Two-phase Detonations Research Articles

Semi-confined layered kerosene/air two-phase detonations bounded by nitrogen gas

A two-dimensional numerical study is conducted on the semi-confined cellular detonations propagating through a layer of two-phase kerosene/air reactant bounded by an inert gas. By fixing a global equivalence ratio, a series of cases are simulated to investigate the effects of the background vapor/liquid droplet equivalence ratios (φg and φd) and droplet diameters. The results show that the propagation and failure of the layered detonation are strongly affected by the equivalence ratios and droplet diameters. When φg is 0.8, layered detonations can propagate at a droplet size of 5, 10, and 20 µm, while it fails when the droplet size is increased to 40 µm. When φg is less than 0.8, the self-sustained layered detonation can only be obtained with a small droplet size of 5 µm and a high φg above 0.5. The detonated fuel fraction and droplet contribution efficiency are found to be sensitive to the droplet diameter. It is found that the transverse detonation is a manifestation of the self-sustained ability of detonation waves. The loss of triple points leads to the appearance of transverse detonation whereas the transverse detonation can generate new triple points and stabilize the detonation front. The transverse detonation can significantly enhance the mass transfer and heat release even though it occurs behind the sonic line, which promotes the detonation re-initiation. Besides, it is found that h/λ=2.90 (h is reactant layer height and λ is cell width) is the critical value for the successful propagation of layered detonations in this study, which agrees well with the existing experiments. In addition, reflection efficiency is introduced and is effective in predicting the strength of the weak confinement.

Numerical simulation of two-dimensional detonation propagation in partially pre-vaporized n-heptane sprays

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

Eulerian-Lagrangian modelling of detonative combustion in two-phase gas-droplet mixtures with OpenFOAM: Validations and verifications

A hybrid Eulerian-Lagrangian solver RYrhoCentralFoam is developed based on OpenFOAM® to simulate detonative combustion in two-phase gas-liquid mixtures. For Eulerian gas phase, RYrhoCentralFoam enjoys second order of accuracy in time and space discretizations and is based on finite volume method on polyhedral cells. The following developments are made based on the standard compressible flow solver rhoCentralFoam in OpenFOAM®: (1) multi-component species transport, (2) detailed fuel chemistry for gas phase combustion, and (3) Lagrangian solver for gas-droplet two-phase flows and sub-models for liquid droplets. To extensively verify and validate the developments and implementations of the solver and models, a series of benchmark cases are studied, including non-reacting multi-component gaseous flows, purely gaseous detonations, and two-phase gas-droplet mixtures. The results show that the RYrhoCentralFoam solver can accurately predict the flow discontinuities (e.g. shock wave and expansion wave), molecular diffusion, auto-ignition and shock-induced ignition. Also, the RYrhoCentralFoam solver can accurately simulate gaseous detonation propagation for different fuels (e.g. hydrogen and methane), about propagation speed, detonation frontal structures and cell size. Sub-models related to the droplet phase are verified and/or validated against analytical and experimental data. It is also found that the RYrhoCentralFoam solver is able to capture the main quantities and features of the gas-droplet two-phase detonations, including detonation propagation speed, interphase interactions and detonation frontal structures. As our future work, RYrhoCentralFoam solver can also be extended for simulating two-phase detonations in dense droplet sprays.

Two-phase reaction model of a gas-aluminum particles mixture detonation

ABSTRACT The reaction model of aluminum particles is the key to successfully simulate the two-phase detonation of aluminum suspensions. In this study, by considering the decomposition of the aluminum oxide (Al2O3) product at high temperature, the reaction model for aluminum particles is improved and is incorporated into the numerical code. Then numerical simulations for two-phase detonations of Al/air mixtures and Al/O2 mixtures are performed, respectively, the simulated results for the peak pressure and the speed of the two-phase detonation wave are in agreement with the experimental results, which demonstrate the validity of the improved aluminum reaction model. Moreover, the detonation parameters and the distributions of the physical quantities around the detonation wave are analyzed.

Application of CE/SE method to gas-particle two-phase detonations under an Eulerian-Lagrangian framework

This study aims to extend the original Eulerian space-time conservation element and solution element (CE/SE) method to the Eulerian-Lagrangian framework to solve the gas-particle two-phase detonation problems. The gas-aluminum particle two-phase detonations are numerically investigated by the developed Eulerian-Lagrangian code, in which the gas-phase compressible Euler equations are solved by our in-house CE/SE scheme based on quadrilateral meshes. Additionally, the particle-phase Lagrangian equations, together with the stiff source terms of interphase interactions and chemical reactions, are explicitly integrated via the operator-splitting technique. A dynamic data structure is introduced to store particle information to overcome the tremendous communication costs when applying message passing interface parallel to the Eulerian-Lagrangian framework. The code is shown to be of better parallel efficiency in moderate-scale computations than that uses static arrays. Comparisons with previous one-dimensional and two-dimensional simulation results and experimental observations are conducted to demonstrate the accuracy and reliability of the developed Eulerian-Lagrangian CE/SE code in gas-particle two-phase detonation simulations. Moreover, the code is also applied to simulate polydisperse gas-particle detonations which is close to a realistic scenario, and significant differences in detonation characteristics are found when compared with the monodisperse counterparts. The great demands of using the Eulerian-Lagrangian method to obtain more physics-consistent gas-particle detonation results are addressed, which the traditional Eulerian-Eulerian simulations fail to observe.

A hybrid two-phase mixture model of detonation diffraction with compliant confinement

A multi-material two-phase hybrid model of heterogeneous explosives, with a reaction rate that is proportional to the gas-phase pressure excess above an ignition threshold, is examined computationally. The explosive is confined within a compliant inert, and the focus is on the behavior of an established detonation as it rounds a 90° corner and undergoes diffraction. The numerical approach, a variant of Godunovʼs method, is designed to capture interfaces between materials that can undergo phase change, and extends previous work of the authors on rigidly-confined two-phase detonations. The dependence of the post-diffraction conduct on the strength of the confinement is explored by holding the reaction-rate prefactor and the ignition threshold fixed, and considering confiners of two different strengths. The aim is to determine whether a detonation that turns the corner successfully when rigidly confined can experience failure when the confinement is compliant.

New numerical algorithms in SUPER CE/SE and their applications in explosion mechanics

The new numerical algorithms in SUPER/CESE and their applications in explosion mechanics are studied. The researched algorithms and models include an improved CE/SE (space-time Conservation Element and Solution Element) method, a local hybrid particle level set method, three chemical reaction models and a two-fluid model. Problems of shock wave reflection over wedges, explosive welding, cellular structure of gaseous detonations and two-phase detonations in the gas-droplet system are simulated by using the above-mentioned algorithms and models. The numerical results reveal that the adopted algorithms have many advantages such as high numerical accuracy, wide application field and good compatibility. The numerical algorithms presented in this paper may be applied to the numerical research of explosion mechanics.

An improved CE/SE scheme for numerical simulation of gaseous and two-phase detonations

A new structure of solution elements and conservation elements based on rectangular mesh was proposed and an improved space-time conservation element and solution element (CE/SE) scheme with second-order accuracy was constructed. Furthermore, the application of improved CE/SE scheme was extended to detonation simulation. Three models were used for chemical reaction in gaseous detonation. And a two-fluid model was used for two-phase (gas–droplet) detonation. Shock reflections were simulated by the improved CE/SE scheme and the numerical results were compared with those obtained by other different numerical schemes. Gaseous and gas–droplet planar detonations were simulated and the numerical results were carefully compared with the experimental data and theoretical results based on C–J theory. Mach reflection of a cellular detonation was also simulated, and the numerical cellular patterns were compared with experimental ones. Comparisons show that the improved CE/SE scheme is clear in physical concept, easy to be implemented and high accurate for above-mentioned problems.

A conservative approximation to compressible two-phase flow models in the stiff mechanical relaxation limit

In this article, we present and analyze a conservative approximation to reduced one-pressure one-velocity models for compressible two-phase flows that contain non-conservative products. This approximation is valid when certain material properties of the two phases are considerably different from each other. Although it cannot be applied to arbitrary mixtures, it is applicable to many heterogeneous mixtures of technological interest. Herein, we derive the Rankine–Hugoniot relations and Riemann invariants for the homogeneous part of the proposed model and develop an exact Riemann solver for it. Further, we investigate the structure of the steady two-phase detonation waves, with inert or reactive solid particles, admitted by the proposed model. Comparisons with the corresponding gaseous detonations are also made. Moreover, we derive a lower limit for the propagation speed of steady two-phase detonations in the case of reactive particles. At the limiting case of very dilute mixtures, this minimum speed tends to the Chapman–Jouguet velocity of gaseous detonations. Finally, we report on numerical simulations of the transmission of a purely gaseous detonation to heterogeneous mixtures containing inert or reactive solid particles. The effect of the solid particles on the structure of the resulting two-phase detonation is discussed in detail.

Phenomenological aspects in explosive powder/gas two-phase detonations

Attempts were made to detonate a special ball-milled TNT powder of about 30-μm particle size thatwas dispersed in air, oxygen, and nitrogen at nominally 1 kg/m3 in a highly instrumented 152-mm-diameter 7.31-m-long horizontal detonation tube. Results were successful in both air and oxygen, but not in nitrogen. New modifications to the detonation tube for this work included implementation of two-color temperature-measuring instrumentation, and the repositioning of some piezoelectric pressure transducers and fiberoptic light-detector probes so that phenomena such as spinning detonation and multiple-front detonations could be better identified and quantified. TIGER Code Chapman-Jouguet (CJ) computations were made for TNT, RDX, and mixtures of TNT and RDX in air, oxygen, and nitrogen at concentrations up to 100 kg/m3. The computed results for TNT in air and oxygen at a concentration of 1 kg/m3 for the detonation velocities, pressures, and temperatures were 2.00 km/s, 4.00 MPa, 3250 K in air and 2.05 km/s, 4.40 MPa, 3740 K in oxygen. Experimental results for TNT powder were 1.82 km/s, 4.06 MPa, 3245 K in air and 1.90 km/s, 4.61 MPa, 4240 K in oxygen; the experimental concentrations, which were monitored with laser optics, were determined to be 1 kg/m3 with an estimated error of ± 10%. Subsequent experiments were conducted with RDX, alone and in mixtures with TNT, in attempts to achieve detonation in nitrogen. These were successful except when the RDX percentage fell below 20% by weight. Results of sucessful detonations of RDX/TNT mixtures indicated multiple-front detonations, suggesting that the TNT was reacting behind the RDX detonation front in such a manner that it supported the overall detonation.

Characterization of shock and reaction fronts in detonations

An instrumental technique has been developed which allows the concomitant measurement of the arrival times of both shock and reaction (flame) fronts in propagating detonations. A combination of fiber-optic probes and light detectors is used to monitor the arrival of the reaction front, whereas piezoelectric pressure gauges monitor the arrival of the pressure pulse from the preceding shock wave. Both signals provide the measurement of the detonation velocity; variance between shock and reaction front velocities implies nonstable detonation (growing or dying detonation) which can be attributed to variation in density, concentration, or homogeneity of the detonating media. This technique is straightforward in the case of pressed or cast formulations but presents difficulties when gas-phase or two-phase detonations are involved. The detonation of near-stoichiometric ethylene–air mixtures in a detonation-tube facility was used to refine the technique and calibrate the instrumentation. The technique was then used to characterize the detonation of two-phase aluminum powder–air mixtures of various concentrations. Compared to the 3-μs induction time between the shock and reaction fronts in the case of ethylene–air mixtures, the induction times for aluminum powder–air mixtures varied from about 1 to over 100 μs. The variation in induction time was attributed to several factors: extended heating time to ignition of the particles due to inhomogeneity of the two-phase mixtures; variation in particle size; and variable aluminum-oxide surface coating thickness. The concentration of aluminum powder in the air was monitored dynamically using instrumentation that related the concentration of aluminum to the attenuation of a laser beam through the mixture. A mean, or overall, value was also estimated by determining the mass flow rate and overall discharge time using photographic coverage. In the former case, in order to obtain meaningful signals for these high-concentration two-phase systems it was necessary to reduce the pathlength of the laser beam through the mixture to a small fraction of the total width of the tube. Hence, the observed concentration measurements did not necessarily reflect good homogeneity across the width of the tube. Nevertheless, with some modifications this technique can be exceptionally useful for this most difficult measurement.

Static and dynamic impulses generated by two-phase detonations

The influence of the mixture density and the reaction zone length on the static and dynamic impulse of the detonations through wheat dust, RDX dust, and decane droplet air mixtures was studied. A numerical solution of the detailed model of the two-phase detonation initiation and development in the medium, provided the basis for the study. Mixtures with a higher average density were found to produce a significantly greater static impulse, but a reduced dynamic impulse. The reasons for this behavior were discussed.

The Transitional Structure of Detonation Waves in Multi-Phase Reactive Media

Abstract The transitional structure of two-phase detonations initiated by strong blast waves in decane sprays in oxygen and in clouds of wheat and RDX particles in air is investigated numerically. A one-dimensional unsteady code based on the flux corrected transport algorithm is employed. Detailed profiles of mass velocity, particle velocity, sound velocity and Mach number are presented for the reaction zone both prior to and after the establishment of fully developed detonations. With heavy particle loading a broad region of near sonic flow is observed and under proper conditions weak secondary shock waves are generated within the reaction zone.

Relation of chemical and physical processes in two-phase detonations

Both physical and chemical factors influence combusion instabilities and explosions in two-phase systems consisting of fuel liquid drops in a gaseous oxidizer. It is generally agreed that in two-phase detonations, fuel drops are broken up via a mass stripping mechanism and form combustible mixtures of fuel micromist and hot gaseous oxidizer in the wake of each parent drop. The large surface area between the micromist (micron size drops) and the hot oxidizer enable chemical reactions to proceed at a rapid enough rate to support the incident shock front. Therefore, the detonability of two-phase mixtures is affected by both the fuel drop breakup and the chemical energy release rate. An experimental study was undertaken to elucidate the relative importance of the roles of chemical and physical processes. Additives were employed to alter the physical properties (such as viscosity) and the chemical properties (such as ignition delay) of the fuel. In addition, fuel drop size was systemically varied, since this also affects breakup time. The sensitivity of a hydrocarbon fuel drop-air mixture to detonate was significantly increased by using additives which alter the chemical energy release rate and by decreasing the initial fuel drop size.

Theoretical and experimental study of cylindrical shock and heterogeneous detonation waves

A simplified theory of blast initiation of detonations in clouds of fuel in gaseous or droplet form is developed and agrees with the experiments described below. The flow is at first dominated by the strong blast wave but transition from blast to detonation behavior occurs near a critical radius r∗ where the blast energy and the heat of combustion contained in r < r∗ are equal. The complex flow in this transition region cannot be determined analytically. In the simplified theory the details of the transition region are ignored but the flow is represented by the self-similar solution for a strong blast wave for r < r∗ and by the self-similar detonation solution for r > r∗. The development of a sectored shock tube to study cylindrical shock waves and two-phase detonations is described. Data are presented for shock waves as well as for blast initiated detonations of a monodisperse spray of 400 μ kerosene droplets in air at standard conditions. Two regimes of propagation were established experimentally: (1) the subcritical energy regime, where decoupling of shock and reaction zone results in a strong blast wave type decay and, (2) the supercritical energy regime, where the initially overdriven cylindrical detonation decays, at some critical radius, to its Chapman-Jouguet state. Experimentally determined critical radii and steady-state detonation velocity agree very well with theoretical predictions. Detonation velocity was found to be constant at the plane C–J value for radius greater than the critical radius.

Present status of detonations in two-phase systems

A review of two-phase detonations is presented. Similarities and differences with homogeneous detonations are outlined and advances in their understanding are indicated. Because of recent and present interest, particular attention is devoted to spray detonations. However, the survey does include film and solid-gas detonations as well as detonations in monopropellant sprays. Areas in need of further research are outlined.

Time variation in the reaction-zone structure of two-phase spray detonations

A detailed theoretical analysis of the time-varying detonation structure in a monodisperse spray is presented. The theory identifies exprimentally observed reaction-zone overpressures as deriving from blast waves formed theriin by the explosive ignition of the spray droplets, and follows in time the motion, change in strength, and interactions of these blast waves with one another, and with the leading shock. The results are compared with experimental data by modeling the motion of a finite-size circular pressure transducer through the theoretical data field in a x-t space.

Breakup of liquid drops due to convective flow in shocked sprays

An analytical model of the breakup of droplets in a column or a spray subjected to shock waves is presented. The model is based on observation of the breakup of isolated drops and is an extension of the model for a column of droplets previously developed by the authors, wherein droplet motion was ignored. In this model, allowance for the simultaneous stripping and motion of the droplets is made and, in addition, a probability factor, accounting for the probablity of wake-droplet interactions, is included for the spray case. It is shown analytically that, in the range of spacing to drop diameter ratio, S/D 0 =10–25, of importance to two-phase detonations, and for 2≤ M ≤6, the breakup time of the drops can be 55% to 90% of the breakup time of an isolated drop under the same convective flow conditions. Experiments with columns of 1.94-mm water drops at S/D 0 =14.6, under the action of M =2 shocks, indicate, on the basis of the diameter growth, a breakup-time reduction in good agreement with the value of t bc /t b =0.62, predicted analytically, where t b and t bc are the breakup time for isolated drops and drops in column, respectively. Data for similar water columns at higher Mach Numbers up to M =3.3 indicate a qualitative agreement but not as good quantitative agreement as obtained at M =2. Previously published work on the ignition and detonation of 2.6-mm diethylcyclohexane drops in oxygen provides further qualitative verification of the model.

Ignition delay measurements in two-phase detonations

The ignition time delay between the leading shock front and the onset of OH emission from a two-phase detonations of decane-oxygen has been measured. A thin layer of decane was placed on the walls of a 2.22 cm id tube 3-m long which was filled with oxygen or nitrogen-oxygen mixtures to 1/2, 1, or 2 atm. Self-sustaining propagation velocities from 0.9 to 1.9 km/sec were obtained depending on the nitrogen dilution. The ignition delay varied from 250 μsec to 35 μsec — the higher the velocity, the lower the ignition delay, and the higher the initial pressure, the lower the ignition delay. An Arrhenius-type correlation fits the data well and yields a pseudo-activation energy of 4.32 kcal/g mole for 1 atm initial pressure and 5.65 kcal/g mole for 1/2 atm. No evidence of major perturbations due to secondary or transverse waves within the ignition zone was observed.