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Two-dimensional simulations are conducted to investigate the direct initiation of cylindrical detonation in hydrogen/air mixtures with detailed chemistry. The effects of hotspot condition and mixture composition gradient on detonation initiation are studied. Different hotspot pressure and composition are first considered in the uniform mixture. It is found that detonation initiation fails for low hotspot pressures and supercritical regime dominates with high hotspot pressures. Detonation is directly initiated from the reactive hotspot, whilst it is ignited somewhere beyond the nonreactive hotspots. Two cell diverging patterns (i.e., abrupt and gradual) are identified and the detailed mechanisms are analyzed. Moreover, cell coalescence occurs if many irregular cells are generated initially, which promotes the local cell growing. We also consider nonuniform detonable mixtures. The results show that the initiated detonation experiences self-sustaining propagation, highly unstable propagation, and extinction in mixtures with a linearly decreasing equivalence ratio along the radial direction respectively, i.e., 1 to 0.9, 1 to 0.5 and 1 to 0. Moreover, the hydrodynamic structure analysis shows that, for the self-sustaining detonations, the hydrodynamic thickness increases at the overdriven stage, decreases as the cells are generated, and eventually become almost constant at the cell diverging stage, within which the sonic plane shows a sawtooth pattern. However, in the detonation extinction cases, the hydrodynamic thickness continuously increases, and no sawtooth sonic plane can be observed.

Autoignition of n-heptane droplet/vapor/air mixtures behind an oblique shock wave are studied, through Eulerian-Lagrangian method and a skeletal chemical mechanism. The effects of gas/liquid equivalence ratio (ER), droplet diameter, flight altitude, and Mach number on the ignition transient and chemical timescales are investigated. The results show that the ratio of chemical excitation time to ignition delay time can be used to predict the oblique detonation wave (ODW) transition mode. When the ratio is relatively high, the combustion heat release is slow and smooth transition is more likely to occur. In heterogeneous ignition, there are direct interactions between the evaporating droplets and the induction/ignition process, and the chemical explosive propensity changes accordingly. The energy absorption of evaporating droplets significantly retards the ignition of n-heptane vapor. In the two-phase n-heptane mixture autoignition process, the ignition delay time decreases exponentially with flight Mach number, and increases first and then decreases with the flight altitude. As the liquid ER increases, both ignition delay time and droplet evaporation time increase. With increased droplet diameter, the ignition delay time decreases, and the evaporation time increases. Besides, for Mach number is less than 10, the ratio of the chemical excitation time to ignition delay time generally increases with the flight altitude or Mach number. It increases when the liquid ER decreases or droplet diameter increases. When Mach number is sufficiently high, it shows limited change with fuel and inflow conditions. The results from this work can provide insights into spray ODW initiation. The ODW is more likely to be initiated with a smooth transition at high altitude or Mach number. Abrupt transition mode tends to happen when fine fuel droplets are loaded.

The interactions between an incident shock and 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. In this work, parametric studies are performed considering different particle sizes, volume fractions, and curtain thicknesses. It is found that smaller particle size and larger volume fractions lead to stronger reflected shock and weaker transmitted shock. Different expansion stages of the curtain fronts are also studied in detail. Attention is paid to the particle collision effects on the curtain evolution behaviours. 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 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 accelerate large ones and cause velocity scattering. Moreover, increasing the bi-dispersed curtain thickness leads to multiple collision force peaks due to the local particle accumulations, 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 modelled.

Transmission of hydrogen detonation wave (DW) in an inert particle curtain is simulated using the Eulerian-Lagrangian approach with gas-particle two-way coupling. A detailed chemical mechanism is used for hydrogen detonative combustion and parametric studies are conducted based on a two-dimensional computational domain. A detonation map of propagation and extinction corresponding to various particle sizes, concentrations, and curtain thicknesses is plotted. It is shown that the critical curtain thickness decreases considerably when the particle concentration is less than the critical value. The effects of curtain thickness on the trajectories of peak pressure, shock front speed, and heat release rate are examined. Three propagation modes of the DW in particle curtain are found: detonation transmission, partial extinction and detonation reinitiation, and detonation extinction. The chemical explosive mode analysis confirms that a detonation re-initiation event is caused by a re-initiation point with high pressure and explosive propensity, resulting from transverse shock focusing. The influence of particle dimeter and concentration, and curtain thickness on the DW are also examined with peak pressure trajectories, shock speed, and interphase exchange rates of energy and momentum. Furthermore, the evolutions of curtain morphologies are analyzed by the particle velocity, volume fraction, Stokes drag and Archimedes force. This analysis confirms the importance of the drag force in influencing the change of curtain morphologies. Different curtain evolution regimes are found: quasi-stationary regime, shrinkage regime, constant-thickness regime, and expansion regime. Finally, the influences of the curtain thickness on the characteristic time of curtain evolutions are studied.

Spray detonation in n-heptane two-phase mixtures is simulated using Eulerian Lagrangian method. Two-dimensional configuration is considered, and the effects of droplet diameter and liquid equivalence ratio on detonation propagation, structure, and dynamics are investigated. The results show that the average detonation propagation speed first increases and then decreases as liquid equivalence ratio changes, and the speed peaks at higher liquid equivalence ratio for larger droplets. The triple points and transverse detonations vaporize or aerodynamically expel the droplets from their trajectories, resulting in non-uniform distributions of fuel vapor and reaction zones behind the detonation. In addition, droplet dispersion distance in the post-detonation area increases for larger droplets due to lower evaporation. Moreover, small droplets generally lead to higher detonated n-heptane fraction, and fuel detonative combustion directly affects the variations of detonated fuel fraction. For larger droplets, V shaped dependence on liquid equivalence ratio is seen for large droplets, dominated by variations of post-detonation deflagration. It is found that spray detonation structure is significantly influenced by liquid fuel equivalence ratio and droplet diameter. The dependence of key locations in spray detonation structure on liquid fuel properties is also evaluated, e.g., reaction front and sonic plane. Furthermore, the leading shock Mach number slightly decreases with droplet size. When the liquid equivalence ratio is high, spray detonation exhibits pronounced unsteadiness, such as instantaneous or complete extinction. Either extinction is caused by strong heat absorption of evaporating droplets behind the shock. Moreover, localized detonative spot is observed due to the compression of multiple transverse shocks., Comment: 16 figures

Spark ignition of ethanol droplet/vapor/air mixture is studied with a Eulerian-Eulerian method and detailed chemical mechanism. The flame kernel-droplet interaction is quantified with an evaporation completion front (ECF). Two categories of spray flames can hence be defined based on the relative location between the ECF and flame front, i.e., homogeneous and heterogeneous spray flames. An element-based equivalence ratio (ER) at the flame front (flame ER for short) is introduced to measure the gas composition in evaporating sprays. For overall fuel-lean mixtures, quasi-stationary spherical flame (QSSF) occurs due to lean flame ER and the composition at the QSSF front is homogeneous. For overall fuel-rich two-phase mixtures, re-ignition, after the spark-ignited kernel fails, is observed when the droplet diameter is 15 {\mu}m for fuel sprays with both fuel-lean and fuel-rich background gas. This is due to rich flame ER and/or strong evaporative heat loss. Meanwhile, the kernel is born in a heterogeneous mixture and transition into homogeneous state is found. For both overall lean and rich two-phase mixtures, fuel droplets affect the ignitability and flame trajectories. Moreover, ignition energy affects the flame ER and front distance at the early stage of kernel development. Lastly, the minimum ignition energies (MIE) with different gas and overall ERs are investigated.

Methane/coal dust hybrid explosion is one of the common hazards in process and mining industries. In this study, methane detonation propagation in dilute coal char particle suspensions is studied based on Eulerian-Lagrangian method. The effects of char combustion on methane detonation dynamics are focused on. The results show that propagation of the methane detonation wave in coal particle suspensions are considerably affected by particle concentration and size. Detonation extinction occurs when the coal particle size is small and concentration is high. The averaged lead shock speed generally decreases with increased particle concentration and decreased particle size. Mean structure and interphase coupling of hybrid detonation are analysed, based on the gas and particle quantities. It is found that char combustion proceeds in the subsonic region behind the detonation wave and heat release is relatively distributed compared to that from gas phase reaction. The mass and energy transfer rates increase rapidly to the maximum near the reaction front in the induction zone. Moreover, for 1 {\mu}m particles, if the particle concentration is beyond a threshold value, detonation re-initiation occurs after it is quenched at the beginning of the coal dust suspensions. This is caused by hot spots from the shock focusing along the reaction front in a decoupled detonation and these shocks are generated from char combustion behind the lead shock., Comment: arXiv admin note: substantial text overlap with arXiv:2202.02735

Interactions between a propagating hydrogen/air detonation wave and circular water cloud are studied. Eulerian Lagrangian method involving two-way gas-droplet coupling is applied. Different droplet (diameter, concentration) and cloud (diameter) properties are considered. Results show that droplet size, concentration and cloud radius have significant effects on peak pressure trajectory of the detonation wave. Three propagation modes are identified: perturbed propagation, leeward re-detonation, and detonation extinction. Leeward re-detonation is analyzed from unsteady evolutions of gas and liquid droplet quantities. The detonation is re-initiated by a local hot spot from shock focusing of upper and lower diffracted detonations. Disintegration of water droplets proceeds when the detonation wave crosses the cloud. In addition, detonation extinction is featured by quickly fading peak pressure trajectories when the detonation wave passes the larger cloud, and no local autoignition occurs in the shock focusing area. Evolutions of thermochemical structures from the shocked area in an extinction process are also studied. The transfer rates of mass, energy and momentum of detonation success and failure are analyzed. Moreover, parametric studies demonstrate that the critical cloud size to quench a detonation decreases when the droplet concentration is increased. However, when the droplet concentration is beyond 0.84 kg/m3, the critical cloud size is negligibly influenced due to small droplets. Two-phase fluid interfacial instability is observed, and the mechanism of cloud evolution is studied with the distributions of droplet, vorticity, density / pressure gradient magnitudes, and gas velocity., Comment: arXiv admin note: substantial text overlap with arXiv:2202.03675

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.

Utilization of liquid fuels is crucial to enabling commercialization of rotating detonation engines in the near future. In this study, Eulerian-Lagrangian simulations are conducted for rotating detonative combustion with dilute n-heptane sprays and preheated air. Two-dimensional flattened configuration is used and a skeletal chemical mechanism with 44 species and 112 elementary reactions for n-heptane combustion is adopted. The flow structure, droplet distribution, and thermochemical parameters in the refill zone are first analyzed. It is shown that the mixture in the refill zone is heterogeneous, including evaporating droplets, vapor, and air. When the total temperature is below 950 K, the average equivalence ratio increases with the total temperature. When it is higher than 950 K, the average equivalence ratio is almost constant. Subsequently, the chemical explosive mode analysis is applied to identify the controlling reactions and dominant combustion modes in the fuel refill zone and reaction fronts. Results demonstrate that the initiation reaction and low-temperature reaction are dominant in the upstream and downstream of the refill zone, respectively. The intermediate species from low-temperature chemistry is found to be important for the chemical explosive mode in the undetonated mixture. The influence of species diffusion and dispersed droplets is further analyzed. Results show that vapor autoignition facilitated by droplet evaporation occurs in the refill zone. Finally, the effects of the air total temperature on the detonation propagation speed and RDE propulsion performance are investigated. It is found that the detonation propagation speed and specific impulse increase with air total temperature.

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.

Inhibition of hydrogen explosion is crucial to realize its wide applications and fine water spray is an ideal mitigant due to numerous advantages. In this work, interactions between a propagating hydrogen/air detonation wave and circular water cloud are numerically studied. Eulerian-Lagrangian method involving two-way gas-droplets coupling is applied, with a two-dimensional configuration. Different droplet (diameter, concentration) and cloud (diameter) properties are considered. Our results show that droplet size, concentration and cloud radius have significant effects on peak pressure trajectory of the detonation wave. After interacting with cloud, the detonation wave exhibits three propagation modes, including perturbed propagation, leeward re-detonation, and detonation extinction. Leeward re-detonation is analyzed from unsteady evolutions of gas and liquid droplet quantities. The refracted detonation wave inside the cloud is decoupled and propagates more slowly than the one outside the cloud. The detonation re-initiation is from a local hot spot, caused by shock focusing from upper and lower diffracted detonations. Disintegration of water droplets proceeds when the detonation wave crosses the cloud and multiphase interfacial instability is observed due to the difference in effective density of the two fluids. Furthermore, detonation extinction is observed when we consider various water cloud size. It is featured by quickly fading peak pressure trajectories when the detonation passes the cloud, and no local autoignition occurs in the shock focusing area. Evolutions of thermochemical structures from the shocked area in an extinction process are also studied. Moreover, parametric studies considering various droplet concentrations and cloud radii are performed.

In this study, methane detonation propagation in dilute coal particle suspensions is studied based on Eulerian-Lagrangian method. Two-dimensional configuration is considered, and a skeletal chemical mechanism (24 species and 104 reactions) is applied for methane combustion. The gas and particulate phase equations are solved using an OpenFOAM code for two-phase compressible reacting flow, RYrhoCentralFOAM. The effects of char combustion on methane detonation dynamics are investigated and devolatized coal particles are modelled. The results show that propagation of the methane detonation wave in coal particle suspensions are considerably affected by coal particle concentration and size. Detonation extinction occurs when the coal particle size is small and concentration is high. The averaged lead shock speed generally decreases with increased particle concentration and decreased particle size. Mean structure of methane and coal particle hybrid detonation is analysed, based on the gas and particle quantities. It is found that char combustion proceeds in the subsonic region behind the detonation wave and heat release is relatively distributed compared to that from gas phase reaction. Moreover, for 1 {\mu}m particle, if the particle concentration is beyond a threshold value, detonation re-initiation occurs after it is quenched at the beginning of the coal dust suspensions. This is caused by hot spots from the shock focusing along the reaction front in a decoupled detonation and these shocks are generated from char combustion behind the lead shock. A regime map of detonation propagation and extinction is predicted. It is found that the re-initiation location decreases with the particle concentration and approaches a constant value when the concentration exceeds 1000 g/m3. The results from this study are useful for prevention and suppression of methane/coal dust hybrid explosion.

Two-dimensional wedge-stabilized oblique detonations in stoichiometric and fuel-lean H2/O2/Ar mixtures with water mists are studied with Eulerian-Lagrangian method. The effects of water droplet mass flow rate on flow and chemical structures in the induction zone, as well as physical / chemical roles of water vapor, are investigated. The results show that the oblique detonation wave (ODW) can stand in a range of water mass flow rates for both stoichiometric and fuel-lean mixtures. With increased droplet mass flow rate, the deflagration front in the induction zone is distorted and becomes zigzagged, but the transition mode from oblique shock wave (OSW) to ODW does not change. Moreover, the initiation and transition locations monotonically increase, and the OSW and ODW angles decrease, due to droplet evaporation and water vapor dilution in the induction region. For fuel-lean mixtures, the sensitivity of characteristic locations to the droplet loading variations is mild, which signifies better intrinsic stability and resilience to the oncoming water droplets. The chemical explosiveness of the gaseous mixture between the lead shock and reaction front is studied with the chemical explosive method analysis. The smooth transition is caused by the highly enhanced reactivity of the gas immediately behind the curved shock, intensified by the compression waves. Nonetheless, the abrupt transition results from the intersection between the beforehand generated detonation wave in the induction zone and OSW. Besides, the degree to which the gas chemical reactivity in the induction zone for fuel-lean mixtures is reduced by evaporating droplets is generally lower than that for stoichiometric gas. Also, physical and chemical effects of water vapor from liquid droplets result in significant differences in ODW initiation and morphology.

The Eulerian-Lagrangian method is applied to simulate pulsating propagation and extinction of stoichiometric hydrogen/oxygen/argon detonations in ultrafine water sprays. Three detonation propagation modes are found: (1) pulsating propagation, (2) propagation followed by extinction, and (3) immediate extinction. For pulsating detonation, within one cycle, the propagation speeds and the distance between reaction front (RF) and shock front (SF) change periodically. The pulsating phenomenon originates from the interactions between gas dynamics, chemical kinetics, and droplet dynamics inside the induction zone. Multiple pressure waves are emanated from the RF within one cycle, which overtake and intensify the lead SF. An autoigniting spot arises in the shocked gas after the contact surface. The relative locations of SF, RF, shock-frame sonic point, and two-phase contact surface remain unchanged in a pulsating cycle, but their distances have periodic variations. Moreover, the unsteady behaviors of detonation extinction include continuously increased distance between the RF and SF and quickly reduced pressure peaks, temperature, and combustion heat release. The decoupling of RF and SF leads to significantly increasing chemical timescale of the shocked mixture. The hydrodynamic structure also changes considerably when detonation extinction occurs. Moreover, the predicted map of detonation propagation and extinction illustrates that the critical mass loading for detonation extinction reduces significantly when the droplet size becomes smaller. It is also found that for the same droplet size, the average detonation speed monotonically decreases with water mass loading. However, detonation speed and pulsating frequency have a non-monotonic dependence on droplet size under a constant water mass loading.

Two-dimensional numerical simulations with Eulerian-Lagrangian method and detailed chemical mechanism are conducted to study the methane detonation propagation across a water curtain with finite thickness. The critical length of the water curtain with sprayed droplets is determined through parametric simulations with different water mass loadings and droplet sizes. The influence of water curtain length on the methane detonation is examined by the trajectories of peak pressure and time history of average heat release rate. The results indicate that the water curtain not only inhibit the incident detonation wave, but also prevent the detonation re-ignition after the incident wave is quenched. Moreover, unsteady response of gaseous methane detonation to water curtain are analyzed. The detonation re-initiation process behind the water curtain near the critical loading is also captured. In addition, mechanism of detonation inhibition with fine water droplets are discussed. It is found that energy and momentum exchanges start immediately when the detonation wave enters the water curtain area, but the mass transfer starts well behind the detonation wave due to the finitely long droplet heating duration. It is shown that the convective heat transfer by water droplets plays a significant role in quenching a detonation.

Eulerian-Lagrangian simulations are conducted for two-dimensional Rotating Detonative Combustion (RDC) fueled by bi-disperse n-heptane sprays without any fuel pre-vaporization. Parametric studies are performed to study the influences of droplet diameter and droplet distribution on detonation wave are studied. The extinction process of the detonation wave is also been analyzed. It is found that small n-heptane droplets (e.g., 2 um) are completely vaporized in the fuel refilling area. Increasing the droplet diameter causes the droplet to fail to evaporate completely within the fuel refilling area and exist after the detonation wave. A reflected shock can be obsevered after the detonation wave. When the droplet diameter is larger than 10 {\mu}m, the higher pressure after the detonation wave leads to the reactants cannot be sprayed into the combustor, eventually leading to extinction of the detonation wave. In bi-disperse n-heptane sprays, presence of droplets with small diameter maintains the stable propagation of the detonation wave. The average equivalence ratio in the fuel refilling area is lower than total equivalence ratio (up to 0.66 only), and the average equivalence ratio decreases with the increase of droplet diameter in bi-disperse n-heptane sprays. The increase in droplet diameter decreases the detonated fuel fraction and the speed of detonation wave. The speeds of detonation wave in bi-disperse n-heptane sprays are 3-9% lower than the respective gaseous cases. Moreover, propulsion performance of RDC such as thrust and specific impulse decreases with increasing droplet diameter.

Dynamics of ethylene autoignition and Deflagration-to-Detonation Transition (DDT) in a one-dimensional shock tube are numerically investigated using a skeletal chemistry including 10 species and 10 reactions. Different combustion modes are investigated through considering various premixed gas equivalence ratios (0.2 to 2.0) and incident shock wave Mach numbers (1.8 to 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 Multiple Mapping Conditioning / Large Eddy Simulation (MMC-LES) approach is used to simulate a supersonic lifted hydrogen jet flame, which features shock-induced autoignition, shock-flame interaction, lifted flame stabilization, and finite-rate chemistry effects. The shocks and expansion waves, shock-reaction interactions and overall flame characteristics are accurately reproduced by the model. Predictions are compared with the detailed experimental data for the mean axial velocity, mean and root-mean-square temperature, species mole fractions, and mixture fraction at various locations. The predicted and experimentally observed flame structures are compared through scatter plots of species mole fractions and temperature against mixture fraction. Unlike most past MMC-LES which has been applied to low-Mach flames, in this supersonic flame case pressure work and viscous heating are included in the stochastic FDF equations. Analysis indicates that the pressure work plays an important role in autoignition induction and flame stabilization, whereas viscous heating is only significant in shear layers (but still negligibly small compared to the pressure work). The evolutions of particle information subject to local gas dynamics are extracted through trajectory analysis on representative fuel and oxidizer particles. The particles intermittently enter the extinction region and may be deviated from the full burning or mixing lines under the effects of shocks, expansion waves and viscous heating. The chemical explosive mode analysis performed on the Lagrangian particles shows that temperature, the H and OH radicals contribute dominantly to CEM respectively in the central fuel jet, fuel-rich and fuel-lean sides. The pronounced particle Damk\"ohler numbers first occur in the fuel jet / coflow shear layer, enhanced at the first shock intersection point and peak around the flame stabilization point.

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.

This study aims to build a theoretical model to describe the ignition process of spherical spray flame laden with fuel droplets under overall fuel-lean condition. Two characteristic fronts are introduced to reveal where the evaporation starts and ends in the ignition process. The results demonstrate that the flame has been strengthened with extra fuel droplet adding while the minimum ignition energy (MIE) is decreased. The evolution of the two evaporation fronts in the flame kernel and propagating branches has also be revealed coupled with the evaporation zone length., Comment: arXiv admin note: substantial text overlap with arXiv:2103.14227; text overlap with arXiv:2009.12799

Evolution of fuel droplet evaporation zone and its interaction with the propagating flame front are studied in this work. A general theory is developed to describe the evolutions of flame propagation speed, flame temperature, droplet evaporation onset and completion locations in ignition and propagation of spherical flames. The influences of liquid droplet mass loading, heat exchange coefficient (or evaporation rate) and Lewis number on spherical spray flame ignition are studied. Two flame regimes are considered, i.e., heterogeneous and homogeneous flames, based on the mixture condition near the flame front. The results indicate that the spray flame trajectories are considerably affected by the ignition energy addition. The critical condition for successful ignition for the fuel-rich mixture is coincidence of inner and outer flame balls from igniting kernel and propagating flame. The flame balls always exist in homogeneous mixtures, indicating that ignition failure and critical successful events occur only in purely gaseous mixture. The fuel droplets have limited effects on minimum ignition energy, which however increases monotonically with the Lewis number. Moreover, flame kernel originates from heterogeneous mixtures due to the initially dispersed droplets near the spark. The evaporative heat loss in the burned and unburned zones of homogeneous and heterogeneous spray flames is also evaluated, and the results show that for the failed flame kernels, evaporative heat loss behind and before the flame front first increases and then decreases. The evaporative heat loss before the flame front generally increases, although non-monotonicity exists, when the flame is successfully ignited and propagate outwardly. For heterogeneous flames, the ratio of the heat loss from the burned zone to the total one decreases as the flame expands.

Large Eddy Simulation with a Perfectly Stirred Reactor model (LES-PSR) is developed to simulate supersonic combustion with high-enthalpy flow conditions. The PSR model considers the viscous heating and compressibility effects on the thermo-chemical state, through correcting the chemical source term for progress variable and incorporating absolute enthalpy as the control variable for the look-up table. It is firstly validated by using a priori analysis of the viscous heating and compressibility effects. Then an auto-igniting hydrogen flame stabilized in supersonic vitiated co-flowing jet is simulated with LES-PSR method. The results show that the shock wave structure, overall flame characteristics, flame-shock interaction and lift-off height are accurately captured. Good agreements of the velocity and mixture fraction statistics with the experimental data are observed. The results also show that the LES-PSR model can predict the mean temperature and mole fractions of major species quite well in both flame induction and stabilization zones. However, there are some under-predictions of temperature RMS by about 100-150 K, which may be due to the chemical non-equilibrium in the H2/O2-enriched combustion product of the co-flowing jet. The scatter plots of two probe locations respectively from induction and flame zones show that the respective flame structures in mixture fraction space are captured well. However, the flucturations of the temperature and species mole fractions are under-predicted in the flame zone. The shock-induced auto-igniting spots are captured by the PSR model. These spots are highly unsteady and play an important role in flame stabilization. It is also shown that the intense reactions are initiated at mixture fractions around the stoichiometry or fuel-lean values, corresponding to local elevated pressure (1.5-2.0 atm) due to shock compression.

In this paper, two dimensional detonation propagation in partially prevaporized n-heptane sprays is studied by using Eulerian/Lagrangian methods. The effects of droplet preevaporation on the detonation propagation are investigated. The general features and detailed structures of two-phase detonations are well captured with the present numerical methods. The results show that the detonation propagation speed and detonation structures are significantly affected by the preevaporated gas equivalence ratio. The numerical soot foils are used to characterize the influence of preevaporated gas equivalence ratio on the detonation propagation. Regular detonation cellular structures are observed for large preevaporated gas equivalence ratios, but when decreasing the preevaporated gas equivalence ratio, the detonation cellular structures become much more unstable and the average cell width also increases. It is also found that the preevaporated gas equivalence ratio has little effects on the volume averaged heat release when the detonation propagates stably. Moreover, the results also suggest that the detonation can propagate in the two-phase heptane and air mixture without preevaporation, but the detonation would be first quenched and then re-ignited when the preevaporated gas equivalence ratio is small or equal to zero.

One-dimensional numerical simulations based on hybrid Eulerian-Lagrangian method are performed to study the interactions between propagating shocks and dispersed evaporating water droplets. Two-way coupling for exchanges of mass, momentum, energy and vapour species is adopted for the dilute two-phase gas-droplet flows. Interphase interactions and droplet breakup dynamics are investigated with initial droplet diameters of 30, 50, 70 and 90 {\mu}m under an incident shock wave Mach number of 1.3. Novel two-phase flow phenomena are observed when droplet breakup occurs. First, droplets near the two-phase contact surface show obvious dispersed distribution because of the reflected pressure wave that propagates in the reverse direction of the leading shock. The reflected pressure wave grows stronger for larger droplets. Second, spatial oscillations of the gas phase pressure, droplet quantities (e.g., diameter and net force) and two-phase interactions (e.g., mass, momentum, and energy exchange), are observed in the post-shock region when droplet breakup occurs, which are caused by shock / droplet interactions. Third, the spatial distribution of droplets (i.e., number density, volume fraction) also shows strong oscillation in the post-shock region when droplet breakup occurs, which is caused by the oscillating force exerted on the droplets.

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.

Large eddy simulations with three-dimensional finite-volume Conditional Moment Closure (CMC) model are performed for a hydrogen / nitrogen lifted flame with detailed chemical meachanism. The emphasis is laid on the influences of mesh resolution and convection scheme of finite-volume CMC model on predictions of reactive scalar distribution and unsteady flame dynamics. The results show that the lift-off height is underestimated and the reactive scalars (e.g. temperature, H2 and OH) are over-predicted with coarser CMC mesh. It is also found that further refinement of the CMC mesh would not considerably improve the results. The time sequences of the most reactive and stoichiometric OH mass fractions indicate that finer CMC mesh can capture more unsteady details than coarser CMC mesh. Moreover, the coarse CMC mesh has lower conditional scalar dissipation rate, which would promote the ealier auto-ignition of the flame base. Besides, the effects of the convection schemes in the CMC equations on the lifted flame characteristics are also investigated. It is shown that different convection schemes lead to limited differences on the time-averaged temperature, mixture fraction and species mass fractions. Moreover, the RMS values of H2 and OH mass fractions show larger deviation from the measurements with hybrid upwind and central differencing scheme, especially around the flame base. Furthermore, the distributions of the numerical flux on the CMC faces also show obvious distinction between the upwind scheme and the blending scheme. The budget analysis of the individual CMC terms shows that a sequence of CMC faces has comparable contributions with upwind scheme. However, with the hybrid schemes, the instantaneous flux is dominantly from limited CMC faces. The reactivity of a CMC cell is more easily to be affected by its neighbors when the upwind scheme is used.

Rotating detonation combustion (RDC) fuelled with partially pre-vaporized n-heptane sprays and gaseous hydrogen is studied with an Eulerian-Lagrangian method. Our focus is the effects of pre-vaporized n-heptane equivalence ratios and droplet diameters on detonation wave propagation and droplet dynamics in two-phase RDC. The results show that when the droplets are small, they are fully vaporized by the detonation wave. However, when the droplet diameter is relatively large and/or the detonation wave number is bifurcated, liquid droplets are observable beyond the refill zone. Moreover, the detonation speed is considerably influenced by the droplet pre-vaporization and diameter. The velocity deficits vary between 5% and 30%. Over 70% n-heptane is detonated in the simulated cases, and there exists a critical droplet diameter (about 20 um), around which the detonated fuel fraction is minimal. Four droplet trajectories in RDC are identified, which are differentiated by various evaporation times, residence times and interactions between droplets and the basic RDC flow structures. Inside the refill zone, three droplet categories are qualitatively identified. Droplets injected at the right end of the refill zone directly interact with the deflagration surface and meanwhile have relatively long residence time. However, droplets injected closer to the travelling detonation front have insufficient time to be heated and vaporized. Our results also demonstrate that when pre-vaporization level is low and initial droplet diameter is large, the liquid fuel droplets may disperse towards the combustor exit. Furthermore, the droplet dispersion height decreases with liquid fuel pre-vaporization, while increases with droplet diameter.

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.