Two-dimensional Vortex Research Articles

Resonant excitation of single Kelvin–Helmholtz high-order waves in a magnetized electron fluid vortex

Thanks to the isomorphism between the drift-Poisson and Euler equations, inviscid two-dimensional fluid experiments can be performed in magnetized, single-component plasmas in Penning–Malmberg traps. Within this analogy, a trapped electron plasma column is equivalent to a two-dimensional vortex. Here, we focus our attention on the generation of V-states, i.e. $l$ -fold symmetric rotating vorticity patches where the deformation with respect to the circular cross-section has reached the nonlinear regime. We detail a linear theoretical analysis and devise an experimental routine to generate V-states through the precise excitation of single Kelvin–Helmholtz perturbations in a magnetized electron plasma. This technique makes use of suitable multipolar rotating electric fields, which are shown to be able to select the desired wavemode. In particular, with rotating fields, a hardware limitation in the highest accessible mode is removed and nonlinear Kelvin–Helmholtz waves of generic order $l$ can be attained, which pave the way for further investigations on the evolution and stability properties of V-states. Systematic experimental results for the selective mode growth in the linear and nonlinear regimes up to saturation and collapse are discussed.

Two Dimensional Vortex Shedding from a Rotating Cluster of Cylinders

The dynamics of two-dimensional vortex shedding from a rotating cluster of three cylinders was investigated using Computational Fluid Dynamics (CFD) and Dynamic Mode Decomposition (DMD). The cluster was formed from three circles with equal diameters in mutual contact and allowed to rotate about an axis passing through the cluster centroid. While immersed in an incompressible fluid with Reynolds number of 100, the cluster was allowed to rotate at non-dimensionalised rotation rates (Ω) between 0 and 1. The rotation rates were non-dimensionalised using the free-stream velocity and the cluster characteristic diameter, the latter being equal to the diameter of the circle circumscribing the cluster. CFD simulations were performed using StarCCM+. Dynamic Mode Decomposition based on the two-dimensional vorticity field was used to decompose the field into its fundamental mode-shapes. It was then possible to relate the mode-shapes to lift and drag. Transverse and longitudinal mode-shapes corresponded to lift and drag, respectively. Lift–drag polars showed a more complex pattern dependent on Ω in which the flow fields could be classified into three regimes: Ω less than 0.3, greater than 0.5, and between 0.3 and 0.5. In general, the polars formed open curves in contrast to those of static cylinders, which were closed. However, some cases, such as Ω = 0.01, 0.22, and 0.28, formed closed curves. Whether a lift-drag polar was closed or open was deduced to be determined by the ratio of Strouhal numbers calculated using lift and drag time series, with closed curves forming when the ratio is an integer.

Effects of spatial resolution of the data on dynamic mode decomposition and its quantitative analysis

Dynamic mode decomposition (DMD), based on Koopman analysis, is a tool capable of spatiotemporal analysis for various spatial resolutions, from one-dimensional signals to three-dimensional computational fluid dynamics (CFD) and experimental data. Outputs of the DMD consist of amplitudes, frequencies, decaying rates, and spatial modes. However, the effects of spatial resolution (time-series data in one-dimensional signal and spatial grid in two-dimensional data) and quantitative analysis of DMD are limited to one-dimensional signal data. In this study, the effects of spatial resolution with a fixed time scale of data and correction using scaling factors 2/A on DMD amplitudes and A on DMD spatial mode strengths are investigated, where A is the number of the time-series data in one-dimensional signal or the number of the spatial grid in two-dimensional data. First, proofs of the scaling factors for one-dimensional(line layout) and two-dimensional(grid layout) data are presented. Second, the effect of spatial resolution on the amplitudes and spatial mode strengths and their scaled results are confirmed using one-dimensional artificial signal data, two-dimensional artificial signal field data, two-dimensional vortex shedding simulation data, and two-dimensional pulsating flow experimental data with various data resolutions. The results show that the amplitude increases proportionally with the spatial resolution, and the spatial mode strength is inversely proportional to the time series or spatial resolution of the data in all cases. As a result of applying the scaling factors to one-dimensional artificial signal and two-dimensional artificial signal field data, the amplitudes and spatial modes contain the same values regardless of the change in spatial resolutions. The scaled amplitudes and spatial mode strengths on vortex shedding simulation and two-dimensional laminar pulsating jet show good agreements with slight differences, regardless of the spatial resolution change. The proposed scaling factor can be applied to compare data quantitatively obtained with different spatial resolutions.

A New Unsteady Flow Control Technology of Centrifugal Compressor Based on Negative Circulation Concept

The tip leakage vortex (TLV) induced by the tip clearance flow has a significant impact on the performance of centrifugal compressors, causing impeller flow losses and reducing the stall margin. To solve this problem, an unsteady flow control technology called the NCFC method is proposed based on the concept of negative circulation control, realized by a vortex generator placed in a tube connected with the shroud through a hole. The approach is derived from a theoretical study of the compressor TLV by introducing a two-dimensional vortex model. A numerical simulation is then performed to verify the effectiveness of the NCFC method. The result shows that the NCFC method can greatly stabilize the flow field at the blade tip and improve the stall margin and efficiency of the compressor without reducing the total pressure ratio of the compressor, which has the characteristics of both unsteadiness and negative circulation effect. In addition, a HC method with only unsteady excitation effect is also studied for comparison, which only slightly stabilizes the blade tip flow and increases the stall margin of the compressor, suggesting that the NCFC is more effective than the HC. Finally, it is highly recommended to improve the efficiency of any unsteady jet/suction and separation flow interaction.

Effective Lewis number and burning speed for flames propagating in small-scale spatio-temporal periodic flows

Propagation of premixed flames having thick reaction zones in rapidly-varying, small-scale, zero-mean, spatio-temporal periodic flows is considered. Techniques of large activation energy asymptotics and homogenization theory are used to determine the effective Lewis number Leeff and the effective burning speed ratio ST/SL, which are influenced by the flow through flow-enhanced diffusion. The resultant effective diffusivity matrix is, in general, neither a scalar nor a diagonal matrix and therefore induces anisotropic effects on the propagation of multi-dimensional flames. As the flow Peclet number Pe becomes large, the flow-enhanced fuel diffusion coefficient and the thermal diffusivity behave respectively like (PeLe)σ and Peσ, where Le is the Lewis number and σ≤2 is a constant which depends on the flow and the direction of flame propagation. The maximal value σ=2 is achieved for steady, unidirectional, spatially periodic shear flows, while for steady two-dimensional square vortices, we have σ=1/2. In general, the constant σ is determined by solving a linear partial differential equation. The scaling laws for the diffusion coefficients lead to corresponding scaling laws for the effective Lewis number and the effective burning speed ratio of the form Leeff≃Le1−σ and ST/SL∼(Pe/Le)σ/2. Effects of thermal expansion and volumetric heat loss on the flame are also briefly discussed. In particular, it is shown that the quenching limit is enlarged by a factor 1/Leσ for Le<1 and diminished by the same factor for Le>1, due to the flow-enhanced diffusion. The potential implications of the results to better understand turbulent combustion are discussed. A special emphasis is placed on the dependence of the flame on Le in the presence of high-intensity, small-scale flows. In particular, it is shown that this dependence is intimately linked to the flow through Taylor-dispersion like enhanced diffusion, rather than through the traditional molecular diffusion coupled with curvature effects. The flow-dependent effective Lewis number identified may also provide an explanation to the peculiar experimental observation that turbulence appears to facilitate ignition in Le>1 mixtures and to inhibit it in Le<1 mixtures. Novelty and significance statementAn original study, combining asymptotic analysis and homogenization theory, is applied to describe flame propagation in small-scale, spatio-temporal periodic flow fields. Scaling laws are derived for the effective burning speed and the effective Lewis number for high-intensity small-scale flows, which are useful to better understand the behaviour of turbulent premixed flames in the distributed reaction zone regime. The formula for the flow-dependent effective Lewis number identified herein may explain the peculiar experimental observation that turbulence appears to facilitate ignition in Le>1 mixtures and to inhibit it in Le<1 mixtures. The high-intensity small-scale flows are shown to increase the quenching limit due to volumetric heat losses in Le<1 mixtures and decrease it in Le>1 mixtures

Finite-Difference Frequency-Domain Scheme for Sound Scattering by a Vortex with Perfectly Matched Layers

Finite-Difference Frequency-Domain Scheme for Sound Scattering by a Vortex with Perfectly Matched Layers

Two-dimensional vortex dipole solitons in nonlocal nonlinearity with PT-symmetric Scarff-II potential.

We investigate the dynamics and stability of two-dimensional (2D) vortex dipole solitons in nonlocal nonlinearity with PT-symmetric Scarff-II potential. We analyze the solitons with single charge and higher-order charge using analytical and numerical methods. By the variational approach, we can obtain analytical solutions for the model. It is found that the nonlocality degree affects the evolution of the beams. We discover that the vortex dipole solitons will undergo stable deformation rather than maintaining their basic profile when the nonlocality is strong. Moreover, the stability of the vortex dipole solitons depends on the potential depth and there exists a threshold, below which the beams can keep their shapes and propagate stably whether the nonlocality is weak, intermediate, or strong. Numerical simulations are consistent with the analytical results.

Performance evaluation with turbulent flow and heat transfer characteristics in rectangular cooling channels with various novel hierarchical rib schemes

Turbulators, such as ribs, dimples, and pin-fins, play a vital role in the internal cooling efficiency of turbine blades. As a typical turbulator, various rib configurations using a uniform arrangement scheme have indicated high heat transfer enhancement but the friction loss is simultaneously subject to a great increase. In this work, a novel hierarchical arrangement scheme of ribs is developed aiming to improve the cooling efficiency. Adopting the uniform scheme as a baseline, the hierarchical scheme is implemented for six representative rib configurations (including transverse ribs, angled ribs, V-shaped ribs, inverted V-shaped ribs, M-shaped ribs, and inverted M-shaped ribs) and evaluated for its feasibility and generality. For different cooling designs, turbulent flow and heat transfer of the ribbed cooling channel are studied by three-dimensional numerical simulations based on the finite volume method with a constructed turbulence model. It is found that for all rib configurations, the hierarchical scheme can remarkably reduce the friction loss as desired, especially for the inverted V-shaped rib with a reduction of up to 50%. Due to the occurrence of flow separation, secondary flows offered by transverse ribs are characterized by a two-dimensional recirculation vortex behind the rib. For other rib configurations, secondary flows present a typical three-dimensional characteristic including the downwash flows along the inclined rib leg and the longitudinal vortices. The usage of the hierarchical scheme with small ribs strongly suppresses these secondary flows, which contributes to the significant decrease in form drag loss. Meanwhile, using the hierarchical scheme produces a slight heat transfer deterioration commonly, which is because the constrained secondary vortices weaken the turbulent mixing and convection heat transfer. Significantly, for the two W-shaped ribs, the limited secondary vortices but fully developed under the hierarchical scheme achieve a higher heat transfer enhancement. Finally, for all considered ribs, the hierarchical scheme can improve the overall performance factor of (Nu/Nu0)/(f/f0)1/3 by more than 10%, and up to 21.15% for the V-shaped rib. Adjusting design variables, including the decreasing ratio of the rib size and the initial rib size, the hierarchical scheme still provides even higher performance enhancement.

Suppression of vortex shedding in the wake of a circular cylinder through high-frequency in-line oscillation

This paper presents a new flow control approach to suppress the vortex shedding in the wake of a circular cylinder through high-frequency oscillation. The circular cylinder is forced to oscillate in the streamwise direction at high-frequency and low amplitude, corresponding to a high Stokes number (β = 100–1000) and low Keulegan–Carpenter number (KC = 0.001–4). Two-dimensional (2-D) and three-dimensional (3-D) direct numerical simulations of an oscillating circular cylinder in steady current have been carried out in the parameter space of KC, Rec, and β. Our numerical results show that when the flow remains in the two-dimensional vortex shedding regime, the cylinder wake sequentially experiences transitions from the vortex shedding regime to the suppression of the vortex shedding regime and finally to the symmetry breaking regime, with increasing KC. Corresponding wake characteristics and variations of hydrodynamic forces over the three wake regimes are explored. Three quantities that represent shear-layer characteristics, including the length of separating shear layers, the circulation of shear layers and wake recirculation length, reach maxima at the onset of suppression. The physical mechanisms for the suppression of vortex shedding and occurrence of symmetry breaking are also explained. Once the flow becomes 3-D, vortex shedding from the cylinder cannot be suppressed, primarily because the outer shear layers induced by the steady approaching flow are enhanced in 3-D flows. The cylinder oscillation over the frequency range investigated in the present study delays wake transition to 3-D. The cylinder oscillation alters the 3-D vortical structure and its spanwise wavelength significantly.

Singularity resolving in solution of the boundary integral equation in two-dimensional vortex methods

The problem of 2D incompressible flow simulation around airfoils with sharp edges and corner point is considered. The solution of the boundary integral equation with respect to vortex sheet intensity arising in Lagrangian vortex method has weak singularity that cannot be resolved correctly in the framework of the existing Galerkin-type numerical schemes. It is shown that for piecewise-smooth bounded solutions the known schemes allow for solution reconstruction with high quality and provide the 2-nd order of accuracy, while for singular solution their order of accuracy goes down to the 1-st. A numerical scheme is suggested that allows for solution singularity resolving and provides the 2-nd order of accuracy. As a model problem, the added mass tensor components computation is considered, since its exact value is known for the Joukowsky wing airfoil with sharp edge (cusp point).

An unsteady flow control technique based on negative circulation conception and its application to a blade-divergent passage

A two-dimensional vortex model is introduced in this paper in order to understand the characteristics of the shedding vortex in a blade-divergent passage and to mitigate or suppress it by appropriate methods. The performance of this model under the influence of three typical external factors is studied, namely, the main flow extrusion effect, viscous effect, and transport effect. Based on the analysis, a negative circulation unsteady flow control technique is proposed to compensate for the viscous effect, which is known as NCFC. Numerical simulation is performed to verify the effectiveness of the NCFC method. The results show that the NCFC method is superior to the conventional unsteady flow control for improving the performance of the blade-divergent passage in most cases. In addition, there is an optimum injection to suppress the shedding vortex with NCFC, which is about 0.2% of the main flow mass, and NCFC shows to be more efficient than conventional flow control in weakening the shedding vortex. Furthermore, NCFC can effectively inhibit separation flow and is shown to be insensitive to the injection flow mass. Finally, the NCFC method is highly recommended to adapt to the fact that the working conditions often change in practice.

The effect of central gap and wind screens on the aeroelastic stability of long-span bridge decks: Comparison of numerical analyses and experimental results

As long-span bridges are usually built at exposed locations and high winds can cause disruptions to traffic, relatively tall wind screens are often used to protect vehicles which are prone to suffer from wind induced accidents. This paper presents the results of a series of two-dimensional discrete vortex method simulations of laminar incompressible flow past standard aerofoil mono-boxes and twin-boxes, conducted to investigate the aerodynamic impact of wind screens on bridge decks in relation to steady-state and divergent instability (classical flutter) behaviour. A comparison against the outcome of a series of parametric wind tunnel tests is also presented. The quality of the agreement between the numerical simulations and the observed experimental behaviour is such that designers, under certain conditions, could rely on computational bridge aerodynamics at feasibility or early design stages to identify potential instabilities and introduce mitigation measures aimed at optimizing the aerodynamic performance of the deck.

Non-negative aeroacoustic source contributions to radiated sound power

A new approach that determines the contribution of aeroacoustic sources to sound power is presented. The method combines the Lighthill source distribution with an acoustic impedance matrix constructed from radiation kernels of the free-field Green's function. To demonstrate the technique, the flow noise produced by a pair of co-rotating vortices is examined. Results are initially compared with those obtained using Möhring's analogy of two-dimensional vortex sound radiation. The contribution to sound power for each component of the Lighthill tensor is presented for a range of wave numbers and vortex separation distances. For acoustically compact cases, the aeroacoustic source contributions for the diagonal components of the Lighthill tensor show a similar trend observed in sound maps for longitudinal quadruples. In contrast to the acoustically compact cases where the central focal area is mostly unchanged with variation in Mach number, significant variation in the focal areas occurs for non-acoustically compact cases. Using the aeroacoustic source contribution technique, the nature and location of dominant flow noise sources to sound power can be identified.

Modes of interaction of counterflow flames in diluted methane–oxygen mixtures in a closed reactor

The features of the interaction of counterflow flames in diluted methane–oxygen mixtures at a total pressure of up to 200 Torr in a closed reactor were established. It was found that in the mode of interaction of flames propagating in hot reaction products, two-dimensional flame vortices arise due to density stratification; flames, propagating through the initial mixture, interact with the formation of only three-dimensional structures.

Cross-stream migration of a vesicle in vortical flows.

We use numerical simulations to systematically investigate the vesicle dynamics in two-dimensional (2D) Taylor-Green vortex flow in the absence of inertial forces. Vesicles are highly deformable membranes encapsulating an incompressible fluid and they serve as numerical and experimental proxies for biological cells such as red blood cells. Vesicle dynamics has been studied in free-space or bounded shear, Poiseuille, and Taylor-Couette flows in 2D and 3D. Taylor-Green vortex are characterized with even more complicated properties than those flows such as nonuniform flow line curvature, shear gradient. We study the effects of two parameters on the vesicle dynamics: the ratio of the interior fluid viscosity to that of the exterior one and the ratio of the shear forces on the vesicle to the membrane stiffness (characterized by the capillary number). Vesicle deformability nonlinearly depends on these parameters. Although the study is in 2D, our findings contribute to the wide spectrum of intriguing vesicle dynamics: Vesicles migrate inwards and eventually rotate at the vortex center if they are sufficiently deformable. If not, then they migrate away from the vortex center and travel across the periodic arrays of vortices. The outward migration of a vesicle is a new phenomenon in Taylor-Green vortex flow and has not been observed in any other flows so far. Such cross-streamline migration of deformable particles can be utilized in several applications such as microfluidics for cell separation.

Linear stability analysis of a three-dimensional laminar separation bubble on a finite wing

Disturbance amplification in a laminar separation bubble forming on the suction surface of a cantilevered NACA0018 wing at an angle of attack of 6° and Reynolds number of 1.25 × 105 is studied using a combination of particle image velocimetry measurements and local and non-local linear stability analyses. The experimental measurements reveal the formation of largely two-dimensional velocity fluctuations leading to the formation of initially two-dimensional roll-up vortices in the separated shear layer at a nearly constant wavenumber and frequency, despite the substantial reduction in the effective angle of attack near the wing tip. The most amplified wavenumber and its growth rate are accurately predicted by linear stability theory outside of the regions of the separation bubble dominated by three-dimensional end effects, with negligible differences between local and non-local stability analyses. Near the wing root and tip, an increase in the magnitudes of spanwise velocities is observed within the laminar separation bubble, and linear stability calculations predict a relative increase in the amplification of spanwise wavenumbers with the same sign as the spanwise flow. However, the calculations show that the most amplified disturbance remains essentially two-dimensional across the entire wingspan.

Hidden topological transitions in emergent magnetic monopole lattices

Topological defects, called magnetic hedgehogs, realize emergent magnetic monopoles, which are not allowed in the ordinary electromagnetism described by Maxwell's equations. Such monopoles were experimentally discovered in magnets in two different forms: tetrahedral $4Q$ and cubic $3Q$ hedgehog lattices. The spin textures are modulated by the chemical composition, an applied magnetic field, and temperature, leading to quantum transport and optical phenomena through movement and pair annihilation of magnetic monopoles, but the theoretical understanding remains elusive, especially in the regions where different types of hedgehog lattices are competing. Here we propose a theoretical model that can stabilize both tetrahedral and cubic hedgehog lattices, and perform a thorough investigation of the phase diagram while changing the interaction parameters, magnetic field, and temperature, by using a recently developed method that delivers exact solutions in the thermodynamic limit. We find that the model exhibits various types of topological transitions with changes of the density of monopoles and antimonopoles, some of which are accompanied by singularities in the thermodynamic quantities, while the others are hidden with less or no anomaly. We also find another hidden topological transition with pair annihilation of two-dimensional vortices in the three-dimensional system. These results not only provide useful information for understanding the existing experimental data but also challenge the identification of hidden topological transitions and the exploration of emergent electromagnetism in magnetic monopole lattices.

Acoustic reconstruction of the vortex field in the nonuniform temperature field of a simulated furnace

The high-temperature thermal vortex flows generated by the tangential combustion of large-scale coal-fired power plant boilers represent a complex medium that causes acoustic ray bending. In this paper, nonlinear acoustic tomography is combined with particle swarm optimization as a means of reconstructing the two-dimensional thermal vortex field. The nonuniform and large-gradient temperature distribution is the main cause of acoustic ray bending. We establish curved paths of acoustic propagation that are closely related to the temperature distribution. Based on these curved paths, a set of radial basis functions combined with Tikhonov regularization is derived to achieve more accurate reconstruction of the temperature field. The nonuniform temperature field affects the reconstruction of the flow field information. Our model considers a variation in the angle between the direction vector of the acoustic curved paths and the horizontal and vertical components of the flow velocity, and incorporates a priori information and a six-parameter hypersurface into the flow field reconstruction scheme. Particle swarm optimization is applied to minimize the objective function and obtain the vortex velocity field. Numerical experiments show that the proposed mathematical model of acoustic ray bending improves the reconstruction accuracy of the temperature distribution and vortex flow field. The acoustic time-of-flight is experimentally measured through the generalized cross-correlation with different window functions. The temperature and vortex fields reconstructed based on the actual time-of-flight are compared with thermocouple and anemometer measurements to demonstrate the validity and robustness of the proposed reconstruction model.

Mutual friction and diffusion of two-dimensional quantum vortices

We present a microscopic open quantum systems theory of thermally-damped vortex motion in oblate atomic superfluids that includes previously neglected energy-damping interactions between superfluid and thermal atoms. This mechanism couples strongly to vortex core motion and causes dissipation of vortex energy due to mutual friction, as well as Brownian motion of vortices due to thermal fluctuations. We derive an analytic expression for the dimensionless mutual friction coefficient that gives excellent quantitative agreement with experimentally measured values, without any fitted parameters. Our work closes an existing two orders of magnitude gap between dissipation theory and experiments, previously bridged by fitted parameters, and provides a microscopic origin for the mutual friction and diffusion of quantized vortices in two-dimensional atomic superfluids.

Two-dimensional anisotropic vortex–bright soliton and its dynamics in dipolar Bose–Einstein condensates in optical lattice

We study construction and dynamics of two-dimensional (2D) anisotropic vortex–bright (VB) soliton in spinor dipolar Bose–Einstein condensates confined in a 2D optical lattice (OL), with two localized components linearly mixed by the spin–orbit coupling and long-range dipole–dipole interaction (DDI). It is found that the OL and DDI can support stable anisotropic VB soliton in the present setting for arbitrarily small value of norm N. We then present a new method via examining the mean square error of norm share of bright component to implement stability analysis. It is revealed that one can control the stability of anisotropic VB soliton only by adjusting OL depth for a fixed DDI. In addition, the dynamics of the anisotropic VB soliton was studied by applying the kick to them. The mobility of the single kicked VB soliton is Rabbi-like oscillation. However, for the collision dynamics of two kicked anisotropic VB solitons, their properties mainly depend on their initial distance and OL, and they can realize the transition from the bright component to the vortex component. Our work may provide a convenient way to prepare and manipulate anisotropic VB soliton in high-dimensional space.