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The interrelation between Reynolds stresses and their dissipation rate tensors for different Karlovitz number values was analysed using a direct numerical simulation (DNS) database of turbulent statistically planar premixed H2-air flames with an equivalence ratio of 0.7. It was found that a significant enhancement of Reynolds stresses and dissipation rates takes place as a result of turbulence generation due to thermal expansion for small and moderate Karlovitz number values. However, both Reynolds stresses and dissipation rates decrease monotonically within the flame brush for large Karlovitz number values, as the flame-generated turbulence becomes overridden by the strong isotropic turbulence. Although there are similarities between the anisotropies of Reynolds stress and its dissipation rate tensors within the flame brush, the anisotropy tensors of these quantities are found to be non-linearly related. The predictions of three different models for the dissipation rate tensor were compared to the results computed from DNS data. It was found that the model relying upon isotropy and a linear dependence between the Reynolds stress and its dissipation rates does not correctly capture the turbulence characteristics within the flame brush for small and moderate Karlovitz number values. In contrast, the models that incorporate the dependence of the invariants of the anisotropy tensor of Reynolds stresses were found to capture the components of dissipation rate tensor for all Karlovitz number conditions. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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

The predictions of turbulent burning velocity parameterizations for non-unity Lewis number flames have been assessed based on a single-step chemistry Direct Numerical Simulation (DNS) database of premixed Bunsen flames for different values of characteristic Lewis numbers ranging from 0.34 to 1.2. It has been found that the definition of the turbulent burning velocity is strongly dependent on the choice of projected flame brush area in the Bunsen burner configuration. The highest values of normalized turbulent burning velocity are obtained when the projected flame brush area is evaluated using the area of the isosurface of the Reynolds averaged reaction progress variable of 0.1 out of different options, namely the Favre averaged and Reynolds averaged isosurfaces of reaction progress variable of 0.5 and integral of the gradient of Favre and Reynolds averaged reaction progress variable. Because of the axisymmetric nature of the mean flame brush, the normalized turbulent burning velocity has been found to decrease as the burned gas side is approached, due to an increase in flame brush area with increasing radius. Most models for turbulent burning velocity provide comparable, reasonably accurate predictions for the unity Lewis number case when the projected flame brush area is evaluated using the isosurface of the Reynolds averaged reaction progress variable of 0.1. However, most of these parameterizations underpredict turbulent burning velocity values for Lewis numbers smaller than unity. A scaling relation has been utilized to extend these parameterizations for non-unity Lewis numbers. These revised parameterizations have been shown to be more successful than the original model expressions. These modified expressions also exhibit small values of L2-norm of the relative error with respect to experimental data from literature for different Lewis numbers, higher turbulence intensity and thermodynamic pressure levels. [ABSTRACT FROM AUTHOR]

The early stages of flame evolution following successful localised forced ignition of different CH 4 /CO 2 blends in a slot jet configuration have been analysed using three-dimensional direct numerical simulations. The simulations have been conducted for three different concentration levels of CO 2 in the fuel blend composed of CH 4 and CO 2 (ranging from 0% to 20% by volume). The effects of CO 2 concentration have been analysed based on five different energy deposition scenarios which include situations where the mean mixture composition at the ignitor varies, but not its location in space, whereas other cases represent the scenarios where the mean mixture composition within the energy deposition region remains constant, but its spatial location changes with CO 2 concentration. The most favourable region for successful flame development following thermal runaway, from the mixture composition standpoint (i.e. the highest flammability factor), has been found to be displaced close to the nozzle with an increase in CO 2 concentration. The flame development following thermal runaway exhibits initial growth of hot gas kernel followed by downstream advection and eventual flame propagation along with radial expansion with a possibility of flame stabilisation irrespective of the level of CO 2 concentration. The triple flame propagation has been found to play a key role in the upstream flame propagation and eventual stabilisation. The orientation of the local flame normal plays a key role in the flame stabilisation. The lift off height has been found to increase with increasing CO 2 concentration which also adversely affect flame stabilisation for high levels of CO 2 concentration. [ABSTRACT FROM AUTHOR]

The localized forced ignition and subsequent flame propagation have been analyzed for stoichiometric biogas-air mixtures ( C H 4 / C O 2 / a i r blend) with different spatial distributions (uniform, Gaussian and bimodal) and mean levels of C O 2 dilution (i.e. mole fraction of C O 2 ) for different flow conditions (e.g. quiescent laminar condition and different turbulence intensities) using three-dimensional Direct Numerical Simulations. A two-step chemical mechanism with sufficient accuracy is used to capture the effects of C O 2 dilution on the laminar burning velocity of the b i o g a s − a i r m i x t u r e . A parametric analysis in terms of the mean, standard deviation and integral length scale of the initial Gaussian and bimodal distributions of spatial C O 2 dilution in the unburned gas has been conducted. Qualitatively similar behavior has been observed for all three initial spatial distributions of C O 2 . A departure from uniform conditions was found to increase the range of reaction rate magnitudes of C H 4 , which impacts the burned gas volume and, in turn, increases the variability of the outcomes of the ignition event (successful thermal runaway and subsequent self-sustained propagation or misfire). Turbulence intensity and the mean level of dilution were found to have significant impacts on the outcome of the localized forced ignition, and an increase of either quantity acts to reduce the burned gas volume irrespective of mixture composition due to the enhancement of heat transfer from the hot gas kernel, and the heat sink effects of C O 2 , respectively. An increase of the integral length scale l ψ for the spatial distribution of C O 2 dilution increased the probability of a successful outcome of the ignition event. A uniform initial spatial distribution was found to be optimal, and in the case of a departure from non-uniform conditions, larger variability in the outcome are obtained for a Gaussian initial distribution of C O 2 dilution than a bimodal one. The variance of the C O 2 dilution distribution has been found to have a negligible impact on the outcomes observed, as it was dominated by the effects arising from turbulence intensity, nature of initial C O 2 distribution and integral length scale of C O 2 dilution. [ABSTRACT FROM AUTHOR]

Three-dimensional Direct Numerical Simulations (DNS) data has been utilised to analyse statistical behaviours of the scalar dissipation rate (SDR) and its transport for homogeneous methane-air mixture turbulent Moderate or Intense Low oxygen Dilution (MILD) combustion for different O2 dilution levels and turbulence intensities for different reaction progress variable definitions. Additional DNS has been conducted for turbulent premixed flames and passive scalar mixing for the purpose of comparison with the SDR statistics of the homogeneous mixture MILD combustion with that in conventional premixed combustion and passive scalar mixing. It has been found that the peak mean value of the scalar dissipation rate decreases with decreasing O2 concentration for MILD combustion cases. Moreover, SDR magnitudes increase with increasing turbulence intensity for both MILD and conventional premixed combustion cases. The profiles and mean values of the scalar dissipation rate conditioned upon the reaction progress variable are found to be sensitive to the choice of the reaction progress variable definition. This behaviour arises due to the differences in the distributions of the species mass fractions within the flame. The strain rate contribution and the molecular dissipation term are found to be the leading order contributors in the scalar dissipation rate transport for MILD combustion; whereas, in conventional premixed flames, the terms rising from density variation and reaction rate gradient also play leading roles in addition to the strain rate and molecular dissipation contributions. By contrast, the terms due to density gradient and reaction rate gradient remain negligible in comparison to the leading order contributors in MILD combustion cases due to small density variation because of moderate temperature rise and small reaction rate gradient magnitudes. Furthermore, the qualitative behaviour of the strain rate contribution to the SDR transport in premixed flames is significantly different to that in the case of MILD combustion and passive scalar mixing. The findings of the current analysis indicate that the scalar dissipation rate statistics in MILD combustion show several qualitative similarities to the passive scalar mixing despite major differences with the SDR transport in conventional turbulent premixed flames. This further suggests that the scalar dissipation rate models, which were originally proposed in the context of passive scalar mixing, have the potential to be applicable for MILD combustion but the models for the premixed turbulent combustion may not be applicable for MILD combustion of homogeneous mixtures. [ABSTRACT FROM AUTHOR]

The effects of body force on the statistical behaviour of turbulent scalar flux and its closure in the context of Reynolds Averaged Navier–Stokes simulations have been studied using Direct Numerical Simulations (DNS) of statistically planar turbulent premixed flames under different turbulence intensities and Froude numbers. An increase in body force magnitude in the case of unstable density stratification has been found to augment flame wrinkling, burning rate and gradient transport in comparison to a case without body force but with statistically similar unburned gas turbulence. By contrast, an increase in body force magnitude in the case of stable stratification reduces the flame wrinkling, burning rate and gradient transport in comparison to the flame without body force subjected to statistically similar unburned gas turbulence. Based on a-priori DNS analysis, an algebraic closure for turbulent scalar flux has been identified where the Froude number effects are explicitly accounted for. The body force has been found to have significant influence on the statistical behaviours and magnitudes of the terms of the scalar flux transport equation and this effect is particularly strong for the mean pressure gradient term in the scalar flux transport equation. Based on a detailed a priori DNS analysis, suitable model expressions have been identified for the turbulent transport, pressure gradient, dissipation and reaction rate-velocity correlation terms of the scalar flux transport equation by incorporating the effects of body force (e.g. Froude number effects) for improved model performance. [ABSTRACT FROM AUTHOR]

The statistical behaviors of the magnitude of the reaction progress variable gradient (alternatively known as the Surface Density Function (SDF)) and the strain rates, which affect the SDF evolution, have been analyzed using three-dimensional Direct Numerical Simulations (DNS) of spherically expanding flames in globally stoichiometric initially mono-sized droplet-laden mixtures for different initial turbulence intensities and droplet diameters. It has been found that gaseous phase combustion predominantly takes place under fuel–lean mode and this tendency strengthens for large droplets and high turbulence intensities. The mean values of flame displacement speed, dilatation rate and normal strain rate decrease with increasing turbulence intensity and droplet diameter. By contrast, the mean tangential strain rate increases with increasing turbulence intensity for all droplet diameters. The mean normal strain rate induced by flame propagation remains negative but its magnitude decreases with increasing droplet size and turbulence intensity. The mean tangential strain rate induced by flame propagation (alternatively curvature stretch rate) assumes negative values except for the laminar flame with small droplets. The mean effective normal strain rate has been found to assume predominantly positive values and increases with increasing turbulence intensity for the droplet cases considered here. The mean effective tangential strain rate (alternatively stretch rate) is found to assume mostly negative values except for the laminar case with small droplets. The mean effective tangential strain rate decreases with increasing droplet size, which leads to a smaller extent of flame surface area generation for flames with larger droplets. [ABSTRACT FROM AUTHOR]

The localised forced ignition and subsequent flame propagation have been analysed for stoichiometric C H 4 − C O 2 − air mixtures with different spatial distributions and mean levels of C O 2 dilution (i.e. mole fraction of C O 2 in C H 4 / C O 2 blend) for different flow conditions (e.g. quiescent laminar condition and different turbulence intensities) using three-dimensional Direct Numerical Simulations. The C H 4 + C O 2 mixture is taken to represent biogas, as C H 4 and C O 2 are its two principal constituents. A two-step chemical mechanism, which has been demonstrated to capture the effects of C O 2 dilution on the laminar burning velocity with sufficient accuracy, has been used for the purpose of a parametric analysis in terms of the mean value, standard deviation and integral length scale of the initial spatial Gaussian distributions of C O 2 dilution in the unburned gas. An increase of mean C O 2 dilution level was found to reduce the maximum values of temperature and the reaction rate magnitude of C H 4 . Moreover, an increase of mean C O 2 dilution acts to reduce the probability of finding large reaction rate magnitudes of C H 4 , which also leads to a decreasing trend of burned gas volume C O 2 irrespective of flow conditions. Furthermore, an increase in turbulence intensity acts to reduce the burned gas volume irrespective of mixture composition due to the enhancement of heat transfer from the hot gas kernel. However, the initial values of integral length scale and standard deviation of C O 2 dilution variation (i.e. l ψ and σ ψ ) have been found not to have significant influences on the burned gas volume for the parameter range considered here. Although a small value of l ψ promotes high rates of mixing of C O 2 within the unburned gas, the overwhelming probability of finding C O 2 dilution close to its mean value eclipses the effects of l ψ and σ ψ even under laminar conditions, and this trend strengthens further under high turbulence intensities due to enhanced mixing. [ABSTRACT FROM AUTHOR]

The flame-wall interaction in a quasi-steady configuration, where a statistically planar premixed flame is pushed by the inflow of unburned reactants and stabilizes at a distance away from the wall, has been analyzed for different fuel Lewis numbers and inlet turbulence intensities. The extent of flame-wall interaction has been found to increase with increasing inlet turbulence intensity and increasing fuel Lewis number L e F due to the greater extent of flame wrinkling and smaller flame stabilization distance from the wall, respectively. The increasing trend of turbulent flame speed with decreasing fuel Lewis number and increasing inlet turbulence intensity act to increase the wall heat flux magnitude. However, the quenching distance remains comparable to the quenching distance predicted by one-dimensional conventional head-on quenching simulations. It has been found that the wall Stanton number and the skin friction coefficient are of the same order of magnitude, but the Reynolds-Colburn analogy does not remain strictly valid in the case of flame-wall interaction in this configuration. For a given value of bulk mean inlet velocity to laminar burning velocity ratio, the flames with smaller L e F stabilize further away from the wall due to their higher turbulent flame speed and thus the flame-wall interaction events are less frequent for small values of L e F . The drops in temperature and reaction rate magnitude lead to reductions in the values of dilatation rate, normal strain rate, and flame displacement speed in the flame quenching zone; with the increased likelihood of finding negative values for these quantities in the near-wall region. The decrease in displacement speed with decreasing wall-normal distance leads to predominantly positive normal strain rates induced by flame propagation in the quenching zone. These behaviors act to reduce the magnitude of the reaction progress variable gradient in the quenching zone, which has implications on the behaviors of the Flame Surface Density and scalar dissipation rate in the near-wall region. [ABSTRACT FROM AUTHOR]

The effects of droplet diameter, overall (i.e. liquid and gaseous phases) equivalence ratio, and turbulence intensity on the variation of the Minimum Ignition Energy (MIE) for localized forced ignition of uniformly dispersed mono-sized n-heptane droplet-laden mixtures under homogeneous isotropic decaying turbulence have been analyzed based on Direct Numerical Simulation (DNS) data. The MIE was evaluated just for (i) obtaining thermal runway irrespective of the fate of the resulting flame kernel, and (ii) also for a successful self-sustained flame propagation without the assistance of an external energy source following the energy deposition by the ignitor. It has been found that the MIE requirement increases with increasing turbulence intensity and this trend for the MIE increase is especially significant for large values of turbulence intensity. The MIE requirement increases with increasing initial droplet diameter and with decreasing overall equivalence ratio. The MIE requirements for droplet-laden mixtures have been found to be greater than the corresponding value for homogeneous mixture with the same nominal values of initial turbulence intensity and equivalence ratio for the parameter range considered here. This behavior arises due to the deposited energy being partially utilized to supply the latent heat of evaporation and also due to the predominantly fuel-lean composition of the gaseous flammable mixture. This tendency of obtaining fuel-lean mixture strengthens with increasing (decreasing) initial droplet diameter (overall equivalence ratio). It has also been demonstrated that combustion takes place predominantly in the fuel-lean premixed mode although there is a finite probability of having non-premixed combustion in all cases. Moreover, there is a small probability of fuel-rich combustion occurring for small droplets, especially under fuel-rich overall equivalence ratios. The stochastic nature of the ignition event has been demonstrated by considering different realizations of statistically similar turbulent flow fields. The conditions giving rise to a successful thermal runaway/self-sustained flame propagation have been identified by a detailed analysis of the energy budget. [ABSTRACT FROM AUTHOR]

The implications of elevated pressure on the statistical behavior of the flame surface density (FSD) transport statistics together with the behavior of selected established sub-models of the unclosed terms of the FSD transport equation have been analyzed in the context of large eddy simulation. For this purpose, five turbulent premixed Bunsen flames have been considered from an existing database. Four of the Bunsen flames are characterized by different pressure levels and are located on the boundary of the wrinkled and the corrugated flamelet (CF) regimes to allow for the possibility and clear identification of combustion instabilities that are often observed at high pressures. The fifth flame is in the thin reaction zones regime and serves as a reference case for the purpose of comparison. For a given filter width to flame thickness ratio, the terms of the FSD transport equation and their models behave in a qualitatively similar manner for different pressure levels. However, as the flame thickness decreases with increasing pressure, it is unlikely that a high pressure flame will be simulated for the same spatial resolution (i.e. LES filter width) normalized by flame thickness as that of an atmospheric flame. It is more likely that the spatial resolution remains constant and in this case, the modeling becomes much more challenging for higher pressures: the magnitudes of the sub-grid contributions increase for larger filter width to flame thickness ratio and thus the accuracy of sub-grid modeling is expected to play a more important role in determining the fidelity of the simulations. The flames considered in this work feature a relatively low ratio of turbulent velocity fluctuations to laminar flame speed, and under these conditions, positive values of the sub-grid curvature term and negative values of the strain rate term are observed toward the leading edge of the flame brush. This behavior cannot be captured by the well-established existing models for the sub-grid curvature term as these model expressions yield deterministically negative values. Similarly, existing models for the tangential strain term yield deterministically positive values. Detailed explanations have been provided for the observed behaviors of the unclosed terms of the FSD transport equations and their respective model predictions. [ABSTRACT FROM AUTHOR]

The validity of Damköhler's second hypothesis, which was originally proposed for premixed combustion for conditions where the large scale turbulent timescale remains smaller than the chemical timescale and the integral length scale remains smaller than the flame thickness, has been assessed for a range of Damköhler and Karlovitz numbers (i.e. 0.2 ≤ D a ≤ 3.0 and 0.58 ≤ K a ≤ 33.34) using a three-dimensional DNS database of statistically planar turbulent premixed flames subjected to forced unburned gas turbulence. It has been found that Damköhler's first hypothesis remains valid for all cases considered in this work irrespective of the combustion regime. By contrast, Damköhler's second hypothesis does not hold in the strict sense for the thin reaction zones regime flames with small values of Damköhler number. However, the ratio of the turbulent flame speed normalised by laminar burning velocity and the square root of the ratio of turbulent diffusivity to mass diffusivity converges to a value of the order of unity for the flames with high turbulence intensity and low Damköhler number in the thin reaction zones regime. Under this condition, Damköhler's second hypothesis, in an order of magnitude sense, can be considered to be valid alongside Damköhler's first hypothesis. A scaling analysis has been carried out using the equilibrium of the tangential strain rate and curvature terms in the Flame Surface Density transport equation to demonstrate that Damköhler's second hypothesis can be expected to be valid only in an order of magnitude sense for the thin reaction zones regime flames with small values of Damköhler number. [ABSTRACT FROM AUTHOR]

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 ∗ and increases the probability of finding negative S d ∗ 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. [ABSTRACT FROM AUTHOR]

The 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. [ABSTRACT FROM AUTHOR]

Laminar and turbulent spherically expanding n-heptane flames in mono-sized fuel droplet-mists have been simulated for a range of different overall equivalence ratios and droplet diameters using three-dimensional Direct Numerical Simulations (DNS). Flame wrinkling and the evolutions of flame surface area and burned gas volume have been investigated for spherically expanding spray and gaseous premixed flames with the same initial burned gas radius and overall equivalence ratios. It has been found that droplet-induced wrinkling for laminar flame kernels strengthens with increasing overall equivalence ratio and droplet diameter. However, the effects of droplet-induced flame wrinkling are masked by wrinkling induced by fluid motion in turbulent spherically expanding spray flames. The gaseous phase mixture within the flame has been found to have smaller equivalence ratios (predominantly fuel-lean) in comparison to the overall equivalence ratio for globally stoichiometric and fuel-rich droplet cases and this tendency strengthens with increasing droplet diameter. By contrast, it is possible to obtain higher local equivalence ratio values than the overall equivalence ratio in globally fuel-lean spray flames. The presence of droplets in the globally fuel-lean cases enhances the growth of flame surface area under laminar and turbulent conditions. However, for the laminar globally stoichiometric spray flame, flame surface area for small droplets grows faster than the corresponding laminar premixed flame and this tendency is observed also for turbulent globally fuel-rich spray flames. It has been found that the burned gas mass increases for large (small) droplets for overall fuel-lean (fuel-rich) mixtures for flame propagation in droplet-laden mixtures, which is in qualitative agreement with previous experimental findings. [ABSTRACT FROM AUTHOR]

Abstract The validity of Damköhler's first hypothesis, which relates the turbulent flame speed to turbulent flame surface area under the condition where the integral length scale of turbulence is greater than the flame thickness, has been assessed using three-dimensional Direct Numerical Simulations (DNS) of turbulent premixed Bunsen burner flames over a range of values of Reynolds number, pressure and turbulence intensity. It has been found for the Bunsen configuration that the proportionality between volume-integrated burning rate and the overall flame surface area is not strictly maintained according to Damköhler's first hypothesis. The discrepancy is found to originate physically from the local stretch rate dependence of displacement speed, and this helps to explain differences observed previously between flames with and without mean curvature. Approximating the local density-weighted flame propagation speed with the unstrained laminar burning velocity is shown to be inaccurate, and can have a significant influence on the prediction of the overall burning rate for flames with non-zero mean curvature. Using a two-dimensional projection of the actual scalar gradient for flame area evaluation is shown to exacerbate the loss of proportionality between volume-integrated burning rate and the overall flame surface area. The current analysis identifies the conditions under which Damköhler's hypothesis remains valid and the necessary correction for non-zero mean flame curvature. Further, it has been demonstrated that surface-weighted stretch effects on displacement speed need to be accounted for in order to ensure the validity of Damköhler's hypothesis under all circumstances. Finally, it has been found that the volume-integrated density-weighted scalar dissipation rate remains proportional to the overall burning rate for all flames considered here irrespective of the value of Reynolds number, pressure and turbulence intensity. However, this proportionality is lost when the scalar dissipation rate is evaluated using the two-dimensional projection of the actual scalar gradient. [ABSTRACT FROM AUTHOR]

Direct numerical simulations (DNS) of oblique wall quenching of a turbulent V-flame and head-on quenching (HOQ) of a statistically planar flame by isothermal inert walls have been utilized to analyze the statistics of wall heat flux, flame quenching distance in terms of the distributions of flow topologies and their contributions to the wall heat flux. The flow topologies have been categorized into eight generic flow configurations (i.e., S1-S8) in terms of three invariants of the velocity gradient tensor (i.e., first, second and third P, Q, and R, respectively). It has been found that nodal (i.e., strain rate dominated) flow topologies are major contributors to the wall heat flux when it attains large magnitude in the HOQ configuration, whereas focal (i.e., vorticity-dominated) topologies contribute significantly to the wall heat flux in the case of oblique flame quenching. These differences in the heat transfer mechanisms contribute to the differences in wall heat flux and flame quenching distance between HOQ and oblique quenching configurations. The maximum wall heat flux magnitude in the case of oblique flame quenching has been found to be greater than that in the corresponding turbulent HOQ case. By contrast, the minimum wall Peclet number, which quantifies the flame quenching distance, in the case of oblique quenching has been found to be smaller than that in the case of HOQ. [ABSTRACT FROM AUTHOR]

The statistical behaviours of sub-grid flux of reaction progress variable has been assessed for premixed turbulent flames with global Lewis number Le (=thermal diffusivity/mass diffusivity) ranging from 0.34 to 1.2 using a Direct Numerical Simulation (DNS) database of freely propagating statistically planar flames. It is known that the sub-grid scalar flux shows counter-gradient transport when the velocity jump across the flame due to heat release overcomes the effects of turbulent velocity fluctuation. The results show that the sub-grid scalar flux components exhibit counter-gradient transport for all cases considered here. The extent of counter-gradient transport increases with increasing filter width Δ and decreasing value of Le . This is due to the fact that flames with Le ≪ 1 (e.g. Le = 0.34) exhibit thermo-diffusive instabilities, which in turn increases the extent of counter-gradient transport. The effects of heat release and flame normal acceleration weaken with increasing Le . Several established algebraic models have been assessed in comparison to the sub-grid scalar flux components extracted from explicitly filtered DNS data in terms of their correlation coefficients at the vector level and their mean variation conditional on the Favre-filtered progress variable. The gradient transport closure does neither capture the quantitative nor the qualitative behaviour of the different sub-grid scalar flux components for all filter widths in all cases considered here. Models which account for local flame normal acceleration perform better, especially when the flame remains completely unresolved. In particular those models that account for the alignment of local resolved velocity and scalar gradients by using a tensor diffusivity, perform relatively better than the other alternative models irrespective of Le . [ABSTRACT FROM AUTHOR]

The strain rate contribution in the generalized flame surface density (FSD)transport equation remains a leading order unclosed source term, which plays a pivotal role in the modeling oftransport for all filter widthsin the context of large eddy simulations (LES). To date, most FSD-based closures have been proposed for flames without differential diffusion effects of heat and mass, characterized by a global Lewis number equal to unity (i.e.,). The effects of differential diffusion arising due to non-unity Lewis number on the FSD transport have rarely been analyzed in existing literature. In the present analysis, the statistical behaviors of the strain rate term of the FSD transport equation have been analyzed using a DNS database of freely propagating statistically planar turbulent premixed flames with a global Lewis number ranging from 0.34 to 1.2 (i.e.,= 0.34–1.2). The FSD strain rate term has been split into components originating from the gradients of Favre-filtered velocity components (i.e.,), strain rate contribution due to chemical heat release (i.e.,) and sub-grid processes (i.e.,). The contributions ofandassume positive values throughout the flame brush for all values of. The performances of the existing models forandhave been assessed for flames with different values of global Lewis number. The contribution ofremains positive throughout the flame brush for the= 0.6, 0.8, 1.0, and 1.2 flames but the variation oftowards the burned gas side of the flame brush for theflame remains qualitatively different in comparison to the other cases considered here. The effects ofon the local alignment of reaction progress variable gradient with principal strain rates are responsible for the observed influences of Lewis number on the sub-grid strain rate term. The existing models have been found to be inadequate for the purpose of capturing the qualitative behaviors of the sub-grid strain rate termforflames. Here a new model has been proposed based on a-priori analysis of explicitly filtered DNS data, which has been demonstrated to capture both the qualitative and quantitative behaviors offor all values offor flames withranging from 0.34 to 1.2. [ABSTRACT FROM PUBLISHER]

A compressible single step chemistry Direct Numerical Simulation (DNS) database of freely propagating premixed flames has been used to analyze different entropy generation mechanisms. The entropy generation due to viscous dissipation within the flames remains negligible in comparison to the other mechanisms of entropy generation. It has been found that the entropy generation increases significantly due to turbulence and the relative magnitudes of the augmentation of entropy generation and burning rates under turbulent conditions ultimately determine the value of turbulent second law efficiency in comparison to the corresponding laminar values. It has been found that the entropy generation mechanisms due to chemical reaction, thermal conduction and mass diffusion in turbulent flames strengthen with decreasing global Lewis number in comparison to the corresponding values in laminar flames. The ratio of second law efficiency under turbulent conditions to its corresponding laminar value has been found to decrease with increasing global Lewis number. An increase in heat release parameter significantly augments the entropy generation due to thermal conduction, whereas other mechanisms of entropy generation are marginally affected. However, the effects of augmented entropy generation due to thermal conduction at high values of heat release parameter are eclipsed by the increased change in availability due to chemical reaction, which leads to an increase in the second law efficiency with increasing heat release parameter for identical flow conditions. The combustion regime does not have any major influence on the augmentation of entropy generation due to chemical reaction, thermal conduction and mass diffusion in turbulent flames in comparison to corresponding laminar flames, whereas the extent of augmentation of entropy generation due to viscous dissipation in turbulent conditions in comparison to corresponding laminar flames, is more significant in the thin reaction zones regime than in the corrugated flamelets regime. However, the ratio of second law efficiency under turbulent conditions to its corresponding laminar value does not get significantly affected by the regime of combustion, as viscous dissipation plays a marginal role in the overall entropy generation in premixed flames. [ABSTRACT FROM AUTHOR]

Statistically planar turbulent stratified flames for different initial intensities of decaying turbulence have been simulated for global equivalence ratios <φ> = 0.7 and <φ> = 1.0 using three-dimensional simplified chemistry–based direct numerical simulations (DNS). The simulation parameters are chosen in such a manner that all the cases considered here represent low Damköhler number thin reaction zones regime combustion. The DNS data have been used to analyze the statistical behaviors of the turbulent fluxes of fuel mass fraction Y F and mixture fraction ξ, and their variances and covariances. It has been found that turbulent scalar flux of fuel mass fraction predominantly exhibits gradient-type transport in all cases considered in the current study, but countergradient-type transport has also been observed in the globally stoichiometric flame for small values of turbulence intensity where the flame normal acceleration due to chemical heat release overcomes the effects of turbulent velocity fluctuation. Models have been identified for the turbulent fluxes of fuel mass fraction Y F and mixture fraction ξ, and their variances and covariances, which are shown to satisfactorily capture the qualitative and quantitative behaviors of the corresponding quantities extracted from DNS data. It has been shown that the accurate modeling of the scalar fluxes of fuel mass fraction and mixture fraction plays a key role in the modeling of scalar fluxes of the fuel mass fraction variance and the covariance of fuel mass fraction and mixture fraction. [ABSTRACT FROM AUTHOR]

Abstract: Direct Numerical Simulations of expanding flame kernels following localized ignition in decaying turbulence with the fuel in the form of a fine mist have been performed to identify the effects of the spray parameters on the possibility of self-sustained combustion. Simulations show that the flame kernel may quench due to fuel starvation in the gaseous phase if the droplets are large or if their number is insufficient to result in significant heat release to allow for self-sustained flame propagation for the given turbulent environment. The reaction proceeds in a large range of equivalence ratios due to the random location of the droplets relative to the igniter location that causes a wide range of mixture fractions to develop through pre-evaporation in the unreacted gas and through evaporation in the preheat zone of the propagating flame. The resulting flame exhibits both premixed and non-premixed characteristics. [Copyright &y& Elsevier]

• Performances of filtered reaction rate of progress variable closures are assessed. • Direct Numerical Simulation data of MILD CH4/air combustion is considered. • Phenomenological, Statistical, Flame surface description closures are considered. • The sub-grid PDF of progress variable can be approximated by beta-PDF. • Scalar Dissipation Rate models for passive scalar mixing are inadequate here. • An Eddy Dissipation Concept model shows promising performance for LES. A priori Direct Numerical Simulation (DNS) assessment of the closures for the filtered reaction rate and the Favre-filtered scalar dissipation rate (SDR) for large eddy simulations (LES) of homogenous and stratified mixture MILD combustion has been performed. It has been found that the probability density function of the reaction progress variable can be adequately predicted using the beta function for both homogenous and stratified mixture MILD combustion. It has also been found that a scalar dissipation rate closure characteristic of passive scalar mixing may not be suitable for homogenous and stratified mixture MILD combustion. The predictions of different filtered reaction rate closures have been assessed with respect to DNS data in this study. The Eddy Dissipation Concept (EDC), Eddy-Break Up (EBU) model, and SDR-based reaction rate closures for Reynolds Averaged Navier-Stokes simulations have been extended for MILD combustion in the context of LES. The SDR-based reaction rate closure captures the qualitative behaviour but overpredicts the filtered reaction rate for both homogenous and stratified mixture MILD combustion. The EBU-based reaction rate and flame surface density (FSD) closures did not capture the qualitative behaviour of the filtered reaction rate for both homogenous and stratified mixture MILD combustion. By contrast, the EDC model with bridging functions, which ensures asymptotic behaviour, shows the potential to provide reasonable predictions of the filtered reaction rate for a wide range of filter widths in the cases investigated here. [ABSTRACT FROM AUTHOR]

The performances of different models for sub-grid scalar flux for premixed turbulent combustion in the context of Large Eddy Simulations (LES) have been assessed based on a Direct Numerical Simulation (DNS) database of freely propagating turbulent premixed flames with a range of different values of R e t where Damköhler and Karlovitz numbers are altered independently of each other to bring about the variation of R e t , whereas the heat release parameter τ is kept unaltered. It has been found that the sub-grid scalar flux exhibits local counter-gradient transport for all cases considered here. However, the extent of counter-gradient transport decreases with decreasing values of filter width Δ and for increasing values of the ratio of the root-mean-square turbulent velocity fluctuation to the unstrained laminar burning velocity u ′ / S L . The performance of several algebraic models has been assessed with respect to explicitly filtered DNS data. The standard gradient hypothesis based model does not adequately capture both the qualitative and quantitative behaviours of sub-grid scalar flux for all cases for all filter widths. The models which account for local flame normal acceleration perform better than the standard gradient hypothesis model. In general the performance of the models, which account for the alignment of local resolved velocity and scalar gradients, remains relatively better than the performance of the other existing models. Detailed physical explanations have been provided for the observed model performances. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

• Carrier phase DNS of turbulent V-shaped flames propagating into droplet-laden mixtures. • Effects of initial droplet diameter at different axial locations from the flame holder are analysed. • Reaction zone structure and flame propagation characteristics are analysed. • Statistics in droplet cases are compared to that in the corresponding premixed flame. 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. [ABSTRACT FROM AUTHOR]