Mean Reaction Rate Research Articles

Close Intimacy between PtIn Clusters and Zeolite Channels for Ultrastability toward Propane Dehydrogenation.

Propane dehydrogenation (PDH) serves as a pivotal intentional technique to produce propylene. The stability of PDH catalysts is generally restricted by the readsorption of propylene which can subsequently undergo side reactions for coke formation. Herein, we demonstrate an ultrastable PDH catalyst by encapsulating PtIn clusters within silicalite-1 which serves as an efficient promoter for olefin desorption. The mean lifetime of PtIn@S-1 (S-1, silicalite-1) was calculated as 37317 h with high propylene selectivity of >97% at 580 °C with a weight hourly space velocity (WHSV) of 4.7 h-1. With an ultrahigh WHSV of 1128 h-1, which pushed the catalyst away from the equilibrium conversion to 13.3%, PtIn@S-1 substantially outperformed other reported PDH catalysts in terms of mean lifetime (32058 h), reaction rates (3.42 molpropylene gcat-1 h-1 and 341.90 molpropylene gPt-1 h-1), and total turnover number (14387.30 kgpropylene gcat-1). The developed catalyst is likely to lead the way to scalable PDH applications.

Particle-resolved numerical simulations of char particle combustion in isotropic turbulence

In the present study, two-dimensional particle-resolved numerical simulations of char particle combustion are performed. A series of cases are considered, with varying turbulence intensities and heterogeneous reaction rates. The impact of turbulence and Stefan flow on char particle combustion is examined. It is shown that the cases with higher turbulence intensity and heterogeneous reaction rate exhibit higher mean gas-phase temperatures and reaction rates. The range of the Stefan flow Reynolds number (ReS) increases as the value of heterogeneous reaction rate increases. Additionally, higher turbulence intensity is associated with an increased range of ReS. The drag force coefficient of burning particles is analyzed. The results show that turbulence induces fluctuations of drag force coefficient, and increasing the turbulent velocity broadens the drag force coefficient fluctuation amplitude. The particle drag force is increased with increasing heterogeneous reaction rate. The pressure and viscous components of the drag force are examined. It is revealed that the increase of heterogeneous reaction rate alters the pressure distribution on the particle surface, resulting in the increase of pressure drag force, while the viscous drag force remains almost unchanged.

Turbulence Effects on the Statistical Behaviour and Modelling of Flame Surface Density and the Terms of Its Transport Equation in Turbulent Premixed Flames

The influence of the ratio of integral length scale to flame thickness on the statistical behaviours of flame surface density (FSD) and its transport has been analysed using a Direct Numerical Simulation database of three-dimensional statistically planar turbulent premixed flames for different turbulence intensities. It has been found that turbulent burning velocity based on volume-integration of reaction rate and flame surface area increase but the peak magnitudes of the FSD and the terms of the FSD transport term decrease with an increase in length scale ratio for a given turbulence intensity. The flame brush thickness and flame wrinkling increase with an increase in length scale ratio for all turbulence intensities. However, the qualitative behaviours of the unclosed terms in the FSD transport equation remain unaltered by the length scale ratio and in all cases the tangential strain rate term and the curvature term act as leading order source and sink, respectively. A decrease in length scale ratio for a given turbulence intensity leads to a decrease in Damköhler number and an increase in Karlovitz number. This has an implication on the alignment of reactive scalar gradient with local strain rate eigenvectors, which in turn increases positive contribution of the tangential strain rate term with a decrease in length scale ratio. Moreover, an increase in Karlovitz number increases the likelihood of negative contribution of the curvature term. Thus, the magnitude of the negative contribution of the FSD curvature term increases with a decrease in length scale ratio for a given turbulence intensity. The model for the tangential strain rate term, which explicitly considers the scalar gradient alignment with local principal strain rate eigenvectors, has been shown to be more successful than the models that do not account for the scalar gradient alignment characteristics. Moreover, the existing model for the curvature and propagation term needed modification to account for greater likelihood of negative values for higher Karlovitz number. However, the models for the unclosed flux of FSD and the mean reaction rate closure are not significantly affected by the length scale ratio.

A Priori Direct Numerical Simulation Assessment of MILD Combustion Modelling in the Context of Reynolds Averaged Navier–Stokes Simulations

A priori Direct Numerical Simulation (DNS) assessment of mean reaction rate closures for reaction progress variable in the context of Reynolds Averaged Navier–Stokes (RANS) simulations has been conducted for MILD combustion of homogeneous (i.e., constant equivalence ratio), methane-air mixtures. The reaction rate predictions according to statistical (e.g., presumed probability density function), phenomenological (e.g., eddy-break up (EBU), eddy dissipation concept (EDC) and the scalar dissipation rate (SDR) based approaches), and flame surface description (e.g., Flame Surface Density) based closures are compared. The performance of the various reaction rate closures has been assessed by comparing the models’ predictions to the corresponding quantities extracted from DNS data. It has been found that the usual presumed probability density function (PDF) approach using the beta-function predicts the PDF of the reaction progress variable in homogenous mixture MILD combustion throughout the flame brush for all cases considered here provided that the scalar variance is accurately predicted. The accurate estimation of scalar variance requires the solution of a modelled transport equation, which depends on the closure of Favre-averaged SDR. A linear relaxation based algebraic closure for the Favre-averaged SDR has been found to capture the behaviour of the Favre-averaged SDR in the current homogenous mixture MILD combustion setup. It has been found that the EBU, SDR and FSD-based mean reaction rate closures do not adequately predict the mean reaction rate of the reaction progress variable for the parameter range considered here. However, a variant of the EDC closure, with model coefficients expressed as functions of micro-scale Damköhler and turbulent Reynolds numbers, has been found to be more successful in predicting the mean reaction rate of reaction progress variable compared to other modelling methodologies for the range of turbulence intensities and dilution levels considered here.

Effects of Mixture Distribution on the Structure and Propagation of Turbulent Stratified Slot-Jet Flames

The influence of mixture stratification on the development of turbulent flames in a slot-jet configuration has been analysed using Direct Numerical Simulation data. Mixture stratification was imposed at the inlet by varying the equivalence ratio between 0.6 and 1.0 with different alignments to the reaction progress variable gradient: aligned gradients (back-supported), opposed gradients (front-supported) and misaligned gradients. An additional premixed case with a global equivalence ratio of 0.8 was simulated for comparison. The flame is shortest for the front-supported case, followed by the premixed flame, with the back-supported and misaligned gradient flames being the tallest and of comparable size. This behaviour has been explained in terms of the variations of the mean equivalence ratio within the flame and the volume-integrated reaction rate in the streamwise direction. The difference in mixture composition for these cases results in significant variations in the burning rate, flame area, flame wrinkling and flame brush thickness in the streamwise direction. The globally front-supported case has the highest volume-integrated burning rate and flame area, while the back-supported case has the lowest. The misaligned scalar gradient case exhibits qualitatively similar behaviour to that of the globally back-supported case. The burning intensity is unity for a major part of the flame length but assumes values greater than unity towards the flame tip where the effects of flame curvature become strong. All cases predominantly exhibit the premixed mode of combustion within the flamelet regime, so flamelet assumption-based reaction rate closures, originally proposed for premixed combustion, were evaluated using a priori analysis. The terms which require improved closures have been identified and existing closures have been improved where necessary. It was found that the global nature of mixture stratification does not influence the performance of the mean reaction rate closures or the parameterisation of marginal probability density functions of scalars in turbulent stratified mixture combustion.

Monte Carlo simulation of ion kinetics in nitrogen and oxygen plasmas under non-uniform electric field conditions

The kinetics of N4+ and O− ions was numerically studied in nitrogen and oxygen plasmas in a highly non-uniform electric field. Mean ion energy and reaction rate coefficients in a background gas at pressures from 1 to 10 Torr were calculated through a Monte Carlo simulation. The ion characteristics followed the local reduced electric field at high pressures, whereas nonhydrodynamic effects leading to a nonlocal dependence of the mean ion energy and rate coefficients on the field were obtained at low pressures. As a result, the rates of N4+ ion dissociation, electron detachment from O− ions, and charge exchange in collisions between O− and O2 lagged the local field value. The non-local effect on the ion rate coefficients was more profound when the field decreased in space. We suggested a simplified method of describing ion rates in spatially varying electric fields on the basis of the Monte Carlo simulation of these rates for uniform electric field conditions and mean ion energy calculations in non-uniform fields. This method is similar to the local-mean-energy approximation utilized for describing electron swarm parameters in varying electric fields. The results of the simplified method were compared with the results of the direct Monte Carlo simulation.

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.

Extensive Discussions of the Eddy Dissipation Concept Constants and Numerical Simulations of the Sandia Flame D

The indisputable wide use of the Eddy Dissipation Concept (EDC) implies that the resulting mean reaction rate is reasonably well modeled. To model turbulent combustions, an amount of EDC constants that differ from the original values was proposed. However, most of them were used without following the nature of the model or considering the effects of the modification. Starting with the energy cascade and the EDC models, the exact original primary and secondary constants are deduced in detail in this work. The mean reaction rate is then formulated from the primary constants or the secondary constants. Based on the physical meaning of fine structures, the limits of the EDC constants are presented and can be used to direct the EDC constant modifications. The effects of the secondary constant on the mean reaction rate are presented and the limiting turbulence Reynolds number used for the validity of EDC is discussed. To show the effects of the constants of the EDC model on the mean reaction rate, 20 combinations of the primary constants are used to simulate a laboratory-scale turbulent jet flame, i.e., Sandia Flame D. After a thorough and careful comparison with experiments, case 8, with a secondary constant of 6 and primary constants of 0.1357 and 0.11, can aptly reproduce this flame, except for in the over-predicted mean OH mass fraction.

Energy integral equation for premixed flame-wall interaction in turbulent boundary layers and its application to turbulent burning velocity and wall flux evaluations

An integral form of the energy conservation equation has been derived from the first principle for low Mach number conditions for statistically steady premixed flame-wall interaction within turbulent boundary layers. The validity of this equation has been demonstrated based on three-dimensional Direct Numerical Simulation data of statistically stationary oblique quenching of a turbulent premixed V-shaped flame in a channel flow configuration as a result of its interaction with an inert isothermal wall. It has been found that the wall heat flux and the integral of chemical heat release in the wall normal direction within the turbulent thermal boundary layer are the major contributors in the energy integral equation, and their difference is accounted for by the advection contribution. The magnitudes of the wall heat flux increase, and integral of heat release rate across the thermal boundary layer decrease with increasing distance from the leading edge of the boundary layer as a result of flame quenching. The integral form of the energy conservation equation has been utilised to demonstrate that the Nusselt number (or Stanton number) for wall heat transfer is intrinsically related to the turbulent burning velocity in the case of flame-wall interaction within turbulent boundary layers. A Flame Surface Density based reaction rate closure, modified to account for the near-wall behaviour, has been utilised to estimate the mean Nusselt number in the case of flame-wall interaction within turbulent boundary layers, which revealed that the modelling limitations of the mean reaction rate closure may give rise to inaccuracies in the estimation of the mean Nusselt number. By contrast, the measurements of mean velocity, temperature, and wall heat flux can be utilised to estimate the turbulent burning velocity within the turbulent boundary layer using the newly derived energy integral equation.

Computations of a Bluff-Body Stabilised Premixed Flames Using ERN Method

Combustible carbon-based energy is still prevailing as the world’s leading energy due to its high energy density. However, the oxidation of these hydrocarbons disturbs the natural carbon cycle greatly by increasing greenhouse gases. As emission legislation becomes more rigorous, lean premixed combustion becomes promising because it can reduce nitrogen oxides (NOx) and Carbon Monoxide (CO) emissions without compromising efficiency. However, utilising lean premixed flames in industrial combustors is not easy because of its thermo-acoustic instabilities associated with pressure fluctuations and the non-linearity in the mean reaction rate. Therefore, reliable predictive combustion models are required to predict emissions with sensible computational costs to use the mode efficiently in designing environmentally friendly combustion systems. Along with the promising methodologies capable of modelling turbulent premixed flames with low computational costs is the ERN-RANS framework. Thus, this study aims to compute a bluff-body stabilised premixed flames close to blow-Off using the ERN-RANS framework. As a result, a satisfactory agreement is reached between the predicted and measured values.

Analysis of EDC constants for predictions of methane MILD combustion

The indisputable wide use of the Eddy Dissipation Concept (EDC) indicates that the mean reaction rate is reasonably modeled for MILD (Moderate or Intense Low-oxygen Dilution) and conventional combustions. However, RANS (Reynolds-Averaged Navier-Stokes) modelling with the standard EDC constants tends to over-predict maximum temperatures when applied to the MILD combustion regime. Therefore, there is a modification need of the EDC constants to predict properly the mean reaction rate, and then the maximum temperatures. The relation of the mean reaction rate and the EDC constants, including the primary and the secondary, is presented. A lab-scale methane MILD combustion furnace (MCF) with non-preheated air from literature is chosen for the validation of the EDC constants. The modification is done with one of the secondary EDC constants ranging from 1 to 28 where the primary constant is kept at CD1=0.1357. Predictions with the secondary EDC constant of 4 agree quite well with the measurements of the MILD combustion in this furnace. The modified EDC constant of 2 are suggested for the predictions of the conventional combustion in this furnace. Finally, based on the excess temperature or the normalized root mean square excess temperature (NRET), a criterion for the attainment of MILD combustion in this furnace is suggested.

A comparison between head-on quenching of stoichiometric methane-air and hydrogen-air premixed flames using Direct Numerical Simulations

Head-on quenching of statistically planar stoichiometric methane-air and hydrogen-air flames has been compared based on a Direct Numerical Simulation (DNS) database. Due the absence of OH at the wall CO cannot be oxidised anymore which leads to the accumulation of carbon monoxide in the near-wall region during flame quenching of stoichiometric methane-air flames. Furthermore, for both fuels, low-temperature reactions at the wall have been found to give rise to accumulation of HO2 and H2O2 during flame quenching. As a result of this, a non-zero heat release rate can be observed at the wall during flame-wall interaction and this effect is particularly strong for the head-on quenching of the stoichiometric hydrogen-air premixed flame. The minimum Peclet number (i.e. normalised flame quenching distance) and the normalised wall heat flux magnitude are found to be smaller in the stoichiometric hydrogen-air flame than in the stoichiometric methane-air premixed flame. Moreover, it has been found that the flame quenching distance tends to decrease under turbulent conditions for the head-on quenching of the stoichiometric hydrogen-air premixed flame but the quenching distances for laminar and turbulent conditions remain comparable for the stoichiometric methane-air premixed flame. The mean reaction rate of reaction progress variable is not properly predicted in the near-wall region by well-known closures for the Flame Surface Density (FSD) or scalar dissipation rate (SDR). For FSD based mean reaction rate closure, it has been observed that recently proposed, simple chemistry DNS based, near-wall corrections perform satisfactorily for both fuels for the detailed chemistry case without adjustment of the model parameters. However, the previously proposed near-wall modification to an algebraic SDR closure based on simple chemistry data performs satisfactorily for the head-on quenching of stoichiometric methane-air premixed flame but it is found to be less effective in the case of the head-on quenching of stoichiometric hydrogen-air premixed flame. Moreover, the prediction of the mean heat release rate for head-on quenching of the stoichiometric hydrogen-air premixed flame cannot be achieved by the mean reaction rate closure of the reaction progress variable based on the mass fraction of a major species because of the important role played by intermediate species in the heat release rate at the wall.

Flame Surface Density based mean reaction rate closure for Reynolds averaged Navier Stokes methodology in turbulent premixed Bunsen flames with non-unity Lewis number

The Flame Surface Density (FSD) based mean reaction rate closure proposed by Prof. K.N.C. Bray and co-workers in the context of Reynolds Averaged Navier-Stokes simulations has been a-priori analysed using a Direct Numerical Simulation (DNS) database of turbulent premixed Bunsen flames with different characteristic Lewis numbers representing the strict flamelet regime (i.e. high Damköhler number and low Karlovitz number combustion). The statistical behaviours of stretch factor, orientation factor and wrinkling length scale have been assessed for non-unity Lewis number conditions to identify their Lewis number dependencies. The assumption of presumed bimodal distribution has been found to be rendered invalid close to the nozzle exit where the unresolved wrinkling remains relatively small even when the flow parameters at the nozzle exit represent high Damköhler number and low Karlovitz number conditions. Although the PDF of reaction progress variable shows some resemblance to a bimodal distribution away from the nozzle exit, the Bray-Moss-Libby expressions which can be derived for infinitely large values of Damköhler number have been found to show considerable deviations from the Reynolds averaged reaction progress variable and reaction progress variable variance extracted from DNS data even though these cases represent the wrinkled/corrugated flamelets regime combustion based on nozzle exit conditions. This suggests that it might be necessary to solve a modelled scalar variance transport equation even in the strict flamelet regime instead of using the algebraic relation for the scalar variance. It has been found that the characteristic Lewis number has a major influence on the orientation factor, wrinkling length scale, and the stretch factor. Furthermore, these parameters are found to be (sometimes strong) functions of the axial distance from the nozzle exit. Known parameterisations for the wrinkling length scale and the stretch factor have been shown to be unable to capture the correct variation across the flame brush based on a-priori analysis of DNS data. The variability of the orientation factor and the inadequacy of existing relations to approximate other quantities such as the stretch factor, wrinkling factor and the Reynolds averaged reaction progress variable have the potential to severely limit the performance of algebraic FSD based mean reaction rate closures in turbulent premixed flames within the flamelet regime.

Scrutinizing proposed extensions to the Eddy Dissipation Concept (EDC) at low turbulence Reynolds numbers and low Damköhler numbers

Recent proposals to modify or extend the Eddy Dissipation Concept are investigated and compared to the standard EDC. The results with respect to the underlying principles of EDC are examined. A total of four different variants of the extended EDC are available, expressing locally determined values for two model coefficients that are constants in the standard EDC. The effects on the fine-structure region mass fraction and the fine structure time scale are demonstrated with resulting effects on the mixing and species mean reaction rate. It is found that the constraints imposed on the locally determined coefficients are more important for the results than the formulated dependencies of turbulence Reynolds number and microscale Damköhler number. Furthermore, some of the versions require a less-than-unity limitation for the fine-structure mass fraction for wide ranges of the Reynolds number. All the modified model versions maintain the EDC cascade model, and their relations to this model are investigated. A finding is that some versions maintain very high viscous effects at high turbulence Reynolds numbers. Comparison with the standard EDC shows that some of the effects motivating the extensions are already present in the standard EDC. Initially, a short cascade for low turbulence Reynolds numbers is derived from the existing EDC cascade model, which was developed for high Reynolds numbers. The resulting changes are small, and the need for a modification still remains.

Species reaction rate modelling based on physics-guided machine learning

Deep neural network (DNN) is applied to mean reaction rate modelling. Two DNN structures, species-dependent (SD) and species-independent (SI), are considered.11Code and data to use the trained deep neural network models in this work are available at https://github.com/minamoto-group/PGDNN_RANS_model_Nakazawa_etal. Due to the explicit inclusion of all species variables in the input layer for SD-DNN, this model may consider relationships of different chemical species. However, the prediction can be performed only for simulations with chemical mechanisms considering the same set of species as the one used in training data. SI-DNN circumvents this constraint, and can be used for any set of species appearing in the combustion. For the efficient learning and better prediction performance, two physics-guided loss functions are proposed and employed, which consider mass conservation of the mixture and elemental species in a specific formulation that yields a larger number of constraint conditions. These DNNs are trained and validated using direct numerical simulation (DNS) data of three different turbulent premixed planar flames, and tested using DNS results of a fourth turbulent premixed planar flame and turbulent premixed V-flame to assess the robustness of the present models for an unknown combustion configuration as well as unknown turbulent combustion conditions.

Assessment of Bray Moss Libby formulation for premixed flame-wall interaction within turbulent boundary layers: Influence of flow configuration

Three-dimensional direct numerical simulations (DNS) of two different flow configurations have been performed for premixed flames interacting with chemically inert isothermal walls at the unburned gas temperature in fully developed turbulent boundary layers. The first configuration is an oblique flame-wall interaction (FWI) of a V-flame in a turbulent channel flow and the second configuration is a head-on quenching planar flame in a turbulent boundary layer. These simulations are representative of stoichiometric methane-air mixture at unity Lewis number under atmospheric conditions. The turbulence in the non-reacting conditions for these simulations is representative of the friction velocity based Reynolds number of Reτ=110. Differences in the statistical behaviours of the mean values of progress variable, temperature, and density during the FWI process have been reported for the two configurations. It is found that the mean flame brush thickens in the near wall region leading to significant departures from the strict Bray Moss Libby (BML) formulation limit during the FWI process and that is reflected in the probability density function (PDF) distributions of c for both flame configurations. The closures from the BML formulation for Reynolds averaged progress variable c¯ and the Favre averaged variance of the progress variable c′′2˜ have also been investigated and it is found that these closures need to be modified to account for the FWI process even when the flame away from the wall represents high Damköhler number premixed turbulent combustion. Furthermore, the statistical behaviours of the quantities required for Flame Surface Density (FSD) based mean reaction rate closure including the flame orientation factor σy, the flamelet length scale Ly and the flame stretch factor I0 have been interrogated from the DNS data for the two flame configurations. The flamelet length scale and the stretch factor extracted from the DNS data are compared with the closures for these quantities proposed in the literature. It is found that σy exhibits significant spatial variation for both cases. The existing closures for Ly and I0 which exhibit the best quantitative agreement with DNS data have been identified. It has been found that the models for Ly and I0 have scopes for further improvement to enable satisfactory predictions of these quantities during the FWI process within turbulent boundary layers.

Statistics of local and global flame speed and structure for highly turbulent H[formula omitted]/air premixed flames

A statistical analysis is conducted for turbulent hydrogen-air premixed flames at a range of Karlovitz numbers up to 1,126 by direct numerical simulations (DNS) with detailed chemistry. The local and global burning velocities are evaluated and the deviation from the laminar flame speed is assessed. It is found that the global turbulent flame speed is largely determined by the integral length scale than the turbulent Karlovitz number, due to the flame surface area enhancement. The turbulent flame speed in all examined cases correlates well with the flame surface area, according to Damköhler’s first hypothesis; even at Karlovitz number well above 1,000, reaction zones stay intact and only the preheat zone is broadened by the strong turbulence level. The statistical analysis with the probability density function (PDF) for the displacement speed shows that the highest probability of the local flame speed coincides with the one-dimensional unstretched flame speed. Despite some deviations, the mean flame structures and reaction rate of hydrogen of the higher Ka cases are found to resemble those of the laminar flame, and this further confirms that the turbulent flame brush topology is mainly determined by the large scale turbulence behavior. The results also suggest that the engineering modeling based on the flamelet concept may be valid for a wider range of Ka conditions.

Heat transfer augmentation by recombination reactions in turbulent reacting boundary layers at elevated pressures

A study of a reacting boundary layer flow with heat transfer at conditions typical for configurations at elevated pressures has been performed using a set of direct numerical simulations. Effects of wall temperatures are investigated, representative for cooled walls of gas turbines and sub-scale rocket engines operating with hydrocarbon as fuels. The results show that exothermic chemical reactions induced by the low-enthalpy in the boundary layer take place predominantly in the logarthimic sub-layer. The majority of the heat release is attributed to the exothermic recombination of OH and CO to produce CO2 and H2O. The recombination reactions result in an increase of the wall heat loads by up to 20% compared to the inert flow. The gas composition experiences strong deviations from the chemical equilibrium conditions. In fact, a quenching of the major species is observed within the viscous sub-layer and the transition region. Analysis of chemical time-scales shows that the location of quenched composition coincides with the region where the Damköhler number decreases below unity. Within the viscous sub-layer, a secondary reaction zone is detected, involving the production of formyl and formaldehyde radicals that provide an additional source of energy release. The analysis of the reaction paths showed that reactions with zero activation energy are responsible for this change in gas composition, which also account for the initial branching of hydrocarbon fuels decomposition according to previous auto-ignition studies. The effect of the secondary recombination reactions is more prominent for the lower wall temperature case. Finally, the role of turbulent fluctuations on the species net chemical production rates is evaluated, showing a strong correlation between species and temperature fluctuations. This leads to a pronounced deviation of the mean reaction rates ω˙(Yk,T)¯ from the reaction rates obtained under the assumption of laminar finite rate.

A hybrid BML-fractal approach for the mean reaction rate modelling of accidental gas explosions in partially confined obstructed geometries

We propose a new approach to model the mean reaction rate of premixed turbulent flames when simulating accidental gas explosions with computational fluid dynamics (CFD). The combination between Bray–Moss–Libby (BML) approach and the fractal concept was evaluated. The fractal concept is used for closing the integral length scale of wrinkling in the BML formulation replacing the utilisation of empirical functions. The proposed expression accounts for the effect of local length scales of turbulence on the flame front via the fractal outer and inner cut-offs, which were taken respectively as the integral length scale of turbulence and the Gibson length scale. The initial laminar phase of flame propagation is described by a laminar combustion model and the onset of the transition from the laminar to turbulent combustion is assumed to take place at a threshold value of the turbulent Reynolds number. The approach is implemented and evaluated within an in-house developed code called STOKES (Shock Towards Kinetic Explosion Simulator) that solves the full set of Navier–Stokes equations. The equations are parameterised according to the porosity distributed resistance (PDR) method in which the porous mesh accounts for the presence of small obstacles that are responsible for turbulence generation during an explosion. Simulations are carried out for vented explosions of both methane–air and propane–air mixtures in partially obstructed chambers. Results are compared with experimental data, FLACS simulations and a typical model for the length of wrinkling which uses an empirical function instead of the fractal approach. Comparisons lead to overall good agreement, indicating that the proposed model can be used in numerical simulations of accidental explosions to support consequence modelling in the framework of risk analysis.

Simulations of turbulent acetone spray flames using the conditional source term estimation (CSE) approach

Turbulent dilute acetone spray flames are simulated in an Eulerian–Lagrangian framework using Conditional Source-term Estimation (CSE) for closure of the mean reaction rate. The objective of this work is to assess the performance of the coupled CSE-spray approach, investigated for the first time for the selected configuration. One non-reacting case and four non-premixed flames, AcF1–AcF3 and AcF5 are chosen. Detailed tabulated chemistry is included. Predictions of mean axial velocity, gas temperature and spray statistics are compared with available experimental data. Good agreement between the predicted gas temperatures and experimental values is found. The peak temperature tends to be overpredicted and shifted radially outwards in the simulations, in particular farther downstream. Same trends are observed in all flames, but the predictions deteriorate with flame AcF5. Possible sources of discrepancy are inaccurate turbulent mixing field, increased level of premixing for flame AcF5, the neglect of spray effect in the chemistry tabulation and a larger experimental uncertainty in the temperatures in the high-temperature regions. The mean droplet velocity profiles are in good agreement with the experiments for the four flames. However, the velocity was underpredicted, in particular near the centreline, for flames AcF1 and AcF2.