Search

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.

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.

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.

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.

Recent research efforts have focused on the usage of lean hydrogen–air mixtures in Homogeneous Charge Compression Ignition (HCCI) engines. In this work we investigate the effect of temperature stratification on the occurrence of differential diffusion during the autoignition of a lean premixed hydrogen–air mixture at high pressure, constant volume conditions. We employ a Direct Numerical Simulation methodology including hydrogen–air finite-rate chemistry and molecular transport based on a Lewis number formulation for individual species [E.R. Hawkes, R. Sankaran, P.P. Pebay, J.H. Chen, Combust. Flame 145 (1–2) (2006) 145–159]. At the highest level of temperature stratification tested, we find that differential diffusion has an impact on the heat release rate. Early in the ignition, regions with mixture fraction higher than the initial value are created by differential diffusion and they subsequently burn to achieve higher temperatures, which can be accounted for by simple equilibrium calculations. Later in the ignition process, differential diffusion enhances heat release rate along positively stretched fronts and reduces it for negatively stretched regions. Finally, it is found that mixture fraction is not a conserved scalar due to differential diffusion.