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Abstract The flow field around a generic multi-swept delta wing configuration is investigated under transonic flow conditions, both experimentally and numerically. A special focus is on the analysis of vortex/vortex and vortex/sho...
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Abstract The flow field around a generic multi-swept delta wing configuration is investigated under transonic flow conditions, both experimentally and numerically. A special focus is on the analysis of vortex/vortex and vortex/shock interactions at moderate angles of attack. In the present study, the Mach number is varied between Ma=0.50\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textrm{Ma} = {0.50}$$\end{document} and Ma=1.41\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textrm{Ma} = {1.41}$$\end{document} and the angle of attack is varied between α=8∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha = 8^\circ$$\end{document} and α=28∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha = 28^\circ$$\end{document}. Numerical results are validated using experimental surface pressure data from pressure taps, as well as forces and moments based on strain gauge measurements. For selected cases, velocity field data from particle image velocimetry (PIV) measurements are available as well. Over a broad range of angle of attack and Mach number, strong vortex/vortex interactions, including vortex braiding and vortex merging, occur. The location of vortex merging is moving downstream with increasing angle of attack and increasing Mach number. Additionally, at Ma=0.85\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textrm{Ma} = {0.85}$$\end{document}, vortex/shock interaction occurs above the wing. For moderate angles of attack, shock-induced vortex breakdown is observed.
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The flow behind two side-by-side circular cylinders is experimentally investigated based on laser-illuminated flow-visualization, particle image velocimetry and hot-wire measurements. The flow is classified as three regimes: singl...
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The flow behind two side-by-side circular cylinders is experimentally investigated based on laser-illuminated flow-visualization, particle image velocimetry and hot-wire measurements. The flow is classified as three regimes: single street (the cylinder center-to-center spacing T/d < 1.2), asymmetrical flow (1.2 < T/d < 2.0) and two coupled street (T/d > 2.0). Special attention is given to the regime of 1.2 < T/d < 2.0, which is characterized by one narrow and one wide wake. It is found that the flow structure and its downstream evolution are closely linked to the phase relationship between the gap vortex in the wide wake and that in the narrow wake. When the gap vortex in the wide wake leads in phase, the two opposite-signed vortices in the narrow wake are typically engaged in pairing, which yields a relatively low-pressure region between them, thus drawing in the gap vortex along with fluid in the wide wake. This vortex interaction may act to stabilize the gap flow deflection. When lagging behind in phase, the gap vortex in the wide wake fails to merge with the vortices in the narrow wake. Interactions between vortices in the two wakes lead to the changeover of the gap flow deflection from one side to another. It is further noted that, for L/d > 2.0, the flow structure change from the anti-phase to in-phase mode starts with a phase shift between gap vortices. The dynamical role of gap bleeding between cylinders for L/d < 1.2 is also examined.
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The present work describes the vortex–vortex interactions observed during laboratory experiments, where a single regular water wave is allowed to travel over a discontinuous rigid bed promoting the generation of both near-bed and...
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The present work describes the vortex–vortex interactions observed during laboratory experiments, where a single regular water wave is allowed to travel over a discontinuous rigid bed promoting the generation of both near-bed and surface vortices. While near-bed vortices are generated by the flow separation occurring at the bed discontinuity, surface vortices are induced by the wave breaking in conjunction with a breaking-induced jet. A ‘backward breaking’ (previously observed in the case of solitary waves) occurs at the air–water interface downstream of the discontinuity and generates a surface anticlockwise vortex that interacts with the near-bed clockwise vortex. With the vortex–vortex interaction influenced by many physical mechanisms, a point-vortex model, by which vortices evolve under both self-advection (in relation to both free surface and seabed) and mutual interaction, has been implemented to separately investigate the vortex- and wave-induced dynamics. The available data indicate that both self-advection and mutual interaction are the governing mechanisms for the downward motion of the surface vortex, with the effect of the breaking-induced jet being negligible. The same two mechanisms, combined with the mean flow, are responsible for the almost horizontal and oscillating path of the near-bed vortex. The investigation of the vortex paths allow us to group the performed tests into three distinct classes, each characterized by a specific range of wave nonlinearity. The time evolution of the main variables characterizing the vortices (e.g. circulation, kinetic energy, enstrophy, radius) and their maximum values increase with the wave nonlinearity, such dependences being described by synthetic best-fit formulas.
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Discrete vortex rings impinging on concave hemispherical cavities were explored experimentally. Planar laser-induced fluorescence, two-dimensional particle image velocimetry and flow visualization techniques were employed. Five di...
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Discrete vortex rings impinging on concave hemispherical cavities were explored experimentally. Planar laser-induced fluorescence, two-dimensional particle image velocimetry and flow visualization techniques were employed. Five different ratios of vortex ring to hemisphere cavity radius ($gamma$) were investigated, namely, $gamma = 1/4,1/3,2/5,$$1/2, 2/3$. For $gamma = 1/4,1/3, 2/5$, the geometric confinement of the primary ring due to the hemispherical cavity induced loop-like instabilities in the secondary ring, which led to head-on collision and ejection of the looped ends as they orbited the primary ring. As the hemispherical cavity decreased in diameter (increasing $gamma$), the dynamics were altered significantly due to the increased generation of vorticity along the edge of the hemisphere. For $gamma = 1/2$, vorticity produced at the edge/lip of the hemisphere ultimately disrupted the classical formation of a secondary vortex ring from the wall-bounded vorticity. For $gamma = 2/3$, the primary ring and hemisphere radius were close enough in size that the interaction was dominated by direct impact of the primary ring with the lip of the cavity. The primary vortex ring produced a vortex ring at the lip of the hemisphere that ultimately separated from the cavity, orbited around the primary ring, and then self-advected in the direction opposite to the primary vortex ring trajectory. A detailed investigation of the dynamics provided.
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Polarized vortical structures (i.e. with axial flow, thus coiled vortex lines) are generic to turbulent flows – hence the importance of their dynamics, interactions and cascade. Direct numerical simulations of two anti-parallel p...
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Polarized vortical structures (i.e. with axial flow, thus coiled vortex lines) are generic to turbulent flows – hence the importance of their dynamics, interactions and cascade. Direct numerical simulations of two anti-parallel polarized vortex tubes are performed for vortex Reynolds numbers $Re$ ($\equiv \varGamma /\nu$) up to $9000$ and initial polarization strength $q$ (ratio of peak axial to azimuthal velocities) between $0$ and $4/3$. For both counter- and co-polarized cases, although the reconnection is delayed as $q$ increases – mainly due to weakened self-induction – it is more rapid and more complete for small $q$. Enstrophy growth and energy cascade are suppressed for weak polarization ($q < 1/2$) due to depleted nonlinearity, but are enhanced for strong polarization ($q > 1/2$) due to instability and/or transient growth. When counter-polarized, numerous structures with both positive and negative helicity densities (i.e. $\pm h$) are generated. For large $q$, strong axial flows opposite to the initial flows occur – causing polarization reversals. For the co-polarized cases, although $+h$ predominates, $-h$ structures also form and interact with positive ones – leading to helicity cascade to small scales. As $Re$ increases, small scales are more numerous: for counter-polarized cases, the threads undergo successive reconnections in a cascade – akin to the unpolarized case; for co-polarized cases, the newly formed vortex ring breaks up with numerous hairpin vortices wrapping around it. Increasing $q$ alters the energy spectrum in the inertial range with a scaling varying from $k^{-5/3}$ for the unpolarized case to $k^{-7/3}$ for the strongly polarized case, which seems to be associated with the enhanced vortex spiralling. In addition, for the strongly co-polarized cases, a $k^{-4/3}$ helicity spectrum develops. Furthermore, most of the energy and helicity in the inertial range with scale $L$ transfer to scales between $0.3L$ and $0.4L$. Therefore, polarization can significantly alter the dynamics of vortex reconnection as well as turbulence cascade.
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The dynamics of axial flow is investigated in initially two-dimensional (2-D) concentrated line vortices that are subsequently cut by a thin wall. The vortices are formed in the wake of an airfoil oscillating sinusoidally at small...
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The dynamics of axial flow is investigated in initially two-dimensional (2-D) concentrated line vortices that are subsequently cut by a thin wall. The vortices are formed in the wake of an airfoil oscillating sinusoidally at small amplitude, and their circulation and peak vorticity are controlled by the choice of oscillation frequency. The flow field is quantified in terms of the spatio-temporal evolution of axial (spanwise) velocity using one-component molecular tagging velocimetry, and simultaneous measurements of spanwise vorticity and axial velocity at selected planes away from the cutting wall using stereoscopic molecular tagging velocimetry. Results show that the characteristics of the vortices cut by the wall are initially in good agreement with the baseline 2-D vortices. However, as the axial flow develops near the cutting wall and propagates away from it farther downstream, the structure of the initially 2-D Gaussian-shaped vortices quickly changes to a highly distorted region(s) of vorticity near the wall. Data over planes one and two core radii away from the wall reveal appreciable axial velocity both toward and away from the wall, whereas at locations farther away the axial velocity is primarily away from the wall. The data reveal the existence of small amplitude area-varying waves that propagate away from the wall along the vortex core. These disturbances are associated with local changes in the vortex axial velocity and peak vorticity. The propagation speed of these disturbances is found to agree with predictions using the analytical model of Lundgren & Ashurst (J. Fluid Mech., vol. 200, 1989, pp. 283–307).
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In this paper, axial interaction of a vortex ring with a thin circular cylinder has been studied. An apparatus to generate clean vortex rings, free of piston and stopping vortex effects, has been used. Flow visualization and parti...
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In this paper, axial interaction of a vortex ring with a thin circular cylinder has been studied. An apparatus to generate clean vortex rings, free of piston and stopping vortex effects, has been used. Flow visualization and particle image velocimetry (PIV) experiments are carried out to determine and compare the characteristics of free and interacting vortex rings in the Reynolds number (defined with the circulation of the free travelling vortex ring) range of 2270 < R-e Gamma < 6790. It is observed that due to the presence of the cylinder, there is an increase in the velocity of the vortex ring. Also, noticeable changes in the characteristic properties of vortex ring such as core circulation, core diameter and ring diameter have been observed. Changes in these parameters are explained by two changes in the flow field between the vortex ring and the cylinder due to axial interactions: 0) displacement of the streamlines and (ii) acceleration in the induced velocity field in this region. These two mutually opposing effects determine the changes in the primary vortex ring properties that take place during interaction. To justify these experimental observations quantitatively, an analytical study of the interaction under an inviscid assumption is performed. The inviscid analysis does predict the increase in velocity during the interaction, but fails to predict the values observed in the present experiments. However, when the theory is used to correct the velocity change through incorporation of the effects of an axisymmetric induced boundary layer region over the cylinder, modelled as an annular vortex sheet of varying strength, the changes in the translational velocities of the vortex rings match closely with the experimental values.
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The internal structure of vortex rings and helical vortices is studied using asymptotic analysis and numerical simulations in cases where the core size of the vortex is small compared to its radius of curvature, or to the distance...
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The internal structure of vortex rings and helical vortices is studied using asymptotic analysis and numerical simulations in cases where the core size of the vortex is small compared to its radius of curvature, or to the distance to other vortices. Several configurations are considered: a single vortex ring, an array of equally-spaced rings, a single helix and a regular array of helices. For such cases, the internal structure is assumed to be at leading order an axisymmetric concentrated vortex with an internal jet. A dipolar correction arises at first order and is shown to be the same for all cases, depending only on the local vortex curvature. A quadrupolar correction arises at second order. It is composed of two contributions, one associated with local curvature and another one arising from a non-local external 2-D strain field. This strain field itself is obtained by performing an asymptotic matching of the local internal solution with the external solution obtained from the Biot-Savart law. Only the amplitude of this strain field varies from one case to another. These asymptotic results are thereafter confronted with flow solutions obtained by direct numerical simulation (DNS) of the Navier-Stokes equations. Two different codes are used: for vortex rings, the simulations are performed in the axisymmetric framework; for helices, simulations are run using a dedicated code with built-in helical symmetry. Quantitative agreement is obtained. How these results can be used to theoretically predict the occurrence of both the elliptic instability and the curvature instability is finally addressed.
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This study examines the two-dimensional interaction of two unequal co-rotating viscous vortices in uniform background shear. Numerical simulations are performed for vortex pairs having various circulation ratios $varLambda _0 = va...
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This study examines the two-dimensional interaction of two unequal co-rotating viscous vortices in uniform background shear. Numerical simulations are performed for vortex pairs having various circulation ratios $varLambda _0 = varGamma _{1,0}/varGamma _{2,0} = (omega _{1,0}/omega _{2,0})(a^2_{1,0}/a^2_{2,0}) leqslant 1$, corresponding to different initial characteristic radii $a_{i,0}$ and peak vorticities $omega _{i,0}$ of each vortex $i=1,2$, in shears of various strengths $zeta _0 = omega _S/omega _{2,0}$, where $omega _S$ is the constant vorticity of the shear. Two primary flow regimes are observed: separations ($zeta _0 < zeta _{sep} < 0$), in which the vortices move apart continuously, and henditions ($zeta _0 > zeta _{sep}$), in which the interaction results in a single vortex (where $zeta _{sep}$ is the adverse shear strength beyond which separation occurs). Vortex motion and values of $zeta _{sep}(varLambda _0)$ are well-predicted by a point-vortex model for unequal vortices. In vortex-dominated henditions, shear varies the peak–peak distance $b$, and vortex deformation. The main convective interaction begins when core detrainment of one vortex is established, and proceeds similarly to the no-shear ($zeta _0 = 0$) case: merger occurs if the second vortex also detrains, engendering mutual entrainment; otherwise straining out occurs. Detrainment requires persistence of straining of both sufficient magnitude, as indicated by relative straining above a consistent critical value, $(S/omega )_i > (S/omega )_{cr}$, where $S$ is the strain rate magnitude at the vorticity peak, and conducive direction. Hendition outcomes are assessed in terms of an enhancement factor $varepsilon equiv varGamma _{end}/varGamma _{2,start}$. Although $varepsilon$ generally varies with $zeta _0$, $(a^2_{1,0} /a^2_{2,0} )$ and $(omega _{1,0}/omega _{2,0})$ in a complicated manner, this variation is well-characterized by the pair's starting enstrophy ratio, $Z_2/Z_1$. Within a transition region between merger and straining out (approximately $1.65 < Z_2/Z_1 < 1.9$), shear of either sense may increase $varepsilon$.
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The dynamics of interacting vortex filaments in an incompressible fluid, which are nearly parallel, have been approximated in the Klein-Majda-Damodaran model. The regime considers the deflection of each filament from a central axi...
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The dynamics of interacting vortex filaments in an incompressible fluid, which are nearly parallel, have been approximated in the Klein-Majda-Damodaran model. The regime considers the deflection of each filament from a central axis; that is to say, the vortex filaments are assumed to be roughly parallel and centred along parallel lines. While this model has attracted a fair amount of mathematical interest in the recent literature, particularly concerning the existence of certain specific vortex filament structures, our aim is to generalise several known interesting filament solutions, found in the self-induced motion of a single vortex filament, to the case of pairwise interactions between multiple vortex filaments under the Klein-Majda-Damodaran model by means of asymptotic and numerical methods. In particular, we obtain asymptotic solutions for counter-rotating and co-rotating vortex filament pairs that are separated by a distance, so that the vortex filaments always remain sufficiently far apart, as well as intertwined vortex filaments that are in close proximity, exhibiting overlapping orbits. For each scenario, we consider both co- and counter-rotating pairwise interactions, and the specific kinds of solutions obtained for each case consist of planar filaments, for which motion is purely rotational, as well as travelling wave and self-similar solutions, both of which change their form as they evolve in time. We choose travelling waves, planar filaments and self-similar solutions for the initial filament configurations, as these are common vortex filament structures in the literature, and we use the dynamics under the Klein-Majda-Damodaran model to see how these structures are modified in time under pairwise interaction dynamics. Numerical simulations for each case demonstrate the validity of the asymptotic solutions. Furthermore, we develop equations to study a co-rotating hierarchy of many satellite vortices orbiting around a central filament. We numerically s
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