects

Abstract

3D Direct Numerical Simulations of propagation of a single-reaction wave in forced, statistically stationary, homogeneous, isotropic, and constant-density turbulence, which is not affected by the wave, are performed in order to investigate the influence of the wave development on scaling (power) exponents for the turbulent consumption velocity U T as a function of the rms turbulent velocity u , laminar wave speed S L , and a ratio L 11 /δ F of the longitudinal turbulence length scale L 11 to the laminar wave thickness δ F. Fifteen cases characterized by u /S L = 0.5, 1.0, 2.0, 5.0, or 10.0 and L 11 /δ F = 2.1, 3.7, or 6.7 are studied. Obtained results show that, while U T is well and unambiguously defined in the considered simplest case of a statistically 1D planar turbulent reaction wave, the wave development can significantly change the scaling exponents. Moreover, the scaling exponents depend on a method used to compare values of U T , i.e., the scaling exponents found by processing the DNS data obtained at the same normalized wave-development time may be substantially different from the scaling exponents found by processing the DNS data obtained at the same normalized wave size. These results imply that the scaling exponents obtained from premixed turbulent flames of different configurations may be different not only due to the well-known effects of the mean-flame-brush curvature and the mean flow non-uniformities, but also due to the flame development, even if the different flames are at the same stage of their development. The emphasized transient effects can, at least in part, explain significant scatter of the scaling exponents obtained by various research groups in different experiments, thus, implying that the scatter in itself is not sufficient to reject the notion of turbulent burning velocity. Keywords Premixed turbulent combustion • Burning velocity • Consumption velocity • Turbulent flame development • DNS Nomenclature a heat diffusivity of a mixture c combustion progress variable

Evolution equations for the decomposed components of displacement speed in a reactive scalar field

“…(2.29) or its equivalent (2.30), were applied to analyse two different DNS data sets obtained from statistically 1-D, initially planar, single-reaction waves propagating in a homogeneous, isotropic, statistically stationary forced turbulence. One data set (case B in the following) was selected from a big DNS database (Yu, Lipatnikov & Bai 2014;Yu, Bai & Lipatnikov 2015b;Elperin et al 2016;Yu & Lipatnikov 2017a,b;Sabelnikov, Yu & Lipatnikov 2019;Yu & Lipatnikov 2019a) obtained from dynamically passive reaction waves. Such a wave affects neither the fluid density nor the fluid viscosity.…”

Surface-averaged quantities in turbulent reacting flows and relevant evolution equations

“…(27), (29), and (30), are applicable to explore heavily disturbed turbulent reaction waves. For this purpose, these equations are applied to analyze a representative highly turbulent case (case C in the following) selected from a large DNS database computed earlier [14,15,[74][75][76][77][78][79].…”

“…In our earlier DNS's [14,15,[76][77][78][79], propagation of a statistically one-dimensional (1D), planar, single-reaction wave in a homogeneous, isotropic, statistically stationary forced turbulence was simulated in the case of a dynamically passive wave, i.e., a wave that did not change the fluid density and viscosity, therefore, did not affect turbulence. The invoked simplifications allowed us to sample better statistics, as will be discussed later, and to investigate a large number of substantially different cases.…”

“…Since the DNS attributes are discussed in detail elsewhere [14,15,[74][75][76][77][78][79], we will restrict ourselves to a very brief summary of the simulations.…”

“…In order to study a fully developed turbulent reaction wave, a planar wave c s (x, 0) = c L (ξ ) is initially (t = 0) released at t /(100 t ) realizations. Such a method, i.e., simulations of M independent transient fields, significantly increases the sampling counts for calculating transient statistics and was already applied to studying self-propagation of an infinitely thin front [74,75] and a reaction wave of nonzero thickness [14,15,[76][77][78][79] in homogeneous isotropic turbulence.…”