The term 'vortex breakdown', as used in the reported investigation, refers to a disturbance characterized by the formation of an internal stagnation point on the vortex axis, followed by reversed flow in a region of limited axial extent. Two forms of vortex breakdown, which predominate, are shown in photographs. One form is called 'near-axisymmetric' (sometimes 'axisymmetric'), and the other is called 'spiral'. A survey is presented of work published since the 1972 review by Hall. Most experimental data taken since Hall's review have been in tubes, and the survey deals primarily with such cases. It is found that the assumption of axial-symmetry has produced useful results. The classification of flows as supercritical or subcritical, a step that assumes symmetry, has proved universally useful. Experiments show that vortex breakdown is always preceded by an upstream supercritical flow and followed by a subcritical wake. However, a comparison between experiments and attempts at prediction is less than encouraging. For a satisfactory understanding of the structure of vortex breakdown it is apparently necessary to take into account also aspects of asymmetry.

The structure of vortex breakdown

Analyse theorique et experimentale des conditions de stabilite et d'eclatement de tourbillons isoles incompressibles pour des valeurs elevees du nombre de Reynolds. On rappelle des methodes d'experimentation en laboratoire qui ont ete utilisees. On decrit les deux types principaux d'eclatements de tourbillons. On discute de l'importance de la symetrie par rapport a l'axe. On donne un bref apercu de la theorie de l'onde transcritique

Vortex stability and breakdown - Survey and extension

Experiments have been performed on the tip vortex trailing from a rectangular NACA 0012 half-wing. Preliminary studies showed the vortex to be insensitive to the introduction of a probe and subject only to small wandering motions. Meaningful velocity measurements could therefore be made using hot-wire probes.Detailed analysis of the effects of wandering was performed to properly reveal the flow structure in the core region and to give confidence in measurements made outside the core. A theory has been developed to correct mean-velocity profiles for the effects of wandering and to provide complete quantitative estimates of its amplitude and contributions to Reynolds stress fields. Spectral decomposition was found to be the most effective method of separating these contributions from velocity fluctuations due to turbulence.Outside the core the flow structure is dominated by the remainder of the wing wake which winds into an ever-increasing spiral. There is no large region of axisymmetric turbulence surrounding the core and little sign of turbulence generated by the rotational motion of the vortex. Turbulence stress levels vary along the wake spiral in response to the varying rates of strain imposed by the vortex. Despite this complexity, the shape of the wake spiral and its turbulent structure reach an approximately self-similar form.On moving from the spiral wake to the core the overall level of velocity fluctuations greatly increases, but none of this increase is directly produced by turbulence. Velocity spectra measured at the vortex centre scale in a manner that implies that the core is laminar and that velocity fluctuations here are a consequence of inactive motion produced as the core is buffeted by turbulence in the surrounding spiral wake. Mean-velocity profiles through the core show evidence of a two-layered structure that dies away with distance downstream.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112096001929

The structure and development of a wing-tip vortex

▪ Abstract This review surveys the formation, motion, and persistence of trailing vortices as relevant to the safety and productivity of air travel. It highlights findings or shifts made since Widnall's (1975) review in this series. This review also examines the predictability of the vortices (particularly in terms of lifespan), the durability of multiple vortex pairs, the controversy between expectations of vortex decay and of vortex collapse, the many types of turbulence that may influence the flow, the rich interplay between the rotational and the axial velocity fields in the vortex, the various atmospheric and ground-related factors that dominate the late behavior, a few instances of wakes rising back, and the still unexplained bursting of the vortices. The article also briefly covers prospects for detection and control.

Airplane trailing vortices

Arguments are presented to show that the concept of gradient diffusion is inapplicable to mixing in turbulent shear layers. A new model is proposed for treating molecular mixing and chemical reaction in such flows at high Reynolds number. It is based upon the experimental observations that revealed the presence of coherent structures and that showed that fluid elements from the two streams are distributed unmixed throughout the layer by large-scale inviscid motions. The model incorporates features of the strained flame model and makes use of the Kolmogorov cascade in scales. Several model predictions differ markedly from those of diffusion models and suggest experiments for testing the two approaches.

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A Simple Model of Mixing and Chemical Reaction in a Turbulent Shear Layer

The tip vortex of a laminar flow wing was studied at a sectional lift‐to‐drag ratio of 60. The vortex Reynolds number was Γ0/ν=7.8×104, where Γ0 is the total circulation and ν is the kinematic viscosity. At and near the wing the vortex core was turbulent with an axial jet. Downstream of the wing the jet rapidly dissipated and a wake developed in the core and intensity of turbulent velocities decreased. From 13 to 40 chord length periodic oscillations dominated the velocity fluctuations with little background turbulence. These instabilities had a symmetric and a helical mode with wavelength of the same order as the core diameter. In this range of distances along the vortex core the maximum axial, swirl, and fluctuating velocities vary slowly. At 40 chord lengths behind the wing there is a rapid change in these velocities. This change of state of the vortex core is accompanied by change of velocity fluctuations from periodic to turbulent. The core showed spatial excursions. Measurements up to 80 chord lengths downstream showed no self‐similar decay.

Experiments on vortex stability

An ensemble of instantaneous temperature profiles across a two‐dimensional heated jet was obtained by shooting a fine platinum resistance thermometer across the jet at speeds much higher than the local velocity of the jet. Each recording of the ensemble was shifted to have a common center, and ensemble averages were obtained counting only the profiles for which the spatial location in question was inside the jet. This conditional averaging produced mean and mean‐square fluctuations which are quite flat across the jet, indicating that the fluid inside the jet is well‐mixed. Visual inspection of instantaneous records showed no cold spots in the jet. Ensemble averages were also measured by aligning the edge or beginning of the instantaneous profiles. This led to a sharper rise in the mean temperature profile and an overshoot in the mean‐square temperature fluctuations. This indicates that mixing across the turbulent‐nonturbulent interface is stronger than in the main body of the jet.

Param Indar Singh

Papers

Experiments on vortex stability

Turbulent mixing in a two‐dimensional jet