Effects of Lewis Number on Conditional Fluid Velocity Statistics in Low Damköhler Number Turbulent Premixed Combustion: A Direct Numerical Simulation Analysis

The effects of global Lewis number Le on the statistics of fluid velocity components conditional in unburned reactants and fully burned products in the context of Reynolds Averaged Navier Stokes simulations have been analysed using a Direct Numerical Simulations (DNS) database of statistically planar turbulent premixed flames with a low Damkohler number and Lewis number ranging from 0.34 to 1.2. The conditional velocity statistics extracted from DNS data have been analysed with respect to the well-known Bray-Moss-Libby (BML) expressions which were derived based on bi-modal probability density function of reaction progress variable for high Damkohler number flames. It has been shown that the Lewis number substantially affects the mean velocity and the velocity fluctuation correlation conditional in products, with the effect being particularly pronounced for low Le. As far as the mean velocity and the velocity fluctuation correlation conditional in reactants are concerned, the BML expressions agree reasonably well with the DNS data reported in the present work. Based on a priori analysis of present and previously reported DNS data, the BML expressions have been empirically modified here in order to account for Lewis number effects, and the non-bimodal distribution of reaction progress variable. Moreover, it has been demonstrated for the first time that surface averaged velocity components and Reynolds stresses conditional in unburned reactants can be modelled without invoking expressions involving the Lewis number, as these surface averaged conditional quantities remain approximately equal to their conditionally averaged counterparts in the unburned mixture

Statistics of conditional fluid velocity in the corrugated flamelets regime of turbulent premixed combustion: A Direct Numerical Simulation study

The statistics of mean fluid velocity components conditional in unburned reactants and fully burned products in the context of Reynolds Averaged Navier Stokes (RANS) simulations have been studied using a Direct Numerical Simulation database of statistically planar turbulent premixed flame representing the corrugated flamelets regime combustion. Expressions for conditional mean velocity and conditional velocity correlations which are derived based on a presumed bimodal probability density function of reaction progress variable for unity Lewis number flames are assessed in this study with respect to the corresponding quantities extracted from DNS data. In particular, conditional surface averaged velocities (ui)¯Rs and the velocity correlations (uiu)j¯Rs in the unburned reactants are demonstrated to be effectively modelled by the unconditional velocities (ui)¯R and velocity correlations (uiuj)¯R, respectively, for the major part of turbulent flame brush with the exception of the leading edge. By contrast, conditional surface averaged velocities (ui)¯Ps and the velocity correlations (uiu)j¯Ps in fully burned products are shown to be markedly different from the unconditional velocities (ui)¯P and velocity correlations (uiuj)¯P, respectively

Speed selection for traveling-wave solutions to the diffusion-reaction equation with cubic reaction term and Burgers nonlinear convection

The problem of traveling wave (TW) speed selection for solutions to a generalized Murray-Burgers-KPP-Fisher parabolic equation with a strictly positive cubic reaction term is considered theoretically and the initial boundary value problem is numerically solved in order to support obtained analytical results. Depending on the magnitude of a parameter inherent in the reaction term (i) the term is either a concave function or a function with the inflection point and (ii) transition from pulled to pushed TW solution occurs due to interplay of two nonlinear terms; the reaction term and the Burgers convection term. Explicit pushed TW solutions are derived. It is shown that physically observable TW solutions, i.e., solutions obtained by solving the initial boundary value problem with a sufficiently steep initial condition, can be determined by seeking the TW solution characterized by the maximum decay rate at its leading edge. In the Appendix, the developed approach is applied to a non-linear diffusion-reaction equation that is widely used to model premixed turbulent combustion

A direct numerical simulation study of vorticity transformation in weakly turbulent premixed flames

Database obtained earlier in 3D Direct Numerical Simulations (DNS) of statistically stationary, 1D, planar turbulent flames characterized by three different density ratios σ is processed in order to investigate vorticity transformation in premixed combustion under conditions of moderately weak turbulence (rms turbulent velocity and laminar flame speed are roughly equal to one another). In cases H and M characterized by σ = 7.53 and 5.0, respectively, anisotropic generation of vorticity within the flame brush is reported. In order to study physical mechanisms that control this phenomenon, various terms in vorticity and enstrophy balance equations are analyzed, with both mean terms and terms conditioned on a particular value c of the combustion progress variable being addressed. Results indicate an important role played by baroclinic torque and dilatation in transformation of average vorticity and enstrophy within both flamelets and flame brush. Besides these widely recognized physical mechanisms, two other effects are documented. First, viscous stresses redistribute enstrophy within flamelets, but play a minor role in the balance of the mean enstrophy Ω ¯ ¯ ¯ within turbulent flame brush. Second, negative correlation u ′ ⋅∇Ω ′ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ between fluctuations in velocity u and enstrophy gradient contributes substantially to an increase in the mean Ω ¯ ¯ ¯ within turbulent flame brush. This negative correlation is mainly controlled by the positive correlation between fluctuations in the enstrophy and dilatation and, therefore, dilatation fluctuations substantially reduce the damping effect of the mean dilatation on the vorticity and enstrophy fields. In case L characterized by σ = 2.5, these effects are weakly pronounced and Ω ¯ ¯ ¯ is reduced mainly due to viscosity. Under conditions of the present DNS, vortex stretching plays a minor role in the balance of vorticity and enstrophy within turbulent flame brush in all three cases

Numerical simulations of turbulent combustion

Turbulent burning of gaseous fuels is widely used for energy conversion in stationary power generation, e [...

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

While quantities conditioned to an isosurface of reaction progress variable c, which characterizes fluid state in a turbulent reacting flow, have been attracting rapidly growing interest in the recent literature, a mathematical and physical framework required for research into such quantities has not yet been elaborated properly. This paper aims at filling two fundamental gaps in this area, i.e., (i) ambiguities associated with a definition of a surface-averaged quantity and (ii) the lack of rigorous equations that describe evolutions of such quantities. In the first (theoretical) part of the paper, (a) analytical relations between differently defined (area-weighted and unweighted) surface-averaged quantities are obtained and differences between them (quantities) are discussed, (b) a unified method for deriving an evolution equation for bulk area-weighted surface-averaged value of a local characteristic φ of a turbulent reacting flow is developed, and (c) the method is applied for deriving evolution equations for the bulk area-weighted surface-averaged reaction-surface density |∇c|, local reactionwave thickness 1/|∇c|, and local displacement speed Sd , i.e., the speed of an isosurface of the c(x,t) field with respect to the local flow. In the second (numerical) part of the paper, direct numerical simulation data obtained recently from a highly turbulent reaction wave are analyzed in order to (1) highlight substantial differences between area-weighted and unweighted surface-averaged quantities and (2) show that various terms in the derived evolution equations are amenable to accurate numerical evaluation in spite of appearance of the so-called zero-gradient points [C. H. Gibson, Phys. Fluids 11, 2305 (1968)] in a highly turbulent medium. Finally, the obtained analytical and numerical results are used to shed light on the paradox of local flame thinning and broadening which is widely discussed in the turbulent combustion literature

A new mathematical framework for describing thin-reaction-zone regime of turbulent reacting flows at low Damk\uf6hler number

Recently, Sabelnikov et al. (2019) developed a phenomenological theory of propagation of an infinitely thin reaction sheet, which is adjacent to a mixing layer, in a constant-density turbulent flow in the case of a low Damk\uf6hler number. In the cited paper, the theory is also supported by Direct Numerical Simulation data and relevance of such a physical scenario to highly turbulent premixed combustion is argued. The present work aims at complementing the theory with a new mathematical framework that allows for appearance of thick mixing zones adjacent to an infinitely thin reaction sheet. For this purpose, the instantaneous reaction-progress-variable c(x,t) is considered to consist of two qualitatively different zones, that is, (i) mixture of products and reactants, c(x,t)<1, where molecular transport plays an important role, and (ii) equilibrium products, c(x,t)=1. The two\ua0zones are separated by an infinitely thin reaction sheet, where c(x,t)=1 and |nabla c| is fixed in order for the molecular flux into the sheet to yield a constant local consumption velocity equal to the speed of the unperturbed laminar reaction wave. Exact local instantaneous field equations valid in the entire spaceare derived for the conditioned (to the former, mixing, zone) reaction progress variable,\ua0its second moment, and instantaneous characteristic functions. Averaging of these equations yields exact, unclosed transport equations for the conditioned reaction-progress-variable moments and\ua0Probability Density Function (PDF), as well as a boundary condition for the PDF at the reaction sheet.\ua0The closure problem for the derived equations is beyond the scope of the paper

Flame folding and conditioned concentration profiles in moderately intense turbulence

While the flamelet paradigm offers the opportunity to simplify computations of mean species concentrations in turbulent flames, a widely\ua0accepted criterion of the validity of this paradigm has not yet been elaborated. In this regard, different physical mechanisms are discussed, and\ua0flame folding is one of them. The present work aims at exploring the eventual influence of flame folding on the local flame structure in a turbulent flow. For this purpose, a new diagnostic technique was applied to processing complex-chemistry direct numerical simulation data obtained earlier from a lean hydrogen-air turbulent flame [Dave and Chaudhuri, J. Fluid Mech. 884, A46 (2020)]. The technique consists of counting crossing numbers Nf for a cold boundary of the local reaction zone and a ray normal to the mean flame brush, followed by analyzing statistics sampled from rays characterized by Nf>2. More specifically, profiles of species mole fractions, temperature, heat release\ua0rate, and species production rates, conditioned to combustion progress variable and either Nf or axial distance dx between two neighboring reaction zones, are sampled and compared with the counterpart profiles obtained from the laminar flame. Results show that these doubly conditioned profiles are close to each other for various crossing numbers or for various axial distances even if the distance is as small as halflaminar flame thickness. The lack of a substantial effect of the crossing number or the axial distance on the doubly conditioned profiles implies that small-scale flame folding does not limit the validity of the flamelet paradigm

An extended flamelet-based presumed probability density function for predicting mean concentrations of various species in premixed turbulent flames

Direct Numerical Simulation (DNS) data obtained by Dave and Chaudhuri (2020) from a lean, complex-chemistry, hydrogen-air flame associated with the thin-reaction-zone regime of premixed turbulent burning are analyzed to perform a priori assessment of predictive capabilities of the flamelet approach for evaluating mean species concentrations. For this purpose, dependencies of mole fractions and rates of production of various species on a combustion progress variable c, obtained from the laminar flame, are averaged adopting either the actual Probability Density Function (PDF) P(c) extracted from the DNS data or a common presumed β-function PDF. On the one hand, the results quantitatively validate the flamelet approach for the mean mole fractions of all species, including radicals, but only if the actual PDF P(c) is adopted. The use of the β-function PDF yields substantially worse results for the radicals’ concentrations. These findings put modeling the PDF P(c) on the forefront of the research agenda. On the other hand, the mean rate of product creation and turbulent burning velocity are poorly predicted even adopting the actual PDF. These results imply that, in order to evaluate the mean species concentrations, the flamelet approach could be coupled with another model that predicts the mean rate and turbulent burning velocity better. Accordingly, the flamelet approach could be implemented as post-processing of numerical data yielded by that model. Based on the aforementioned findings and implications, a new approach to building a presumed PDF is developed. The key features of the approach consist in (i) adopting a re-normalized flamelet PDF for intermediate values of c and (ii) directly using the mean rate of product creation to calibrate the presumed PDF. Capabilities of the newly developed PDF for predicting mean species concentrations are quantitively validated for all species, including radicals