Diesel flame lift-off stabilization in the presence of laser-ignition: a numerical study

Diesel flame lift-off and stabilization in the presence of laser-ignition were numerically investigated with the method of Eulerian stochastic fields. The aim was to scrutinise the interaction between the lifted diesel flame and an ignition kernel upstream of the lifted flame. The numerical simulation was carried out in a constant-volume combustion vessel with n-heptane as fuel. The process was studied previously in an experiment employing Diesel #2 as the fuel in the same combustion vessel. In the experiment a lifted flame was first established at a position downstream of the nozzle. An ignition kernel was then initiated using a high-energy pulse laser at a position upstream of the natural lift-off position of the diesel flame. The laser-ignition kernel was modelled using a high-temperature (～2000 K) hot spot. In both experiment and simulations the upstream front of the ignition kernel was shown to remain around the initial laser ignition site for a substantially long period of time, while the downstream front of the ignition kernel propagates rapidly towards the natural lift-off position downstream of the laser ignition site. The lift-off position oscillated before the final stabilization at the natural lift-off position. The structures and the propagation speed of the reaction fronts in the laser-ignition kernel and the main flame were analysed. Two different stabilization mechanisms, the auto-ignition mechanism and the flame propagation mechanism, were identified for the naturally lifted flame and the laser-induced reaction front, respectively. A mechanism was proposed to explain the oscillation of the lift-off position.     

Ignition of hydrogen in unsteady nonpremixed flows

The effects of unsteady strain on hydrogen (H₂) ignition in nonpremixed flows are investigated with both experimental measurements and numerical computations. A mixing layer is established in a counterflow configuration with a fuel stream containing N₂–diluted H₂ (X_H2=0.08) flowing against heated air. A reproducible ignition process is initiated by introducing atomic oxygen into the mixing layer with a pulsed ArF excimer laser, which photodissociates heated O₂ from the oxidizer stream. The temporal evolution of OH during ignition is measured by planar laser-induced fluorescence. Following the induction phase, the measured OH mole fraction increases rapidly to a super-equilibrium value that is 60% greater than the OH mole fraction in a steady diffusion flame. The peak OH mole fraction occurs at approximately 6 ms after the excimer laser pulse. To study the OH time history under transient strain, the fuel stream is pulsed at a fixed time after the initiation of ignition. The response of the ignition kernel is extremely sensitive to the time delay of the flow transient. The unsteady strain can delay the ignition time or extinguish the kernel. Comparisons between computations and experiments are made for the evolution of OH during autoignition both for steady and unsteady strain. For both steady and unsteady strain, the transient one-dimensional counterflow computations show excellent agreement with the experiment in terms of predicting ignition delays and the rate of OH accumulation during the induction period. The computations also capture the super-equilibrium OH during the transition to the formation of a steady flame, although not to the degree observed experimentally. The computations are further used to understand the influence of unsteady strain on the kernel evolution. It is found that the degree of super-equilibrium OH is sensitive to strain transients applied close to the time of thermal runaway.     

Dynamics of triple-flames in ignition of turbulent dual fuel mixture: A direct numerical simulation study

Pilot-ignited dual fuel combustion involves a complex transition between the pilot fuel autoignition and the premixed-like phase of combustion, which is challenging for experimental measurement and numerical modelling, and not sufficiently explored. To further understand the fundamentals of the dual fuel ignition processes, the transient ignition and subsequent flame development in a turbulent dimethyl ether (DME)/methane-air mixing layer under diesel engine-relevant conditions are studied by direct numerical simulations (DNS). Results indicate that combustion is initiated by a two-stage autoignition that involves both low-temperature and high-temperature chemistry. The first stage autoignition is initiated at the stoichiometric mixture, and then the ignition front propagates against the mixture fraction gradient into rich mixtures and eventually forms a diffusively-supported cool flame. The second stage ignition kernels are spatially distributed around the most reactive mixture fraction with a low scalar dissipation rate. Multiple triple flames are established and propagate along the stoichiometric mixture, which is proven to play an essential role in the flame developing process. The edge flames gradually get close to each other with their branches eventually connected. It is the leading lean premixed branch that initiates the steady propagating methane-air flame. The time required for the initiation of steady flame is substantially shorter than the autoignition delay time of the methane-air mixture under the same thermochemical condition. Temporal evolution of the displacement speed at the flame front is also investigated to clarify the propagation characteristics of the combustion waves. Cool flame and propagation of triple flames are also identified in this study, which are novel features of the pilot-ignited dual fuel combustion.     

Flame propagation monitoring in an engine by an optical technique

A Schlieren laser technique has been used to investigate the transit time of the flame front at selected locations inside a running automotive engine. Thus we get information on the flame speed and the delay between ignition and formation of the front in a very simple fashion without disturbing the combustion itself. The only obvious requirement is that the engine has optical access, and the proposed technique can thus be used whenever other optical diagnostic techniques are used. We also present some examples of the results we obtained.     

Effects of flash boiling injection on in-cylinder spray,mixing and combustion of a spark-ignition direct-injection engine

Higher engine efficiency and ever stringent pollutant emission regulations are considered as the most important challenges for today's automotive industry. Fast evaporation and combustion technique has caused unprecedented attention due to its potential to solve both of the above challenges. Flash boiling, which features a two-phase flow that constantly generates vapor bubbles inside the liquid spray is ideal to achieve fast evaporation and combustion inside direct-injection (DI) gasoline engines. In this study, three spray conditions, including liquid, transitional flash boiling and flare flash boiling spray were studied for comparison under cold start condition in a spark-ignition direct-injection (SIDI) optical gasoline engine. Optical access into the combustion chamber includes a quartz linear and a quartz insert on the piston. In separate experiments, we recorded the crank angle resolved spray morphology using laser scattering technique, and distribution of fuel before ignition employing laser induced fluorescence technology, as well as time-resolved color images of flame with high-speed camera. The spray morphology during the intake stroke shows stronger plume-plume and plume-air interaction under flash boiling condition, as well as smaller penetration. Then around the end of compression (before ignition), the fuel distribution is also shown to be more homogeneous with less cyclic variation under flash boiling. Finally, from the color images of the flame, it was found that with the increase of superheat degree, the diffusion rate of blue flame (generated by excited molecules) is higher, which is considered to be related with the larger fractal dimension of the flame front. Also, the combustion is more complete with less yellow flame under flash boiling.     

Modeling evaporation effects in conditional moment closure for spray autoignition

Simulations of an n-heptane spray autoigniting under conditions relevant to a diesel engine are performed using two-dimensional, first-order conditional moment closure (CMC) with full treatment of spray terms in the mixture fraction variance and CMC equations. The conditional evaporation term in the CMC equations is closed assuming interphase exchange to occur at the droplet saturation mixture fraction values only. Modeling of the unclosed terms in the mixture fraction variance equation is done accordingly. Comparison with experimental data for a range of ambient oxygen concentrations shows that the ignition delay is overpredicted. The trend of increasing ignition delay with decreasing oxygen concentration, however, is correctly captured. Good agreement is found between the computed and measured flame lift-off height for all conditions investigated. Analysis of source terms in the CMC temperature equation reveals that a convective–reactive balance sets in at the flame base, with spatial diffusion terms being important, but not as important as in lifted jet flames in cold air. Inclusion of droplet terms in the governing equations is found to affect the mixture fraction variance field in the region where evaporation is the strongest, and to slightly increase the ignition delay time due to the cooling associated with the evaporation. Both flame propagation and stabilization mechanisms, however, remain unaffected.     

Development and validation of an n-dodecane skeletal mechanism for spray combustion applications

n-Dodecane is a promising surrogate fuel for diesel engine study because its physicochemical properties are similar to those of the practical diesel fuels. In the present study, a skeletal mechanism for n-dodecane with 105 species and 420 reactions was developed for spray combustion simulations. The reduction starts from the most recent detailed mechanism for n-alkanes consisting of 2755 species and 11,173 reactions developed by the Lawrence Livermore National Laboratory. An algorithm combining direct relation graph with expert knowledge (DRGX) and sensitivity analysis was employed for the present skeletal reduction. The skeletal mechanism was first extensively validated in 0-D and 1-D combustion systems, including auto-ignition, jet stirred reactor (JSR), laminar premixed flame and counter flow diffusion flame. Then it was coupled with well-established spray models and further validated in 3-D turbulent spray combustion simulations under engine-like conditions. These simulations were compared with the recent experiments with n-dodecane as a surrogate for diesel fuels. It can be seen that combustion characteristics such as ignition delay and flame lift-off length were well captured by the skeletal mechanism, particularly under conditions with high ambient temperatures. Simulations also captured the transient flame development phenomenon fairly well. The results further show that ignition delay may not be the only factor controlling the stabilisation of the present flames since a good match in ignition delay does not necessarily result in improved flame lift-off length prediction.     

Detailed measurements of transient two-stage ignition and combustion processes in high-pressure spray flames using simultaneous high-speed formaldehyde PLIF and schlieren imaging

This study investigates the low- and high-temperature ignition and combustion processes in a high-pressure spray flame of n-dodecane using simultaneous 50-kHz formaldehyde (HCHO) planar laser-induced fluorescence (PLIF) and 100-kHz schlieren imaging. The PLIF measurements were facilitated through the use of a pulse-burst-mode Nd:YAG laser, producing a 355-nm pulse-train with 300 pulses at 70 mJ/pulse, separated by 20-µs, in a 6-ms burst. The high-speed HCHO PLIF signal was imaged using a non-intensified CMOS camera with dynamic background emission correction. The acquisition rate of this HCHO PLIF diagnostic is unique to the research community, and when combined with high-speed schlieren imaging, provides unprecedented opportunity for analysis of the spatiotemporal evolution of fuel jet penetration and low- and high-temperature ignition processes relevant to internal combustion engine conditions. The present experiments are conducted in the Sandia constant-volume preburn vessel equipped with a new Spray A injector. The influences of ambient conditions are examined on the ignition delay times of the two-stage ignition events, HCHO structures, and lift-off length values. Consistent with past studies of traditional Spray A flames, the formation of HCHO is first observed in the jet peripheries where the equivalence ratio (Φ) is expected to be leaner and hotter and then grows in size and in intensity downstream into the jet core where Φ is expected to be richer and colder. The measurements demonstrate that the formation and propagation of HCHO from the leaner to richer region leads to high-temperature ignition events, supporting the identification of a phenomenon coined “cool-flame wave propagation” during the transient ignition process. Subsequent high-temperature ignition is found to consume the previously formed HCHO in the jet head, while the formation of HCHO persists in the fuel-rich zone near the flame base over the entire combustion period.     

High-pressure fuel spray ignition behavior with hot surface interaction

Fuel-flexible aircraft propulsion systems using compression ignition engines will require novel strategies for reducing the ignition delay of low-reactivity fuels to feasible timescales. Hot surface ignition of fuel sprays has been implemented in some practical situations, but the complex nature of flame formation within the spray structure poses significant challenges. In order to design next-generation ignition devices, the capacity of hot surface heating elements to promote fuel spray ignition must be investigated. In this study, a rapid compression machine (RCM) was used to examine the ignition process of a single kerosene-based F-24 jet fuel spray with a cylindrical heating element inserted into the spray periphery. The experiments, performed with moderately high injection pressures of 40 MPa, have demonstrated two modes of ignition governed by surface temperature and insertion depth of the heating element. There exists an optimal position where the heating element tip is located in the fuel vapor cone around the liquid spray. For this configuration, a critical surface temperature was identified (～1250 K), above which short ignition delays associated with a “spray ignition” mode are consistently achieved. In this case, a local ignition flame kernel propagates downstream to the flame lift-off length before full ignition of the spray. In comparison, below the critical temperature a slower “volumetric” mode results. The extended ignition delays associated with this mode may be impractical for compression ignition engines operating at high speeds and increased altitude.     

Gas-phase spontaneous ignition of hydrocarbons

The ignition of hydrocarbons at low temperatures is experimentally studied in a rapid-mixture-injection static reactor. The ignition process was monitored using a high-speed color video camera. It was found that, at low temperatures, ignition starts in kernels, a feature also characteristic of methods for measuring the ignition delay time at high and medium temperatures (shock tube, rapid compression machine). Kernel-mode ignition is associated with gas-dynamic phenomena inherent in different techniques of heating the gas to the desired temperature. Ignition in the kernel is of chain-thermal nature. The emergence of a visible kernel can be considered the beginning of hot flame propagation. It is shown that, in the self-ignition mode, the propagation of the flame front from the initial kernel occurs by the induction mechanism, proposed by Ya.B. Zel’dovich, rather than by the diffusion-heat-conduction mechanism. Introduction of a platinum wire into the reactor produces a catalytic effect in the negative temperature coefficient region, while virtually unaffecting the ignition delay at lower temperatures.     

Two-sided ignition of a thin PMMA sheet in microgravity

Numerical computations and a series of experiments were conducted in microgravity to study the ignition characteristics of a thin polymethylmethacrylate (PMMA) sheet (thicknesses of 0.2 and 0.4 mm) using a CO₂ laser as an external radiant source. Two separate ignition events were observed, including ignition over the irradiated surface (frontside ignition), and ignition, after some delay, over the backside surface (backside ignition). The backside ignition was achieved in two different modes. In the first mode, after the laser was turned off, the flame shrank and stabilized closer to the fuel surface. This allowed the flame to travel from the frontside to the backside through the small, open hole generated by the laser’s vaporization of PMMA. In the second mode, backside ignition was achieved during the laser irradiation. The numerical calculation simulating this second process predicts fresh oxygen supply flows from the backside gas phase to the frontside gas phase through the open hole, which mixes with accumulated hot MMA fuel vapor which is ignited as a second flame in the frontside gas phase above the hole. Then, the flame initiated from the second ignition travels through the hole to ignite the accumulated flammable mixture in the backside gas phase near the hole, attaining backside ignition. The first backside ignition mode was observed in 21% oxygen and the second backside ignition mode in 35%. The duration of the laser irradiation appears to have important effects on the onset of backside ignition. For example, in 21% oxygen, the backside ignition was attained after a 3 s laser duration but was not observed after a 6 s laser duration (within the available test time of 10 s). Longer laser duration might prevent two-sided ignition in low oxygen concentrations.     

Laser spark ignition of a jet diffusion flame

In this work we report preliminary results on the laser ignition of a jet diffusion flame with jet flow rates ranging from 35 (Re=1086) to 103 cm³/s (Re=3197). The laser spark energy of about 4 mJ was used for all the tests. The relative amounts of fuel and air concentrations at the laser focus have been estimated using a variant of laser-induced breakdown spectroscopy. The ignition and the flame blow out times were measured using the time-resolved OH emission. Ignition times in the range from 3 to about 10 ms were observed depending on the experimental conditions and they increased towards the rich as well as the lean sides. The early time and late-time OH emissions indicate that chemical reactions during the initial stage of the blast wave expansion are not immediately responsible for the ignition. The ultimate fate of an ignition depends on the reactions at later times which determines whether the gas could undergo a transition from hot plasma to a propagating flame.     

Numerical simulation of a mixed-mode reaction front in a PPC engine

The ignition process, mode of combustion and reaction front propagation in a partially premixed combustion (PPC) engine running with a primary reference fuel (87% iso-octane, 13% n-heptane by volume) is studied numerically in a large eddy simulation. Different combustion modes, ignition front propagation, premixed flame and non-premixed flame, are observed simultaneously. Displacement speed of CO iso-surface propagation describes the transition of premixed auto-ignition to non-premixed flame. High temporal resolution optical data of CH₂O and chemiluminescence are compared with simulated results. A high speed ignition front is seen to expand through fuel-rich mixture and stabilize around stoichiometry in a non-premixed flame while lean premixed combustion occurs in the spray wake at a much slower pace. A good qualitative agreement of the distribution of chemiluminescence and CH₂O formation and destruction shows that the simulation approach sufficiently captures the driving physics of mixed-mode combustion in PPC engines. The study shows that the transition from auto-ignition to flame occurs over a period of several crank angles and the reaction front propagation can be captured using the described model.     

Effects of turbulence-chemistry interactions on auto-ignition and flame structure for n-dodecane spray combustion

The Engine Combustion Network (ECN) spray A under diesel engine conditions is investigated with a non-adiabatic 5D Flamelet Generated Manifolds (FGM) model with the consideration of detailed chemical kinetic mechanisms. The enthalpy deficit due to droplet vapourisation is considered by employing an additional controlling parameter in the FGM library. In this FGM model, β-PDF is used for the PDF integration over the control variable space. Validation results in non-reacting conditions indicate relatively good agreement between the predicted and experimental data in terms of liquid and vapour penetrations and mixture fraction spatial distribution. In reacting conditions, the effects of variance of mixture fraction and progress variable were examined. The ignition delay time and the quasi-steady flame structure are both affected by the variances. The variance of mixture fraction delays the ignition process and the variance of progress variable accelerates it. For mixture fraction, the ignition process is quicker at any stage in the case of neglecting variance. While things are more complex for progress variable, the ignition process is advanced in the case of neglecting variance at early times, but surpassed by the case of β-PDF later and until auto-ignition. When variance of mixture fraction is considered, the OH mass fraction shows a wide spatial distribution. While if not, a very thin flame is observed with a higher peak in OH, and a very large lift-off length. The variance of progress variable has little impact on the global flame structure, but makes the flame lift-off length much shorter. This study confirms the general observation, that the variance of mixture fraction is of higher importance in high temperature non-premixed combustion, however, we found that the variance of progress variable is far from negligible.     

Simultaneous rainbow schlieren deflectometry and OH* chemiluminescence imaging of a diesel spray flame in constant pressure flow rig

The physical and chemical phenomena that take place during fuel injection, entrainment and fuel-air mixing, cool-flame and ignition reaction, and combustion in diesel sprays still require extensive study. Global parameters such as liquid and vapor jet penetration lengths and spreading rates render useful yet still limited information. Understanding of the temporal evolution of the spray as it progresses through various steps is needed to develop advanced clean combustion modes and high-fidelity predictive models with sufficient accuracy. In this study, high-speed rainbow schlieren deflectometry (RSD) and OH* chemiluminescence are used to simultaneously image fuel-air mixing, cool-flame reactions, ignition, flame propagation and stabilization, and combustion in a transient diesel-like flame. A constant pressure flow rig (CPFR) is used to conduct multiple injections in quick succession to obtain a statistically relevant dataset. n-heptane was injected at nominal supply pressure of 1000 bar from a single-hole diesel injector into ambient at pressure of 30 bar and temperature of 800 K. About 500 injections were performed and analyzed to reveal structural features of non-reacting and reacting regions of the spray, quantify jet penetration and spreading rates, and study cool-flame behavior, ignition, flame propagation and stabilization at lift-off length, and combustion at upstream and downstream locations.     

Numerical simulations of the ignition of n-heptane droplets in the transition diameter range from heterogeneous to homogeneous ignition

Spontaneous ignition of single n-heptane droplets in a constant volume filled with air is numerically simulated with the spherical symmetry. The volume is closed against mass, species, and energy transfer. The numerical model is fully transient. It continues calculation even after the droplet has completely vaporized, and therefore can predict pre-vaporized ignition. Initial pressure and initial air temperature are fixed at 3 MPa and 773 K, respectively. The droplet is initially at room temperature, and its diameter is between 1 and 100 μm. When the overall equivalence ratio is fixed to be sufficiently large, there exists no ignition limit in terms of initial droplet diameter d₀, and the ignition delay takes a minimum value at certain d₀. In such a case, transition from the heterogeneous ignition to the homogeneous ignition with decreasing d₀ is observed. When d₀ is fixed to be so small that the ignition would not occur in an infinite volume of air, the ignition delay takes a minimum value at certain , which is less than unity. Two-stage ignition behavior is investigated with this model. Ignition delay of a cool flame has the dependence on d₀ that is similar to that of ignition delay of a hot flame when is unity. When is almost zero, the ignition limit for cool flame in terms of d₀ is not identified unlike that for hot flame.     

Computational investigations of the coupling between transient flame dynamics and thermo-acoustic instability in a self-excited resonance combustor

Combustion instability due to thermo-acoustic interactions is a critical combustion problem that requires a thorough understanding because of its adverse impact on stable and reliable operation of combustors in high-speed propulsion devices like gas turbines and rockets. This work conducts computational investigations of the coupling between the transient flame dynamics such as the ignition delay and local extinction and the thermo-acoustic instability developed in a self-excited resonance combustor to gain deep insights into the mechanisms of thermo-acoustic instability. A 2D modelling framework that employs different flamelet models (the steady flamelet model and the flamelet/progress variable approach) is developed to enable the examination of the effect of the transient flame dynamics caused by the strong coupling of the turbulent mixing and finite-rate chemical kinetics on the occurrence of thermo-acoustic instability. The models are validated by using the available experimental data for the pressure signal. Parametric studies are performed to examine the effect of the occurrence of the transient flame dynamics, the effect of artificial amplification of the Damköhler number, and the effect of neglecting mixture fraction fluctuations on the predictions of the thermo-acoustic instability. The parametric studies reveal that the occurrence of transient flame dynamics has a strong influence on the onset of the thermo-acoustic instability. Further analysis is then conducted to localise the effect of a particular flame dynamic event, the ignition delay, on the thermo-acoustic instability. The reverse effect of the occurrence of the thermo-acoustic instability on the transient flame dynamics in the combustor is also investigated by examining the temporal evolution of the local flame events in conjunction with the pressure wave propagation. The above observed two-way coupling between the transient flame dynamics (the ignition delay) and the thermo-acoustic instability provides a plausible mechanism of the self-excited and sustained thermo-acoustic instability observed in the combustor despite the fact that the results are obtained from 2D simulations. The same analysis is expected to be extensible to fully 3D simulations.     

Ethanol turbulent spray flame response to gas velocity modulation

A numerical investigation of the interaction between a spray flame and an acoustic forcing of the velocity field is presented in this paper. In combustion systems, a thermoacoustic instability is the result of a process of coupling between oscillations in heat released and acoustic waves. When liquid fuels are used, the atomisation and the evaporation process also undergo the effects of such instabilities, and the computational fluid dynamics of these complex phenomena becomes a challenging task. In this paper, an acoustic perturbation is applied to the mass flow of the gas phase at the inlet and its effect on the evaporating fuel spray and on the flame front is investigated with unsteady Reynolds averaged Navier-Stokes numerical simulations. Two flames are simulated: a partially premixed ethanol/air spray flame and a premixed pre-vaporised ethanol/air flame, with and without acoustic forcing. The frequencies used to perturb the flames are 200 and 2500 Hz, which are representative for two different regimes. Those regimes are classified based on the Strouhal number St = (D/U)f_f: at 200 Hz, St = 0.07, and at 2500 Hz, St = 0.8. The exposure of the flame to a 200 Hz signal results in a stretching of the flame which causes gas field fluctuations, a delay of the evaporation and an increase of the reaction rate. The coupling between the flame and the flow excitation is such that the flame breaks up periodically. At 2500 Hz, the evaporation rate increases but the response of the gas field is weak and the flame is more stable. The presence of droplets does not play a crucial role at 2500 Hz, as shown by a comparison of the discrete flame function in the case of spray and pre-vaporised flame. At low Strouhal number, the forced response of the pre-vaporised flame is much higher compared to that of the spray flame.     

Numerical investigation of pulverized coal particle group combustion using tabulated chemistry

The ignition and combustion of coal particle groups are investigated numerically in a laminar flow reactor. The Flamelet Generated Manifold method is extended to account for the complex mixture of gases being released during devolatilization, which is calculated with a competing two-step model. A second mixture fraction is introduced to include the mixing with the second methane fuel stream. The interactions of the gas phase with particles are modeled within a fully coupled Euler-Lagrange framework. To investigate the influence of particle groups on ignition and combustion, successively increasing densities of particle streams have been analyzed. The ignition delay time is increased significantly by higher particle densities. This delay is validated successfully with the available measurements. Moreover, the shape of the volatile flame was found to be strongly influenced by the particle number density inside the flame. A transition from spherical flames around single particles to a conical flame around the particle cloud could be found in numerical results as well as in experiments. As the primary mechanism for the substantial ignition delay and the formation of the flame, the increased heat transfer from the gas-phase to the particle group, resulting in lower gas-phase temperatures, was identified.     

Theoretical analysis on the forced ignition of a quiescent mixture by repetitive heating pulse

Recently, forced ignition by nanosecond-repetitive-pulsed-discharge (NRPD) has received great attention since it can greatly promote ignition. However, there is no theoretical analysis on ignition induced by multiple heating pulses such as NRPD. Therefore, this work attempts to provide a theoretical interpretation on the ignition of a quiescent, flammable mixture by multiple discharges and to assess the effects of repetitive pulse on ignition characteristics. Based on fully transient formulation, analytical expressions describing ignition kernel propagation induced by multiple pulses are derived. The key parameters of multiple pulse heating, such as energy distribution among individual pulse, intermittent duration between neighboring pulse and total pulse numbers are appropriately incorporated, and their effects on ignition characteristics are assessed. It is found that because of memory effect, the flame kernel continues to propagate after switching off the external heating source. Sequentially introducing identical heating pulses at appropriate intermittent duration repetitively exploits the memory effect during ignition kernel development and thus extends propagating distance of the flame front. The repetitive pulse heating can promote ignition capability due to the flame revitalization effect, i.e., ignition reinforcement to the flame front thanks to additional thermal energy supplied by subsequent pulse. This is consistent with the synergistic effect of NRPD observed in previous experimental studies. In particular, as the pulse number increases, the minimum ignition energy decreases and approaches to an asymptotic value. In the limit of large pulse number, it is found that the integration of the implicit expressions describing the ignition kernel evolution does not depend on the pulse number explicitly. This substantiates the invariance of minimum ignition energy with heating pulse number. The present theory explains the effects of multiple discharges on ignition and provides insights on ignition enhancement.