Numerical investigation on three-dimensional shock wave reflection over two perpendicularly intersecting wedges

The three-dimensional (3D) shock wave reflections over two perpendicularly intersecting wedges are numerically studied in this paper, using the finite volume method which is based on the MUSCL-Hancock interpolation technique and self-adaptive unstructured mesh. Two kinds of 3D Mach stem structures are demonstrated by the numerical simulations for different shock Mach numbers and wedge angles. A four-shock or three-shock wave configuration appears in the vicinity of the corner of the wedges.     

非定常激波三维双楔面反射的数值研究

采用基于MUSCL-Hancock插值的有限体积方法, 在非结构自适应网格上求解三维Euler方程, 研究了非定常激波在三维垂直双楔面上的反射现象. 研究结果表明, 由于三维效应的影响, 通过二维非定常激波反射理论预测的三维马赫反射区域范围存在着一定的局限, 在该区域范围内出现了一种非典型的三维突起结构, 即第二类三维马赫干. 另外, 对于不同的激波马赫数和楔面倾角组合, 非定常激波在三维双楔面上会形成具有四波结构的三维马赫反射或具有三波结构的三维规则反射.      

Numerical study of the oscillations induced by shock/shock interaction in hypersonic double-wedge flows

In this paper, the shock pattern oscillations induced by shock/shock interactions over double-wedge geometries in hypersonic flows were studied numerically by solving 2D inviscid Euler equations for a multi-species system. Laminar viscous effects were considered in some cases. Temperature-dependent thermodynamic properties were employed in the state and energy equations for consideration of the distinct change of the thermodynamic state. It was shown that the oscillation results in high-frequency fluctuations of heating and pressure loads over wedge surfaces. In a case with a relatively lower free-stream Mach number, the shock/shock interaction structure maintains a seven-shock configuration during the entire oscillation process. On the other hand, the oscillation is accompanied by a transition between a six-shock configuration (regular interaction) and a seven-shock configuration (Mach interaction) in a case with a higher free-stream Mach number. Numerical results also indicate that the critical wedge angle for the transition from a steady to an oscillation solution is higher compared to the corresponding value in earlier numerical research in which the perfect diatomic gas model was used.      

Three-dimensional shock wave reflection over a corner of two intersecting wedges

This paper presents an experimental and numerical investigation of three-dimensional shock wave reflections over a corner of two wedges intersecting perpendicularly in a shock tube. Experiments were conducted in a diaphragmless shock tube equipped with double-exposure diffuse holographic interferometry in which the time interval between the first and second exposure was set to be . This arrangement clearly visualized complex configurations of three-dimensional shock wave reflections. A numerical study was also carried out for interpreting these holographic interferometric observations by using the Weighted Average Flux (WAF) method to solve the three-dimensional unsteady compressible Euler equations. It was found that along the line of the intersection of these two wedges, two Mach stems intersected each other resulting in the formation of a Mach stem which leaned forward. Received 30 June 1996 / Accepted 6 October 1996     

The reflection of a shock wave over a cone

An investigation was made of the reflection of planar shock waves from cones. 86 cones, the half apex angle of which varied from 10° to 52° at every 0.5°, were installed in a 60 mm×150 mm diaphragmless shock tube equipped with holographic interferometry. The diaphragmless shock tube had a high degree of reproducibility with which the scatter of shock wave Mach number was within ±0.25% for shock wave Mach number ranging from 1.16 to approximately 2.0. The reflection of shock waves over cones was visualized using double exposure holographic interferometry. Whitham's geometrical shock wave dynamics was used to analyse the motion of Mach stems over cones. It is found that for relatively smaller apex angles of cones trajectory angles of resulting irregular reflections coincide with the so-called glancing incidence angles and their Mach stems appear to be continuously curved from its intersection point with the incident shock wave, which shows the chractericstic of von Neumann reflection. The domain of the existence of the von Neumann reflection was analytically obtained and was found to be broadened much more widely than that of two-dimensional reflections of shock waves over wedges.     

Investigation of the hysteresis phenomena in steady shock reflection using kinetic and continuum methods

The problem of transition of planar shock waves over straight wedges in steady flows from regular to Mach reflection and back was numerically studied by the DSMC method for solving the Boltzmann equation and finite difference method with FCT algorithm for solving the Euler equations. It is shown that the transition from regular to Mach reflection takes place in accordance with detachment criterion while the opposite transition occurs at smaller angles. The hysteresis effect was observed at increasing and decreasing shock wave angle. Received September 1, 1995 / Accepted November 20, 1995     

Mach stem hysteresis: Experiments addressing a novel explanation of clumpy astrophysical jet emission

Recent time-series observations of shock waves in stellar jets taken with the Hubble Space Telescope reveal localized bright knots that persist over nearly 15 years. While some of these features represent shock fronts caused by variable velocities in the flow, others appear at the intersection points between distinct bow shocks. Theoretically, when the angle between two intersecting shocks exceeds a certain critical value, a third shock (Mach stem) should form. Because Mach stems form perpendicular to the direction of flow, incoming particles encounter a normal shock instead of an oblique one, which results in brighter emission at this location. To study this phenomenon in a controlled laboratory setting, we have carried out experiments on the Omega laser aimed at understanding the formation, growth, and destruction of Mach stems in the warm dense plasma regime. Our experimental results indicate how the growth rate depends upon included angle, and numerical simulations indicate that it may be possible to stabilize an already-formed Mach stem below the critical angle when certain conditions are satisfied.     

DIAMOND PORT JET INTERACTION WITH SUPERSONIC FLOW

Interaction flow field of the sonic air jet through diamond shaped orifices at different incidence angles （10 degrees, 27.5 degrees, 45 degrees and 90 degrees） and total pressures （0.10 MPa and 0. 46 MPa） with a Mach 5.0 freestream was studied experimentally. A 90 degrees circular injector was examined for comparison. Crosssection Mach number contours were acquired by a Pitot-cone five-hole pressure probe. The results indicate that the low Mach semicircular region close to the wall is the wake region. The boundary layer thinning is in the areas adjacent to the wake. For the detached case, the interaction shock extends further into the freestream, and the shock shape has more curvature, also the low-Mach upwash region is larger. The vortices of the plume and the height of the jet interaction shock increase with increasing incidence angle and jet pressure. 90 degrees diamond and circular injector have stronger plume vorticity, and for the circular injector low-Mach region is smaller than that for the diamond injector. Tapered ramp increases the plume vorticity, and the double ramp reduces the level of vorticity. The three-dimensional interaction shock shape was modeled from the surface shock shape, the center plane shock shape, and crosssectional shock shape. The shock total pressure was estimated with the normal component of the Mach number using normal shock theory. The shock induced total pressure losses decrease with decreasing jet incidence angle and injection pressure, where the largest losses are incurred by the 90 degrees, circular injector.     

Three-dimensional effects on regular reflection in steady supersonic flows

The reflection of shock waves between two symmetrical wedges is investigated for the case of three-dimensional flows. Oblique shadowgraphs at various optical angles of yaw and pitch were used to examine the nature of fully three-dimensional flows, with wedge aspect ratios as low as 0.25 being considered. These images were used to construct surface models of the overall flow field for various reflection patterns and aspect ratios, which provides a visual indication of the flow field shape. For a Mach number of 3.1, and suitable wedge angles, the flow field with regular reflection on the tunnel centreline and Mach reflection further out is examined. The point of transition from regular reflection to the peripheral Mach surfaces is identified for various wedge angles and aspect ratios. It is shown that the transition points move outwards from the central plane as the aspect ratio decreases. This shows that three-dimensional flows favor regular reflection, because of the increasing curvature of the incident shock as the wedge becomes narrower, causing a decrease in the local angle of incidence. The height of the Mach stem is shown to be highly dependent on the geometry of the test wedge models. The Mach stem height decreases with aspect ratio due to the three-dimensional relieving effect, where the increase in lateral flow relieves the pressure over the surfaces of the wedges. Experimental evidence of the existence of the strong oblique shock solution in steady flows is presented.Received: 7 July 2003, Revised: 20 October 2003, Accepted: 6 November 2003, Published online: 10 February 2004PACS: 47.40.Nm Correspondence to: B.W. Skews     

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。     

Collective Bow Shock Ahead of a Transverse System of Spheres in a Supersonic Flow Behind a Moving Shock Wave

The results of investigating the dynamics and physical conditions of formation of a collective bow shock ahead of a system of spheres with the line of centers normal to the supersonic flow behind a traveling shock wave are presented. Two types of shock-wave patterns that necessarily precede the formation of the collective shock wave and correspond to regular and Mach interaction of the bow shocks were detected experimentally. On the basis of a local gasdynamic-discontinuity interference theory, quantitative criteria of the existence of these regimes and of the formation of a common shock wave are determined. These criteria are confirmed in a series of experiments for the transitional regimes.     

A shock tube research facility for high-resolution measurements of compressible turbulence

A new shock tube facility with a 30.5 cm (1 ft) inside diameter is currently in operation that allows for high-spatial-resolution measurements of compressible turbulence. Small scales of turbulence behave very differently from large scales when they interact with shock or expansion waves. Highly resolved measurements can provide new information on the interaction at small scales. Another notable characteristic of the present facility is the ability to control the flow velocity behind the reflected shock through the porosity of the reflecting wall. Tests showed good flow quality with sufficiently long observation times. Measurements of piecewise average skin friction over short segments of the tube indicated strong viscous effects very close to the diaphragm where the shock is developing. The skin friction and the shock propagation speed virtually remained constant inside the working section of the shock tube in all investigated flow cases, even in low Mach number cases where viscous effects are stronger. The experimental results are compared with numerical simulations, including the effects of the reflecting porous wall and viscous effects.     

Effect of Partial Closure of the Channel on the Pressure Pulse in a Shock Wave Emerging from a Duct

The temporal-spatial development of the flow pattern behind a shock wave emerging from open-ended and half-closed ducts at M₀=1.15 to 3.0 Mach number is investigated both experimentally and numerically and the action of the diffracted wave on a barrier placed at different distances from the duct exit is studied. Flow toeplerograms are obtained and the pressure on the barrier is measured. The distinctive features of the interaction between the shock wave and a barrier mounted perpendicular to the duct axis are established. It is found that partial closing of the duct results in a decrease in the barrier pressure in the case of a strong shock (M₀ > 2.2) and leads to a pressure decrease when a weak shock is diffracted (M₀=1.1 to 1.7). A dependence characterizing the dynamic action of the shock wave on the barrier and specifying the threshold value of a combination of the shock Mach number and the distance from the barrier determining whether the pressure pulse on the barrier increases or decreases, is obtained.     

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.     

Near field shock structure of dual co-axial jets

Experimental results on the shock structure of dual co-axial jets are presented. The effects of the geometric parameters of the inner nozzle, jet static pressure ratio (ratio of the exit plane static pressures of the inner and outer nozzles) and the ratio of outer to inner nozzle throat area on the shock structure were studied. A superimposed outer and inner jet structure was observed in the schlieren photographs. The inner flow is compressed by the outer flow resulting in the formation of a Mach disc and an exit shock. A parameter incorporating the effect of Mach number of the inner nozzle and jet static pressure ratio was found to correlate the observations regarding the Mach disc location.     

可压缩流向涡与激波轴对称干扰的数值模拟

用ＮＳ方程数值模拟了可压缩流向涡和激波轴对称相互作用现象．数值模拟包括定常和非定常两种情况,计算结果分别与相应的实验进行了比较．结果表明数值模拟成功地捕捉到了激波和旋涡相互作用过程中发生的激波波面变形,激波振荡,涡核变大以及激波波后出现驻点、回流区等流场特征．提出了判断流向涡与运动激波相互作用中旋涡破碎的准则     

Shock wave diffraction on multi-facetted and curved walls

The two-dimensional diffraction of a shock wave over a wall made up of a series of plane and/or curved sections is considered. The analysis is based on the theory presented by, for the interaction of an originally plane shock wave with a corner. A method is presented by which the shock profile may be determined for a wall of any shape and for any incident Mach number, in regions where the characteristics form a simple wave. Comparisons are made between experimental measurements and theoretical predictions for convex walls consisting of a number of facets, and for circular arcs, for a range of incident shock wave Mach numbers. It is shown that the theory gives a satisfactory prediction of the wave shape, which improves as the Mach number increases. Modifications in the flow field behind the shock, compared to that for a simple corner made up of two plane walls is discussed, particularly relating to flow separation. For circular arc concave walls a inverse Mach reflection results experimentally, leading to regular reflection, for which the theory is of no use. PACS 47.40.Nm     

On flows behind shock waves reflected from a solid wall

The flow fields associated with the interaction of a normal shock wave with a plane wall kept at a constant temperature were studied based on kinetic theory which can describe appropriately the shock structure and its reflection process. With the use of a difference scheme, the time developments of the distributions of the fluid dynamic quantities (velocity, temperature, pressure and number density of the gas) were obtained numerically from the BGK model of the Boltzmann equation subject to the condition of diffusive-reflection at the wall for several cases of incident Mach number:M ₁=1.2, 1.5, 2.0, 3.0, 4.0, 5.0 and 6.0. The reflection process of the shocks is shown explicitly together with the resulting formation of the flow fields as time goes on. The nonzero uniform velocity toward the wall occurring between the viscous boundary layer and the reflected shock wave is found to be fairly large, the magnitude of which is of the order of several percent of the velocity induced behind the incident shock, decreasing as the incident Mach number increases. It is also seen that a region of positive velocity (away from the wall) within the viscous boundary layer manifests itself in the immediate vicinity of the wall, which is distinct for larger incident Mach numbers. Some of the calculated density profiles are compared with available experimental data and also with numerical results based on the Navier-Stokes equations. The agreement between the three results is fairly good except in the region close to the wall, where the difference in the conditions of these studies and the inappropriateness of the Navier-Stokes equations manifest themselves greatly in the gas behavior.This article was processed using Springer-Verlag TEX Shock Waves macro package 1990.     

气相爆轰波正反射激波加速研究

实验采用压力传感器测量了指定点压力时间曲线。数值模拟基于二维反应欧拉方程和基元反应模型,采用二阶附加半隐的龙格-库塔法和5阶WENO格式分别离散时间和空间导数项,获得了指定点数值压力时间曲线。理论分析基于爆轰理论和激波动力学,分析了气相爆轰波反射过程所涉及的复杂波系演变并获得了反射激波速度。结果表明:本文数值模拟和理论计算定性上重复并解释了实验现象。气相爆轰波在右壁面反射后,右行稀疏波加速反射激波。其加速原因是:尽管激波波前声速减小,但激波马赫数增大,波前气流速度减小。在低初压下,可能还由于爆轰波后未反应或部分反应气体的作用,导致反射激波加速幅度比高初压下大。     

准定常强激波反射马赫杆突出变形准则的探讨

分析了滑移线延长线与楔面交点附近的流动特点,研究了准定常强激波反射中马赫杆的变形,建立了马赫杆突出变形消失的过渡准则,并用激波极曲线方法进行了求解。对马赫杆的变形过程进行了描述,研究了比热比、马赫数的变化对马赫杆突出变形消失条件的影响,并对突出变形消失区域与终点双马赫反射区域进行了比较。结果表明:马赫杆突出变形的消失是低比热比介质中出现的一种激波反射现象。马赫杆突出变形的消失,导致出现一种新的无射流、直马赫杆的双马赫反射结构。