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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 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.

This paper addresses a continuous-time continuous-space chance-constrained stochastic optimal control (SOC) problem via a Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE). Through Lagrangian relaxation, we convert the chance-constrained (risk-constrained) SOC problem to a risk-minimizing SOC problem, the cost function of which possesses the time-additive Bellman structure. We show that the risk-minimizing control synthesis is equivalent to solving an HJB PDE whose boundary condition can be tuned appropriately to achieve a desired level of safety. Furthermore, it is shown that the proposed risk-minimizing control problem can be viewed as a generalization of the problem of estimating the risk associated with a given control policy. Two numerical techniques are explored, namely the path integral and the finite difference method (FDM), to solve a class of risk-minimizing SOC problems whose associated HJB equation is linearizable via the Cole-Hopf transformation. Using a 2D robot navigation example, we validate the proposed control synthesis framework and compare the solutions obtained using path integral and FDM.

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...

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.

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...

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.

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.

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.

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.

Simulations of ion and electron transport in flames routinely adopt plasma fluid models, which require transport coefficients to compute the mass flux of charged species. In this work, the mobility and diffusion coefficient of thermal electrons in atmospheric premixed methane/air flames are calculated and analyzed. The electron mobility is highest in the unburnt region, decreasing more than threefold across the flame due to mixture composition effects related to the presence of water vapor. Mobility is found to be largely independent of equivalence ratio and approximately equal to 0.4 m 2 V −1 s −1 in the reaction zone and burnt region. The methodology and results presented enable accurate and computationally inexpensive calculations of transport properties of thermal electrons for use in numerical simulations of charged species transport in flames.

Homogeneous charge compression ignition (HCCI) engine technology promises to reduce NOx and soot emissions while achieving high thermal efficiency. Temperature and mixture stratification are regarded as effective means of controlling the start of combustion and reducing the abrupt pressure rise at high loads. Probability density function methods are currently being pursued as a viable approach to modeling the effects of turbulent mixing and mixture stratification on HCCI ignition. In this paper we present an assessment of the merits of three widely used mixing models in reproducing the moments of reactive scalars during the ignition of a lean hydrogen/air mixture ( Φ = 0.1 , p = 41 atm , and T = 1070 K ) under increasing temperature stratification and subject to decaying turbulence. The results from the solution of the evolution equation for a spatially homogeneous joint PDF of the reactive scalars are compared with available direct numerical simulation (DNS) data [E.R. Hawkes, R. Sankaran, P.P. Pebay, J.H. Chen, Combust. Flame 145 (1–2) (2006) 145–159]. The mixing models are found able to quantitatively reproduce the time history of the heat release rate, first and second moments of temperature, and hydroxyl radical mass fraction from the DNS results. Most importantly, the dependence of the heat release rate on the extent of the initial temperature stratification in the charge is also well captured.

Uncertainty quantification (UQ) methods are implemented to obtain a quantitative characterization of the evolution of electrons and ions during the ignition of methane–oxygen mixtures under lean and stoichiometric conditions. The GRI-Mech 3.0 mechanism is combined with an extensive set of ion chemistry pathways and the forward propagation of uncertainty from model parameters to observables is performed using response surfaces. The UQ analysis considers 22 uncertain rate parameters, which include both chemi-ionization, proton transfer, and electron attachment reactions as well as neutral reactions pertaining to the chemistry of the CH radical. The uncertainty ranges for each rate parameter are discussed. Our results indicate that the uncertainty in the time evolution of the electron number density is due mostly to the chemi-ionization reaction CH + O ⇌ HCO+ + E− and to the main CH consumption reaction CH + O2 ⇌ O + HCO. Similar conclusions hold for the hydronium ion H3O+, since electrons and H3O+ account for more than 99% of the total negative and positive charge density, respectively. Surprisingly, the statistics of the number density of charged species show very little sensitivity to the uncertainty in the rate of the recombination reaction H3O+ + E− → products, until very late in the decay process, when the electron number density has fallen below 20% of its peak value. Finally, uncertainties in the secondary reactions within networks leading to the formation of minor ions (e.g., C2H3O+, HCO+, OH−, and O−) do not play any role in controlling the mean and variance of electrons and H3O+, but do affect the statistics of the minor ions significantly. The observed trends point to the role of key neutral reactions in controlling the mean and variance of the charged species number density in an indirect fashion. Furthermore, total sensitivity indices provide quantitative metrics to focus future efforts aiming at improving the rates of key reactions responsible for the formation of charges during hydrocarbon combustion. Accepted version

This research was funded by King Abdullah University of Science and Technology (KAUST) and made use of the computational resources managed by KAUST Supercomputing Lab (KSL).

Combustion of fossil fuels is likely to continue for the near future due to the growing trends in energy consumption worldwide. The increase in efficiency and the reduction of pollutant emissions from combustion devices are pivotal to achieving meaningful levels of carbon abatement as part of the ongoing climate change efforts. Computational fluid dynamics featuring adequate combustion models will play an increasingly important role in the design of more efficient and cleaner industrial burners, internal combustion engines, and combustors for stationary power generation and aircraft propulsion. Today, turbulent combustion modelling is hindered severely by the lack of data that are accurate and sufficiently complete to assess and remedy model deficiencies effectively. In particular, the formation of pollutants is a complex, nonlinear and multi-scale process characterized by the interaction of molecular and turbulent mixing with a multitude of chemical reactions with disparate time scales. The use of direct numerical simulation (DNS) featuring a state of the art description of the underlying chemistry and physical processes has contributed greatly to combustion model development in recent years. In this paper, the analysis of the intricate evolution of soot formation in turbulent flames demonstrates how DNS databases are used to illuminate relevant physico-chemical mechanisms and to identify modelling needs.

The counterflow configuration is a canonical stagnation flow, featuring two opposed impinging round jets and a mixing layer across the stagnation plane. Although counterflows are used extensively in the study of reactive mixtures and other applications where mixing of two streams is required, quantitative data on the scaling properties of the flow field are lacking. The aim of this work is to characterize the velocity and mixing fields in isothermal counterflows over a wide range of conditions. The study features both experimental data from particle image velocimetry and results from detailed axisymmetric simulations. The scaling laws for the nondimensional velocity and mixture fraction are obtained as a function of an appropriate Reynolds number and the ratio of the separation distance of the nozzles to their diameter. In the range of flow configurations investigated, the nondimensional fields are found to depend primarily on the separation ratio and, to a lesser extent, the Reynolds number. The marked d...

The turbulent flow originating downstream of the Kelvin-Helmholtz instability in a mixing layer has great relevance in many applications, ranging from atmospheric physics to combustion in technical devices. The mixing of a substance by the turbulent velocity field is usually involved. In this paper, a detailed statistical analysis of fluctuations of a passive scalar in the fully developed region of a turbulent mixing layer from a direct numerical simulation is presented. Passive scalar spectra show inertial ranges characterized by scaling exponents $\ensuremath{-}4/3$ and $\ensuremath{-}3/2$ in the streamwise and spanwise directions, in agreement with a recent theoretical analysis of passive scalar scaling in shear flows [Celani et al., J. Fluid Mech. 523, 99 (2005)]. Scaling exponents of high-order structure functions in the streamwise direction show saturation of intermittency with an asymptotic exponent ${\ensuremath{\zeta}}_{\ensuremath{\infty}}=0.4$ at large orders. Saturation of intermittency is confirmed by the self-similarity of the tails of the probability density functions of the scalar increments at different scales $r$ with the scaling factor ${r}^{\ensuremath{-}{\ensuremath{\zeta}}_{\ensuremath{\infty}}}$ and by the analysis of the cumulative probability of large fluctuations. Conversely, intermittency saturation is not observed for the spanwise increments and the relative scaling exponents agree with recent results for homogeneous isotropic turbulence with mean scalar gradient. Probability density functions of the scalar increments in the three directions are compared to assess anisotropy.

A Direct Numerical Simulation (DNS) of soot formation in an n-heptane/air turbulent nonpremixed flame has been performed to investigate unsteady strain effects on soot growth and transport. For the first time in a DNS of turbulent combustion, Polycyclic Aromatic Hydrocarbons (PAH) are included via a validated, reduced chemical mechanism. A novel statistical representation of soot aggregates based on the Hybrid Method of Moments is used [M.E. Mueller, G. Blanquart, H. Pitsch, Combust. Flame 156 (2009) 1143–1155], which allows for an accurate state-of-the-art description of soot number density, volume fraction, and morphology of the aggregates. In agreement with previous experimental studies in laminar flames, Damkohler number effects are found to be significant for PAH. Soot nucleation and growth from PAH are locally inhibited by high scalar dissipation rate, thus providing a possible explanation for the experimentally observed reduction of soot yields at increasing levels of mixing in turbulent sooting flames. Furthermore, our data indicate that soot growth models that rely on smaller hydrocarbon species such as acetylene as a proxy for large PAH molecules ignore or misrepresent the effects of turbulent mixing and hydrodynamic strain on soot formation due to differences in the species Damkohler number. Upon formation on the rich side of the flame, soot is displaced relative to curved mixture fraction iso-surfaces due to differential diffusion effects between soot and the gas-phase. Soot traveling towards the flame is oxidized, and aggregates displaced away from the flame grow primarily by condensation of PAH on the particle surface. In contrast to previous DNS studies based on simplified soot and chemistry models, surface reactions are found to contribute barely to the growth of soot, for nucleation and condensation processes occurring in the fuel stream are responsible for the most of soot mass generation. Furthermore, the morphology of the soot aggregates is found to depend on the location of soot in mixture fraction space. Aggregates having the largest primary particles populate the region closest to the location of peak soot growth. On the contrary, the aggregates with the largest number of primary particles are located much further into the fuel stream.

A large-scale simulation of aerosol nucleation and growth in a turbulent mixing layer is performed and analyzed with the aim of elucidating the key processes involved. A cold gaseous stream is mixed with a hot stream of vapor, nanometer sized droplets nucleate as the vapor becomes supersaturated, and subsequently grow as more vapor condenses on their surface. All length and time scales of fluid motion and mixing are resolved and the quadrature method of moments is used to describe the dynamics of the condensing, non-inertial droplets. The results show that a region of high nucleation rate is located near the cold, dry stream, while particles undergo intense growth via condensation on the hot, humid vapor side. Supersaturation and residence times are such that number densities are low and neither coagulation nor vapor scavenging due to condensation are significant. The difference in Schmidt numbers of aerosol particles (approximated as infinity) and temperature and vapor (near unity) causes a drift of the aerosol particles in scalar space and contributes to a large scatter in the conditional statistics of aerosol quantities. The spatial distribution of the aerosol reveals high volume fraction on the hot side of the mixing layer. This distribution is due to drift against the mean and is related to turbulent mixing, which displaces particles from the nucleation region (cold side) into the growth region (hot side). Such a mechanism is absent in laminar flows and is a distinct feature of turbulent condensing aerosols.

The turbulent flow originating from the interaction between two parallel streams with different velocities is studied by means of direct numerical simulation. Rather than the more common temporal evolving layer, a spatially evolving configuration, with perturbed laminar inlet conditions is considered. The streamwise evolution and the self-similar state of turbulence statistics are reported and compared to results available in the literature. The characteristics of the transitional region agree with those observed in other simulations and experiments of mixing layers originating from laminar inlets. The present results indicate that the transitional region depends strongly on the inlet flow. Conversely, the self-similar state of turbulent kinetic energy and dissipation agrees quantitatively with those in a temporal mixing layer developing from turbulent initial conditions [M. M. Rogers and R. D. Moser, “Direct simulation of a self-similar turbulent mixing layer,” Phys. Fluids 6, 903 (1994)]. The statistical features of turbulence in the self-similar region have been analysed in terms of longitudinal velocity structure functions, and scaling exponents are estimated by applying the extended self-similarity concept. In the small scale range (60 400), the mean shear and large coherent structures result in a significant deviation from predictions based on homogeneous isotropic turbulence theory. In this second scaling range, the numerical values of the exponents agree quantitatively with those reported for a variety of other flows characterized by strong shear, such as boundary layers, as well as channel and wake flows.

A highly resolved Direct Numerical Simulation of a spatially developing turbulent mixing layer is presented. In the fully developed region, the flow achieves a turbulent Reynolds number Reλ = 250, high enough for a clear separation between large and dissipative scales, so for the presence of an inertial range. Structure functions have been calculated in the self-similar region using velocity time series and Taylor's frozen turbulence hypothesis. The Extended Self-Similarity (ESS) concept has been employed to evaluate relative scaling exponents. A wide range of scales with scaling exponents and intermittency levels equal to homogeneous isotropic turbulence has been identified. Moreover an additional scaling range exists for larger scales; it is characterized by smaller exponents, similar to the values reported in the literature for flows with strong shear.

Combustion theory and modelling 22(3), 480 - 504 (2018). doi:10.1080/13647830.2018.1424353, Published by Taylor and Francis, London

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.

The intricate nature of detailed kinetic mechanisms for plasma-assisted combustion motivates the development of high-fidelity surrogates to simplify their use in extensive numerical simulations. This chapter presents a machine-learning approach based on the coupling of Principal Component Analysis (PCA) with Gaussian Process Regression (GPR) to produce a reliable reduced-order representation of the detailed plasma-combustion physics. The entire state-space is expressed in function of a selected number of principal components using a non-linear Gaussian regression model. This machine-learning framework allows for a superior dimensionality compression compared to conventional data-driven reduction strategies based solely on principal component analysis. The performance of the present technique is assessed for the simulation of ethylene-air ignition by nanosecond repetitive pulsed discharges.