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Detonation wave driven by aerosolized liquid RP-2 spray
Abstract
Detonation-based engines such as Rotating Detonating Engines (RDEs) have been of significant interest for aerospace propulsion. However, most detonation-related studies have focused on gaseous reactants with the majority of investigations focusing on liquid water interactions with gaseous detonations and shocks. This study explores the dynamics of detonation waves driven by aerosolized liquid fuel sprays. An unlike-doublet impinging-jet injector is used to atomize RP-2 and water into aerosolized liquid droplet cloud of measured droplet size distribution where the detonation wave interacts with the cloud mixture. Evidence of RP-2 driving the detonation phenomenon is quantified using dynamic pressure measurements and four simultaneous optical diagnostic measurements: high-speed schlieren, CH* chemiluminescence, formaldehyde planar laser-induced fluorescence (PLIF), and particle Mie scatter. The results show formaldehyde and CH* generation along with a substantial increase in pressure and wave speed when the detonation wave interacts with the RP2 mixture cloud. On the contrary, the detonation pressure and wave speed decrease are observed when the detonation wave interacts with the water droplet cloud. The investigation provides supporting information on liquid fuel droplet burning and heat release driving the detonation wave.
... An extensive analysis was conducted on the design and optimization of nozzles [21][22][23][24][25] and inlets [26][27][28]. Advanced measurement and diagnostic techniques such as high-speed photography [29,30], OH-PLIF [31][32][33], and OH*/CH*-chemiluminescencem [34][35][36] were implemented to address the issue of measurement of the extreme environment inside the combustion chamber of the RDE. ...
... The value for volume-fraction is estimated based on the liquid fuel injection rate and is approximately 9 × 10 −5 . Even though realistic RDEs would employ liquid injectors which result in a wide distribution of droplets size and velocity [56], to fundamentally understand the effect of injected droplet size on mixing, vaporization, and detonation propagation, a monodisperse injection is considered here. The initialization procedure of the detonation wave in the periodic channel is carefully designed to minimize any numerical artifacts. ...
Considering the recent interest in the use of liquid fuel in rotating detonation engines, there is a need to understand the interactions of a detonation wave with liquid fuel.
Detonation propagation in a three-dimensional periodic channel is simulated in this work using Eulerian-Lagrangian reactive simulations.
To model the non-homogeneity of combustion, discrete injectors for gaseous hydrogen fuel are used, and the liquid spray is injected along with the air from a continuous plenum.
The results show that when the hydrogen injection rate is reduced to a certain condition, the detonation wave is unable to sustain, but the injection of the kerosene spray helps it sustain and the system transitions from a pure gaseous detonation to a hydrogen-driven kerosene-sustained detonation.
Effect of droplet injection diameter and the fuel mass-flow rate are also studied.
Hydrogen promotes the vaporization and the burning of kerosene droplets.
Kerosene vaporization is a relatively slow process and the vapor burns as either a weak detonation or through the post-shock region, which in turn provides sufficient energy for detonation propagation.
Therefore, the contributions of both fuels are interlinked and responsible for sustaining the continuous propagation of the detonation wave.
... Subsequently, Jourdaine et al. [35] investigated a detonation in a reactive dispersed liquid n-heptane droplet cloud using an Eulerian-Eulerian two-dimensional numerical simulation. Recent work by Malik et al. [36] explored the interaction of a detonation wave with a liquid RP-2 spray with simultaneous CH* chemiluminescence, schlieren, planar laser-induced fluorescence (PLIF), and laser Mie scattering, which showed the incoming detonation wave being supported by the liquid RP-2 spray. The works surrounding droplet detonation interaction primarily investigate the influence on the detonation flow field, wave velocity, and final droplet size distribution; however, they do not explore the dynamics of the droplet breakup physics. ...
The deformation and breakup characteristics of liquid rocket propellant 2 (RP-2) droplets are experimentally investigated in a shock tube. The RP-2 droplets are subjected to a weak shock wave, a strong shock, and a detonation wave to deduce the impacts of high-speed and supersonic reacting flows on droplet deformation and breakup. High-speed shadowgraph and schlieren imaging techniques are employed to characterize droplet morphologies, deformation rates, and displacement of the droplet centroid. The results reveal that the transition from a shock wave to a detonation suppresses the deformation of the droplet and augments small-scale breakup. A shift in dominant breakup mechanisms is linked to a significant increase in the Weber number due to an increase in flow velocities and temperatures when transitioning to the detonation case. The experimental data are combined with a droplet stability analysis to predict the “child” (or fragments of the initial “parent” droplet) droplet sizes of each test condition. The child droplet size is shown to decrease as the flow regime transitions toward a detonation. An analytical mass stripping model was also used to determine that the total mass stripped from the parent droplet increased when approaching supersonic reacting conditions. The child droplet sizes and mass stripping rate will ultimately influence evaporation timescales and ignition in supersonic reacting flows, which is important for the development of detonation-based propulsion and power systems.
Spatiotemporal visualization of instantaneous flame structures in a hydrogen-fueled axisymmetric supersonic combustor was investigated using multiview planar laser-induced fluorescence of the hydroxyl radical, coupled with high-speed photography and pressure measurement. The axisymmetric cavity generates a loop-shaped recirculation flow and shear layer that sustains the flame. An irregular and wrinkled flame loop with a central hole is formed near the loop-shaped region. Due to turbulent disturbances, multiple small-scale holes and fragmented flames are randomly distributed in the flame loop or near the wrinkled flame front. The combustion near the cavity shear layer is more likely to be stronger and sustained. As the thickness of the cavity shear layer increases along the axial direction, the flame loop is expanded toward the core flow and the cavity. The flame base anchors near the cavity leading edge with a low global equivalence ratio (GER). The increased GER expands the flame loop to compress the high-speed core flow dramatically, promoting the flame base to propagate upstream along the hydrogen jet wake. The flame base is unable to anchor near the thin boundary layer. Consequently, it propagates reciprocally to enhance the combustion oscillation that disturbs the flame structure dramatically. The flame structure becomes more complex and tendentially fragmented, which increases the fractal dimension, especially near the middle part of the combustor. In comparison, the flame structure near the ramp is more resistant to disturbances due to the dramatic expansion of local flame loop, extending the favorable combustion environment. Despite the instantaneous flame structure being severely wrinkled and even tendentially fragmented, it is primarily sustained within a relatively regular loop region near the cavity recirculation flow and the cavity shear layer.
Stable detonation initiation and combustion are critical in the operation of oblique detonation wave (ODW) engine, especially when the engine is subjected to disturbances. In this paper, the sweeping jet is implemented on the wedge to provide an active flow control method for ODW and the combustion zone behind the waves. Numerical simulations are conducted on basis of two-dimensional URANS equations with detailed chemistry reactions. The results indicate that applying the sweeping jet method can reliably induce the ODW at a wedge angle of 18°, resulting in a 25% reduction in initiation length compared to scenarios without jet. It is attributed to the energy input derived from periodic directional changes. Furthermore, the characteristics of initiation and combustion are investigated under different jet positions and total pressures. In the case where the jet total pressure is fixed at 300 kPa, it is observed that there is minimal variation in both the initiation length and combustion area with the sweeping jet position. When the jet position is held constant and the total pressure of the jet varies between 200 and 400 kPa, it is evident that the initiation length and combustion area are more stable under the sweeping jet conditions compared to steady jet cases. This enhanced stability is attributed to the exceptional mixing performance. Specifically, the turbulent kinetic energy within the reaction region and at the injector outlet is enhanced when subjected to the sweeping jet. The present work ends by emphasizing the effectiveness of the sweeping jet in facilitating the formation of ODW, which may provide an understanding for exploring solutions for reliable and stable detonation initiation and combustion.
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Abstract:
The shock-induced atomization and burning of liquid fuel droplets are paramount for hypersonic propulsion and detonation-based combustion systems. The present work experimentally explores the atomization and aerobreakup of liquid RP-2 droplets in a hypersonic shock tube. The shock tube is operated with normal shocks propagating between Mach 5–10 interacting with RP-2 droplets with diameters between 200 and 300 µm. The droplet deformation and breakup dynamics are characterized by ultra-high-speed 5 MHz shadowgraph imaging diagnostics. For all hypersonic shock-droplet interactions, the droplets first undergo structural deformations with subsequent breakup occurring from a shear-stripping mechanism along the periphery of the droplet. The structural changes and droplet deformation rate are found to be self-similar among all cases, and the rate of deformation collapsed to a unified non-dimensional timescale. The complete breakup time of the fuel droplets were analyzed, and theoretical scaling arguments were used to quantify the effects of the Mach number, Weber number, and Ohnesorge number. The experimental data is then used to develop a modified boundary layer stripping model to estimate the breakup time of liquid drops. The model leverages the concept of displacement and momentum thickness to provide a numerical solution to estimate droplet breakup times when exposed to a high-speed gas stream. The model is compared to the experimental RP-2 data and water data available in the literature. The model predicts the breakup time for a range of droplet sizes between 200 and 2000 µm within a reasonable accuracy. The results can be used to optimize liquid fuel injection for hypersonic and detonation-based combustion systems.
Traditional exhaust-gas turbocharging exhibits hysteresis under variable working conditions. To achieve rapid-intake supercharging, this study investigates the synergistic coupling process between the detonation and diesel cycles using gasoline as fuel. A numerical simulation model is constructed to analyze the detonation characteristics of a pulse-detonation combustor (PDC), followed by experimental verification. The comprehensive process of the flame’s deflagration-to-detonation transition (DDT) and the formation of the detonation wave are discussed in detail. The airflow velocity, DDT time, and peak pressure of detonation tubes with five different blockage ratios (BR) are analyzed, with the results imported into a one-dimensional GT-POWER engine model. The results indicate that the generation of detonation waves is influenced by flame and compression wave interactions. Increasing the airflow does not shorten the DDT time, whereas increasing the BR causes the DDT time to decrease and then increase. Large BRs affect the initiation speed of detonation in the tube, while small BRs impact the DDT distance and peak pressure. Upon connection to the PDC, the transient response rate of the engine is slightly improved. These results can provide useful guidance for improving the transient response characteristics of engines.
This research quantifies the evolution of pressure for fast burning regimes characterized by various degrees of compressibility and involving turbulent flames and shocks. The experimental exploration is conducted in a Turbulent Shock Tube facility, where the level of flame compressibility is controlled by varying the equivalence ratio of the hydrogen-air mixture. High-speed particle image velocimetry, chemiluminescence, schlieren, and pressure measurements are simultaneously acquired to capture the rise in stagnation pressure for various regimes from fast flames to shock-flame complexes. The pressure and velocity measurements are used to analyze combustion regimes on the Rankine-Hugoniot diagram that shows the flame-driven compression for a range of fast flame conditions evolving toward detonation onset. Various levels of compression are dependent on the level of shock-flame coupling and flame velocities. Lower degrees of compressibility show 52% efficiency of an ideal ZND cycle with 40% thermal efficiency, while shock-flame complexes are shown to produce 81% of the work produced by an ideal ZND cycle with 53% thermal efficiency.
The present experimental study investigates the shear stripping breakup of single droplets in subsonic and supersonic gaseous flows. In contrast to most research that places emphasis on the Weber number (We), we focus on the individual effects exerted by flow Mach (M∞) and Reynolds numbers (Re). Millimeter-sized droplets made of either ethylene glycol or water are exposed to shock-induced flows. Shadowgraph and schlieren images of the breakup process are recorded by an ultra-high-speed camera. The experimental We is constrained at 1100, while M∞ is varied from 0.3 to 1.19 and Re from 2600 to 24,000. A systematic analysis of the experiment series reveals that the breakup pattern alters with M∞ although a constant We is maintained. The classical stripping behavior with fine mist shed from the peripheral sheet changes to rupture of multiple bags along the periphery at M∞ = 0.63, and further to stretching of ligament structures from the leeward surface at M∞ = 1.19. The corresponding breakup initiation is delayed and the resultant fragments are sized less uniformly and distributed over a narrower spread. In terms of the early-stage deformation, droplets experience less intense flattening and slower sheet growth at higher M∞. The change of Re introduces additional variations, but only to a minor extent.
Graphical abstract:
Detonation experiments are conducted in a 52 square channel with an ethylene–air gaseous mixture with dispersed liquid water droplets. The tests were conducted with a fuel–air equivalence ratio ranging from 0.9 to 1.1 at atmospheric pressure. An ultrasonic atomizer generates a polydisperse liquid water spray with droplet diameters of 8.5–12 \upmu \hbox {m}, yielding an effective density of 100–120 . Pressure signals from seven transducers and cellular structure are recorded for each test. The detonation structure in the two-phase mixture exhibits a gaseous-like behaviour. The pressure profile in the expansion fan is not affected by the addition of water. A small detonation velocity deficit of up to 5 % was measured. However, the investigation highlights a dramatic increase in the cell size () associated with the increase in the liquid water mass fraction in the two-phase mixture. The detonation structure evolves from a multi-cell to a half-cell mode. The analysis of the decay of the post-shock pressure fluctuations reveals that the ratio of the hydrodynamic thickness over the cell size () remains quite constant, between 5 and 7. A slight decrease of this ratio is observed as the liquid water mass fraction is increased, or the ethylene–air mixture is made leaner.
By using laser-induced fluorescence to visualize liquid drops that are suddenly exposed to supersonic gas streams, we show that the previously available experimental results, which are based on the shadowgraph method, allowed misinterpretations that have lead to inappropriate conceptualizations (and theory) of the physics that govern breakup at high Weber numbers (We>103)—instead of the Rayleigh–Taylor piercing, the dominant mechanism is shear-induced motion with a significant radial component and instabilities on the so-generated, stretched liquid sheet. At low Weber numbers (We
The calculation of the detonation velocity in monodisperse mixtures of kerosene droplets and gaseous oxygen is described. The stationary Z-N-D detonation wave model is used. It is proposed that only that part of the fuel, which has been shattered by the high speed gas flow can react instantaneously at the C-J plane. The part of the fuel which burns behind the C-J plane does not have any effect on the detonation wave velocity. The C-J plane position is determined by the ignition time delay.The amount of fuel supporting the detonation was calculated using experimentally determined expressions for the variation of the velocity and the mass of the shattering droplets.Results of the calculations show good agreement with published experimental results.
Two-dimensional (2-D) numerical simulations based on the Eulerian–Lagrangian method that take droplet break-up into account are conducted to clarify the mean structure of gaseous detonation laden with a dilute water spray. The premixed mixture is a slightly diluted stoichiometric hydrogen–oxygen mixture at low pressure. The simulated results are analysed via 2-D flow fields and statistical Favre spatiotemporal averaging techniques. Gaseous detonation with water droplets (WD) propagates stably with a velocity decrease compared with the dry Chapman–Jouguet speed. The mean structure of gaseous detonation with dilute water spray shares a similar structure as the one without water spray. However, the hydrodynamic thickness is changed due to the interaction with water spray. Overall interphase exchanges (mass, momentum and energy) that take place within the hydrodynamic thickness induce a decrease of the detonation velocity and lower the level of fluctuations downstream of the mean leading shock wave. Droplet break-up occurs downstream of the induction zone and in our case, the water vapour from the evaporation of water spray does not affect the reactivity of gaseous detonation. The laminar master equation for gaseous detonation laden with inert WD shows that the hydrodynamic thickness should rely on the gaseous sound speed, and works well as the working mixture is weakly unstable and its cellular structure is regular. The droplet flow regimes and break-up modes have also been determined. The characteristic lengths of detonation and interphase exchanges have been ordered under the present simulation conditions and have been shown to be intimately intertwined.
Achieving unconfined supersonic explosions
In some forms of supernovae and chemical explosions, a flame moving at subsonic speeds (deflagration) spontaneously evolves into one driven by a supersonic shock (detonation), vastly increasing the power output. The mechanism of this deflagration-to-detonation transition (DDT) is poorly understood. Poludnenko et al. developed an analytical model to describe DDTs, then tested it with lab experiments and numerical simulations. Their model successfully reproduced the DDT seen in the experiments and predicted a DDT in type Ia supernovae, which is consistent with observational constraints. The same mechanism may apply to DDTs in any unconfined explosion.
Science , this issue p. eaau7365
Experimental and numerical study of the detonation has been conducted in heterogeneous reactive two-phase media made of liquid isooctane sprays dispersed in gaseous oxidizing atmospheres. Influence of the oxidizer composition on conditions of detonation formation and propagation regimes, with particular attention on the existence of the so-called cellular structure, has been studied.
Experiments have been performed under standard initial conditions of temperature and pressure (293 K, 1 bar) in a 4-m long vertical, square cross-section (53 × 53 mm²) detonation tube. The mean isooctane droplet size was of about 30 µm. When oxidizing mixture was made of air (O2 + βN2 with β = 3.76), three detonation regimes have been observed with increasing equivalence ratio: a spinning regime, a marginal one with half a cell structure, and a normal multi-headed detonation regime. At smaller dilution ratio (β = 2 and 1), only the multi-headed detonation regime was observed, with smaller cell size. When nitrogen is replaced by argon as inert diluent, the detonation structure is multi-headed; the cellular structure is more regular and the cell size is smaller than with nitrogen.
Numerical simulations have been performed with the EFAE code, with taking in consideration the chemical composition of the oxidizing phase and the effects of the two-phase mixture richness. Results of 2D and 3D numerical simulations, as a function of the equivalence ratio and the dilution, display propagation regimes and detonation cell sizes in reasonable agreement with the experimental results.
The propagation of a detonation wave in a tube containing a single stream of 2600‐μ‐diam diethylcyclohexane droplets dispersed in gaseous oxygen has been studied with streak and space resolved photography, special pressure transducers, and thin‐film heat‐transfer gauges. The detonation wave, which reached a velocity of 4100 ft/sec, consisted of a planar shock front followed by secondary shocks and a gradual decrease in pressure as heat is added. A detailed history of an individual drop within the reaction zone is presented. Under the observed conditions a 2600‐μ‐drop disintegrates continuously over a period of 500 μsec. Combustion is initiated in the wake of the drops at 65 μsec after the passage of the shock with the reaction zone considered completed in 670 μsec. One‐dimensional equations for a two‐phase Chapman‐Jouguet detonation wave with mass and heat addition within the reaction zone, and momentum and heat transfer out of the reaction zone are derived. Comparison of the experiments with the theoretical prediction yields a reasonable agreement.
Programs that simulate constant volume explosions and ZND profiles are very important tools for making predictions on the outcome of expensive experiments. Each of these programs uses the post-shock state as initial conditions for its computation. The post-shock state which is the second intersection of the Rayleigh line and the reactant Hugoniot can be found analytically for gas mixtures with constant properties, but must be solved iteratively for gas mixtures with temperature dependent properties. Our software has traditionally iterated on a single variable, the density ratio, to find the post-shock state. Unfortunately, for very strong shock waves, the output of this single variable algorithm is incorrect. Reynolds' STANJAN program also has the capability of calculating the post-shock state and is successful in a much wider range than our one variable method. This report outlines the algorithms that STANJAN uses to calculate both the post-shock state and the Chapman-Jouguet detonation velocity.
http://deepblue.lib.umich.edu/bitstream/2027.42/6816/5/bac9845.0001.001.pdf http://deepblue.lib.umich.edu/bitstream/2027.42/6816/4/bac9845.0001.001.txt
Solutions to the differential equations governing the structure of a steady‐state detonation in a spray are obtained both numerically and by means of analytical approximations for the case in which the droplets in the spray burn heterogeneously. It is shown that, for reasonable droplet burning rates, the detonation structure corresponds almost precisely to the spray analog of the von Neumann hypothesis of a shock wave followed by a deflagration zone. The size of the burning region is demonstrated to be large enough to cast doubt upon the stability of a spray detonation not supported to a significant extent by purely gaseous reactions.
Methods designed to quench a detonation wave in a pipe usually rely on some passive device which often presents an unacceptable impedance to the normal pipe flow. One method which overcomes this problem is a triggered water spray barrier, the principles of which are examined in the present study.Experimental data on detonation quenching were obtained in a vertical tube, 76 mm diameter, fitted with various spray generators. The empirical relations of Ranger and Nicholls were then used to calculate the rate at which water is stripped from a droplet in the shock flow field to form a micromist, thus enabling the energy loss from the wavefront in heating and vapourising the micromist to be found. Application of the Shchelkin criterion to the quenching mechanism shows that a 20% energy loss is required from the wavefront. This requirement is met at distances ranging from 0.2 to 1.0 cell lengths which is in reasonable agreement with the expected position of the CJ plane.
Applications of detonations to propulsion are reviewed. First, the advantages of the detonation cycle over the constant pressure combustion cycle, typical of conventional propulsion engines, are discussed. Then the early studies of standing normal detonations, intermittent (or pulsed) detonations, rotating detonations, and oblique shock-induced detonations are reviewed. This is followed by a brief discussion of detonation thrusters, laser- supported detonations and oblique detonation wave engines. Finally, a more detailed review of research during the past decade on ram accelerators and pulsed detonation engines is presented. The impact of the early work on these recent developments and some of the outstanding issues are also discussed. In this paper, the status of propulsion applications of detonations is reviewed. First, a cycle analysis is performed to show that the ef- é ciencyof a detonation cycleisclosetothat of the constant-volume Humphrey cycle, which is much more efécient than the constant- pressure Brayton cycle,characteristicof most conventional propul- sion systems. Other advantages of detonations are also discussed. Then a review of the early attempts to use detonations for propul- sionispresented.Aftera briefdiscussionof the possible reasonsfor the successes and failures of the early attempts, more recent work during the 1980s on oblique detonation wave engines is reviewed. This is followed by a detailedanalysis of the ram acceleratorin the detonative mode and the pulsed detonation engine, a topic of great current interest. Finally, some observations from the lessons learnt in the past and their potential implications for further development of detonations for propulsion applications are presented.
In this review, we consider and unify all aspects of the dynamics of Newtonian and viscoelastic liquid drops in high-speed gas flows, including shock waves. The path to understanding is opened by novel, laser-induced fluorescence visualizations at spatial resolutions of up to 200 pixels for millimeter and exposure times as low as 5 ns. The central role of the competition between Rayleigh-Taylor and Kelvin-Helmholtz instabilities is assessed in the frame of rich aerodynamics, from low subsonic to supersonic, and the multitude of characteristic length scales and timescales at play with varying liquid properties. Acceleration and liquid redistribution (drop deformation) early in the evolution set the stage for this competition, and we insist on an interpretation of the drag coefficient that is physically meaningful. Two principal breakup regimes (patterns of bodily loss of coherence) are identified depending on whether the gas finds its way through the liquid mass, causing gross disintegration, or goes aroun...
Recent experimental results on the development and propagation of detonation in sprays of liquid diethylcyclohexane (DECH) in gaseous oxygen are presented. Three drop sizes are used: 290 μ, 940 μ and 2600 μ. It is found that the smaller the drop size, the faster the detonation develops into a steady state. The steady velocity for mixtures ranging from 0.2–1.0 in equivalence ratio, is found to be lower than the ideal Chapman-Jouguet velocity. The difference is 2–10% for the 290-μ and the 940-μ sprays, and 30%–35% for the 2600-μ. Heat-transfer measurements and inferred frictional losses to the walls are used, in conjunction with a reaction length assumed to be controlled by the break-up of the drops, to arrive at a relationship between the experimental and the ideal (no loss) velocities. The relationship shows direct dependence of velocity difference on drop size and results in a calculated difference of 4%, 10%, and 26% for the 290-μ, 940-μ, and 2600-μ sprays, respectively.Schlieren and direct light photographs of the phenomenon are also presented. They show a rather complicated structure of the flow field behind the front due to the interaction of the gaseous convective flow and the initially stationary drops.
The breakup of viscous and viscoelastic drops in the high speed airstream behind a shock wave in a shock tube was photographed with a rotating drum camera giving one photograph every 5 μs. From these photographs we created movies of the fragmentation history of viscous drops of widely varying viscosity, and viscoelastic drops, at very high Weber and Reynolds numbers. Drops of the order of one millimeter are reduced to droplet clouds and possibly to vapor in times less than 500 μs. The movies may be viewed at http://www.aem.umn.edu /research/Aerodynamic_Breakup. They reveal sequences of breakup events which were previously unavailable for study. Bag and bag-and-stamen breakup can be seen at very high Weber numbers, in the regime of breakup previously called ‘catastrophic’. The movies allow us to generate precise displacement–time graphs from which accurate values of acceleration (of orders 104 to 105 times the acceleration of gravity) are computed. These large accelerations from gas to liquid put the flattened drops at high risk to Rayleigh–Taylor instabilities. The most unstable Rayleigh–Taylor wave fits nearly perfectly with waves measured on enhanced images of drops from the movies, but the effects of viscosity cannot be neglected. Other features of drop breakup under extreme conditions, not treated here, are available on our Web site.
A theoretical model including a detailed chemical kinetic reaction mechanism, for hydrogen and hydrocarbon oxidation is used to examine the effects of variations in initial pressure and temperature on the kinetic induction properties of gaseous fuel-oxidizer mixtures. Fuels considered include hydrogen, methane, ethane, ethylene, and acetylene. Induction lengths are computed for initial pressures between 0.01 and 10.0 atmospheres and initial temperatures between 200 K and 500 K. These induction lengths are then compared with available experimental data for critical energy and critical tube diameter for initiation of spherical detonation, as well as detonation limits in linear tubes. Combined with earlier studies concerning variations in fuel-oxidizer equivalence ratio and degree of dilution with N2, the model provides a unified treatment of fuel oxidation kinetics in detonations.
New experimental and analytical results are reported for the problem of liquid drop shattering. Breakup is observed to occur as a result of the interaction between a drop and the convective flowfield established by the passage of a shock wave over it. The purpose of this investigation, which supplements and extends previous experimental and theoretical studies, is to establish the influence of various parameters on the rate of disintegration and on the time required for breakup to occur. Photographic, drop displacement, and break-up time information is presented for a range of conditions which involve shock waves moving at Mach numbers Ms = 1.5-3.5 in air over water drops having diameters of 750-4000μ. A model is formulated for the breakup phenomenon by considering that it results from a boundary-layer stripping mechanism. The experimental determination of the variation of drop shape and of drop velocity with time is used together with the analytical results to compute the disintegration rate. © 1969 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.