Valery Okulov

Helical vortices in swirl flow

Helical vortices in swirl flow are studied theoretically and experimentally. A theory of helical vortices has been developed. It includes the following results: an analytical solution describing an elementary helical vortex structure – an infinitely thin filament; a solution for axisymmetrical vortices accounting for the helical shape of vortex lines and different laws of vorticity distribution; a formula for calculation of the self-induced velocity of helical vortex rotation (precession) in a cylindrical tube; an explanation of the zone with reverse flow (recirculation zone) arising in swirl flows; and the classification of vortex structures. The experimental study of helical vortices was carried out in a vertical hydrodynamical vortex chamber with a tangential supply of liquid through turning nozzles. Various vortex structures were formed owing to changing boundary conditions on the bottom and at the exit section of the chamber. The hypothesis of helical symmetry is confirmed for various types of swirl flow. The stationary helical vortex structures are described (most of them for the first time) the features of which agree with the results and predictions of the theoretical model developed. They are the following: a rectilinear vortex; a composite columnar vortex; helical vortices screwed on the right or on the left; a vortex with changing helical symmetry; a double helix – two entangled vortex filaments of the same sign.

Stability of helical tip vortices in a rotor far wake

As a means of analysing the stability of the wake behind a multi-bladed rotor the stability of a multiplicity of helical vortices embedded in an assigned flow field is addressed. In the model the tip vortices in the far wake are approximated by infinitely long helical vortices with constant pitch and radius. The work is a further development of a model developed in Okulov ( J. Fluid Mech. , vol. 521, p. 319) in which the linear stability of N equally azimuthally spaced helical vortices was considered. In the present work the analysis is extended to include an assigned vorticity field due to root vortices and the hub of the rotor. Thus the tip vortices are assumed to be embedded in an axisymmetric helical vortex field formed from the circulation of the inner part of the rotor blades and the hub. As examples of inner vortex fields we consider three generic axial columnar helical vortices, corresponding to Rankine, Gaussian and Scully vortices, at radial extents ranging from the core radius of a tip vortex to several rotor radii. The analysis shows that the stability of tip vortices largely depends on the radial extent of the hub vorticity as well as on the type of vorticity distribution. As part of the analysis it is shown that a model in which the vortex system is replaced by N tip vortices of strength Γ and a root vortex of strength − N /Γ is unconditionally unstable.

Maximum efficiency of wind turbine rotors using Joukowsky and Betz approaches

On the basis of the concepts outlined by Joukowsky nearly a century ago, an analytical aerodynamic optimization model is developed for rotors with a finite number of blades and constant circulation distribution. In the paper, we show the basics of the new model and compare its efficiency with results for rotors designed using the optimization model of Betz.

Helical structure of longitudinal vortices embedded in turbulent wall-bounded flow

Embedded vortices in turbulent wall-bounded flow over a flat plate, generated by a passive rectangular vane-type vortex generator with variable angle β to the incoming flow in a low-Reynolds-number flow ( Re = 2600 based on the inlet grid mesh size L = 0.039 m and free stream velocity U ∞ = 1.0 ms −1 ), have been studied with respect to helical symmetry. The studies were carried out in a low-speed closed-circuit wind tunnel utilizing stereoscopic particle image velocimetry (SPIV). The vortices have been shown to possess helical symmetry, allowing the flow to be described in a simple fashion. Iso-contour maps of axial vorticity revealed a dominant primary vortex and a weaker secondary one for 20° ≤ β ≤ 40°. For angles outside this range, the helical symmetry was impaired due to the emergence of additional flow effects. A model describing the flow has been utilized, showing strong concurrence with the measurements, even though the model is decoupled from external flow processes that could perturb the helical symmetry. The pitch, the vortex core size, the circulation and the advection velocity of the vortex all vary linearly with the device angle β. This is important for flow control, since one thereby can determine the axial velocity induced by the helical vortex as well as the swirl redistributing the axial velocity component for a given device angle β. This also simplifies theoretical studies, e.g. to understand and predict the stability of the vortex and to model the flow numerically.

The velocity field induced by a helical vortex tube

The influence of finite-core thickness on the velocity field around a vortex tube is addressed. An asymptotic expansion of the Biot-Savart law is made to a higher order in a small parameter, the ratio of core radius to curvature radius, which consists of the velocity field due to lines of monopoles and dipoles arranged on the centerline of the tube. The former is associated with an infinitely thin core and is featured by the circulation alone. The distribution of vorticity in the core reflects on the strength of dipole. This result is applied to a helical vortex tube, and the induced velocity due to a helical filament of the dipoles is obtained in the form of the Kapteyn series, which augments Hardin’s [Phys. Fluids 25, 1949 (1982)] solution for the monopoles. Using a singularity-separation technique, a substantial part of the series is represented in a closed form for both the mono- and the dipoles. It is found from numerical calculation that the smaller the helix pitch is, the larger the relative influe...

Optical diagnostics of intermittent flows

The efficiency of combined use of different optical techniques for flow diagnostics is demonstrated with the practically important case of intense swirling flows. It is shown that, when applied separately, commonly used optical measuring techniques, such as laser Doppler anemometry and particle image velocimetry, frequently give erroneous results, especially for the transition flow and developed nonstationary flow. However, their combined use in diagnostics of unsteady (intermittent) flows significantly improves both the temporal and spatial resolution of measurements. Such a complex approach is for the first time applied for diagnostics of the flow pattern in a closed cylinder with a rotating end face with the aim of studying the changeover from the steady axisymmetric to unsteady asymmetric flow over a wide range of flow parameters. It is found that such a transition is notable for azimuthal disturbances with characteristic modes and frequencies.

PIV and LDA measurements of the wake behind a wind turbine model

In the present work we review the results of a series of measurements of the flow behind a model scale of a horizontal axis wind turbine rotor carried out at the water flume at Technical University of Denmark (DTU). The rotor is three-bladed and designed using Glauert theory for tip speed ratio λ =5 with a constant design lift coefficient along the span, CLdesign= 0.8. The measurements include dye visualization, Particle Image Velocimetry and Laser Doppler Anemometry. The wake instability has been studied in the range λ =3 – 9 at different cross-sections from the very near wake up to 10 rotor diameters downstream from the rotor. The initial flume flow was subject to a very low turbulence level with a uniform velocity profile, limiting the influence of external disturbances on the development of the inherent vortex instability. Using PIV measurements and visualizations, special attention was paid to detect and categorize different types of wake instabilities and the development of the flow in the near and the far wake. In parallel to PIV, LDA measurements provided data for various rotor regimes, revealing the existence of three main regular frequencies governing the development of different processes and instabilities in the rotor wake. In the far wake a constant frequency corresponding to the Strouhal number was found for the long-scale instabilities. This Strouhal number is in good agreement with the well-known constant that usually characterizes the oscillation in wakes behind bluff bodies. From associated visualizations and reconstructions of the flow field, it was found that the dynamics of the far wake is associated with the precession (rotation) of a helical vortex core. The data indicate that Strouhal number of this precession is independent of the rotor angular speed.

Flow diagnostics downstream of a tribladed rotor model

This paper presents results of a study of vortex wake structures and measurements of instantaneous 3D velocity fields downstream of a triblade turbine model. Two operation modes of flow around the rotor with different tip speed ratios were tested. Initially the wake structures were visualized and subsequently quantitative data were recorded through velocity field restoration from particle tracks using a stereo PIV system.The study supplied flow diagnostics and recovered the instantaneous 3D velocity fields in the longitudinal cross section behind a tribladed rotor at different values of tip speed ratio. This set of data provided a basis for testing and validating assumptions and hypothesis regarding classical theories of rotors.

Optimum operating regimes for the ideal wind turbine

We here present new results on the classical work of the optimum rotor. The emphasis is put vortex theory for which we have developed a new analytical method to determine the loading on an optimum win turbine rotor. The introduction of the work is a repetition of results using momentum theory. This is included in order to validate and compare the new model at simplified situations, such as a rotor operating without swirl and/or a rotor with infinite many blades.

Wake effect on a uniform flow behind wind-turbine model

LDA experiments were carried out to study the development of mean velocity profiles of the very far wake behind a wind turbine model in a water flume. The model of the rotor is placed in a middle of the flume. The initial flume flow is subjected to a very low turbulence level, limiting the influence of external disturbances on the development of the inherent wake instability. The rotor is three-bladed and designed using Glauerts optimum theory at a tip speed ratio λ =5 with a constant of the lift coefficient along the span, CL= 0.8. The wake development has been studied in the range of tip speed ratios from 3 to 9, and at different cross-sections from 10 to 100 rotor radii downstream from the rotor. By using regression techniques to fit the velocity profiles it was possible to obtain accurate velocity deficits and estimate length scales of the wake attenuation. The data are compared with different analytical models for wind turbine wakes.