聚心火焰与激波相互作用的数值研究

基于带化学反应的2维轴对称Euler方程,利用带有monotonized centered(MC)限制器的波传播算法,在两端敞开的圆桶中对惰性介质的聚心激波和氢气-空气混合物的聚心火焰与激波的相互作用进行了数值模拟。数值结果表明,在惰性介质中激波在轴心的每次汇聚均可成长为马赫干,马赫干的追赶使激波得到一定程度的增强,但整体还呈下降趋势。在氢气-空气混合物中,燃烧诱导的激波,由于与火焰的反复作用,使激波在轴心处产生马赫干的频率和强度皆高于惰性介质中的情形。同时,火焰在与激波的相互作用过程中发生失稳变形,使其形状呈扁平头部的蘑菇云。     

Study on Mach stems induced by interaction of planar shock waves on two intersecting wedges

The properties of Mach stems in hypersonic corner flow induced by Mach interaction over 3D inter-secting wedges were studied theoretically and numerically. A new method called “spatial dimension reduction” was used to analyze theoretically the location and Mach num-ber behind Mach stems. By using this approach, the problem of 3D steady shock/shock interaction over 3D intersecting wedges was transformed into a 2D moving one on cross sec-tions, which can be solved by shock-polar theory and shock dynamics theory. The properties of Mach interaction over 3D intersecting wedges can be analyzed with the new method, including pressure, temperature, density in the vicinity of triple points, location, and Mach number behind Mach stems. Theoretical results were compared with numerical results, and good agreement was obtained. Also, the influence of Mach number and wedge angle on the properties of a 3D Mach stem was studied.     

A revised three-shock solution for the Mach reflection of weak shocks (1.1<M i<1.5)

It is well known that the classical three-shock theory of von Neumann (1943) does not adequately describe the configuration of the shocks close to the triple-point of a Mach reflection of an incident shock with a Mach number less than about 1.5. The assumptions on which the three-shock theory is based have been examined and several of them are shown to be invalid. The assumption that may be of most significance is that the normal components of the flows behind the reflected and the Mach stem shocks are parallel. Dropping this assumption removes an essential equation in the three-shock solution. An alternative assumption, based on experimental observation, is that there is an approximate linear relationship between the pressure behind the reflected shock and the triple-point trajectory angle. This assumption permits a revised three-shock solution which gives results that are in agreement with experimental observations of reflections of incident shocks with Mach numbers between 1.1 and 1.5.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Submerged shocks in conical gas flows in the presence of a mach shock-wave configuration

The results of a numerical study of a new type of singularities in the Mach shock-wave structure realized in supersonic nonsymmetric conical flows over V-wings with a bow shock attached to the leading edges are presented. Within the framework of the ideal gas model we study the changes in the shock system on transition, with increase in the sweep angle, from the region of nonsymmetric Mach interaction of the shocks attached to the leading edges of the wing to the region of special flow patterns, where on the windward cantilever surface a rarefaction flow is realized rather than a flow with an internal shock. It is shown, in particular, that in the region with special wing flow patterns a Mach system of shocks with a submerged shock proceeding from the branch point above the windward cantilever may exist.     

Simulation of the Mach reflection in supersonic flows by the CE/SE method

This study employs the Space-Time Conservation Element and Solution Element (CE/SE) method to determine the influence of downstream flow conditions on Mach stem height. The results indicate that the Mach stem height depends on the incident shock wave angle and the distance between the trailing edge and the symmetry plane. Furthermore, it is shown that the downstream length ratio and the trailing edge angle do not affect the Mach stem height nor the Mach reflection (MR) configuration, and the Space-Time Conservation Element and Solution Element method is able to simulate the MR as well as many other numerical schemes. Communicated by K. Takayama PACS 47.40.Nm     

A weak shock wave reflection over wedges

When a weak shock wave reflects from wedges its reflection pattern does not appear to be a simple Mach reflection. This reflection pattern is known to be von Neumann Mach reflection in which a Mach stem can not necessarily be straight. In this paper the local change of the Mach stem curvature was experimentally and numerically investigated. A distinct triple point, at which the curvature becomes infinite as appears in a simple Mach reflection, was not observed but the Mach stem curvature became a maximum between foot of the Mach stem and a point, P₁, at which an incident shock met with a reflected shock. Maximum curvature point P₂ and P₁ do not coincide for small wedge angles and tend to merge over a certain wedge angle. Experimental results agreed with numerical results. The trajectory angle of P₂ was found to be expressed well by Whitham's shock-shock angle.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

A simple physical theory of weak Mach reflection over plane surfaces

It is shown that simple physical principles coupled with the inviscid shock jump relations can be applied to the problem of weak Mach reflection to the extent that the triple point path can be predicted from the incident shock Mach number , gas specific heat ratio and the inclination angle of the reflecting surface to the shock normal. Comparison with the Euler code data and with experiments show close agreement for conditions both far and close to transition and that the general shape of the reflected and Mach stem shocks follow simple curves except in the neighbourhood of the triple point. The conflict at the triple point in matching the flow deflection angles and pressures across the contact discontinuity remains. It is shown however that the simple model presented here gives a close match to the cfd and experimental overall shock and contact surface shapes although it cannot predict these or the flow properties in any detail. Received 10 May 1999 / Accepted 17 December 1999     

金属铅在斜冲击波对碰加载下动态行为的数值模拟

高强度冲击加载作用下金属材料的动态物理行为是当前冲击波领域基础研究和工程应用最为关注的焦点。采用光滑粒子法(SPH)开展不同位置起爆诱发的斜冲击波对碰加载金属铅的二维数值模拟研究,得到了金属铅内入射斜冲击波的角度和强度,并利用极曲线方法理论上导出发生马赫反射时的临界入射角和入射马赫数关系。根据计算结果可知,金属铅内入射斜波对碰后将发生马赫反射。随着起爆位置与金属铅表面距离的增加,不仅金属铅内入射冲击波强度和入射角增加,而且形成的马赫杆宽度也在增加。由自由面速度剖面给出了马赫杆宽度及张角,结果与理论预测的结果吻合较好。     

Baroclinic vortex sheet production by shocks and expansion waves

Vortex sheet production by shocks and expansion waves refracting at a density discontinuity was examined and compared using an analytical solution and numerical simulations. The analytical solution showed that with a small exception, vortex sheet strength is generally stronger in fast/slow shock refractions. In contrast, expansion waves generated a stronger vortex sheet in slow/fast refractions. This difference results in larger vorticity deposited by shocks in fast/slow refractions and by expansion waves in slow/fast refractions. Shock refractions become irregular and the analytical solution fails when either incident, transmitted or reflected shock, exceeded the angle limit for an attached shock. To investigate vortex sheet production outside the range of analytical solutions and to verify the applicability of the planar-interface analytical solution to a curved interface, shock refraction through a sinusoidal interface was numerically simulated in the shock frame of reference. It is found that variation in the local incidence angle along the curved interface creates pressure waves that affect the level of deposited vorticity. This contributes to the difference between predictions from local analysis and numerical computation. Furthermore, an interesting behavior of the shock and expansion wave-deposited vorticity in supersonic ramp flow was discovered. When the high- and low-density streams were swapped, while keeping the incident flow Mach numbers constant, a vortex sheet of equal magnitude but of opposite sign was generated.     

Focusing of Strong Shocks in an Annular Shock Tube

Focusing of strong shock waves in a gas-filled thin convergence chamber with various forms of the reflector boundary is investigated experimentally and numerically. The convergence chamber is mounted at the end of the horizontal co-axial shock tube. The construction of the convergence chamber allows the assembly of the outer chamber boundaries of various shapes. Boundaries with three different shapes have been used in the present investigation—a circle, an octagon and a smooth pentagon. The shock tube in the current study was able to produce annular shocks with the initial Mach number in the range M _s = 2.3 − 3.6. The influence of the shape of the boundary on the shape and properties of the converging and reflected shock waves in the chamber has then been investigated both experimentally and numerically. It was found that the form of the converging shock is initially governed by the shape of the reflector and the nonlinear interaction between the shape of the shock and velocity of shock propagation. Very close to the center of convergence the shock obtains a square-like form in case of a circular and octagonal reflector boundary. This is believed to stem from the instability of the converging shock front triggered by the disturbances in the flow field. The outgoing, reflected shocks were also observed to be influenced by the shape of the boundary through the flow ahead as created by the converging shocks.     

带隔板装药爆轰波马赫反射理论研究和数值模拟

基于三波理论和Whitham方法对带隔板装药爆轰波相互作用后发生的正规反射和非正规反射进行了理论分析,给出了爆轰波发生马赫反射时临界入射角和马赫杆增长角等参数的变化规律,提出了马赫杆高度的计算模型。基于凝聚炸药爆轰Jones-Wilkins-Lee(JWL)模型和冲击起爆的Lee-Tarver模型,利用有限元计算软件对带隔板装药爆轰波的传播过程进行了数值模拟。结果表明,发生马赫反射后,随着爆轰波的传播,马赫杆的高度不断增加。数值模拟结果与理论计算结果吻合较好,说明本文中采用的理论模型和数值模拟方法能够较准确地描述带隔板装药爆轰波马赫反射的传播过程。     

Hysteresis phenomenon in supersonic flow past a system of cylinders

The interaction between the bow shocks ahead of a system of bodies in a supersonic flow is numerically investigated. Flow past cylinders with parallel axes lying in the plane perpendicular to the flow direction is calculated. Three different shock interaction patterns are obtained in modeling flow past an infinite periodic lattice, namely, the regular and Mach-type regimes and a regime with flow choking. In the case of two bodies a collective bow shock is formed. Transition between the flow patterns with variation in the freestream Mach number and the spacing between the cylinders is studied. Regular-to-Mach-configuration transition and vice versa occurs at particular angles of inclination of the bow shock at the interaction point determined by the criterion of a maximum flow deflection angle and the von Neumann criterion, respectively.     

An experimental and theoretical study of converging polygonal shock waves

An experimental investigation was carried out to explore the possibility of producing converging polygonal shocks in an essentially two-dimensional cavity. Previous calculations by Apazidis and Lesser (1996) suggested that such configurations could be produced by reflecting a cylindrical outgoing shock from a smoothly altered circular boundary, the alteration having n-gonal symmetry. In the experiments the outgoing shock was produced by a spark discharge which yielded shocks in the Mach number range from 1.1 to 1.7 at a radius just prior to the reflection. Polygonal shocks were observed as predicted by using a modified form of geometrical shock dynamics, derived in the above paper. In addition, the modified theory was used to calculate the results of an experiment carried out by Sturtevant and Kulkarny (1976). The results of the numerical calculations were found to be in substantial agreement with both experiments, suggesting that the modifications in geometrical shock dynamics for non-uniform flow ahead of an advancing shock are useful in the case of shock focusing. The experiment also showed that the polygonal shapes were stable in the examined range of shock Mach numbers, a result that may be of importance for a number of practical situations in which shock focusing is present. Received 9 October 2001 / Accepted 7 January 2002 – Published online 11 June 2002     

An experimental investigation of the sonic criterion for transition from regular to Mach reflection of weak shock waves

The signal speed, namely the local sound speed plus the flow velocity, behind the reflected shocks produced by the interaction of weak shock waves (M _i < 1.4) with rigid inclined surfaces has been measured for several shock strengths close to the point of transition from regular to Mach reflection. The signal speed was measured using piezo-electric transducers, and with a multiple schlieren system to photograph acoustic signals created by a spark discharge behind a small aperture in the reflecting surfaces. Both methods yielded results with equal values within experimental error. The theoretical signal speeds behind regularly reflected shocks were calculated using a non-stationary model, and these agreed with the measured results at large angles of incidence. As the angle of incidence was reduced, for the same incident shock Mach number, so as to approach the point of transition from regular to Mach reflection, the measured values of the signal speed deviated significantly from the theoretical predictions. It was found, within experimental uncertainty, that transition from regular to Mach reflection occurred at the experimentally observed sonic point, namely, when the signal speed was equal to the speed of the reflection point along the reflecting surface. This sonic condition did not coincide with the theoretical value.     

Stability and analogy of shock wave reflection in steady flow

Numerical simulations have been performed to investigate the stability of shock wave reflection in supersonic steady flow. Wall deflection control has been applied just downstream of the reflection point in the regular reflection configuration. The results provide the magnitude of the disturbance required to cause transition from one configuration to the other throughout the range of incident shock angle. An argument focusing on the subsonic region generated behind the Mach stem in the Mach reflection configuration explains the mechanism of the transition. Numerical results show that both regular and Mach reflections are possible in the dual-solution domain, and also indicate the presence of the hysteresis effect. The transition processes and the stability of the possible states are shown to be described consistently by an analogy based on the potential energy of a particle on a surface. The necessity of more sophisticated experimental investigations is emphasized to verify the argument about the stability of shock reflections and proposed analogy. Received 17 March 1997 / Accepted 26 February 1998     

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A simple, robust, and accurate HLLC-type Riemann solver for the compressible Euler equations at various Mach numbers is built. To cure shock instability of the HLLC solver at strong shocks, a pressure-control technique, which plays a role in limiting the propagation of erroneous pressure perturbation, is proposed. With an all Mach correction method for the compressible Euler system, the proposed method is further extended to compute flow problems at low Mach numbers. The proposed all Mach HLLC-type scheme has been implemented and used to compute a variety of flow problems ranging from hypersonic compressible to low Mach incompressible flow regimes. Various numerical results demonstrate that the obtained all Mach HLLC-type scheme is both accurate and stable for all speed ranges.     

Self-similar hypervelocity shock interactions with oblique contact discontinuities

The two-dimensional inviscid refraction of a shock wave at an oblique contact discontinuity is self-similar; i.e. it depends only upon the variables , . We transform the compressible Euler equations into the self-similar () coordinates and solve the resulting boundary-value problem by an implicit equilibrium flux method. We present results for strong shock ( where M is the incident shock Mach number) interactions with an oblique contact discontinuity separating an inert gas from a gas which exhibits high-temperature gas chemistry effects. To model high-temperature effects we employ Lighthill's ideal dissociating gas (IDG) model. Comparison between the frozen and equilibrium limits, both of which are self-similar, indicate large changes in peak density and temperatures. Significant differences in the overall flow pattern between the frozen and equilibrium limits are observed for interfaces with low negative Atwood ratio and high positive Atwood ratio. Results from a local analysis are presented when the shock refraction is regular. The critical angle at which the transition from regular to irregular refraction occurs is slightly larger for the equilibrium chemistry case. Received 6 September 1996 / Accepted 20 May 1997     

Merging of two independent diffracting shock waves

A preliminary experimental and numerical investigation into the interaction between two independent shock waves emerging perpendicular to each other into a common space is presented. It is arranged that two shock tubes have a common diffracting edge, so that the two waves arrive at the edge simultaneously. The shock Mach number was 1.31. The merging three-dimensional diffracting shocks reflect regularly off each other, but as they become more curved due to diffraction the angle between them changes and Mach reflection develops. L-shaped vortices are shed at the two free edges of each tube exit. As they meet, they merge and interact in a complex manner with each other.     

气相爆轰波在障碍物上Mach反射的实验验证

本文公布了气相爆轰波沿收缩管道传播时发生Mach反射的实验证据。在爆轰波通过的管道中安装不同楔角的楔块,形成管道的收缩。爆轰波在通过楔块时会发生Mach反射。利用烟熏玻璃片记录到了爆轰波Mach反射时形成的三波点迹线及其两侧胞格尺寸和密度的变化。据我们掌握的资料,这是首次用胞格结构变化的记录证实,气相爆轰波与无化学反应的空气中的冲击波一样,在一定的入射条件下会发生Mach反射。这一实验结果可使我们更深入了解爆轰波的本质,也为数值模拟气相爆轰波在障碍物上Mach反射现象提供了可对比的依据。     

Shock wave structure for a fully ionized plasma

We study planar shock wave structure in a two-temperature model of a fully ionized plasma that includes electron heat conduction and energy exchange between electrons and ions. For steady flow in a reference frame moving with the shock, the model reduces to an autonomous system of ordinary differential equations which can be numerically integrated. A phase space analysis of the differential equations provides an additional insight into the structure of the solutions. For example, below a threshold Mach number, the model produces continuous solutions, while above another threshold Mach number, the solutions contain embedded hydrodynamic shocks. Between the threshold values, the appearance of embedded shocks depends on the electron diffusivity and the electron–ion coupling term. We also find that the ion temperature may achieve a maximum value between the upstream and downstream states and away from the embedded shock. We summarize the methodology for solving for two-temperature shocks and show results for several values of shock strength and plasma parameters in order to quantify the shock structure and explore the range of possible solutions. Such solutions may be used to verify hydrodynamic codes that use similar plasma physics models.