Reactive Navier Stokes Equations Research Articles

Effect of composition gradient on detonation initiation in fuel-rich hydrogen-air mixtures in an obstructed channel

Numerical simulations were performed to study the effect of composition gradient and obstacle arrangement on detonation initiation in fuel-rich hydrogen-air mixtures. A third-order WENO method with adaptive mesh refinement (AMR) was used to solve the unsteady, fully-compressible, reactive Navier-Stokes equations coupled to a calibrated chemical-diffusive model (CDM). An obstructed channel at a blockage ratio of 0.3 filled with non-uniform hydrogen-air mixtures of an average H2 concentration 50 vol% was considered. The results show that unilateral obstacle arrangement is more conducive to flame acceleration (FA) and DDT than bilateral obstacle arrangement for both homogeneous and inhomogeneous mixtures. For inhomogeneous mixtures, the flame accelerates faster, and the detonation onset time is shorter when obstacles are placed on the sidewall with a hydrogen concentration closer to the stoichiometric ratio than the those when obstacles are placed on the other sidewall. However, the placement of unilateral obstacles on either the upper or lower sidewall does not significantly affect the DDT run-up distance. Besides, for fuel-rich inhomogeneous hydrogen-air mixtures, detonation tends to be initiated in the regions of high H2 concentration. Idealized models were introduced to simplify the intricate interactions of the reaction waves and flow fields to better understand the connection between H2 concentration distribution and detonation initiation. The analysis suggests that the minimum shock strength required for detonation initiation decreases with increasing equivalence ratio. This is supported by a kinetics analysis with detailed reaction model, which shows that ignition delay increases with decreasing equivalence ratio when detonation is about to be initiated.

Micro-jetting and Transverse Waves in Oblique Detonations

We present a highly-resolved 2D numerical simulation of a wedge-induced Oblique Detonation Wave (ODW) using a 9-species 21-reaction chemical kinetic mechanism for a stoichiometric H2-air mixture. Adaptive Mesh Refinement (AMR) is leveraged to obtain a resolution close to the continuum limit at the finest level (Δxfinest=0.78μm=20λ, where λ is the mean-free path of the fuel–air mixture), which spans the ODW front and its transverse waves. The simulation is performed for a sufficiently large domain, enabling us to unveil the multi-zonal structure of the ODW. We capture, for the first time, the onset of microscopic hypersonic jets (micro-jets) far downstream of the wedge tip associated with cellular structures resembling those of a multi-headed Normal Detonation Wave (NDW). In contrast, the upstream “cell-like” structure (christened as “pseudo-cellular” hence) are found to be devoid of these micro-jets with a morphology similar to that of single-headed NDWs, such as spinning/zig-zag detonations in tubes/2D channels, respectively. A detailed investigation into the transverse-shock structure downstream reveals that a colliding pair of transverse waves lead to the micro-jetting phenomenon. The absence of one of the pair of transverse waves in the upstream region results in the observed pseudo-cellular structures. The origin of these transverse waves in an ODW, unclear in previous literature, is shown to arise from coalescing and strengthening of Compression Waves (CWs) that are produced from two distinct mechanisms. During the “early” phase of the ODW stabilization, CWs are formed as a result of local blast events. In the subsequent “middle” phase, these are formed as a result of the shear-layer instabilities coupling with the local shock structure, leading to the so-called left-running transverse waves (LRTWs) upstream and the right-running transverse waves (RRTWs) downstream. The identified mechanisms offer a plausible explanation on why ODWs exhibit a multi-zonal morphology.Novelty and Significance StatementThe present study is one of the very few studies in the Oblique Detonation Wave (ODW) literature that includes multi-step chemistry while solving for the compressible reacting Navier-Stokes equations on a large simulation domain revealing the multi-zonal structure of the ODW. Furthermore, the resolution employed for the study approaches the continuum limit, making it on-par with the current state-of-the-art for ODW simulation. For the first time, this study has demonstrated the existence of microscopic hypersonic jets (micro-jets) far downstream of the wedge tip in a wedge-induced ODW and a method to isolate them in numerical simulations, leading to insights on the broader micro-jetting phenomenon in detonations. The existence of a cell-like (which we term as “pseudo-cellular”) region bearing similarity with that of single-headed spinning detonations is also noted due to the absence of a transverse wave family upstream. The exact physical mechanisms leading to the formation of transverse waves in ODW are also investigated, which were previously ambiguous in the literature.

Discrete Boltzmann model with split collision for nonequilibrium reactive flows

Abstract A multi-relaxation-time discrete Boltzmann model (DBM) with split collision is proposed for both subsonic and supersonic compressible reacting flows, where chemical reactions take place among various components. The physical model is based on a unified set of discrete Boltzmann equations that describes the evolution of each chemical species with adjustable acceleration, specific heat ratio, and Prandtl number. On the righ-hand side of discrete Boltzmann equations, the collision, force, and reaction terms denote the change rates of distribution functions due to self- and cross-collisions, external forces, and chemical reactions, respectively. The source terms can be calculated in three ways, among which the matrix inversion method possesses the highest physical accuracy and computational efficiency. Through Chapman-Enskog analysis, it is proved that the DBM is consistent with the reactive Navier-Stokes equations, Fick's law and Stefan-Maxwell diffusion equation in the hydrodynamic limit. Compared with the one-step-relaxation model, the split collision model offers a detailed and precise description of hydrodynamic, thermodynamic, and chemical nonequilibrium effects. Finally, the model is validated by six benchmarks, including multicomponent diffusion, mixture in the force field, Kelvin-Helmholtz instability, flame at constant pressure, opposing chemical reaction, and steady detonation.

Three-dimensional shock–flame interactions: effect of wall friction

Multi-dimensional numerical simulations were performed to study the interactions between shock wave and premixed flame. The three-dimensional (3D) fully-compressible, reactive Navier–Stokes equations were solved using a high-order numerical method on a dynamically adapting mesh. The effect of wall friction on the shock–flame interaction was examined by varying wall boundary condition on sidewall. The simulations agree with previous experiment in terms of flame perturbation and flame evolution. The results show two effects of wall friction on flame–shock interaction: (1) flame stretching and (2) damping of local flame perturbation very close to the no-slip wall. The stretch effect leads to non-uniform development of the perturbated flame and consequently a significantly higher growth rate in both global flame perturbation and averaged pressure in the no-slip case compared to the free-slip case. By contrast, the damping effect locally moderates the flame perturbation in close proximity to the no-slip wall because less vorticity is deposited on this part of flame during shock–flame interaction. Quantitative analysis of vortex dynamics suggests that vorticity generation that is produced by baroclinic torque and enhanced by the dilation term during shock–flame interaction causes a growth of flame perturbation via Richtmyer–Meshkov instability. Nevertheless, the vorticity generation is greatly weakened in close proximity to the no-slip wall by the viscous torque and viscous dissipation terms due to friction.

Effects of swirling inflow on the stability and combustion mode of rotating detonations

In this study, a novel approach for enhancing the stability of rotating detonation waves (RDWs) with the use of a swirling inflow strategy is presented. A series of numerical simulations are carried out by solving the two-dimensional reactive Navier–Stokes equations. The effects of the swirling angle on the stability of the RDWs and the combustion mode are analyzed. The results show that the formation of the burnt gas bumps is suppressed by the implementation of a swirling inflow. The swirling inflow also contributes to an increased homogeneity of the reactant within the fuel refill zone. As a result, a remarkable enhancement of the stability of the RDWs in terms of their oscillations in heights and inclined angles is achieved without an apparent compromise of the heights of the RDWs. The propagation speeds of the RDWs are controllable within a wide range approximately from 81% to 114% of the Chapman–Jouguet detonation speed by adjusting the swirling angle. Moreover, the oscillations in the instantaneous fuel consumption rates of both detonative and deflagrative combustion are dominated by the oscillation in the height of the RDW; hence, the swirling inflow reduces the oscillations in these two fuel consumption rates and subsequently the detonation fraction. Consequently, the smoothness of the performance output in terms of specific impulses can be significantly improved with a reduced standard deviation of oscillation up to 84% by the implementation of swirling inflows, and the averaged specific impulse only encounters a small deficit of no more than 7.4%.

Numerical investigation of detonation initiation in a modeled rotating detonation engine

In experimental studies, single-wave mode and two counter-rotating wave mode are often observed in rotating detonation combustors. To investigate the mechanism behind different propagation modes, high-resolution numerical simulations of two-dimensional detonation in hydrogen/air mixtures are conducted by solving the reactive Navier–Stokes equations with a detailed chemical mechanism. The numerical results show that the occurrence of the dual-wave detonation propagation mode is positively influenced by an increase in both the channel width and the initial pressure. The dual-wave modes are observed when increasing the channel width, and it is found that the dual-wave modes are caused by increasing the residual premixed gas height near the inner wall. When increasing the initial pressure, the initial peak detonation heat release increases, which leads to the increase in the hot spot intensity formed, and it is found that the dual-wave modes are mainly caused by the interactions between the initial detonation wave and the inner wall. However, the initial equivalent ratio appears to have a relatively minor impact on the detonation propagation mode due to a relatively narrow range variation of physical properties. The peak heat release rate exerts a greater influence on the change of the propagation mode than the induction time does through a wider range test on rotating detonation engines' working condition. Moreover, the velocities and the cell sizes of detonation waves propagating in different directions with different channel widths are also analyzed, revealing that the characteristics of the detonation waves propagating in different directions are nearly the same.

Numerical study on the reinitiation mechanism of detonation propagating through double slits in a planar channel

In this study, numerical simulations were performed to investigate the reinitiation of diffracted detonation waves through a double-slit-plate. A planar detonation wave was set to propagate through a channel of a height of 50 mm filled with the stoichiometric mixture of hydrogen and oxygen at 20 kPa. Several slit-plates with different slit widths and slit spacing were considered to explore the effects of slit geometry on reinitiation and its underlying mechanisms. For this, two-dimensional multi-species reactive Navier–Stokes equations were solved using a finite volume solver. The results revealed that upon diffraction, the detonation waves become decoupled and subsequently exhibit one of three distinct phenomena depending on the specific slit geometry. These phenomena include reinitiation by shock–shock interaction (RSSI), reinitiation by shock-wall interaction (RSWI), and complete suppression. It was found that a residual transverse wave is crucial in generating a detonation kernel. In cases where this residual transverse wave is absent, the detonation kernel fails to develop. As a result, only complete suppression of the detonation wave was observed. The narrow slit widths effectively suppress residual transverse waves through the steep expansion that occurs as the detonation front passes through the slit. Moreover, larger slit spacing resulted in further expansion of the shock front before the collision, due to the increased time delay for the shock waves to intersect. As a result, it was found that a larger slit spacing is unfavorable for the formation of a detonation kernel. Yet, in this regard, it is important to note that the onset of RSSI was not guaranteed even with a detonation kernel. Rather, the onset of RSSI was highly dependent on the curvature of the main detonation trajectory. RSSI was inhibited in cases where the forward propagating detonation wave experienced significant expansion due to the large curvature of the main detonation wave trajectory. Smaller slit spacing was found to be particularly unfavorable for RSSI as they exhibit more divergent curves. Overall, this study illustrates that the reinitiation mechanisms of detonation show two different pathways in the transition to detonation from decoupled shock waves and reaction fronts upon diffraction propagating through double slit configurations, and enhances understanding of RSSI by providing insights into the complex interplay between slit geometry, detonation kernel formation, and curvature of detonation wave based on highly-resolved numerical simulations using detailed chemistry. The findings from this study have implications towards the design and optimization of systems involving detonation propagation and suppression.Novelty and significanceThis study focuses on the reinitiation mechanism of detonation propagating through double slits in a planar channel. Specifically, this numerical study aims to understand the critical behaviors that occur when the slit width and the cell width of the detonation are comparable, based on the previously reported experiment. Reinitiation by shock–shock interaction which had previously been limited in understanding was explained in detail and the effects of slit geometry were examined. It is worth noting that there is a lack of in-depth explanations in the literature regarding the double slit configuration with various dimensions of slit-plates. Moreover, this investigation deals with smaller scales of slit width compared to the well-known critical length scale of a planar channel which is about ten times of cell width. As a result, the findings of this study offer further insights for optimizing the design of detonation arrestors.

Detailed simulations of one-dimensional detonation propagation in dilute n-heptane spray and air mixtures

One-dimensional numerical simulations based on the hybrid Eulerian–Lagrangian approach are performed to investigate detonation dynamics in two-phase gas-droplet n-heptane/air mixtures with and without liquid fuel pre-vaporization. The reactive Navier–Stokes equations considering the two-way coupling for interphase exchanges of mass, momentum, energy, and species are solved with a skeletal mechanism consisting of 44 species and 112 reactions. The effects of n-heptane droplet diameter and equivalence ratio (ER) on average detonation speed and mode are studied. For pre-vaporization cases, the average detonation speed first decreases and then increases with droplet diameter ranging from 2.5 to 40 μm, which is minimum at 7.5–10 μm due to the competition between fuel vapor addition and droplet evaporative heat absorption. However, the average speed increases monotonically as the droplet ER increases from 0.2 to 1.2. A further increase in the droplet ER (e.g., 2.4) would lead to detonation suppression in the presence of large droplets (e.g., above 30 μm). The detonation is fully quenched when the droplet ER is 3.2. Similar observations are also made for the pure sprayed cases without n-heptane pre-vaporization, where the average speed increases rapidly for droplet ER of 0.2–0.8 and slowly for ER of 0.8–1.6. Various detonation modes are observed with respect to droplet diameter and equivalence ratio, either with or without fuel pre-vaporization. Generally, the pure sprayed cases show more irregular behaviors in detonation propagation. The laden droplets provide a new approach to control the intrinsically unstable or highly irregular behaviors of pure gas or pure sprayed detonations. The finite, small disturbances from the spatially non-uniform droplets, and enrichment from the droplet evaporative mass addition, are two essential mechanisms for the mitigation of the pulsating detonation.

Detonation wave structure and thrust variation of a ram accelerator with different projectile velocities

A study was conducted to investigate the effect of velocity on the detonation wave structure and thrust of a ram accelerator using a simulation of a premixed, reacting flow over a conical projectile. The simulation involved solving the compressible reactive Navier-Stokes equations with a detailed chemical model in a channel with a supersonic stoichiometric hydrogen-oxygen inflow. Results showed that at projectile velocities lower than the Chapman-Jouguet detonation velocity, a thermally choked unstart occurs. As the projectile velocity increases, the overdriven detonation mode, trans-detonative mode, and super-detonative mode successively form. The maximum thrust was achieved at the lower velocity limit under the overdriven normal detonation condition, but decreased continuously as an oblique detonation wave formed. The super-detonative mode was distinguished by the smoothness of the tail thrust derived from the recirculation zone and ignition before the conical ramp led to an unstart at the upper velocity limit.

On the mechanism of “tulip flame” formation: The effect of ignition sources

The initial stages of hydrogen–air flame propagation in tubes and the mechanism of tulip flame formation are investigated using a high-order numerical code to solve the fully compressible reactive Navier–Stokes equations for a spark or planar igniting flame at the closed end of a tube and propagating to the opposite closed or open end. It is shown that the mechanism of tulip flame formation is universal for both sparked and planar ignited flames in tubes with both ends closed. Flame front inversion results from the tulip-shaped profile of the unburned gas axial velocity near the flame front, which is the result of the superposition of the unburned gas flow generated by the accelerating flame and the reverse flow generated by the rarefaction wave during flame deceleration. In a half-open tube, this mechanism is valid for spark ignited flames. In the case of planar ignition, there is no rarefaction wave, but the growth of bulges on the sidewalls leads to the formation of a tulip flame.

Pore-scale resolved simulation of quenching, acceleration, and transition to detonation of hydrogen explosions by metal foams

Pore-scale simulations of quenching, acceleration, and transition to detonation of gaseous hydrogen explosions by metal foams were performed. The model solves the three dimensional compressible reactive Navier-Stokes equations with detailed chemistry in a closed square channel with a metal foam placed inside. The structures of the foam were fully resolved using an immersed boundary method. Stoichiometric mixtures of hydrogen-oxygen and hydrogen-air were considered. An explosion in the channel was initiated with a high-pressure and high-temperature spark. The simulation results show that the explosion can be quenched, accelerate, or transition to detonation depending on the foam pores-per-inch (PPI). Hydrogen-air explosions were quenched with foams of ∼39 PPI or higher due to heat losses from the flame, which is consistent with experimental observations. The explosion was not quenched by foams with low PPI. Instead the low PPI foams exacerbated the explosion by causing flame acceleration. Worse, a 78 PPI foam caused a stoichiometric H2 and O2 mixture to transition to detonation. Hydraulic resistance due to products venting away from the flame surface was found to produce strong pressure gradients within the foam. This causes a self-pressurizing effect that grows as the flame propagates further into the foam. The pressure within the foam grows and steepens into a shock. The shock initiated the detonation by a Mach reflection, which is similar to deflagration-to-detonation transition mechanisms in traditional obstacle-laden channels. Statement of SignificanceMetal foam structures are often used as devices to inhibit flames in scenarios where explosion hazards are a concern. Direct numerical simulations were performed to increase understanding of how flames and explosions interact with metal foams. The simulation results show that high pores-per-inch (PPI) foams quench the explosion by removing heat from the flame. Lower PPI foams can have the opposite effect and exacerbate the explosion by promoting flame acceleration or even transition to detonation. Flames self-pressurize as they propagate through low PPI foams due to hydrodynamic friction and gas-dynamic effects from flowing product gases. In extreme cases, the pressure waves near the flame can steepen into a shock and initiate a detonation. These results indicate that improperly selected metal foam flame arresters can exacerbate the explosion.

A study of the occurrence of DDT in an array of obstacles: Combined effects of longitudinal and transverse obstacle spacings

Combustion wave propagation in a channel containing a stoichiometric hydrogen-air mixture and an array of obstacles was investigated, aiming to explore the effects of longitudinal (ls) and transverse (ts) spacings of the obstacles on the occurrence of deflagration-to-detonation transition (DDT). A high-order numerical algorithm and adaptive mesh refinement were adopted to solve reactive Navier-Stokes equations. The spacings, ls and ts, are varied from 1.2 to 6 times the obstacle diameter (do = 12.7 mm). The results show that the occurrence of DDT is largely dependent on ts. The DDT is likely to occur when the ratio of transverse obstacle gap to detonation cell size d/λ ≥ 0.64. The DDT run-up distance and time are closely related to ls and ts. For large ts, the DDT occurrence time increases with ls. However, the DDT distance may decrease significantly as ls increases when ls is relatively small, due to frequent local explosions in the isolated pockets of unreacted material. A requirement for the generation of these isolated explosions can be quantified as (ls/ts)2(12–4br) < 1, where br is the blockage ratio of the channel. For small ts, the increase of DDT distance with ls/ts slows down notably when ls/ts exceeds a threshold, because there is a mechanism characterized by large fluctuations in flame surface area that promotes the occurrence of DDT in the case with a large enough ls/ts.

Characterization of refill region and mixing state immediately ahead of a hydrogen-air rotating detonation using LES

The extraordinary complexity of real Rotating Detonation Combustors (RDC) demands a deep knowledge of each phenomenon involved in the wave development and propagation. Since the reactants are typically injected separately, a key element for the combustor design optimization is understanding the refilling process and the reactants mixing. However, due to the harsh environment and high working frequencies of RDCs, the experimental diagnostics is usually limited, so high-fidelity simulations represent an essential tool to complement the measurements with detailed insights into the flow. In the present work, the non-premixed RDC installed at TU Berlin is simulated with the AVBP code by solving the fully-compressible, spatially-filtered reactive Navier-Stokes equations. The complete hydrogen and air injection system is included in the numerical model to accurately describe both the reactants mixing and the complex turbulent flow field in the resulting refill region. This study shows how both the injection system configuration and its transient interaction with the wave are fundamental for the reactants mixing, as they directly influence the refilled gas properties. Limiting the imbalances between the blockage dynamics of the fuel and oxidizer ducts and optimizing the fuel injectors can improve considerably the homogeneity of the fresh mixture, and consequently the leading shock strength and reasonably the pressure gain. In fact, the detailed analysis of the detonation front speed shown a higher instability near the chamber base for the periodic presence of unmixed reactants. Nevertheless, the unstable root of the front does not affect the whole wave speed, and remaining part propagates steadily thanks to the tangential mixture uniformity. Moreover, the local speed distribution does not appear directly related to the small-scale mixture properties, indicating a higher sensibility to the annulus curvature rather than to the local gas state.

Dimensional analysis and simplified modeling for the cellular structure of premixed gas-phase detonation numerical simulations with single-step kinetics

The current study presents a new simplified model for predicting the detonation cell dimensions obtained by multidimensional gas-phase detonation numerical simulations. Firstly, we present a dimensional analysis of the problem under several simplifying assumptions. We reveal that the normalized detonation cell width and length are approximately governed by only three dimensionless groups. Guided by this result, we develop a simple and analytical blast wave model that is governed by the exact same dimensionless groups. Then, we explore the influence of these dimensionless groups on the regular cellular structure obtained by gas-phase detonation numerical solutions. More specifically, we solve the 2-D compressible reactive Navier–Stokes equations with single-step kinetics and a calorically perfect gas equation of state, and analyze in detail the resulting numerical soot foils. According to these simulation results, we calibrate our new blast wave model to capture the numerically-obtained normalized detonation cell width and length within a maximum relative error of less than 20%. We further validate the new blast wave model against results from the literature and discuss in detail the new model limitations. Also, we show that the blast wave model can be coupled with a new optimization procedure for calibrating flow and reaction parameters to capture realistic detonation properties. Finally, we demonstrate that gas-phase detonation numerical simulations, with parameters derived via the new optimization procedure, can replicate the experimentally measured cell width with a maximum relative error of less than 15%.

Flame Acceleration in Stoichiometric CH4/H2/air Mixtures with Different Hydrogen Blend Ratios in an Obstructed Channel

ABSTRACT Adding a certain percentage of hydrogen into the natural gas pipeline network is regarded as an efficient way to store and transport hydrogen. CH4-H2 binary fuel is also considered to be an important means of hydrogen utilization. In this paper, flame acceleration (FA) in stoichiometric CH4/H2/air mixtures with various hydrogen blend ratios (i.e., Hbr = 0%, 20%, 50%, 80%, and 100%) was studied experimentally and numerically. In the experiments, high-speed photography was used to record the FA process. In the numerical simulations, the two-dimensional, fully-compressible, reactive Navier-Stokes equations were solved using a high-order algorithm on a dynamically adapting mesh. The chemical reaction and diffusive transport of the mixtures were described by a calibrated chemical-diffusive model. The numerical predictions agree reasonably with the experimental measurements. The results show that a larger hydrogen blend ratio leads to a faster FA. The difference in FA due to hydrogen blending mainly depends on the property change of the fuel mixtures, the increase of flame surface area and the interactions between flame and pressure waves, corresponding to three different stages. In addition, the heat loss to the channel walls and obstacle surfaces has an impact on the FA process, especially in the mixtures with low hydrogen blend ratios (i.e., Hbr ≤ 20%). This is related to the weakening of interactions between pressure waves and flame under isothermal boundary condition.

Experimental and numerical study of flame acceleration and DDT in a channel with continuous obstacles

Flame acceleration and deflagration-to-detonation transition (DDT) in obstructed channels is an important subject of research for propulsion and explosion safety. Experiment and numerical simulation of DDT in a stoichiometric hydrogen–oxygen mixture in a channel equipped with continuous triangular obstacles were conducted in this work. In the experiment, high-speed schlieren photography was used to record the evolution of reaction front and strong pressure waves. A pressure transducer was used to record the pressure build-up. In the numerical simulation, a high-order numerical method was used to solve the fully compressible reactive Navier–Stokes equations coupled with a calibrated chemical-diffusive model. The calculations are in good agreement with experimental observations. The result shows that the triangular obstacles can significantly promote flame acceleration and provide conditions for the occurrence of DDT. In the early stages of flame acceleration, the main cause for flame roll-up and distortion is the effect of vortices generated in the gaps between neighbouring triangular obstacles. The scales and velocities of vortices are determined by the positive feedback process between combustion-generated flow and flame propagation. The continuous triangular obstacles create an intricate flow field and increase the complexity of shock reflections. This complicated flow leads to local detonation initiation through different mechanisms, i.e. flame-flame collisions and flame-shock interactions. Successive local detonation ignitions and failures are produced in the obstacle gaps due to the continuous layout of the triangular obstacles. It was found that successive local detonation ignitions are critical for the eventual success of DDT formation because the shock waves generated by them continually strengthen the leading shock. The detonation failure or survival due to diffraction depends on the height of the narrow space (h*) between the bulk flame and obstacle vertex, and can be quantitatively characterised by the ratio of the space height to detonation cell size (), h*/.

Influence of longitudinal obstacle spacing on the deflagration-to-detonation transition through a bank of obstacles in a hydrogen-air mixture

Flame acceleration and deflagration-to-detonation transition (DDT) in a channel containing an array of staggered cylindrical obstacles and a stoichiometric hydrogen-air mixture were studied by solving the fully-compressible reactive Navier-Stokes equations using a high-order numerical algorithm and adaptive mesh refinement. Four different longitudinal spacings (ls) of the neighboring obstacle rows (i.e., ls = 15.28, 19.1, 25.4, and 38.2 mm, corresponding to 1.2, 1.5, 2 and 3 times of obstacle diameter, respectively) were used to examine the effect of obstacle spacing on flame acceleration and DDT. The results show that the main mechanisms of flame acceleration and transition to detonation in all the cases studied are consistent. While the flame acceleration is caused by the growth of flame surface area in the initial stage, it is governed by shock-flame interactions in the later stage when shock waves are generated. The focusing of strong shocks at flame front is responsible for the initiation of detonation. It was found that the flame propagation speed and the DDT run-up distance and time are highly dependent on ls. Specifically, the flame acceleration declines as ls increases, since a larger ls leads to less disturbance of flow by obstacles per unit channel length. For detonation initiation, both the run-up distance and time increase with the increase of ls. It is interesting to note that the DDT distance and time increase significantly as ls increases from 19.1 mm to 25.4 mm. This is related to the slowdown of the increase rate of energy release over a period before DDT occurs under large ls condition, because every time the flame passes over an obstacle row the shock-flame interaction is delayed and numerous isolated pockets of unburned gas material are formed.

Effects of staggered opposed hot jets on the initiation and propagation of gaseous detonation in a supersonic combustible inflow

In this paper, the detonation initiation mechanism of a supersonic combustible mixture triggered by a staggered opposing combined hot jets was performed. Two-dimensional reactive Navier–Stokes equations with a one-step Arrhenius chemistry model were solved using a structured adaptive mesh refinement framework. The results show that a high temperature and pressure region triggers a rapid detonation initiation after the jet-induced bow shock focusing. Further analysis showed that there is a large baroclinic torque behind the local detonation wave induced by the staggered hot jet, which leads to a large Richtmyer–Meshkov instability at the end of the unburned jet, and the generated periodic shedding vortex structure thereby enhances the diffusion effect in the unburned region. However, the released heat cannot support the propagation of the detonation wave. In addition, different jet intensity distribution schemes and jet spacing will change the ignition point position. It is worth noting that the distance of detonation initiation can be significantly shortened by reducing the front jet intensity while maintaining the total jet energy. Increasing the jet spacing will significantly slow down the detonation initiation process.

Minimum ignition energy of hydrogen–ammonia blends in air

We present a numerical analysis to calculate the minimum ignition energy of hydrogen–ammonia blends in air at both under and over atmospheric pressure. Unlike previous calculations, we used the full compressible and reactive Navier–Stokes equations coupled with detailed chemical kinetics (San Diego mechanism for hydrogen, complemented with the San Diego chemistry for nitrogen). The effect of the size of the energy deposition region and the deposition time are considered to determine the most efficient method to ignite the mixture. Our calculations also evaluate the impact of the gas compressibility on the minimum ignition energy after a sudden energy deposition. The results are validated first by comparing the minimum ignition energy of pure hydrogen–air mixtures as a function of the equivalence ratio ϕ with available experimental data and previous numerical results. Then, fuel blends made of mixtures of hydrogen and ammonia (NH3) are considered to calculate the minimum ignition energy as a function of fuel composition, equivalence ratio and pressure. The full range of ammonia volumetric content in the blend is varied between the extreme cases of pure hydrogen and pure ammonia. For each fuel blend, we computed a wide range of equivalence ratios ϕ that, in the case of pure hydrogen at atmospheric conditions, ranged from ϕ=7 to ϕ≃0.07, near the lean flammability limit, to theoretically explain the experimental evidence of ultra-lean flames reported in the literature.

Detonation simulations in supersonic flow under circumstances of injection and mixing

The unsteady, reactive Navier-Stokes equations with a detailed chemical mechanism of 11 species and 27 steps were employed to simulate the mixing, flame acceleration and deflagration-to-detonation transition (DDT) triggered by transverse jet obstacles. Results show that multiple transverse jet obstacles ejecting into the chamber can be used to activate DDT. But the occurrence of DDT is tremendously difficult in a non-uniform supersonic mixture so that it required several groups of transverse jets with increasing stagnation pressure. The jets introduce flow turbulence and produce oblique and bow shock waves even in an inhomogeneous supersonic mixture. The DDT is enhanced by multiple explosion points that are generated by the intense shock wave focusing of the leading flame front. It is found that the partial detonation front decouples into shock and flame, which is mainly caused by the fuel deficiency, nevertheless the decoupled shock wave is strong enough to reignite the mixture to detonation conditions. The resulting transverse wave leads to further mixing and burning of the downstream non-equilibrium chemical reaction, resulting in a high combustion temperature and intense flow instabilities. Additionally, the longitudinal and transverse gradients of the non-uniform supersonic mixture induce highly dynamic behaviors with sudden propagation speed increase and detonation front instabilities.