Calculation of shock wave propagation in water containing reactive gas bubbles

The entry of a shock wave from air into water containing reactive gas (stoichiometric acetylene–oxygen mixture) bubbles uniformly distributed over the volume of the liquid has been numerically investigated using equations describing two-phase compressible viscous reactive flow. It has been demonstrated that a steady-state supersonic self-sustaining reaction front with rapid and complete fuel burnout in the leading shock wave can propagate in this bubbly medium. This reaction front can be treated as a detonation-like front or “bubble detonation.” The calculated and measured velocities of the bubble detonation wave have been compared at initial gas volume fraction of 2 to 6%. The observed and calculated data are in satisfactory qualitative and quantitative agreement. The structure of the bubble detonation wave has been numerically studied. In this wave, the gas volume fraction behind the leading front is approximately 3–4 times higher than in the pressure wave that propagates in water with air bubbles when the other initial conditions are the same. The bubble detonation wave can form after the penetration of the shock wave to a small depth (~300 mm) into the column of the bubbly medium. The model suggested here can be used to find optimum conditions for maximizing the efficiency of momentum transfer from the pressure wave to the bubbly medium in promising hydrojet pulse detonation engines.     

炸药爆轰驱动超高速击波管的数值摸拟

 高能炸药（HE）柱壳沿轴向传播的稳定态爆轰，在置于炸药柱壳内部的泡沫塑料（工作流体）中产生很强的轴向击波，达到极高的压力和能量密度。适当设计，可使工作流体的流动接近一稳定态，与炸药爆轰以相同的相速度前进。击波阵面后的工作流体可用Nozzle流动方程很好地描述^[1]，Nozzle收缩段中的流动不受散开段流动的影响。利用这一性质，可以设计出达到极高压力和能量密度的超高速击波管，并且不受管壁物质强度的限制。数值模拟计算给出了上述稳定态物理图象，并显示出开始阶段轴向击波的形成过程及其后对稳定态的逼近，计算结果及物理图象与理论分析符合得很好。     

低温下JB-9014钝感炸药DSD参数研究

 爆轰冲击波动力学（Detonation Shock Dynamics,DSD）是目前研究爆轰波非理想传播的有效途径。利用DSD的广义几何光学模型,研究了大长径比药柱中爆轰波非理想传播现象,根据-30 ℃下直径为10～30 mm药柱的直径效应实验数据,利用遗传算法确定了低温下JB-9014钝感炸药的DSD参数。由DSD参数计算得到了JB-9014药柱中的定态波形和爆速,计算结果与实验结果符合。     

Detonation of explosives containing heavy inert particles

The physical and mathematical aspects of the theory of a detonation wave containing heavy inert particles are considered. The detonation wave intensity and structure are determined by the relaxation of velocities of both the reactive explosive and the inert admixture. The generalized Jouguet condition is formulated for the velocity of a self-sustained detonation wave. The results of analytical treatment and the model numerical solutions of the problem of the detonation wave velocity selection and the wave structure determination are presented as a function of the ratio of the characteristic times of the heat evolution and the two-component flow velocity relaxation. A limiting case of the fast particle drag is represented by the shock wave structure determined by relaxation of the two-component flow velocity.     

Detonation type waves in phase (chemical) transformation processes in condensed matter

Fast self sustained waves (autowaves) associated with chemical or phase transformations are observed in many situations in condensed matter. They are governed neither by diffusion of matter or heat (as in combustion processes) nor by a travelling shock wave (as in gaseous detonation). Instead, they result from a coupling between phase transformation and the stress field, and may be classified as gasless detonation autowaves in solids. We propose a simple model to describe these regimes. The model rests on the classical equations of elastic deformations in a 1-dimensional solid bar, with the extra assumption that the phase (chemical) transformation induces a change of the sound velocity. The transformations are assumed to occur through a chain branched mechanism, which starts when the mechanical stress exceeds a given threshold. Our investigation shows that supersonic autowaves exist in this model. In the absence of diffusion (dissipation factor, losses), a continuum of travelling wave solutions is found. In the presence of diffusion, a steady state supersonic wave solution is found, along with a slower wave controlled by diffusion. Received 15 October 1998     

Experimental characterization of detonation initiation modes in a confined chamber flush-mounted with small-diameter ignition tubes

This work reports the experimental characterization of detonation initiation modes in a confined chamber in respect to the different types of reacting waves generated in various small-diameter ignition tubes. Depending on the length of the tube and mixtures composition, four types of reacting waves can be generated and utilized to initiate detonation in the main chamber, namely the over-driven detonation ignition wave, CJ detonation ignition wave, high-speed deflagration ignition wave and deflagration ignition wave. Based on the mechanisms of detonation initiation in the main chamber, four initiation modes can be observed: the direct initiation, the local explosion initiation, and the fast and slow deflagration-to-detonation transition (DDT) initiation. By comparing the detonation initiation positions and flame-tip velocities, the first two modes show appreciably shorter initiation distances compared to the DDT modes. The over-driven detonation ignition wave is shown to yield a high probability of direct initiation, while contrary to expectation, the high-speed deflagration ignition wave exhibits superior initiation performance compared to the CJ detonation ignition wave. It is illustrated that the energy decay through diffraction and the effect of precursor shock wave reflection on the wall of the rectangular chamber are viable factors responsible for this observation. The deflagration ignition wave is also shown to be able to rapidly initiate the detonation near the inlet of the chamber, albeit with a lower success rate.     

A generic travelling wave solution in dissipative laser cavity

A large family of cosh-Gaussian travelling wave solution of a complex Ginzburg–Landau equation (CGLE), that describes dissipative semiconductor laser cavity is derived. Using perturbation method, the stability region is identified. Bifurcation analysis is done by smoothly varying the cavity loss coefficient to provide insight of the system dynamics. He’s variational method is adopted to obtain the standard sech-type and the not-so-explored but promising cosh-Gaussian type, travelling wave solutions. For a given set of system parameters, only one sech solution is obtained, whereas several distinct solution points are derived for cosh-Gaussian case. These solutions yield a wide variety of travelling wave profiles, namely Gaussian, near-sech, flat-top and a cosh-Gaussian with variable central dip. A split-step Fourier method and pseudospectral method have been used for direct numerical solution of the CGLE and travelling wave profiles identical to the analytical profiles have been obtained. We also identified the parametric zone that promises an extremely large family of cosh-Gaussian travelling wave solutions with tunable shape. This suggests that the cosh-Gaussian profile is quite generic and would be helpful for further theoretical as well as experimental investigation on pattern formation, pulse dynamics and localization in semiconductor laser cavity.     

Numerical investigation on detonation cell evolution in a channel with area-changing cross section

The two-dimensional cellular detonation propagating in a channel with area- changing cross section was numerically simulated with the dispersion-controlled dissipative scheme and a detailed chemical reaction model. Effects of the flow expansion and compression on the cellular detonation cell were investigated to illustrate the mechanism of the transverse wave development and the cellular detonation cell evolution. By examining gas composition variations behind the leading shock, the chemical reaction rate, the reaction zone length, and thermodynamic parameters, two kinds of the abnormal detonation waves were identified. To explore their development mechanism, chemical reactions, reflected shocks and rarefaction waves were discussed, which interact with each other and affect the cellular detonation in different ways.     

New exact travelling wave solutions of the generalized zakharov equations

A direct algebraic method is introduced for constructing exact travelling wave solutions of nonlinear partial differential equations with complex phases. The scheme is implemented for obtaining multiple soliton solutions of the generalized Zakharov equations, and then new exact travelling wave solutions with complex phases are obtained. In addition, by using new exact solutions of an auxiliary ordinary differential equation, new exact travelling wave solutions for the generalized Zakharov equations are obtained.     

Symmetry groups and spiral wave solution of a wave propagation equation

We study a third-order nonlinear evolution equation, which can be transformed to the modified KdV equation, using the Lie symmetry method. The Lie point symmetries and the one-dimensional optimal system of the symmetry algebras are determined. Those symmetries are some types of nonlocal symmetries or hidden symmetries of the modified KdV equation. The group-invariant solutions, particularly the travelling wave and spiral wave solutions, are discussed in detail, and a type of spiral wave solution which is smooth in the origin is obtained.     

氢气-空气混合物中瞬态爆轰过程的二维数值模拟

 对高温火团引发的氢气-空气混合气的瞬态爆轰过程进行了二维数值模拟,考虑了H₂-O₂-N₂的详细化学反应动力学机理,该机理包含了19个基元反应和9种组分。采用分裂格式处理带化学反应的Euler方程,其中使用全耦合的TVD格式求解流场,使用基于Gear算法的微分方程解法器求解化学反应过程。计算结果表明：在H₂∶O₂∶N₂＝0.4∶0.4∶0.2（摩尔比）的混合气中,高温气团初始温度为T/T₀=5.3时可诱导爆轰,爆轰波以2 300 m/s的速度传播,同时爆轰波阵面在管壁会形成反射波。还对计算的爆轰波后组分的浓度和温度进行了讨论,为理解爆轰波后结构提供信息。     

基于裸光纤探头的双点光子多普勒测速系统

全光纤光子多普勒速度测量(PDV)系统是一种新型的激光测速系统,可广泛用于冲击波、爆轰波以及其他短时高速运动物体的速度测量。多点测量可以获得靶面不同位置的速度,以测量靶面的形变。为提高测量的空间分辨率,提出使用裸光纤束为PDV系统的探头,并在实验上实现了空间分辨率为375μm的双点速度测量。裸光纤探头的间距较小,一个探头的测量结果可能受到另一个探头反射光的干扰。理论和实验的研究结果表明,当靶面各点速度相同时,测量结果不受干扰光的影响;当各点速度不同时,其测速误差不但与两被测点的速度差有关,还与传感光和干扰光的光强和相位有关。     

Towards nonlinear stability of sources via a modified Burgers equation

Coherent structures are solutions to reaction-diffusion systems that are time-periodic in an appropriate moving frame and spatially asymptotic at x=±∞ to spatially periodic travelling waves. This paper is concerned with sources which are coherent structures for which the group velocities in the far field point away from the core. Sources actively select wave numbers and therefore often organize the overall dynamics in a spatially extended system. Determining their nonlinear stability properties is challenging as localized perturbations may lead to a non-localized response even on the linear level due to the outward transport. Using a Burgers-type equation as a model problem that captures some of the essential features of sources, we show how this phenomenon can be analysed and asymptotic nonlinear stability be established in this simpler context.     

Rigorous asymptotic stability of a Chapman - Jouguet detonation wave in the limit of small resolved heat release

We study the rigorous asymptotic stability of a Chapman - Jouguet (CJ) detonation wave in the limit of small resolved heat release (SRHR). We show that the solution exists globally and that the solution converges uniformly to a shifted CJ detonation wave as t + for initial data which are small perturbations of the CJ detonation wave. A CJ detonation wave is characterized by the property that the speed at the end of it is sonic. A similar phenomenon occurs for a shock profile when the flux function is nonconvex. We use the weighted energy method to overcome the difficulty. The proper choice of the weight cancels the degenerate property of the CJ detonation at the tail. The nonmonotonic part, or the expansive part, of the profile caused by the chemical reaction is treated by the characteristic energy estimate under the assumption of SRHR.     

Structural characteristics of detonation expansion from a small channel to a larger one

We report on numerical simulations of the evolution of two-dimensional detonation waves that are expanded from a small channel to a larger one. In accordance with experimental data, the simulations predict three different types of evolution, namely, supercritical, critical and subcritical detonations. In a supercritical detonation, the reaction zone remains always attached to the precursor shock, whereas in a critical one it temporarily detaches and then re-attaches to the front. In the subcritical type, the extinction is permanent, i.e., the detonation quenches. The effects of the fuel’s activation energy and the channel-width ratio are studied via a parametric study. It is found that sufficiently large values of these two parameters can result to flows of the critical and even the subcritical type. Finally, three-dimensional simulations have also been performed and are briefly discussed herein.     

Bifurcations and new exact travelling wave solutions for the bidirectional wave equations

By using the method of dynamical system, the bidirectional wave equations are considered. Based on this method, all kinds of phase portraits of the reduced travelling wave system in the parametric space are given. All possible bounded travelling wave solutions such as dark soliton solutions, bright soliton solutions and periodic travelling wave solutions are obtained. With the aid of Maple software, numerical simulations are conducted for dark soliton solutions, bright soliton solutions and periodic travelling wave solutions to the bidirectional wave equations. The results presented in this paper improve the related previous studies.     

Thermal tests of a pulse-detonation high-speed burner

The steady-state temperatures of the elements of a high-speed pulse-detonation burner (HSPDB) running on a natural gas-air mixture were measured in the course of long-term tests of the burner operating in the pulse-detonation mode without forced cooling at a frequency of 2 Hz. Knowledge of the steady-state temperatures is required for the development of an energy-efficient forced cooling system for the HSPDB. The experiments have shown that the maximum steady-state temperature (～500°C) is reached after approximately 200 s of operation at internal elements of the HSPDB, more specifically, turbulizing obstacles placed in that part of the burner duct through which the detonation wave travels periodically. The HSPDB wall in this part of the burner duct is heated to 420°C within ～1000 s. In the part of the burner duct through which the deflagration wave travels periodically, the HSPDB walls and internal elements are heated to a steady-state temperature not exceeding 330°C. The results show that the forced cooling of the HSPDB is generally required only for those parts of the burner duct through which the detonation wave passes periodically.     

来流温度影响驻定爆轰波结构和性能的数值研究

 采用数值模拟的方法研究了超音速来流撞击圆锥体诱导的驻定爆轰波的结构和性能,讨论了不同初始来流温度下,爆轰波结构和波后压力的变化。结果表明,随着来流初始温度的降低,爆轰波的增压比逐渐增加,有利于提高驻定爆轰发动机的推进性能。当初始温度较高时,爆轰波阵面呈现光滑平直的形态,而初始温度较低时,爆轰波呈现出明显的三波点结构,且温度越低,三波点数量越多排列越紧密,这些具有较高压力的三波点对爆轰波波后压力的变化起到了重要作用。     

Aluminum oxidation in shock and detonation waves

Experimental data on the detonation velocity of aluminized explosives and the temperature of the material behind the shock wave front in condensed media, including aluminum-oxidizer mixtures were examined. It was demonstrated that the oxidation of aluminum to the highest oxide behind the front of shock and detonation waves is limited by the dissociation of aluminum oxides at temperatures above 3.5 kK.     

Burgers方程的声速点故障问题

研究了在Burgers方程跨声速稀疏波计算中遇到的sonic point glitch问题,对它产生的原因及其与数值格式熵条件的关系进行了分析.对若干著名格式,按照是否满足熵条件进行了分类.为了消除sonic point glitch现象,提出了一种新的两步分裂方法,并用这种方法改进了一系列典型格式.数值试验表明这是一种很好的消除sonic point glitch的方法.