Interaction Of Vortex Structures Research Articles

CABARET scheme in velocity-pressure formulation for two-dimensional incompressible fluids

The CABARET method was generalized to two-dimensional incompressible fluids in terms of velocity and pressure. The resulting algorithm was verified by computing the transport and interaction of various vortex structures: a stationary and a moving solitary vortex, Taylor-Green vortices, and vortices formed by the instability of double shear layers. Much attention was also given to the modeling of homogeneous isotropic turbulence and to the analysis of its spectral properties. It was shown that, regardless of the mesh size, the slope of the energy spectra up to the highest-frequency harmonics is equal ?3, which agrees with Batchelor's enstrophy cascade theory.

The role of wake stiffness on the wake-induced vibration of the downstream cylinder of a tandem pair

AbstractWhen a pair of tandem cylinders is immersed in a flow the downstream cylinder can be excited into wake-induced vibrations (WIV) due to the interaction with vortices coming from the upstream cylinder. Assi, Bearman & Meneghini (J. Fluid Mech., vol. 661, 2010, pp. 365–401) concluded that the WIV excitation mechanism has its origin in the unsteady vortex–structure interaction encountered by the cylinder as it oscillates across the wake. In the present paper we investigate how the cylinder responds to that excitation, characterising the amplitude and frequency of response and its dependency on other parameters of the system. We introduce the concept ofwake stiffness, a fluid dynamic effect that can be associated, to a first approximation, with a linear spring with stiffness proportional to$\mathit{Re}$and to the steady lift force occurring for staggered cylinders. By a series of experiments with a cylinder mounted on a base without springs we verify that such wake stiffness is not only strong enough to sustain oscillatory motion, but can also dominate over the structural stiffness of the system. We conclude that while unsteady vortex–structure interactions provide the energy input to sustain the vibrations, it is the wake stiffness phenomenon that defines the character of the WIV response.

On the use of time-resolved particle image velocimetry for the investigation of rod–airfoil aeroacoustics

The present study investigates an experimental methodology to determine aeroacoustic emission from vortex–structure interaction by means of Time-resolved Particle Image Velocimetry (TR-PIV). The aeroacoustic investigation is conducted on a rod–airfoil configuration at Re=6000 based on the rod diameter. The time-resolved velocity field obtained from 2D PIV is employed to evaluate the instantaneous planar pressure field by spatial integration of the Navier–Stokes equations under the assumption of 2D incompressible flow. The instantaneous pressure field computed on a control surface approximating that of the physical airfoil is used as source term of Curle's aeroacoustic analogy in both a distributed and a lumped formulation to obtain the far-field acoustic prediction. The spanwise coherence function of velocity and pressure fluctuations is determined by means of additional experiments, and is applied to weight the contributions at different frequencies. Results are compared with far-field microphone measurements in terms of spectra and directivity pattern. A good agreement is observed for the tonal component corresponding to the periodic interaction of the Kármán vortices with the airfoil leading edge. The contributions at higher frequencies also show an acceptable agreement when the spanwise coherence is taken into account.

Numerical and Experimental Studies on the Supersonic Coaxial Jet Mixing

Coaxial nozzles are an integral part of many engineering systems where mixing of different fluid streams is required. Single noncircular nozzles have been shown to have better mixing characteristics than their axisymmetric counterparts. Therefore, a combination of such nozzles into coaxial configurations is promising. The aim of the present study is to quantitatively determine the effects of the geometry of the primary supersonic jet on the mixing characteristics with the secondary high speed subsonic jet. Measurements of pressure profiles at several positions along central axis of jets using identical facilities and nominally identical experimental conditions were done. The mixing is dominated by the vortex structures that are present in the inner shear layers. The interaction of the vortex structures govern the growth, and entrainment, and mixing of the jet. Also, the experimental results show that the radial and centerline pressure profiles through various coaxial jets has good correlation with the CFD simulation.

Nonlinear dynamics of drift structures in a magnetized dissipative plasma

A study is made of the nonlinear dynamics of solitary vortex structures in an inhomogeneous magnetized dissipative plasma. A nonlinear transport equation for long-wavelength drift wave structures is derived with allowance for the nonuniformity of the plasma density and temperature equilibria, as well as the magnetic and collisional viscosity of the medium and its friction. The dynamic equation describes two types of nonlinearity: scalar (due to the temperature inhomogeneity) and vector (due to the convectively polarized motion of the particles of the medium). The equation is fourth order in the spatial derivatives, in contrast to the second-order Hasegawa-Mima equations. An analytic steady solution to the nonlinear equation is obtained that describes a new type of solitary dipole vortex. The nonlinear dynamic equation is integrated numerically. A new algorithm and a new finite difference scheme for solving the equation are proposed, and it is proved that the solution so obtained is unique. The equation is used to investigate how the initially steady dipole vortex constructed here behaves unsteadily under the action of the factors just mentioned. Numerical simulations revealed that the role of the vector nonlinearity is twofold: it helps the dispersion or the scalar nonlinearity (depending on their magnitude) to ensure the mutual equilibrium and, thereby, promote self-organization of the vortical structures. It is shown that dispersion breaks the initial dipole vortex into a set of tightly packed, smaller scale, less intense monopole vortices-alternating cyclones and anticyclones. When the dispersion of the evolving initial dipole vortex is weak, the scalar nonlinearity symmetrically breaks a cyclone-anticyclone pair into a cyclone and an anticyclone, which are independent of one another and have essentially the same intensity, shape, and size. The stronger the dispersion, the more anisotropic the process whereby the structures break: the anticyclone is more intense and localized, while the cyclone is less intense and has a larger size. In the course of further evolution, the cyclone persists for a relatively longer time, while the anticyclone breaks into small-scale vortices and dissipation hastens this process. It is found that the relaxation of the vortex by viscous dissipation differs in character from that by the frictional force. The time scale on which the vortex is damped depends strongly on its typical size: larger scale vortices are longer lived structures. It is shown that, as the instability develops, the initial vortex is amplified and the lifetime of the dipole pair components-cyclone and anticyclone-becomes longer. As time elapses, small-scale noise is generated in the system, and the spatial structure of the perturbation potential becomes irregular. The pattern of interaction of solitary vortex structures among themselves and with the medium shows that they can take part in strong drift turbulence and anomalous transport of heat and matter in an inhomogeneous magnetized plasma.

On the wake-induced vibration of tandem circular cylinders: the vortex interaction excitation mechanism

The mechanism of wake-induced vibrations (WIV) of a pair of cylinders in a tandem arrangement is investigated by experiments. A typical WIV response is characterized by a build-up of amplitude persisting to high reduced velocities; this is different from a typical vortex-induced vibration (VIV) response, which occurs in a limited resonance range. We suggest that WIV of the downstream cylinder is excited by the unsteady vortex–structure interactions between the body and the upstream wake. Coherent vortices interfering with the downstream cylinder induce fluctuations in the fluid force that are not synchronized with the motion. A favourable phase lag between the displacement and the fluid force guarantees that a positive energy transfer from the flow to the structure sustains the oscillations. If the unsteady vortices are removed from the wake of the upstream body then WIV will not be excited. An experiment performed in a steady shear flow turned out to be central to the understanding of the origin of the fluid forces acting on the downstream cylinder.

Two vortex interaction patterns in a turbine rotor

The article analyses the unsteady interaction of vortex structures in a turbine rotor passage. In the form of sample cases, two high pressure steam turbine stages are examined: a standard stage, used as the reference, which reveals regular performance characteristics and distributions of flow parameters, and a low-efficiency stage, in which a large separation zone is observed in the rear part of the rotor passage. In the latter case the combined interaction of all vortices has been found to take an extremely complex course and be a source of remarkable flow fluctuations. The methodology applied for extracting particular vortex structures from the general flow pattern bases on comparing entropy distributions with corresponding velocity vectors. The reported vortex interaction patterns are believed to be representative for a variety of turbine constructions of both land, and marine applications.

Interstage Flow Interactions and Loss Generation in a Two-Stage Shrouded Axial Turbine

The aerodynamics and kinematics of flow structures, including the loss generation mechanisms, in the interstage region of a two-stage partially shrouded axial turbine are examined. The nonaxisymmetric partial shroud introduces highly three-dimensional unsteady interactions, the details of which must be understood in order to optimize the design of the blade/shroud. Detailed measurements of the steady and unsteady pressure and velocity fields are obtained using a two-sensor fast response aerodynamic probe and stereoscopic particle image velocimetry. These intrusive and nonintrusive measurement techniques yield a unique data set that describes the details of the flow in the interstage region. The measurements show that a highly three-dimensional interaction occurs between the passage vortex and a vortex caused by the recessed shroud platform design. Flow coming from the blade passage suddenly expands and migrates radially upward in the cavity region, causing a localized relative total pressure drop. Interactions of vortex and wake structures with the second stator row are analyzed by means of the combination of the measured relative total pressure and nondeterministic pressure unsteadiness. The analysis of the data gives insight on unsteady loss mechanisms. This study provides improved flow understanding and suggests that the design of the blade/shroud and second stator leading edge may be further improved to reduce unsteady loss contribution.

About possible mechanisms of influence of gas bubbles on characteristics of turbulent boundary layer

Two different mechanisms responsible for the were revealed impact of gas bubbl injected into a boundary layer on the shear stress on the wetted surfaces. Both mechanisms exist due to extremely high sensitivity of bubbles even to very low pressure gradients and due to a high value of the virtual mass and coefficient of viscous drag for bubbles. The first mechanism manifests itself at the interaction of vortex structures with bubbles in the near-wall layer y+ < 250. The second mechanism is due to pressure gradient along the wetted surface. Ascertainment of these mechanisms explains the known discrepancies in the experimental results on gas saturation obtained on different experimental setups.

Variational principle for frozen-in vorticity interacting with sound waves.

General properties of conservative hydrodynamic-type models are treated from positions of the canonical formalism adopted for liquid continuous media. A variational formulation is found for motion and interaction of frozen-in localized vortex structures and acoustic waves in a special description where dynamical variables are, besides the Eulerian fields of the fluid density and the potential component of the canonical momentum, also the shapes of frozen-in lines of the generalized vorticity. This variational principle can serve as a basis for approximate dynamical models with reduced number of degrees of freedom.

Sediment suspension due to waves

A simulation of the turbulent flow and sediment dynamics in the boundary layer originated close to the seabed by a first‐order Stokes wave is performed. The flow field is obtained by the numerical integration of Navier‐Stokes and continuity equations while sediment trajectories are computed via a simplified model that assumes a one‐way coupling. Hence the results describe situations characterized by low concentrations and small values of the Stokes particle number. The investigation of the interaction of turbulent vortex structures with sediment shows that particles are picked up from the bed and carried into suspension when the low‐speed streaks start to break up and to generate small incoherent vortices that increase mixing effects. The low‐speed streaks are generated close to the seabed at the end of the accelerating phases, when the flow velocity is maximum, and breakdown during the decelerating phases of the cycle. The effects of turbulence structure and sediment characteristics on pickup and deposition rates are investigated and quantified by varying the values of the parameters which control the phenomenon.

Dynamics of Vortex Interactions in Two-Dimensional Flows

The dynamics and interaction of like-signed vortex structures in two dimensional flows are investigated by means of direct numerical solutions of the two-dimensional Navier–Stokes equations. Two vortices with distributed vorticity merge when their distance relative to their radius, d/R0, is below a critical value, ac. Using the Weiss-field, ac is estimated for vortex patches. Introducing an effective radius for vortices with distributed vorticity, we find that 3.3 < ac < 3.5 independently of the vorticity distribution. The evolution of spiral vorticity filaments in the merging process is effectively producing small scale structures and the relation to the enstrophy “cascade” in developed 2D turbulence is discussed. The influence of finite viscosity on the merging is also investigated. Additionally, we examine vortex interactions on a finite domain, and discuss the results in connection with the formation of “vortex crystals”.

A Nonlinear Dynamics Analysis of Vortex-Structure Interaction Models

Vortex-structure interaction models are studied in the work presented here. The third- order model by Hartlen and Currie (HC model) can reproduce the correct response amplitude, while a fifth-order model by Landl predicts the observed hysterisis effect. Using concepts from nonlinear dynamics and bifurcation theory, the range of possible dynamics of the models is investigated in parameter space; essentially, a class of nonlinear oscillators deriving “naturally” from the HC model is studied. It is found that perturbations of the HC model in parameter space lead to qualitatively physically meaningful dynamics. Forced excitation of the HC model is the highlight of the work. In this case, it is shown that a subharmonic lock-in predicted by the model may be related to a three-dimensional secondary subharmonic instability of a periodic flow. Experimental results are presented for comparison.

The study of vortex ring/wall interaction for artificial nose improvement

Normal and oblique collisions of a vortex ring with a wall have been studied experimentally and numerically with the aim of analyzing the interaction of vortex structures with the solid boundary and to understand the effect of the impact angle alpha and the Reynolds number Re on the development of the azimuthal instabilities. The application of such analysis is relevant, for instance, in systems for artificial olfaction (Davide et al., 1994). In fact these devices consist of a box having a sensor array at its bottom wall, devoted to detect the presence of certain substances in the test mixture. The efficiency of the sensor depends on the concentration of the substance that reaches the surface; this requires that the fluid injected in the box organizes into structures that arrive at the wall as much coherent as possible. The vortex ring has been chosen as the advecting structure because its high degree of coherence in the laminar range, allows the mixture to be transported on the sensing surface. During the impingement the vortex ring generates an oppositely-signed vortical layer and the mutual induction between the primary ring and the vorticity induced at the wall is the leading process for the eventual break-down of the structure. The eigenvalues of the velocity gradient tensor have allowed to study the stabilizing effect of impact angle through the topological features of the field. Finally the vortex structure identification allowed to study the vortex dynamics in the vicinity of the wall in order to perform a measure of the stability of the field.

A study of the numerical stability of the method of contour dynamics

The inviscid interaction of vortex structures has been studied extensively to elucidate many of the important features of high Reynolds number flows and turbulence. Contour dynamics was developed specifically to study the evolution of the boundaries of uniform vortices, and has been used to study a wide variety of flows. The method is a lagrangian one, and typically a discrete dynamical system is obtained by representing the boundary by a finite collection of points. We examine the linear stability features of a typical method by considering perturbations to a circular, uniform vortex. We find a spurious branch to the numerical dispersion relation that indicates points will oscillate along the boundary without any distortion in its shape. Numerical results for the full equations show that the amplitudes of these particular modes grow slowly in time.

Numerical simulations of acoustic-vortex interactions in a central-dump ramjet combustor

A potentially important source of large pressure oscillations in compact ramjets is a combustion instability induced by the interaction of large-scale vortex structures with the acoustic modes of the ramjet. These interactions have been studied using time-dependent, compressible numerical simulations of cold flow in an idealized ramjet consisting of an axisymmetric inlet and combustor. The simulations indicate a strong coupling between the flowfield and the acoustics of both the inlet and the combustor. Vortex rollup is observed near the entrance to the combustor at the first longitudinal acoustic mode of the combustor. A low-frequency mode is also observed in the simulations. This mode is determined by the acoustics of the inlet and causes major changes in the merging pattern of the vortices.