Regularization of reaction progress variable for application to flamelet-based combustion models

Many combustion models that are based on the flamelet paradigm employ a reaction progress variable. While such a progress variable is well defined for one-step reaction kinetics, this is typically not the case for complex chemical mechanisms. Consequently, several expressions for a progress variable have been utilized. In this paper a formal method for the generation of a reaction progress variable is proposed that is optimal with respect to a set of constraints. The potential of the method is demonstrated in applications to partially premixed and diffusion flames, and the extension to premixed combustion is discussed. It is shown that the proposed method can lead to significant improvements in the definition of an optimal progress variable over conventional formulations, essentially eliminating the expert knowledge previously required in identifying such quantities.     

Modelling compression ignition engines by incorporation of the flamelet generated manifolds combustion closure

Tabulated chemistry models allow to include detailed chemistry effects at low cost in numerical simulations of reactive flows. Characteristics of the reactive fluid flows are described by a reduced set of parameters that are representative of the flame structure at small scales so-called flamelets. For a specific turbulent combustion configuration, flamelet combustion closure, with proper formulation of the flame structure can be applied. In this study, flamelet generated manifolds (FGM) combustion closure with progress variable approach were incorporated with OpenFOAM® source code to model combustion within compression ignition engines. For IC engine applications, multi-dimensional flamelet look-up tables for counter flow diffusive flame configuration were generated. Source terms of non-premixed combustion configuration in flamelet domain were tabulated based on pressure, temperature of unburned mixture, mixture fraction, and progress variable. A new frozen flamelet method was introduced to link one dimensional reaction diffusion space to multi-dimensional Computational Fluid Dynamics (CFD) physical space to fulfill correct modelling of thermal state of the engine at expansion stroke when charge composition was changed after combustion and reaction rates were subsided. Predictability of the developed numerical framework were evaluated for Sandia Spray A (constant volume vessel), Spray B (light duty optical Diesel engine), and a heavy duty Diesel engine experiments under Reynolds averaged Navier Stokes turbulence formulation. Results showed that application of multi-dimensional FGM combustion closure can comprehensively predict key parameters such as: ignition delay, in-cylinder pressure, apparent heat release rate, flame lift-off , and flame structure in Diesel engines.     

A generalized flame surface density modelling approach for the auto-ignition of a turbulent non-premixed system

Auto-ignition of turbulent non-premixed systems is encountered in practical devices such as diesel internal combustion engines. It remains a challenge for modellers, as it exhibits specific features such as unsteadiness, flame propagation and combustion far from stoichiometric conditions. In this paper, a two-dimensional DNS database of an igniting H₂/O₂/N₂ mixing layer, including detailed chemistry and transport, is extensively post-processed in order to gain physical insight into the flame structure and dynamics during auto-ignition. The results are used as a framework for the development of a generalized flame surface density modelling approach by integrating the equations over all possible mixture fraction values. The mean reaction rate is split into two contributions: a generalized flame surface density and a mean reaction rate per unit generalized flame surface density. The unsteadiness of the ignition phenomenon is accounted for via a generalized progress variable. Closures for the generalized surface average of the reaction rate and for the generalized progress variable are proposed, and the modelling approach is tested a priori versus the DNS data. The use of a laminar database for the chemistry coupled to the mean turbulent field via the generalized progress variable shows very promising results, capturing the correct ignition delay and the premixed peak in the turbulent mean heat release rate evolution. This allows confidence in future inclusion and validation of this approach in a RANS-CFD code.     

Effects of turbulence-chemistry interactions on auto-ignition and flame structure for n-dodecane spray combustion

The Engine Combustion Network (ECN) spray A under diesel engine conditions is investigated with a non-adiabatic 5D Flamelet Generated Manifolds (FGM) model with the consideration of detailed chemical kinetic mechanisms. The enthalpy deficit due to droplet vapourisation is considered by employing an additional controlling parameter in the FGM library. In this FGM model, β-PDF is used for the PDF integration over the control variable space. Validation results in non-reacting conditions indicate relatively good agreement between the predicted and experimental data in terms of liquid and vapour penetrations and mixture fraction spatial distribution. In reacting conditions, the effects of variance of mixture fraction and progress variable were examined. The ignition delay time and the quasi-steady flame structure are both affected by the variances. The variance of mixture fraction delays the ignition process and the variance of progress variable accelerates it. For mixture fraction, the ignition process is quicker at any stage in the case of neglecting variance. While things are more complex for progress variable, the ignition process is advanced in the case of neglecting variance at early times, but surpassed by the case of β-PDF later and until auto-ignition. When variance of mixture fraction is considered, the OH mass fraction shows a wide spatial distribution. While if not, a very thin flame is observed with a higher peak in OH, and a very large lift-off length. The variance of progress variable has little impact on the global flame structure, but makes the flame lift-off length much shorter. This study confirms the general observation, that the variance of mixture fraction is of higher importance in high temperature non-premixed combustion, however, we found that the variance of progress variable is far from negligible.     

Effects of equivalence ratio variation on lean,stratified methane–air laminar counterflow flames

The effects of equivalence ratio variations on flame structure and propagation have been studied computationally. Equivalence ratio stratification is a key technology for advanced low emission combustors. Laminar counterflow simulations of lean methane–air combustion have been presented which show the effect of strain variations on flames stabilized in an equivalence ratio gradient, and the response of flames propagating into a mixture with a time-varying equivalence ratio. ‘Back supported’ lean flames, whose products are closer to stoichiometry than their reactants, display increased propagation velocities and reduced thickness compared with flames where the reactants are richer than the products. The radical concentrations in the vicinity of the flame are modified by the effect of an equivalence ratio gradient on the temperature profile and thermal dissociation. Analysis of steady flames stabilized in an equivalence ratio gradient demonstrates that the radical flux through the flame, and the modified radical concentrations in the reaction zone, contribute to the modified propagation speed and thickness of stratified flames. The modified concentrations of radical species in stratified flames mean that, in general, the reaction rate is not accurately parametrized by progress variable and equivalence ratio alone. A definition of stratified flame propagation based upon the displacement speed of a mixture fraction dependent progress variable was seen to be suitable for stratified combustion. The response times of the reaction, diffusion, and cross-dissipation components which contribute to this displacement speed have been used to explain flame response to stratification and unsteady fluid dynamic strain.     

Investigation of the Livengood–Wu integral for modelling autoignition in a high-pressure bomb

The reaction progress variable, which is widely used in premixed and diffusion combustion studies, comprises a set of pre-selected intermediate species to denote reaction progress. Progress towards autoignition can also be traced by the Livengood–Wu (LW) integral. Autoignition occurs when the LW integral attains a value of unity. This concept is further explored by applying it to an inhomogeneous mixture scenario, to determine the time and place of autoignition occurrence. A semidetailed mechanism (137 species and 633 reactions) for n-heptane/iso-octane/toluene is used in this study. Two numerical schemes based on the LW integral are proposed and incorporated into a computational fluid dynamics platform, to model autoignition in a 3D configuration, when a spray is injected into a constant volume bomb under diesel engine conditions. Tabulated chemistry, a traditional method of modelling autoignition using information from pre-calculated igniting diffusion flames, is also used for comparison purposes. The associated predicted pressure profiles are compared with experimental measurements.     

Using self-similar properties of turbulent premixed flames to downsize chemical tables in high-performance numerical simulations

Detailed chemical mechanisms have to be incorporated in turbulent combustion modelling to predict flame propagation, ignition, extinction or pollutant formation. Unfortunately, hundreds of species and thousands of elementary reactions are involved in hydrocarbon chemical schemes and cannot be handled in practical simulations, because of the related computational costs and the need to model the complexity of their interaction with turbulent motions. Detailed chemistry may be handled using look-up tables, where chemical parameters such as reaction rates and/or species mass fractions are determined from a reduced set of coordinates, progress variables or mixture fractions, as proposed in ILDM, FPI or FGM methods. Nevertheless, these tables may require large computer memory spaces and non-negligible access times. This issue becomes of crucial importance when running on massively parallel computers: to implement these databases in shared memories would induce a large number of data exchanges, reducing the overall code performance; on the other hand duplicating databases in every local processor memory may become impossible either for large databases or small local memories. This work proposes to take advantage of the self-similar behaviour of turbulent premixed flames to reduce the size of these chemical databases, specifically when running on massively parallel machines, under the FPI (Flame Prolongation of ILDM) framework. Several approaches to reduce the database are investigated and discussed both in terms of memory requirements and access times. A very good compromise is obtained for methane–air turbulent premixed flames, where the size of the database is decreased by a factor of 1000, while the access time is reduced by about 60%.     

Effects of body force on the statistical behaviour and modelling of scalar variance in turbulent premixed flames

The effects of body force/external pressure gradient on the statistical behaviours of the reaction progress variable variance and the terms of its transport equation have been investigated for different turbulence intensities using DNS data of statistically planar flames. Since the extent of flame wrinkling increases with the strengthening of body force promoting unstable stratification, the scalar variance has been found to decrease under strong body force promoting stability. This trend is particularly strong for low turbulence intensities where the probability density function of the reaction progress variable cannot be approximated by a bimodal distribution. Therefore, an algebraic relation for the reaction progress variable variance, derived based on a presumed bimodal probability density function of reaction progress variable, cannot be used for general flow conditions. The contributions of chemical reaction and scalar dissipation rates in the scalar variance transport equation remain leading order source and sink, respectively for all cases irrespective of the strength and direction of the body force. The counter-gradient type transport is found to weaken with increasing body force magnitude when the body force is directed from the heavier unburned gas to the lighter burned gas side of the flame brush, and vice versa. Although a scalar dissipation rate-based reaction rate closure can be utilised to model the reaction rate contribution to the scalar variance transport accurately, the dissipation rate contribution due to the gradient of the Favre-averaged reaction progress variable cannot be ignored and it plays a key role for large magnitudes of body force promoting stable stratification. An algebraic closure of the scalar dissipation rate, originally proposed for high Damköhler number combustion, has been modified for the thin reaction zones regime combustion by incorporating the effects of Froude number. This model has been shown to predict the scalar dissipation rate accurately for all cases considered here.     

Laser diagnostics and their interplay with computations to understand turbulent combustion

Laser diagnostics for fundamental investigation of turbulent combustion are discussed in the context of collaborative research that has been conducted over the past decade to contribute toward the development and experimental validation of predictive science-based models for turbulent flames. The emphasis is on simultaneous application of multiple laser techniques in flames having relatively simple fuels and flow geometries, as well as separate application of complementary diagnostics in the same flames. Data needs and design considerations for turbulent combustion model-validation experiments are outlined. Examples are given of ways in which the interplay of experiments and computations on “standard” turbulent flames has led to better understanding of these flames and also a better understanding of the capabilities of laser diagnostics and models to accurately capture the effects of turbulence-chemistry interactions. Issues of spatial resolution, differential diffusion, and LES validation are discussed, and perspectives on current research challenges are offered.     

Large eddy simulation of the low temperature ignition and combustion processes on spray flame with the linear eddy model

Large eddy simulation coupled with the linear eddy model (LEM) is employed for the simulation of n-heptane spray flames to investigate the low temperature ignition and combustion process in a constant-volume combustion vessel under diesel-engine relevant conditions. Parametric studies are performed to give a comprehensive understanding of the ignition processes. The non-reacting case is firstly carried out to validate the present model by comparing the predicted results with the experimental data from the Engine Combustion Network (ECN). Good agreements are observed in terms of liquid and vapour penetration length, as well as the mixture fraction distributions at different times and different axial locations. For the reacting cases, the flame index was introduced to distinguish between the premixed and non-premixed combustion. A reaction region (RR) parameter is used to investigate the ignition and combustion characteristics, and to distinguish the different combustion stages. Results show that the two-stage combustion process can be identified in spray flames, and different ignition positions in the mixture fraction versus RR space are well described at low and high initial ambient temperatures. At an initial condition of 850 K, the first-stage ignition is initiated at the fuel-lean region, followed by the reactions in fuel-rich regions. Then high-temperature reaction occurs mainly at the places with mixture concentration around stoichiometric mixture fraction. While at an initial temperature of 1000 K, the first-stage ignition occurs at the fuel-rich region first, then it moves towards fuel-richer region. Afterwards, the high-temperature reactions move back to the stoichiometric mixture fraction region. For all of the initial temperatures considered, high-temperature ignition kernels are initiated at the regions richer than stoichiometric mixture fraction. By increasing the initial ambient temperature, the high-temperature ignition kernels move towards richer mixture regions. And after the spray flames gets quasi-steady, most heat is released at the stoichiometric mixture fraction regions. In addition, combustion mode analysis based on key intermediate species illustrates three-mode combustion processes in diesel spray flames.     

A novel linear transformation model for the analysis and optimisation of chemical kinetics

In this study, a novel model for the analysis and optimisation of numerical and experimental chemical kinetics is developed. Concentration–time profiles of non-diffusive chemical kinetic processes and flame speed profiles of fuel–oxidiser mixtures can be described by certain characteristic points, so that relations between the coordinates of these points and the input parameters of chemical kinetic models become almost linear. This linear transformation model simplifies the analysis of chemical kinetic models, hence creating a robust global sensitivity analysis and allowing quick optimisation and reduction of these models. Firstly, in this study the model is extensively validated by the optimisation of a syngas combustion model with a large data set of imitated ignition experiments. The optimisation with the linear transformation model is quick and accurate, revealing the potential for decreasing the numerical costs of the optimisation process by at least one order of magnitude compared to established methods. Additionally, the optimisation on this data set demonstrates the capability of predicting reaction rate coefficients more accurately than by currently known confidence intervals. In a first application, methane combustion models are optimised with a small experimental set consisting of OH(A) and CH(A) concentration profiles from shock tube ignition experiments, species profiles from flow reactor experiments and laminar flame speeds. With the optimised models, especially the predictability for the flame speeds of mixtures of hydrogen, carbon monoxide and methane can be increased compared to established models. With the analysis of the optimised models, new information on the low pressure reaction coefficient of the fall-off reaction H+CH₃(+M)?CH₄(+M) is determined. In addition, the optimised combustion model is quickly and efficiently reduced to validate a new rapid reduction scheme for chemical kinetic models.     

Self-similar behavior and chemistry tabulation of burnt-gas diluted premixed flamelets including heat-loss

In many combustion systems, the reactive gases feeding the reaction zones are diluted by burnt products, to favor flame stabilization, homogenize the temperature distribution and reduce pollutant emission. The objective of this paper is to discuss a premixed flamelet detailed chemistry tabulation strategy for vitiated and non-adiabatic combustion. Dilution by burnt products is parameterized here with two controlling quantities: the amplitude of the heat-loss in the burnt gases, for instance at walls, and the level of reactant vitiation. The chemical response of premixed flames to variations of these parameters is studied and it is shown that most chemical properties of burnt-gas diluted flames feature self-similar behavior, which can be used to dramatically downsize chemical tables based on canonical flamelets. The self-similar behavior of the flamelets is studied for both molecular diffusion and chemical source budgets in a progress variable composition space. It is found that two different scaling relations are needed to ensure self-similar behavior of both major and radical species.     

Highly energetic and flammable metallic glasses

Energetic materials are solids that release a large amount of energy in combustion. The evaluation depends on both combustion heat and ignition temperature. Conventional non-metallic materials have low ignition temperature but small combustion heat,whereas metals have large combustion heat but high ignition temperatures. We show that many metallic glasses, combining the merits of both metals and non-metals, have large combustion heat, approximately twice that of the non-metals, and low ignition temperature that is several hundreds of Kelvin lower than that of the metals. The ease in igniting metallic glass results from the low thermal conductivity of the materials and the storage of energy in their liquid-like atomic structure. Metallic glass ribbons outweigh metallic nanoparticles due to their high production efficiency, low cost and nontoxicity. The findings suggest that metallic glasses are alternative energetic materials.     

Astrophysical combustion

There are three main astrophysical combustion systems: the evolution of stars, formation of interstellar dust and particulates, and the transition to hadrons in the early universe. These are described in terms of general combustion concepts, such as ignition, laminar and turbulent flames, detonations, multiphase flows, and particle and soot formation. Viewed in this way, the universe and many of its most important astronomical components are combustion systems, and we should use these as naturally occurring laboratories for exploring new and familiar combustion regimes. A more detailed discussion focuses on one type of combustion system, the ignition and development of turbulent flames in Type Ia supernovae, and the importance of the transition to a detonation.     

The compositional structure of highly turbulent piloted premixed flames issuing into a hot coflow

Simultaneous line measurements of major species and temperature by the Raman–Rayleigh technique, combined with CO two-photon laser-induced fluorescence and crossed-plane OH planar laser-induced fluorescence have been applied to a series of flames in the Piloted Premixed Jet Burner (PPJB). The PPJB is capable of stabilizing highly turbulent premixed jet flames through the use of a stoichiometric pilot and a large coflow of hot combustion products. Four flames with increasing jet velocities and constant jet equivalence ratios are examined in this paper. The characteristics of these four flames range from stable flame brushes with reaction zones that can be described as thin and “flamelet-like” to flames that have thickened reaction zones and exhibit extinction re-ignition behaviour. Radial profiles of the mean temperature are reported, indicating the mean thermal extent of the pilot and spatial location of the mean flame brush. Measurements of carbon monoxide (CO) and the hydroxyl radical (OH) reveal a gradual decrease in the conditional mean as the jet velocity is increased and the flame approaches extinction. Experimental results for the conditional mean temperature gradient show a progressive trend of reaction zone thickening with increasing jet velocities, indicating the increased interaction of turbulence with the reaction zone at higher turbulence levels. For the compositions examined, the product of CO and OH mole fractions ([CO][OH]) is shown to be a good qualitative indicator for the net rate of production of carbon dioxide. The axial variation of [CO][OH] is shown to correlate well with the mean chemi-luminescence of the flames including the extinction re-ignition regions. The experimental findings reported in this paper further support the hypothesis of an initial ignition region followed by extinction and re-ignition regions for certain PPJB flames.