Reconnections of vortex filaments

The process of break-down and reconnection of vortex filaments is considered by the method of three-dimensional vortex singularities (vortons) in various situations, including oblique interaction of a vortex ring with a boundary in shear flow, shedding of a vortex ring from a horseshoe vortex, instability of elliptic vortex ring, Crow instability of two perturbed antiparallel vortex filaments, merging and subsequent splitting of vortex rings. Special attention is paid to the global integrals (vorticity, momentum, angular momentum) and to the inviscid dissipation of energy. The visualization of the effective vortex core, created by the interference of the vorticity fields of vortons, is presented. The comparisons with other methods of simulation of three-dimensional vortex interactions and with the observations have been made.     

BIOMECHANICAL MODELING OF SURFACE WRINKLING OF SOFT TISSUES WITH GROWTH-DEPENDENT MECHANICAL PROPERTIES

This paper explores growth induced morphological instabilities in biological soft materials.In view of that the growth of a living tissue not only changes its geometry but also can alter its mechanical properties,we suggest a refined volumetric growth model incorporating the effects of growth on the mechanical properties of materials.Analogy between this volumetric growth model and the conventional thermal stress model is addressed for both small and finite deformation problems,which brings great ease for the finite element analysis based on the suggested model.Examples of growth induced surface wrinkling behavior in soft composites,including coreshell soft cylinders and three-layered soft tissues,are explored.The results and discussions foresee possible applications of the model in understanding the correlation between the morphogenesis and growth of soft biological tissues(e.g.skins and tumors),as well as in evaluating the deformation and surface instability behavior of soft artificial materials induced by swelling/shrinkage.     

超临界CO_2作用下煤体膨胀变形规律试验研究

为解决采用应变片对超临界CO_2作用下煤体膨胀变形进行点测量时,试验结果离散性大、超临界CO_2作用导致应变片易脱离破损等问题,自主研发了具有施加热流力载荷功能的膨胀体积应变测量装置,对不同温度、压力的超临界CO_2作用下,煤体膨胀体积变形规律进行研究。结果表明:煤体膨胀体积应变随超临界CO_2作用时间增加呈现先增大后趋于稳定的变化规律;当孔隙压力不变时,膨胀体积应变随超临界温度的升高而增加,温度越高,达到稳定膨胀变形所需时间越长;当温度不变时,随着超临界孔隙压力增加,膨胀体积应变也随之增大,但达到稳定膨胀变形所需时间随孔隙压力的升高呈先增加后减少的趋势;超临界CO_2作用下,煤体体积应变随温度和孔隙压力均呈"S型"Logistic函数规律变化;膨胀体积应变对超临界温度和孔隙压力的变化率具有分区性,其变化率大小排序依次为:近临界区跨临界区高临界区。     

Biochemomechanical poroelastic theory of avascular tumor growth

Tumor growth is a complex process involving genetic mutations, biochemical regulations, and mechanical deformations. In this paper, a thermodynamics-based nonlinear poroelastic theory is established to model the coupling among the mechanical, chemical, and biological mechanisms governing avascular tumor growth. A volumetric growth law accounting for mechano-chemo-biological coupled effects is proposed to describe the development of solid tumors. The regulating roles of stresses and nutrient transport in the tumor growth are revealed under different environmental constraints. We show that the mechano-chemo-biological coupling triggers anisotropic and heterogeneous growth, leading to the formation of layered structures in a growing tumor. There exists a steady state in which tumor growth is balanced by resorption. The influence of external confinements on tumor growth is also examined. A phase diagram is constructed to illustrate how the elastic modulus and thickness of the confinements jointly dictate the steady state of tumor volume. Qualitative and quantitative agreements with experimental observations indicate the developed model is capable of capturing the essential features of avascular tumor growth in various environments.     

Impact of buoyancy on vortex ring development in the near field

The development of a buoyant vortex ring in the near field was examined experimentally, and the findings were compared with those of a non-buoyant ring with a similar Reynolds number. The experiments were performed in a water tank, and the vortices were produced by a cylindrical tube of aspect ratio 2. Laser sheet flow visualization and PIV measurements were carried out. In the near field, the initial column of the buoyant fluid breaks down due to the presence of Rayleigh–Taylor instability at the buoyant fluid interface. Subsequently, a large diameter vortex ring with a large spreading rate, compared with the non-buoyant ring, emerges. The celerity of buoyant vortex continued to decrease throughout the range examined, in contrast to the constant celerity of the non-buoyant ring. The vorticity in the core of buoyant and non-buoyant vortex rings is symmetric and has a Gaussian distribution. However, the buoyant vortex ring evolves into a thin core ring, whereas the non-buoyant ring becomes a thick core ring shortly after the ring formation. This difference is brought on by the rapid entrainment and the significant growth of the buoyant ring following the breakup of the initial formation.     

Swelling instability of surface-attached gels as a model of soft tissue growth under geometric constraints

The purpose of this work is to provide a theoretical analysis of the mechanical behavior of the growth of soft materials under geometrical constraints. In particular, we focus on the swelling of a gel layer clamped to a substrate, which is still the subject of many experimental tests. Because the constrained swelling process induces compressive stresses, all these experiments exhibit surface instabilities, which ultimately lead to cusp formation. Our model is based on fixing a neo-Hookean constitutive energy together with the incompressibility requirement for a volumetric, homogeneous mass addition. Our approach is developed mostly, but not uniquely, in the plane strain configuration. We show how the standard equilibrium equations from continuum mechanics have a similarity with the two-dimensional Stokes flows, and we use a nonlinear stream function for the exact treatment of the incompressibility constraint. A free energy approach allows the extension both to arbitrary hyperelastic strain energies and to additional interactions, such as surface energies. We find that, at constant volumetric growth, the threshold for a wavy instability is completely governed by the amount of growth. Nevertheless, the determination of the wavelength at threshold, which scales with the initial thickness of the gel layer, requires the coupling with a surface effect. Our findings, which are valid in proximity of the threshold, are compared to experimental results. The proposed treatment can be extended to weakly nonlinearities within the aim of the theory of bifurcations.     

Formation and evolution of vortex rings induced by interactions between shock waves and a low-density bubble

The deformation and instability of a low-density spherical bubble induced by an incident and its reflected shock waves are studied by using the large eddy simulation method. The computational model is firstly validated by experimental results from the literature and is further used to examine the effect of incident shock wave strength on the formations and three-dimensional evolutions of the vortex rings. For the weak shock wave case (Ma?=?1.24), the baroclinic effect induced by the reflected shock wave is the key mechanism for the formation of new vortex rings. The vortex rings not only move due to the self-induced effect and the flow field velocity, but also generate azimuthal instability due to the pressure disturbance. For the strong shock wave case (Ma?=?2.2), a boundary layer is formed adjacent to the end wall owing to the approach of vortex ring, and unsteady separation of the boundary layer near the wall results in the ejection and formation of new vortex rings. These vortex rings interact in the vicinity of the end wall and finally collapse to a complicated vortex structure via azimuthal instability. For both shock wave strength cases, the evolutions of vortex rings due to the instability lead to the formation of the complicated structure dominated by the small-scale streamwise vortices.     

Global stability behaviour for the BEK family of rotating boundary layers

Numerical simulations were conducted to investigate the linear global stability behaviour of the Bödewadt, Ekman, von Kármán (BEK) family of flows, for cases where a disc rotates beneath an incompressible fluid that is also rotating. This extends the work reported in recent studies that only considered the rotating-disc boundary layer with a von Kármán configuration, where the fluid that lies above the boundary layer remains stationary. When a homogeneous flow approximation is made, neglecting the radial variation of the basic state, it can be shown that linearised disturbances are susceptible to absolute instability. We shall demonstrate that, despite this prediction of absolute instability, the disturbance development exhibits globally stable behaviour in the BEK boundary layers with a genuine radial inhomogeneity. For configurations where the disc rotation rate is greater than that of the overlying fluid, disturbances propagate radially outwards and there is only a convective form of instability. This replicates the behaviour that had previously been documented when the fluid did not rotate beyond the boundary layer. However, if the fluid rotation rate is taken to exceed that of the disc, then the propagation direction reverses and disturbances grow while convecting radially inwards. Eventually, as they approach regions of smaller radii, where stability is predicted according to the homogeneous flow approximation, the growth rates reduce until decay takes over. Given sufficient time, such disturbances can begin to diminish at every radial location, even those which are positioned outwards from the radius associated with the onset of absolute instability. This leads to the confinement of the disturbance development within a finitely bounded region of the spatial–temporal plane.     

An experimental study of viscous vortex rings

The work focuses on the problem of stability and viscous decay of single vortex rings. A tentative classification scheme is proposed for vortex rings which is based on extensive hot-wire measurements of velocity in the ring core and wake, and flow visualization, viz. laminar, wavy, turbulence-producing, and turbulent. Prediction of vortex ring type is shown to be possible, at least approximately, based on the vortex ring Reynolds number alone. Linear growth rates of ring diameter with time are observed for all types of vortex rings, with different growth rates occurring for laminar and turbulent vortex rings. Data on the viscous decay of vortex rings are used to provide experimental confirmation of the accuracy of Saffman's equation for the velocity of propagation of a vortex ring.The work reported herein is supported through a grant of the Natural Sciences and Engineering Research Council of Canada. Special thanks are due to CAPES (Brazil) for the award of a scholarship to the senior author.     

单模态Richtmyer-Meshkov不稳定性数值模拟

采用VOF(Volume of Fluid)方法和PPM(Piecewise Parabolic Method)方法,发展了可用于可压缩多介质粘性流体动力学问题的数值模拟方法MVPPM(Multi-Viscous-Fluid Piecewise Parabolic Method)。利用MVPPM对多个具有不同初始扰动振幅的二维和三维单模态RM(Richtmyer-Meshkov)不稳定性模型进行了数值计算,并与理论模型的计算结果进行了比较。结果表明,无论二维还是三维情况,当初始扰动振幅相对于波长较小的时候,计算的扰动振幅和增长率与理论模型的计算结果一致。当初始扰动波长不变而振幅逐渐增大时,界面振幅和增长率也逐渐增大。对于具有相同初始扰动的情况,三维计算结果在线性段与二维计算结果相同,但是在非线性段比二维结果大,说明非线性和三维效应在RM不稳定性发展过程中起着重要作用。     

Evolution of a forced counter rotating vortex pair for two selected forcing frequencies

In this paper, results from an experimental study of the natural and forced evolution of a pair of counter rotating wing-tip vortices are reported. The vortices were generated using a pair of opposed wing-tips in a wind tunnel and measurements made up to 77 tip-spacings downstream of the models at a chord Reynolds number of 1.3 × 10⁵. The wake was interrogated using 2D particle image velocimetry and the long-wave Crow instability observed. Velocity data were recorded throughout the lifetime of the instability from initial growth through linking, formation of vortex rings and their subsequent decay. Forcing was achieved using pulsed air jets blowing in the span-wise direction from the wing tip and imparting spatially periodic perturbations to the vortices. Forcing at a frequency within the range amplified by the Crow instability was found to enhance the instability growth rate whereas forcing at a frequency outside the amplified range was found to inhibit instability growth. In the latter case the imparted wavelength was observed to die out with a preferred wavelength growing in its place.     

Micromechanical analysis of volumetric growth in the context of open systems thermodynamics and configurational mechanics. Application to tumor growth

We adopt in this paper the physically and micromechanically motivated point of view that growth (resp. resorption) occurs as the expansion (resp. contraction) of initially small tissue elements distributed within a host surrounding matrix, due to the interfacial motion of their boundary. The interface motion is controlled by the availability of nutrients and mechanical driving forces resulting from the internal stresses that built in during the growth. A general extremum principle of the zero potential for open systems witnessing a change of their mass due to the diffusion of nutrients is constructed, considering the framework of open systems thermodynamics. We postulate that the shape of the tissue element evolves in such a way as to minimize the zero potential among all possible admissible shapes of the growing tissue elements. The resulting driving force for the motion of the interface sets a surface growth models at the scale of the growing tissue elements, and is conjugated to a driving force identified as the interfacial jump of the normal component of an energy momentum tensor, in line with Hadamard’s structure theorem. The balance laws associated with volumetric growth at the mesoscopic level result as the averaging of surface growth mechanisms occurring at the microscopic scale of the growing tissue elements. The average kinematics has been formulated in terms of the effective growth velocity gradient and elastic rate of deformation tensor, both functions of time. This formalism is exemplified by the simulation of the avascular growth of multicell spheroids in the presence of diffusion of nutrients, showing the respective influence of mechanical and chemical driving forces in relation to generation of internal stresses.     

TBM滚刀刀圈硬度与岩石匹配性能试验

为了研究TBM滚刀刀圈硬度与岩石匹配性能对滚刀刀圈磨损量及磨损去除机制的影响机理,将四种材料相同但硬度不同的滚刀刀圈试样分别与同一种TBM工程中典型的花岗岩试样进行匹配磨损试验.试验结果表明:材料相同硬度不同的刀圈,其微观组织结构存在一定的差异,刀圈硬度对刀圈磨损量及磨损去除机制有显著影响.随着刀圈硬度的增加,刀圈的磨损量呈先减小后增大的变化趋势且硬度最高的刀圈的磨损量最大.当刀圈硬度较低时,刀圈的磨损以显微切削去除机制为主,且在一定范围内随着刀圈硬度的增加,显微切削去除作用减弱,刀圈的耐磨性更好;但当刀圈硬度高于一定值后,刀圈的磨损去除机制发生转变,刀圈磨损以韧性断裂剥落去除机制为主,刀圈的耐磨性急剧变差.     

Swell-induced surface instability of hydrogel layers with material properties varying in thickness direction

Upon swelling in a solvent, a thin hydrogel layer on a rigid substrate may become unstable, developing various surface patterns. Recent experimental studies have explored the possibilities to generate controllable surface patterns by chemically modifying the molecular structures of the hydrogel near the surface. In this paper, we present a theoretical stability analysis for swelling of hydrogel layers with material properties varying in the thickness direction. As a specialization of the general procedure, hydrogel bilayers with different combinations of the material properties are examined in details. For a soft-on-hard bilayer, the onset of surface instability is determined by the short-wave limit, similar to a homogeneous layer. In contrast, for a hard-on-soft bilayer, a long-wave mode with a finite wavelength emerges as the critical mode at the onset of surface instability, similar to wrinkling of an elastic thin film on a compliant substrate, and the critical swelling ratio is much lower than that for a homogeneous hydrogel layer. A smooth transition of the critical mode is predicted as the volume fraction of the top layer changes, linking surface instability of a homogeneous layer to thin film wrinkling as two limiting cases. The results from the present study suggest that both the critical condition and the instability mode depend sensitively on the variation of the material properties in the thickness direction of the hydrogel layer.     

Gravitational instability of thin gas layer between two thick liquid layers

We consider the problem of gravitational instability (Rayleigh–Taylor instability) of a horizontal thin gas layer between two liquid half-spaces (or thick layers), where the light liquid overlies the heavy one. This study is motivated by the phenomenon of boiling at the surface of direct contact between two immiscible liquids, where the rate of the “break-away” of the vapor layer growing at the contact interface due to development of the Rayleigh–Taylor instability on the upper liquid–gas interface is of interest. The problem is solved analytically under the assumptions of inviscid liquids and viscous weightless vapor. These assumptions correspond well to the processes in real systems, e.g., they are relevant for the case of interfacial boiling in the system water-n-heptane. In order to verify the results, the limiting cases of infinitely thin and infinitely thick gas layers were considered, for which the results can be obviously deduced from the classical problem of the Rayleigh–Taylor instability. These limiting cases are completely identical to the well-studied cases of gravity waves at the liquidliquid and liquid–gas interfaces. When the horizontal extent of the system is long enough, the wavenumber of perturbations is not limited from below, and the system is always unstable. The wavelength of the most dangerous perturbations and the rate of their exponential growth are derived as a function of the layer thickness. The dependence of the exponential growth rate on the gas layer thickness is cubic.     

The in-plane loading of rigid disc inclusion embedded in a crack

The paper examines the in-plane loading of a disc shaped rigid disc inclusion which is embedded in bonded contact with the plane surfaces of a penny-shaped crack. The mixed boundary value problem governing the elastostatic problem is reduced to the solution of a system of coupled integral equations, which are solved numerically to determine results of engineering interest. These results include the in-plane stiffness of the disc inclusion and the crack opening mode stress intensity factor at the boundary of the penny-shaped crack.     

On the Effect of Pipe Boundary Layer Growth on the Formation of a Laminar Vortex Ring Generated by a Piston/Cylinder Arrangement

The growth of a boundary layer at the nozzle wall during laminar vortex ring formation by a nozzle flow generator (piston/cylinder arrangement) is analysed theoretically and numerically and used for modelling the formation of real vortex rings. The predictions of the model are in good agreement with previous experimental and numerical results. Received 19 January 2000 and accepted 17 August 2001     

Coaxial interactions of two vortex rings or of a ring with a body

Inviscid coaxial interactions of two vortex rings, including head-on collisions and leapfrogging motions, are considered using a contour dynamics technique. Interactions of vortex rings with solid bodies are also investigated by combining the contour dynamics technique with a boundary integral equation method. Numerical results show that a clean, successful passage motion is possible for two vortex rings with not too thick cores. In both cases of head-on collisions and leapfrogging motions, very large core deformations are observed when two vortex rings get close to each other. A head-tail structure is formed in the later stage of a head-on collision of two fat vortices. Numerical results also show that a vortex ring will stretch and slow down when it moves toward a solid boundary, will shrink and speed up when it moves away from a solid boundary, and will either translate steadily or approach an oscillating asymptotic state when it is far away from any boundaries. The project supported by The National Education Commission of China and NASA under cooperative grant agreement #NCC5-34.     

涡激诱导并列双圆柱碰撞数值模拟研究

圆柱类结构物的涡激振动是工程中较为常见的一种现象,如果圆柱结构物之间的距离较小, 就会产生涡激诱导碰撞现象,而涡激碰撞会比涡激振动对结构物疲劳破坏产生更严重的威胁.采用浸入边界法模拟流体中的动边界问题,避免了传统贴体网格方法在求解流体中存在固体间碰撞问题时出现数值求解不稳定问题,采用有限元方法对圆柱的运动和碰撞进行求解,通过数据回归方法建立了流体流动条件下的润滑模型,对不同间隙比下涡激诱导并列双圆柱振动及碰撞过程进行了数值模拟, 数值结果表明,如果两圆柱产生了碰撞将会有连续的碰撞发生, 碰撞时出现了多阶频率,振动主频率要比无碰撞时大, 两圆柱碰撞时的相对速度比自由来流速度小;当两圆柱相互接近时, 随着涡环分离角度的逐渐倾斜, 横向流体力先逐渐减小,当两圆柱间涡环开始相互影响发生挤压时, 横向流体力开始逐渐增大;当两圆柱开始反弹时, 两圆柱间形成了低压区, 改变了横向流体阻力的方向,使两圆柱又产生了接近运动,如此反复从而产生了碰撞后横向流体力和圆柱速度的振荡现象.