Density-weighted Displacement Speed Research Articles

Evolution of Displacement Speed Statistics During Head-On Flame-Wall Interaction within Turbulent Boundary Layers

ABSTRACT The statistical behaviours of the density-weighted displacement speed and its curvature and strain rate dependence during head-on interaction of statistically planar premixed flames have been analysed based on Direct Numerical Simulations. The analysis has been conducted within turbulent boundary layers featuring inert walls, under both isothermal and adiabatic wall boundary conditions. The flame quenches due to heat loss when it reaches close to the wall in the case of isothermal wall boundary condition. By contrast, the flame can propagate all the way to the wall before extinguishing due to the consumption of reactants in the case of adiabatic wall boundary conditions. Thus, the effects of thermal expansion, quantified by dilatation rate, and flame normal acceleration during flame-wall interaction in the case of the isothermal wall are weaker than that in the case of the adiabatic wall case due to flame quenching. This gives rise to significant differences in the curvature and strain rate dependences of the reactive scalar gradient magnitude, which affects the statistical behaviours of the reaction and normal diffusion components of density-weighted displacement speed including their mean values, widths of their probability density functions, and their local strain rate and curvature dependences. It has been found that the interaction of near-wall vortical structures with flame surface increases the range of curvature variation during head-on interaction, which acts to widen the probability density function of the density-weighted displacement speed. This trend is relatively stronger for the isothermal wall boundary condition because of the larger variation of the reaction rate component of the density-weighted displacement speed due to local flame quenching, which also acts to widen the range of the density-weighted displacement speed variation in comparison to that in the case of adiabatic wall boundary conditions. Although the qualitative nature of curvature, strain rate, and stretch rate dependences of the density-weighted displacement speed remain unaffected by the wall boundary condition, the strength of the correlation changes with the progress of head-on interaction. It has been found that the negative correlation between the density-weighted displacement speed and flame curvature weakens with the progress of head-on interaction, which gives rise to a reduction in the strength of the correlation between the density-weighted displacement speed and flame stretch rate. Similarly, the correlation between the tangential strain rate and the density-weighted displacement speed weakens with the progress of head-on interaction. Detailed physical explanations are provided for these behaviours, and their modeling implications are indicated.

Effects of liquid water injection on flame surface topology and propagation characteristics in spray flames: A direct numerical simulation analysis

The effects of water injection on flame surface topology and local flame propagation characteristics have been analyzed for statistically planar turbulent n-heptane spray flames with an overall (i.e., liquid + gaseous) equivalence ratio of unity using carrier-phase direct numerical simulations. Most fuel droplets have been found to evaporate as they approach the flame even though some droplets can survive until the burnt gas side is reached, whereas water droplets do not significantly evaporate ahead of the flame and the evaporation of water droplets starts to take place in the reaction zone and is completed within the burnt gas. However, the gaseous-phase combustion occurs predominantly in fuel–lean mode although the overall equivalence ratio remains equal to unity. The water injection has been found to suppress the fuel droplet-induced flame wrinkling of the progress variable isosurface under the laminar condition, and this effect is particularly strong for small water droplets. However, turbulence-induced flame wrinkling masks these effects, and thus, water injection does not have any significant impact on flame wrinkling for the turbulent cases considered here. The higher rate of evaporation and the associated high latent heat extraction for smaller water droplets induce stronger cooling effects, which weakens the effects of chemical reaction. This is reflected in the decrease in the mean values of density-weighted displacement speed with decreasing water droplet diameter. The weakening of flame wrinkling as a result of injection of small water droplets is explained through the curvature dependence of the density-weighted displacement speed. The combined influence of cooling induced by the latent heat extraction of water droplets and flame surface flattening leads to a decrease in volume-integrated burning rate with decreasing water droplet diameter in the laminar cases, whereas the cooling effects are primarily responsible for the drop in burning rate with decreasing water droplet diameter in the turbulent cases.

On flame speed enhancement in turbulent premixed hydrogen-air flames during local flame-flame interaction

Local flame displacement speed Sd of a turbulent premixed flame is of fundamental and practical interest. For H2-air flames, the interest is further accentuated given the recent drive towards the development of zero-carbon combustors for both power and aircraft engine applications. The present study investigates several three-dimensional Direct Numerical Simulation (3D DNS) cases of premixed H2-air turbulent flames to theoretically model the Sd at negative curvatures, building upon recent works. Two of the four DNS cases presented are simulated at atmospheric pressure and two at elevated pressure. The DNS cases at different turbulence Reynolds numbers (Ret) and Karlovitz numbers (Ka) are generated using detailed chemistry. It has been shown in the previous studies that at atmospheric pressure, the density-weighted flame displacement speed Sd˜ is enhanced significantly over its laminar value (SL) at large negative curvature κ due to flame-flame interactions. The current work justifiably employs an imploding cylindrical laminar flame configuration to represent the local flame surfaces undergoing flame-flame interaction in a 3D turbulent flame. Therefore, to acquire a deep understanding of the interacting flame dynamics at large negative curvatures, one-dimensional (1D) simulations of an inwardly propagating cylindrical H2-air laminar premixed flame, with detailed chemistry at the corresponding atmospheric and elevated pressure conditions are performed. In particular, the 1D simulations emphasized the transient nature of the flame structure during these interactions. Based on the insights from the 1D simulations, we utilize an analytical approach to model the Sd˜ at these regions of extreme negative κ of the 3D DNS. The analytical approach is formulated to include the effect of variable density, convection and the inner reaction zone motion. The joint probability density function (JPDF) of Sd˜ and κ and the corresponding conditional averages obtained from 3D DNS showed clear negative correlation between Sd˜ and κ at all pressures. The obtained model successfully predicts the variation of 〈Sd˜|κ〉 with κ for the regions on the flame surface with large negative curvature (κδL≪−1) at atmospheric as well as at elevated pressure, with good accuracy. This showed that the 1D cylindrical, interacting flame model is a fruitful representation of a local flame-flame interaction that persists in a 3D turbulent flame, and is able to capture the intrinsically transient dynamics of the local flame-flame interaction. The 3D DNS cases further showed that even in the non-interacting state at κ=0, on average Sd˜ can deviate from SL. Sd˜ at κ=0 is a manifestation of the internal flame structure, controlled by turbulence transport in the large Ka regime. Therefore, the correlation of 〈Sd˜〉/SL with the the normalized gradient of the progress variable, 〈|∇c^|c0〉 at κ=0 is explored.

A Numerical Study on Premixed Turbulent Planar Ammonia/Air and Ammonia/Hydrogen/Air Flames: An Analysis on Flame Displacement Speed and Burning Velocity

The economic storage and transportation of ammonia (NH3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {NH}_3$$\\end{document}), and its capability to be thermally decomposed to hydrogen (H2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {H}_2$$\\end{document}) make it a potential carbon-free synthetic fuel for the future. To comprehend the fundamental characteristics of NH3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {NH}_3$$\\end{document} as a primary fuel enriched with H2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {H}_2$$\\end{document} under low turbulent premixed flame conditions, three quasi direct numerical simulations (quasi-DNS) with detailed chemistry and the mixture-averaged transport model are conducted under decaying turbulence herein. The Karlovitz number is fixed to 4.28 for all the test conditions. The blending ratio (α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document}), specifying the hydrogen concentration in the ammonia/hydrogen mixture, varies from 0.0 to 0.6. The results reveal that the mean value of the density-weighted flame displacement speed (Sd∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S_{\ extrm{d}}^{*}$$\\end{document}) is similar to (higher than) the unstrained premixed laminar burning velocity (SL0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S_{\ extrm{L}}^{0}$$\\end{document}) for NH3/\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {NH}_3/$$\\end{document}air flame (NH3/H2/\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {NH}_3/\\hbox {H}_2/$$\\end{document}air flames). Furthermore, the performance of two extrapolation relations for estimating Sd∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S_{\ extrm{d}}^{*}$$\\end{document} as linear and non-linear functions of flame front curvature is discussed thoroughly. The performances of both models are almost similar when evaluating the data near the leading edge of the flame. However, the non-linear one offers more accurate results near the trailing edge of the flame. The results show that the mean flame stretch factor increases with increasing the blending ratio, suggesting that the mean flamelet consumption velocity deviates from SL0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S_{\ extrm{L}}^{0}$$\\end{document} by enriching the mixture with H2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {H}_2$$\\end{document}. The mean value of the local equivalence ratio (ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi$$\\end{document}) for the turbulent NH3/\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {NH}_3/$$\\end{document}air flame is almost equal to its laminar counterpart, while it deviates significantly for NH3/H2/\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {NH}_3/\\hbox {H}_2/$$\\end{document}air flames. In addition, the local equivalence ratio for the flame front with positive curvature values is higher than the negatively curved regions for NH3/H2/\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {NH}_3/\\hbox {H}_2/$$\\end{document}air flames due to H2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {H}_2$$\\end{document} preferential diffusion. Furthermore, the results indicate that hydrogen is consumed faster in positively curved regions compared to the negatively curved zones due to enhanced reaction rates of specific chemical reactions.

A study of flame dynamics and structure in premixed turbulent planar NH3/H2/air flames

Ammonia (NH3) has received considerable attention as a near future carbon-free synthetic fuel due to its economic storage/transportation/distribution, and its potential to be thermally decomposed to hydrogen (H2). To promote the low burning velocity and heat of combustion of ammonia, one viable option is to enrich pure ammonia with hydrogen. In this study, two quasi direct numerical simulations (quasi-DNS) with detailed chemistry and the mixture-averaged transport model are examined to study stoichiometric planar ammonia/hydrogen/air flames under decaying turbulence. The reactants temperature and pressure are set to 298 K and 1 atm, respectively. The initial turbulent Karlovitz number is changed from 4.3 to 16.9, implying that all the test conditions are located within the thin reaction zones combustion regime. The results indicate that the density-weighted flame displacement speed ([Formula: see text]), on average, is higher than the unstrained premixed laminar burning velocity ([Formula: see text]) value for both test cases. This suggests that the flame elements propagate faster than their laminar flame counterpart. With increasing the Karlovitz number, the turbulent burning velocity and the wrinkled flame surface area increase by about 35%. Furthermore, the mean flame stretch factor defined as the ratio of the turbulent to the laminar burning velocity divided by the ratio of the wrinkled to the unwrinkled flame surface area is equal to 1.08. This indicates that the local flamelet velocity value, on average, is higher than the unstrained premixed laminar burning velocity. In addition, the results show that the mean value of the local equivalence ratio for the turbulent conditions is higher than its laminar counterpart due to the preferential diffusion of hydrogen and turbulent mixing. Furthermore, the net production rate of hydrogen is shown to be negatively correlated with the flame front curvature suggesting that the local burning rate is intensified in positively curved regions.

Effects of water droplet injection on turbulent premixed flame propagation: a direct numerical simulation investigation

The influence of water droplet injection on the propagation rate of statistically planar stoichiometric n-heptane-air flames has been analysed based on three-dimensional carrier phase Direct Numerical Simulations for different turbulence intensities and different initially mono-sized droplets. It has been found that most water droplets do not completely evaporate within the flame due to their large latent heat of evaporation for the conditions considered here. Thus, the cooling effect due to the extraction of latent heat during the evaporation of water droplets dominates over the dilution of the concentration of reactants and gives rise to smaller reaction rate of reaction progress variable and thicker flame front than in the corresponding premixed turbulent flame without droplets. These effects (a) strengthen with decreasing droplet size due to higher rate of evaporation for smaller droplets, but (b) weaken with an increase in turbulence intensity. The interaction of water droplets with the flame affects the density-weighted displacement speed through its reaction and molecular diffusion components and the magnitudes of these components remain much greater than the components due to cross-scalar dissipation rate and two-phase coupling. The flame-water droplet interaction for the parameter range considered here acts to reduce the mean density-weighted displacement speed, consumption speed and turbulent flame speed, and this reduction becomes increasingly prominent with decreasing droplet diameter. However, it has been found that the presence of water droplets does not alter the qualitative nature of the strain rate and curvature dependences of both density-weighted displacement speed and consumption speed for the range of parameters considered here, but the correlation strength is altered by the presence of water droplets.

Effects of low-temperature chemical reactions on ignition kernel development and flame propagation in a DME-air mixing layer

The impact of chemical reactions at low-temperature (i.e., low-temperature chemistry, LTC) and LTC-induced cool flames on autoignition and premixed flame propagation has been investigated extensively. However, much less analysis is made to explore the role of LTC in forced ignition of non-premixed fuel/oxidizer systems. The objective of this work is to assess and interpret the effects of LTC on ignition kernel development and subsequent flame transition in a quiescent DME-air mixing layer. A series of two-dimensional simulations are conducted for forced ignition by a hot spot. It is found that under elevated initial temperatures and pressures, a cool flame or a warm flame can be directly ignited depending on the hot spot temperature Tig. When Tig is relatively low, a three-staged ignition process is observed where the cool, warm and hot flames are initiated sequentially. A novel penta-brachial flame structure is identified consisting of a trailing warm flame and a trailing cool flame attached to the hot triple flame. A parametric study is conducted to examine the effects of mixture layer thickness and hot spot size and location on ignition kernel development. It is found that the mixture layer thickness has little influence on the cool flame initiation but it substantially affects the subsequent warm flame or hot flame initiation. It is demonstrated that the mixture fraction range covered by the hot spot has a strong impact on subsequent flame initiation. Moreover, different ignition modes (e.g., ignition failure, only hot flame initiation and only cool flame initiation) can be achieved via changing the hot spot configuration. Furthermore, the analysis of cool flame displacement speed indicates that the cool flame initiated by the hot spot is a self-sustained partially premixed flame. Its density-weighted displacement speed changes linearly with flame stretch. These results provide useful insights into how LTC affects non-premixed ignition.

Inner Flame Front Structures and Burning Velocities of Premixed Turbulent Planar Ammonia/Air and Methane/Air Flames

Ammonia (mathrm {NH_3}) has attracted interest as a future carbon-free synthetic fuel due to its economic storage and transportation. In this study, quasi direct numerical simulations (quasi-DNS) with detailed-chemistry have been performed in 3-D to examine the flame thickness and assess the validity of Damköhler’s first hypothesis for premixed turbulent planar ammonia/air and methane/air flames under different turbulence levels. The Karlovitz number is systematically changed from 4.26 to 12.06 indicating that all the test conditions are located within the thin reaction zones combustion regime. Results indicate that the ensemble average values of the preheat zone thickness deviate slightly from the thin laminar flamelet assumption, while the reaction zone regions remain relatively intact. Following the balance equation of reaction progress variable gradient, normal strain rate and the tangential diffusion component of flame displacement speed variation in the normal direction to the flame surface are found to be responsible for thickening the flame. However, the sum of reaction and normal diffusion components of flame displacement speed variation in the normal direction to the flame surface is in charge of flame thinning for ammonia/air and methane/air flames. In addition, the validity of Damköhler’s first hypothesis is confirmed by indicating that the ratio of the turbulent burning velocity to the unstrained premixed laminar burning velocity is relatively equal to the ratio of the wrinkled to the unwrinkled flame surface area. Furthermore, the probability density functions of the density-weighted flame displacement speed show that the bulk of flame elements propagate identical to the unstrained premixed laminar flame.

Local flame displacement speeds of hydrogen-air premixed flames in moderate to intense turbulence

Comprehensive knowledge of local flame displacement speed, Sd, in turbulent premixed flames is crucial towards the design and development of hydrogen fuelled next-generation engines. Premixed hydrogen-air flames are characterized by significantly higher laminar flame speed compared to other conventional fuels. Furthermore, in the presence of turbulence, Sd is enhanced much beyond its corresponding unstretched, planar laminar value SL. In this study, the effect of high Karlovitz number (Ka) turbulence on density-weighted flame displacement speed, Sd˜, in a H2-air flame is investigated. Recently, it has been identified that flame-flame interactions in regions of large negative curvature govern large deviations of Sd˜ from SL, for moderately turbulent flames. An interaction model for the same has also been proposed. In this work, we seek to test the interaction model’s applicability to intensely turbulent flames characterized by large Ka. To that end, we investigate the local flame structures: thermal, chemical structure, the effect of curvature, along the direction that is normal to the chosen isothermal surfaces. Furthermore, relative contributions of the transport and chemistry terms to Sd˜ are also analyzed. It is found that, unlike the moderately turbulent premixed flames, where enhanced Sd˜ is driven by interactions among complete flame structures, Sd˜ enhancement in high Ret and high Ka flame is predominantly governed by local interactions of the isotherms. It is found that enhancement in Sd˜ in regions of large negative curvature occurs as a result of these interactions, evincing that the interaction model is useful for high Ka turbulent premixed flames as well.

Assessment of Extrapolation Relations of Displacement Speed for Detailed Chemistry Direct Numerical Simulation Database of Statistically Planar Turbulent Premixed Flames

A three-dimensional Direct Numerical Simulation (DNS) database of statistically planar H_{2} - air turbulent premixed flames with an equivalence ratio of 0.7 spanning a large range of Karlovitz number has been utilised to assess the performances of the extrapolation relations, which approximate the stretch rate and curvature dependences of density-weighted displacement speed S_{d}^{*}. It has been found that the correlation between S_{d}^{*} and curvature remains negative and a significantly non-linear interrelation between S_{d}^{*} and stretch rate has been observed for all cases considered here. Thus, an extrapolation relation, which assumes a linear stretch rate dependence of density-weighted displacement speed has been found to be inadequate. However, an alternative extrapolation relation, which assumes a linear curvature dependence of S_{d}^{*} but allows for a non-linear stretch rate dependence of S_{d}^{*}, has been found to be more successful in capturing local behaviour of the density-weighted displacement speed. The extrapolation relations, which express S_{d}^{*} as non-linear functions of either curvature or stretch rate, have been found to capture qualitatively the non-linear curvature and stretch rate dependences of S_{d}^{*} more satisfactorily than the linear extrapolation relations. However, the improvement comes at the cost of additional tuning parameter. The Markstein lengths LM for all the extrapolation relations show dependence on the choice of reaction progress variable definition and for some extrapolation relations LM also varies with the value of reaction progress variable. The predictions of an extrapolation relation which involve solving a non-linear equation in terms of stretch rate have been found to be sensitive to the initial guess value, whereas a high order polynomial-based extrapolation relation may lead to overshoots and undershoots. Thus, a recently proposed extrapolation relation based on the analysis of simple chemistry DNS data, which explicitly accounts for the non-linear curvature dependence of the combined reaction and normal diffusion components of S_{d}^{*}, has been shown to exhibit promising predictions of S_{d}^{*} for all cases considered here.

Effects of Mean Inflow Velocity and Droplet Diameter on the Propagation of Turbulent V-Shaped Flames in Droplet-Laden Mixtures

Three-dimensional carrier phase Direct Numerical Simulations of V-shaped n-heptane spray flames have been performed for different initially mono-sized droplet diameters to investigate the influence of mean flow velocity on the burning rate and flame structure at different axial locations from the flame holder. The fuel is supplied as liquid droplets through the inlet and an overall (i.e., liquid + gaseous) equivalence ratio of unity is retained in the unburned gas. Additionally, turbulent premixed stoichiometric V-shaped n-heptane flames under the same turbulent flow conditions have been simulated to distinguish the differences in combustion behaviour of the pure gaseous phase premixed combustion in comparison to the corresponding behaviour in the presence of liquid n-heptane droplets. It has been found that reacting gaseous mixture burns predominantly under fuel-lean mode and the availability of having fuel-lean mixture increases with increasing mean flow velocity. The extent of flame wrinkling for droplet cases has been found to be greater than the corresponding gaseous premixed flames due to flame-droplet-interaction, which is manifested by dimples on the flame surface, and this trend strengthens with increasing droplet diameter. As the residence time of the droplets within the flame decreases with increasing mean inflow velocity, the droplets can survive for larger axial distances before the completion of their evaporation for the cases with higher mean inflow velocity and this leads to greater extents of flame-droplet interaction and droplet-induced flame wrinkling. Mean inflow velocity, droplet diameter and the axial distance affect the flame brush thickness. The flame brush thickens with increasing droplet diameter for the cases with higher mean inflow velocity due to the predominance of fuel-lean gaseous mixture within the flame. However, an opposite behaviour has been observed for the cases with lower mean inflow velocity where the smaller extent of flame wrinkling due to smaller values of integral length scale to flame thickness ratio arising from higher likelihood of fuel-lean combustion for larger droplets dominates over the thickening of the flame front. It has been found that the major part of the heat release arises due to premixed mode of combustion for all cases but the contribution of non-premixed mode of combustion to the total heat release has been found to increase with increasing mean inflow velocity and droplet diameter. The increase in the mean inflow velocity yields an increase in the mean values of consumption and density-weighted displacement speed for the droplet cases but leads to a decrease in turbulent burning velocity. By contrast, an increase in droplet diameter gives rise to decreases in turbulent burning velocity, and the mean values of consumption and density-weighted displacement speeds. Detailed physical explanations have been provided to explain the observed mean inflow velocity and droplet diameter dependences of the flame propagation behaviour.

A direct numerical simulation of Jet A flame kernel quenching

Abstract The safe operation of aeronautical engines requires an understanding of flame ignition, propagation and extinction. In this study, direct numerical simulations are performed using a 29 species reduced chemical mechanism for jet fuel surrogate Jet A to understand the flame quenching process. Initially laminar spherical flames of varying sizes and equivalence ratios are subject to an identical periodic domain of decaying and isotropic high intensity turbulence with a turbulent Reynolds number of 2400. All cases become quenched, except for the larger kernel with lower Karlovitz number. An analysis of the flame structure shows broadened preheat zone, flame shortening on the product side, differential species diffusion and partial fuel pyrolysis in the fresh mixture. Two extinction mechanisms are identified arising from flame shortening and high flame stretch. Flame shortening occurs due to turbulence-chemistry interactions that resemble the flame–flame interaction in a laminar counterflow reactant-to-reactant configuration, which contorts and breaks up the ignition kernel. Flame stretch is a local effect that attenuates the heat release rate and causes the flame to retreat towards the product mixtures, similar to what has been observed for reactant-to-product laminar counterflow flames. Chemical explosive mode analysis was also performed to quantify the flame structure and local combustion mode. The diffusion–reaction balance in pinched-off flame islands favors extinction of these smaller structures, while auto-ignition modes are observed within the flame kernel after fresh mixture is engulfed and preheated in the product kernel. Statistics of the density-weighted displacement speed conditional on local combustion mode indicates strong correlation between the local extinction mode and negative displacement speed. The local balance between diffusion and reaction ultimately determines the propensity for local extinction in both laminar and turbulent flames, the extent of which has an impact on global flame propagation.

Displacement speed statistics in an open turbulent jet spray flame

In this study, a three-dimensional Direct Numerical Simulation of an open turbulent jet spray flame has been used to investigate the statistical behaviour of displacement speed Sd and its components to provide physical explanations for the observed behaviours at different axial locations downstream of the jet exit. The open turbulent jet spray flame exhibits fuel-lean conditions close to the jet exit but fuel-rich conditions have been observed further downstream due to the evaporation of fuel droplets. For the axial locations considered, combustion takes place under low Damköhler number conditions. The displacement speed of reaction progress variable isosurfaces shows qualitatively similar behaviour for all axial locations considered – predominantly positive across the major part of the flame but with small, potentially negative, values towards the burned-gas-side. The components of displacement speed arising from chemical reaction rate and flame normal molecular diffusion remain leading order contributors and the competition between these determines the mean behaviour of displacement speed. These observations are consistent with studies of turbulent spray flames in canonical configurations and low Damköhler number turbulent premixed and stratified flames. This suggests that flow geometry in the absence of mean curvature might not be important in determining the mean behaviour of displacement speed and its components. Therefore, the modelling methodologies employed for turbulent stratified flames can potentially be extended for turbulent spray flames. However, the modelling methodologies, which implicitly assume equality between the surface-weighted values of density-weighted displacement speed and local laminar burning velocity, might be rendered invalid for turbulent spray flames.

Effects of the cold wall boundary on the flame structure and flame speed in premixed turbulent combustion

The near-wall flame structure is analyzed based on the direct numerical simulation (DNS) data of a statistically stationary counterflow-like flame-wall interaction (FWI) configuration. According to the relative orientation between the flame normal and the wall normal, a flame element can be either head-on or entrained. Within the quenching zone of FWI, the flame elements are more likely to be entrained, while the head-on flame elements are more likely to appear beyond the influence zone. The flame in the quenching zone thickens considerably which has implications on the variation of the displacement speed of different progress variable isosurfaces. To characterize the dynamics of the local flame elements, a local mean density-weighted displacement speed across the flame front is introduced and investigated. Moreover, the scalar dissipation rates conditional on non-dimensional temperature and progress variable are found to be considerably different in the quenching zone because of significant differences in the distributions of progress variable and non-dimensional temperature in the near-wall region.

A direct numerical simulation analysis of turbulent V-shaped flames propagating into droplet-laden mixtures

Three-dimensional Direct Numerical Simulations (DNS) data has been used to analyse the gaseous phase combustion behaviour in a V-shaped flame configuration where fuel is supplied in the form of droplets such that an overall (i.e. liquid+gaseous) equivalence ratio of unity is maintained in the unburned gas. The analysis has been carried out for different initially mono-sized droplet diameters. A gaseous premixed V-shaped flame with the same flow conditions has been utilised to compare the flame propagation in V-shaped spray flames with a corresponding gaseous premixed flame case. It has been found that combustion in the gaseous phase mainly takes place under fuel-lean mode and the probability of finding fuel-lean burning increases with increasing droplet diameter. However, the mean equivalence ratio of the predominantly fuel-lean mixture increases with increasing axial distance from the flame holder. The presence of droplets has been found to give rise to dimples on the reaction progress variable isosurfaces, and the effects of droplet–induced flame wrinkling are reflected by the widening of the curvature probability density functions for large droplets. The heat release has been found to arise mainly from the premixed mode of combustion. Detailed analysis of reaction progress variable transport has been used to explain the mean variations of consumption speed and density-weighted displacement speed with the axial distance from the flame holder. The mean values of consumption speed, density-weighted displacement speed and turbulent burning velocity have been found to decrease with increasing droplet diameter. The flame speed statistics have been utilised to explain that the enhancement of the burning rate cannot be equated to the enhancement of the flame surface area in turbulent droplet-laden V-shaped flames.

Applicability of extrapolation relations for curvature and stretch rate dependences of displacement speed for statistically planar turbulent premixed flames

A three-dimensional Direct Numerical Simulation (DNS) database of statistically planar turbulent premixed flames covering the wrinkled/corrugated flamelets and the thin reaction zones regimes of premixed turbulent combustion has been utilised to assess the performances of the extrapolation relations, which approximate the stretch rate and curvature dependences of density-weighted displacement speed . It has been found that remains negatively correlated with curvature and exhibits a significantly non-linear relation with stretch rate for all cases considered here. As a result of these behaviours, an extrapolation relation, which assumes a linear stretch rate dependence of density-weighted displacement speed has been found to be inadequate. However, an alternative extrapolation relation which assumes a linear curvature dependence of has been found to be more successful in capturing local behaviour of the density-weighted displacement speed because it allows for a non-linear stretch rate dependence of . The extrapolation relations, which express as non-linear functions of either curvature or stretch rate, have been found to perform better than the linear extrapolation relations. The Markstein length for all the extrapolation relations except for the one, which assumes a linear stretch rate dependence of , has been found to be in good agreement with an analytical expression for . An extrapolation relation which involves solving a non-linear equation in terms of stretch rate has been found to be sensitive to the initial guess and an alternative high-order polynomial-based extrapolation relation gives rise to overshoots and undershoots and thus the goodness of fit of these relations suffers for high turbulence intensities. An alternative extrapolation relation has been proposed in this analysis, which explicitly accounts for the non-linear curvature dependence of the combined reaction and normal diffusion components of and satisfactorily captures the statistical behaviours of for all cases considered here.

Lewis Number Effects on Flame Speed Statistics in Spherical Turbulent Premixed Flames

The influences of characteristic Lewis number hbox{Le} on the statistics of density-weighted displacement speed and consumption speed in spherically expanding turbulent premixed flames have been analysed using three-dimensional direct numerical simulations data for hbox{Le} = 0.8 , 1.0 and 1.2 under statistically similar flow conditions. It has been found that the extents of flame wrinkling and burning increase with decreasing hbox{Le} , which is reflected in increasing trends of mean and most probable values of both density-weighted displacement and consumption speed. Moreover, in all cases the marginal probability density functions of density-weighted displacement speed show finite probabilities of obtaining negative values, whereas consumption speed remains deterministically positive. The strain rate and curvature dependences of scalar gradient and temperature have been found to be strongly dependent on hbox{Le} , and these statistics, along with the interrelation between strain rate and curvature, influence the local strain rate and curvature responses of consumption speed and both reaction and normal diffusion components of density-weighted displacement speed. Density-weighted displacement speed and curvature have been found to be negatively correlated, whereas positive correlations are obtained between density-weighted displacement speed and tangential strain rate for all flames considered here. The positive correlation between temperature and curvature arising from differential diffusion of heat and mass in the hbox{Le} = 0.8 case induces a positive correlation between consumption speed and curvature, whereas these correlations are negative in the hbox{Le} = 1.2 flame. The statistical behaviour of density-weighted displacement speed has been utilised to demonstrate that Damköhler’s first hypothesis does not strictly hold for spherically expanding turbulent premixed flames.

Propagation of Spherically Expanding Turbulent Flames into Fuel Droplet-Mists

The effects of droplet diameter and the overall (liquid+gas) equivalence ratio on flame topology and propagation statistics in spherically expanding turbulent n-heptane spray flames have been analysed based on three-dimensional Direct Numerical Simulations (DNS) data. It has been found that the range of both mean and Gauss curvatures of the flame surface, and the probability of finding saddle topologies increase with increasing droplet diameter and overall equivalence ratio. The presence of droplets affects the displacement speed and consumption speed statistics principally through the reaction rate of the mixture composition in the reaction zone. The magnitudes of the components of density-weighted displacement speed arising from mixture inhomogeneity and droplet evaporation remain small in comparison to the magnitudes of the reaction rate and molecular diffusion rate components. The presence of large droplets decreases the mean density-weighted displacement speed $$ {S}_d^{\ast } $$ and increases the probability of finding negative $$ {S}_d^{\ast } $$ values, except for overall fuel-lean equivalence ratios. The mean consumption speed shows an increasing trend with increasing droplet diameter for fuel-lean overall equivalence ratios, whereas the mean consumption speed decreases with increasing droplet diameter for overall stoichiometric and fuel-rich mixtures. The mean consumption speed remains greater than the mean density-weighted displacement speed for all cases considered here. An alternative flame speed, which represents the growth rate of the flame surface area, has been found to provide an approximate measure of mean consumption flame speed. By contrast, an alternative flame speed, which represents the growth rate of burned gas volume, has been found to approximate the mean density-weighted displacement speed for large droplets in the case of stoichiometric and fuel-rich overall equivalence ratios.

Effects of Reaction Progress Variable Definition on the Flame Surface Density Transport Statistics and Closure for Different Combustion Regimes

ABSTRACTThe implications of the choice of reaction progress variable on the performances of the flame surface density (FSD) based mean reaction rate closure and the well-established sub-models of the FSD transport have been analysed in context of Reynolds Averaged Navier Stokes simulations. For this purpose, a detailed chemistry direct numerical simulation (DNS) database of freely-propagating statistically planar air flames (with an equivalence ratio of 0.7) spanning the corrugated flamelets (CF), thin reaction zones (TRZ) and broken reaction zones (BRZ) regimes of premixed turbulent combustion has been considered. The FSD and the unclosed terms of its transport equation have been analysed for reaction progress variables defined based on normalised and mass fractions and temperature. The performances of the closures for turbulent flux of FSD, and tangential strain rate term have been found to be mostly unaffected by the choice of reaction progress variable. However, the well-established existing models for the unresolved tangential strain rate term have been found not to perform well for the cases representing the CF and TRZ regimes of premixed combustion. The performance of a well-established existing model for the combined propagation and curvature terms has been found to be significantly dependent on the choice of reaction progress variable. Furthermore, the surface-averaged value of the density-weighted displacement speed cannot be approximated by the corresponding unstretched laminar flame value especially for the flames in the BRZ regime. Detailed explanations have been provided for the observed behaviours of the FSD based reaction rate closure and sub-models for the unclosed terms of the FSD transport equation in different combustion regimes for different choices of reaction progress variable.

Constant volume n-Heptane autoignition using One-Dimensional Turbulence

Constant volume premixed lean n-Heptane/air autoignition at high pressure is investigated using the One-Dimensional Turbulence (ODT) model. The configuration consists of a 1D fixed volume domain with a prescribed velocity spectrum and temperature fluctuations superimposed on an initial uniformly elevated scalar field. The sensitivity of the heat release rate and pressure evolution to the initial temperature distribution is studied by imposing different initial temperature fields while holding the mean, RMS and integral length scale of the field constant. Three detailed chemical mechanisms are employed for the prediction of autoignition and heat release rate. To mitigate the high computational cost associated with the calculation of the chemical source terms in the stiff complex mechanisms, an approach based on the Strang-Splitting method is presented. Finally, a study of the ODT model uncertainty is carried out. For validation, ODT results are compared to 2D DNS data from Yoo et al. (2011) for the temporal evolution of heat release rate, pressure and density-weighted displacement speed. Ensemble averaged ODT results show good agreement with the DNS data. ODT results generated from varying the initial temperature fields show that the ignition delay time is highly sensitive to the initial temperature field. The ODT model uncertainty study shows that dispersion due to the stochastic nature of the model is considerably smaller than the dispersion resulting from varying the initial temperature field. Overall, this study demonstrates that ODT accurately captures the evolution of complex chemistry reactive flows in constant volume autoignition simulations and that once validated, ODT is an efficient tool that can be used to carry out parametric studies not feasible by DNS.