An experimental investigation of the propagation mechanism of critical deflagration waves that lead to the onset of detonation

The reflection of a CJ detonation from a perforated plate is used to generate high speed deflagrations downstream in order to investigate the critical conditions that lead to the onset of detonation. Different perforated plates were used to control the turbulence in the downstream deflagration waves. Streak Schlieren photography, ionization probes and pressure transducers are used to monitor the flow field and the transition to detonation. Stoichiometric mixtures of acetylene–oxygen and propane–oxygen were tested at low initial pressures. In some cases, acetylene–oxygen was diluted with 80% argon in order to render the mixture more “stable” (i.e., more regular detonation cell structure). The results show that prior to successful detonation initiation, a deflagration is formed that propagates at about half the CJ detonation velocity of the mixture. This “critical” deflagration (which propagates at a relatively constant velocity for a certain duration prior to the onset of detonation) is comprised of a leading shock wave followed by an extended turbulent reaction zone. The critical deflagration speed is not dependent on the turbulence characteristics of the perforated plate but rather on the energetics of the mixture like a CJ detonation (i.e., the deflagration front is driven by the expansion of the combustion products). Hence, the critical deflagration is identified as a CJ deflagration. The high intensity turbulence that is required to sustain its propagation is maintained via chemical instabilities in the reaction zone due to the coupling of pressure fluctuations with the energy release. Therefore, in “unstable” mixtures, critical deflagrations can be supported for long durations, whereas in “stable” mixtures, deflagrations decay as the initial plate generated turbulence decays. The eventual onset of detonation is postulated to be a result of the amplification of pressure waves (i.e., turbulence) that leads to the formation of local explosion centers via the SWACER mechanism during the pre-detonation period.     

Direct blast initiation of spherical gaseous detonations in highly argon diluted mixtures

In this study, direct initiation of spherical detonations in highly argon diluted mixtures is investigated. Direct initiation is achieved via a high voltage capacitor spark discharge and the critical energy is estimated from the analysis of the current output. Stoichiometric acetylene–oxygen mixtures highly diluted with 70% argon is used in the experiment. Previous investigations have suggested that detonations in mixtures that are highly diluted with argon have been shown to be “stable” in that the reaction zone is at least piecewise laminar described by the ZND model and cellular instabilities play a minor role on the detonation propagation. For the acetylene–oxygen mixture that is highly diluted with argon, the experimental results show that the critical energy where the detonation is “stable” is in good agreement with the Zel’dovich criterion of the cubic dependence on the ZND reaction length, which can be readily determined using the chemical kinetic data of the reaction. The experimental results are also compared with those estimated using Lee’s surface energy model where empirical data on detonation cell sizes are required. Good agreement is found between the experimental measurement and theoretical model prediction, where the breakdown of the 13λ relationship for critical tube diameter – and hence a different propagation and initiation mechanism – is elucidated in highly argon diluted mixtures and this appears to indicate that cellular instabilities do not have a prominent effect on the initiation process of a stable detonation.     

Detonation propagation with velocity deficits in narrow channels

Propagation limits of detonations in narrow channels have been studied with a focus on velocity deficits and variation in cell widths. A channel was formed by a pair of metal plates of 1500 mm length which were inserted in a detonation tube of 50.5 mm inner diameter. Test gases were hydrogen–oxygen mixtures diluted with argon or nitrogen, which were selected as representatives of regular and irregular mixture systems. The velocity deficits predicted using the concept of negative boundary layer displacement thickness were compared to those obtained experimentally. From good agreement between the predicted and the experimental velocity deficits, the cell width enlarged in the channel was calculated using the induction zone length behind the decelerated leading shock front. Although this calculation underestimates the cell widths, the calculated cell widths were found to be well predicted when they were multiplied by an appropriate proportionality factor. It is found that for given mixtures, a combination of the calculated velocity deficit and the number of cells in a channel contributes to the prediction of propagation limits of detonations.     

Near limit behavior of the detonation velocity

The behavior of the detonation velocity near the limits is investigated. Circular tubes of diameters 65, 44 and 13 mm are used. To simulate a quasi two-dimensional rectangular geometry thin annular channels are also used. The annular channels are formed by a 1.5 m long insert of a smaller diameter tube into the larger outer diameter detonation tube. Premixed mixtures of C₂H₂ + 2.5O₂ + 70%Ar, CH₄ + 2O₂ and C₂H₂ + 5N₂O + 50%Ar are used in the present study. The high argon dilution stoichiometric C₂H₂ + 2.5O₂ mixture has a regular cell size and piecewise laminar reaction zone and thus referred to as “stable”. The other two mixtures give highly irregular cell pattern and a turbulent reaction zone and are hence, referred to as “unstable” mixtures. Pressure transducers and optical fibers spaced 10 cm apart along the tube are used for pressure and velocity measurements. Cell size of the three mixtures studied is also determined using smoked foils in both the circular tubes and annular channels. The ratio d/λ (representing the number of cells across the tube diameter) is found to be an appropriate sensitivity parameter to characterize the mixture. The present results indicate that well within the limit, the detonation velocity is generally a few percent below the theoretical Chapman–Jouguet (CJ) value. As the limit is approached, the velocity decreases rapidly to a minimum value before the detonation fails. The narrow range of values of d/λ of the mixture where the velocity drops rapidly is found to correspond to the range of values for the onset of single headed spinning detonations. Thus we may conclude that the onset of single headed spin can be used as a criterion for defining the limits. Spinning detonations are also observed near the limits in annular channels.     

Statistical analysis of detonation wave structure

Hydrocarbon fueled detonations are imaged in a narrow channel with simultaneous schlieren and broadband chemiluminescence at 5 MHz. Mixtures of stoichiometric methane and oxygen are diluted with various levels of nitrogen and argon to alter the detonation stability. Ethane is added in controlled amounts to methane, oxygen, nitrogen mixtures to simulate the effects of high-order hydrocarbons present in natural gas. Sixteen unique mixtures are characterized by performing statistical analysis on data extracted from the images. The leading shock front of the schlieren images is detected and the normal velocity is calculated at all points along the front. Probability distribution functions of the lead shock speed are generated for all cases and the moments of distribution are computed. A strong correlation is found between mixture instability parameters and the variance and skewness of the probability distribution; mixtures with greater instability have larger skewness and variance. This suggests a quantitative alternative to soot foil analysis for experimentally characterizing the extent of detonation instability. The schlieren and chemiluminescence images are used to define an effective chemical length scale as the distance between the shock front and maximum intensity location along the chemiluminescence front. Joint probability distribution functions of shock speed and chemical length scale enable statistical characterization of coupling between the leading shock and following reaction zone. For more stable, argon dilute mixtures, it is found that the joint distributions follow the trend of the quasi-steady reaction zone. For unstable, nitrogen diluted mixtures, the distribution only follows the quasi-steady solution during high-speed portions of the front. The addition of ethane is shown to have a stabilizing effect on the detonation, consistent with computed instability parameters.     

Initiation and sustaining mechanisms of stabilized Oblique Detonation Waves around projectiles

Direct initiations and stabilizations of three-dimensional conical detonation waves were attained by launching spheres with 1.06–1.31 times the C–J velocities into detonable mixtures. We conducted high time-resolution Schlieren visualizations of the whole processes over unsteady initiations to stable propagations of the stabilized Oblique Detonation Waves (ODWs) using a high-speed camera. The detonable mixtures were stoichiometric oxygen mixtures with acetylene, ethylene or hydrogen. They were diluted with argon in a 50% volumetric fraction, and a 75% diluted mixture was also tested for the acetylene/oxygen. The direct initiation of detonation by the projectile and the DDT process like the re-initiation appeared in the initiation process of stabilized ODW. This process eventually led to the stabilized ODW supported by the projectile velocity and the ringed shape detonation wave originating in the re-initiation. We modeled the spatial evolution of stabilized ODW after the re-initiation based on its C–J velocity and angle. The model qualitatively reproduced the measured development rate of stabilized ODW. We also discussed about the detonation stability for the curvature effect arising from the three-dimensional nature of stabilized ODW around the projectile. The curvature effect attenuated the detonation wave below its C–J velocity at the vicinity of projectile. The propagation limits of curvature effect will be responsible for the criticality to attain the stabilized ODWs. By accessing the detailed distributions of propagation velocities and curvature radiuses, the critical curvature radiuses normalized by the cell sizes experimentally revealed to be 8–10 or 15–18 for mixtures diluted with each 50% argon or 75% argon/krypton.     

Numerical study on three-dimensional C-J detonation waves: detailed propagating mechanism and existence of OH radical

An unsteady three-dimensional simulation is performed for a hydrogen/air C–J detonation in a rectangular tube, where a detailed chemical reaction model is used to reveal the C–J detonation structure. In this simulation, detailed propagating detonation structures for a diagonal mode are described in three-dimensions. The detonation front structures, the line of triple points, and the strong explosions at the corners of the rectangular tube are revealed by using a three-dimensional numerical visualization. From the spatial isosurface profiles of H₂ mass fraction, it is confirmed that the triple point lines have a role of “shutter” to generate unburned gas pockets and become of a ring shape behind the detonation front due to its explosion. The explosion process and its influence on an induction delay are observed by visualizing the spatial isosurface profiles of OH mass fraction. Moreover, a high “peninsula-shaped” OH mass fraction area, which has been experimentally reported, is reproduced on the side wall of the rectangular tube.     

Spinning detonation and velocity deficit in small diameter tubes

Detonation velocities and soot patterns of H₂/O₂ mixtures were measured in glass tubes of 3, 6 and 10 mm diameters at pressures ranging from 70 to 400 Torr and equivalence ratios of 0.5–1.5. It was confirmed that the transition from a multi-head to a spinning detonation occurred at the pressure where the cell size is equal to the length of circumference. At this transition pressure, the velocity was 95% of the C-J detonation. Stable spinning detonations were observed at wide range of initial pressures below the transition point. Detonation velocities were continuously decreasing with decreasing initial pressures in this pressure region. Spinning detonations with velocities down to 85% of the C-J detonation were observed. Those deficits in detonation velocities were well predicted by the modified ZND model with full detailed chemical kinetics. Heat and momentum losses were taking into account in this model. Validity of the modified ZND model to define the limit of detonation propagation was discussed.     

Gas-phase and catalytic combustion in heat-recirculating burners

An experimental study of a spiral counterflow “Swiss roll” burner was conducted, with emphasis on the determination of extinction limits and comparison of results with and without bare-metal Pt catalyst. A wide range of Reynolds numbers (Re) were tested using propane–air mixtures. Both lean and rich extinction limits were extended with the catalyst, though rich limits were extended much further. With the catalyst, combustion could be sustained at Re as low as 1.2 with peak temperatures as low as 350 K. A heat transfer parameter characterizing the thermal performance of both gas-phase and catalytic combustion at all Re was identified. At low Re, the “lean” extinction limit was actually rich of stoichiometric, and rich-limit had equivalence ratios exceeded 40 in some cases. No corresponding behavior was observed without the catalyst. Gas-phase combustion, in general, occurred in a “flameless” mode near the burner center. With or without catalyst, for sufficiently robust conditions (high Re, near-stoichiometric) not requiring heat recirculation, a visible flame would propagate out of the center, but this flame could only be re-centered if the catalyst were present. Gas chromatography indicated that at low Re, even in extremely rich mixtures, CO and non-propane hydrocarbons did not form. For higher Re, where both gas-phase and catalytic combustion could occur, catalytic limits were slightly broader but had much lower limit temperatures. At sufficiently high Re, catalytic and gas-phase limits merged. It is concluded that combustion at low Re in heat-recirculating burners greatly benefits from catalytic combustion with the proper choice of mixtures that are different from those preferred for gas-phase combustion. In particular, the importance of providing a reducing environment for the catalyst to enhance O₂ desorption, especially at low Re where heat losses are severe thus peak temperatures are low, is noted.     

Detonation properties of stoichiometric gaseous n-heptane/oxygen/argon mixtures

A study of detonation velocity and cellular structure for stoichiometric heptane/oxygen and for some stoichiometric heptane/oxygen/argon mixtures is carried out in a shock tube at low initial pressure. The critical conditions for the detonation onset and for the propagation of a self-sustained detonation wave are determined. A simplified form of the ZND model used in conjunction with a validated detailed kinetic model leads to the determination of the proportionality factor, A, between the detonation cell width, λ, and the induction distance, Δ, in the detonation wave. This A factor is of practical importance to estimate the detonation properties of n-heptane based mixtures including n-heptane/air. The prediction of detonation cell size λ for n-heptane based mixtures is discussed according to the recent semi-empirical detonation model of Gavrikov et al. The cell sizes predicted according to this detonation model are underestimated by a factor of about 8. The limitations of this model are underlined when applied to n-heptane based mixtures.     

Explosive characteristics of tetrafluoroethylene

The minimum energies required to initiate the combustion of gaseous tetrafluoroerthy1ene (TFE) and mixtures thereof with nitrogen, argon, and helium at various initial pressures and temperatures are determined. Flame transition from the gas to the liquid phase of TFE is investigated. Liquid TFE is demonstrated to be virtually nondetonable. The fuel-lean flammability and detonability limits of TFE-air mixtures under normal conditions are demonstrated to be identical, 12.2 vol %.     

Schlieren “PIV” for turbulent flows

The possibility of using commercial PIV equipment combined with schlieren optics to measure the velocity fields of turbulent flows is explored. Given a sufficiently high Reynolds number and adequate refractive flow differences, turbulent eddies can serve as the PIV “particles” in a schlieren image or shadowgram. The PIV software analyzes motion between consecutive schlieren or shadowgraph frames to obtain velocity fields. Velocimetry examples of an axisymmetric sonic helium jet in air and a 2D turbulent boundary layer at Mach 3 are shown. Due to optical path integration, axisymmetric flows require the inverse Abel transform to extract center-plane velocity data. Conditions for optimum schlieren sensitivity are examined. In its present embodiment, “schlieren PIV” is not useful for laminar flows nor for fully 3D flows. Otherwise it functions much like standard PIV under conditions where individual particles are not resolved and velocimetry is instead based on correlation of the motion of turbulent structures. “Schlieren PIV” shows significant promise for general refractive turbulent flow velocimetry if its integrative nature can be overcome through sharp-focusing optics.     

An experimental investigation of the onset of detonation

An experimental configuration is devised in the present investigation whereby the condition at the final phase of the deflagration to detonation transition (DDT) process can be generated reproducibly by reflecting a CJ detonation from a perforated plate. The detonation products are transmitted downstream through the plate, generating a turbulent reaction front that mixes with the unburned mixture and that drives a precursor shock ahead of it at a strength of about M = 3. The gasdynamic condition that is generated downstream of the perforated plate closely corresponds to that just prior to the onset of detonation in the DDT process. The turbulence parameters can be controlled by varying the geometry of the perforated plate; thus, the condition leading to the onset of detonation can be experimentally investigated. A one-dimensional theoretical analysis of the steady wave processes was first performed, and the experimental results show good agreement, indicating that the present experimental condition can be theoretically described. Two different detonation tube geometries (one with a square cross-section of 300 mm by 300 mm and the other with a circular cross-section of 150 mm) are used to demonstrate the independence of the tube diameter at the critical condition for DDT. Perforated plates with different hole diameters (d = 8, 15, and 25 mm) were tested, and the hole spacing to hole diameter ratio was maintained at 0.5. Different hydrogen–air mixtures were tested at normal temperature and pressure. For the plate with 8 mm holes, the onset of detonation is never observed. For the plate with 15 mm holes, successful initiation of a detonation is achieved for 0.8 < < 1.75 in both detonation tubes. For the plate with 25 mm holes, detonation initiation is observed for 0.7 < < 2.1 in the square detonation tube and for 0.8 < < 1.6 in the smaller circular detonation tube.     

Asymptotic description of solitary wave trains in fully nonlinear shallow-water theory

We derive an asymptotic formula for the amplitude distribution in a fully nonlinear shallow-water solitary wave train which is formed as the long-time outcome of the initial-value problem for the Su–Gardner (or one-dimensional Green–Naghdi) system. Our analysis is based on the properties of the characteristics of the associated Whitham modulation system which describes an intermediate “undular bore” stage of the evolution. The resulting formula represents a “non-integrable” analogue of the well-known semi-classical distribution for the Korteweg–de Vries equation, which is usually obtained through the inverse scattering transform. Our analytical results are shown to agree with the results of direct numerical simulations of the Su–Gardner system. Our analysis can be generalised to other weakly dispersive, fully nonlinear systems which are not necessarily completely integrable.     

Nucleation and growth mechanism for flame synthesis of MoO2 hollow microchannels with nanometer wall thickness

The growth and morphological evolution of molybdenum-oxide microstructures formed in the high temperature environment of a counter-flow oxy-fuel flame using molybdenum probes is studied. Experiments conducted using various probe retention times show the sequence of the morphological changes. The morphological row begins with micron size objects exhibiting polygonal cubic shape, develops into elongated channels, changes to large structures with leaf-like shape, and ends in dendritic structures. Time of probe–flame interaction is found to be a governing parameter controlling the wide variety of morphological patterns; a molecular level growth mechanism is attributed to their development. This study reveals that the structures are grown in several consecutive stages: material “evaporation and transportation”, “transformation”, “nucleation”, “initial growth”, “intermediate growth”, and “final growth”. XRD analysis shows that the chemical compositions of all structures correspond to MoO₂.     

K–K excitations on as “primary” superfields

We show that the K–K spectrum of IIB string on is described by “twisted chiral” superfields, naturally described in “harmonic superspace”, obtained by taking suitable gauge singlets polynomials of the D3-brane boundary superconformal field theory.To each p-order polynomial is associated a massive K–K short representation with states. The quadratic polynomial corresponds to the “supercurrent multiplet” describing the “massless” bulk graviton multiplet.     

The application of ultrasound radiation to the synthesis of nanocrystalline metal oxide in a non-aqueous solvent

Highly crystalline metal oxide nanoparticles of TiO₂, WO₃, and V₂O₅ were synthesized in just a few minutes by reacting transition metal chloride with benzyl alcohol using ultrasonic irradiation under argon atmosphere in a non-aqueous solvent. The sonochemical process was conducted at a relatively low temperature, 363 K. A unique crystallization process of these nanoparticles has been observed and characterized by powder X-ray diffraction (PXRD), high resolution scanning electron microscopy (HRSEM), and BET. The particles’ size and shape measured from HRSEM reveal “quasi” zero-dimensional, spherical TiO₂ particles in the range of 3–7 nm. The V₂O₅ particles have a “quasi” one-dimensional ellipsoidal morphology, with lengths in the range of 150–200 nm and widths varying between 40 and 60 nm. The WO₃ particles were obtained as “quasi” two-dimensional platelets with square shapes having facets ranging from 30 to 50 nm. The thickness of these platelets was between 2 and 7 nm. The mechanism of the reactions leading to these three metal oxide nanoparticles in a non-aqueous system is substantiated by Nuclear Magnetic Resonance (NMR), and Electron Spin Resonance (ESR).     

Stable bonds and unstable bonds in Y(Pr)-123 system

The Pr content dependence of the bond lengths of Y–Cu, Y–O, O–O, Cu–O, Ba–Cu and Ba–O in PrBa₂Cu₃O_y are analyzed and discussed in detail. The different valence bonds can be divided into two groups: stable bonds and unstable bonds. Since the bond lengths and angles between every two ions among O2, Cu2 and O3 are very stable, we conclude that the three ions form an unchangeable triangle when the Pr doping changes. The triangle is called “fixed triangle”. This “fixed triangle” can slightly rotate around the Cu2 ions. It is just this rotation that leads to the unstable bonds. As the increase of the Pr content, the bond lengths between the two Cu(2)–O planes becomes larger and larger, the Cu(2)–O planes bend towards the Ba–O plane. The bonds lengths between the Cu(2)–O and Ba–O planes vary oppositely from those of Cu(2)–O, and become shorter and shorter. These changes connected with the superconductivity are discussed.     

Studies on the valveless scheme to produce high-frequency detonations with different purge methods

Producing high-frequency detonations is an important topic for pulse detonations which has received considerable attentions. The valveless scheme has been verified to be able to obtain high-frequency detonations more than 100 Hz. This work has been conducted to investigate the possibility to achieve a higher detonation frequency and clarify the limits of stable operations preliminarily for the valveless scheme with different purge methods. Oxygen, ethylene, and nitrogen or liquid water are utilized as oxidizer, fuel, and purge medium in the experiments while two injection configurations are employed. The maximum detonation frequencies of 180 Hz and 330 Hz have been achieved in stable operations for two different injection configurations when nitrogen is used as the purge gas. The ceiling frequency for stable detonations is 300 Hz if nitrogen is replaced by liquid water, which indicates that water vapor is capable to create an efficient buffer zone to ensure stable operations. The results imply that the injection configuration also has a great impact on the ceiling stable detonation frequency. Three operating modes have been observed in this study, i.e., a stable detonation mode, an unstable detonation mode, and a deflagration mode. In the unstable mode, failure of detonation initiation occurs frequently and one interesting phenomenon is that the detonation frequency is reduced by half exactly when insufficient filling happens. The supply pressure ratios of oxidizer to fuel and purge to fuel are obtained for different operating modes when the purge method is changed. Furthermore, the equivalence ratios have been also studied for different operating modes which reveals that the range will change when different purge methods and injection configurations are employed. According to the equivalence ratio and the mass flow rates, an equivalent volume fraction of oxygen is defined and its range for the stable detonation mode is clarified.