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.     

A theoretical study of premixed turbulent flame development

Flame development in a statistically stationary and uniform, planar, one-dimensional turbulent flow is theoretically studied. A generalized balance equation for the mean combustion progress variable, which includes turbulent diffusion and pressure-driven transport terms, as well as the mean rate of product creation, is introduced and analyzed by invoking the sole assumption of a self-similar flame structure, well-supported by numerous experiments. The assumption offers the opportunity to simplify the problem by splitting the aforementioned partial differential equation into two ordinary differential equations, which separately model spatial variations of the progress variable and time variations of flame speed and thickness. The self-similar profile of the progress variable, obtained in numerous experiments, is theoretically predicted. Closures of the normalized pressure-driven transport term and mean rate of product creation are obtained. The closed balance equation shows that turbulent diffusion dominates during the initial stage of flame development, followed by the transition to counter-gradient transport in a sufficiently developed flame. A criterion of the transition is derived. The transition is promoted by the heat release and pressure-driven transport. Fully developed mean flame brush thickness and speed are shown to decrease when either density ratio or pressure-driven transport increases. Solutions for the development of the thickness are obtained. The development is accelerated by the pressure-driven transport and heat release.     

Large Eddy Simulation of a turbulent lifted flame using multi-modal manifold-based models: Feasibility and interpretability

A general model for multi-modal turbulent combustion is achievable with two-dimensional manifold equations that use the mixture fraction and a generalized progress variable as coordinates. Information about the underlying mode of combustion is encoded in three scalar dissipation rates that appear as parameters in the two-dimensional equations. In this work, Large Eddy Simulation (LES) of a multi-modal turbulent lifted hydrogen jet flame in a vitiated coflow is performed using this new turbulent combustion model, leveraging both convolution-on-the-fly and In-Situ Adaptive Tabulation for computational tractability. The simulation predicts a lifted flame consistent with observations from past experiments. The feasibility of such a model implemented in LES is examined, and the cost per timestep is found to be comparable to conventional one-dimensional manifold-based models describing one asymptotic mode of combustion. Additionally, the model provides clear interpretability, allowing for combustion mode analysis to be performed with ease by evaluating the scalar dissipation rates and generalized progress variable source term. This analysis is used to show that the flame is stabilized by autoignition and has a trailing nonpremixed flame. Furthermore, transport of progress variable from the most reactive mixture fraction towards richer mixtures at the centerline is found to be important.     

Stagnation-point polydisperse spray flame ignition

A theory of stagnation-point flow polydisperse spray flame ignition by an isothermal hot surface is presented for the first time. The configuration investigated consists of a mixture of fuel droplets and air flowing against an isothermal hot surface (such as a hot ignition probe). The polydisperse spray of droplets is modelled using the sectional approach. A single global chemical reaction is assumed for the case when ignition occurs. The mathematical analysis makes use of a small parameter that is exploited for an asymptotic approach. An analytical criterion for ignition is derived which includes effects of the flow field, the reactants and all the fuel spray-related parameters, including the initial size distribution of the spray's droplets. Numerical calculations disclose how the actual droplet size distribution impacts on the critical stagnation point temperature necessary to promote ignition. Additionally, the analytical estimates are compared with predictions of a numerical finite difference code with very satisfactory agreement.     

Computational investigations of the coupling between transient flame dynamics and thermo-acoustic instability in a self-excited resonance combustor

Combustion instability due to thermo-acoustic interactions is a critical combustion problem that requires a thorough understanding because of its adverse impact on stable and reliable operation of combustors in high-speed propulsion devices like gas turbines and rockets. This work conducts computational investigations of the coupling between the transient flame dynamics such as the ignition delay and local extinction and the thermo-acoustic instability developed in a self-excited resonance combustor to gain deep insights into the mechanisms of thermo-acoustic instability. A 2D modelling framework that employs different flamelet models (the steady flamelet model and the flamelet/progress variable approach) is developed to enable the examination of the effect of the transient flame dynamics caused by the strong coupling of the turbulent mixing and finite-rate chemical kinetics on the occurrence of thermo-acoustic instability. The models are validated by using the available experimental data for the pressure signal. Parametric studies are performed to examine the effect of the occurrence of the transient flame dynamics, the effect of artificial amplification of the Damköhler number, and the effect of neglecting mixture fraction fluctuations on the predictions of the thermo-acoustic instability. The parametric studies reveal that the occurrence of transient flame dynamics has a strong influence on the onset of the thermo-acoustic instability. Further analysis is then conducted to localise the effect of a particular flame dynamic event, the ignition delay, on the thermo-acoustic instability. The reverse effect of the occurrence of the thermo-acoustic instability on the transient flame dynamics in the combustor is also investigated by examining the temporal evolution of the local flame events in conjunction with the pressure wave propagation. The above observed two-way coupling between the transient flame dynamics (the ignition delay) and the thermo-acoustic instability provides a plausible mechanism of the self-excited and sustained thermo-acoustic instability observed in the combustor despite the fact that the results are obtained from 2D simulations. The same analysis is expected to be extensible to fully 3D simulations.     

Laser-based investigation of flame surface density and mean reaction rate during flame-wall interaction at elevated pressure

Velocities and flame front locations are measured simultaneously in a turbulent, side-wall quenching (SWQ) V-shaped flame during flame-wall interaction (FWI) at 1 and 3 bar by means of particle image velocimetry (PIV) and planar laser-induced fluorescence of the OH radical (OH-PLIF). The turbulent flame brush is characterized based on the spatial distribution of the mean reaction progress variable and a common direct method is used to derive the flame surface density (FSD) from the two-dimensional data by image processing. As the near-wall reaction zone is limited to a smaller region closer to the wall at higher pressure, higher peak values are observed in the FSD at 3 bar. A second definition of the FSD adapted for flames exposed to quenching is utilized similar to previous studies emphasizing the impact of FWI. The influence of the wall on the flame front topology is investigated based on a flame front-conditioned FSD and its variability within the data set. In a last step, an estimate of the mean reaction rate is deduced using an FSD model and evaluated in terms of integral and space-averaged values. A decreasing trend of integral mean reaction rate in regions with increasing flame quenching is observed for both operating conditions, but more pronounced at 3 bar. Space-averaged mean reaction rates, however, increase in the quenching region, as the size of the reaction zone decreases.     

A DNS assessment of linear relations between filtered reaction rate,flame surface density,and scalar dissipation rate in a weakly turbulent premixed flame

Linear relations between (i) filtered reaction rate and filtered flame surface density (FSD) and (ii) filtered reaction rate and filtered scalar dissipation rate (SDR), which are widely used in Large Eddy Simulation (LES) research into premixed turbulent combustion, are examined by processing DNS data obtained from a statistically 1D planar flame under weakly turbulent conditions that are most favourable for the two approaches (flamelet combustion regime, single-step chemistry, equidiffusive mixture, adiabatic burner, and low Mach number). The analysis well supports the former approach provided that the filtered reaction rate is combined with filtered molecular transport term. In such a case, both the RANS and LES FSD approaches are based on local relations valid within weakly perturbed flamelets. Accordingly, simply recasting RANS expressions to a filtered form works well. On the contrary, while the FSD and SDR approaches appear to be basically similar at first glance, the analysis does not support the latter one, but shows that a ratio of the filtered reaction rate to the filtered SDR is strongly scattered within the studied flame brush, with its conditionally mean value varying significantly with Favre-filtered combustion progress variable. As argued in the paper, these limitations of the LES SDR approach stem from the fact that it is based on a relation valid after integration over weakly perturbed flamelets, but this relation does not hold locally within such flamelets. Consequently, when a sufficiently small filter is applied to instantaneous fields, the filter may contain only a part of the local flamelet, whereas the linear relation holds solely for the entire flamelet and may not hold within the filtered flamelet volume. Thus, the present study implies that straightforwardly recasting well-established RANS equations to a filtered form is a flawed approach if the equations are based on integral features of local burning.     

Simultaneous rainbow schlieren deflectometry and OH* chemiluminescence imaging of a diesel spray flame in constant pressure flow rig

The physical and chemical phenomena that take place during fuel injection, entrainment and fuel-air mixing, cool-flame and ignition reaction, and combustion in diesel sprays still require extensive study. Global parameters such as liquid and vapor jet penetration lengths and spreading rates render useful yet still limited information. Understanding of the temporal evolution of the spray as it progresses through various steps is needed to develop advanced clean combustion modes and high-fidelity predictive models with sufficient accuracy. In this study, high-speed rainbow schlieren deflectometry (RSD) and OH* chemiluminescence are used to simultaneously image fuel-air mixing, cool-flame reactions, ignition, flame propagation and stabilization, and combustion in a transient diesel-like flame. A constant pressure flow rig (CPFR) is used to conduct multiple injections in quick succession to obtain a statistically relevant dataset. n-heptane was injected at nominal supply pressure of 1000 bar from a single-hole diesel injector into ambient at pressure of 30 bar and temperature of 800 K. About 500 injections were performed and analyzed to reveal structural features of non-reacting and reacting regions of the spray, quantify jet penetration and spreading rates, and study cool-flame behavior, ignition, flame propagation and stabilization at lift-off length, and combustion at upstream and downstream locations.     

Investigation of lengthscales, scalar dissipation, and flame orientation in a piloted diffusion flame by LES

This work investigates the structure of a diffusion flame in terms of lengthscales, scalar dissipation, and flame orientation by using large eddy simulation. This has been performed for a turbulent, non-premixed, piloted methane/air jet flame (Flame D) at a Reynolds-number of 22,400. A steady flamelet model, which was represented by artificial neural networks, yields species mass fractions, density, and viscosity as a function of the mixture fraction. This will be shown to suffice to simulate such flames. To allow to examine scalar dissipation, a grid of 1.97 × 10⁶ nodes was applied that resolves more than 75% of the turbulent kinetic energy. The accuracy of the results is assessed by varying the grid-resolution and by comparison to experimental data by Barlow, Frank, Karpetis, Schneider (Sandia, Darmstadt), and others. The numerical procedure solves the filtered, incompressible transport equations for mass, momentum, and mixture fraction. For subgrid closure, an eddy viscosity/diffusivity approach is applied, relying on the dynamic Germano model. Artificial turbulent inflow velocities were generated to feature proper one- and two-point statistics. The results obtained for both the one- and two-point statistics were found in good agreement to the experimental data. The PDF of the flame orientation shows the tilting of the flame fronts towards the centerline. Finally, the steady flamelet approach was found to be sufficient for this type of flame unless slowly reacting species are of interest.     

Numerical study of transient evolution of lifted jet flames: partially premixed flame propagation and influence of physical dimensions

Three-dimensional (3D) unsteady Reynolds-averaged Navier–Stokes simulations of a spark-ignited turbulent methane/air jet flame evolving from ignition to stabilisation are conducted for different jet velocities. A partially premixed combustion model is used involving a correlated joint probability density function and both premixed and non-premixed combustion mode contributions. The 3D simulation results for the temporal evolution of the flame's leading edge are compared with previous two-dimensional (2D) results and experimental data. The comparison shows that the final stabilised flame lift-off height is well predicted by both 2D and 3D computations. However, the transient evolution of the flame's leading edge computed from 3D simulation agrees reasonably well with experiment, whereas evident discrepancies were found in the previous 2D study. This difference suggests that the third physical dimension plays an important role during the flame transient evolution process. The flame brush's leading edge displacement speed resulting from reaction, normal and tangential diffusion processes are studied at different typical stages after ignition in order to understand the effect of the third physical dimension further. Substantial differences are found for the reaction and normal diffusion components between 2D and 3D simulations especially in the initial propagation stage. The evolution of reaction progress variable scalar gradients and its interaction with the flow and mixing field in the 3D physical space have an important effect on the flame's leading edge propagation.     

Investigation of the ignition processes of a multi-injection flame in a Diesel engine environment using the flamelet model

In this work, the first flamelet analysis is conducted of a highly resolved DNS of a multi-injection flame with both auto-ignition and ignition induced by flame-flame interaction. A novel method is proposed to identify the different combustion modes of ignition processes using generalized flamelet equations. The state-of-the-art DNS database generated by Rieth et al. (US National Combustion Meeting, 2019) for a multi-injection flame in a Diesel engine environment is investigated. Three-dimensional flamelets are extracted from the DNS at different time instants with a focus on auto-ignition and interaction-ignition processes. The influences of mixture field interactions and the scalar dissipation rate on the ignition process are investigated by varying the species composition boundary conditions of the transient flamelet equations. Budget analyses of the generalized flamelet equations show that the transport along the mixture fraction iso-surface is insignificant during the auto-ignition process, but becomes important when interaction-ignition occurs, which is further confirmed through a flamelet regime classification method.     

A novel method to automate FGM progress variable with application to igniting combustion systems

This paper introduces a new method to formulate reaction progress variables for the application of FGM in combustion systems. The method involves a multiobjective optimisation to find a reaction progress variable that accurately reproduces complex reactive phenomenon of interest. In our current research, the method is applied to igniting non-premixed flames. The optimised progress variable combinations are evaluated for their accuracy in reproducing detailed chemistry results for the ignition of hydrocarbon fuels. Comparisons are made against conventional progress variable formulations used in the literature. The current approach takes into consideration the table resolution and error reduction for the application of FGM in combustion problems. Methods that rely on maximising the smoothness of the manifold or ensuring monotonic increase in progress variables alone are shown to be insufficient to capture ignition. The possibility of optimising the progress variable with emphasis on accurately resolving a particular zone or phase of combustion, such as ignition, while maintaining minimum data loss is demonstrated. Through its application in a number of igniting counterflow flames, the effectiveness of the current method is verified. Progress variables optimised using specific flame databases are shown to accurately reproduce the ignition delays even with moderate variations in boundary conditions of the respective flames.     

Effects of subgrid scale and combustion modelling on flame structure of a turbulent premixed flame within LES and tabulated chemistry framework

The effects of combustion and SubGrid Scale (SGS) modelling on the overall flame characteristics of a turbulent premixed flame are investigated. This is achieved in terms of mean flow statistics, variances and flame surfaces. In particular, the chemical flame structure is analysed and compared. The Artificially Thickened Flame (ATF) approach coupled with the Flamelet Generated Manifolds (FGMs) and Filtered TAbulated Chemistry for LES (F-TACLES) approaches are used for this investigation. A Germano like procedure for dynamical calculation of SGS wrinkling is used which ensures the conservation of the total flame surface for both models. It turns out that using the dynamic SGS wrinkling model improves the results. Although the results of both combustion models in terms of statistics, mean and variances show very good agreement, the resolved flame surfaces hide different dynamic behaviour.     

Simultaneous observation of liquid phase distribution and flame front evolution during the ignition transient of a LOX/GH2-combustor

Phenomena such as flame propagation, flame/spray interaction and flame stabilization during the transient ignition process in a cryogenic model rocket combustor are investigated on sub-millisecond time scale. Diagnostic techniques developed to characterize the stationary spray flame are applied to investigate the transient evolution of the LOX-spray and the flame front during the ignition process. Ignition is initiated by focusing a pulsed laser into the combustion chamber. Thus, ignition time as well as the position of ignition is well defined. This and the exact control of the delay between ignition and detection time allowed the observation of the evolution of the flame front. The distribution of the liquid oxygen phase and the velocity of LOX droplets and ligaments are determined by light sheet techniques using a double-pulsed laser system. Simultaneously the position of the flame front is measured by recording the spontaneous emission of the OH-radical. By varying the delay timet between ignition and detection in a series of test runs, the transient ignition phenomena has been investigated in the interval from 0 to 5 ms after ignition.     

Measurements of three-dimensional mean flame surface area ratio in turbulent premixed Bunsen flames

A data processing scheme with particular emphasis on proper flame contour smoothing is developed and applied to measure the three-dimensional mean flame surface area ratio in turbulent premixed flames. The scheme is based on the two-sheet imaging technique such that the mean flame surface area ratio is an average within a window covering a finite section of the turbulent flame brush. This is in contrast to the crossed-plane tomograph technique which applies only to a line. Two sets of Bunsen flames have been investigated in this work with the turbulent Reynolds number up to 4000 and the Damköhler number ranging from less than unity to close to 10. The results show that three-dimensional effects are substantial. The measured three-dimensional mean flame surface area ratio correlates well with a formula similar to the Zimont model for turbulent burning velocity but with different model constants. Also, the mean flame surface area ratio displays a weak dependency on turbulence intensity but a strong positive dependency on the turbulence integral length scale.     

Modeling of flame lift-off length in diesel low-temperature combustion with multi-dimensional CFD based on the flame surface density and extinction concept

Low-Temperature Combustion (LTC) is becoming a promising technology for simultaneously reducing soot and NOx emissions from diesel engines. LTC regimes are evaluated by the flame lift-off length – the distance from the injector orifice to the location of hydroxyl luminescence closest to the injector in the flame jet. Various works have been dedicated to successful simulations of lifted flames of a diesel jet by use of various combustion modeling approaches. In this work, flame surface density and flamelet concepts were used to model the diesel lift-off length under LTC conditions. Numerical studies have been performed with the ECFM3Z model, n-Heptane and diesel fuels to determine the flame lift-off length and its correlation with soot formation under quiescent conditions. The numerical results showed good agreement with experimental data, which were obtained from an optically accessible constant volume chamber and presented at the Engine Combustion Network (ECN) of Sandia National Laboratories. It was shown that at a certain distance downstream from the injector orifice, stoichiometric scalar dissipation rate matched the extinction scalar dissipation rate. This computed extinction scalar dissipation rate correlated well with the flame lift-off length. For the range of conditions investigated, adequate quantitative agreement was obtained with the experimental measurements of lift-off length under various ambient gas O₂ concentrations, ambient gas temperatures, ambient gas densities and fuel injection pressures. The results showed that the computed lift-off length values for most of the conditions lay in a reasonable range within the quasi-steady lift-off length values obtained from experiments. However, at ambient temperatures lower than 1000 K, the lift-off length values were under-predicted by the numerical analysis. This may be due to the use of the droplet evaporation model as it is believed that evaporation has a strong effect on the lift-off length.     

Large-eddy simulation of a bluff-body stabilised turbulent premixed flame using the transported flame surface density approach

A premixed propane–air flame stabilised on a triangular bluff body in a model jet-engine afterburner configuration is investigated using large-eddy simulation (LES). The reaction rate source term for turbulent premixed combustion is closed using the transported flame surface density (TFSD) model. In this approach, there is no need to assume local equilibrium between the generation and destruction of subgrid FSD, as commonly done in simple algebraic closure models. Instead, the key processes that create and destroy FSD are accounted for explicitly. This allows the model to capture large-scale unsteady flame propagation in the presence of combustion instabilities, or in situations where the flame encounters progressive wrinkling with time. In this study, comprehensive validation of the numerical method is carried out. For the non-reacting flow, good agreement for both the time-averaged and root-mean-square velocity fields are obtained, and the Karman type vortex shedding behaviour seen in the experiment is well represented. For the reacting flow, two mesh configurations are used to investigate the sensitivity of the LES results to the numerical resolution. Profiles for the velocity and temperature fields exhibit good agreement with the experimental data for both the coarse and dense mesh. This demonstrates the capability of LES coupled with the TFSD approach in representing the highly unsteady premixed combustion observed in this configuration. The instantaneous flow pattern and turbulent flame behaviour are discussed, and the differences between the non-reacting and reacting flow are described through visualisation of vortical structures and their interaction with the flame. Lastly, the generation and destruction of FSD are evaluated by examining the individual terms in the FSD transport equation. Localised regions where straining, curvature and propagation are each dominant are observed, highlighting the importance of non-equilibrium effects of FSD generation and destruction in the model afterburner.     

LES/FGM investigation of ignition and flame structure in a gasoline partially premixed combustion engine

This paper presents a joint numerical and experimental study of the ignition process and flame structures in a gasoline partially premixed combustion (PPC) engine. The numerical simulation is based on a five-dimension Flamelet-Generated Manifold (5D-FGM) tabulation approach and large eddy simulation (LES). The spray and combustion process in an optical PPC engine fueled with a primary reference fuel (70% iso-octane, 30% n-heptane by volume) are investigated using the combustion model along with laser diagnostic experiments. Different combustion modes, as well as the dominant chemical species and elementary reactions involved in the PPC engines, are identified and visualized using Chemical Explosive Mode Analysis (CEMA). The results from the LES-FGM model agree well with the experiments regarding the onset of ignition, peak heat release rate and in-cylinder pressure. The LES-FGM model performs even better than a finite-rate chemistry model that integrates the full-set of chemical kinetic mechanism in the simulation, given that the FGM model is computationally more efficient. The results show that the ignition mode plays a dominant role in the entire combustion process. The diffusion flame mode is identified in a thin layer between the ultra fuel-lean unburned mixture and the hot burned gas region that contains combustion intermediates such as CO. The diffusion flame mode contributes to a maximum of 27% of the total heat release in the later stage of combustion, and it becomes vital for the oxidation of relatively fuel-lean mixtures.