凝聚炸药爆轰波在高声速材料界面上的折射现象分析

凝聚炸药爆轰在边界高声速材料约束下传播时,爆轰波会在约束材料界面上产生复杂的折射现象.本文针对凝聚炸药爆轰波在高声速材料界面上的折射现象展开理论和数值模拟分析.首先通过建立在爆轰ZND模型上的改进爆轰波极曲线理论给出爆轰波折射类型,然后发展一种求解爆轰反应流动方程的基于特征理论的二阶单元中心型Lagrange计算方法来数值模拟典型的爆轰波折射过程.从改进爆轰波极曲线理论和二阶Lagrange方法数值模拟给出的结果看出,凝聚炸药爆轰波在高声速材料界面上的折射类型有四种:反射冲击波的正规折射、带束缚前驱波的非正规折射、带双Mach反射的非正规折射、带λ波结构的非正规折射.     

Influence of the adiabatic index on switching between different types of shock wave reflection in a steady supersonic gas flow

A comprehensive pattern of different types of shock wave reflection in a steady supersonic gas flow is analytically constructed with regard to a new wave configuration found by the authors-negative-angle irregular reflection. A double Mach reflection with a negative reflection angle in a steady supersonic gas flow is numerically obtained for the first time.     

Flow visualization and density measurement of compressible flows by a laser speckle method

Laser speckle method is a well known technique that is useful for both visualization and quantitative measurement. This technique was applied to the density measurement of Mach reflection of shock waves in the present experiment. The Object of the measurement is the density field of simple Mach reflection in relatively low shock Mach number. The non-uniform flow field is divided into three regions by incident, Mach and reflected shock waves. A shock tube was employed in the present experiment. Wedges of 20 degrees and 45 degrees were placed in the test section. YAG laser was employed as a light source. Speckle photograph was taken by a digital still camera. Simple subtraction between the reference and flow images shows a shock pattern and a degree of the correlation of speckle pattern in the flow field. Thus, we can obtain a visualized flow image showing a configuration of Mach reflection from speckle photograph. Speckle photographs which was obtained in the experiments were processed with cross-correlation method. A reconstructed density gradient vector map of Mach reflection was obtained. Comparing the experimental result with numerical one, the measured density gradient shows a good agreement with theoretical prediction.     

Gasdynamic design of a two-dimensional supersonic inlet with the increased flow rate factor

A two-dimensional inlet of external compression with the increased flow rate factor at high supersonic velocities is constructed by the method of gasdynamic design. Its feature is that a flow with the initial oblique shock wave and the subsequent centered isentropic compression wave is formed over the external compression ramp of the inlet. These waves interact with one another so that a resulting stronger oblique shock wave and a velocity discontinuity arise in front of the entrance to the inlet internal duct. An example of an inlet configuration with the design flow regime corresponding to the Mach number M_d = 7 is considered. The characteristics of this inlet were obtained in the range of the free-stream Mach numbers M = 4–7 with the use of a Navier—Stokes code for turbulent flow. They are compared with characteristics of an equivalent conventional shocked inlet. As computations have shown, the inlet with the isentropic compression wave has much higher values of flow rate factor φ at Mach numbers M < M_d. So, for example, at M = 4 the value φ ≈ 0.72 for it is by 33 % higher in comparison with φ ≈ 0.54 for the equivalent shocked inlet.     

Generalized hydrodynamic theory of shock waves: Mach-number dependence of inverse shock width for nitrogen gas

A generalized hydrodynamic theory of shock wave structures is presented for rigid diatomic gases. The theory yields shock solutions for all Mach numbers. The accuracy of the theory is examined for nitrogen gas as an example. Excellent agreement with experiment is obtained for the inverse shock widths for the entire range of Mach number studied by experiment. The comparison made shows that we are now in possession of a successful continuum theory of shock waves in molecular gases for all Mach numbers.     

Detonation re-initiation mechanism following the Mach reflection of a quenched detonation

This experimental study addresses the re-initiation mechanism of detonation waves following the Mach reflection of a shock–flame complex. The detonation diffraction around a cylinder is used to reproducibly generate the shock–flame complex of interest. The experiments are performed in methane–oxygen. We use a novel experimental technique of coupling a two-in-line-spark flash system with a double-frame camera in order to obtain microsecond time resolution permitting accurate schlieren velocimetry. The first series of experiments compares the non-reactive sequence of shock reflections with the reflection over a rough wall under identical conditions. It was found that the hot reaction products generated along the rough wall are entrained by the wall jet into a large vortex structure behind the Mach stem. The second series of experiments performed in more sensitive mixtures addressed the sequence of events leading to the detonation establishment along the Mach and transverse waves. Following ignition and jet entrainment, a detonation first appears along the Mach stem while the transverse wave remains non-reactive. The structure of the unburned tongue however indicates local instabilities and hot spot formation, leading to the rapid reaction of this gas. Numerical simulations are also reported, confirming the sequence of ignition events obtained experimentally.     

无粘流中能捕捉较弱的接触间断和激波的反扩散差分格式

在研究弱入射激波遇到对称楔以后的马赫反射现象时,激波管实验不易测出很弱的接触间断,也不易捕捉到马赫反射与正规反射转换的条件。文章一方面研究了可压流体力学欧拉方程的数值方法,首先是用反扩散法改进接触间断的计算;另一方面根据格式粘性的特性和它引出的很微小的熵的变化规律来显示很弱的接触间断和反射激波。这样才易于将对三波点的分析推进一步。文[5,6]曾预言了一种反散波是连续的压缩波的新的激波反射类型。我们设想并根据计算初步确认这新类型反射实际应该是简单马赫反射,反射波虽弱仍是激波。     

平面激波经下降台阶后的马赫效应

As a plane shock wave with shock mach number Mi propagates down a backward step of height H (fig 1) a part of the shock front turns to be curvilinear It reflects from the horizontal part behind step.This unsteady regular reflection eventually becomes Mach reflection.We present here the results of shock tube experiment (M_i ≤ 2.20) and numerical simulation of this phenomena, say the transition from regular reflection (RR) to Mach reflection (MR).The dependence of the position of transition L_k and critical angle of transition ω_Ck on strength of the impinging plane shock M_i and height of step H are analysed.Our experimental and numerical results are compared with the theoretical criLerion of transition of Iton & Itaya^[15].It should be mentioned that the numerical method of FLIC type with triangular mesh developed in^[13] is successful.     

Mach reflection for the two-dimensional Burgers equation

We study shock reflection for the two 2D Burgers equation. This model equation is an asymptotic limit of the Euler equations, and retains many of the features of the full equations. A von Neumann type analysis shows that the 2D Burgers equation has detachment, sonic, and Crocco points in complete analogy with gas dynamics. Numerical solutions support the detachment/sonic criterion for transition from regular to Mach reflection. There is also strong numerical evidence that the reflected shock in the 2D Burgers Mach reflection forms a smooth wave near the Mach stem, as proposed by Colella and Henderson in their study of the Euler equations.     

Waves in interplanetary shocks: a wind/WAVES study

We describe results from the first statistical study of waveform capture data during 67 interplanetary (IP) shocks with Mach numbers ranging from approximately 1-6. Most of the waveform captures and nearly 100% of the large amplitude waves were in the ramp region. Although solitary waves, Langmuir waves, and ion acoustic waves (IAWs) are all observed in the ramp region of the IP shocks, large amplitude IAWs dominate. The wave amplitude is correlated with the fast mode Mach number and with the shock strength. The observed waves produced anomalous resistivities from approximately 1-856 Omega.m (approximately 10(7) times greater than classical estimates.) The results are consistent with theory suggesting IAWs provide the primary dissipation for low Mach number shocks.     

爆轰波在炸药-金属界面上的折射分析

针对爆轰波在炸药-金属界面上折射时由实验获得的金属折射冲击波压力与经典爆轰波极曲线理论预测的压力存在显著差异这一问题, 本文展开了进一步的理论和数值模拟分析研究. 首先通过分析指出经典爆轰波极曲线理论的缺陷, 并对爆轰波极曲线理论进行了改进, 改进爆轰波极曲线理论给出了炸药爆轰波折射类型以及折射冲击作用点处的压力值. 然后发展了一个基于次特征理论来数值求解爆轰反应流动控制方程的二阶中心型Lagrange方法, 并数值模拟了一个典型的炸药爆轰波折射实验. 改进爆轰波极曲线理论和数值模拟分析结果表明, 爆轰波折射类型有三种:反射冲击波的正规折射、带Mach反射的非正规折射、无反射波的正规折射, 并且金属折射冲击波压力值随入射角增大而单调减小.     

Diffraction of a two-shock configuration by a convex cylindrical surface

The subject of this work is numerical investigation into the diffraction of a shock-wave configuration by a convex cylindrical surface. The diffraction is a stage of interaction of a shock wave with a two-dimensional body. It is preceded by the stage of shock wave reflection from the front surface of the body, the back surface of which has a convex cylindrical shape. The two-or three-shock configuration formed on the front surface diffracts by the back cylindrical surface. The emphasis is on studying the diffraction of the two-shock wave configuration with the diffraction angle varying continuously. The object under study a wedge with an inclined front surface and convex cylindrical back surface. The results of numerical investigation are obtained by integrating the Euler equations. Flow features associated with the simultaneous diffraction of the incident and reflected shock waves are revealed. The evolution of the gasdynamic system (stagnation wave + TU layer) arising inside the diffraction area is studied. Breakaway and vorticity initiation are considered. It is shown that the positions of the line of separation and TU layer change in the course of diffraction. They merge together at the stage of steady flow. Comparison is made between the flow formed upon diffraction of the two-shock configuration by the cylindrical surface and the flow generated upon diffraction by horizontal and vertical surfaces.     

Interaction of shock waves with bubble-liquid drops

The regular reflection of an air shock wave from a spherical drop of a bubble liquid is studied. In the framework of an extended equilibrium model, the effect of the shock waves on single drops of various shapes and on drop ensembles (drop screens) is numerically investigated. It is shown that, when subjected to shock waves, bubble-liquid drops and drops of a bubble-free liquid collapse in a radically different way.     

Stability of supersonic boundary layer on a porous plate with a flexible coating

The development of disturbances in the boundary layer of compressible gas on a flexible surface has been investigated in the linear and nonlinear approximations (the weakly nonlinear stability theory). The regimes of moderate (the Mach number M = 2) and high (M = 5.35) supersonic velocities as well as a model of a porous wall, on which a flexible film is spanned, have been considered. The boundary conditions for disturbances with regard for their transformation by a flexible porous coating have been derived. The character of the variation of the coefficients of the stream-wise growth of linear oscillations of different nature (the vortex waves of the first mode and the acoustic waves of the second mode) is shown. The direction and the degree of their deformations are determined by the flexible coating parameters. It is found that at moderate Mach numbers, the stabilization of disturbances and the diminution of increments occur, whereas at high M on a surface with a film, the acoustic components are destabilized, which may lead to an earlier onset of nonlinear processes. The nonlinear interactions in three-wave symmetric triplets between the vortex waves at M = 2 and between the waves of different nature at M = 5.35 are considered. In the latter case, the plane acoustic wave is the pumping wave, which excites the three-dimensional subharmonic components of vortex nature.     

Application of the wavenumber jump condition to the normal and oblique interaction of a plane acoustic wave and a plane shock

A kinematic approach is considered whereby the wavenumber jump conditions in conjunction with the appropriate dispersion relations is applied to the investigation of the normal and oblique interaction of a plane acoustic wave with a plane shock wave. For the normal interaction of an acoustic wave with a stationary plane shock a logarithmic shift in the wave spectra is obtained. For the normal interaction with a moving shock front it is shown that for shock Mach numbers above a critical value, the frequency of the transmitted wave becomes negative. This results in the fact that the crests of the transmitted signal arrive at a fixed observer in a reverse order to their generation. Finally, the oblique interaction of an acoustic wave with a stationary shock is considered. The “Snell's Law” for the transmitted wave is derived and two special angles of incidence are identified. The first is a no-refraction angle: i.e., the transmitted wave angle is the same as the incident wave angle. The second is a critical angle such that for incident angles greater than this critical angle there is no transmitted wave. A necessary and sufficient condition for the existence of a transmitted wave is derived in terms of the speed of sound and Mach number of the fluid and the frequency and tangential wavenumber component of the incident wave.The dynamics aspects of the interaction concerning the determination of the frequency independent transmission coefficients and shock displacements are determined for the simple case of the normal interaction with a moving shock as an illustration.     

Dispersive nature of high mach number collisionless plasma shocks: Poynting flux of oblique whistler waves

Whistler wave trains are observed in the foot region of high Mach number quasiperpendicular shocks. The waves are oblique with respect to the ambient magnetic field as well as the shock normal. The Poynting flux of the waves is directed upstream in the shock normal frame starting from the ramp of the shock. This suggests that the waves are an integral part of the shock structure with the dispersive shock as the source of the waves. These observations lead to the conclusion that the shock ramp structure of supercritical high Mach number shocks is formed as a balance of dispersion and nonlinearity.     

内聚锥形激波的非均匀强化与结构演变特征

以高超声速内转式进气道流动中的激波汇聚问题为背景,考虑工程实际中的来流和壁面几何条件这两个关键因素,分别提出了以来流攻角为研究参数的非轴向来流内锥流动模型,和以长/短轴比为研究参数的椭圆入口内锥流动模型.采用激波风洞实验观测和数值模拟相结合的方法,揭示了两类流动中激波的非均匀汇聚特征.结果表明:由来流攻角引起的激波初始沿周向强度分布的不均匀性会在汇聚过程中被放大,迎风面和背风面的激波差异不断加剧;来流攻角越大,初始激波强度不均匀性越强,在汇聚过程中激波面越容易出现不连续的拐折,且出现拐折后激波的汇聚效应会被削弱.由椭圆入口形成的等强度激波在初始时周向的几何不均匀性使激波在汇聚过程中出现沿长/短轴方向的强度差异,激波沿长轴方向上的强度增加更迅速;椭圆长/短轴比越大,激波初始几何不均匀性越强,在汇聚过程中长/短轴两个方向激波强度差异凸显得越快,波面越容易出现不连续的拐折,进而削弱激波的汇聚.在偏离轴对称达到一定程度时,这两种条件下的激波汇聚都会出现汇聚中心处从Mach反射向规则反射的转变.      

Initiation and propagation of detonation waves in combustible high speed flows

The initiation and propagation of detonation waves in combustible high speed flows were studied experimentally. A planar detonation wave traveling in an initiation tube was transmitted into a test section where a combustible high speed flow was induced by an incident shock wave generated in a shock tube. In this study, the flow Mach numbers were obtained as 0.9 and 1.2. The experimental results show that depending on the flow velocity, the apparent propagation velocity of a detonation wave is higher in the upstream and lower in the downstream direction than the CJ velocity. Smoked plate records reveal cellular patterns deformed in the flow direction, and the calculated aspect ratios of the cell were found to agree well with the experimental ones on the basis of the assumption that the velocity of the transverse wave is not affected by the flowing mixture. By analyzing the shock-wave diffraction at the position where there is an abrupt change in the area, on the basis of Whitham’s theory, it was deduced that in the present experimental set-up, the detonation was initiated by the reflection of the diffracted shock waves on the sidewalls of the test section. The agreement between the experimental and calculated results regarding the position of the cellular patterns on the smoked plate record indicated that the position of detonation initiation in high speed flows is shifted downstream due to the flow velocity.     

Shock tube exit flow fields through thin membranes

The flow field characteristics that form for a shock wave propagating through a membrane-like termination at the exit of a shock tube are studied. The strength of the shock wave reflected back into the tube, as well as the strength of the shock wave transmitted, is examined. Six different materials are used, ranging from copper and aluminium foils to a variety of elastic and plastic sheets, in a few cases with different initial pressure differentials. High-speed shearing interferometry imaging is done of the external flow. Three principal characteristics are present in the transmitted flow: a diffracted shock wave, an expansion wave and a re-compression shock wave. It is found that the prominence of these features varies depending on the material type. For the later flow development and material rupture, there are a number of principal characteristics: small vortices, secondary shock waves, a vortex ring, oblique waves and a Mach disc.     

Classification of shock wave reflections from a wedge. Part 1: Boundaries and domains of existence for different types of reflections

Classification of various types of the reflections of a shock wave over straight wedge is supposed. The idea about entire reflection phenomenon as a result of interaction of two processes—the shock wave refection process and the flow deflection process—serves as a basis for the classification. To recognize the types of reflection, changes in the shapes of the reflected wave, Mach stem and contact surface are taken into account. The boundaries and domains of existence for various types of reflection are reported. New names for some types of reflection are proposed.