Three-dimensional Vortex Dynamics Research Articles

Flow-induced oscillations of pitching swept wings: stability boundary, vortex dynamics and force partitioning

We study experimentally the aeroelastic instability boundaries and three-dimensional vortex dynamics of pitching swept wings, with the sweep angle ranging from 0 $^\circ$ to 25 $^\circ$ . The structural dynamics of the wings are simulated using a cyber-physical control system. With a constant flow speed, a prescribed high inertia and a small structural damping, we show that the system undergoes a subcritical Hopf bifurcation to large-amplitude limit-cycle oscillations (LCOs) for all the sweep angles. The onset of LCOs depends largely on the static characteristics of the wing. The saddle-node point is found to change non-monotonically with the sweep angle, which we attribute to the non-monotonic power transfer between the ambient fluid and the elastic mount. An optimal sweep angle is observed to enhance the power extraction performance and thus promote LCOs and destabilize the aeroelastic system. The frequency response of the system reveals a structural-hydrodynamic oscillation mode for wings with relatively high sweep angles. Force, moment and three-dimensional flow structures measured using multi-layer stereoscopic particle image velocimetry are analysed to explain the differences in power extraction for different swept wings. Finally, we employ a physics-based force and moment partitioning method to correlate quantitatively the three-dimensional vortex dynamics with the resultant unsteady aerodynamic moment.

Three-dimensional vortex dynamics and transitional flow induced by a circular cylinder placed near a plane wall with small gap ratios

The flow past a cylinder in proximity to a plane wall is investigated numerically for small gap ratios. Three vortex dynamic processes associated with different hairpin vortex generation mechanisms are identified for the first time, and the wake-induced turbulent transition is analysed. The vortex shedding is suppressed at $G/D = 0.1$ , while the spanwise vortex is generated via a Kelvin–Helmholtz instability and evolves into hairpin vortices. For $G/D= 0.3$ , the upper and lower rollers alternatively shedding from the cylinder, interact with the secondary vortex. The split secondary vortex merges with the upper roller and results in a new vortex downstream, which develops into hairpin vortices. When $G/D = 0.9$ , the secondary vortex interacts with the lower roller and then evolves into hairpin vortices. A tertiary vortex induced by the secondary vortex is observed, rotating in the opposite direction to the secondary vortex the wake-induced transitions share the same route. The velocity fluctuations deviate from the optimal growth theory in the pre-transitional region. In the transitional region low-frequency disturbances penetrate the sheltering edge to generate streaks where the disturbance energy declines. In the turbulent region the logarithmic layer is formed, indicating that the turbulent equilibrium is established.

Random vortex dynamics via functional stochastic differential equations

In this paper, we present a novel, closed, three-dimensional random vortex dynamics system, which is equivalent to the Navier–Stokes equations for incompressible viscous fluid flows. The new random vortex dynamics system consists of a stochastic differential equation which is, in contrast with the two-dimensional random vortex dynamics equations, coupled to a finite-dimensional ordinary functional differential equation. This new random vortex system paves the way for devising new numerical schemes (random vortex methods) for solving three-dimensional incompressible fluid flow equations by Monte Carlo simulations. In order to derive the three-dimensional random vortex dynamics equations, we have developed two powerful tools: the first is the duality of the conditional distributions of a couple of Taylor diffusions, which provides a path space version of integration by parts; the second is a forward type Feynman–Kac formula representing solutions to nonlinear parabolic equations in terms of functional integration. These technical tools and the underlying ideas are likely to be useful in treating other nonlinear problems.

An investigation of bluff body flow structures in variable velocity flows

The present study explores three-dimensional vortex-dynamics past a wall-attached bluff body kept in a variable velocity field with numerical simulations. A trapezoidal pulse of mean velocity, consisting of acceleration phase from rest followed by constant velocity phase and deceleration phase to rest, is imposed at the inlet of the computational domain similar to the experimental study of Das et al. [“Unsteady separation and vortex shedding from a laminar separation bubble over a bluff body,” J. Fluids Struct. 40, 233–245 (2013)]. For a wide range of Reynolds numbers (96≤Reb≤2390), acceleration Reynolds numbers (196≤Rea≤978), and deceleration Reynolds numbers (310≤Red≤1522), different stages of flow evolution are systematically analyzed. The flow evolution starts with the formation of a primary vortex followed by a two-dimensional circular array of spanwise vortex tubes by inflectional shear-layer instability. At a sufficiently high Reynolds number, the shear layer vortices originated from two-dimensional fluctuations deformed by three-dimensional instabilities, giving fragmented streamwise vorticity. In addition, long-wavelength “tongue-like structures” and short-wavelength “rib-like structures” are evident near the top wall and the bluff body, respectively. The streamwise vorticity generation equation indicates that the spanwise vortex tubes initially tilt, resulting in streamwise vorticity, further amplified by the vortex stretching process. The distinct flow features, including mode shape, frequency, and growth rate associated with the shear-layer instability, are identified using the dynamic mode decomposition (DMD) algorithm. Using the maximum growth rate criteria, the DMD technique successfully separates the coherent shear layer modes associated with two-dimensional shear layer instability from the flow field.

Wakes of rotorcraft in advancing flight: A large-eddy simulation study

We perform the large-eddy simulation of the flow past a helicopter rotor to support the investigation of rotorcraft wake characteristics and decay mechanisms. A hybrid Lagrangian–Eulerian vortex particle–mesh method is employed to simulate the wake development with the blades modeled using immersed lifting lines. The validity of the numerical approach is first evaluated through a comparison of the rotor trim parameters with experimental results. Then, the rotor wake at low, medium, and high advance ratios is simulated up to 30 rotor diameters. The wake generation and roll-up are described (i) qualitatively using rotor polar plots and three-dimensional (3D) vortex dynamics visualizations and (ii) quantitatively using classical integral diagnostics in cross sections. The highly 3D unsteady near wake transitions to a system dominated by two parallel vortices over a distance that depends on the advance ratio. This process is accelerated by the multiple interactions between successive tip vortices, supporting the generation of self-induced turbulence and uncovering a mechanism of vorticity alignment along the streamwise axis. The vortices in the far wake are compared to typical aircraft ones and exhibit less compact cores and faster decaying energy. Finally, we illustrate the loss of time periodicity in the far wake using the power spectral density of the kinetic energy, and the backscattering of energy from high rotor harmonics to lower frequencies, as complementary evidence of the intense vortex interaction activity.

The role of rotary motion on vortices in reverse flow

The physics of a rotary wing in forward flight are highly complex, particularly when flow separation is involved. The purpose of this work is to assess the role of three-dimensional (3-D) vortex dynamics, with a focus on Coriolis forces, in the evolution of vortices in the reverse flow region of a rotating wing. High-fidelity numerical simulations were performed to recreate the flow about a representative rotating wing in forward flight. A vorticity transport analysis was performed to quantify and compare the magnitudes of 2-D flow physics, vortex tilting and Coriolis effects in the resulting flow fields. Three-dimensional vortex dynamics was found to have a very small impact on the growth and behaviour of vortices in the reverse flow region; in fact, the rate of vortex growth was successfully modelled using a simple 2-D vortex method. The small role of 3-D physics was attributed to the Coriolis and vortex tilting terms being approximately equal and opposite to one another. This ultimately lead to vortex behaviour that more closely resembled a surging wing as opposed to a conventional rotating wing, a feature unique to the reverse flow region.

A scaling for vortex formation on swept and unswept pitching wings

We examine the dynamics of the leading-edge vortex (LEV) on a rapidly pitching plate with the aim of elucidating the underlying flow physics that dictates the stability and circulation of the LEV. A wide variety of flow conditions is considered in the present study by systematically varying the leading-edge sweep angle ($\unicode[STIX]{x1D6EC}=0^{\circ }$,$11.3^{\circ }$,$16.7^{\circ }$) and the reduced frequency ($f^{\ast }=0.064{-}0.151$), while keeping the pitching amplitude and the Reynolds number fixed. Tomographic particle image velocimetry is used to characterise the three-dimensional fluid motion inside the vortex core and its relation to the LEV stability and growth. A series of control volume analyses are performed to quantify the relative importance of the vorticity transport phenomena taking place inside the LEV to the overall vortex development. We show that, near the wing apex where tip effects can be neglected, the vortex develops in a nominally two-dimensional manner, despite the presence of inherently three-dimensional vortex dynamics such as vortex stretching and compression. Furthermore, we demonstrate that the vortex formation time and circulation growth are well-described by the principles of optimal vortex formation number, and that the occurrence of vortex shedding is dictated by the relative energetics of the feeding shear layer and the resulting vortex.

Aeroacoustic source mechanisms of a wavy leading edge undergoing vortical disturbances

High-accuracy numerical simulations are performed to study aeroacoustic source mechanisms of wavy leading edges (WLEs) on a thin aerofoil undergoing vortical disturbances. This canonical study is based on a prescribed spanwise vortex travelling downstream and creating secondary vortices as it passes through the aerofoil’s leading edge. The primary aim of the study is to precisely understand the relationships between the vortex-induced velocity perturbation and the wall pressure fluctuation on the WLE geometry. It is observed that by increasing the size (amplitude) of the WLE the source strength at the peak region is reduced rapidly to a certain point, followed by a saturation stage, while at the root (trough) it remains fairly consistent regardless of the WLE size. This observation is demonstrated to be the consequence of three-dimensional vortex dynamics taking place along the WLE. One of the most profound features is that a system of horseshoe-like secondary vortices are created from the WLE peak region upon the impingement of the prescribed vortex. It is found that the horseshoe vortices produce a significantly non-uniform velocity perturbation in front of the WLE leading to the disparity in the source characteristics between the peak and root. The alterations to the impinging velocity perturbation are carefully analysed and related to the wall pressure fluctuation in this study. In addition, a semi-analytic model based on Biot–Savart’s law is developed to better understand and explain the role of the horseshoe vortex systems and the source mechanisms.

An acentric rotation of two helical vortices of the same circulations

The aim of this paper is to test the possibility of a secondary solution of the acentric rotation of helical vortex pairs with the same pitch, sign and strength. The investigation addresses the three-dimensional vortex dynamics of thin vortex filaments. As a result of the current investigation, this secondary solution with acentric vortex positions in the helical pairs is found. This fact was not discussed in previous studies, and the existence of the new equilibrium solution for the helical vortex pairs is an original result.

Large-eddy simulation and wind-tunnel measurement of aerodynamics and aeroacoustics of a horizontal-axis wind turbine

Large-eddy simulation of the whole three-dimensional vortex dynamics and noise radiation around a horizontal-axis wind turbine has been studied and analyzed together with wind-tunnel experimental measurement. A computational framework that takes into account of the true shape of the wind turbine blade geometry for calculating the aerodynamics and aeroacoustics is developed and validated against the experimental data. The LES results generally agree well with the experimental data in terms of both the aerodynamics and aeroacoustics statistics. The formation and development of the complex three-dimensional wake vortexes are captured and analyzed, and the aerodynamic noise is further studied based on the flow field using the FW–H method. It is found that noise generation and acoustic radiation are closely associated with the generation and evolution of these vortex structures. The blade tip region is the main resource area of the aero-noise and the acoustic radiation intensity of the rotor decreases rapidly downstream.

Analysis of vortex splitting characteristics in the wake of an inclined flat plate using Hilbert–Huang transform

Three-dimensional vortex dynamics in the wake behind a flat plate at 20○ angle of attack are explored by means of the Hilbert–Huang transform. While a completely regular vortex shedding is observed at Reynolds number Re = 500 with a distinct shedding frequency and only a single subharmonic frequency, a complex shedding behavior is observed at Re = 525 and above. The low-frequency variations of the energy content and frequency in time are deduced from the Hilbert spectra. The low-frequency modulations along the span of the plate are substantially increased from Re = 525 to Re = 800. The mean marginal spectra reveal that the energy in the low-frequency band increases with increasing Re. A corresponding reduction of the energy content in the high-frequency band is observed at the highest Reynolds number.

Three-dimensional vortex dynamics and convective heat transfer in circular and chevron impinging jets

This paper describes an experimental investigation at Reynolds number equal to 5000 on circular and chevron impinging jets by means of time-resolved tomographic particle image velocimetry (TR-TOMO PIV) and infrared (IR) thermography. TR-TOMO PIV experiments are performed at kilo-hertz repetition rate in a tailored water jet facility where a plate is placed at a distance of 4 diameters from the nozzle exit. Using air as working fluid, time-averaged convective heat transfer is measured on the impinged plate by means of IR thermography with the heated-thin-foil heat transfer sensor for nozzle-to-plate distances ranging from 2 to 10 diameters. The circular impingement shows the shedding and pairing of axisymmetric toroidal vortices with the later growth of azimuthal instabilities and counter-rotating streamwise vortices. In the chevron case, instead, the azimuthal coherence is replaced by counter-rotating pairs of streamwise vortices that develop from the chevron notches. The heat transfer performances of the chevron impingement are compared with those of the circular one, analyzing the influence of the nozzle-to-plate distance on the distribution of Nusselt number. The chevron configuration leads to enhanced heat transfer performances for all the nozzle-to-plate distances hereby investigated with improvements up to 44% at the center of the impinged area for nozzle-to-plate distance of 4. Such enhancements are discussed in relation to the streamwise structures that, compared with the toroidal vortices, are associated with an earlier penetration of turbulence towards the jet axis and a higher arrival speed.

Three-dimensional vortex dynamics in oscillatory flow separation

The dynamics of coherent columnar vortices and their interactions in an oscillatory flow past an obstacle are examined experimentally. The main focus is on the low Keulegan–Carpenter number range (0.2 < KC < 2), where KC is the ratio between the fluid particle excursion during half an oscillation cycle and the obstacle size, and for moderate Reynolds numbers (700 < Rev < 7500). For this parameter range, a periodic unidirectional vortex pair ejection regime is observed, in which the direction of vortex propagation is set by the initial conditions of the oscillations. These vortex pairs provide a direct mechanism for the transfer of momentum and enstrophy to the outer region of rough oscillating boundary layers. Vortices are observed to be short-lived relative to the oscillation time scale, which limits their propagation distance from the boundary. The instability mechanisms leading to vortex decay are elucidated via flow visualizations and digital particle image velocimetry (DPIV). Dye visualizations reveal complex three-dimensional vortex interactions resulting in rapid vortex destruction. These visualizations suggest that one of the instabilities affecting the spanwise vortices is an elliptical instability of the strained vortex cores. This is supported by DPIV measurements which identify the spatial structure of the perturbations associated with the elliptical instability in the divergence field. We also identify regions in the periphery of the vortex cores which are unstable to the centrifugal instability. Vortex longevity is quantified via a vortex decay time scale, and the results indicate that vortex pair lifetimes are of the order of an oscillation period T.

Birth of three-dimensionality in a pulsed jet through a circular orifice

The pulsed flow about a circular non-centred orifice inside a cylindrical duct is analysed to obtain insight into the basic three-dimensional vortex dynamics that may be expected behind natural cardiac valves. The problem is approached by a highresolution numerical simulation. Results show how a small finite eccentricity generates af ully three-dimensional vortex wake that evolves quite differently from that found under an axisymmetric approximation. The flow field is analysed in terms of velocity and vorticity fields. The vortex wake structure is that of an initially quasi-axisymmetric vortex ring that progressively deforms into a three-dimensional structure, and whose vortex lines tend to reconnect with the boundary-layer-induced vorticity. The vortex structure explains secondary circulation and the presence of a diastolic backflow jet localized behind the longer orifice edge, in agreement with previous experimental observations. Possible relevance of the results to flows of cardiovascular interest is discussed.

Three-Dimensional Vortex Dynamics in a Shear-Driven Rectangular Cavity

We investigate the vortical flow structure which has evolved in a rectangular cavity defined by a depth-to-width aspect ratio of 1:1 and a span-to-width aspect ratio of 3:1. The vortical system of interest consists of a dominant eddy, secondary motions, and spiraling spanwise motion. The objective of this study was to broaden knowledge of: 1) how the Taylor-Görtler vortices emerge and modify the flow structure; 2) why the left vortex differs from its right counterpart in each unsymmetric pair of TGL vortices. Most importantly, the intent of this study is to discuss the formation of flow instabilities from the energy standpoint.

Nonlinear axisymmetric and three-dimensional vorticity dynamics in a swirling jet model

The mechanisms of vorticity concentration, reorientation, and stretching are investigated in a simplified swirling jet model, consisting of a line vortex along the jet axis surrounded by a jet shear layer with both azimuthal and streamwise vorticity. Inviscid three-dimensional vortex dynamics simulations demonstrate the nonlinear interaction and competition between a centrifugal instability and Kelvin–Helmholtz instabilities feeding on both components of the base flow vorticity. Under axisymmetric flow conditions, it is found that the swirl leads to the emergence of counter-rotating vortex rings, whose circulation, in the absence of viscosity, can grow without bounds. Scaling laws are provided for the growth of these rings, which trigger a pinch-off mechanism resulting in a strong decrease of the local jet diameter. In the presence of an azimuthal disturbance, the nonlinear evolution of the flow depends strongly on the initial ratio of the azimuthal and axisymmetric perturbation amplitudes. The long term dynamics of the jet can be dominated by counter-rotating vortex rings connected by braid vortices, by like-signed rings and streamwise braid vortices, or by wavy streamwise vortices alone.

Three-dimensional vorticity dynamics in a swirling jet

Three-dimensional aspects of vorticity concentration, reorientation, and stretching are investigated in a simplified swirling jet model, consisting of a line vortex along the jet axis surrounded by a jet shear layer with both azimuthal and streamwise vorticity. Inviscid three-dimensional vortex dynamics simulations demonstrate the nonlinear interaction and competition between a centrifugal instability and Kelvin-Helmholtz instabilities feeding on both components of the base flow vorticity. The nonlinear evolution of the flow depends strongly on the initial ratio of the azimuthal and axisymmetric perturbation amplitudes. The long term dynamics of the jet can be dominated by counterrotating vortex rings connected by braid vortices, by like-signed rings and streamwise braid vortices, or by wavy streamwise vortices alone.

EXPERIMENTAL AND NUMERICAL STUDY OF THE ATOMIZATION OF A PLANAR LIQUID SHEET

The disintegration of a water sheet into a spray has been studied with the objective of improving the understanding of the fundamental mechanisms of atomization. Flow visualization, frequency analysis, and LDV are used to identify and characterize the importance of vortex interactions in the atomization process, reflected in the formation of liquid filaments. A three-dimensional vortex dynamics simulation has been developed to model the instability growth in the flow. Preliminary results support the hypothesis that it is the interaction between the vorticity generated by the high-speed air and the vorticity present inside the liquid sheet, generated in the nozzle, which leads to complex disintegration phenomena.

Free vortex calculations using analytical/numerical matching with solution pyramiding

The motion of a free vortex system is predicted using a novel method called analytical/numerical matching (ANM). Analytical/numerical matching is a hybrid mathematical and numerical technique that results in a new problem formulation with high accuracy and increased computational efficiency. The approach capitalizer on the disparity of characteristic length scaler that occur in many fluid dynamics problems. Accordingly, many problems can be decomposed into two distinct problems involving a local high-resolution near field, often solvable analytically, end a global, low-resolution far field, solved numerically. The ANM technique breaks the free vortex problem into these local and global problems each of which are easier end more efficient to solve than the traditional problem formulation. In addition, the ANM decomposition can be repeated to form a hierarchy of nested problems of increasing resolution using a method called pyramiding. The ANM method with pyramiding, called ANM/P, is studied to assess its accuracy and computational efficiency for two-dimensional and three-dimensional vortex dynamics problems. In calculations of vortex sheet rollup end vortex ring motion and interactions, this method war found to be relatively easy to implement end exhibited reductions in computational time from a factor of three to more than an order of magnitude

Three-dimensional vortex dynamics in a rectangular sudden expansion

A detailed experimental study of flow in a rectangular sudden expansion using both active and passive forcing techniques has been made. The configuration consists of a 2:1-aspect-ratio rectangular channel which undergoes a sudden expansion such that the backward-facing step height (h) is uniform, and equal to the minor side of the inlet channel. Passive forcing was provided by the system geometry; the rectangular vortex rings formed in the shear layer of the expanding jet undergo self-induction, deforming the jet cross-section and introducing transverse velocities not found in plane or axisymmetric configurations. Active forcing was induced by periodic fluctuations in the system flow rate at the jet natural frequency. This served to enhance the unusual three-dimensional effects and phase-lock the flow for ensemble analysis. The results presented here include a description of the evolution of an isolated vortex in this configuration obtained from flow visualization of a suddenly started jet, as well as forced steady-state three-component velocity measurements which are used to characterize the flow field. The evolution of a rectangular vortex ring in the jet shear layer is traced, and both fluctuating and time-constant transverse velocities are related to the passage of the vortex structures.