Hydrodynamic structure of a vortex ring

Hot-wire anemometry and high-speed motion-picture photography have been used in an experimental study of the structure of a vortex ring in air. The velocity field and streamline pattern have been determined, together with the vorticity distribution. It has been shown that the vorticity is almost entirely localized in the region of the core of the vortex ring and quickly diminishes with distance from the core. Analysis of the experimental results permits a conclusion concerning the nonstationarity of vortex rings.The authors thank V. K. Sheremetov and V. A. Kosinov for their assistance.     

Model of two-dimensional vortex motion with an entrainment mechanism

A model for describing the vertically averaged vortex motions of an incompressible viscous fluid with an arbitrary vertical structure of the bottom Ekman boundary layer is proposed. An approach similar to that adopted in [1] is used: the second moments of the deviations from the average velocities required in order to close the vorticity equation are calculated by means of the Ekman solution for gradient flows, which makes it possible to take the integral bottom boundary layer effect into account. As a result, these terms lead to a specific form of nonlinear friction with a coefficient that depends on the vorticity of the average flow. In the particular case of a constant vertical turbulent transfer coefficient the inaccuracies of the model described in [1] can be eliminated. The generalized vorticity equation obtained has solutions of the vorticity spot type with a uniform internal vorticity distribution, which can be effectively investigated by means of appropriate algorithms [2]. The mechanism of entrainment at the vorticity front is illustrated with reference to the example of the evolution of vorticity spots. An exact solution of the problem of the evolution of an elliptic vortex (generalized Kirchhoff vortex), which in the case of fairly strong anticyclonic vorticity degenerates first into a line segment (vortex sheet) and then into a point vortex, is constructed. Equations describing the dynamics of an elliptic vorticity spot in an external field with a linear dependence of the velocity on the horizontal coordinates and generalizing the classical Chaplygin-Kida model [3, 4] are constructed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 49–56, November–December, 1992.     

Diffusion of a ring vortex

The diffusion of a ring vortex is investigated in the present paper with allowance for the influence of the initial radius of the toroidal vorticity distribution on the flow structure. The statement of the problem in such a formulation makes it possible to classify and reinterpret results obtained previously. A vortex pair is studied together with a vortex ring. The toroidal vorticity and stream function distributions are obtained analytically. The self-induced lift velocity of the ring vortex is found. The influence of inertial terms is investigated numerically.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 10–15, November–December, 1987.     

Experimental study of three-dimensional vortex structures in translating and rotating plates

Motivated by the unsteady force generation of flying animals, vortex formation and vorticity transport processes around small aspect-ratio translating and rotating plates with a high angle of attack are investigated. Defocusing Digital Particle Image Velocimetry was employed to explore the structure and dynamics of the vortex generated by the plates. For both translating and rotating cases, we observe the presence of a spanwise flow over the plate and the consequent effect of vorticity transport due to the tilting of the leading-edge vortex. While the spanwise flow is confined inside the leading-edge vortex for the translating case, it is widely present over the plate and the wake region of the rotating case. The distribution of the spanwise flow is a prominent distinction between the vortex structures of these two cases. As the Reynolds number decreases, due to the increase in viscosity, the leading-edge and tip vortices tend to spread inside the area swept by the rotating plate. The different vorticity distributions of the low and high Reynolds number cases are consistent with the difference in measured lift forces, which is confirmed using the vorticity moment theory.     

Study of vortex breakdown by particle tracking velocimetry (PTV) Part 3: Time-dependent structure and development of breakdown-modes

This third part of the study deals with the time-dependent nature of vortex breakdown. The results show the unsteady velocity and vorticity field of the initiation and development of breakdown and transition between both predominant breakdown modes, the bubble and the spiral. During the development to breakdown, the generated amount of circumferential vorticity follows the theoretical prediction by Brown and Lopez (1990). This confirms the idea of positive feedback as the key-mechanism leading to vortex breakdown. We regard the bubble-type as the fundamental breakdown type, that is stationary and nearly axisymmetric. The circumferential vorticity is distributed in a form of an elliptical vortex-ring-like structure. Starting from this stage, an increase of volume flux to a higher Reynolds number leads to the transition to the spiral-type with an initial stretching of the vortex ring-like structure and a subsequent change to an asymmetric circumferential vorticity distribution. This in combination with the inductive effect causes the front stagnation point to be deflected radially away and later to rotate around the centerline. Consequently the approaching vortex core is radially deflected in opposite direction and evolves in a spiral path. The idea of a second positive feedback-mechanism gives a possible explanation for the transition. Following this theory the asymmetry of circumferential vorticity will trigger itself at a certain degree by the interaction with the inductively affected stagnation point and its influence on the approaching vortex core. This self-enhancing process will finally lead to the spiral-type breakdown in which the radial distance between rotating stagnation point and deflected vortex core is of the order of the characteristic vortex core radius. The reversed transition from the spiral to a stable bubble-type can be regenerated by decreasing the Reynolds number down to the value that corresponds to the stable bubble state. The flow structure evolves nearly in the time-reversed way as during transition from bubble towards the spiral.     

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.     

A combined vortex and panel method for numerical simulations of viscous flows: a comparative study of a vortex particle method and a finite volume method

This paper describes and compares two vorticity‐based integral approaches for the solution of the incompressible Navier–Stokes equations. Either a Lagrangian vortex particle method or an Eulerian finite volume scheme is implemented to solve the vorticity transport equation with a vorticity boundary condition. The Biot–Savart integral is used to compute the velocity field from a vorticity distribution over a fluid domain. The vorticity boundary condition is improved by the use of an iteration scheme connected with the well‐established panel method. In the early stages of development of flows around an impulsively started circular cylinder, and past an impulsively started foil with varying angles of attack, the computational results obtained by the Lagrangian vortex method are compared with those obtained by the Eulerian finite volume method. The comparison is performed separately for the pressure fields as well. The results obtained by the two methods are in good agreement, and give a better understanding of the vorticity‐based methods. Copyright © 2005 John Wiley & Sons, Ltd.     

A three‐dimensional vortex particle‐in‐cell method for vortex motions in the vicinity of a wall

A new vortex particle‐in‐cell method for the simulation of three‐dimensional unsteady incompressible viscous flow is presented. The projection of the vortex strengths onto the mesh is based on volume interpolation. The convection of vorticity is treated as a Lagrangian move operation but one where the velocity of each particle is interpolated from an Eulerian mesh solution of velocity–Poisson equations. The change in vorticity due to diffusion is also computed on the Eulerian mesh and projected back to the particles. Where diffusive fluxes cause vorticity to enter a cell not already containing any particles new particles are created. The surface vorticity and the cancellation of tangential velocity at the plate are related by the Neumann conditions. The basic framework for implementation of the procedure is also introduced where the solution update comprises a sequence of two fractional steps. The method is applied to a problem where an unsteady boundary layer develops under the impact of a vortex ring and comparison is made with the experimental and numerical literature. Copyright © 2001 John Wiley & Sons, Ltd.     

Numerical study of vortex reconnection for two anti-parallel vortex tubes

By direct numerical simulation of the Navier-Stokes equations we investigate the reconnection of two antiparallel vortex tubes. A new type of perturbation of the initial vorticity field is given which is different from that presented in Refs. [8] and [9]. The formation and the evolution of the “curved vortex belts”, their mutual action with the “bridges” are found. These are important phenomena not studied by others. The project supported by the LNM of Institute of Mechanics, Academia Sinica and The National Natural Science Foundation of China     

Dynamics of thin vortex rings in a low-viscosity fluid

In order to describe the unsteady flow of a viscous fluid induced by a toroidal vorticity distribution we use the two-scale expansion method [6], By this means we obtain a vorticity distribution in the core of the thin vortex ring that is consistent with the external potential flow. The time dependence of the flow characteristics obtained confirms the experimental results for the inertial regime. The interaction of coaxial vortex rings is investigated as an example.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.5, pp. 52–59, September–October, 1992.     

Adaptive Euler simulations of airfoil–vortex interaction

A grid redistribution method is used together with an improved spatially third‐order accurate Euler solver to improve the accuracy of direct Euler simulations of airfoil–vortex interaction. The presented numerical results of two airfoil–vortex interaction cases indicate that with combination of the two methods, the numerical diffusion of vorticity inherent in the direct Euler simulations is drastically reduced without increasing the number of grid points. With some extra works due to grid redistribution, the predicted vortex structure is well preserved after a long convection and much sharper acoustic wave front resulting from airfoil–vortex interaction is captured. Copyright © 2006 John Wiley & Sons, Ltd.     

Singular interaction of vortex filaments

The reconnection process of two vortex filaments is analyzed using the viscous vorticity equation and several assumptions. Analysis is confined to a local region where the interaction takes place, and the velocity field is expanded in polynomials. The expansion coefficients are functions of time, and their behavior is obtained from the vorticity equation. The significance of this phenomenon in aeroacoustic noise generation is discussed.     

Nonlinear wind-up in a strained planar vortex

The response of a Gaussian vortex to a strong external strain field is examined using two complementary numerical schemes. When the strain is weak previous calculations have shown that a rebound phenomenon is operative: after enstrophy is transferred from the mean to the azimuthal component by the straining there is a reversal during which a significant fraction of the enstrophy moves back from the azimuthal component to the mean. Concomitantly the perturbation vorticity undergoes spiral wind-up and develops a short-scale radial structure which becomes ever finer with time. We show that the rebound behaviour is suppressed by strong strain and that the intricate radial structure is simultaneously inhibited. We also give some indication of the modifications that are introduced when a strongly strained vortex is allowed to relax after the forcing field is switched off.     

Evolution of an initially columnar vortex terminating normal to a no-slip wall

The early evolution of an initially columnar vortex normal to a solid wall was examined. The vortex was generated by a pair of flaps in a water tank. Detrimental effects from the wall during the vortex generation were avoided by producing the vortex normal to a free surface and subsequently bringing a horizontal plate into contact with the surface. Digital particle image velocimetry (DPIV) measurements of the velocity and vorticity, together with laser induced fluorescence (LIF) visualizations, in a meridional plane revealed a toroidal structure with the appearance of an axisymmetric vortex breakdown bubble. Agreement was found between the measurements and numerical simulations of the axisymmetric Navier–Stokes equations. The results show that the flow in the effusive corner region is dominated by a Bödewadt-type spatially oscillatory boundary layer within the core region and a potential-like vortex boundary layer at large radii. The toroidal structure results from the interaction between these two boundary layers, leading to the roll up of a dominant shear layer within the Bödewadt structure, and does not develop from the columnar vortex itself.     

Wave generation on an interface by vortex disturbances in a shear flow

A linear problem of oscillations of an interface in a two-layer system, in which the upper layer is at rest and the lower layer has a constant velocity shear, is considered. The dynamic perturbations in the lower layer are represented as the sum of vortex and wave disturbances (disturbances with zero vorticity). It is shown that in the shear flow the evolution of the vortex disturbances with a nonsmooth or a singular initial vorticity distribution can result in the resonant excitation of waves on the interface. The occurrence of the resonance corresponds to the coincidence of the oscillation frequencies of the perturbations of both classes. In the absence of hydrodynamic instability of the shear flow, the resonant excitation can be one of the main mechanisms of wave generation in two-layer systems.     

Wave/vortex decompositions in stably stratified flows

The slowly evolving vortex part of stably stratified flows, both homogeneous and of shear-layer type, is extracted using a diagnostic decomposition of the velocity field based upon the potential vorticity. Comparisons with a decomposition theoretically valid for the linear regime are also made. For the homogeneous flows considered here, the vortex part apparently strongly interacts with the wave field, whatever the decomposition in use. A numerical wave filtering process is applied to simulate the flow dynamics driven by the vortex part only. The resulting vortex flow is the same for each decomposition. In the shear layers, by contrast, only the decomposition based upon the potential vorticity is able to extract the vortex part of the flow, whether the shear layer is moderately or strongly stratified. We propose an argument to account for the fact that a highly energetic vortex part is more likely to be found in a strongly stratified shear layer.This work has been supported by EDF (Direction des Etudes et Recherches, Laboratoire National d'Hydraulique) under Contract No. 2J6773.     

Flow past confined delta-wing type vortex generators

This paper presents the results of an experimental study of flow structure in horizontal equilateral triangular ducts having double rows of half delta-wing type vortex generators mounted on the duct’s slant surfaces. The test ducts have the same axial length and hydraulic diameter of 4 m and 58.3 mm, respectively. Each duct consists of double rows of half delta wing pairs arranged either in common flow-up or common flow-down configurations. Flow field measurements were performed using a Particle Image Velocimetry Technique for hydraulic diameter based Reynolds numbers in the range of 1000-8000. The secondary flow field differences generated by two different vortex generator configurations were examined in detail. The secondary flow is found stronger behind the second vortex generator pair than behind the first pair but becomes weaker far from the second pair in the case of Duct1. However, the strength of the secondary flow is found nearly the same behind the first and the second vortex generator pair as well as far from the second vortex generator pair in the case of Duct2. Both ducts are able to create a counter-rotating and a second set of twin foci. Duct2 is able to create the second set of twin foci in an earlier streamwise location than Duct1, as these foci are well-known to their heat transfer augmentation. A larger vortex formation area and a greater induced vorticity field between vortex pairs are observed for Duct2 compared with Duct1. As the induced flow field between the vortex pairs increases the heat transfer, and as the flow field between the vortex cores is found larger in the case of Duct2, therefore, it is expected to obtain better heat transfer characteristics for Duct2 compared with Duct1.     

Head on collisions of compressible vortex rings on a smooth solid surface

An experimental study has been conducted on the effects of distance variation on the impingement process of compressible vortex rings on a stationary solid wall. An experimental incident Mach number of 1.61 was used. Qualitative and quantitative studies compared the impingement and interaction flow characteristics of a compressible vortex ring with a stationary, solid, smooth surface at three distances: 1.66, 3.33, and 5.00 inner diameters. The three distances corresponded to an under-developed vortex ring (1.66 inner diameters), a vortex ring at its development threshold (3.33 inner diameters), and a fully developed one (5.00 inner diameters). Qualitative schlieren results showed that the surface distance affected the shock/vortex interaction process along with the impingement process of the vortex ring and the flow structure of its trailing jet. Quantitative data were extrapolated to evaluate the propagation velocity of the vortex ring prior to impingement. The boundary layer thickness was also estimated. Particle image velocimetry studies showed the main and secondary vortices to have opposite vorticity, with the magnitude of the vorticity of the secondary vortices being approximately half of that of the main vortex. Surface pressure results reveal the symmetrical properties of the impinging flow, along with a direct correlation between the maximum pressure measured at the instant the vortex ring impingement and an increase in surface distance.     

On the three-dimensional nature of the orthogonal blade–vortex interaction

An orthogonal blade–vortex interaction has been visualised using stereo particle image velocimetry. Significant changes to the vortex axial flow w component velocity are observed during the interaction, with a deceleration on the lower surface of the blade where the vortex axial flow is towards the blade surface. Over this surface the interaction process close to the blade surface spreads the vorticity out to the areas of oppositely signed blade w component, and the results suggest a non-uniform spreading over the leading edge region of the blade, with a tendency for a spanwise transport of vorticity. Over the upper surface of the blade, the vortex axial flow velocity increases and the vortex core shrinks slightly. During the lower surface interaction the vorticity and velocity vectors become significantly realigned with respect to one another, while this is not observed for the upper surface interaction.