轴对称钝物体的尾涡结构

本文对于圆球和70°角斜切尾钝头旋成体的尾涡结构作了流态显示和部分热线测量,流态显示结果表明,这类钝物体尾迹中的三维尾涡结构均呈现为一列相互锁定的“涡链”状结构,每一个涡元素自身并不闭合,呈“发卡”形,并与后继的涡相连接,对于70°斜切尾钝头旋成体模型,由于其斜切尾有固定三维尾涡面卷起和脱落方位的作用,故呈现出规则的三维尾涡结构。而圆球模型,由于涡面卷起和涡脱落的方位是随机旋转的,因此“涡链”呈现为被任意扭曲的千姿百态,流态照片各不相同,圆球尾迹的这种既有周期性又有随机旋转的特性,在热线测量的结果中也有所反映。     

Perturbed Motion of a Centrally Symmetric Point Vortex System

The types of motion in a system of point vortices initially located at the vertices of a 2n-sided regular polygon, produced by a spatially periodic perturbation, in the presence of which the vortices are positioned at the corners of two regular concentric n-sided polygons, are described.     

Existence of Minima¶for Nonconvex Functionals¶in Spaces of Functions¶Depending on the Distance from the Boundary

We prove that some nonconvex functionals admit a unique minimum in a functional space of functions which depend only on the distance from the boundary of the (plane) domain where they are defined. The domains considered are disks and regular polygons. We prove that the sequence of minima of the functional on the polygons converges to the unique minimum on the circumscribed disk as the number of sides tends to infinity. Our method also allows us to determine the explicit form of the minima. (Accepted January 19, 1999)     

Singular vortices in regular flows

A review of the theory of quasigeostrophic singular vortices embedded in regular flows is presented with emphasis on recent results. The equations governing the joint evolution of singular vortices and regular flow, and the conservation laws (integrals) yielded by these equations are presented. Using these integrals, we prove the nonlinear stability of a vortex pair on the f-plane with respect to any small regular perturbation with finite energy and enstrophy. On the β-plane, a new exact steady-state solution is presented, a hybrid regular-singular modon comprised of a singular vortex and a localized regular component. The unsteady drift of an individual singular β-plane vortex confined to one layer of a two-layer fluid is considered. Analysis of the β-gyres shows that the vortex trajectory is similar to that of a barotropic monopole on the β-plane. Non-stationary behavior of a dipole interacting with a radial flow produced by a point source in a 2D fluid is examined. The dipole always survives after collision with the source and accelerates (decelerates) in a convergent (divergent) radial flow.     

Coaxial axisymmetric vortex rings: 150 years after Helmholtz

This article addresses the fascinating 150 years history of the classical Helmholtz paper that laid the foundation of the vortex dynamics. Among general theorems on vortex motion, this memoir contains the special section on circular vortex filaments and axisymmetric vortex rings, in particular. The objective of this article is both to clarify some purely mathematical questions connected with the Dyson model of coaxial vortex rings in inviscid incompressible fluid and to provide a historical overview of achievements in experimental, analytical, and numerical studies of vortex rings interactions. The model is illustrated by several examples both of regular and chaotic motion of several vortex rings in an unbounded fluid.     

Numerical study of the turbulent channel flow under space-dependent electromagnetic force control at different Reynolds numbers

In this paper, the control of turbulent channel flow by space-dependent electromagnetic force and the mechanism of drag reduction are investigated with the direct numerical simulation(DNS) methods for different Reynolds numbers. A formulation is derived to express the relation between the drag and the Reynolds shear stress. With the application of optimal electromagnetic force, the in-depth relations among characteristic structures in the flow field, mean Reynolds shear stress, and the effect of drag reduction for different Reynolds numbers are discussed. The results indicate that the maximum drag reductions can be obtained with an optimal combination of parameters for each case of different Reynolds numbers. The regular quasi-streamwise vortex structures, which appear in the flow field, have the same period with that of the electromagnetic force.These structures suppress the random velocity fluctuations, which leads to the absolute value of mean Reynolds shear stress decreasing and the distribution of that moving away from the wall. Moreover, the wave number of optimal electromagnetic force increases,and the scale of the regular quasi-streamwise vortex structures decreases as the Reynolds number increases. Therefore, the rate of drag reduction decreases with the increase in the Reynolds number since the scale of the regular quasi-streamwise vortex structures decreases.     

An accurate interface reconstruction method using piecewise circular arcs

A novel piecewise circular interface construction (PCIC) method for accurate reconstruction of interface in a two‐phase flow problem is proposed. This is under the framework of a fixed grid, volume of fluid approach applied on a two‐dimensional semistaggered structured grid. Fluid interface in each mixed cell is represented using a geometric template of piecewise circular arc. Data corresponding to arc center coordinates and radius are first predicted using curve fitting methods and corrected with the help of volume fraction constraints. Further corrections are carried out to achieve function (c0) continuity at cell boundaries. The proposed method does not require additional calculations for the determination of curvature (for calculation of surface tension force), since it is obtained as part of reconstruction process itself. For dynamic interface construction, simple analytical expressions are derived to construct edge matched flux polygons. Area of intersection of flux polygons with area covered by primary fluid is determined to effect geometric advection across a PCIC interface. Accuracy of this method is demonstrated by the reconstruction of standard static and dynamically evolving interface problems. Accuracy levels superior to most interface reconstruction methods using PLIC and schemes using higher order curves are established. Finally, the capability to handle a complex two‐phase flow problem simulation viz the four‐vortex flow field, where interface undergoes breakage and coalescence, is also demonstrated.     

Branching of a horseshoe vortex around surface-mounted rectangular cylinders

Flow visualizations and surface pressure measurements are performed to study the branching phenomenon of a horseshoe vortex upstream of a series of rectangular cylinders with aspect ratios ranging from 0 to 17. The Reynolds numbers are 500 for visualization experiments and 1990 to 6650 for wind tunnel surface pressure measurements. The flow visualization results indicate that a horseshoe vortex will first evolve into a wavy structure and for aspect ratios which are equal or larger than 10, the wavy horseshoe vortex will branch itself into smaller regular vortices. The waviness disappears as soon as branching occurs. The number of the branched smaller vortices increases as the aspect ratio increases further. Received: 31 March 1998/Accepted: 29 June 1999     

Three dimensional reconstruction of coherent structures using image processing techniques

An algorithm for reconstructing three dimensional images of coherent structures using a commercially available video image processing system is presented. The principal advantages of this work are low cost and minimal development time. The image processing system comes complete with frame grabbing and four software programs needed for image reconstruction. The process entails: grabbing individual video frames comprising a single three dimensional image of a vortex, converting each frame to a polygon, ordering successive polygons to reconstruct the vortex skeleton, and generating a surface for full three dimensional reconstruction. The processing system also includes a computer movie studio for creating animations, and a video editing system for producing professional quality video presentations.Support of the Office of Naval Research (Grant No. N00014-92-J-1020) through Dr. Edwin P. Rood is gratefully acknowledged.     

Formation of a regular sequence of vortex loops around a rotating disk in stratified fluid

A regular system of vortex loops in annular flow behind the edge of a disk of 6–11 cm in diameter rotating in stratified fluid is first visualized using the shadowgraph techniques (classical method with the Foucault knife and the “filament-in-focus” method). Clearly outlined vortex loops are observed in strongly and weakly stratified fluids over a wide range of the angular disk rotation velocities. The dimensions of the vortex flow region depend on the stratification (buoyancy period), the angular velocity of rotation, and the disk diameter. Extended lengthy filaments which form spiral and irregular patterns inside the loops are clearly expressed in the fine flow structure. The filaments connect the neighboring loops. The trajectories of motion of the upper edges of the loops, i.e., the sources of short internal waves, are traced.     

Singularity analysis at the vertex of polygonal quantum wire inclusions

Singular behavior near the vertex/corner of polygonal inclusions in anisotropic piezoelectric planes is identified and investigated. Using a recently derived exact closed-form solution, the elastic and electric fields associated with regular polygon-shaped quantum wires are analyzed in detail, revealing the effect of factors such as material orientation, type of eigenstrain, and number of sides of polygons on the singular behavior. Our study shows that by adjusting these factors properly, one could avoid the singular behavior or reduce the level of singularity, which could be of significance in the design and fabrication of the semiconductor devices.     

Low Mach number prediction of the acoustic signature of fractal-generated turbulence

In this work, we compare the acoustic properties of a fractal square grid with those of a regular grid by means of a hybrid approach based on Lighthill’s analogy and Direct Numerical Simulation (DNS). Our results show that the sound levels corresponding to our fractal square grid of three fractal iterations are significantly reduced by comparison to a regular grid of same porosity and mesh-based Reynolds number. We also find a well-defined peak at a Strouhal number between 0.2 and 0.3 in the acoustic spectrum of our fractal square grid which is absent in the case of our regular grid. We explain this effect in terms of a new criterion for quasi-periodic vortex shedding from a regular or fractal grid.     

Study of periodically excited bubbly jets by PIV and double optical sensors

Interactions between large coherent structures and bubbles in two-phase flow can be systematically observed in a periodically excited bubbly jet. Controlled excitation at fixed frequency causes large eddy structures to develop at regular intervals. Thus, interactions between large vortices and bubbles can be studied with PIV and double optical sensors (DOS) using phase-averaging techniques. A number of results on the time and space dependence of velocities and void fractions are presented revealing physical interactions between the liquid flow field and bubble movement as well as feedbacks from bubble agglomeration on the development of flow structures. A clear indication of bubble trapping inside the vortex ring is the generation of a bubble ring that travels with the same velocity as the vortex ring. The DOS results indicate clustering of the bubbles in coherent vortex structures, with a periodic variation of void fraction during the excitation period.     

Elementary aspects of vortex motion

Several aspects of vortex motion are considered, with a special stress on the present status of idealization, such as point vortices or vortex filament. As an introduction, elements of vortices induced by the transient flow past an obstacle are considered and their role and development are stated.

Following this introduction, a general survey of the issues in this symposium is made sketchily. As an example, the motion of point vortices in the presence of an external flow or a boundary is discussed on the basis of the Hamiltonian formalism. The cases of linear flow and semicircular boundary are taken as examples of regular and chaotic motions. Secular behaviour of a pair of vortices in the flow is remarked.     

剥蚀引起的球锥体两相绕流效应

基于多学科理论建立了极端环境下球锥体烧蚀、剥蚀的数理模型。利用离散涡方法计算流场与球锥表面压力分布,采用三方程烧蚀模型计算热化学控制机制下的烧蚀速率;引入颗粒轨道模型求解剥蚀颗粒的运动,编程计算高温高压燃烧室内球锥形烧蚀试件的绕流场及剥蚀颗粒的运动轨迹。研究表明：烧蚀对球锥体的绕流影响显著,球锥体的涡云较快地转变为不对...     

Exotic vortex wakes—point vortex solutions

Von Kármán was the first to present a quantitative model of the “vortex street” wake as a double row of point vortices, to determine which configurations propagate in the direction of the rows, and to consider the linear stability theory for such states. In the early literature one works with infinite rows of vortices. The vortex street is assumed to continue to infinity both upstream and downstream. Another analytical approach is to use periodic boundary conditions in the direction of the wake. This representation was used by Domm in his analysis of the instability of the Kármán vortex street. Birkhoff and Fisher in 1959 were the first to treat vortices in a periodic strip as a dynamical system in its own right. We have used the periodic system to address problems of vortex wake patterns, in particular vortex wakes that are more complicated than the traditional two-vortices-per-strip configurations. We use the term “exotic” for such wakes. We submit that this approach can yield a number of insights, including results of direct relevance to experiments, in the same sense that von Kármán's analysis has been helpful to the understanding of the regular vortex street wake, and we present the results obtained to date following this program.     

Fluctuating fluid forces acting on a circular cylinder and interference with a plane wall

The flow around a circular cylinder placed close to a horizontal plane wall was investigated experimentally. Fluctuations of lift and drag of the cylinder and wall interference effects were studied in terms of the gap height between the cylinder and wall and the thickness of the turbulent wall boundary layer. The fluctuating fluid forces acting on the cylinder sharply increased, and the regular vortex shedding, i.e. Kárman vortex streets, started to form beyond a critical gap height. The formation of Kárman vortex streets was abruptly interrupted when the bottom of the cylinder came in contact with the outer layer of the boundary layer developed on the wall. This critical gap height correlated well with the thickness of the boundary layer.     

Effects of sound on flow separation from blunt flat plates

The effect of sound on the flow around plates with semicircular or square leading edges and square trailing edges located in a low turbulence open jet has been studied. In all circumstances the length of the leading edge separation bubbles associated with square leading edge plates was found to oscillate. When sound was applied to the flow around these plates, the leading edge shear layers reattached closer to the leading edge and the oscillations in bubble length occurred at the applied sound frequency, generating patches of concentrated vorticity in the boundary layers. These vorticity patches moved downstream near the plate surface and then beyond the trailing edge to form vortex cores in a street with a Strouhal number equal to the applied sound value. Sometimes these vortex streets are unstable and break down into streets with Strouhal numbers approaching those observed without sound. These effects of sound were not observed in the flow around plates with semicircular leading edges. Without sound, square leading edge plates of intermediate length did not shed regular vortex streets.     

On the jet formation through a leaky glottis

The present experimental study aims at analyzing the jet formation of the glottal jet flow using a model of a leaky glottis. Experiments were performed in a flow channel with dynamic models of the vocal folds in order to measure the glottal waveform and the velocity distribution in the supraglottal region using High Speed Particle Image Velocimetry (HSPIV). Proper Orthogonal Decomposition (POD) of the vortex Q-criterion was performed in order to detect the energetically most significant large-scale vortex structures and their appearance in the jet flow. The spectral analysis of the glottal waveforms results in an increased spectral decay with more prominent peaks at higher frequencies in the case of a leaky glottis compared to a completely closing reference case. Vortex induced fluctuation frequencies have similar spectral content in both cases as they appear as trains of vortex packets in a regular manner over the glottal cycle. However, when removing the false vocal folds in the leaky glottis model, coherence of vortex generation is lost over the motion cycle. Thus, the presence of the false vocal folds retains most of the vortex induced characteristics in the source spectrum even when the vocal folds do not close fully.