Nonstationary shock reflection over nonstraight surfaces: an approach with a method of multiple steps

Shock reflection phenomena over nonstraight surfaces have been investigated. The models used in this experiment are ordinary circular cylindrical concave and convex wedges and step-like wedges which simulate the former. The step-like wedges were used to investigate the process of reflected-wave formation over circular cylindrical wedges (method of multiple steps). The reflected-wave structure has been photographed with a schlieren apparatus. The formation of the reflected wave over circular cylindrical wedges is physically well understood by comparing it with shock reflection over step-like wedges. In particular, the reason why the reflected wave over a concave circular cylindrical wedge is very weak away from the reflection point is elucidated. Moreover, the structure and the formation mechanism of the so-called transitioned regular reflection (TRR) are illustrated in detail. As a by-product, based on acoustic theory, analytical formulae for the transition wedge angle are found. They are in good agreement with experiments. Received Received 28 February 1996 / Accepted 7 August 1996     

One case of the equilibrium of a system of radial cracks

The plane-elasticity problem of the equilibrium of a system of uniformly distributed cracks of equal length intersecting in a single point is considered. The system is located with concentrated forces applied to the tips of the wedges cut out by the cracks and acting along the bisectrices of the wedges. An analytical expression is found for the singularity coefficient of the stress field at the tip of the cracks.     

水陆两栖飞机典型横截面入水撞击实验研究

选取当今世界几种水陆两栖飞机典型横截面为研究对象,通过进行不同投放高度和不同质量的楔形体入水冲击实验,动态测量楔形体入水冲击过程中的压力并记录自由液面变化情况,研究了不同实验件的自由液面变化、冲击压力随时间变化及局部压力分布规律等。通过对比分析,发现带舭弯的弧形横截面型式有利于降低水陆两栖飞机在复杂海况下的着水冲击载荷,可作为水陆两栖飞机设计的参考线型。     

On the computation of the near-tip stress intensities for three-dimensional wedges via two-state M-integral

Singular stress fields around three-dimensional wedges are examined, and the near-tip intensity is calculated via the two-state M-integral with the aid of the domain integral representation. Two numerical examples demonstrate the effectiveness and accuracy of the present scheme for computing the stress intensities of singular stresses near the generic three-dimensional wedges.     

An unstructured-mesh-based finite element simulation of wave interactions with non-wall-sided bodies

An unstructured-mesh-based finite element method is employed to simulate two-dimensional nonlinear interactions between waves and non-wall-sided floating structures. The velocity potential theory is adopted and the potential is obtained at each time step through solving a matrix equation based on the Galerkin method. The boundary conditions on the free surface are satisfied in the Lagrangian form and the information is updated through the fourth-order Runge–Kutta method. Remeshing based on B-splines is applied regularly to avoid over-distorted elements, and smoothing based on a method using the energy of a curve defined through its nodes is applied to improve the stability of the results. Comparison is made with published results for transient wave motion in a tank to validate the present method. Extensive simulation is made for wedge-shaped bodies in vertical and horizontal motions, and comparison is made with the solution from second-order theory. Results are also provided for wedges in a tank, for wedges in large motion relative to water depth and for twin wedges.     

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.     

Numerical investigation of flow past a system of two sweptback compression wedges

Supersonic flow past a three-dimensional configuration consisting of two neighboring wedges with sweptback leading edges mounted on a preliminary compression surface is numerically investigated. The case of sweptback wedges is considered, when their beveled surfaces deflect the compressed flows to opposite directions. The calculations are carried out on the basis of the averaged Navier-Stokes equations, together with the SST k-? turbulence model, at the freestream Mach number M = 6. The results obtained are compared with the data for inviscid flow calculated using the Euler equations. The flow pattern features, due to the interaction in the plane of symmetry between the shocks formed by the wedges and the shock-induced three-dimensional quasiconical separations of the turbulent boundary layer on the preliminary compression surface along the swept leading edges, are established. Within these separation zones the flow is directed away from the plane of symmetry of the configuration and is characterized by considerably greater values of the transverse velocity component, as compared with the flow outside of the separation zone.     

复合材料尖劈和接头端部奇性场的反平面问题研究

提出了一个基于位移的分析尖劈端部奇性位移场和应力场反平面问题的非协调元特征法．该方法与过去原有求解裂纹尖端近似场的有限元特征法有几点不同：(1)导出虚功原理的出发点为二维扇区的散度原理;(2)有限元的单元形式为非协调元;(3)尖劈端部邻域内的位移场假定没有采用奇异变换技术．运用该方法给出了求解正交各向异性复合材料尖劈端部附近奇性应力指数、奇性位移和应力角分布函数的算例．计算结果表明,该方法较原来的有限元特征法所用的单元少而且精度高．     

Turbulent channel flow with 2D wedges of random height on one wall

Direct numerical simulations (DNS) of a turbulent channel flow with 2D wedges of random height on the bottom wall have been performed. In addition, two other simulations have been carried out to assess the effect of the geometry on the overlying flow. In the first simulation, the four smallest elements were removed while in the other, a uniform distribution of wedges with the same area was used. Two Reynolds numbers were studied, Re_b=2500 and Re_b=5000 which correspond in case of smooth walls to Re_τ=180 and 300, respectively. Roughness on the wall induces separated regions, the reattachment occurring on the walls of the wedges or on the bottom wall. The pressure gradients on the walls increase the ejections and inrushes towards the wall. As a consequence the flow is more isotropic. The mechanism inducing an improved isotropy has been explained in term of the spectra and budgets of Reynolds stress. The comparison of the 3 surfaces has shown that near the wall, the uniformly distributed roughness represents only a poor approximation of the surface with wedges of random height. The Reynolds stresses, pressure distribution and spectra on the modified wall agree well with those on the random surface. Energy spectra show the pitch to height ratio of the largest elements to be the more appropriate geometrical parameter to describe the geometry.     

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.     

STRESS SINGULARITY ANALYSIS OF MULTI-MATERIAL WEDGES UNDER ANTIPLANE DEFORMATION

With the help of the coordinate transformation technique, the symplectic dual solving system is developed for multi-material wedges under antiplane deformation. A virtue of present method is that the compatibility conditions at interfaces of a multi-material wedge are expressed directly by the dual variables, therefore the governing equation of eigenvalue can be derived easily even with the increase of the material number. Then, stress singularity on multi-material wedges under antiplane deformation is investigated, and some solutions can be presented to show the validity of the method. Simultaneously, an interesting phenomenon is found and proved strictly that one of the singularities of a special five-material wedge is independent of the crack direction.     

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.      

A Mathematical Analogy and a Unified Asymptotic Formulation for Singular Elastic and Electromagnetic Fields at Multimaterial Wedges

In the present contribution, the mathematical analogy existing between the singular stress field in elasticity due to antiplane loading and the singular electromagnetic fields in electromagnetism is derived with reference to the problem of isotropic multimaterial wedges. These configurations, where dissimilar sectors converge to the same vertex, are commonly observed in composite materials and may lead to singularities. The proposed analogy permits to extend several elastic solutions for the power of the stress-singularity already available in the elasticity literature to the analogous electromagnetic problems and viceversa. Finally, electromagnetic structures that cannot be treated according to the proposed analogy, such as those related to bi-isotropic multimaterial wedges, are discussed.     

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     

A crack emanating from the tip of bonded dissimilar materials

1.IntroductionBondedstructurescanbewidelyfoundindifferentareas,suchasweldedpressurevessels,reinforcedconcretemembers,groutingsoftfoundationandsolidrocketpropellants.etc.Thestudy'ofthesingularityofbondedstructuresisespeciallyimp6rtantnotonlyforsafedesignbutalsoforconstruction.DeinpseyandSinclairl61studiedthegeneraleaseofN-materialcompositewedges,andprovedthat'ingeneralthereexistsstresssingularitynearthetipofthewedges,andtheorderofthesingularitydependsontheelasticconstantsandthelocalgeometry.Fo…     

铁道车辆用新型减振材料的摩擦磨损行为研究

对铁道车辆摩擦减振系统所用斜楔和磨耗板新型材料进行了磨损试验研究,并分析了其摩擦磨损行为.结果表明,T10与ADI球铁、奥贝灰铸铁和高分子材料配副的耐磨性均优于45#钢与ADI球铁配副,磨耗板材料的相对耐磨性均优于斜楔,T10与高分子材料配副具有最佳的摩擦磨损性能.     

Anisotropic Elasticity and Multi-Material Singularities

Multi-material wedges associated with convergence of geometrical and material discontinuity lines generally show singular stress fields around the vertex of the wedge. In this paper, the eigenvalue problem for a multi-material wedge composed of several anisotropic elastic sectors is formulated in a completely generally manner, including the cases of degenerate and extra-degenerate material sectors, and various types of edge conditions for both open and closed wedges. General representation of the elasticity solution in a degenerate or extra-degenerate anisotropic sector requires higher-order eigenmodes (generalized eigenfunctions) in addition to zeroth-order eigenmodes. Such higher-order eigenmodes are obtained from appropriate analytical expressions of the zeroth-order eigenmode by using the derivative rule. The analysis is applied to one bisector wedge and one trisector wedge in a three-layer cracked composite model to obtain accurate elasticity solutions of the singular stress fields. These solutions were determined using the traction data generated on a circular collocation path by a conventional finite element analysis.     

楔形体入水时域解的复边界元数值分析

基于速度势理论,利用复数变量边界元法对二维楔形体常速入水冲击的时域解进行了数值研究。 以相似解作为数值计算的初始条件,采用时域解射流线性近似处理方法,利用复数变量边界元法进行求解,以 减少计算量和数值误差。深入讨论了扩展坐标系求时域解、射流处理、网格划分和网格更新等关键技术。最 后数值计算了不同斜升角楔形体入水时的自由液面隆起、射流飞溅和压力分布,经与相似解结果作比较,自由 液面隆起轮廓基本吻合,而压力分布更符合实际情况,从而证明了模型及分析方法的正确性。     

Interaction of intersecting shocks with a flat-plate boundary layer in the presence of an entropy layer

Gas flow and heat transfer on the surfaces of sharp and blunt plates is experimentally investigated in the presence of two forward-looking wedges at the Mach numbers M = 5, 6, and 8 and the Reynolds numbers up to Re_∞L = 27×10⁶. It is shown that the entropy layer generated by a small bluntness of the leading edge of the plate can considerably change the heat transfer, the gas pressure, and the friction in the zone of interference of the shock with the plate boundary layer. Under certain conditions a small plate bluntness can also lead to a qualitative change in the flow structure. The effect of constriction of the channel between the wedges on the interference flow is studied.     

Logarithmic singularity of an elastic composite wedge subjected to out-of-the-plane extensional strain

When an elastic composite wedge is not under a plane strain deformation, an out-of-the-plane extensional strain exists. The singularity analysis for the stresses at the apex of the composite wedge reduces to a system of non-homogeneous linear equations. When the composite wedge consists of two anisotropic elastic materials, it is shown that the stresses have the (ln r) term for all combinations of wedge angles with few exceptions. The same is true when the materials are isotropic except that the (ln r) term may appear in the form of r(ln r) in the displacements only. For these isotropic composite wedges therefore the stresses are bounded, though not continuous, at the apex. However, there are isotropic composite wedges for which the stress singularity is logarithmic. Conditions are given for isotropic composite wedges for which the stresses are (a) uniform, (b) non-uniform but bounded and (c) logarithmic. Unlike the r^−λ singularity, the existence of the (ln r) term does not depend on the complete boundary conditions.