Helmholtz Vortices Research Articles

Instability of separated shear layer around levitated freestream-aligned circular cylinder

In the present study, characteristics of a shear layer around a freestream-aligned circular cylinder and the relationship between the shear layer motion and the aerodynamic force were investigated under supportless condition. A 0.3-m magnetic suspension and balance system was employed, and experiments were conducted without a mechanical supporting device. Velocity fields were measured using particle image velocimetry with a sufficient temporal and spatial resolution, and high-frequency velocity fluctuations caused by small Kelvin–Helmholtz (KH) vortices were captured. The power spectral densities of velocity fluctuations represent phenomena such as KH vortex convection, vortex pairing, and convection of multiple vortices. Furthermore, fluctuations of the shear layer position were investigated. The results illustrate that the dominant frequency of the shear layer position is lower than the frequency of the velocity, and it shows good agreement with the characteristic frequency of lift force fluctuations. The present results together with the report in the previous study illustrate that the pressure fluctuations are considered to drive both fluctuations of the shear layer position and lateral aerodynamic force.

Turbulent flow over a cylinder confined in a channel at Re = 3,900

This paper presents data from numerical simulation of the flow over a cylinder confined in a channel at Reynolds number of 3,900. Direct numerical simulation (DNS) of the flow field from blockage ratio of 0 (i.e. the canonical flow over an unconfined cylinder) up to blockage ratio of 0.7 have been performed. At large blockage ratios, an adverse pressure gradient develops and the boundary layer on the channel walls separates and interacts with the cylinder wake. It is observed that the interaction gives rise to complex flow dynamics, affecting the size of the wake, making the wake asymmetric and also resulting in a decrease in the intensity of the turbulent fluctuations in the shear layer. Analysis of the spectra of the turbulent near wake shows an increase of the shedding frequency of the Kármán vortices as blockage ratio is increased. This occurs up to around blockage ratio of 0.7 where it is observed that the formation and shedding of coherent Kármán vortices no longer occur. For all except the blockage ratio of 0.5 case, the frequency of the shear layer is well approximated by the natural frequency of the shear layer instabilities obtained from linear stability theory. In all of these cases, there is a peak of energy associated with subharmonics of the shear layer frequency indicating pairing of the Kelvin–Helmholtz vortices in the shear layer.

Characteristics of enhanced mixing induced by plate jet actuation in supersonic flow

The fast and efficient mixing of fuel and oxidizers under supersonic conditions is of great importance for improving the performance of scramjet engines. The mixing process in the inner flow of a scramjet combustor is heavily inhibited by compressibility effects. In this paper, the novel strategy of plate jet actuation is proposed, and its effects on mixing augmentation are analyzed by employing numerical programs developed in-house. The fine vortex structures induced by the plate jet actuation are well captured, and the dynamic behaviors of newly observed T-shaped structures are analyzed in detail. It is found that in plate jet actuation flow, Kelvin–Helmholtz (K–H) vortices induced by K–H instability coexist with T-shaped structures induced by jet actuation instability. The interaction of adjacent T-shaped structures leads to the distortion and breakup of large-scale structures, which can obviously improve the interfaces of upper and lower streams. The distribution of the turbulence intensity along the streamwise direction suggests that with the introduction of plate jet actuation, more intense fluctuations occur in the flow. The growth process of mixing layer thickness indicates that with plate jet actuation, a sharp increase in mixing thickness can be achieved in the near flow field. The results of structural topology analysis show that upper plate jet actuation can produce structures with larger sizes, and the distortion and penetration process of these structures can entrain more upper and lower streams into the mixing region. It is suggested that the present proposed strategy is a good candidate for mixing enhancement with the application of scramjet combustors.

Nudging-based data assimilation of the turbulent flow around a square cylinder

We investigate the estimation of the turbulent flow around a canonical square cylinder at $Re=22\,000$ based on temporally resolved but spatially sparse velocity data and solving the unsteady Reynolds-averaged Navier–Stokes (URANS) equations. Flow reconstruction from sparse data is achieved through the application of a nudging data assimilation technique. It involves the introduction of a feedback control term in the momentum equations which allows us to drive URANS predictions towards reference data, which are here extracted from a direct numerical simulation. Such a data assimilation approach induces negligible supplementary computational cost compared with that of a standard URANS simulation. The influence of the spatial resolution of the reference data on the reconstruction performances is systematically investigated. Using a spacing of the order of one cylinder length between data points, we already observe synchronisation of the low-frequency vortex shedding between the full reference flow and the one that is estimated by URANS. The present data assimilation procedure allows us to compensate for deficiencies in standard URANS calculations and leads to a significant decrease in temporal and spectral errors as computed by spectral proper orthogonal decomposition. Furthermore, high accuracy in terms of mean-flow prediction by URANS is achieved. When considering spacings between measurements that are of the order of the wavelength of the Kelvin–Helmholtz vortices, such phenomena in the shear layers at the top and bottom of the cylinder are correctly estimated, while they are not self-sustained in standard URANS. The influence of the structure of the feedback control term in the data assimilation procedure is also investigated.

Stacked Electron Diffusion Regions and Electron Kelvin–Helmholtz Vortices within the Ion Diffusion Region of Collisionless Magnetic Reconnection

Abstract The structure of the electron diffusion region (EDR) is essential for determining how fast the magnetic energy converts to plasma energy during magnetic reconnection. Conventional knowledge of the diffusion region assumes that the EDR is a single layer embedded within the ion diffusion region (IDR). This paper reports the first observation of two EDRs that stack in parallel within an IDR by the Magnetospheric Multiscale mission. The oblique tearing modes can result in these stacked EDRs. Intense electron flow shear in the vicinity of two EDRs induced electron Kelvin–Helmholtz vortices, which subsequently generated kinetic-scale magnetic peak and holes, which may effectively trap electrons. Our analyses show that both the oblique tearing instability and electron Kelvin–Helmholtz instability are important in three-dimensional reconnection since they can control the electron dynamics and structure of the diffusion region through cross-scale coupling.

Transition to chaos in a reduced-order model of a shear layer

The present work studies the nonlinear dynamics of a shear layer, driven by a body force and confined between parallel walls, a simplified setting to study transitional and turbulent shear layers. It was introduced by Nogueira & Cavalieri (J. Fluid Mech., vol. 907, 2021, A32), and is here studied using a reduced-order model based on a Galerkin projection of the Navier–Stokes system. By considering a confined shear layer with free-slip boundary conditions on the walls, periodic boundary conditions in streamwise and spanwise directions may be used, simplifying the system and enabling the use of methods of dynamical systems theory. A basis of eight modes is used in the Galerkin projection, representing the mean flow, Kelvin–Helmholtz vortices, rolls, streaks and oblique waves, structures observed in the cited work, and also present in shear layers and jets. A dynamical system is obtained, and its transition to chaos is studied. Increasing Reynolds number $Re$ leads to pitchfork and Hopf bifurcations, and the latter leads to a limit cycle with amplitude modulation of vortices, as in the direct numerical simulations by Nogueira & Cavalieri. Further increase of $Re$ leads to the appearance of a chaotic saddle, followed by the emergence of quasi-periodic and chaotic attractors. The chaotic attractors suffer a merging crisis for higher $Re$ , leading to a chaotic dynamics with amplitude modulation and phase jumps of vortices. This is reminiscent of observations of coherent structures in turbulent jets, suggesting that the model represents a dynamics consistent with features of shear layers and jets.

Large‐scale turbulent mixing at a mesoscale confluence assessed through drone imagery and eddy‐resolved modelling

AbstractConfluences are sites of intense turbulent mixing in fluvial systems. The large‐scale turbulent structures largely responsible for this mixing have been proposed to fall into three main classes: vertically orientated (Kelvin–Helmholtz) vortices, secondary flow helical cells and smaller, strongly coherent streamwise‐orientated vortices. Little is known concerning the prevalence and causal mechanisms of each class, their interactions with one another and their respective contributions to mixing. Historically, mixing processes have largely been interpreted through statistical moments derived from sparse pointwise flow field and passive scalar transport measurements, causing the contribution of the instantaneous flow field to be largely overlooked. To overcome the limited spatiotemporal resolution of traditional methods, herein we analyse aerial video of large‐scale turbulent structures made visible by turbidity gradients present along the mixing interface of a mesoscale confluence and complement our findings with eddy‐resolved numerical modelling. The fast, shallow main channel (Mitis) separates over the crest of the scour hole's avalanche face prior to colliding with the slow, deep tributary (Neigette), resulting in a streamwise‐orientated separation cell in the lee of the avalanche face. Nascent large‐scale Kelvin–Helmholtz instabilities form along the collision zone and expand as the high‐momentum, separated near‐surface flow of the Mitis pushes into them. Simultaneously, the strong downwelling of the Mitis is accompanied by strong upwelling of the Neigette. The upwelling Neigette results in ∼50% of the Neigette's discharge crossing the mixing interface over the short collision zone. Helical cells were not observed at the confluence. However, the downwelling Mitis, upwelling Neigette and separation cell interact to generate considerable streamwise vorticity on the Mitis side of the mixing interface. This streamwise vorticity is strongly coupled to the large‐scale Kelvin–Helmholtz instabilities, which greatly enhances mixing. Comparably complex interactions between large‐scale Kelvin–Helmholtz instabilities and coherent streamwise vortices are expected at other typical asymmetric confluences exhibiting a pronounced scour hole.

Dynamic mode decomposition and Koopman spectral analysis of boundary layer separation-induced transition

In the present work, dynamic mode decomposition (DMD) and Koopman spectral analysis are applied to flat plate particle image velocimetry experimental data. Experiments concerning separated-flow transition process were carried out in a test section allowing the variation of the Reynolds number (Re), the adverse pressure gradient (APG) and the free-stream turbulence intensity (Tu). The analysis accounts for two different Re numbers, two different Tu levels, and a fixed APG condition inducing flow separation, as it may occur in low pressure turbine-like conditions. For every flow condition, instantaneous velocity fields clearly show the formation of Kelvin–Helmholtz (KH) vortices induced by the KH instability. The most effective definition of the observable matrix for Koopman analysis able to characterize these vortices is addressed first for a reference Tu and Re number condition. Successively, the robustness of DMD and Koopman modal decomposition has been examined for different Tu levels and Re numbers. On a short time trace (10 KH periods), the Koopman analysis is shown to identify the proper KH vortex shedding frequency and wavelength for every condition tested, while DMD fails especially with low Tu and high Re. To validate the results on a longer time trace, a statistical analysis of the dominant unstable eigenvalues captured by the two procedures is successively performed considering several temporal blocks for different inflow conditions. Overall, the Koopman analysis always performs better than DMD since it finds a larger number of unstable eigenvalues at the KH instability frequency and wavelength.

On the Growth and Development of Non‐Linear Kelvin–Helmholtz Instability at Mars: MAVEN Observations

AbstractIn this study, we have analyzed Mars Atmosphere and Volatile EvolutioN (MAVEN) observations of fields and plasma signatures associated with an encounter of fully developed Kelvin–Helmholtz (K–H) vortices at the northern polar terminator along Mars' induced magnetosphere boundary. The signatures of the K–H vortices event are: (a) quasi‐periodic, “bipolar‐like” sawtooth magnetic field perturbations, (b) corresponding density decrease, (c) tailward enhancement of plasma velocity for both protons and heavy ions, (d) co‐existence of magnetosheath and planetary plasma in the region prior to the sawtooth magnetic field signature (i.e., mixing region of the vortex structure), and (e) pressure enhancement (minimum) at the edge (center) of the sawtooth magnetic field signature. Our results strongly support the scenario for the non‐linear growth of K–H instability along Mars’ induced magnetosphere boundary, where a plasma flow difference between the magnetosheath and induced‐magnetospheric plasma is expected. Our findings are also in good agreement with 3‐dimensional local magnetohydrodynamics simulation results. MAVEN observations of protons with energies greater than 10 keV and results from the Walén analyses suggests the possibility of particle energization within the mixing region of the K–H vortex structure via magnetic reconnection, secondary instabilities or other turbulent processes. We estimate the lower limit on the K–H instability linear growth rate to be ∼5.84 × 10−3 s−1. For these vortices, we estimate the instantaneous atmospheric ion escape flux due to the detachment of plasma clouds during the late non‐linear stage of K–H instability to be ∼5.90 × 1026 particles/s. Extrapolation of loss rates integrated across time and space will require further work.

Numerical research on effect of dislocated turbine rims on hot gas ingestion

The flow characteristics in the rim clearances of turbines are sensitive to the turbine rim structures. From this standpoint, rotor–stator cavity models with dislocated clearances are proposed in this study to reveal the effect of dislocated turbine rim lips on hot gas ingestion and the clearance flow characteristics. The results show that the rim clearance flow is unstable, and Kelvin–Helmholtz vortices are induced by the relatively large difference in circumferential velocity of the flow fields inside and outside the rim seal. Moreover, the dislocated turbine rim lips decrease the effectiveness of the rim seal. Ultimately, the responses of the flow characteristics to the dislocated rims are determined to be primarily reflected in the effect of the forward or backward step flow on the Kelvin–Helmholtz vortices in turbine rims.

Spatial and temporal dynamics of a supersonic mixing layer with a blunt base

A supersonic mixing layer with a blunt base is of practical significance to engineering. Two flow configurations with splitter thicknesses of 1 mm (TN) and 5 mm (TK) are simulated using large eddy simulation. The cluster-based network model (CNM) projects the supersonic mixing layer into a ten-centroid based low-dimensional dynamical system. The CNM’s outputs of TN and TK cases are compared in order to better understand the spatial and temporal physics. The given baseline case (TN) demonstrates a quasi-steady dynamics with a periodic visit between ten centroids. Each cluster occupies a nearly uniform space region and is also populated with equal probability. The CNM identifies ten centroids associated with these two flow regimes observed in the TK case: Kelvin–Helmholtz vortex and vortex pairing. According to the resolved centroids, increasing the thickness of the splitter plate complicates the flow structures and expands the high-dimensional state space. The CNM presents probable state transitions, revealing that the temporal dynamics in the whole field exhibits highly intermittent behaviors, with large shape modifications but small fluctuations in turbulent kinetic energy. In the near-wake field, the reattachment point and shock wave behave similarly that they move downstream and upstream alternatively. The blunt base supersonic mixing layer, in aggregate, increases the turbulent kinetic energy by 20.5%.

On the algebra and groups of incompressible vortex dynamics

An algebraic representation for 2D and 3D incompressible, inviscid fluid motion based on the continuous Nambu representation of Helmholtz vorticity equation is introduced. The Nambu brackets of conserved quantities generate a Lie algebra. Physically, we introduce matrix representations for the components of the linear momentum (2D and 3D), the circulation (2D) and the total flux of vorticity (3D). These quantities form the basis of the vortex-Heisenberg Lie algebra. Applying the matrix commutator to the basis matrices leads to the same physical relations as the Nambu bracket for this quantities expressed classically as functionals. Using the matrix representation of the Lie algebra we derive the matrix and vector representations for the nilpotent vortex-Heisenberg groups that we denote by VH(2) and VH(3). It turns out that VH(2) is a covering group of the classical Heisenberg group for mass point dynamics. VH(3) can be seen as central extension of the abelian group of translations. We further introduce the Helmholtz vortex group V(3), where additionally the angular momentum is included. Regarding application-oriented aspects, the novel matrix representation might be useful for numerical investigations of the group, whereas the vector representation of the group might provide a better process-related understanding of vortex flows.

Gravity currents propagating at the base of a linearly stratified ambient

Gravity currents produced from a full-depth lock release propagating at the base of a linearly stratified ambient are investigated by means of newly conducted three-dimensional high-resolution simulations in conjunction with corresponding two-dimensional simulations and laboratory experiments. A passive tracer is implemented in the simulations to quantitatively measure the energies associated with the current and the ambient. The density of heavy fluid within the lock is ρ̃C, the density in the ambient of depth H̃ varies linearly from ρ̃b at the bottom to ρ̃0 at the top, and the ambient has an intrinsic frequency Ñ. Attention is focused on the initial slumping stage, during which the gravity currents propagate at a constant velocity Ṽ and the internal Froude number is defined as Fr=Ṽ/ÑH̃. The dynamics of the subcritical gravity currents, i.e., Fr<1/π, and the supercritical gravity currents, i.e., Fr>1/π, are qualitatively different and are examined with the help of three-dimensional and two-dimensional high-resolution simulations. For the subcritical gravity currents, the flow is dominated by the internal wave, the Kelvin–Helmholtz vortices are inhibited, and the two-dimensional simulation agrees well with and serves as a good surrogate model for the three-dimensional simulation in the slumping stage. For the supercritical gravity currents, the Kelvin–Helmholtz vortices are pronounced and prone to breakup into three-dimensional structures in the slumping stage. On the one hand, for the supercritical gravity currents, the kinetic energy associated with the current and the potential energy associated with the ambient are accurately captured by the two-dimensional simulation. On the other hand, the transition distance for the slumping stage and dissipation rate in the system are underpredicted while the kinetic energy associated with the ambient and the potential energy associated with the current are overpredicted by the two-dimensional simulation for the supercritical gravity currents. Therefore, information derived from the two-dimensional simulation for the supercritical gravity currents must be treated with care. The high-resolution simulations in this study also complement the existing shallow-water formulation, which has been reported to agree well with the two-dimensional simulations with good physical assumptions and simple mathematical models.

Film cooling in the trailing edge cutback with different land shapes and blowing ratios

The cutback was widely used in advanced gas turbines to protect the trailing edge. The land was a main structure in the cutback region. Therefore, the present study describes a numerical investigation on the film cooling performance in the cutback region with various land shapes (straight- expanding land, arch- expanding land, contracting- expanding land and campaniform land) and blowing ratios (0.2, 0.8 and 1.25). According to the numerical validation, the detached eddy simulations agreed well with the experimental results compared to other turbulence models. The flow structure, film cooling effectiveness and total pressure loss in the cutback region were displayed. Results indicated that the main flow separation vortex, cooling separation vortex, Kelvin- Helmholtz vortex and counter rotating vortices were strongly associated with the land shape and blowing ratio. The Kelvin- Helmholtz vortex was invisible at low blowing ratio and was small at the campaniform land shape. The contracting- expanding land resulted in weak counter rotating vortices within the cutback region. The stronger counter-rotating vortices brought lower film cooling effectiveness. Therefore, the contracting- expanding land provided relatively high film cooling effectiveness for most blowing ratios. The different land shape also caused different total pressure losses both in the cooling passage and main flow.

Kinetic Features for the Identification of Kelvin–Helmholtz Vortices in In Situ Observations

Abstract The boundaries identification of Kelvin–Helmholtz vortices in observational data has been addressed by searching for single-spacecraft small-scale signatures. A recent hybrid Vlasov–Maxwell simulation of Kelvin–Helmholtz instability has pointed out clear kinetic features that uniquely characterize the vortex during both the nonlinear and turbulent stage of the instability. We compare the simulation results with in situ observations of Kelvin–Helmholtz vortices by the Magnetospheric Multiscale satellites. We find good agreement between simulation and observations. In particular, the edges of the vortex are associated with strong current sheets, while the center is characterized by a low value for the magnitude of the total current density and strong deviation of the ion distribution function from a Maxwellian distribution. We also find a significant temperature anisotropy parallel to the magnetic field inside the vortex region and strong agyrotropies near the edges. We suggest that these kinetic features can be useful for the identification of Kelvin–Helmholtz vortices in in situ data.

Shallow mixing layers between non-parallel streams in a flat-bed wide channel

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Large eddy simulation of the fluid–structure interaction in an abstracted aquatic canopy consisting of flexible blades

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Vortex system around a step cylinder in a turbulent flow field

The vortex system around the step surface of a step cylinder with a diameter ratio D/d=2 at Reynolds number (ReD) 3900 was investigated by directly solving the three-dimensional Navier–Stokes equations. Formation mechanisms and vortex dynamics of the complex vortex system were studied by performing a detailed investigation of both the time-averaged and instantaneous flow fields. For the time-averaged flow, including the known junction and edge vortices, in total, four horseshoe vortices were observed to form above the step surface in front of the upper small cylinder. The crossflow width of the four horseshoe vortices varies differently as they convect downstream. Moreover, we captured a pair of base vortices and a backside horizontal vortex in the rear part of the step surface behind the small cylinder. For the instantaneous flow, hairpin vortices were found to form between the legs of two counter-rotating horseshoe vortices located on the same side of the step cylinder. Furthermore, in the small step cylinder wake, Kelvin–Helmholtz vortices were observed to shed at an unexpectedly high shedding frequency.

SPOD analysis of noise-generating Rossiter modes in a slat with and without a bulb seal

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Resolvent-based predictions for turbulent flow over anisotropic permeable substrates

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