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It is well known that Navier-Stokes equations are not valid for those high-Knudsen and high-Mach flows, in which the local thermodynamically non-equilibrium effects are dominant. To extend the non-equilibrium describing the ability of macroscopic equations, Nonlinear Coupled Constitutive Relation (NCCR) model was developed from Eu’s generalized hydrodynamic equations to substitute linear Newton’s law of viscosity and Fourier’s law of heat conduction in conservation laws. In the NCCR model, how to solve the decomposed constitutive equations with reasonable computational cost is a key ingredient of this scheme. In this paper, an analytic method is proposed firstly. Compared to the iterative procedure in the conventional NCCR model, the analytic method not only obtains exact roots of the decomposed constitutive polynomials, but also preserves the nonlinear constitutive relations in the original framework of NCCR methods. Numerical tests to assess the efficiency and accuracy of the proposed method are conducted for argon shock structures, Couette flows, two-dimensional hypersonic flows over a cylinder and three-dimensional supersonic flows over a three-dimensional sphere. These superior advantages of the current method are expected to render itself a powerful tool for simulating the hypersonic rarefied flows and microscale flows of high Knudsen number for engineering applications.

Understanding and characterizing ignition of flammable mixtures by hot particles is important for assessing and reducing the risk of accidental ignition and explosion in industry and aviation. Recently, many studies have been conducted for ignition of gaseous mixtures by hot particles. However, the effects of low-temperature chemistry (LTC) on ignition by hot particles received little attention. LTC plays an important role in the ignition of most hydrocarbon fuels and may induce cool flames. The present study aims to numerically assess the effects of LTC on ignition by the hot particles. We consider the transient ignition processes induced by a hot spherical particle in quiescent and flowing stoichiometric dimethyl ether/air mixtures. 1D and 2D simulations, respectively, are conducted for the ignition process by hot-particles in quiescent and flowing mixtures. A detailed kinetic model including both LTC and high-temperature chemistry (HTC) is used in simulations. The results exhibit a premixed cool flame to be first initiated by the hot particle. Then a double-flame structure with both premixed cool and hot flames is observed at certain conditions. At zero or low inlet flow velocities, the hot flame catches up and merges with the leading cool flame. At high inlet flow velocities, the hot flame cannot be initiated due to the short residence time and large convective loss of heat and radicals. Comparing the results with and without considering LTC confirms that LTC accelerates substantially ignition via HTC in a certain range of hot particle temperatures. The mechanism of ignition promotion by LTC is interpreted by analyzing the radical pool produced by the LTC and HTC surrounding the hot particle. Moreover, the influence of inlet flow velocity on ignition by hot particles is assessed. Non-monotonic change of ignition delay time with flow velocity is observed and discussed.

In this work, oblique detonation of n-heptane/air mixture in high-speed wedge flows is simulated by solving the reactive Euler equations with a two-dimensional (2D) configuration. This is a first attempt to model complicated hydrocarbon fuel ODWs with a detailed chemistry (44 species and 112 reactions). Effects of freestream equivalence ratios and velocities are considered, and the abrupt and smooth transition from oblique shock to detonation are predicted. Ignition limit, ODW characteristics, and predictability of the transition mode are discussed. Firstly, homogeneous constant-volume ignition calculations are performed for both fuel-lean and stoichiometric mixtures. The results show that the ignition delay generally increases with the wedge angle. However, a negative wedge angle dependence is observed, due to the negative temperature coefficient effects. The wedge angle range for successful ignition of n-heptane/air mixtures decreases when the wedge length is reduced. From 2D simulations of stationary ODWs, the initiation length generally decreases with the freestream equivalence ratio, but the transition length exhibits weakly non-monotonic dependence. Smooth ODW typically occurs for lean conditions (equivalence ratio < 0.4). The interactions between shock / compression waves and chemical reaction inside the induction zone are also studied with the chemical explosive mode analysis. Moreover, the predictability of the shock-to-detonation transition mode is explored through quantifying the relation between ignition delay and chemical excitation time. It is demonstrated that the ignition delay (excitation time) increases (decreases) with the freestream equivalence ratio for the three studied oncoming flow velocities. Smaller excitation time corresponds to stronger pressure waves from the ignition location behind OSW.

The present work investigates forced ignition and oscillating propagation of spray flame in a mixture of fine ethanol droplets and air. Eulerian-Eulerian method with two-way coupling is used and detailed chemical mechanism is considered. Different droplet diameters and liquid fuel equivalence ratios (ER) are studied. The evaporation completion front (ECF) is defined to study the interactions between the evaporation zone and flame front. The gas composition at the flame front is quantified through an effective ER. The results show that the kernel trajectory is considerably affected by droplet size and liquid ER. Generally, the flame ER reaches the maximum when the ECF start to move from the spherical center. It gradually decreases and reaches a constant value when the flame freely propagates. Quasi-stationary spherical flame is observed when the liquid ER is low, whilst kernel extinction/re-ignition appears when liquid ER is high. These flame behaviors are essentially affected by the heat conduction and species diffusion timescales between the droplet evaporation zone and flame front. The dependence of the minimum ignition energy (MIE) on liquid ER is U-shaped and there is an optimal liquid equivalence ratio range (ERo) with the smallest MIE. Long and short ignition failure modes are observed, respectively for small and large liquid ERs. When liquid ER is less than ERo (long failure mode), larger energy is required to initiate the kernel due to very lean composition near the spark. For liquid ER larger than ERo (short mode), ignition failure is caused by strong evaporative heat loss and rich gas composition due to heavy droplet loading.

The interactions between an incident shock and a moderately dense particle curtain are simulated with the Eulerian–Lagrangian method. A customized solver based on OpenFOAM is extended with an improved drag model and collision model and then validated against two benchmark experiments. The results show that the collision model has a limited impact on curtain morphology compared with the improved drag model. In this work, parametric studies are performed considering different particle sizes, volume fractions, and curtain thicknesses. Smaller particle sizes and larger volume fractions lead to stronger reflected shock and weaker transmitted shock. Attention is paid to the particle collision effects on the curtain evolution behaviors. According to our results, for the mono-dispersed particle curtain, the collision effects on curtain front behaviors are small, even when the initial particle volume fraction is as high as 20%. This is due to the positive velocity gradient across the curtain after the shock wave passage, leading to the faster motion of downstream particles than the upstream ones, and hence, no collision occurs. For the bi-dispersed particle curtain, the collision effects become important in the mixing region of different-size particles. Collisions decelerate small particles while accelerating large ones and cause velocity scattering. Moreover, increasing the bi-dispersed curtain thickness leads to multiple collision force peaks, which is the result of the delayed separation of different particle groups. Our results indicate that the collision model may be unnecessary to predict curtain fronts in mono-dispersed particles, but in bi-dispersed particles, the collision effects are important and, therefore, must be modeled.

In this study, we develop a simplified theoretical model for flame initiation, propagation and extinction in premixed gas mixture containing water droplets, by considering water droplet evaporation in pre-flame or/and post-flame zones. The Eulerian droplet model with simplified evaporation sub-model is employed, while for gas phase the assumptions of constant-density, quasi-steady and large activation energy are made. Analytical correlations describing different flame regimes and transitions among flame balls, propagating spherical flames and planar flames are then derived to investigate the spherical flame initiation, propagation and extinction, with emphasis on the effects of water droplet evaporation on spherical flames at different Lewis numbers. Five different flame regimes are observed and discussed for droplets evaporation in pre-flame or/and post-flame zones. It is found that the droplets with larger heat exchange coefficient are more effective in reducing flame propagation speed and temperature but increasing the vaporization front. Moreover, the cooling effect of evaporation heat loss plays an important role on flame regimes and their transitions. At the relatively large heat exchange coefficient, the total evaporation heat loss from pre-flame and post-flame zones reaches its maximum at an intermediate flame radius. The cooling effect is strong enough to quench the flame and results in the self-extinguishing flame. In addition, the combined effects of stretch rate and Lewis number compete with the evaporation heat loss from droplet evaporation. For small Lewis number, the flammability limits can be achieved through self-extinguishing flames, whereas for large Lewis number the flames approach their flammability limits in their evolution into planar flames. For ignition of spherical flames, if the droplet-laden mixture is intrinsically non-flammable, although a propagating flame kernel can be initiated, however it would still be quenched due to evaporation heat loss at a critical radius. The minimum ignition energy increases with heat exchange coefficient and Lewis number.

Dynamics of ethylene autoignition and deflagration-to-detonation transition (DDT) are first numerically investigated in a one-dimensional shock tube using a reduced chemistry including 10 species and 10 reactions. Different combustion modes are investigated through considering various premixed gas equivalence ratios (0.2 [Formula: see text] 2.0) and incident shock wave Mach numbers (1.8[Formula: see text]3.2). Four ignition and DDT modes are observed from the studied cases, i.e., no ignition, deflagration combustion, detonation after reflected shock, and deflagration behind the incident shock. For detonation development behind the reflected shock, three autoignition hot spots are formed. The first one occurs at the wall surface after the re-compression of the reflected shock and contact surface, which further develops to a reaction shock because of “the explosion in the explosion” regime. The other two are off the wall, respectively, caused by the reflected shock/rarefaction wave interaction and reaction induction in the compressed mixture. The last hot spot develops to a reaction wave and couples with the reflected shock after a DDT process, which eventually leads to detonation combustion. For deflagration development behind the reflected shock, the wave interactions, wall surface autoignition hot spot as well as its induction of reaction shock are qualitatively similar to the mode of detonation after incident shock reflection, before the reflected shock/rarefaction wave collision point. However, only one hot spot is induced after the collision, which also develops to a reaction wave but cannot catch up with the reflected shock. For deflagration behind the incident shock, deflagration combustion is induced by the incident shock compression whereas detonation occurs after the shock reflection. The chemical timescale increases after the reflected shock/contact surface collision, whereas decreases behind the incident and reflected shocks, as well as after the reflected shock/rarefaction wave interaction. Therefore, mixture reactivity behind the reflected shock is weakened by the contact surface, but is intensified by the rarefaction wave. The multi-dimensionality characteristics, including reflected shock/boundary layer interactions, reflected shock bifurcation, destabilization, and detonation, are further present in a two-dimensional configuration. Planar autoignition occurs because of reflected shock compression and detonation combustion is formed first in the central region due to the collision of the reflected shock wave/reflected compression wave. The left and right bifurcations of the separation region in the wall boundary layer are then sequentially ignited.

Effects of low-temperature chemistry induced by ultrafine water droplet evaporation on reaction front development from an ignition spot with temperature gradient are studied in this work. The Eulerian-Eulerian method is used to simulate the gas-liquid two-phase reactive flows and the physical model is one-dimensional spherical reactor with stoichiometric gaseous n-heptane/air mixture and ultrafine monodisperse water droplets (initial diameter 5 micrometres). Homogeneous ignitions of two-phase mixtures are first simulated. The water droplets can complete evaporation in the reactor prior to ignition, and hence pronouncedly reduce gas temperature, which may induce the low-chemistry reactions. It is found that the turnover temperature for negative temperature coefficient range increases with droplet volume fraction. Three-stage ignitions are present when the volume fraction is beyond a critical value, i.e., low-temperature, intermediate-temperature, and high-temperature ignitions. The chemical explosive mode analysis also confirms the low-chemistry reactions induced by the evaporation of ultrafine water droplets. Then reaction front development from an ignition spot with temperature gradient in two-phase mixtures is analysed based on one-dimensional simulations. Different modes for reaction front origin in the spot are identified, based on the initial gas temperature and lower turnover temperature. Specifically, the reaction front can be initiated at the left and right ends of the ignition spot, and inside it. Detailed reaction front developments corresponding to the above three modes are discussed. Besides, the pressure wave from high-temperature ignition is important, compared to those from low- and intermediate-chemistries.

Two-dimensional numerical simulations with Eulerian-Lagrangian method are conducted to study propagation and extinction of stoichiometric hydrogen/air detonations in fine water sprays. Parameterized by water mass loading and initial droplet size, a detonation extinction map is developed. Detonation extinction would occur with larger mass loading and/or smaller droplet size. General features of gas phase and water droplets and local detonation frontal structures are well captured. Numerical soot foils are used to characterize the influence of mass loading and droplet size on the detonation wave. The results also show that the detonation cell size increases with increased mass loading or decreased droplet size. Analysis on unsteady detonation extinction process is performed with the evolutions of detonation frontal structure, spatial distribution of thermochemical variables and interphase transfer rates (mass, energy, and momentum). Moreover, the chemical explosive mode analysis reveals that for stable detonation, thermal runaway dominates behind the Mach stem, while chemical propensities of auto-ignition and thermal runaway appear alternately behind the incident wave. When the induction zone length increases as the reaction front (RF) and shock front (SF) are decoupled, localized burned pockets surrounded by the autoignition chemical explosive mode can be observed. In addition, the interactions between detonation wave and water droplets demonstrate that the energy and momentum transfer have more direct interaction with SF and RF than the mass transfer. The interphase transfer rates increase with the water mass loading. Under the same mass loading, the smaller the droplet size, the larger the interphase transfer rates. However, the size of fine water droplets has a limited influence on the interphase momentum exchange.

A trapped vortex cavity with a radial V-gutter flameholder is adopted to expand the flame stability of an augmentor. The improvement of flame stabilization limits is achieved experimentally by replacing the traditional slotted air-jet with the discrete-hole air-jet. The atomization characteristics of the air-assisted multi-point injector and the numerical fluid-structure are conducted to explain the results. Results indicate that a remarkable enhancement of the flame stability with discrete-hole air-jet is obtained in all conditions, while the slotted air-jet for the cavity leads to a failed ignition at 343 K except for the Mach number of 0.3. As the same passing area of the air-jet, the larger the aperture of the discrete hole, the better the flame stabilization performance. An increasing trend of lean blowout equivalence ratio is contributed by the increased Mach number. Whereas, the Mach number growth will lead to a reduction of lean ignition equivalence ratio at 343 K and 473 K, and a downward parabola is observed at 573 K. Eventually, the optimal flame stability performance is achieved in by the larger discrete space distance, which promotes the fuel/air mixture with the help of the recirculation zones between discrete holes.

One-dimensional numerical simulations based on hybrid Eulerian-Lagrangian approach are performed to investigate the interactions between propagating shock waves and dispersed evaporating water droplets in two-phase gas-droplet flows. Two-way coupling for interphase exchanges of mass, momentum and energy is adopted. Parametric study on shock attenuation, droplet evaporation, motion and heating is conducted, through considering various initial droplet diameters (5-20 {\mu}m), number densities (2.5 x 1011 - 2 x 1012 1/m3) and incident shock Mach numbers (1.17-1.9). It is found that the leading shock may be attenuated to sonic wave and even subsonic wave when droplet volume fraction is large and/or incident shock Mach number is low. Attenuation in both strength and propagation speed of the leading shock is mainly caused by momentum transfer to the droplets that interact at the shock front. Total pressure recovery is observed in the evaporation region, whereas pressure loss results from shock compression, droplet drag and pressure gradient force behind the shock front. Recompression of the region between the leading shock and two-phase contact surface is observed when the following compression wave is supersonic. After a critical point, this region gets stable in width and interphase exchanges in mass, momentum, and energy. However, the recompression phenomenon is sensitive to droplet volume fraction and may vanish with high droplet loading. For an incident shock Mach number of 1.6, recompression only occurs when the initial droplet volume fraction is below 3.28 x 10-5.

Propagation of weakly stretched spherical flames in partially pre-vaporized fuel sprays is theoretically investigated in this work. A general theory is developed to describe flame propagation speed, flame temperature, droplet evaporation onset and completion locations. The influences of liquid fuel and gas mixture properties on spherical spray flame propagation are studied. The results indicate that the spray flame propagation speed is enhanced with increased droplet mass loading and/or evaporation heat exchange coefficient (or evaporation rate). Opposite trends are found when the latent heat is high, due to strong evaporation heat absorption. Fuel vapor and temperature gradients are observed in the post-flame evaporation zone of heterogeneous flames. Evaporation completion front location considerably changes with flame radius, but the evaporation onset location varies little relative to the flame front when the flame propagates. For larger droplet loading and smaller evaporation rate, the fuel droplet tends to complete evaporation behind the flame front. Flame bifurcation occurs with high droplet mass loading under large latent heat, leading to multiplicity of flame propagation speed, droplet evaporation onset and completion fronts. The flame enhancement or weakening effects by the fuel droplet sprays are revealed by enhanced or suppressed heat and mass diffusion process in the pre-flame zone. Besides, for heterogeneous flames, heat and mass diffusion in the post-flame zone also exists. The mass diffusion for both homogeneous and heterogeneous flames is enhanced with decreased Lewis number. The magnitude of Markstein length is considerably reduced with increased droplet loading. Moreover, post-flame droplet burning behind heterogeneous flame influences the flame propagation speed and Markstein length when the liquid fuel loading is relatively low.

The Large Eddy Simulation (LES) and three dimensional CMC (3D-CMC) model are applied to simulate the Sydney swirl-stabilized non-premixed methane flames with different levels of local extinction. The CMC model is implemented with a finite volume formulation, unstructured mesh and detailed chemistry. The statistics of velocity, mixture fraction, and major species mass fractions in both physical and mixture fraction space demonstrate very good agreement with the measured results. The level of local extinction with increased fuel bulk velocity velocities is reasonably captured. In addition, the location where flame extinction first occurs also agrees with the experimental observations. However, the statistics of the hydroxyl mass fraction, a very sensitive indicator of local extinction, have some differences from the experimental data. Budget analysis of individual terms in the CMC equation for the hydroxyl mass fraction shows that conditional convection in the CMC model has a significant role in inducing both local extinction and re-ignition events. The conditional dilatation flux contributes only when the local heat release rate is significant.

Propagation of one-dimensional planar flames laden with fuel droplets is theoretically investigated in this work. Localized homogeneous and heterogeneous flames are considered, characterized by different relative locations of dispersed droplets and propagating flame front. With the assumption of large activation energy for the chemical reaction, correlations describing flame propagation speed, flame temperature, evaporation onset front and completion front are derived. The influences of droplet and fuel properties on propagation of fuel-droplet-laden planar flames are studied. The results indicate that the flames are enhanced under fuel-lean conditions but weakened under fuel-rich conditions. Both effects are intensified with increased droplet mass loading. Fuel vapor and temperature gradient are observed in the post-flame evaporation zone of heterogeneous flames. Evaporation completion front location is considerably affected by the droplet diameter, but the evaporation onset front varies little with droplet properties. Flame bifurcation occurs with high droplet mass loading under fuel-rich mixture, leading to multiplicity of flame propagation speed as well as droplet evaporation onset and completion fronts. Sprayed fuels with larger latent heat of vaporization would weaken the flame enhancement effect under fuel-lean conditions, due to larger evaporation heat loss. Moreover, for homogeneous flames, evaporative heat loss only occurs in the pre-flame zone. However, for heterogeneous flames, heat loss from the post-flame evaporation zone becomes dominant for relatively large droplets. Besides, for fuel-lean mixtures laden with medium-sized fuel droplets, the propagation speed of heterogeneous flames increases with Lewis number, due to the enhanced fuel vapor diffusion in the post-flame zone.

The Multiple Mapping Conditioning/Large Eddy Simulation (MMC-LES) model is extended for the first time to high-speed, compressible flow conditions and validated against non-reacting and reacting experimental data from a model supersonic combustor. The MMC-LES method solves the subgrid joint composition filtered density function through a Monte Carlo approach, and it permits a low-cost numerical implementation using a sparse distribution of stochastic Lagrangian particles. The sensitivity of results to the particle resolution is examined, and similar to past low-speed applications of MMC-LES, that sensitivity is found to be low. In comparison to the model equations for subsonic turbulent combustion conditions, the pressure work and viscous heating effects have been incorporated here to account for the effects of compressibility. As expected, the viscous heating effects are small for this flow case and can be ignored, while the pressure work is not negligible and makes a significant contribution at expansion fans and shock fronts where the magnitude of the pressure derivative term in non-reacting/reacting cases is as much as 23.8%/24.5% and 19.2%/18.6% of the stochastic particle standardized enthalpy, respectively. The MMC-LES predictions show good quantitative agreement with the available experimental data for the mean and root-mean-square of axial velocity, mean temperature, and wall pressure. Good qualitative comparison to the data is also observed for major flow characteristics, including location and size of shocks, expansion fans, and recirculation zone, and combustion characteristics such as flame lift-off distance. Although the effects of the pressure work on the mean flame lift-off distance are negligible, they have a significant influence on the predicted spatial fluctuations of the flame base.

The outwardly propagating spherical flames in premixed gas containing water droplets are theoretically studied in this work. The correlations between the flame propagation speed, droplet distribution and flame radius are derived, based on the large activation energy and quasi-planar flame assumptions. With this, flame bifurcation and multiplicity are analysed, focusing on the effects of initial droplet mass loading, evaporative heat loss and Lewis number. Meanwhile, the model can predict different gaseous flame types and liquid droplet distributions, as well as the bifurcations and transitions between them. It is shown that the spherical flame propagation is strongly affected by water droplet properties. When initial loading and/or heat loss coefficient are small, there is only one normal stable flame. Two stable flames arise when they increase, i.e. normal and weak flames. Increased droplet loading mainly affects the weak flame, resulting in decreased propagation speed, increased values of evaporation onset and completion fronts. However, increased heat loss affects both normal and weak flames, and flame bifurcation is observed for large heat loss. Droplet properties also greatly influence the weak flame transition between different regimes. Our results also show that Lewis number has significant influence on droplet-laden spherical flame propagation, in terms of flame bifurcation and regime transition. The Lewis number would affect the flame propagation jointly with the positive stretch rate and/or the evolving temperature gradients near the flame front through the interactions with the dispersed evaporating droplets. Furthermore, the magnitudes of Markstein length of the normal flames decrease when Lewis number approaches unity. However, those of the weak flames are mostly negative, indicating the enhancement over the shown Lewis number range. The larger magnitudes of Markstein length of weak flames show stronger sensitivity to stretch than those of normal flames. Finally, different flame types seen from our theoretical analysis are summarised.

The Large Eddy Simulation (LES) / Conditional Moment Closure (CMC) model with detailed chemistry is used for modelling spark ignition and flame propagation in a turbulent methane jet in ambient air. Two centerline and one off-axis ignition locations are simulated. We focus on predicting the flame kernel formation, flame edge propagation and stabilization. The current LES/CMC computations capture the three stages reasonably well compared to available experimental data. Regarding the formation of flame kernel, it is found that the convection dominates the propagation of its downstream edge. The simulated initial downstream and radial flame propagation compare well with OH-PLIF images from the experiment. Additionally, when the spark is deposited at off-centerline locations, the flame first propagates downstream and then back upstream from the other side of the stoichiometric iso-surface. At the leading edge location, the chemical source term is larger than others in magnitude, indicating its role in the flame propagation. The time evolution of flame edge position and the final lift-off height are compared with measurements and generally good agreement is observed. The conditional quantities at the stabilization point reflect a balance between chemistry and micro-mixing. This investigation, which focused on model validation for various stages of spark ignition of a turbulent lifted jet flame through comparison with measurements, demonstrates that turbulent edge flame propagation in non-premixed systems can be reasonably well captured by LES/CMC.

Large eddy simulation (LES) with three-dimensional conditional moment closure (CMC) subgrid model for combustion is applied to simulate a swirl-stabilized nonpremixed methane flame with localized extinction, with special focus on the effects of heat loss to the burner surface. The convective wall heat loss is modeled through introducing a source term in the conditionally filtered total enthalpy equation for the CMC cells adjacent to the wall. The mean heat flux is high on the middle surface of the bluff body, but relatively low near its edges. The turbulent heat flux based on the gradient of the resolved temperature is relatively low compared to the laminar counterpart, but increases with the turbulent intensity. The heat loss facilitates the occurrences of extinction and re-ignition for the CMC cells immediately adjacent to the wall, evidenced by comparing flame structures in the near-wall CMC cells. This can be directly linked to the increase of the mean conditional scalar dissipation near the wall in the heat loss case. Furthermore, the degree of local extinction near the bluff body measured by conditional reactedness at stoichiometry is intensified due to the wall heat loss. However, the results also show that there is negligible influence of wall heat loss on the probability density function (PDF) of the lift-off height, demonstrating the dominance of aerodynamic effects on flame stabilization. The results are in reasonable agreement with experimental measurements.

The Large Eddy Simulation (LES)/three-dimensional Conditional Moment Closure (3D-CMC) model with detailed chemistry and finite-volume formulation is employed to simulate a swirl-stabilized non-premixed flame with local extinction. The results demonstrate generally good agreement with the measurements concerning velocity, flame shape, and statistics of flame lift-off, but the penetration of fuel jet into the recirculation zone is under-predicted possibly due to the over-predicted swirl velocities in the chamber. Localized extinctions are seen in the LES, in agreement with experiment. The local extinction event is shown by very low heat release rate and hydroxyl mass fraction and reduced temperature, and is accompanied by relatively high scalar dissipation. In mixture fraction space, CMC cells with strong turbulence-chemistry interaction and local extinction show relatively large fluctuations between fully burning and intermediate distributions. The probability density functions of conditional reactedness, which shows how far the conditionally-filtered scalars are from reference fully burning profiles, indicate that for CMC cells with local extinction, some reactive scalars demonstrate pronounced bimodality while for those cells with strong reactivity the PDFs are very narrow.

Motivated by recent interests in plasma assisted combustion (PAC), theoretical investigation on the ignition of pre-mixture by radical deposition is performed. Thermally sensitive intermediate kinetics are considered and the governing equations for temperature and mass fractions of fuel and radical are solved analytically. The correlation depicting the evolution of flame kernel resulted from radical and/or heat deposition is derived. Based on this correlation, we study the flame bifurcation and critical condition for the ignition caused by radical as well as heat deposition. The emphasis is placed on investigating the effects of fuel and radical Lewis numbers. For ignition by radical deposition only, it is demonstrated that the fuel Lewis number has a pronounced influence on the flame propagation and flame bifurcation. With the increase of the fuel Lewis number, new flame branches and bifurcations are observed. It is found that there are two regimes in the change of the minimum chemical ignition power with the fuel Lewis number. Unlike the fuel Lewis number, the radical Lewis number only has a quantitative influence on the flame bifurcation and critical ignition condition. For ignition by radical and thermal deposition, the flame trajectory and flame bifurcation are found to be strongly affected by additional heat deposition. The minimum chemical and thermal ignition powers are compared, and the ignition efficiency of pure chemical ignition and pure thermal ignition is shown to strongly depend on the fuel and radical Lewis numbers. Moreover, the validity of theoretical results describing the effects of fuel and radical Lewis numbers on the minimum ignition energy is confirmed qualitatively by transient numerical simulations including thermal expansion and detailed chemistry.