The initial stage of dam-break flow

The liquid flow and the free surface shape during the initial stage of dam breaking are investigated. The method of matched asymptotic expansions is used to derive the leading-order uniform solution of the classical dam-break problem. The asymptotic analysis is performed with respect to a small parameter which characterizes the short duration of the stage under consideration. The second-order outer solution is obtained in the main flow region. This solution is not valid in a small vicinity of the intersection point between the initially vertical free surface and the horizontal rigid bottom. The dimension of this vicinity is estimated with the help of a local analysis of the outer solution close to the intersection point. Stretched local coordinates are used in this vicinity to resolve the flow singularity and to derive the leading-order inner solution, which describes the formation of the jet flow along the bottom. It is shown that the inner solution is self-similar and the corresponding boundary-value problem can be reduced to the well-known Cauchy–Poisson problem for water waves generated by a given pressure distribution along the free surface. An analysis of the inner solution reveals the complex shape of the jet head, which would be difficult to simulate numerically. The asymptotic solution obtained is expected to be helpful in the analysis of developed gravity-driven flows.     

Starting flow generated by the impulsive start of a floating wedge

The initial stage of the plane unsteady flow caused by the impulsive vertical motion of a wedge initially floating on an otherwise flat free surface is investigated with the help of a combination of numerical and asymptotic methods. The liquid is assumed ideal and incompressible and its flow potential. Compressible effects give a negligible contribution to the flow close to the entering body at the stage considered in the present paper. The vertical velocity of the body is constant after the impulsive start. The flow domain is divided into an outer region, where the first-order solution is given by the pressure-impulse theory, and inner regions close to the intersection points between the free surface and the moving body. The relative displacement of the body plays the role of a small parameter. The inner solution is matched with the outer one. The outer solution is given in quadratures but the inner solution, which is shown to be nonlinear and self-similar, can be found only numerically. With the aim of deriving the inner solution, the inner region is divided into three parts. In the far-field zone the solution is given in terms of its asymptotic behavior while, in the jet region, attached to the wedge, the flow is described by a second-order shallow-water approximation. In the intermediate region a boundary-element method is used, which is suitably coupled with the solutions in both the jet and the far-field regions through an iterative pseudo-time stepping procedure. The procedure is dependent on the deadrise angle of the wedge. If the angle is equal or smaller than π/4, eigensolutions appear in the far-field asymptotics and their amplitudes are recovered together with the solution. The approach is applied to different values of the wedge deadrise angle. The obtained results can be used to improve the prediction of the hydrodynamic loads acting on floating bodies, the velocity of which changes rapidly.     

Asymptotic estimates of hydrodynamic loads in the early stage of water entry of a circular disk

The hydrodynamic loads generated during the entry of a circular disk into deep water are evaluated with the help of the method of matched asymptotic expansions. It is assumed that the liquid is initially at rest and the disk is floating on the still liquid surface. Then the disk suddenly starts its downward motion. The study is carried out under the assumption of an ideal and incompressible liquid. Attention is focused on the initial stage of the entry process. The solution is sought in the form of an asymptotic expansion of the velocity potential with the non-dimensional displacement of the disk being a small parameter of the problem. Gravity and surface-tension effects are shown to be of minor significance. Owing to the flow singularity at the edge of the disk, an inner problem is formulated and its solution is matched with the second-order outer velocity potential to achieve a uniformly valid solution. It is shown that the initial asymptotics of the hydrodynamic loads involves terms with ${h^{-\frac{1}{3}}}$ and log h where h(t) is the non-dimensional displacement of the disk. Both terms are unbounded in the limit of small penetration depth of the disk. The theoretical estimates are validated versus fully nonlinear numerical simulations of the problem during the later stage of the process. It is shown that the derived asymptotic estimates remain accurate, even for moderate displacements of the disk. The relative difference between the theoretical estimate of the hydrodynamic force and its numerical prediction is less than 5% when the penetration depth is smaller than ${\frac{1}{20}}$ of the disk radius. A way to use the theoretical estimates for practical applications is proposed and comparisons with experimental data available in the literature are also presented.     

Shallow-Water Impact Problems

Impact by a box-like structure onto shallow water is analysed with the help of asymptotic methods. The analysis is based on both the asymptotic approach by Korobkin [1], which was derived originally for blunt-body impact, and the experimental results by Bukreev [2]. The flow region is divided into six parts: the region beneath the entering body, the region close to the bottom edge, the region of inertial flow of the liquid, the jet root, the splash jet and outer region. The flows inside each of the subdomains have their own peculiarities and are analysed separately. The matching conditions make it possible to obtain a uniformly valid asymptotic solution of the impact problem. The main attention is paid to the flow patterns and pressure distributions. It was found that the pressure inside the jet root can be comparable with the pressure beneath the entering body and can even exceed it. The effects of the shape of the body bottom and of the body flexibility on the liquid flow and the pressure distribution are investigated.     

Free convection on a heated vertical plate: The solution for small Prandtl number

The solution of the equations for the free-convection boundary-layer flow on a vertical plate with a prescribed power-law heating is considered for small values of the Prandtl number σ. It is shown that the boundary layer divides up into two regions. There is a thin inner region, of thickness O{ie273-1}, in which, to leading order, the temperature is a constant, but which is not determined from the inner solution. This gives rise to a large temperature on the plate of O{ie273-2}. This inner region drives a flow in a much thicker inviscid outer region, of thickness of O{ie273-3}. At the outer edge of this outer region the ambient conditions are attained, and it is the matching between the two regions which determines the plate temperature.     

An experimental investigation of modes of flow under conditions of evaporation of liquid on a vertical heating surface

An experimental investigation is performed of the effect of temperature head on the flow of evaporating film of liquid, defined by the wetting line or by ribs, on a vertical heating surface. The experiments are performed under conditions of evaporation of R11 Freon in a medium of own vapor on a vertical copper plate, including the presence of ribbing. The visualization of flow is performed. Analysis is made of the effect of the evaporation intensity in the neighborhood of liquid-vapor-wall contact line on the conditions of film discontinuity and on the pattern of resultant streamer flow. It is demonstrated that, rather than spreading, the liquid in the case of streamer flow on the heating surface contracts downstream even for a close-to-zero equilibrium wetting angle. This is due to intense evaporation of liquid in the region of liquid-vapor-wall contact line, where the liquid film exhibits a minimal thickness, to the variation of curvature of the interface in this region, and to the emergence of thermal contact angle. The dependence of thermal contact angle on temperature head is determined. Dynamic measurements are performed of the local thickness of flowing films of liquid using a capacitance meter, and spectral analysis is performed of waves which arise because of instability of film flow on the evaporating film surface.     

分析金属装甲弹道极限的两阶段模型

基于大量弹道试验分析,考虑靶板背面自由边界的影响,提出一个分析刚性尖头弹垂直撞击中等厚度理想弹塑性材料靶板弹道极限的两阶段工程模型。由圆柱形空腔膨胀理论和功能原理导出第一阶段延性扩孔耗能表达式,按薄靶板最小穿透能量的简化分析模型计算第二阶段耗能,由两阶段总的耗能最小确定第一阶段的侵彻深度,从而得到最小穿透能量的解析解。经与金属装甲弹道试验比较,表明两阶段工程模型计算结果与试验吻合较好,比现有单一延性扩孔模型精度高。     

考虑裂纹效应的弹性板振动分析模型

针对含裂纹板的动力学问题,提出了一种耦合裂纹效应的弹性板动力学建模方法。该方法依据变形等效原则用虚拟外部载荷代替裂纹作用,并通过力学平衡原理建立了耦合裂纹项的弹性板运动方程,且基于Rice和Levy应力关系式推导出裂纹项表达式;在此基础上,结合Galerkin法和Berger经验,把含裂纹弹性板振动系统简化成一单自由度非线性振动模型进行动力学特性分析。通过算例探讨了裂纹尺度、阻尼以及激励力位置对弹性板振动特性的影响。结论表明,裂纹尺度和板尺寸对振动非线性作用明显,动应力幅值受阻尼与激励力位置的控制。     

The motion of the free-surface separation point during the initial stage of horizontal impulsive displacement of a floating circular cylinder

The initial stage of unsteady two-dimensional flow caused by the impulsive horizontal motion of a floating circular cylinder is investigated by using methods of asymptotic analysis. Initially the cylinder is half-submerged and the liquid free surface is flat and horizontal. The liquid is of infinite depth. Then the cylinder suddenly starts to move horizontally with a speed given as a function of time. The liquid is assumed ideal and incompressible and its flow potential. The initial flow is provided by pressure-impulse theory, with an account of a possible separation of the liquid free surface from the trailing face of the rigid surface of the cylinder. The initial position of the separation point on the surface of the moving body is determined by using the condition that the fluid velocity is finite at the separation point (Kutta condition). The motion of the separation point along the surface of the cylinder is numerically determined with the help of the second-order outer solution of the problem and the Kutta condition at the moving separation point. It is shown that the length of the wetted part of the cylinder surface increases at a rate proportional to the speed of the cylinder. The speed of the separation point depends on the Froude number. The pressure on the wetted part of the cylinder can be below the atmospheric pressure for relatively high speed.     

Fundamental solution of a circular rigid punch problem for a half plane

A fundamental solution (a Green's function) of a circular rigid punch problem is derived. The punch on a half plane contacts smoothly at both ends of the contact region and a concentrated force or a point dislocation apply at an arbitrary point. Two cases where the punch is kept vertically and the punch is inclined are considered. Complex stress functions and a mapping function are used and a closed form solution is derived. Some results of stress distribution, contact length and resultant moment on the contact region are shown in figures.     

The emptying of channels and reservoirs accompanied by boiling

The emptying of channels and reservoirs filled with boiling up or gas-saturated liquid is theoretically studied within barotropic equations of state. It is assumed that phase transitions occur in the equilibrium mode. Analytically and numerically obtained solutions are used to analyze the effect of initial temperature in the reservoir in the case of boiling up liquid, as well as of the Ostwald absorption coefficient for gas-saturated liquid, on the parameters of flow at the outlet from channels and reservoirs. For the final stage of emptying of channels, where the inertial force is unimportant, a self-similar solution is constructed with due regard for the inversion of flow from bubbly-foamy to vapor-droplet. The effect of inversion on the intensity of emptying is investigated.     

Interfacial structure of steel–aluminum bonding plate under non–equilibrium rapid solidification

A steel–aluminum solid–liquid bonding plate is prepared using a non–equilibrium rapid solidification method (including four kinds of processes such as roughening the steel plate surface, immersing influx at the steel plate surface, short–time bonding and rapid solidification). The interfacial structure of the bonding plate is investigated by means of electron probe microanalysis and X–ray diffraction. The results show that the interfacial structure of the bondingplate under non–equilibrium rapid solidiication is quite different from that of the bonding plate in conventional steel–aluminum solid–liquid bonding, i.e. the interface of the bonding plate under non-equilibrium rapid solidification ismade up of an aluminum-rich region (in the form of a group of Fe₄Al₁₃ teeth that grow from the contact surface to the steel side) at the bulge of steel plate surface and an aluminum–poor region (in the form of Fe–Al solid solution of which the Al content is less than 3.5 wt%) at the concave surface of the steel plate alternately.     

Structural intensity study of plates under low-velocity impact

The transmissions of transient energy flow and dynamic transient response of plate structures under low-velocity impact are presented. The structural intensity approach is used to study the transient dynamic characteristics of plate structures under low-velocity impact. In the dynamic impact response analysis, nine-node degenerated shell elements with assumed shear and membrane strain fields are adopted to model the target and impactor. The dynamic contact-impact algorithm and the governing equations for both the target and impactor are derived based on the updated Lagrangian approach. Explicit integration algorithm has been adopted in the time integration process. The novel structural intensity streamline representation is introduced to interpret energy flow paths for transient dynamic response of plates under low-velocity impact. The effects of plates with and without structural damping on the energy flow and energy path are discussed. Numerical results, including contact force, deflection histories and transient energy flow vectors as well as structural intensity streamlines, show that the present method and representation are an efficient approach for exploring dynamic response for plate structures subjected to low-velocity impact.     

Shear flow over a particulate or fibrous plate

Simple shear flow over a porous plate consisting of a planar array of particles is studied as a model of flow over a membrane. The main objective is to compute the slip velocity defined with reference to the velocity profile far above the plate, and the drift velocity induced by the shear flow underneath the plate. The difference between these two velocities is shown to be proportional to the thickness of the plate. When the geometry of the particle array is anisotropic, the directions of the slip and drift velocity are generally different from the direction of the overpassing shear flow. An integral formulation is developed to describe flow over a plate consisting of a periodic lattice of particles with arbitrary shape, and integral representations for the velocity and pressure are developed in terms of the doubly-periodic Green's function of three-dimensional Stokes flow. Based on the integral representation, asymptotic expressions for the slip and drift velocity are derived to describe the limit where the particle size is small compared to the inter-particle separation, and numerical results are presented for spherical and spheroidal particles of arbitrary size. The asymptotic results are found to be accurate over an extended range of particle sizes. To study the limit of small plate porosity, the available solution for shear flow over a plane wall with a circular orifice is used to describe flow over a plate with a homogeneous distribution of circular perforations, and expressions for the slip and drift velocity are derived. Corresponding results are presented for axial and transverse shear now over a periodic array of cylinders arranged distributed in a plane. Streamline pattern illustrations confirm that a negative drift velocity is due to the onset of eddies between closely-spaced particles.     

Pressure drop and flashing mechanisms in refrigerant expansion devices

This paper examines a novel pressure drop mechanism as well as flow choking conditions that determine mass flow rate in refrigerant expansion devices. For this study, an ideal situation is considered where an expansion device such as a short tube orifice or a thermostatic expansion valve is modeled as an ideal isentropic nozzle. In addition, a liquid with a certain initial degree of superheat is first expanded in the converging nozzle down to the exit section without any phase transition. At the exit section where the metastable liquid jet flashes to produce a complex axisymmetric two-phase flow, a shock wave may terminate the overall expansion process. The model presented here is based on experimental observations in short nozzles, where the metastable liquid in the central core undergoes a sudden phase transition in the interfacial region, giving rise to a high-speed two-phase flow. A simple 1-D analysis of the radial evaporation wave based on the theory of discontinuities from gas dynamics leads to the Chapman–Jouguet (C-J) solution. Flow choking issues are examined and numerical examples are presented for three common refrigerants: R134a, R-22, and R-600a. Results suggest that the evaporation wave may be the flow controlling mechanism in these devices.     

低速大质量球头弹冲击下薄板穿甲破坏机理数值分析

为探讨薄板穿甲破坏机理,采用动态非线性有限元,结合弹道冲击试验,分析了薄板在低速大质量球头弹体冲击下的穿甲破坏过程及其变形机理,薄板的变形吸能规律及破坏模式,并将有限元分析结果与实验结果进行了比较,有限元分析结果与实验结果吻合良好.结果表明:薄板穿甲破坏过程大致可分为三个阶段,即隆起变形阶段,碟形变形阶段和弹体贯穿阶段.其中薄板的隆起变形主要由剪力和弯矩引起的;隆起变形结束后,碟形变形区膜力逐渐增大,超过动态屈服极限,并随冲击速度的减小而增大,到弹道极限附近成为最主要的广义应力;低速冲击下碟型变形是靶板主要的变形吸能方式.大质量低速球头弹冲击下薄板的穿甲破坏模式可归纳为三种:隆起-碟形变形,隆起-碟形变形-贯穿破坏和隆起-贯穿破坏.     

基于FEPG有限元分析系统的树脂充模过程模拟

为优化复杂预成型体结构的液体成型工艺,基于有限元法/生死节点法模拟了复合材料液体模塑成型过程树脂流动,并针对典型矩形平板、圆板结构、I型加筋壁板充模过程进行了仿真与验证。结果表明:典型矩形平板和圆板结构的充模过程模拟结果与理论解一致性较好,验证了生死节点法跟踪树脂流动前锋的有效性。含有方腔的变厚度圆柱体和正方体三维实体结构的充模过程模拟验证了有限元方法对三维结构的适用性。基于有限元法/生死节点法的液体充模过程模拟方法对于复杂求解区域具有更好适应性,可用于复杂实体结构的液体模塑成型工艺过程树脂流动规律预测、指导模具设计及工艺优化。      

横向常磁场中铁磁圆板的主共振特性与静载效应

针对横向常磁场中铁磁圆板的主共振问题进行研究.基于电磁基本理论,得到薄板在常磁场中所受的磁体力和洛伦兹力,应用哈密顿变分原理,推导出磁场中铁磁圆板磁弹性耦合横向振动微分方程.常磁场中铁磁圆板受到的磁体力为静载荷,根据伽辽金法得到周边夹支边界条件下铁磁圆板在静载荷作用下的初挠度,进一步应用多尺度法对周期载荷作用下的非线性...     

Mechanics of powders in the initial rearrangement stage of liquid-phase sintering

The mechanical response of powders in the initial rearrangement stage of liquid-phase sintering (LPS), where capillary force is the driving force for densification, is discussed in this paper. The model which is described in detail elsewhere [Xu, K., Mehrabadi, M.M., 1997, A micromechanical model for the initial rearrangement stage of liquid-phase sintering, Mech. Mater. 25, 137–157.] can be used to determine the dependence of the overall volume change on such factors as local liquid volume, uniformity of liquid distribution, contact angle, initial particle distance, initial confining pressure, particle size and viscosity. Here, the discussion is limited to the influence of macroscopic liquid volume ratio on the volume change behavior of the powder system. The results obtained are in qualitative agreement with the observation.     

The impact of a rigid sphere with an elastic layer of finite thickness

Summary The problem of the impact of a rigid sphere with an elastic isotropic layer is considered in the initial stage of dynamic interaction. The initial stage is characterized by the fact that the velocity of the displacement of the intersection points of the sphere with the upper boundary of the layer is larger than the velocity of longitudinal waves, hence the free surface normal to the contact domain with the body is undisturbed. The method of successive approximations as well as the ray method, according to which the solution behind the fronts of incident and reflected waves is constructed in terms of power series (ray expansions), are used as methods of solution. In the problem under consideration, we used one-term ray expansions whereby the main characteristics of the shock interaction have been obtained, and the possibility of localized damage of the material of the layer at the points lying along the central ray has been examined.