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The direct moment closure (DMC) approach for modeling the filtered chemical source terms in large eddy simulation of turbulent combustion is comprehensively assessed by using direct numerical simulation data of a turbulent premixed flame with a skeletal chemistry. In this approach, closure is achieved by linearizing the chemical source terms using the Taylor series expansions. Different from traditional method, the exponential term is treated as a single variable in the expansion, and the filtered chemical reaction rate can be readily modeled with the first-order and second-order moments, plus higher-order correlations. The a-priori investigations demonstrate that the DMC model is able to reasonably represent the chemical reaction rates, and the second-order correlation of reactive scalars can be well modeled with the algebraic gradient-type model. Compared to the first-order moment closure, the second-order one makes a significant improvement on the predictions. These improvements are also observed in the a-posteriori study in which the premixed flame can be better resolved by the second-order moment closure model. Consequently, the second-order moment closure model provides an alternative for turbulent combustion modeling and is recommended to be used as an improvement to the laminar chemistry closure model. The sensitivity of the DMC approach to the grid size needs further investigation.

The peak flame surface density within the turbulent flame brush is central to turbulent premixed combustion models in the flamelet regime. This work investigates the evolution of the peak surface density in spherically expanding turbulent premixed flames with the help of direct numerical simulations at various values of the Reynolds and Karlovitz number. The flames propagate in decaying isotropic turbulence inside a closed vessel. The effects of turbulent transport, transport due to mean velocity gradient, and flame stretch on the peak surface density are identified and characterized with an analysis based on the transport equation for the flame surface density function. The three mechanisms are governed by distinct flow time scales; turbulent transport by the eddy turnover time, mean transport by a time scale related to the pressure rise in the closed chamber, and flame stretch by the Kolmogorov time scale. Appropriate scaling of the terms is proposed and shown to collapse the data despite variations in the dimensionless groups. Overall, the transport terms lead to a reduction in the peak value of the surface density, while flame stretch has the opposite effect. In the present configuration, a small imbalance between the two leads to an exponential decay of the peak surface density in time. The dimensionless decay rate is found to be consistent with the evolution of the wrinkling scale as defined in the Bray-Moss-Libby model.

Detailed kinetics mechanisms for plasma-assisted combustion contain numerous species and reactions that model the interplay between non-equilibrium plasma processes and hydrocarbon oxidation. While physically accurate and comprehensive, such detailed mechanisms are impractical for simulations of unsteady multi-dimensional plasma discharges and their effect on reactive mixtures in practical devices. In this work, we develop and apply a novel methodology for the reduction of large detailed plasma-assisted combustion mechanisms to smaller skeletal ones. The methodology extends the Directed Relation Graph with Error Propagation (DRGEP) approach in order to consider the energy branching characteristics of plasma discharges during the reduction. Ensuring tight error tolerances on the relative proportions of energy lost by the electrons to the various classes of impact processes (i.e. vibrational and electronic excitation, ionization, and impact dissociation) is key to preserving the correct discharge physics in the skeletal mechanism. To this end, new targets that include energy transfers are defined and incorporated in DRGEP. The performance of the novel framework, called P-DRGEP, is assessed for the simulation of ethylene-air ignition by nanosecond repetitive pulsed discharges at conditions relevant to supersonic combustion and flame holding in scramjet cavities, i.e. from 600 K to 1000 K, 0.5 atm, and equivalence ratios between 0.75 and 1.5. P-DRGEP is found to be greatly superior to the traditional reduction approach applied to plasma-assisted ignition in that it generates a smaller skeletal mechanism with significantly lower errors. For ethylene-air ignition at the target conditions, P-DRGEP generates a skeletal mechanism with 54 species and 236 reactions, resulting in a 84% computational speed-up for ignition simulations, while guaranteeing errors below 10% on the time required for ignition following the first pulse, 1% on the mean electron energy, between 4 and 35% on electron energy losses depending on the process, and 5% on the laminar flame speed., SCOPUS: ar.j, info:eu-repo/semantics/published

The surface of turbulent premixed flames is fractal within a finite range of scales and the fractal dimension and inner cutoff scale are key components of fractal turbulent combustion closures. In such closures, the estimate for the surface area is sensitive to the value of the inner fractal cutoff scale, whose modeling remains unclear and for which both experimental and numerical contradictory evidence exists. In this work, we analyze data from six direct numerical simulations of spherically expanding turbulent premixed flames at varying Reynolds and Karlovitz numbers. The flames propagate in decaying isotropic turbulence and fall in the flamelet regime. Past an initial transient, we find that the fractal dimension reaches an asymptotic value between 2.3 and 2.4 in good agreement with previous results at similar conditions. A minor dependence of the fractal dimension on the Reynolds and Karlovitz numbers is observed and explained by the relatively low values of the Reynolds number and narrow inertial and fractal ranges. The inner fractal cutoff scale Δ* is found to scale as Δ * / l ∼ Re λ − 1.14 , where l is the integral scale of turbulence and Reλ is the Reynolds number based on the Taylor micro-scale computed in the turbulence on the reactants’ side. The scaling is robust and insensitive to the Karlovitz number over the range of values considered in this study. An important implication is that the ratio Δ*/η grows with Reynolds number (η is the Kolmogorov scale), albeit at a rather slow rate that may explain the widespread observation that 4 ≤ Δ*/η ≤ 10. This suggests that Δ*, although smaller than λ, is not a dissipative length scale for the flame surface and scaled solely by η. Finally, a dissipative threshold scale that remains constant once normalized by η is identified.

The ignition of methane/air and ethylene/air mixtures by nanosecond pulsed discharges (NSPD) is investigated numerically using a zero-dimensional isochoric adiabatic reactor. A combustion kinetics model is coupled with a non-equilibrium plasma mechanism, which features vibrational and electronic excitation, dissociation, and ionization of neutral particles (O2 and N2) via electron impact. A time to ignition metric τ is defined, and ignition simulations encompassing a wide range of pressures (0.5–30 atm) and pulsing conditions for each fuel are executed. For each fuel, it is found that τ depends primarily on initial pressure and energy deposition rate, and scaling laws are derived. In order to quantify the benefit gained from plasma-assisted ignition (PAI), τ is compared with a thermal ignition time. It is found that for both fuels, PAI leads to a faster ignition at low pressures, while at higher pressures (p0 ≥ 5 atm), methane/air ignition becomes inefficient (meaning a longer ignition time for the same input energy compared to thermal ignition). Ethylene/air PAI shows only a modest deterioration. The drop in performance with pressure is found to be due to the mean electron energy achieved during the pulse, which shows an inverse relationship with pressure, leading to fewer excited species and combustion radicals. The poor performance of methane/air mixture ignition at high pressure is explained by an analysis of the reaction pathways. At high pressures (p0 ∼ 30 atm), H is consumed mostly to form hydroperoxyl (HO2), leading to a bottleneck in the formation of formyl (HCO) from formaldehyde (CH2O). Instead, for ethylene/air ignition, at both low and high pressures there exist several bypass pathways that facilitate the formation of HCO and CO directly from various intermediates, explaining the more robust performance of PAI for ethylene at pressure.

A flamelet model is applied to the simulation of axisymmetric counterflow laminar flames including gravitational acceleration and the geometrical details of main nozzles and annular shrouds. The fl...

Modeling suites for Large-Eddy Simulations of soot evolution in turbulent flames include a number of submodels describing the chemistry of soot precursors, particle dynamics, heterogeneous soot chemistry, turbulent mixing, and combustion. To understand the reasons for model failure and to enhance the overall model performance, it is necessary to identify and subsequently improve model components with a leading order effect on the overall error. In this work, errors in soot predictions associated with flamelet-based combustion models are isolated and quantified in a combined a-priori and partial a-posteriori analysis using large-scale Direct Numerical Simulation (DNS) data of a sooting turbulent jet diffusion flame. Gas-phase quantities entering the calculation of the soot source terms and hence coupling the combustion model to the soot model are analyzed in the DNS first. The performance of a Flamelet/Progress Variable model with respect to these quantities is then analyzed a-priori for two DNS cases employing a mixture-averaged transport model and unity Lewis numbers. Then, the soot evolution along Lagrangian trajectories extracted from the DNS is re-computed using rate coefficients directly taken from the DNS and from the flamelet table. In the context of this partial a-posteriori analysis, flamelet-induced errors are also compared to errors induced by the chemical soot model. The soot surface growth and oxidation rate coefficients are reasonably well predicted by the flamelet library. Considerably larger errors in the model-predicted soot mass originate from the tabulated quantities entering the calculation of PAH-based soot growth rates. However, these errors can be reduced to a few percent if the rate is appropriately scaled with the mass fraction of polycyclic aromatic hydrocarbons (PAH). However, this requires the solution of a transport equation for the PAH mass fraction, and modeling the source term in this equation is shown to be challenging. Overall, the largest uncertainties can be attributed to the chemical mechanism for PAH formation and the model for the PAH source term.

Turbulence and mixing statistics are investigated in a set of flames at a jet Reynolds number of 15000 achieving a Taylor’s scale Reynolds number in the range 100 ≤Reλ ≤ 150. In particular, the impact on small scale turbulence statistics of different levels of flame extinction, induced imposing different Damkohler numbers in the three simulated cases, is investigated. It is found that the non-dimensional scalar dissipation depends on the Damkohler number slightly. This deviation from self-similarity manifests itself as a decrease of the non-dimensional scalar dissipation with increasing occurrence of localized extinction events. This is caused by the decrease of molecular diffusion due to the lower flame temperatures in the low Damkohler number cases. Probability density functions of the scalar dissipation χ show important deviations from the log-normal distribution. The left tail of the pdf scales as χ1/2 while the right tail scales as $e^{-c\chi ^{\alpha }}$ , as shown for incompressible turbulence. In all flames, the vorticity vector displays a pronounced tendency to align with the direction of the intermediate strain and the gradient of mixture fraction aligns with the most compressive strain. Conditioning on the local values of mixture fraction and heat release does not affect the statistics. The alignment statistics of vorticity are in agreement with those in homogeneous isotropic turbulence while they show some difference compared to previous results in non premixed flames. The alignment between strain and mixture fraction gradient differs slightly from the homogeneous isotropic turbulent case but agree remarkably well with previous results observed in homogeneous shear incompressible flows.

Dissipation element (DE) analysis is a method for analyzing scalar fields in turbulent flows. DEs are defined as a coherent region in which all gradient trajectories of a scalar field reach...

Flamelet models, which enable the storing of precomputed detailed chemistry into lookup tables, are widely used in combustion simulations. They allow the computation of accurate results at low comp...

Direct Numerical Simulations (DNS) are conducted to study the statistics of flame surface stretch in turbulent jet premixed flames. Emphasis is placed on the rates of surface production and destruction and their scaling with the Reynolds number. Four lean methane/air turbulent slot jet flames are simulated at increasing Reynolds number and up to Re ≈ 22 × 103, based on the bulk velocity, slot width, and the reactants’ properties. The Karlovitz number is held approximately constant and the flames fall in the thin reaction zone regime. The simulations feature finite rate chemistry and mixture-average transport. Our data indicate that the area of the flame surface increases up to the streamwise position corresponding to 80% of the average flame length and decreases afterwards as surface destruction overtakes production. It is observed that the tangential rate of strain is responsible for the production of flame surface in the mean and surface destruction is due to the curvature term. In addition, it is found that these two terms are both significantly larger than their difference, i.e., the net surface stretch.The statistics of the tangential strain rate are in good agreement with those for infinitesimal material surfaces in homogeneous isotropic turbulence. Once scaled by the Kolmogorov time scale, the means of both contributions to stretch are largely independent of location and equal across flames with different values of the Reynolds number. Surface destruction is due mostly to propagation into the reactants where the surface is folded into a cylindrical shape with the center of curvature on the side of the reactants. The joint statistics of the displacement speed and curvature of the reactive surface are nuanced, with the most probable occurrence being that of a negative displacement speed of a flat surface, while the surface averaged displacement speed is positive as expected.

We present a novel moving immersed boundary method (IBM) and employ it in direct numerical simulations (DNS) of the closed-vessel swirling von Karman flow in laminar and turbulent regimes. The IBM extends direct-forcing approaches by leveraging a time integration scheme, that embeds the immersed boundary forcing step within a semi-implicit iterative Crank–Nicolson scheme. The overall method is robust, stable, and yields excellent results in canonical cases with static and moving boundaries. The moving IBM allows us to reproduce the geometry and parameters of the swirling von Karman flow experiments in (F. Ravelet, A. Chiffaudel, and F. Daviaud, JFM 601, 339 (2008)) on a Cartesian grid. In these DNS, the flow is driven by two-counter rotating impellers fitted with curved inertial stirrers. We analyze the transition from laminar to turbulent flow by increasing the rotation rate of the counter-rotating impellers to attain the four Reynolds numbers 90, 360, 2000, and 4000. In the laminar regime at Reynolds number 90 and 360, we observe flow features similar to those reported in the experiments and in particular, the appearance of a symmetry-breaking instability at Reynolds number 360. We observe transitional turbulence at Reynolds number 2000. Fully developed turbulence is achieved at Reynolds number 4000. Non-dimensional torque computed from simulations matches correlations from experimental data. The low Reynolds number symmetries, lost with increasing Reynolds number, are recovered in the mean flow in the fully developed turbulent regime, where we observe two tori symmetrical about the mid-height plane. We note that turbulent fluctuations in the central region of the device remain anisotropic even at the highest Reynolds number 4000, suggesting that isotropization requires significantly higher Reynolds numbers.

In the flamelet regime of turbulent premixed combustion the enhancement in the burning rates originates primarily from surface wrinkling. In this work we investigate the Reynolds number dependence of burning rates of spherical turbulent premixed methane/air flames in decaying isotropic turbulence with direct numerical simulations. Several simulations are performed by varying the Reynolds number, while keeping the Karlovitz number the same, and the temporal evolution of the flame surface is compared across cases by combining the probability density function of the radial distance of the flame surface from the origin with the surface density function formalism. Because the mean area of the wrinkled flame surface normalized by the area of a sphere with radius equal to the mean flame radius is proportional to the product of the turbulent flame brush thickness and peak surface density within the brush, the temporal evolution of the brush and peak surface density are investigated separately. The brush thickness is shown to scale with the integral scale of the flow, evolving due to decaying velocity fluctuations and stretch. When normalized by the integral scale, the wrinkling scale defined as the inverse of the peak surface density is shown to scale with Reynolds number across simulations and as turbulence decays. As a result, the area ratio and the burning rate are found to increase as , in agreement with recent experiments on spherical turbulent premixed flames. We observe that the area ratio does not vary with turbulent intensity when holding the Reynolds number constant.

A series of Direct Numerical Simulations (DNS) of lean methane/air flames was conducted in order to investigate the enhancement of the turbulent flame speed and modifications to the reaction layer structure associated with the systematic increase of the integral scale of turbulence $l$ while the Karlovitz number and the Kolmogorov scale are kept constant. Four turbulent slot jet flames are simulated at increasing Reynolds number and up to $Re \approx 22000$, defined based on the bulk velocity, slot width, and the reactants' properties. The turbulent flame speed $S_T$ is evaluated locally at select streamwise locations and it is observed to increase both in the streamwise direction for each flame and across flames for increasing Reynolds number, in line with a corresponding increase of the turbulent integral scale. In particular, the turbulent flame speed $S_T$ increases exponentially with the integral scale for $l$ up to about 6 laminar flame thicknesses, while the scaling becomes a power-law for larger values of $l$. These trends cannot be ascribed completely to the increase in the flame surface, since the turbulent flame speed looses its proportionality to the flame area as the integral scale increases; in particular, it is found that the ratio of turbulent flame speed to area attains a power-law scaling $l^{0.2}$. This is caused by an overall broadening of the reaction layer for increasing integral scale, which is not associated with a corresponding decrease of the reaction rate, causing a net enhancement of the overall burning rate. This observation is significant since it suggests that a continuous increase in the size of the largest scales of turbulence might be responsible for progressively stronger modifications of the flame's inner layers even if the smallest scales, i.e., the Karlovitz number, are kept constant.

The positive effect of plasma discharges on ignition and flame stability motivates the development of detailed kinetic mechanisms for high-fidelity simulations of plasma-assisted combustion. Because of their hierarchical nature, combustion processes require a large number of chemical species and pathways to describe hydrocarbon oxidation. In order to simulate kinetic enhancement by non-thermal electrons, additional species and processes are included, which model the ionization and excitation of neutral molecules. From a practical perspective, integrating large kinetics mechanisms is computationally burdensome due to the temporal stiffness of the nonlinear combustion dynamics and the memory requirements associated with the high number of species. In order to alleviate computational costs, a dimensionality reduction approach is proposed based on principal component analysis. The methodology is demonstrated on a detailed kinetics mechanism for plasma-assisted combustion excited by a nanosecond pulse discharge. Data are collected from a zero-dimensional two-temperature reactor model, whereby a nanosecond pulse generates a population of excited-state molecules and radicals in argon and air mixtures with hydrocarbon fuels. The data from the detailed mechanism are used to describe the evolution of the plasma and mixture based on principal components. Several skeletal mechanisms consisting of a much smaller number of species are assembled and their accuracy is compared against the detailed one. The performance of selected skeletal mechanisms is found satisfactory for the simulation of plasma-assisted ignition in unsteady, three-dimensional reactive flows.

info:eu-repo/semantics/published

Coflow diffusion flames are a canonical laboratory-scale flame configuration, which is routinely employed in fundamental combustion studies on flame stabilization, chemical kinetics, and pollutants’ emissions. In particular, pressurized coflow flames are used to study the effect of pressure on soot formation. In this work, we explore the opportunity to scale sooting coflow flames at constant Reynolds and Grashof numbers as pressure increases. This is achieved by decreasing the bulk velocity and the diameter of the fuel nozzle with increasing pressure. Despite some minor departures from the ideal scaling due to the effect of radiative heat losses from soot, the coflow flames are shown to be self-similar to a very good approximation. By keeping the Reynolds and Grashof numbers constant, one obtains a set of pressurized flames, which have self-similar nondimensional flow fields. Self-similarity is observed experimentally via direct photography and documented thoroughly by direct numerical simulation of steady axisymmetric coflow flames of methane and air at pressures from 1 to 12 atm. Although the study does not include data on soot yields, the implications for soot formation are explored with emphasis on the field of scalar dissipation rate and on the residence time, temperature, and mixture fraction experienced by a parcel of fluid moving along the centerline and along a streamline on the flame’s wing. We explain how the proposed approach to scaling pressurized flames facilitates the analysis of the effect of pressure on soot formation.

Current-voltage, or i–V, curves are used in combustion to characterise the ionic structure of flames. The objective of this paper is to develop a detailed modelling framework for the quantitative p...

A new skeletal mechanism, consisting of 16 species and 72 reactions, has been developed for lean methane–air premixed combustion from the GRI-Mech 3.0. The skeletal mechanism is validated for eleva...

The thickness of the turbulent flame brush is central to the modeling of premixed turbulent combustion and the theory of turbulent diffusion is often applied to explain the growth of the brush with varying success. However, numerous studies have shown that the brush evolves differently from the dispersion of material points on the account of flame propagation, density changes across the front, and hydrodynamic instabilities. Modifications to turbulent diffusion theory to incorporate these effects are challenging since the theory is Lagrangian. In this article, we present an alternate Eulerian framework based on the surface density formalism. We employ the proposed framework to analyze a database of direct numerical simulations of spherical turbulent premixed flames in decaying isotropic turbulence and recover mechanisms for which scaling laws are proposed and assessed against data. We characterize quantitatively two mechanisms: one related to the mean velocity gradient induced by thermal expansion and the other due to flame propagation in the presence of curvature. We demonstrate that the net effect of these two processes is to hinder the growth of the turbulent flame brush in the present configuration. Our analysis supports the notion that the turbulent flame brush does not grow indefinitely, rather it attains a maximum thickness.

The formation, growth, and oxidation of soot are studied in a set of laminar coflow diffusion flames at pressures ranging from 1 to 8 atm. The modeling approach combines detailed finite rate chemical kinetics mechanisms that model the formation of Polycyclic Aromatic Hydrocarbon (PAH) species up to pyrene, and a bivariate method of moments that describes soot particles and aggregates by their volume and surface area. The spatial distribution of soot observed experimentally and that predicted numerically are in good qualitative agreement with the peak soot volume fraction located at the flame tip and soot appearing on the flame wings and closer to the nozzle as pressure increases. A detailed analysis of the effect of hydrodynamics and mixing on soot formation is presented. We show that the scalar dissipation rate is lower for the higher pressure flames, promoting the formation of PAH species and soot. Thus, the observed increase in soot volume fraction across flames with increasing pressure is not due solely to mixture density and kinetics effects, rather is affected by hydrodynamics and mixing processes also. Similarly, our results indicate that the decrease in the scalar dissipation rate contribute to changing the location where soot forms in the flame, with soot formation occurring closer to the nozzle and outward on the flame’s wings as pressure increases. Radiative heat losses are found to lower the flame temperature, inducing a reduction of the PAH species and associated rates of soot formation. However, heat losses are responsible for a slightly longer flame, which allows for more soot. The overall effect is a modest variation of soot volume fraction if radiation is included.

A modeling framework based on Direct Simulation Monte Carlo (DSMC) is employed to simulate the evolution of the soot particle size distribution in turbulent sooting flames. The stochastic reactor describes the evolution of soot in fluid parcels following Lagrangian trajectories in a turbulent flow field. The trajectories are sampled from a Direct Numerical Simulation (DNS) of a n-heptane turbulent nonpremixed flame. The DSMC method is validated against experimentally measured size distributions in laminar premixed flames and found to reproduce quantitatively the experimental results, including the appearance of the second mode at large aggregate sizes and the presence of a trough at mobility diameters in the range 3–8 nm. The model is then applied to the simulation of soot formation and growth in simplified configurations featuring a constant concentration of soot precursors and the evolution of the size distribution in time is found to depend on the intensity of the nucleation rate. Higher nucleation rates lead to a higher peak in number density and to the size distribution attaining its second mode sooner. The ensemble-averaged PSDF in the turbulent flame is computed from individual samples of the PSDF from large sets of Lagrangian trajectories. This statistical measure is equivalent to time-averaged, scanning mobility particle size (SMPS) measurements in turbulent flames. Although individual trajectories display strong bimodality as in laminar flames, the ensemble-average PSDF possesses only one mode and a long, broad tail, which implies significant polydispersity induced by turbulence. Our results agree very well with SMPS measurements available in the literature. Conditioning on key features of the trajectory, such as mixture fraction or radial locations does not reduce the scatter in the size distributions and the ensemble-averaged PSDF remains broad. The results highlight and explain the important role of turbulence in broadening the size distribution of particles in turbulent sooting flames.

We developed a novel two-step hierarchical method for the Bayesian inference of the rate parameters of a target reaction from time-resolved concentration measurements in shock tubes. The method was applied to the calibration of the parameters of the reaction of hydroxyl with 2-methylfuran, which is studied experimentally via absorption measurements of the OH radical’s concentration following shock-heating. In the first step of the approach, each shock tube experiment is treated independently to infer the posterior distribution of the rate constant and error hyper-parameter that best explains the OH signal. In the second step, these posterior distributions are sampled to calibrate the parameters appearing in the Arrhenius reaction model for the rate constant. Furthermore, the second step is modified and repeated in order to explore alternative rate constant models and to assess the effect of uncertainties in the reflected shock’s temperature. Comparisons of the estimates obtained via the proposed methodology against the common least squares approach are presented. The relative merits of the novel Bayesian framework are highlighted, especially with respect to the opportunity to utilize the posterior distributions of the parameters in future uncertainty quantification studies.

The opportunity for ignition assistance by a pulsed applied voltage is investigated in a canonical one-dimensional configuration. An incipient ignition kernel, formed by localized energy deposition into a lean mixture of methane and air at atmospheric pressure, is subjected to sub-breakdown electric fields (E/N ≈ 100 Td) by a DC potential applied across the domain, resulting in non-thermal behavior of the plasma formed during the discharge. A two-fluid approach is employed to couple thermal neutrals and ions to the non-thermal electrons. A two-temperature plasma mechanism describing gas phase combustion, excitation of neutral species, and high-energy electron kinetics is employed to account for non-thermal effects. Charged species transported from the ignition zone drift rapidly through the domain, augmenting the magnitude of the electric field in the fresh gas during the pulse through a dynamic-electrode effect, which results in an increase in the energy of the electrons in the fresh mixture with increasing time. Enhanced fuel and oxidizer decomposition due to electron impact dissociation and interaction with excited neutrals generate a pool of radicals, mostly O and H, in the fresh gas ahead of the flame’s preheat zone. In the configuration considered, the effect of the nanosecond pulse is to increase the mass of fuel burned at equivalent times relative to the unsupported ignition through enhanced radical generation, resulting in an increased heat release rate in the immediate aftermath of the pulse.

The i − V curve describes the current drawn from a flame as a function of the voltage difference applied across the reaction zone. Since combustion diagnostics and flame control strategies based on electric fields depend on the amount of current drawn from flames, there is significant interest in modeling and understanding i − V curves. We implement and apply a detailed model for the simulation of the production and transport of ions and electrons in one-dimensional premixed flames. An analytical reduced model is developed based on the detailed one, and analytical expressions are used to gain insight into the characteristics of the i − V curve for various flame configurations. In order for the reduced model to capture the spatial distribution of the electric field accurately, the concept of a dead zone region, where voltage is constant, is introduced, and a suitable closure for the spatial extent of the dead zone is proposed and validated. The results from the reduced modeling framework are found to be in good agreement with those from the detailed simulations. The saturation voltage is found to depend significantly on the flame location relative to the electrodes, and on the sign of the voltage difference applied. Furthermore, at sub-saturation conditions, the current is shown to increase linearly or quadratically with the applied voltage, depending on the flame location. These limiting behaviors exhibited by the reduced model elucidate the features of i − V curves observed experimentally. The reduced model relies on the existence of a thin layer where charges are produced, corresponding to the reaction zone of a flame. Consequently, the analytical model we propose is not limited to the study of premixed flames, and may be applied easily to others configurations, e.g. nonpremixed counterflow flames.

Turbulence statistics from two three-dimensional direct numerical simulations of planar n -heptane/air turbulent jets are compared to assess the effect of the gas-phase species diffusion model on flame dynamics and soot formation. The Reynolds number based on the initial jet width and velocity is around 15, 000, corresponding to a Taylor scale Reynolds number in the range 100 ≤ Re λ ≤ 150. In one simulation, multicomponent transport based on a mixture-averaged approach is employed, while in the other the gas-phase species Lewis numbers are set equal to unity. The statistics of temperature and major species obtained with the mixture-averaged formulation are very similar to those in the unity Lewis number case. In both cases, the statistics of temperature are captured with remarkable accuracy by a laminar flamelet model with unity Lewis numbers. On the contrary, a flamelet with a mixture-averaged diffusion model, which corresponds to the model used in the multi-component diffusion three-dimensional DNS, produces significant differences with respect to the DNS results. The total mass of soot precursors decreases by 20–30% with the unity Lewis number approximation, and their distribution is more homogeneous in space and time. Due to the non-linearity of the soot growth rate with respect to the precursors’ concentration, the soot mass yield decreases by a factor of two. Being strongly affected by coagulation, soot number density is not altered significantly if the unity Lewis number model is used rather than the mixture-averaged diffusion. The dominant role of turbulent transport over differential diffusion effects is expected to become more pronounced for higher Reynolds numbers.

Summary The analysis of reactive systems in combustion science and technology relies on detailed models comprising many chemical reactions that describe the conversion of fuel and oxidizer into products and the formation of pollutants. Shock-tube experiments are a convenient setting for measuring the rate parameters of individual reactions. The temperature, pressure, and concentration of reactants are chosen to maximize the sensitivity of the measured quantities to the rate parameter of the target reaction. In this study, we optimize the experimental setup computationally by optimal experimental design in a Bayesian framework. We approximate the posterior probability density functions (pdf) using truncated Gaussian distributions in order to account for the bounded domain of the uniform prior pdf of the parameters. The underlying Gaussian distribution is obtained in the spirit of the Laplace method, more precisely, the mode is chosen as the maximum a posteriori (MAP) estimate, and the covariance is chosen as the negative inverse of the Hessian of the misfit function at the MAP estimate. The model related entities are obtained from a polynomial surrogate. The optimality, quantified by the information gain measures, can be estimated efficiently by a rejection sampling algorithm against the underlying Gaussian probability distribution, rather than against the true posterior. This approach offers a significant error reduction when the magnitude of the invariants of the posterior covariance are comparable with the size of the bounded domain of the prior. We demonstrate the accuracy and superior computational efficiency of our method for shock-tube experiments aiming to measure the model parameters of a key reaction, which is part of the complex kinetic network describing the hydrocarbon oxidation. In the experiments, the initial temperature and fuel concentration are optimized with respect to the expected information gain in the estimation of the parameters of the target reaction rate. We show that the expected information gain surface can change its “shape” dramatically according to the level of noise introduced into the synthetic data. The information that can be extracted from the data saturates as a logarithmic function of the number of experiments, and few experiments are needed when they are conducted at the optimal experimental design conditions. Furthermore, inversion of the legacy data indicates the validity and robustness of our designs. Copyright © 2016 John Wiley & Sons, Ltd.

The interaction between scales is investigated in a turbulent mixing layer. The large-scale amplitude modulation of the small scales already observed in other works depends on the crosswise location. Large-scale positive fluctuations correlate with a stronger activity of the small scales on the low speed-side of the mixing layer, and a reduced activity on the high speed-side. However, from physical considerations we would expect the scales to interact in a qualitatively similar way within the flow and across different turbulent flows. Therefore, instead of the large-scale fluctuations, the large-scale gradients modulation of the small scales has been additionally investigated. INTRODUCTION AND MOTIVATION In the present work the interaction between turbulence scales in a mixing layer is investigated at relatively high Reynolds number (1). The interaction between the large and the small scales has been the topic of several studies. Recent investigations showed that in a boundary layer the large scales of turbulence modulate the small-scale motions (2) (3). Close to the wall, large-scale positive fluctuations are associated with a stronger activity of the small-scale motions, whereas they are related with reduced small-scale activity in the outer region. The top-down interaction between large and small scales presents an important phase delay, and therefore it is not concurrent (4). These findings were based on time series from hot-wire anemometry. The interaction between scales was studied experimentally in a jet by Fiscaletti et al. (5), using hot-wire anemometry, and PIV. It was found that the small-scale signal is stronger in amplitude if it is conditioned on positive large-scale fluctuations. Surprisingly, the strength of the small-scale amplitude modulation in the spatial signal obtained with PIV was only 25% of the value obtained from the time signal from hot-wire anemometry. The elevated level of the amplitude modulation from hot-wire anemometry was attributed to the fixed spectral band filter used to obtain the large- and the small-scale signals, which does not consider the local convection velocity. Moreover, the inhomogeneous distribution of the structures of vorticity, and their preferential location in high velocity regions of the flow could explain the spatial amplitude modulation. Buxton & Ganapathisubramani (2014) (6) investigated experimentally the fully developed region of a mixing layer. They found that negative large-scale fluctuations coincide with regions characterized by a high amplitude of the small-scale signal. Large and small scales appear therefore to interact similarly to the outer region of the turbulent boundary layer. The work did not consider different crosswise locations within the mixing layer. Therefore, the first goal of the present study is the investigation of the interaction between the large and the small scales of turbulence at different crosswise locations in the mixing layer. A strong flow dependency with respect to the nature of the scale interaction, i.e. increased vs decreased small activity with positive large scale fluctuations, has been observed (Bandyopadhyay & Hussein 1984, (2)). In addition, the location within the same flow seems to affect large-scale amplitude modulation. On the other hand, this appears at conflict with the classical theories of turbulence, according to which the transfer of turbulent kinetic energy across the scales is a universal process. Then, we would expect the scale interactions to be qualitatively similar across flows. Recent findings have related the activity of the viscous scales to the large-scale shear layers within the flow ((7), (8)). Large-scale shear layers, characterized by strong velocity gradients are expected to play an important role in the cascade of turbulent kinetic energy. As a second goal of this work, we intend to examine possible interactions between the large-scale gradients (rather than the large-scale velocity used before) and the small scales of turbulence, by determining the correlation between the large-scale gradients and the local activity of the small scales (local enstrophy). METHODS

We investigate two methods to build a polynomial approximation of a model output depending on some parameters. The two approaches are based on pseudo-spectral projection (PSP) methods on adaptively constructed sparse grids, and aim at providing a finer control of the resolution along two distinct subsets of model parameters. The control of the error along different subsets of parameters may be needed for instance in the case of a model depending on uncertain parameters and deterministic design variables. We first consider a nested approach where an independent adaptive sparse grid PSP is performed along the first set of directions only, and at each point a sparse grid is constructed adaptively in the second set of directions. We then consider the application of aPSP in the space of all parameters, and introduce directional refinement criteria to provide a tighter control of the projection error along individual dimensions. Specifically, we use a Sobol decomposition of the projection surpluses to tune the sparse grid adaptation. The behavior and performance of the two approaches are compared for a simple two-dimensional test problem and for a shock-tube ignition model involving 22 uncertain parameters and 3 design parameters. The numerical experiments indicate that whereas both methods provide effective means for tuning the quality of the representation along distinct subsets of parameters, PSP in the global parameter space generally requires fewer model evaluations than the nested approach to achieve similar projection error. In addition, the global approach is better suited for generalization to more than two subsets of directions.

A steady, laminar stagnation flow configuration is adopted to investigate numerically the interaction between condensing aerosol particles and gas-phase transport across a canonical mixing layer. The mixing rates are varied by adjusting the velocity and length scales of the stagnation flow parametrically. The effect of mixing rates on particle concentration, polydispersity, and mean droplet diameter is explored and discussed. This numerical study reveals a complex response of the aerosol to varying flow times. Depending on the flow time, the variation of the particle concentration in response to varying mixing rates falls into one of the two regimes. For fast mixing rates, the number density and volume fraction of the condensing particles increase with residence time (nucleation regime). On the contrary, for low mixing rates, number density decreases with residence time and volume fraction reaches a plateau (condensation regime). It is shown that vapor scavenging by the aerosol phase is key to explaining the transition between these two regimes. The results reported here are general and illustrate genuine features of the evolution of aerosols forming by condensation of supersaturated vapor from heat and mass transport across mixing layers.

The effect of Damkohler number on turbulent nonpremixed sooting flames is investigated via large scale direct numerical simulation in three-dimensional n -heptane/air jet flames at a jet Reynolds number of 15,000 and at three different Damkohler numbers. A reduced chemical mechanism, which includes the soot precursor naphthalene, and a high-order method of moments are employed. At the highest Damkohler number, local extinction is negligible, while flames holes are observed in the two lowest Damkohler number cases. Compared to temperature and other species controlled by fuel oxidation chemistry, naphthalene is found to be affected more significantly by the Damkohler number. Consequently, the overall soot mass fraction decreases by more than one order of magnitude for a fourfold decrease of the Damkohler number. On the contrary, the overall number density of soot particles is approximately the same, but its distribution in mixture fraction space is different in the three cases. The total soot mass growth rate is found to be proportional to the Damkohler number. In the two lowest Da number cases, soot leakage across the flame is observed. Leveraging Lagrangian statistics, it is concluded that soot leakage is due to patches of soot that cross the stoichiometric surface through flame holes. These results show the leading order effects of turbulent mixing in controlling the dynamics of soot in turbulent flames.

A set of tribrachial flames of n-heptane/air is simulated with finite rate chemistry and detailed transport in a realistic laminar jet configuration for which experimental data are available. The flames differ by the temperature of the unburnt mixture and stabilization height, which controls the mixture fraction gradient ahead of the flame front. The simulations reproduce the lift-off heights in the experiments, showing that the flame stabilizes further downstream as the unburnt temperature decreases. For the lowest unburnt temperature, resulting in a weak mixture fraction gradient at the tribrachial point, positive stretch along the rich premixed wing leads to an increase in the rate of chemical reaction in the whole flame. The tribrachial flame burning velocity exceeds that in the unstretched, one-dimensional flame. For the highest temperature, the flame stabilizes closest to the nozzle. Large flame tilt, large mixture fraction gradient, and small radius of curvature lead to a reduction in the heat release rate and the flame propagates slower than its one-dimensional counterpart. The observed behavior is explained with a detailed analysis of the flame geometry, differential diffusion effects, flame stretch, and transport of heat and mass from the burnt gases to the flame front.

Cations and anions are formed as a result of chemi-ionization processes in combustion systems. Electric fields can be applied to reduce emissions and improve combustion efficiency by active control of the combustion process. Detailed flame ion chemistry models are needed to understand and predict the effect of external electric fields on combustion plasmas. In this work, a molecular beam mass spectrometer (MBMS) is utilized to measure ion concentration profiles in premixed methane-oxygen-argon burner-stabilized atmospheric flames. Lean and stoichiometric flames are considered to assess the dependence of ion chemistry on flame stoichiometry. Relative ion concentration profiles are compared with numerical simulations using various temperature profiles, and good qualitative agreement was observed for the stoichiometric flame. However, for the lean flame, numerical simulations misrepresent the spatial distribution of selected ions greatly. Three modifications are suggested to enhance the ion mechanism and improve the agreement between experiments and simulations. The first two modifications comprise the addition of anion detachment reactions to increase anion recombination at low temperatures. The third modification involves restoring a detachment reaction to its original irreversible form. To our knowledge, this work presents the first detailed measurements of cations and flame temperature in canonical methane-oxygen-argon atmospheric flat flames. The positive ion profiles reported here may be useful to validate and improve ion chemistry models for methane-oxygen flames.

External electric fields may reduce emissions and improve combustion efficiency by active control of combustion processes. In-depth, quantitative understanding of ion chemistry in flames enables predictive models to describe the effect of external electric fields on combustion plasma. This study presents detailed cation profile measurements in low-pressure, burner-stabilized, methane/oxygen/argon flames. A quadrupole molecular beam mass spectrometer (MBMS) coupled to a low-pressure ( P = 30 Torr) combustion chamber was utilized to measure ion signals as a function of height above the burner. Lean, stoichiometric and rich flames were examined to evaluate the dependence of ion chemistry on flame stoichiometry. Additionally, for the first time, cataloging of flame cations is performed using a high mass resolution time-of-flight mass spectrometer (TOF-MS) to distinguish ions with the same nominal mass. In the lean and stoichiometric flames, the dominant ions were H 3 O + , CH 3 O 2 + , C 2 H 7 O + , C 2 H 3 O + and CH 5 O + , whereas large signals were measured for H 3 O + , C 3 H 3 + and C 2 H 3 O + in the rich flame. The spatial distribution of cations was compared with results from numerical simulations constrained by thermocouple-measured flame temperatures. Across all flames, the predicted H 3 O + decay rate was noticeably faster than observed experimentally. Sensitivity analysis showed that the mole fraction of H 3 O + is most sensitive to the rate of chemi-ionization CH + O ↔ CHO + + E − . To our knowledge, this work represents the first detailed measurements of positive ions in canonical low-pressure methane flames.

The formation, growth, and transport of soot is investigated via large scale numerical simulation in a three-dimensional turbulent non-premixed n -heptane/air jet flame at a jet Reynolds number of 15,000. For the first time, a detailed chemical mechanism, which includes the soot precursor naphthalene and a high-order method of moments are employed in a three-dimensional simulation of a turbulent sooting flame. The results are used to discuss the interaction of turbulence, chemistry, and the formation of soot. Compared to temperature and other species controlled by oxidation chemistry, naphthalene is found to be affected more significantly by the scalar dissipation rate. While the mixture fraction and temperature fields show fairly smooth spatial and temporal variations, the sensitivity of naphthalene to turbulent mixing causes large inhomogeneities in the precursor fields, which in turn generate even stronger intermittency in the soot fields. A strong correlation is apparent between soot number density and the concentration of naphthalene. On the contrary, while soot mass fraction is usually large where naphthalene is present, pockets of fluid with large soot mass are also frequent in regions with very low naphthalene mass fraction values. From the analysis of Lagrangian statistics, it is shown that soot nucleates and grows mainly in a layer close to the flame and spreads on the rich side of the flame due to the fluctuating mixing field, resulting in more than half of the total soot mass being located at mixture fractions larger than 0.6. Only a small fraction of soot is transported towards the flame and is completely oxidized in the vicinity of the stoichiometric surface. These results show the leading order effects of turbulent mixing in controlling the dynamics of soot in turbulent flames. Finally, given the difficulties in obtaining quantitative data in experiments of turbulent sooting flames, this simulation provides valuable data to guide the development of models for Large Eddy Simulation and Reynolds Average Navier Stokes approaches.

The thin interface separating the inner turbulent region from the outer irrotational fluid is analysed in a direct numerical simulation of a spatially developing turbulent mixing layer. A vorticity threshold is defined to detect the interface separating the turbulent from the non-turbulent regions of the flow, and to calculate statistics conditioned on the distance from this interface. The conditional statistics for velocity are in remarkable agreement with the results for other free shear flows available in the literature, such as turbulent jets and wakes. In addition, an analysis of the passive scalar field in the vicinity of the interface is presented. It is shown that the scalar has a jump at the interface, even stronger than that observed for velocity. The strong jump for the scalar has been observed before in the case of high Schmidt number (Sc). In the present study, such a strong jump is observed for a scalar with Sc ≈ 1. Conditional statistics of kinetic energy and scalar dissipation are presente...

The effects of an electric field on the collision rates, energy exchanges and transport properties of electrons in premixed flames are investigated via solutions to the Boltzmann kinetic equation. The case of high electric field strength, which results in high-energy, non-thermal electrons, is analysed in detail at sub-breakdown conditions. The rates of inelastic collisions and the energy exchange between electrons and neutrals in the reaction zone of the flame are characterised quantitatively. The analysis includes attachment, ionisation, impact dissociation, and vibrational and electronic excitation processes. Our results suggest that Townsend breakdown occurs for E/N = 140 Td. Vibrational excitation is the dominant process up to breakdown, despite important rates of electronic excitation of CO, CO2 and N2 as well as impact dissociation of O2 being apparent from 50 Td onwards. Ohmic heating in the reaction zone is found to be negligible (less than 2% of peak heat release rate) up to breakdown field stre...

A Lagrangian particle scheme is applied to the solution of soot dynamics in turbulent nonpremixed flames. Soot particulate is described using a method of moments and the resulting set of continuum advection-reaction equations is solved using the Lagrangian particle scheme. The key property of the approach is the independence between advection, described by the movement of Lagrangian notional particles along pathlines, and internal aerosol processes, evolving on each notional particle via source terms. Consequently, the method overcomes the issues in Eulerian grid-based schemes for the advection of moments: errors in the advective fluxes pollute the moments compromising their realizability and the stiffness of source terms weakens the stability of the method. The proposed scheme exhibits superior properties with respect to conventional Eulerian schemes in terms of stability, accuracy, and grid convergence. Taking into account the quality of the solution, the Lagrangian approach can be computationally more economical than commonly used Eulerian schemes as it allows the resolution requirements dictated by the different physical phenomena to be independently optimized. Finally, the scheme posseses excellent scalability on massively parallel computers.

The scale dependence of the statistical alignment tendencies of the eigenvectors of the strain-rate tensor ei, with the vorticity vector ω, is examined in the self-preserving region of a planar turbulent mixing layer. Data from a direct numerical simulation are filtered at various length scales and the probability density functions of the magnitude of the are examined. It is observed that alignment cosines between the two unit vectors |ei·ω| the alignment tendencies are insensitive to the concurrent large-scale velocity fluctuations, but are quantitatively affected by the nature of the concurrent large-scale velocity-gradient fluctuations. It is confirmed that the small-scale (local) vorticity vector is preferentially aligned in parallel with the large-scale (background) extensive strain-rate eigenvector e1, in contrast to the global tendency for ω to be aligned in parallel with the intermediate strain-rate eigenvector [Hamlington et al., Phys. Fluids 20, 111703 (2008)]. When only data from regions of the flow that exhibit strong swirling are included, the so-called high-enstrophy worms, the alignment tendencies are exaggerated with respect to the global picture. These findings support the notion that the production of enstrophy, responsible for a net cascade of turbulent kinetic energy from large scales to small scales, is driven by vorticity stretching due to the preferential parallel alignment between ω and nonlocal e1 and that the strongly swirling worms are kinematically significant to this process.