Interaction Of Vortex Pairs Research Articles

The interaction of longitudinal vortex pairs with a turbulent boundary layer

In this study, we demonstrate an efficient approach to investigating the interaction of vortex pairs on a turbulent boundary layer. Our aim is to assess how vortex characteristics impact the downstream flow. Wall-modelled large eddy simulations are used together with an inlet defined by a Batchelor vortex model superimposed on a turbulent boundary layer profile, generated using synthetic turbulence and a precursor Reynolds-averaged Navier–Stokes calculation. This set-up allows for the efficient testing of multiple configurations whilst providing adequate resolution of outer boundary layer and the vortex–vortex interactions. After validating the methodology, we report a set of simulations for both co- and counter-rotating vortex pairs at different separations and asymmetric strengths. The separation distance between the vortices was found to have a significant effect upon the merging of the vortices. Asymmetric strength vortex pairs, analogous to vortex generators in yaw, demonstrate performance independent of flow direction for small angles. Detailed analysis of this flow provides insight into turbulence generation mechanisms and Reynolds stress anisotropy – valuable reference data for the development of lower-order models. Skin-friction enhancement is shown to be more effective for counter-rotating vortex pairs than co-rotating pairs of the same strength and spacing. Additionally, a wider spacing between the initial vortex positions results in a faster rise in the skin-friction coefficient.

Topological bifurcations of vortex pair interactions

Abstract

Experiments on asymmetric vortex pair interaction with the ground

The interaction between the asymmetric vortex pair and the ground was experimentally investigated in a closed-circuit water channel for the current study. Particle image velocimetry tests were conducted to achieve the velocity measurements of flow fields at various crossflow planes. The vortex pair, with the reference circulation Reynolds number ReΓ ≈ 4490, was tested with various initial heights (h0/b0 = 1.5, 1.0 and 0.5) and circulation ratios (λ = 0.36:1, 1:0.36, 0.6:1, 1:0.6), with it being found that according to different interaction effects, the trajectory and merger of the vortex pair could be significantly affected. As the primary vortex pair approached the ground, a high turbulent kinetic energy region was observed between the secondary and primary vortical structures, which suggests violent interaction and accelerated circulation decay of the primary vortex. In addition, depending on the distribution of secondary vorticity and image vortices to the moving coordinate system, merging-promoting or -inhibiting effects were observed, which eventually affected the evolution of the primary vortex pair.

Collinear interaction of vortex pairs with different strengths—Criteria for leapfrogging

We formulate a system of equations that describe the motion of four vortices made up of two interacting vortex pairs, where the absolute strengths of the pairs are different. Each vortex pair moves along the same axis in the same sense. In much of the literature, the vortex pairs have equal strength. The vortex pairs can either escape to infinite separation or undergo a periodic leapfrogging motion. We determine an explicit criterion in terms of the initial horizontal separation of the vortex pairs given as a function of the ratio of their strengths to describe a periodic leapfrogging motion when interacting along the line of symmetry. In the Appendix, we also contrast a special case of interaction of a vortex pair with a single vortex of the same strength in which a vortex exchange occurs.

Effects of Strake Shape on the Vortex Pair Interaction of a Double-Delta Wing

Effects of Strake Shape on the Vortex Pair Interaction of a Double-Delta Wing

Vorticity topology of vortex pair interactions at low Reynolds numbers

Abstract We investigate vortex merging at low Reynolds numbers from a topological point of view. We identify vortices as local extremal points of vorticity and follow the motion and bifurcation of these points as time progresses. We consider both two-dimensional simulations of the vorticity transport equation and an analytical study of the core growth model. The merging process of identical vortices is shown to occur through a pitchfork bifurcation and for asymmetric vortices one vortex merges with a saddle through a cusp (perturbed pitchfork) bifurcation. Excellent agreement between the core growth model and the numerical simulations is observed. For higher Reynolds numbers, filamentation becomes dominant hence limiting the predictive value of the core growth model. A complete investigation of merging in the core growth model is conducted for all possible vortex strengths. Simple, analytical expressions are derived for bifurcation curves, merging time, and vortex positions depending on systems parameters.

Interactions and scattering of quantum vortices in a polariton fluid

Quantum vortices, the quantized version of classical vortices, play a prominent role in superfluid and superconductor phase transitions. However, their exploration at a particle level in open quantum systems has gained considerable attention only recently. Here we study vortex pair interactions in a resonant polariton fluid created in a solid-state microcavity. By tracking the vortices on picosecond time scales, we reveal the role of nonlinearity, as well as of density and phase gradients, in driving their rotational dynamics. Such effects are also responsible for the split of composite spin–vortex molecules into elementary half-vortices, when seeding opposite vorticity between the two spinorial components. Remarkably, we also observe that vortices placed in close proximity experience a pull–push scenario leading to unusual scattering-like events that can be described by a tunable effective potential. Understanding vortex interactions can be useful in quantum hydrodynamics and in the development of vortex-based lattices, gyroscopes, and logic devices.

A quantitative assessment of viscous asymmetric vortex pair interactions

The interactions of two like-signed vortices in viscous fluid are investigated using two-dimensional numerical simulations performed across a range of vortex strength ratios, $\unicode[STIX]{x1D6EC}=\unicode[STIX]{x1D6E4}_{1}/\unicode[STIX]{x1D6E4}_{2}\leqslant 1$, corresponding to vortices of circulation, $\unicode[STIX]{x1D6E4}_{i}$, with differing initial size and/or peak vorticity. In all cases, the vortices evolve by viscous diffusion before undergoing a primary convective interaction, which ultimately results in a single vortex. The post-interaction vortex is quantitatively evaluated in terms of an enhancement factor, $\unicode[STIX]{x1D700}=\unicode[STIX]{x1D6E4}_{end}/\unicode[STIX]{x1D6E4}_{2,start}$, which compares its circulation, $\unicode[STIX]{x1D6E4}_{end}$, to that of the stronger starting vortex, $\unicode[STIX]{x1D6E4}_{2,start}$. Results are effectively characterized by a mutuality parameter, $MP\equiv (S/\unicode[STIX]{x1D714})_{1}/(S/\unicode[STIX]{x1D714})_{2}$, where the ratio of induced strain rate, $S$, to peak vorticity, $\unicode[STIX]{x1D714}$, for each vortex, $(S/\unicode[STIX]{x1D714})_{i}$, is found to have a critical value, $(S/\unicode[STIX]{x1D714})_{cr}\approx 0.135$, above which core detrainment occurs. If $MP$ is sufficiently close to unity, both vortices detrain and a two-way mutual entrainment process leads to $\unicode[STIX]{x1D700}>1$, i.e. merger. In asymmetric interactions and mergers, generally one vortex dominates; the weak/no/strong vortex winner regimes correspond to $MP<,=,>1$, respectively. As $MP$ deviates from unity, $\unicode[STIX]{x1D700}$ decreases until a critical value, $MP_{cr}$ is reached, beyond which there is only a one-way interaction; one vortex detrains and is destroyed by the other, which dominates and survives. There is no entrainment and $\unicode[STIX]{x1D700}\sim 1$, i.e. only a straining out occurs. Although $(S/\unicode[STIX]{x1D714})_{cr}$ appears to be independent of Reynolds number, $MP_{cr}$ shows a dependence. Comparisons are made with available experimental data from Meunier (2001, PhD thesis, Université de Provence-Aix-Marseille I).

A large eddy simulation of the breakup and atomization of a liquid jet into a cross turbulent flow at various spray conditions

A three-dimensional large eddy simulation (LES) is conducted to investigate the breakup and atomization of a liquid jet into a cross turbulent flow for several variants of a liquid-gas momentum flux ratio by varying the liquid injection velocity and cross flow temperature. The spray-field dynamics are treated using a combined Eulerian-Lagrangian approach in which the gas phase is discretized using a density-based, finite-volume approach. A Kelvin-Helmholtz and Rayleigh-Taylor (KH-RT) hybrid wave breakup model is implemented to simulate the liquid column and droplet breakup process. While the KH model is applied to the liquid column breakup (primary breakup), the RT model is implemented to the breakup of the small droplets (secondary breakup). The detail flow structures of the counter-rotating vortex pair (CVP) and vortex interaction behind the injector are observed. The spray penetration depth in the crossflow compares well with the experimental data and similar to empirical equations. The Sauter mean diameter (SMD) distribution is analyzed along the flow downstream representing somewhat different, and an analytical correlation model is proposed to pre-evaluate the SMD in the flowfield.

Turbulence/chemistry interactions in a ramp-stabilized supersonic hydrogen–air diffusion flame

Hybrid large-eddy / Reynolds-averaged Navier–Stokes simulations of turbulence / chemistry interactions occurring within a ramp-injected, hydrogen-fueled scramjet combustor are presented in this work. The experimental geometry is one of several studied at the Universty of Virginia as part of the National Center for Hypersonic Combined Cycle Propulsion and consists of an isolator, a combustor, and an extender section. Data collected includes coherent anti-Stokes Raman spectroscopy (CARS) measurements of major species composition and temperature at several streamwise planes, stereoscopic particle image velocimetry (PIV) measurements, hydroxyl planar-induced fluorescence (OH-PLIF) imagery, wall pressure distributions, and line-of-sight profiles of temperature and water concentration obtained using tunable diode laser spectroscopy (TDLAS). This paper focuses on an equivalence ratio of 0.17, which does not produce enough heat release to force a shock train into the isolator. The computational methods utilize a hybrid fourth-order central-difference / upwind strategy to enable accurate resolution of turbulent structures and employ a nine-species hydrogen oxidation mechanism. Generally accurate predictions of temperature, velocity, and nitrogen mole fraction are achieved through a ‘laminar chemistry’ assumption for the filtered species production rates, though results do improve slightly with the use of a simple turbulence / chemistry subgrid closure model. The predictions are most sensitive to the choice of isolator inflow boundary condition, with the use of a recycling / rescaling technique to sustain turbulent fluctuations resulting in an ‘over-mixing’ effect immediately downstream of the fuel injector. Turbulence–chemistry interactions in the flameholding region are examined from the standpoint of laminar flamelet theory. A region of high scalar dissipation rate, coincident with the breakdown of the fuel plume and the interaction of a reflected shock wave with the plume, inhibits flame propagation, forming a ‘hole’ in the flame. Advection of cooler fluid downstream into regions of moderate scalar dissipation enlarges the ‘hole’, but eventually the flame reconnects. These results point to one potential disadvantage of fuel-air mixing technologies that enhance axial vorticity – even if conditions for combustion are favorable, high strain rates generated by the interaction and breakdown of vortex pairs can lead to flame suppression.

Scattering of a vortex pair by a single quantum vortex in a Bose–Einstein condensate

We analyze the scattering of vortex pairs (the particular case of 2D dark solitons) by a single quantum vortex in a Bose–Einstein condensate with repulsive interaction between atoms. For this purpose, an asymptotic theory describing the dynamics of such 2D soliton-like formations in an arbitrary smoothly nonuniform flow of a ultracold Bose gas is developed. Disregarding the radiation loss associated with acoustic wave emission, we demonstrate that vortex–antivortex pairs can be put in correspondence with quasiparticles, and their behavior can be described by canonical Hamilton equations. For these equations, we determine the integrals of motion that can be used to classify various regimes of scattering of vortex pairs by a single quantum vortex. Theoretical constructions are confirmed by numerical calculations performed directly in terms of the Gross–Pitaevskii equation. We propose a method for estimating the radiation loss in a collision of a soliton-like formation with a phase singularity. It is shown by direct numerical simulation that under certain conditions, the interaction of vortex pairs with a core of a single quantum vortex is accompanied by quite intense acoustic wave emission; as a result, the conditions for applicability of the asymptotic theory developed here are violated. In particular, it is visually demonstrated by a specific example how radiation losses lead to a transformation of a vortex–antivortex pair into a vortex-free 2D dark soliton (i.e., to the annihilation of phase singularities).

Characterization of the vortex-pair interaction law and nonlinear mobility effects

Employing nematic liquid crystals in a homeotropic cell with a photosensitive wall, dissipative vortex pairs are selectively induced by external illumination and the interaction law is characterized for pairs of opposite topological charges. Contrary to the phenomenological fit with a force inversely proportional to the distance, the data provide evidence that nonlinear mobility effects must be taken into account. The observations lead to a reconciliation of experiments with theory.

Simulation of viscous flows with undulatory boundaries: Part II. Coupling with other solvers for two-fluid computations

We extend the direct numerical simulation (DNS) capability developed in [D. Yang, L. Shen, Simulation of viscous flows with undulatory boundaries: Part I. Basic solver, J. Comput. Phys. (submitted for publication) ] to the simulation of two-fluid interaction with deformable interface. Two approaches are used to couple the DNS of one fluid with the simulation of another fluid. In the first, the DNS is coupled with a potential-flow based wave solver that uses a high-order spectral (HOS) method. This coupled method is applied to simulate the interaction of turbulent wind with surface waves, including single wave train and broadband wavefield. Validation with previous theoretical and experimental studies shows the accuracy and efficiency of this coupled DNS-HOS method for capturing the essential physics of wind–wave interaction. In the second approach, both of the fluids are simulated by the DNS and are coupled by an efficient iterative scheme, in which the continuity of velocity and the balance of stress are enforced at the interface. The performance of this coupled DNS–DNS method is demonstrated and validated by several test cases including: interfacial wave between two viscous fluids, water surface wave over highly viscous mud flow with interfacial wave, and interaction of two-phase vortex pairs with a deformable interface. Comparison with existing theoretical and numerical results confirms the accuracy of this coupled DNS–DNS method. Finally, this method is applied to study the interaction of air and water turbulence. The nonlinear development of interfacial wave by the excitation of the air and water turbulence, and the wave effect on the instantaneous and statistical characteristics of the turbulence are elucidated.

Flow structures in flat plate boundary layer induced by pulsed plasma actuator

The flow field in the flat plate boundary layer induced by the pulsed plasma actuator was simulated by solving the Navier-Stokes equations with a phenomenological DBD plasma model. The effects of actuation strength, wave form and frequency on the flow structures induced by the unsteady pulsed plasma actuator were investigated. The results indicated that a series of vortex pairs were formed in the boundary layer, and decayed in downstream convection following the exponential law. The strength of vortex pair was dominated by the effective plasma actuation strength, and the vortex streamwise spacing depended on the actuation frequency. If the duty cycle is not so large that interaction of adjacent vortex pairs can be negligible, then the actuation wave form has little influence on the vortex pair induced by the unsteady plasma actuator.

Interaction of a shock wave with two counter-rotating vortices: Shock dynamics and sound production

In the present paper the interaction of a planar shock wave with a pair of counter-rotating vortices is studied by means of extensive numerical simulations. The main objective of the study is to characterize the shock pattern and the nature of the acoustic field. For the purpose of shedding some light into the mechanism of sound generation, the acoustic analogy developed by the present authors for the interaction of a shock wave with an isolated vortex has been extended to the case of a vortex pair, so as to obtain a closed form solution for the acoustic far field pressure in the limit of weak vortices. The effect of various parameters, such as the shock and vortex strengths and the initial vortex separation distance has been investigated, and their influence on the dynamics has been assessed. In addition, we have also considered both the case of passing and colliding pairs. In the case of a colliding pair five types of interactions are found to occur, depending upon the value of the interaction parameter, defined as the ratio of the vortex pair intensity over the shock strength. With regard to the acoustic field, the simulations have shown that the latter is the result of two mechanisms: the one directly associated to the interaction itself, and the one related to the coupling process of the vortex pair. The former mechanism is controlling if the interaction is weak, while for strong interactions the acoustic field is also controlled by the sound generated through the coupling process. For all cases the acoustic pressure field exhibits a multipolar directivity pattern with at least four sound peaks along the radial direction; however, if the vortex pair intensity is large the sound waves trailing the precursor are not clearly distinguishable. Shock wave–passing vortex pair interactions exhibit only three types of shock patterns, as in the case of shock wave–isolated vortex interaction; however, the acoustic field exhibits the same features as in the colliding case.

Digital particle velocimetry technique for free-surface boundary layer measurements: Application to vortex pair interactions

A variation of the digital particle image velocimetry (DPIV) technique was developed for the measurement of velocity at a free surface for low Froude number flows. The two-step process involves first determining the location of the free surface in the digital images of the seeded flow using the fast Fourier transform-based method of surface elevation mapping (SEM), which takes advantage of total internal reflection at the interface. The boundary-fitted DPIV code positions the interrogation windows below the computed location of the interface to allow for extrapolation of interfacial velocities. This technique was designed specifically to handle large surface-parallel vorticity which can occur when the Reynolds number is large and surface-active materials are present. The SEM technique was verified on capillary-gravity waves and the full boundary-fitted DPIV technique was applied to the interaction of vortex pairs with a free surface covered by an insoluble monolayer. The local rise and fall of the free surface as well as the passage and return of a contamination front was clearly observed in the DPIV data.

Simulations and analysis of the coupling process of compressible vortex pairs: Free evolution and shock induced coupling

In the present paper the dynamics of the coupling process of compressible vortex pairs is analyzed by means of extensive numerical simulations. The objective of the study is to determine the effects of the initial vortex spatial structure and of the compressibility. Different vortex structures have been considered and their influence on the vorticity dynamics has been assessed. In the case of free evolution, the numerical simulations show that two vortices in close contact evolve toward a vortex dipole; however, the structure of the resulting dipole depends upon the initial inner core structure and on the vortex intensity. In the presence of shock wave–vortex pair interaction the coupling process depends upon the strength of the shock and the type of pair. In the case of a colliding pair, the process obeys either a two- or a three-stage mechanism depending upon the shock strength, and nonlinear couples form regardless of the initial vortex Mach number. If the interacting shock is strong, the vortex pair experiences a three-stage evolution, whereby the intermediate stage is characterized by the occurrence of a transient nonsymmetric couple. In the case of passing pair, the coupling mechanism proceeds in four stages. In particular, we observe the formation of satellite vortices, whose interaction with the primary vortex during the transient gives rise to the formation of a nonsymmetric dipole and a subsequent temporary tripole due to the feeding of shear produced vorticity. The final stage of the interaction is characterized by the formation of a nonlinear dipole.

The Effects of Aircraft Wake Dynamics on Contrail Development

Results of large-eddy simulations of the development of young persistent ice contrails are presented, concentrating on the interactions between the aircraft wake dynamics and the ice cloud evolution over ages front a few seconds to approx. 30 min. The 3D unsteady evolution of the dispersing engine exhausts, trailing vortex pair interaction and breakup, and subsequent Brunt-Vaisala oscillations of the older wake plume are modeled in detail in high-resolution simulations, coupled with it bulk microphysics model for the contrail ice development. The simulations confirm that the early wake dynamics can have a strong influence on the properties of persistent contrails even at late times. The vortex dynamics are the primary determinant of the vertical extent of the contrail (until precipitate ton becomes significant): and this together with the local wind shear largely determines the horizontal extent. The ice density, ice crystal number density, and a conserved exhaust tracer all develop and disperse in different fashions from each other. The total ice crystal number can be significantly reduced due to adiabatic compression resulting from the downward motion of the vortex system, even for ambient conditions that are substantially supersaturated with respect to ice. The fraction of the initial ice crystals surviving, their spatial distribution and the ice mass distribution are all sensitive to the aircraft type, ambient humidity, assumed initial ice crystal number, and ambient turbulence conditions. There is a significant range of conditions for which a smaller transport such as a B737 produces as significant a persistent contrail as a larger transport such as a B747, even though the latter consumes almost five times as much fuel. The difficulties involved in trying to minimize persistent contrail production are discussed.

Sound sources in the interactions of two inviscid two-dimensional vortex pairs

The sources of sound during the interactions of two identical two-dimensional inviscid vortex pairs are investigated numerically by using the vortex sound theory and the method of contour dynamics. The sound sources are identified and then separated into two independent components, which represent the contributions from the vortex centroid dynamics and the microscopic vortex core dynamics. Results show that the sound generation mechanism of the latter is independent of the type of vortex pair interaction, while that of the former depends on the jerks, accelerations and vortex forces on the vortex pairs. The power developed by the vortex forces is found to be important in the generation of sound when the vortex cores are severely deformed and their centroids are close to each other. The isolated source terms also explain the appearance of wavy oscillations on the time variations of the sound source strengths in the vortex ring and the two-dimensional vortex interaction systems.

The interaction of skewed vortex pairs: a model for blow-up of the Navier–Stokes equations

The interaction of two propagating vortex pairs is considered, each pair being initially aligned along the positive principal axis of strain associated with the other. As a preliminary, the action of accelerating strain on a Burgers vortex is considered and the conditions for a finite-time singularity (or ‘blow-up’) are determined. The asymptotic high Reynolds number behaviour of such a vortex under non-axisymmetric strain, and the corresponding behaviour of a vortex pair, are described. This leads naturally to consideration of the interaction of the two vortex pairs, and identifies a mechanism by which blow-up may occur through self-similar evolution in an interaction zone where scale decreases in proportion to (t* − t)1/2, where t* is the singularity time. The relevance of Leray scaling in this interaction zone is discussed.