Mark Ulitsky

A spectral study of differential diffusion of passive scalars in isotropic turbulence

In a companion paper, we applied the eddy-damped quasi-normal Markovian (EDQNM) turbulence theory to the mixing of two inert passive scalars with different diffusivities in stationary isotropic turbulence. This paper showed that a rigorous application of the EDQNM approximation leads to a scalar covariance spectrum that violates the Cauchy-Schwartz inequality over a range of wavenumbers. The violation results from the improper functionality of the inverse diffusive time scales that arise from the Markovianization of the time evolution of the triple correlations. The modified inverse time scale they proposed eliminates this problem and allows meaningful predictions of the scalar covariance spectrum both with and without a uniform mean gradient. This study uses the modified EDQNM model to investigate the spectral dynamics of differential diffusion. Consistent with recent DNS results by Yeung, we observe that whereas spectral transfer is predominantly from low to high wavenumbers, spectral incoherence, being of molecular origin, originates at high wavenumbers and is transferred in the opposite direction by the advective terms

Relative importance of coherent structures vs background turbulence in the propagation of a premixed flame

Abstract For premixed flames in the “flamelet” regime, where turbulence length scales are significantly greater than the flame thickness, it has been asserted that the principal contribution to flame surface area is generated by vortical structures present in the reacting gas mixture. Several direct numerical simulation (DNS) studies of premixed combustion implicitly follow this assumption by only considering a flame interacting with a single, well-defined vortical structure; however, the important issue of whether the majority of flame surface area is actually caused by vortical structures, as opposed to the featureless background turbulence has not been satisfactorily addressed. We consider this question using direct numerical simulations (DNS). As shown by She, Jackson and Orszag ( Nature 344:226, 1990), scrambling the phase of the velocity field in Fourier space (or wave number space) eliminates coherent structures from the turbulent field. Consequently, DNS provides an opportunity to evaluate the importance of coherent structures by comparing flames propagating through Navier-Stokes turbulence with those passing through phase-scrambled (coherent-structure-free) turbulence. The idea of scrambling the phasing of the velocity components is extremely attractive since the scrambled velocity field is free of any coherent vortical structures yet is nearly identical to the Navier-Stokes velocity in all other respects. The results show that the turbulent burning velocity is predominantly influenced by the featureless background turbulence over the range of parameters considered, although there is approximately a 4–7% increase in the flame speed that results from the presence of structures. The topologies of the flame surfaces from the scrambled and unscrambled turbulence are also very similar.

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 applied to a modified Kuramoto–Sivashinsky field equation to develop a spectral model for investigating the single and two-point scalar statistics associated with a flame front (treated as a passive scalar interface) propagating through isotropic turbulence. As a result of the presence of a uniform mean gradient in the scalar field, all correlations involving the scalar were found to be functions of both the wave number, k, and μ, the cosine of the angle between the k vector and the mean gradient vector. An infinite Legendre expansion separated out the wave number and angle dependencies, where the first term in each series accounted for the isotropic contribution to the correlations and the higher order terms accounted for the anisotropy introduced as a result of the mean gradient. It was found that while strong anisotropy existed in the scalar field at short times, at steady state the scalar field became nearly isotropic. A parameter st...

Comparison between a spectral and probability density function model for turbulent reacting flows

This study compares the performance of a newly developed spectral model based on the eddy damped quasi-normal Markovian (EDQNM) theory with a standard probability density function (PDF) model for the case of two initially unmixed reactants undergoing a finite-rate bimolecular reaction. The two models were chosen because they involve complementary treatments of the nonlinearities and mixing terms. That is, nonlinearities are exactly treated in the PDF and mixing is modeled, whereas the opposite is true for EDQNM. The predictions of the two models are compared to direct numerical simulations. The results show that the PDF model is capable of describing the mixing of the major species reasonably well, but fails to describe the correlations between the reactants and the products even qualitatively. This suggests that the mixing model in the PDF is adequate for describing mixing between major species, but is incapable of describing mixing of the more spatially segregated product species. The EDQNM model does a slightly better job of describing the mixing of reactant species and a much better job of describing mixing of the product species. Presumably the improvement is associated with the more accurate description of the interscale dynamics that are especially important for the segregated products. The implication is that a model that combines the strengths of the EDQNM for describing mixing and the PDF for describing the nonlinearities would yield the best of both worlds.

Comparison of a spectral model for premixed turbulent flame propagation to DNS and experiments

A recently developed spectral model for premixed turbulent combustion in the flamelet regime (based on the EDQNM turbulence theory) has been compared with both direct numerical simulations (DNS) and experimental data. The 1283 DNS is performed at a Reynolds number of 223 based on the integral length scale. Good agreement is observed for both single- and two-point quantities (i.e. ratio of the turbulent to laminar burning velocities, scalar autocorrelation, dissipation and scalar-velocity cross correlation spectra) for the two different values of u′/s L0 considered. The model also predicts the rapid transient behaviour of the flame at early times. An experimental set-up is then described for generating a lean methane-air flame and measuring two-point spatial correlations along the midpoint of the flame brush (i.e. along the C¯=0.5 contour). The experimental measurements in the flamelet regime take the form of a discontinuous or ‘telegraph’ signal. The EDQNM model, in contrast, describes an ‘ensemble’ of flames, and thus is based solely on continuous variables. A theoretical relationship between the correlation obtained from the EDQNM model and the equivalent correlation for a discontinuous (experimental) flame is derived. The relationship is used to enable a meaningful comparison between experimentally observed and model correlations. In general, the agreement is good for the three different cases considered in this study, with most of the error occurring at the lowest Reynolds number (Re L =22). Furthermore, it is shown that considerably more error would result if no attempt is made to convert the ensemble representation in the model to an equivalent single-flame or ‘telegraph’ signal.

Spectral model of premixed flame propagation

A premixed flame propagating under flamelet conditions in turbulent flow is wrinkled by the fluid fluctuations at a multitude of scales. Traditional models of premixed combustion predict the flame speed based on global parameters from the reacting mixture. As a result, there is no information on intermediate to small scales, which are thought to play an increasingly important role in generating flame surface area as the flow becomes more turbulent. In an attempt to incorporate the entire spectrum of possible turbulent and flame length scales, a combustion model based on the eddy damped quasi-normal Markovian (EDQNM) theory has been developed. By applying the theory to the three-dimensional Navier-Stokes and modified Sivashinsky equations, one can derive transport equations for the scalar-velocity cross correlation spectrum as well as the scalar and velocity antocorrelation spectra. In this model, one can examine how flame surface area is affected by turbulent fluctuations over the entire spectrum. The model predicts that the turbulent flame speed is a function of the ratio of the turbulence intensity to the laminar flame velocity (γ) and the turbulence Reynolds number. The sensitivity of the flame speed to the Reynolds number particularly at high values of γ may explain some of the scatter in the data in the literature. The model also predicts a platean in the turbulent flame speed at large values of γ. This is connected to the behavior of the scalar autocorrelation spectrum, which approaches a passive scalar spectrum in the limit γ→∞, thereby yielding a bounded limit for the turbulent flame speed.