Cylindrical Detonation Research Articles

The role of global curvature on the structure and propagation of weakly unstable cylindrical detonations

The role of the global curvature on the structure and propagation of cylindrical detonations is studied allowing and without allowing the development of cellular structures through two-dimensional (2-D) and 1-D simulations, respectively. It is shown that as the detonation transitions from being overdriven to the Chapman–Jouguet (CJ) state, its structure evolves from no cell, to growing cells and then to diverging cells. Furthermore, the increased dimension of the average structure of the cellular cylindrical detonation, coupled with the curved transverse wave, leads to bulk un-reacted pockets as the cells grow, and consequently lower average propagation velocities as compared to those associated with smooth fronts. As the global detonation front expands and its curvature decreases, the extent of the un-reacted pockets diminishes and the average velocity of the cellular cylindrical detonation eventually degenerates to that of the smooth fronts. Consequently, the presence of cellular instability renders detonation more difficult to initiate for weakly unstable detonations.

反応性が変化する混合気中を伝播する発散円筒デトネーションに関する数値解析

反応性が変化する混合気中を伝播する発散円筒デトネーションに関する数値解析

Mathematical modeling of converging detonation waves at multipoint initiation

The methods of mathematical modeling based on the latest experimental data are proposed to conduct a study of the cylindrical detonation process and gas dynamics of the explosion products. The numerical simulation of converging cylindrical detonation waves at multipoint initiation for the recent experiments in IPCP RAS was conducted. The results of the numerical simulation and the experiment are compared.

Experimental investigation of cylindrical detonation wave

One of the methods of experimental investigation of cylindrical detonation wave formed by the multipoint initiation method is presented in this work. The experimental setup was specially developed for this purpose. Two types of “Nanogate” high-speed cameras were used in the experiments. The phenomenological descriptions of initiation process, dynamic of formation of detonation wave and gas dynamic flow of detonation products are presented. This method in combination with the other modern methods will allow carrying out more profound investigations of such problems.

Numerical Study on Direct Initiation of Cylindrical Detonation in H2/O2 Mixtures: Effect of Higher-Order Schemes on Detonation Propagation

ABSTRACTThis aim of this study is to investigate the effect of grid resolution and higher-order accuracy schemes. The size of the reaction induction zone at the time of the local explosion affects the generation of transverse cells. When the reaction zone is large, transverse cells appear. As a result, for calculations in which the grid width is small or for a higher-order scheme, such as a weighted compact nonlinear scheme (WCNS), is used, the cell size increases; an irregular cellular structure is obtained, such as that observed in experiments; and unburned gas pockets and circulation structures caused by Kelvin–Helmholtz instability appear behind the detonation front. In terms of the computational cost, the computational time of 7th-order WCNS is approximately three times that of the 2nd-order monotone upstream-centered schemes for conservation laws (MUSCL) scheme.

Numerical modelling of continuous spin detonation in rich methane-oxygen mixture

A numerical simulation of a two-dimensional structure of the detonation wave (DW) in a rich (equivalence ratio φ=1.5) methane-air mixture at normal initial condition has been conducted. The computations have been performed in a wide range of channel heights. From the analysis of the flow structure and the number of primary transverse waves in the channel, the dominant size of the detonation cell for studied mixture has been determined to be 45÷50 cm. Based on the fundamental studies of multi-front (cellular) structure of the classical propagating DW in methane mixtures, numerical simulation of continuous spin detonation (CSD) of rich (φ=1.2) methane-oxygen mixture has been carried out in the cylindrical detonation chamber (DC) of the rocket-type engine. We studied the global flow structure in DC, and the detailed structure of the front of the rotating DW. Integral characteristics of the detonation process - the distribution of average values of static and total pressure along the length of the DC, and the value of specific impulse have been obtained. The geometric limit of stable existence of CSD has been determined.

Initiation of explosive mixtures having multi-sized structures

Theory of strong blast was used as the basis for the experimental method of determining of the energy of source which provides the initiation of combustible mixture. For mono-fuel mixtures the following parameters were experimentally determined at testing: the critical initiation energy of a cylindrical detonation wave in mixtures 2H2+O2 and C2H2+2.5O2 (exploding wire); the critical initiation energy of a spherical detonation in a mixture of C2H2+2.5O2 (electrical discharge). Similarly, for the double-fuel mixtures of acetylene - nitrous oxide - oxygen (having bifurcation cellular structures) the critical initiation energy of spherical wave was determined also. It was found that for the stoichiometric mixture on both fuel components the critical energy of mixture with the bifurcation structure was undervalued by several times in comparison with the value of the critical energy for the mono-fuel mixture, in which the cell size at a given pressure is determined by the large scale of bifurcation cells. This result shows the decrease of the critical energy with an increase of the number of "hot spots", which are the numerous areas of collision of the transverse waves of large and small scales in a mixture with bifurcation properties.

Influence of Channel Width on Cylindrical Detonation Wave Propagation

Influence of Channel Width on Cylindrical Detonation Wave Propagation

Propagation of detonation wave in hydrogen–air mixture in channels with sound-absorbing surfaces

The possibility of using sound-absorbing surfaces for attenuating the intensity of detonation waves propagating in hydrogen–air mixtures has been experimentally studied in a cylindrical detonation tube open at one end, with an explosive initiated by spark discharge at the closed end. Sound-absorbing elements were made of an acoustic-grade foamed rubber with density of 0.035 g/cm3 containing open pores with an average diameter of 0.5 mm. The degree of attenuation of the detonation wave front velocity was determined as dependent on the volume fraction of hydrogen in the gas mixture.

Analysis of influence design parameters ejector pipe at the detonation specifications engine

The engines that use a detonation cycle have greater thermal efficiency than engines with constant-pressure combustion cycle. The mechanisms of ejector augmentation are evident in secondary air entrainment. The impulse characteristics of a pulse detonation engine (PDE) with ejector were investigated under different parameters. The propagation of a detonation wave in an ejector-augmented pulse detonation rocket engine fueled with a hydrogen-oxygen methane-oxygen and hydrocarbon-oxygen mixture is studied. The straight cylindrical ejector was coaxially installed at different axial locations relative to the exit of the detonation chamber. The use of a non-steady ejector is modeled for pulse detonation engine performance improvement. In this paper, a two-dimensional numerical model is developed to help design the basic geometry and operating parameters of the device. The unsteady flow processes are simulated and compared with a baseline PDE without ejector enhancement. Various features including detonation-shock interaction, detonation diffraction and vortex formation are observed. It is observed that the design of detonation wave flow path in detonation tube, ejector and operating parameters such as Mach numbers are mainly responsible for improving the propulsion performance of PDE.Object оf numerical simulation is the cylindrical detonation chamber with a diameter of Dc = 25 mm and a length of Lc = 100 mm. The cylindrical ejectors with a length of Le = 100 mm and diameters De = 35, 40, 45, 50 that 55 mm were attached to the chamber. Also ejectors with a diameter of De = 35 mm and lengths of Le = 50, 100, 150, 200 that a 250 mm respectively were attached to the chamber. The calculation was performed with a computer program that implements a numerical TVD-scheme. The results of calculations were presented as the dependence of specific thrust impulse Isp/Ispo ratio (Isp ­- specific thrust impulse with ejector nozzle; Ispo - specific thrust impulse of a chamber only) to the ejector-to-PDE diameter ratio (De/Dc), to the ejector-to-PDE length ratio (Le/Lc) and to the displacement of an ejector-to-PDE length ratio ((Ld +Lc)/Lc), where Ld – distance from the input section of the nozzle to the thrust wall of a detonation chamber. The method of a numerical simulation proved the possibility of a significant increase of pulse detonation engine performance through the use of ejector nozzle.

Investigation of the effect of the ejector on the performance of the pulse detonation engine nozzle extension

Influence of an ejector nozzle extension on gas flow at a pulse detonation engine was investigated numerically and experimentally. Detonation formation was organized in stoichiometric hydrogen-oxygen mixture in cylindrical detonation tube. Cylindrical ejector was constructed and mounted at the open end of the tube. Thrust, air consumption and parameters of the detonation were measured in single and multiple regimes of operation. Axisymmetric model was used in numerical investigation. Equations of Navies-Stokes were solved using a finite-difference scheme Roe of second order of accuracy. Initial conditions were estimated on a base of experimental data. Numerical results were validated with experiments data.

Attenuation of a hydrogen-air detonation by acoustic absorbing covering

Using of sound-absorbing surfaces to weaken and decay of a detonation wave in hydrogen-air mixtures was investigated experimentally. Experiments were carried out in a cylindrical detonation tube open at one end. Initiation of the explosive mixture was carried out by a spark discharge, which is located at the closed end of the detonation tube. Acoustical sound absorbing foam element of a specific weight of 0.035 g/cm3 with open pores of 0.5 mm was used. The degree of attenuation of the intensity of the detonation wave front was determined.

Numerical simulation of the fine structure of a cylindrical detonation wave in a hydrogen–air combustible mixture

The modes of propagation in a hydrogen–air combustible mixture of a cylindrical detonation wave formed as a result of the decay of a discontinuity on the boundary of the low-pressure and high-pressure chambers are studied. The simulation is performed in a quasi-one-dimensional nonstationary formulation using the original grid-characteristic method with the explicit separation of strong and weak discontinuities. It is shown that, when approaching the Chapman–Jouguet detonation velocity, the detonation wave propagates in a pulsating mode; that the frequency of fluctuations at large distances depends weakly on the parameters in the high-pressure chamber; and that the step of temperature and density oscillations with respect to the spatial coordinate behind the bow shock wave is close to the experimentally measured dimensions of a detonation cell.

On the structure of self-similar detonation waves in TNT charges

A phase-plane method is proposed to model flow fields bounded by constant-velocity detonation waves propagating in TNT charges. Similarity transformations are used to formulate the problem in the phase plane of non-dimensional sound speed Z versus non-dimensional velocity F. The formulation results in two coupled ordinary differential equations that are solved simultaneously. The solution corresponds to an integral curve Z(F) in the phase plane, starting at the Chapman-Jouguet (CJ) point and terminating at the singularity A, which is the sonic point within the wave. The system is closed by computing thermodynamic variables along the expansion isentrope passing through the CJ point, forming, in effect, the complete equation of state of the thermodynamic system. The CJ condition and isentropic states are computed by the Cheetah thermodynamic code. Solutions are developed for planar, cylindrical, and spherical detonations. Species profiles are also computed; carbon graphite is found to be the predominant component (≈10 mol/kg). The similarity solution is used to initialize a 1D gas-dynamic simulation that predicts the initial expansion of the detonation products and the formation of a blast wave in air. Such simulations provide an insight into the thermodynamic states and species concentrations that create the initial optical emissions from TNT fireballs.

Influence of Detonation Cell Size on Propagation of Cylindrical Detonation Wave

Influence of Detonation Cell Size on Propagation of Cylindrical Detonation Wave

Detonation Transition Around Cylindrical Reflector of Pulse Detonation Engine Initiator

To achieve reliable transmission of detonation waves to a pulse detonation engine combustor (detonation chamber), the authors propose a pulse detonation engine initiator that uses a cylindrical reflector downstream of a predetonator exit. The detonation wave propagates around the reflector to change the wave shape in three transition stages: from a planar detonation wave in the predetonator to an expanding cylindrical detonation wave, from the cylindrical wave to a planar toroidal detonation wave, and from the toroidal wave to a planar detonation wave in the detonation chamber. The cylindrical wave propagates along a cylindrical path between the reflector and front wall of the detonation chamber, and the toroidal wave propagates along an annular path between the reflector and sidewall of the detonation chamber. The purpose of this study was to examine the influence of the gap width of the annular path on the transition stages from cylindrical to toroidal and from toroidal to planar. A series of experiments that filled the entire test section with the driver gas mixture (stoichiometric hydrogen–oxygen mixture) showed that the expanding cylindrical detonation wave was sufficiently strong to survive the rarefaction waves from the corners of the reflector at all of the investigated annular gap widths (5, 10, 15, and 20 mm) and was transmitted to the planar toroidal wave successfully in all cases. When the strength of the cylindrical detonation wave was under a supercritical condition for diffraction at the reflector corner, the necessary filling distance for the driver gas was predicted well by the Whitham theory. A second series of experiments showed the influence of the annular gap width on the detonation transition from the planar toroidal detonation wave to the planar detonation wave. Two different types of detonation transitions termed “continuous transition” and “temporal quenching” were observed. The threshold value of for continuous transition is approximately four.

Methods of re-initiation and critical conditions for a planar detonation transforming to a cylindrical detonation within a confined volume

The conditions necessary for the successful transformation of a planar detonation into a diverging, cylindrical detonation after diffraction into a confined volume have been investigated for four different fuel–oxygen mixtures over a wide range of gap sizes. The test mixtures were H2+0.5O2, C2H2+2.5O2, C2H2+4O2 and C2H4+3O2, and the range of gap size (w) varied from 1 to 45.5mm. This range of mixtures and gap sizes plus the higher fidelity owing to pressure measurements along the endwall allowed greater precision when interpreting the results than what was seen in earlier studies, leading to the identification of a wider range of conditions for the successful transformation of the detonation than what was heretofore assumed. The spontaneous re-initiation and continuous reflected re-initiation mechanisms previously observed by Murray and Lee [8] were confirmed, but the present study improves upon the prior one through the conclusive observation that successful propagation of detonations after multiple reflections from the front and back walls of the confined volume is also possible. When compared with literature data, the current results are in fair agreement when only spontaneous and single-reflected re-initiation modes are considered, but when multiple reflections are included, the go/no-go boundary for successful transmission is much wider than found from the limited literature data available. The demarcation boundary was found to fit the relationship w/λ=0.14w+0.24, with λ being the cell size in the axial tube. In addition to significantly expanding the database on the axial-to-cylindrical detonation transition in a confined volume and obtaining a new correlation for the demarcation condition, the present paper also shows that there is an optimum distance from the exit of the detonation tube to the endwall, approximately equal to one tube diameter, which promotes successful transmission.

Initiation of reactive blast waves by external energy sources

This article is devoted to the analysis of the direct initiation, by concentrated centrally-symmetric external energy sources, of self-sustained detonation waves in gaseous reactive mixtures. The dynamics of the detonation front will be described in the fast reaction limit, when the thickness of the reaction layer that follows the shock front is very small compared with the shock radius. At early times, after starting the external thermal energy deposition, the detonation front, associated with a strongly expanding flow, is overdriven; thus it is reached by expansion waves that decrease its velocity towards the Chapman–Jouguet (CJ) value, for which the expansion waves can no longer reach the front. The decay occurs for detonation radii such that the energy released by the external source equals the heat released by the chemical reaction. For planar detonations the CJ velocity is only approached asymptotically for large times, while for cylindrical and spherical detonations the flow divergence provides an additional decay mechanism associated with the front curvature that causes the transition to the constant CJ velocity to occur at a finite value of the detonation radius. The time evolution of the flow field and the corresponding variation with deposition time of the transition radius is computed for energy sources of constant heating rate. The analysis includes a detailed quantitative description of the near-front flow structure for times close to the transition time, given here for the first time, along with the study of the evolution towards the Zelʼdovich–Taylor cylindrical or spherical self-similar flow structure, which corresponds to a CJ detonation front ideally initiated at the center without any external energy source. The asymptotic decay to CJ is also described for planar detonations initiated with energy sources of constant heating rate and finite nonzero deposition time. A brief discussion will be given on how the reaction may be quenched by the flow divergence effects if the initiating energy is smaller than a critical value, thus failing to generate a self-propagating detonation wave.

Propagation Mechanism of Cylindrical Cellular Detonation

We investigate the evolution of cylindrical cellular detonation with different instabilities. The numerical results show that with decreasing initial temperature, detonation becomes more unstable and the cells of the cylindrical detonation tend to be irregular. For stable detonation, a divergence of cylindrical detonation cells is formed eventually due to detonation instability resulting from a curved detonation front. For mildly unstable detonation, local overdriven detonation occurs. The detonation cell diverges and its size decreases. For highly unstable detonation, locally driven detonation is more obvious and the front is highly wrinkled. As a result, the diverging cylindrical detonation cell becomes highly irregular.

Generation and Dynamics of Sub-Transverse Wave of Cylindrical Detonation

This article shows a numerical simulation of the transverse cell in a H2/O2 diverging cylindrical detonation. An advection upstream splitting method with a diminishing variation scheme (AUSMDV scheme) and a detailed chemical kinetic model of H2/O2 by Petersen and Hanson were used to improve the numerical resolutions for fluid dynamics and for chemical kinetics, respectively. In the numerical results, the irregular cellular pattern and transverse cells were obtained by direct initiation. The numerical results indicated the detailed transverse detonation structure formed the complex Mach configuration, and sub-transverse waves on the transverse detonation were observed. These discussions suggest that the sub-transverse wave on thetransverse detonation destabilizes the cylindrical detonation front due to sub-transverse wave propagation toward the detonation front. This unstable factor from the sub-transverse wave develops the new transverse wave, which traces the fine cell, resulting in the appearance of cell bifurcation.