Large eddy simulation of multi-regime combustion with a two-progress variable approach for carbon monoxide

Simulations of two cases in a novel multi-regime burner configuration are undertaken using a presumed joint probability density function (PDF) approach with tabulated chemistry. The flame conditions are varied by changing the central jet equivalence ratio, which produces different multi-regime combustion modes in the non-premixed inner flame. An outer premixed flame and recirculation zone behind a bluff body are present to supply heat and combustion products to stabilise the inner flame. A two-progress variable approach is tested to improve predictions of carbon monoxide (CO) in the post-flame regions, where CO oxidation occurs. The large eddy simulation set-up and sub-grid combustion model are assessed through comparisons with time-averaged measurements for radial profiles at different streamwise locations. The jet break-up length, the shear layers and the mixture fraction distribution are well captured in both cases. The temperature distribution is well captured for the inner flame in each case but the temperature and mixture fraction are over predicted in the downstream regions of the outer premixed flame, which is due to increased dilatation that suppresses air entrainment. Improved predictions of the CO mass fraction are obtained for the outer premixed flames with the two-progress variable approach. Over predictions are seen in the upstream regions of the inner flame when the CO mass fraction is obtained from a look-up table, suggesting that the CO mass fraction should be transported to include the convection/diffusion balance in regions where there is no flame. Furthermore, transporting the CO mass fraction with a one-progress variable approach produces over predictions in the burnt regions, suggesting a two-progress variable model is needed to capture the consumption region of CO. The multi-regime combustion characteristics are observed to be stronger in flame MRB26b, where non-premixed and rich premixed combustion is present. For flame MRB18b, the non-premixed contribution is smaller and weak stratified combustion is observed.     

Characterization of multi-regime reaction zones in a piloted inhomogeneous jet flame with local extinction

Gradient free regime identification (GFRI) is applied to 1D Raman/Rayleigh/LIF measurements of temperature and major species from the intermediate velocity case of the Sydney piloted inhomogeneous jet flame series to better understand the structure of reaction zones and the downstream evolution of multi-regime characteristics. The GFRI approach allows local reaction zones to be detected and characterized as premixed, dominantly premixed, multi-regime, dominantly non-premixed, or non-premixed flame structures, based on flame markers (mixture fraction, chemical mode, and heat release rate) derived from the experimental data. The statistics of chemical mode zero-crossings, which mark premixed reaction zones, and the relative populations of flame structures are shown to be sensitive to the state of mixing in the near field of the flame and to the level of local extinction farther downstream. Multi-regime structures, where premixed and non-premixed reaction zones occur in close proximity and both contribute to overall heat release, account for nearly half the total population at streamwise locations within the first several jet diameters. There is a rapid transition within the near field whereby the relative population of non-premixed and dominantly non-premixed structures grows from 0.05 to nearly 0.5, and the population of premixed and dominantly premixed structures decreases correspondingly as fluid entering the reaction zone becomes progressively fuel-rich. Local extinction and re-ignition bring a resurgence in premixed-type structures, many of which occur at fuel-lean conditions. There are also modest populations of multi-regime structures, having chemical mode zero-crossings at lean conditions, which would not exist in a fully burning jet flame.     

Improved MMC-LES to compute the structure of a mixed-mode turbulent flame series

An improved version of the Lagrangian multiple mapping conditioning model coupled with large eddy simulation (MMC-LES) is applied to compute the structure of a range of turbulent mixed-mode flames stabilised on the Sydney piloted burner with compositionally inhomogeneous inlet. The calculations are compared with detailed measurements. While premixed MMC-LES models are yet to be developed, the most commonly deployed version and code for MMC-LES uses a mixture-fraction-based approach and a sparse-Lagrangian notional particle method that is most suitable for non-premixed combustion. The improvements reported here are due to (i) a more rigorous density coupling approach, (ii) a more refined mixing time scale, and (iii) selective particle intensification to improve localness in physical space as well as mixture fraction space. This intensification is selectively applied in upstream regions where mixed-mode combustion dominates and is relaxed further downstream as the jet flames transition to a non-premixed flame structure. The computed results show good agreement with experimental data hence confirming the feasibility of the improved MMC-LES approach in being able to account for mixed-mode combustion as well as for finite-rate chemistry effects. These promising results warrant future extension of the selective particle intensification method to become automatically adaptive.     

Modelling of turbulent lifted jet flames using flamelets: a priori assessment and a posteriori validation

This study focuses on the modelling of turbulent lifted jet flames using flamelets and a presumed Probability Density Function (PDF) approach with interest in both flame lift-off height and flame brush structure. First, flamelet models used to capture contributions from premixed and non-premixed modes of the partially premixed combustion in the lifted jet flame are assessed using a Direct Numerical Simulation (DNS) data for a turbulent lifted hydrogen jet flame. The joint PDFs of mixture fraction Z and progress variable c, including their statistical correlation, are obtained using a copula method, which is also validated using the DNS data. The statistically independent PDFs are found to be generally inadequate to represent the joint PDFs from the DNS data. The effects of Z–c correlation and the contribution from the non-premixed combustion mode on the flame lift-off height are studied systematically by including one effect at a time in the simulations used for a posteriori validation. A simple model including the effects of chemical kinetics and scalar dissipation rate is suggested and used for non-premixed combustion contributions. The results clearly show that both Z–c correlation and non-premixed combustion effects are required in the premixed flamelets approach to get good agreement with the measured flame lift-off heights as a function of jet velocity. The flame brush structure reported in earlier experimental studies is also captured reasonably well for various axial positions. It seems that flame stabilisation is influenced by both premixed and non-premixed combustion modes, and their mutual influences.     

Turbulence/flame/wall interactions in non-premixed inclined slot-jet flames impinging at a wall using direct numerical simulation

In the present work, three-dimensional turbulent non-premixed oblique slot-jet flames impinging at a wall were investigated using direct numerical simulation (DNS). Two cases are considered with the Damköhler number (Da) of case A being twice that of case B. A 17 species and 73-step mechanism for methane combustion was employed in the simulations. It was found that flame extinction in case B is more prominent compared to case A. Reignition in the lower branch of combustion for case A occurs when the scalar dissipation rate relaxes, while no reignition occurs in the lower branch for case B due to excessive scalar dissipation rate. A method was proposed to identify the flame quenching edges of turbulent non-premixed flames in wall-bounded flows based on the intersections of mixture fraction and OH mass fraction iso-surfaces. The flame/wall interactions were examined in terms of the quenching distance and the wall heat flux along the quenching edges. There is essentially no flame/wall interaction in case B due to the extinction caused by excessive turbulent mixing. In contrast, significant interactions between flames and the wall are observed in case A. The quenching distance is found to be negatively correlated with wall heat flux as previously reported in turbulent premixed flames. The influence of chemical reactions and wall on flow topologies was identified. The FS/U and FC/U topologies are found near flame edges, and the NNN/U topology appears when reignition occurs. The vortex-dominant topologies, FC/U and FS/S, play an increasingly important role as the jet turbulence develops.     

Modeling curvature effects in turbulent autoigniting non-premixed flames using tabulated chemistry

Turbulent flames are intrinsically curved. In the presence of preferential diffusion, curvature effects either enhance or suppress molecular diffusion, depending on the diffusivity of the species and the direction of the flame curvature. When a tabulated chemistry type of modeling is employed, curvature-preferential diffusion interactions have to be taken into consideration in the construction of manifolds. In this study, we employ multistage stage flamelet generated manifolds (MuSt-FGM) method to model autoigniting non-premixed turbulent flames with preferential diffusion effects included. The conditions for the modeled flame are in MILD combustion regime. To model the above-mentioned curvature-preferential diffusion interactions, a new mixture fraction which has a non-unity Lewis number is defined and used as a new control variable in the manifold generation. 1D curved flames are simulated to create the necessary flamelets. The resulting MuSt-FGM tables are used in the simulation of 1D laminar flames, and then also applied to turbulent flames using 2D direct numerical simulations (DNS). It was observed that when the curvature effects are included in the manifold, the MuSt-FGM results agree well with the detailed chemistry results; whereas the results become unsatisfactory when the curvature effects are ignored.     

On the combined effects of compositional inhomogeneity and ammonia addition to turbulent flames of ethylene

This paper is part of a broader program aimed at investigating the effects of co-firing clean fuels such as ammonia or hydrogen with hydrocarbons. The focus is on soot formation as well as flame stability in turbulent mixed-mode combustion, which is highly relevant in practical combustors. Ammonia substitution for nitrogen results in reduced flame stability, and this is correlated to differences in flame speed and extinction strain rate. While it is known that the addition of ammonia suppresses soot, visual inspection of compositionally inhomogeneous flames of ethylene-ammonia indicates a reduction in ammonia's ability to suppress soot formation. Measurements of soot volume fraction and laser-induced fluorescence in selected UV and visible bands are made along the centreline in selected flames to test this hypothesis. Experimental results are then compared to simulations in laminar diffusion flames, stratified counterflow flames, and partially premixed flames. All results confirm the soot-inhibiting ability of ammonia. Increasing inhomogeneity, leading to higher centreline mixture fractions, enhances soot formation, and the level of enhancement is greater for flames with ammonia than without. Moreover, it is found that partial premixing is ultimately responsible for determining the amount of soot formed as opposed to stratification of fuel mixtures near the pilot.     

Thermal and chemical effects of differential diffusion in turbulent non-premixed H2 flames

As a renewable fuel, hydrogen (H₂) may play an increasingly important role in the development and control of piston and gas turbine engines to achieve zero carbon emissions. Predictive modeling of H₂-fueled combustion processes requires a clear understanding of differential diffusion (DD) due to the high diffusivity of H₂. On the assumption that turbulent mixing is a far more dominant process than molecular mixing, DD effects are typically neglected in turbulent combustion simulations to reduce modeling complications. While this assumption is reasonable for hydrocarbon fuels, it is less valid for H₂ combustion, where DD is significant. In this work, two three-dimensional direct numerical simulations of temporally evolving turbulent H₂ jet flames with and without considering DD are performed and compared with laminar flamelet solutions to assess DD effects under turbulent conditions. The emphasis is placed on assessing the suitability of classical mixture fraction Z and Bilger mixture fraction Z_Bilger as conditioning variables for non-premixed turbulent combustion modeling through analyzing DD effects on flame structure, chemical reactions, and tangential diffusion (TD). Furthermore, the persistence of DD effects under turbulent conditions and the suitability of a conventional DD parameter are investigated by comparing the turbulent flames to laminar flamelet solutions. It is found that conditioning the thermochemical state on Z_Bilger helps to capture DD effects and mitigate the relative contribution of TD, which gives Z_Bilger advantages over Z when employing flamelet modeling. Due to close coupling between DD and local chemical reactions, DD can affect the turbulent/laminar flames in the form of thermal effects due to the change in flame temperature, chemical effects due to the change in chemical reactions, and transport effects due to multiple species with varying diffusivities that could result in the difference between Z and Z_Bilger. While the transport effects are suppressed, significant chemical and thermal effects of DD still persist under turbulent conditions, which indicates that the DD parameter is probably unsuitable for comprehensively characterizing and assessing DD effects on the structure of turbulent non-premixed flames.     

Laser-induced plasma in methane and dimethyl ether for flame ignition and combustion diagnostics

In this paper we report the investigation of the laser-induced breakdown and ignition behaviour of methane/air and dimethyl ether (DME)/air mixtures. Moreover, the optical emission from the induced plasma is utilized for determining the mixture composition quantitatively by means of laser-induced breakdown spectroscopy (LIBS). To the best of the authors’ knowledge, LIBS and laser ignition of DME have not been reported in literature before. The technique under investigation is finally employed for combustion diagnostics in laminar as well as turbulent flames. In the laminar premixed and non-premixed flames the LIBS spectra allow spatially resolved measurements of the equivalence ratio and enable studying the mixing of gases provided through the burner with the surrounding room air. In addition, the breakdown threshold of the applied laser pulse energy yields an estimate for the local temperature. In the turbulent cases single-shot LIBS spectra are recorded at fixed position allowing the derivation of local statistical fluctuations of the equivalence ratio in partially premixed jet flames. The results show that laser-induced breakdowns have a strong potential for flame diagnostics and, under suitable conditions, for the ignition of combustible mixtures.     

Response of non-premixed flames to bulk flow perturbations

This paper describes the dynamics of non-premixed flames responding to bulk velocity fluctuations, and compares the dynamics of the flame sheet position and spatially integrated heat release to that of a premixed flame. The space–time dynamics of the non-premixed flame sheet in the fast chemistry limit is described by the stoichiometric mixture fraction surface, extracted from the solution of the

-equation. This procedure has some analogies to premixed flames, where the premixed flame sheet location is extracted from the G = 0 surface of the solution of the G-equation. A key difference between the premixed and non-premixed flame dynamics, however, is the fact that the non-premixed flame sheet dynamics are a function of the disturbance field everywhere, and not just at the reaction sheet, as in the premixed flame problem. A second key difference is that the non-premixed flame does not propagate and so flame wrinkles are convected downstream at the axial flow velocity, while wrinkles in premixed flames convect downstream at a vector sum of the flame speed and axial velocity. With the exception of the flame wrinkle propagation speed, however, we show that that the solutions for the space–time dynamics of the premixed and non-premixed reaction sheets in high velocity axial flows are quite similar. In contrast, there are important differences in their spatially integrated unsteady heat release dynamics. Premixed flame heat release fluctuations are dominated by area fluctuations, while non-premixed flames are dominated by mass burning rate fluctuations. At low Strouhal numbers, the resultant sensitivity of both flames to flow disturbances is the same, but the non-premixed flame response rolls off slower with frequency. Hence, this analysis suggests that non-premixed flames are more sensitive to flow perturbations than premixed flames at O(1) Strouhal numbers.     

A three mixture fraction flamelet model for multi-stream laminar pulverized coal combustion

A three mixture fraction flamelet model is proposed for multi-stream laminar pulverized coal combustion. The technique of coordinate transformation is utilized to map the flamelet solutions from a unit pyramid space into a unit cubic space to improve the stability of the simulation. The validity of the three mixture fraction flamelet model was assessed on different configurations, including a laminar counterflow pulverized coal/methane flame and a laminar piloted pulverized coal jet flame. The flamelet predictions were compared to the reference results of the detailed chemistry solutions. For the counterflow flame, it was found that the flame temperature and major species mass fractions are correctly predicted by the three mixture fraction flamelet model. However, discrepancies are observed for combustion-mode-sensitive species such as CO and H₂ in the premixed combustion region. The thermo-chemical quantities in the char surface reaction zone cannot be correctly predicted if the mixing between the char off-gas stream and other streams is neglected. For the piloted jet flame, it was shown that the stable thermo-chemical variables can be correctly predicted at the upper and middle stream locations. However, at the downstream location, discrepancies can be observed in certain regions. Overall, the validity of the three mixture fraction flamelet model for multi-stream pulverized coal combustion is confirmed and its performance in turbulent pulverized coal combustion will be tested in future work.     

Tabulated chemistry approaches for laminar flames: Evaluation of flame-prolongation of ILDM and flamelet methods

The present study considers the performance of tabulation methods for numerical simulation of complex chemical kinetics in laminar combusting flows and compares their predictions to results obtained by direct calculation. Two tabulation methods are considered: the Flame Prolongation of Intrinsic low-dimensional manifold (FPI) method and Steady Laminar Flamelet Model (SLFM). The FPI method is of current interest as it is a potentially unifying approach capable of dealing with both premixed and non-premixed flames for gaseous fuels. SLFM tabulation methods are popular for non-premixed flames and form a good basis for comparing the performance of the FPI approach. The performance of each method is also evaluated by comparing the results to the direct simulation of the laminar flames using two chemical kinetic schemes: simplified chemistry involving five species and one reaction and detailed chemistry involving 53 species and 325 reaction steps. As part of the evaluation process, the computational cost of each method is also assessed. The laminar flames considered in this study include: freely propagating laminar premixed flames, a two-dimensional axisymmetric methane–air opposed-jet diffusion flame, and a two-dimensional axisymmetric methane–air co-flow diffusion flame. Both tabulation methods are implemented in a parallel adaptive mesh refinement (AMR) framework for solving the complete set of governing partial differential equations. These equations are solved using a fully-coupled finite-volume formulation on body-fitted multi-block quadrilateral mesh. Significant improvements in terms of reduced computational requirements, as measured by both storage and processing time, are demonstrated for the tabulated methods.     

Direct numerical simulations of rich premixed turbulent n-dodecane/air flames at diesel engine conditions

Rich premixed turbulent n-dodecane/air flames at diesel engine conditions are analyzed using direct numerical simulations. The conditions correspond to a parametric variation of the Engine Combustion Network Spray A (pressure 60 atm; oxidizer oxygen level and temperature 21% and 900 K, respectively; fuel temperature 363 K). Three simulations with equivalence ratios of 3, 5, and 7 are performed with a Karlovitz number (Ka, based on flame time) of order 100 to match the estimated Ka of the rich premixed combustion region in Spray A. At these conditions, the reference laminar flames exhibit a complex structure which involves both low-temperature chemistry (LTC) and high-temperature chemistry over a wide range of length scales. In the presence of turbulence, the flame structure is strongly affected in physical space and the reaction zone exhibits a very complex structure in which broken, distributed, and thin regions co-exist, especially for the leanest case. However, the contribution of the LTC pathway is only weakly affected by turbulence. In progress variable space, the mean flame structure, including the chemical source terms, is found to match remarkably well that of the corresponding unity Lewis number laminar flame, particularly for the $?=$ 3 and 5 cases. This behavior is attributed to the strong turbulent mixing occurring throughout the flames/reaction zones, which suppresses differential diffusion effects. Nevertheless, large conditional fluctuations around the mean chemical source terms are identified. These are found to correlate very well with radical species mass fractions such as OH. In addition, a similar functional dependence is obtained from counterflow laminar flames. As such, it appears from these results that laminar flame models have a potential to be used to represent the thermochemical state of rich premixed turbulent flames under diesel engine conditions.     

Assessing multi-regime combustion in a novel burner configuration with large eddy simulations using tabulated chemistry

Recent investigations on a novel multi-regime burner (MRB) configuration showed significant deviations in the CO flame structure compared to the limiting cases of premixed and non-premixed flames. However, a prior analysis revealed that major species and temperature are captured by both limiting cases (Butz et al., Combust. Flame, 2019 [1]). In the present work, large eddy simulations using an artificial thickened flame approach and tabulated chemistry are performed for the MRB configuration. Simulation results are compared to experimental Raman/Rayleigh/CO-LIF and PIV measurements, confirming the applicability of the modeling approach. Further, simulation results are consistent with the aforementioned prior analysis. Special attention is paid to predicting CO by analyzing the conditional flame structure and the effects of local residence time. This combined CO and residence time analysis reveals that local convective and diffusive transport processes should be resolved simultaneously with the unsteady flow, instead of being tabulated. Substantial improvements in CO are achieved when local transport is considered.     

An experimental study of partially premixed flame sound

The occurrence of oscillating combustion and combustion instability has led to resurgence of interest in the causes, mechanisms, suppression, and control of combustion noise. Noise generated by enclosed flames is of greater practical interest but is more complicated than that by open flames, which itself is not clearly understood. Studies have shown that different modes of combustion, premixed and non-premixed, differ in their sound generation characteristics. However, there is lack of understanding of the region bridging these two combustion modes. This study investigates sound generation by partially premixed flames. Starting from a non-premixed flame, air was gradually added to achieve partial premixing while maintaining the fuel flow rate constant. Methane, ethylene, and ethane partially premixed flames were studied with hydrogen added for flame stabilization. The sound pressure generated by methane partially premixed flames scales with M⁵ compared to M³ for turbulent non-premixed methane flames. Also, the sound pressure generated by partially premixed flames of ethane and ethylene scales as M^4.5. With progressive partial premixing, spectra level increases at all frequencies with a greater increase in the high-frequency region compared to the low-frequency region; flames develop a peak and later a constant level plateau in the low frequency region. The partially premixed flames of methane, ethylene, and ethane generate a similar SPL as a function of equivalence ratio when the fuel volume flow rate is matched. However, when fuel mass flow rate is matched, the ethane and ethylene flames produce a similar SPL, which is lower than that produced by the methane flame.     

A spray flamelet/progress variable approach combined with a transported joint PDF model for turbulent spray flames

A spray flamelet/progress variable approach is developed for use in spray combustion with partly pre-vaporised liquid fuel, where a laminar spray flamelet library accounts for evaporation within the laminar flame structures. For this purpose, the standard spray flamelet formulation for pure evaporating liquid fuel and oxidiser is extended by a chemical reaction progress variable in both the turbulent spray flame model and the laminar spray flame structures, in order to account for the effect of pre-vaporised liquid fuel for instance through use of a pilot flame. This new approach is combined with a transported joint probability density function (PDF) method for the simulation of a turbulent piloted ethanol/air spray flame, and the extension requires the formulation of a joint three-variate PDF depending on the gas phase mixture fraction, the chemical reaction progress variable, and gas enthalpy. The molecular mixing is modelled with the extended interaction-by-exchange-with-the-mean (IEM) model, where source terms account for spray evaporation and heat exchange due to evaporation as well as the chemical reaction rate for the chemical reaction progress variable. This is the first formulation using a spray flamelet model considering both evaporation and partly pre-vaporised liquid fuel within the laminar spray flamelets. Results with this new formulation show good agreement with the experimental data provided by A.R. Masri, Sydney, Australia. The analysis of the Lagrangian statistics of the gas temperature and the OH mass fraction indicates that partially premixed combustion prevails near the nozzle exit of the spray, whereas further downstream, the non-premixed flame is promoted towards the inner rich-side of the spray jet since the pilot flame heats up the premixed inner spray zone. In summary, the simulation with the new formulation considering the reaction progress variable shows good performance, greatly improving the standard formulation, and it provides new insight into the local structure of this complex spray flame.     

Numerical simulation of a mixed-mode reaction front in a PPC engine

The ignition process, mode of combustion and reaction front propagation in a partially premixed combustion (PPC) engine running with a primary reference fuel (87% iso-octane, 13% n-heptane by volume) is studied numerically in a large eddy simulation. Different combustion modes, ignition front propagation, premixed flame and non-premixed flame, are observed simultaneously. Displacement speed of CO iso-surface propagation describes the transition of premixed auto-ignition to non-premixed flame. High temporal resolution optical data of CH₂O and chemiluminescence are compared with simulated results. A high speed ignition front is seen to expand through fuel-rich mixture and stabilize around stoichiometry in a non-premixed flame while lean premixed combustion occurs in the spray wake at a much slower pace. A good qualitative agreement of the distribution of chemiluminescence and CH₂O formation and destruction shows that the simulation approach sufficiently captures the driving physics of mixed-mode combustion in PPC engines. The study shows that the transition from auto-ignition to flame occurs over a period of several crank angles and the reaction front propagation can be captured using the described model.     

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.     

Simulations of laminar non-premixed flames of kerosene with hot combustion products as oxidiser

The effects of hot combustion product dilution in a pressurised kerosene-burning system at gas turbine conditions were investigated with laminar counterflow flame simulations. Hot combustion products from a lean (φ = 0.6) premixed flame were used as an oxidiser with kerosene surrogate as fuel in a non-premixed counterflow flame at 5, 7, 9 and 11 bar. Kerosene-hot product flames, referred to as ‘MILD’, exhibit a flame structure similar to that of kerosene–air flames, referred to as ‘conventional’, at low strain rates. The Heat Release Rate (HRR) of both conventional and MILD flames reflects the pyrolysis of the primary and intermediate fuels on the rich side of the reaction zone. Positive HRR and OH regions in mixture fraction space are of similar width to conventional kerosene flames, suggesting that MILD flames are thin fronts. MILD flames do not exhibit typical extinction behaviour, but gradually transition to a mixing solution at very high rates of strain (above A = 160, 000 s^?1 for all pressures). This is in agreement with literature that suggests heavily preheated and diluted flames have a monotonic S-shaped curve. Despite these differences in comparison with kerosene–air flames, MILD flames follow typical trends as a function of both strain and pressure. Further still, the peak locations of the overlap of OH and CH₂O mass fractions in comparison with the peak HRR indicate that the pixel-by-pixel product of OH- and CH₂O-PLIF signals is a valid experimental marker for non-premixed kerosene MILD and conventional flames.     

A new modeling approach for mixture fraction statistics based on dissipation elements

The probabilty density function (PDF) of the mixture fraction is of integral importance to a large number of combustion models. Here, a novel modelling approach for the PDF of the mixture fraction is proposed which employs dissipation elements. While being restricted to the commonly used mean and variance of the mixture fraction, this model approach individually considers contributions of the laminar regions as well as the turbulent core and the turbulent/non-turbulent interface region. The later region poses a highly intermittent part of the flow which is of high relevance to the non-premixed combustion of pure hydrocarbon fuels. The model assumptions are justified by means of the gradient trajectory based analysis of high fidelity direct numerical simulation (DNS) datasets of two turbulent inert configurations and a turbulent non-premixed jet flame. The new dissipation element based model is validated against the DNS datasets and a comparison with the beta PDF is presented.