A low‐dimensional spectral approach for transient axisymmetric free‐surface flow inside thin cavities of arbitrary shape

A low‐dimensional spectral method is used to solve the transient axisymmetric free surface flow inside thin cavities of arbitrary shape. The flow field is obtained on the basis of the lubrication equations, which are expanded in terms of orthonormal functions over the cavity gap. The formulation accounts for nonlinearities stemming from inertia and front location. The work is of close relevance to the filling stage during die casting, and injection molding, or the flow inside annular (extrusion) dies. Both flows under an imposed flow rate, and an imposed pressure at the cavity entrance are examined. The influence of inertia, aspect ratio, gravity, and wall geometry on the evolution of the front, flow rate, and pressure is assessed particularly in the early stage of flow, when a temporal behavior of the ‘boundary‐layer’ type develops. The multiple‐scale method is applied to obtain an approximate solution at small Reynolds number, Re. Comparison with the exact (numerical) solution indicates a wide range of validity for the multiple‐scale approach, including the moderately small Re range. Copyright © 2002 John Wiley & Sons, Ltd.     

超疏水小球低速入水空泡研究

物体入水问题是一类复杂的流固耦合问题,具有广泛的工程应用背景.物体在跨越自由液面入水的过程中,在一定的条件下,会向水中卷入空气形成空泡,空泡的运动还可能形成指向物体的射流,从而对物体的受力及其运动过程产生影响.超疏水表面能够在物体入水过程中形成多尺度流固耦合作用,进而影响物体的运动和宏观流动现象.而对于小尺度的小球低速入水问题,表面和界面力往往起主导作用.为了在更广的参数空间获得超疏水小球入水空泡类型和小球的运动特性,采用高速摄影实验方法,研究了半径0.175$\sim$10mm的超疏水小球低速入水及空泡动力学行为,获得了小球漂浮振荡、准静态空泡、浅闭合空泡、深闭合空泡和表面闭合空泡5种类型的动力学行为,探讨了这些运动行为与韦伯数We}和邦德数Bo之间的关系,并推导了小球漂浮振荡与下沉现象的无量纲关系.研究结果表明:超疏水小球的入水及空泡动力学行为主要与韦伯数We和邦德数Bo有关.在邦德数Bo $<$ $O$ (10$^{-1})$范围内,表面张力对流动的影响显著,随着韦伯数We}的增大,小球入水及空泡动力学行为依次经历漂浮振荡、准静态闭合、浅闭合、深闭合和表面闭合;在邦德数$O$ (10$^{-1})$<$ Bo} $<$O(1)$范围内,漂浮振荡现象不再发生;当邦德数$Bo>O(1)$后,浅闭合现象也不再发生;小球漂浮振荡与下沉现象的临界关系可以用相似律关系描述.      

超声速燃烧火焰稳定凹腔质量交换特性的数值研究

对超声速冷流条件下用于超燃冲压发动机的凹腔火焰稳定器的质量交换特性进行研 究. 采用混合RANS/LES方法对非定常流场进行数值模拟，考虑了凹腔的长深比和后缘角度两 个关键参数. 计算得到了凹腔剪切层拟序结构的演化过程. 对凹腔压力振荡历程进行幅频分 析，所得到的频率和理论分析结果及一些计算结果十分吻合. 结果表明，凹腔的长深比和后 缘倾角对凹腔质量交换过程都有较大的影响. 凹腔驻留时间随着长深比的增加而增加. 随着 后缘倾角减小，长深比较小的凹腔的驻留时间增加，长深比较大的凹腔则完全相反. 该计算 结果为凹腔设计提供了新认识.     

N表面张力对近固壁二空化泡影响的数值研究

在忽略浮力下，用边界积分方法数值模拟了表面张力对固壁之上且靠近固壁的二轴对称空化泡生长和溃灭的影响，发现在下空泡最大等效半径为上空泡一半情形，若固壁对下空泡的Bjerknes力大于上空泡对下空泡的Bjerknes力，则表面张力的作用将使下空泡溃灭加速，使其向下的液体射流变强变宽；若固壁对下空泡的Bjerknes力小于上空泡对下空泡的Bjerknes力，则表面张力的作用将使下空泡溃灭变慢，使其向上射流变弱变细长；若这两个Bjerknes力近于相等，则表面张力将会对下空泡溃灭有重大作用，如改变下空泡射流的方向甚至形式(如由环状变向下或由向上变环状)，当上空泡等于或小于下空泡时，表面张力将不会对这两个空泡的行为产生显著影响，定性地分析了表面张力作用的机理。     

钟摆状态下湿颗粒坍塌流动行为及其动力相似性

基于建立的湿颗粒离散动力学模型,本文系统研究了钟摆状态下湿颗粒柱在重力驱动下的坍塌流动过程,主要考虑了颗粒粒径、液体表面张力系数和液体含量等参数对系统坍塌流动模式和动力学行为的影响。研究发现,在湿颗粒系统中,颗粒粒径和液体表面张力系数会改变颗粒间的毛细力大小,引起系统发生不同的坍塌流动模式,而液体含量仅定量影响颗粒坍塌后的堆积形态。在此基础上,进一步探讨了不同模式下系统坍塌流动行为与模型参数的相关性,发现无量纲Bond数是决定钟摆状态下湿颗粒物质坍塌流动动力学行为的本质因素。     

非定常空泡闭合区域最大压力的理论研究

当物体在流体中高速运动产生空泡时,空泡通常以回射流的形式闭合在物体表面上,并在闭合位置对物体表面产生流体超压. 在物体表面上的空泡闭合位置一般不是固定的,其位置根据物体运动速度的变化、空泡压力的变化及重力场中的位置等因素而在物体表面发 生快速移动,在非对称情况下,这种移动超压会极大影响运动物体的稳定性. 基于势流理论研究了重力场中非定常垂直空泡闭合区域中最大压力的存在位置,推导了最大压力的理论公式,揭示了最大压力与空泡发 展速度之间的关系,证明了最大压力点的两个特殊流体性质. 最后设计了测量空泡闭合区域最大压力的验证性试验,并将理论计算结果与试 验测量结果进行了对比,验证了理论研究结果.     

空化器出水非定常垂直空泡的研究

对空化器朝水面高速运动产生的非定常垂直空泡进行了理论研究. 建立了受水面和重力影响下的水下垂直空泡长度变化数学方程, 从方程中导出了非定常垂直空泡长度计算公式, 利用公式计算了空化器出水后空泡从脱落、收缩到溃灭的时间. 对带空化器的航行体, 公式还可以计算脱落空泡溃灭高压作用在航行体上的位置, 最后给出了避免溃灭高压作用在航行体上的条件和判据.     

A hybrid spectral/finite‐difference to transient free‐surface flow inside thin symmetric cavities of longitudinally varying thickness

The lubrication theory is extended for transient free‐surface flow of a viscous fluid inside three‐dimensional symmetric thin cavities of thickness that varies in the flow direction. The problem is first formulated for a cavity of arbitrary shape. The moving domain is mapped onto a rectangular domain at each time step of the computation. The pressure, which in this case is governed by the modified Laplace's equation, is expanded in a Fourier series in the spanwise direction. The expansion coefficients are obtained using the finite‐difference method. Only a few modes are usually needed to secure convergence. The flow behaviour is strongly influenced by the cavity thickness. The flows inside a straight, contracting, expanding, and modulated cavities are examined. It is found that while the evolution of the front is always monotonic with time, that of the velocity at the front can be oscillatory if the degree of contraction of the cavity (whether modulated or not) is significant. The velocity of the contact point along the lateral walls is usually larger than that at the front, leading to the straightening of the front. However, for modulated cavities, the front may advance at a faster rate, leading to its own undulation. Copyright © 2005 John Wiley & Sons, Ltd.     

用E-L方法计算圆平头物体垂直入水空泡的面闭合和深闭合

本文根据非线性自由面理论,用E-L方法计算了圆平头物体垂直入水空泡发生、发展、面闭合、拉离和深闭合等一系列连续变化过程。空泡中气体流动分为三个阶段加以处理。采用Riabouchinsky映象板模型,初步解决了高F_r数下数值模拟空泡深闭合的困难。计算结果表明,对于给定的物体头型,F_r数、空气出度数、物体质量数是影响入水空泡发展过程的主要因素。     

A Lagrangian boundary element approach to transient three‐dimensional free surface flow in thin cavities

The lubrication theory is extended for transient free‐surface flow of a viscous fluid inside a three‐dimensional thin cavity. The problem is closely related to the filling stage during the injection molding process. The pressure, which in this case is governed by the Laplace's equation, is determined using the boundary element method. A fully Lagrangian approach is implemented for the tracking of the evolving free surface. The domain of computation is the projection of the physical domain onto the (x, y) plane. This approach is valid for simple and complex cavities as illustrated for the cases of a flat plate and a curved plate. It is found that the flow behavior is strongly influenced by the shape of the initial fluid domain, the shape of the cavity, and inlet flow pressure. Copyright © 2001 John Wiley & Sons, Ltd.     

Identification of Cavities Inside Two-Dimensional Heterogeneous Isotropic Elastic Bodies

In this paper, we discuss the uniqueness in determining cavities (i.e., nonrectilinear cracks) in a heterogeneous isotropic elastic medium in two dimensions. Our main result asserts that there is at most one cavity in the elastic medium which yields the same surface displacements and stresses on an arbitarily small portion of the boundary. The boundaries of cavities are assumed to be piecewise smooth and admit edges where no net force is exerted. The key of the proof is the unique continuation for the isotropic Lamé system and geometric considerations. This revised version was published online in August 2006 with corrections to the Cover Date.     

Dynamics of a cavitational cavity in a non-newtonian fluid

The dynamics of a spherical cavity in a non-Newtonian fluid, described by the Reiner-Rivlin rheological equation [1], is investigated. The equation of radial cavity motion is obtained, where the gas in the cavity is subject to a polytropic law and surface tension is taken into account. The equation of cavity motion is solved numerically for a number of values of the transverse viscosity coefficient. The influence of the transverse viscosity on the collapse process of vapor and gas-filled cavities is shown. Numerical computations are also carried out for the rate of energy dissipation and the pressure distribution in the fluid.Translated from Izvestiya Akademiya Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 170–173, July–August, 1973.The authors are grateful to A. T. Listrove for attention to the research.     

Nonlinear waves in a liquid film on a near-horizontal surface

Nonlinear waves in a liquid film on a slightly inclined rigid plane are studied. A mathematical model is reduced to a system of two evolutionary equations for the layer thickness and the local fluid mass flow. In addition to viscous forces, gravity, and surface tension, the pressure difference over the layer thickness, induced by the gravity force projection on the normal to the underlying surface, is also taken into account. Spatially periodic solutions developing with time from small initial disturbances into regular nonlinear waves are considered. A spectral representation of the solution, the Galerkin method with respect to the uniform coordinate, and subsequent numerical calculation of the corresponding dynamic system on large time intervals are employed. Different variants in the space of the three governing parameters are calculated and some basic mechanisms of nonlinear dynamics of the two-dimensional waves are detected. The calculation results are compared with the existing experimental data. It is shown that the theoretical conclusions can be used to interpret and predict experiments.     

Bubble dynamics in microchannel: An overview of the state-of-the-art

The inception of the boiling, in a pool or flow boiling, is the formation of the vapor bubble at an active nucleation site that plays a crucial role in the boiling process and it becomes critical and unfolds many facets when channel size reduces to submicron. The detailed knowledge of the bubble dynamics is helpful in establishing the thermal and hydraulic flow behavior in the microchannel. In the current paper, bubble dynamics that include bubble nucleation at the nucleation site, its growth, departure, and motion along the flow in a microchannel(s) are discussed in detail. Different models developed for critical cavity radius favorable for bubble nucleation are compiled and observe that models exhibit large deviation. The bubble growth models are compiled and concluded that the development of a more generalize bubble growth model is necessary that would be capable of accounting for inertia controlled and thermal diffusion controlled regions. Bubbles at nucleation sites in a microchannel grow under the influence of various forces such as surface tension, inertia, shear, gravitational and evaporation momentum. Parametric analysis of these forces reckoned that the threshold between macro- to microchannel could be identify through critical analysis of such forces. Eventually, the possible impact of the various factors such as operating conditions, geometrical parameters, thermophysical properties of fluid on bubble dynamics in microchannel has been reported.

     

Flow investigation of circular cylinder having different cavities in shallow water

The control of the unsteady flow structure formed behind a cylinder placed horizontally in shallow water was analyzed experimentally using bare cylinder and cylinders with cavities having square and rectangular geometries, respectively. Reynolds number, Froude number and water height had been chosen as 5000, 0.27 and 90 mm, respectively and also these parameters were kept constant for all experiments. To consider the influence of height (h), the cylinder level was located at various heights from h: 0 mm to 60 mm. Furthermore, cavity angle (a) had been selected from 0°, 80°, 85°, 90° and 95° to consider influence of cavity angle on flow. With the help of Particle Image Velocimetry (PIV), average velocity vectors were measured in two dimensions at many points simultaneously in a planar flow area. The results uncovered that large negative counter was observed at h: 37.5 mm in bare cylinder as well as cylinders having square and rectangular cavities at h: 45 mm. Also, no negative counter was observed for cylinders having rectangular cavity at h: 0 mm and a: 90° and 95° due to the bottom effect. Due to surface effects, a foci point was formed in all cylinders where close to the surface and close to the base. Two foci points and a saddle point were seen as they moved away from the surface for all cylinders. Also, the smallest vortex region was observed for cylinders having rectangular cavity at h: 37.5 mm and a: 90° and 95° in whole cylinders. Also, the highest drag coefficient (C_d) value was obtained for cylinder having square cavity at h: 52.5 mm and a: 80° while the highest drag coefficient value was obtained for cylinder having rectangular cavity at h: 37.5 mm and a: 95°.     

Three‐dimensional transient free‐surface flow of viscous fluids inside cavities of arbitrary shape

The three‐dimensional transient free‐surface flow inside cavities of arbitrary shape is examined in this study. An adaptive (Lagrangian) boundary‐element approach is proposed for the general three‐dimensional simulation of confined free‐surface flow of viscous incompressible fluids. The method is stable as it includes remeshing capabilities of the deforming free‐surface, and thus can handle large deformations. A simple algorithm is developed for mesh refinement of the deforming free‐surface mesh. Smooth transition between large and small elements is achieved without significant degradation of the aspect ratio of the elements in the mesh. The method is used to determine the flow field and free‐surface evolution inside cubic, rectangular and cylindrical containers. These problems illustrate the transient nature of the flow during the mixing process. Surface tension effects are also explored. Copyright © 2003 John Wiley & Sons, Ltd.     

导流板对腔口流体自持振荡影响的研究

腔口流体动力自持振荡的频率和导流板的长度有一定关系。本文通过对跨越腔口非稳定层和自持振荡的理论分析，并通过对不同长度导流板的腔、低速流激自持振荡均方压力谱分析的实验研究，给出流激自持振荡的频率与导流板长度之间的关系。流体动力振荡和腔的声驻波共振耦合时，腔内振荡的均方压力达到最大值。根据流速变化时，均方压力谱峰值频率的偏移，分析了导流板长度对流引起的流一腔系统耦合共振的影响。     

微小缺口/孔洞的激光衍射无损检测

基于裂纹和孔洞的小尺寸特征,提出了微小缺口/孔洞的激光衍射无损探测技术,给出了解析表达式.通过这一技术,对单向拉伸试件中所含单边缺口和中心孔洞在外载作用下的演化过程进行了实时原位检测,获得了缺口/孔洞孔径随载荷的变化曲线及模拟裂纹时裂纹的张开位移、裂纹开裂长度及应力强度因子等一系列断裂参数.     

Capillary cavity flow past a circular cylinder

Cavity flow past a circular cylinder is considered accounting for the surface tension on the cavity boundary. The fluid is assumed to be inviscid and incompressible, and the flow is assumed to be irrotational. The solution is based on two derived governing expressions, which are the complex velocity and the derivative of the complex potential defined in an auxiliary parameter region. An integral equation in the velocity magnitude along the free surface is derived from the dynamic boundary condition. The Brillouin–Villat criterion is employed to determine the location of the point of flow separation. The cases of zero surface tension and zero cavitation number are obtained as limiting cases of the solution. Numerical results concerning the effects of surface tension and cavitation development on the cavity detachment, the drag force and the geometry of the free boundaries are presented over a wide range of the Weber and the cavitation numbers.     

空化可压缩流动空穴溃灭激波特性研究

为深入研究空化可压缩流动中空泡/空泡团溃灭过程中激波产生、传播及其与空穴相互作用规律,本文采用数值模拟方法对空化可压缩流动空穴溃灭激波特性展开了研究.数值计算基于OpenFOAM开源程序,综合考虑蒸汽相和液相的压缩性,通过在原无相变两相可压缩求解器的控制方程中耦合模拟空化汽液相间质量交换的源项,实现了对空化流动的非定常可压缩计算.利用上述考虑汽/液相可压缩性的空化流动求解器,对周期性云状空化流动进行了数值模拟,并重点研究了空穴溃灭激波特性.结果表明:上述数值计算方法可以准确捕捉到空穴非定常演化过程及大尺度脱落空泡云团溃灭激波现象,大尺度脱落空泡云团溃灭过程分为3个阶段:(1) U型空泡团形成; (2) U型空泡团头部溃灭; (3) U型空泡团腿部溃灭.在U 型空泡团腿部溃灭瞬间,观察到激波产生,并向上游和下游传播,向上游传播的激波与空穴相互作用,导致水翼吸力面新生的附着型片状空穴回缩,直至完全溃灭.并且空穴溃灭激波存在回弹现象, 抑制了下一周期的空化发展.