Direct numerical simulations analysis of flame surface density models for nonpremixed turbulent combustion

The book Turbulent Combustion by Norbert Peters is a concise monograph on single-phase gaseous low Mach number turbulent combustion. It is compiled from the author's review papers on this topic plus some additional material. Norbert Peters characterizes turbulent combustion both by the way fuel and air are mixed and by the ratio of turbulent and chemical time scales. This approach leads naturally to detailed models, which are based on results of turbulence modelling and asymptotic flame theory. In both areas Norbert Peters has contributed significantly over the last two decades. The book has four sections. In chapter 1 he discusses briefly the state of the art of combustion models as they are used by different authors. Important turbulent and chemical scales are introduced, which are then used to introduce and explain the different combustion models. He distinguishes between premixed and non-premixed combustion and also between infinitely fast and finite rate chemistry. The current turbulent combustion models are described in order of their complexity and physical accuracy. He explains Eddy BreakUp and Eddy Dissipation Models, the fundamentals of the PDF transport equation, and the laminar flamelet concept applied to non-premixed and premixed turbulent combustion. Then, the Conditional Moment Closure, the Linear Eddy Model, and combustion models used in Large Eddy Simulations are described very briefly. Chapter 2 is devoted to premixed turbulent combustion. After introducing some characteristic dimensionless numbers Peters uses the level set approach and the flamelet concept to formulate a combustion model valid in the thin zone and corrugated reaction zone regimes. He shows parallels between this more fundamental model and standard models like the Bray-Moss-Libby model. He also presents models for the turbulent burning velocity, the Flame Surface Area Ratio, and discusses the effects of gas expansion. Very helpful for the reader's understanding is the presentation of three worked examples of a slot burner, a propagating spherical flame and an oscillating counter flow. Peters' model for premixed turbulent combustion is based on the equations for the mean and the variance of the $G$-equation, some closure relations as well as the flamelet equation for premixed combustion. A numerical example is used to discuss its accuracy. Non-premixed turbulent combustion is the subject matter of chapter 3. Peters uses the mixture fraction variable and asymptotic flame theory to explain the regimes of non-premixed turbulent combustion. Two worked examples of a counterflow diffusion flame and the one-dimensional unsteady laminar mixing layer help the reader to understand the theory. After discussing turbulent jet diffusion flames and introducing the flamelet equation he develops steady and unsteady flamelet models for non-premixed turbulent combustion. In particular, the Eulerian Particle Flamelet Model and the RIF (Representative Interactive Flamelet) Model are discussed. These models have been used to predict pollutant formation in a gas turbine and a direct injection Diesel engine, respectively. Finally, partially premixed combustion is discussed in chapter 4. Lifted turbulent diffusion flames are reviewed and the prediction of the lift-off height is identified as a key problem. This leads directly to the introduction of the concept of a triple flame. Different models for partially premixed combustion are then presented and the numerical simulation and the scaling of lift-off heights in turbulent jet flames are studied. There is no doubt that this book is well written and is an important contribution to combustion literature. Peters uses asymptotic theory and scale separation to develop combustion models from first principles. Also, the book contains a comprehensive review of the current literature on turbulent combustion. It is clearly a `must have' for experienced combustion modellers and experimentalists. The book has not been written for non-experts and beginners; these readers would probably have liked more worked examples and exercises, a list of symbols, some material on the mathematical techniques of asymptotic analysis, and a more detailed discussion of the standard combustion models that are often used in the literature. Also, the numerical aspects of turbulent combustion modelling are not discussed in the book. Nevertheless, the book will be a useful source for advanced courses on combustion. Markus Kraft

Combustion in a CI engine is initiated by self-ignition of fuel–air mixture caused by high pressure and high temperature; a process known as autoignition. Autoignition is a challenging problem to simulate as the temperature increases from initial temperature to the adiabatic flame temperature in a very short duration. Numerical study of a turbulent flow using RANS/LES encounters a closure problem. Accuracy of closure models can be improved through experimental results, theoretical reasoning and direct numerical simulation (DNS) data. A review of DNS of autoignition in a turbulent non-premixed medium is presented in this chapter. As observed from DNS study, autoignition sites in a turbulent non-premixed medium are not randomly distributed but follow a pattern in the mixture fraction-scalar dissipation rate space. Turbulent flow is always three-dimensional in nature. 2D DNS of autoignition shows that ignition delay time increases with increase in initial turbulence intensity, which contradicts with the experimental observation. 3D DNS of autoignition resolves this conflict. The conflict is mainly due to the absence of vortex-stretching phenomenon in 2D DNS. Homogeneous charge compression ignition (HCCI) is being considered as one of the strategies toward improving performance of conventional CI engines. However, HCCI engines suffer from drawbacks like lack of control over combustion and limited operating regime. One of the modifications suggested in the HCCI technology to overcome these drawbacks is the use of stratification in the fuel–air mixture. Therefore, a few DNS studies on autoignition in the stratified medium have been discussed here. Further, discussion on the conditional moment closure (CMC) model and its validation using DNS data has been presented. Ignition delay time predicted by CMC was found to be in good agreement with DNS predictions.

Scalar dissipation rate modelling for Large Eddy Simulation of turbulent premixed flames

Body forces such as buoyancy and externally imposed pressure gradients are expected to have a strong influence on turbulent premixed combustion due to the considerable changes in density between the unburned and fully burned gases. The present work utilises Direct Numerical Simulation data of three-dimensional statistically planar turbulent premixed flames to study the influence of body forces on the statistical behaviour of the flame surface density (FSD) and its evolution within the flame brush. The analysis has been carried out for different turbulence intensities and normalised body force values (i.e., Froude numbers). A positive value of the body force signifies an unstable density stratification (i.e., body force is directed from the heavier unburned gas to the lighter burned gas) and vice versa. It is found that for a given set of turbulence parameters, flame wrinkling increases with an increase in body force magnitude in the unstable configuration. Furthermore, higher magnitudes of body force in the unstable density stratification configuration promote a gradient type transport of turbulent scalar and FSD fluxes, and this tendency weakens in the stable density stratification configuration where a counter-gradient type transport is promoted. The statistical behaviours of the different terms in the FSD transport equation and their closures in the context of Reynolds Averaged Navier–Stokes simulations have been analysed in detail. It has been demonstrated that the effects of body force on the FSD and the terms of its transport equation weakens with increasing turbulence intensity as a result of the diminishing relative strength of body force in comparison to the inertial force. The predictions of the existing models have been assessed with respect to the corresponding terms extracted from the explicitly averaged DNS data, and based on this evaluation, suitable modifications have been made to the existing models to incorporate the effects of body force (or Froude number).

Surface density measurements of turbulent premixed flames in a spark-ignition engine and a bunsen-type burner using planar laser-induced fluorescence

In this work, the performances of two recently developed finite-rate dynamic scale similarity (SS) sub-grid scale (SGS) combustion models (named DB and DC) for non-premixed turbulent combustion are a priori assessed based on three Direct Numerical Simulation (DNS) databases. These numerical experiments feature temporally evolving syngas jet flames with different Reynolds (Re) numbers (2510, 4487 and 9079), experiencing a high level of local extinction. For comparison purposes, the predicting capability of these models is compared with three classical non-dynamic SS models, namely the scale similarity resolved reaction rate model (SSRRRM or A), the scale similarity filtered reaction rate model (SSFRRM or B), and a SS model derived by the “test filtering” approach (C), as well as an existing dynamic version of SSRRRM (DA). Improvements in the prediction of heat release rates using a new dynamic model DC are observed in high Re flame case. By decreasing Re, dynamic procedures produce results roughly similar to their non-dynamic counterparts. In the lowest Re, the dynamic methods lead to higher errors.

Applications of direct numerical simulation to premixed turbulent combustion

On jet-wake flame stabilization in scramjet: A LES/RANS study from chemical kinetic and fluid-dynamical perspectives

The primary objective of the research is to use Direct Numerical Simulations (DNS) to study turbulent non-premixed combustion. In DNS, the fluid mechanical and thermochemical conservation equations are solved by an accurate numerical method, without any averaging or turbulence modeling. In principle, then, DNS could be used to study a turbulent diffusion flame, for example. In practice, however, computational limitations severely restrict the flows that can be simulated. For non-reacting flows, DNS is restricted to simple geometries and moderate Reynolds number. For reacting flows there are severe restrictions on the thermochemistry. Our approach is to use DNS to study very simple turbulent reactive flows, that contain qualitatively the same phenomena real flames. Based on the insights and information gained, statistical models will be developed and tested. These models are then applicable to the turbulent flames of practical importance.

The unsteady flamelet progress variable (UFPV) model has been proposed by Pitsch and Ihme [“An unsteady/flamelet progress variable method for LES of nonpremixed turbulent combustion,” AIAA Paper No. 2005-557, 2005] for modeling the averaged/filtered chemistry source terms in Reynolds averaged simulations and large eddy simulations of reacting non-premixed combustion. In the UFPV model, a look-up table of source terms is generated as a function of mixture fraction Z, scalar dissipation rate χ, and progress variable C by solving the unsteady flamelet equations. The assumption is that the unsteady flamelet represents the evolution of the reacting mixing layer in the non-premixed flame. We assess the accuracy of the model in predicting autoignition and flame development in compositionally stratified n-heptane/air mixtures using direct numerical simulations (DNS). The focus in this work is primarily on the assessment of accuracy of the probability density functions (PDFs) employed for obtaining averaged source terms. The performance of commonly employed presumed functions, such as the dirac-delta distribution function, the β distribution function, and statistically most likely distribution (SMLD) approach in approximating the shapes of the PDFs of the reactive and the conserved scalars is evaluated. For unimodal distributions, it is observed that functions that need two-moment information, e.g., the β distribution function and the SMLD approach with two-moment closure, are able to reasonably approximate the actual PDF. As the distribution becomes multimodal, higher moment information is required. Differences are observed between the ignition trends obtained from DNS and those predicted by the look-up table, especially for smaller gradients where the flamelet assumption becomes less applicable. The formulation assumes that the shape of the χ(Z) profile can be modeled by an error function which remains unchanged in the presence of heat release. We show that this assumption is not accurate.

In-situ tracking of mixture fraction gradient trajectories and unsteady flamelet analysis in turbulent non-premixed combustion

The thickened flame approach for non-premixed combustion: Principles and implications for turbulent combustion modeling

Large eddy simulation of fuel variability and flame dynamics of hydrogen-enriched nonpremixed flames

DNS analysis of boundary layer flashback in turbulent flow with wall-normal pressure gradient

Turbulent combustion is the basic physical phenomenon responsible for efficient energy release by any internal combustion engine. However it is accompanied by other undesirable phenomena such as noise, pollutant species emission or damaging instabilities that may even lead to the system desctruction. It is then crucial to control this phenomenon, to understand all its mecanisms and to master it in industrial systems. For long time turbulent combustion has been explored only through theory and experiment. But the rapid increase of computers power during the last years has allowed an important development of numerical simulation, that has become today an essential tool for research and technical design. Direct numerical simulation has then allowed to rapidly progress in the knowledge of turbulent flame structures, leading to new modelisations for steady averaged simulations. Recently large eddy simulation has made a new step forward by refining the description of complex and unsteady flames. The main problem that arises when performing numerical simulation of turbulent combustion is linked to the description of the flame front. Being very thin, it can not however be reduced to a simple interface as it is the location of intense chemical transformation and of strong variations of thermodynamical quantities. Capturing the internal structure of a zone with a thickness of the order of 0.1 mm in a computation with a mesh step 10 times larger being impossible, it is necessary to model the turbulent flame. Models depend on the chemical structure of the flame, on the ambiant turbulence, on the combustion regime (flamelets, distributed combustion, etc.) and on the reactants injection mode (premixed or not). One finds then a large class of models, from the most simple algebraic model with a one-step chemical kinetics, to the most complex model involving probablity density functions, cross-correlations and multiple-step or fully complex chemical kinetics.