Статті в журналах: "Counter-Rotating Vortex Pair (CRVP)"

1

Abdullah, Kamil, Hazim Fadli Aminnuddin, and Akmal Nizam Mohammed. "Parametric Study on Anti-Vortex Film Cooling Hole Arrangements." Applied Mechanics and Materials 660 (October 2014): 664–68. http://dx.doi.org/10.4028/www.scientific.net/amm.660.664.

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Film cooling has been extensively used to provide thermal protection for the external surface of the gas turbine blades. Numerous number of film cooling holes designs and arrangements have been introduced. The main motivation of these designs and arrangements are to reduce the lift-off effect cause by the counter rotating vortices (CRVP) produce by cylindrical cooling hole. One of the efforts is the introduction of newly found anti-vortex film cooling design. The present study focuses on anti-vortex holes arrangement consists of a main hole and pair of smaller holes. All three holes share a common inlet with the outlet of the smaller holes varies base on it relative position towards the main hole. Three anti-vortex holes arrangements have been considered; downstream anti-vortex hole arrangement (DAV), lateral anti-vortex hole arrangement (LAV), and upstream anti-vortex hole arrangement (UAV). In addition, a single hole (SH) film cooling has also been considered as the baseline. The investigation make used of ANSYS CFX software ver. 14. The investigations are made through Reynolds Average Navier Stokes analyses with the application of shear k-ε turbulence model. The results show that the anti-vortex designs produce significant improvement in term of film cooling effectiveness and distribution. The LAV arrangement shows the best film cooling effectiveness distribution among all considered cases and is consistent for all blowing ratios (BR). The results also unveil the formation of new vortex pair on both side of the primary hole CRVP. Interaction between the new vortices and the main CRVP structure reduce the lift off explaining the increased lateral film effectiveness.

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2

Chang, Jianlong, Xudong Shao, Jiangman Li, and Xiao Hu. "A Comparison of Classical and Pulsating Jets in Crossflow at Various Strouhal Numbers." Mathematical Problems in Engineering 2017 (2017): 1–14. http://dx.doi.org/10.1155/2017/5279790.

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Investigation of the classical and pulsating jet in crossflow (JICF) at a low Reynolds number (Re = 100) has been performed by the LES method based on varied velocity ratios (r= 1~4). Time-averaged particle trajectories are compared in the classical and pulsating JICF. The formation mechanism and the corresponding flow characteristics for the counter-rotating vortex pair (CRVP) have been analyzed. An unexpected “vortex tail” has been found in the JICF at higher velocity ratio due to the enhanced interactions indicated by the increased jet momentum among the CRVP, upright vortices, and shear layers. The analysis of time-averaged longitudinal vorticity including a coupling mechanism between vortices has been performed. The returning streamlines appear in the pulsating JICF, and two extra converging points emerge near the nozzle of the jet at different Strouhal numbers. The temperature profiles based on the iso-surface for the classical and pulsating JICF have been obtained computationally and analyzed in detail.

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3

André, Matthieu A., and Philippe M. Bardet. "Free surface over a horizontal shear layer: vorticity generation and air entrainment mechanisms." Journal of Fluid Mechanics 813 (January 26, 2017): 1007–44. http://dx.doi.org/10.1017/jfm.2016.822.

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Two air entrainment mechanisms driven by vortex instability are reported in the unstable relaxation of a horizontal shear layer below a free surface. This flow is experimentally investigated by means of planar laser-induced fluorescence (PLIF) and particle image velocimetry (PIV) coupled with surface profilometry. PLIF identifies counter-rotating vortex pairs (CRVP) emanating from the surface following the growth of high steepness two-dimensional millimetre-size waves for Reynolds and Weber numbers based on the momentum thickness of 177 to 222 and 7.59 to 13.9, respectively. High spatio-temporal resolution PIV reveals the role of surface-generated vorticity and flow separation in the highly curved trough of the waves on the injection of a CRVP. Air bubbles are entrapped in the wake of these CRVPs at Reynolds number above 190. PIV data and spanwise PLIF images show two initiation mechanisms: primary vortex instability modulating the spanwise location where the flow separates, resulting in the pinch off of an air ligament, and secondary vortex instability turning a CRVP into$\unicode[STIX]{x1D6FA}$-shaped loops pulling the surface down. Instability wavelengths agree with linear stability analysis, and models for these new air entrainment mechanisms are proposed.

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4

YAO, YUFENG. "DIRECT NUMERICAL SIMULATION OF MULTIPLE JETS IN CROSS-FLOW." Modern Physics Letters B 23, no. 03 (January 30, 2009): 249–52. http://dx.doi.org/10.1142/s0217984909018126.

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Direct numerical simulation has been performed to study flow interactions in multiple jets in cross-flow. Configurations considered are twin jets side-by-side and triple jets in tandem. Computations are carried out at the jet to cross-flow velocity ratio of 2.5 and the Reynolds number 225 based on the free-stream quantities and the jet width D . For twin jets, results show that in the vicinity of jet exits, the merging of two counter rotating vortex pairs (CRVP) is strongly dependent on the gap of two jets. Downstream in the far-field, a large single CRVP dominates. The simulation is in qualitatively good agreement with the experimental findings by other researchers. For triple jets, more complicated flow structures are revealed, in which a total of three vortex pairs has been identified, but none of them is dominating. The observations of complex flow structure could assistant relevant industrial applications.

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5

Baek, Seung Il, and Joon Ahn. "Large Eddy Simulation of Film Cooling Involving Compound Angle Holes: Comparative Study of LES and RANS." Processes 9, no. 2 (January 21, 2021): 198. http://dx.doi.org/10.3390/pr9020198.

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A large eddy simulation (LES) was performed for film cooling in the gas turbine blade involving spanwise injection angles (orientation angles). For a streamwise coolant injection angle (inclination angle) of 35°, the effects of the orientation angle were compared considering a simple angle of 0° and 30°. Two ratios of the coolant to main flow mass flux (blowing ratio) of 0.5 and 1.0 were considered and the experimental conditions of Jung and Lee (2000) were adopted for the geometry and flow conditions. Moreover, a Reynolds averaged Navier–Stokes simulation (RANS) was performed to understand the characteristics of the turbulence models compared to those in the LES and experiments. In the RANS, three turbulence models were compared, namely, the realizable k-ε, k-ω shear stress transport, and Reynolds stress models. The temperature field and flow fields predicted through the RANS were similar to those obtained through the experiment and LES. Nevertheless, at a simple angle, the point at which the counter-rotating vortex pair (CRVP) collided on the wall and rose was different from that in the experiment and LES. Under the compound angle, the point at which the CRVP changed to a single vortex was different from that in the LES. The adiabatic film cooling effectiveness could not be accurately determined through the RANS but was well reflected by the LES, even under the compound angle. The reattachment of the injectant at a blowing ratio of 1.0 was better predicted by the RANS at the compound angle than at the simple angle. The temperature fluctuation was predicted to decrease slightly when the injectant was supplied at a compound angle.

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6

Yu, Feiyan, and Savas Yavuzkurt. "Near-Field Simulations of Film Cooling with a Modified DES Model." Inventions 5, no. 1 (March 10, 2020): 13. http://dx.doi.org/10.3390/inventions5010013.

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Modeling the heat transfer characteristics of highly turbulent flow in gas turbine film cooling is important for providing better insights and engineering solutions to the film cooling problem. This study proposes a modified detached eddy simulation (DES) model for better film cooling simulations. First, spatially varying anisotropic eddy viscosity is found from the results of the large eddy simulation (LES) of film cooling. Then the correlation for eddy viscosity anisotropy ratio has been established based on the LES results and is proposed as the modification approach for the DES model. The modified DES model has been tested for the near-field film cooling simulations under different blowing ratios. Detailed comparisons of the centerline and 2D film cooling effectiveness indicate that the modified DES model enhances the spanwise spreading of the temperature field. The DES model leads to deviations of 62.4%, 39.8%, and 33.5% from the experimental centerline effectiveness under blowing ratios of 0.5, 1.0, and 1.5, respectively, while the modified DES reduces the deviations to 51.5%, 26.7%, and 28.9%. The modified DES model provides a promising approach for film cooling numerical simulations. It embraces the advantage of LES in resolving detailed vortical structure dynamics with a moderate computational cost. It also significantly improves the original DES model on the spanwise counter rotating vortex pair (CRVP) spreading, mixing, and effectiveness prediction.

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7

Miyazaki, Takeshi, Masahiro Yamamoto, and Shinsuke Fujishima. "Counter-Rotating Quasigeostrophic Ellipsoidal Vortex Pair." Journal of the Physical Society of Japan 72, no. 8 (August 15, 2003): 1948–62. http://dx.doi.org/10.1143/jpsj.72.1948.

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8

RIVERO, A., J. A. FERRÉ, and FRANCESC GIRALT. "Organized motions in a jet in crossflow." Journal of Fluid Mechanics 444 (September 25, 2001): 117–49. http://dx.doi.org/10.1017/s0022112001005407.

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An experimental study to identify the structures present in a jet in crossflow has been carried out at a jet-to-crossflow velocity ratio U/Ucf = 3.8 and Reynolds number Re = UcfD/v = 6600. The hot-wire velocity data measured with a rake of eight X-wires at x/D = 5 and 15 and flow visualizations using planar laser-induced fluorescence (PLIF) confirm that the well-established pair of counter-rotating vortices is a feature of the mean field and that the upright, tornado-like or Fric's vortices that are shed to the leeward side of the jet are connected to the jet flow at the core. The counter-rotating vortex pair is strongly modulated by a coherent velocity field that, in fact, is as important as the mean velocity field. Three different structures – folded vortex rings, horseshoe vortices and handle-type structures – contribute to this coherent field. The new handle-like structures identified in the current study link the boundary layer vorticity with the counter-rotating vortex pair through the upright tornado-like vortices. They are responsible for the modulation and meandering of the counter-rotating vortex pair observed both in video recordings of visualizations and in the instantaneous velocity field. These results corroborate that the genesis of the dominant counter-rotating vortex pair strongly depends on the high pressure gradients that develop in the region near the jet exit, both inside and outside the nozzle.

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9

Misaka, T., F. Holzäpfel, I. Hennemann, T. Gerz, M. Manhart, and F. Schwertfirm. "Vortex bursting and tracer transport of a counter-rotating vortex pair." Physics of Fluids 24, no. 2 (February 2012): 025104. http://dx.doi.org/10.1063/1.3684990.

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10

García-Azpeitia, Carlos. "Standing waves in a counter-rotating vortex filament pair." Journal of Differential Equations 264, no. 6 (March 2018): 3918–32. http://dx.doi.org/10.1016/j.jde.2017.11.034.

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11

Ryan, Kris, Christopher J. Butler, and Gregory J. Sheard. "Stability characteristics of a counter-rotating unequal-strength Batchelor vortex pair." Journal of Fluid Mechanics 696 (March 6, 2012): 374–401. http://dx.doi.org/10.1017/jfm.2012.55.

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AbstractA Batchelor vortex represents the asymptotic solution of a trailing vortex in an aircraft wake. In this study, an unequal-strength, counter-rotating Batchelor vortex pair is employed as a model of the wake emanating from one side of an aircraft wing; this model is a direct extension of several prior investigations that have considered unequal-strength Lamb–Oseen vortices as representations of the aircraft wake problem. Both solution of the linearized Navier–Stokes equations and direct numerical simulations are employed to study the linear and nonlinear development of a vortex pair with a circulation ratio of$\Lambda = \ensuremath{-} 0. 5$. In contrast to prior investigations considering a Lamb–Oseen vortex pair, we note strong growth of the Kelvin mode$[\ensuremath{-} 2, 0] $coupled with an almost equal growth rate of the Crow instability. Three stages of nonlinear instability development are defined. In the initial stage, the Kelvin mode amplitude becomes sufficiently large that oscillations within the core of the weaker vortex are easily observable and significantly affect the profile of the weaker vortex. In the secondary stage, filaments of secondary vorticity emanate from the weaker vortex and are convected around the stronger vortex. In the tertiary stage, a transition in the dominant instability wavelength is observed from the short-wavelength Kelvin mode to the longer-wavelength Crow instability. Much of the instability growth is observed on the weaker vortex of the pair, although small perturbations in the stronger vortex are observed in the tertiary nonlinear growth phase.

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12

Heister, S. D., J. M. Mcdonough, A. R. Karagozian, and D. W. Jenkins. "The compressible vortex pair." Journal of Fluid Mechanics 220 (November 1990): 339–54. http://dx.doi.org/10.1017/s0022112090003287.

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A numerical solution for the flow field associated with a compressible pair of counter-rotating vortices is developed. The compressible, two-dimensional potential equation is solved utilizing the numerical method of Osher et al. (1985) for flow regions in which a non-zero density exists. Close to the vortex centres, vacuum ‘cores’ develop owing to the existence of a maximum achievable flow speed in a compressible flow field. A special treatment is required to represent these vacuum cores. Typical streamline patterns and core boundaries are obtained for upstream Mach numbers as high as 0.3, and the formation of weak shocks, predicted by Moore & Pullin (1987), is observed.

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13

ORTEGA, J. M., R. L. BRISTOL, and Ö. SAVAŞ. "Experimental study of the instability of unequal-strength counter-rotating vortex pairs." Journal of Fluid Mechanics 474 (January 10, 2003): 35–84. http://dx.doi.org/10.1017/s0022112002002446.

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A rapidly growing instability is observed to develop between unequal-strength counter- rotating vortex pairs. The vortex pairs are generated in a towing tank in the wakes of wings with outboard triangular flaps. The vortices from the wing tip and the inboard tip of the flap form the counter-rotating vortex pair on each side of the wing. The flow fields are studied using flow visualization and particle image velocimetry. Both chord- based and circulation-based Reynolds numbers are of O(105). The circulation strength ratios of the flap- to tip-vortex pairs range from −0.4 to −0.7. The initial sinuous stage of the instability of the weaker flap vortex has a wavelength of order one wing span and becomes observable in about 15 wing spans downstream of the wing. The nearly straight vortex filaments first form loops around the stronger wing-tip vortices. The loops soon detach and form rings and move in the wake under self-induction. These vortex rings can move to the other side of the wake. The subsequent development of the instability makes the nearly quasi-steady and two-dimensional wakes unsteady and three-dimensional over a distance of 50 to 100 wing spans. A rectangular wing is also used to generate the classical wake vortex pair with the circulation ratio of −1.0, which serves as a reference flow. This counter-rotating vortex pair, under similar experimental conditions, takes over 200 spans to develop visible deformations. Velocity, vorticity and enstrophy measurements in a fixed plane, in conjuction with the flow observations, are used to quantify the behaviour of the vortex pairs. The vortices in a pair initially orbit around their vorticity centroid, which takes the pair out of the path of the wing. Once the three-dimensional interactions develop, two-dimensional kinetic energy and enstrophy drop, and enstrophy dispersion radius increases sharply. This rapid transformation of the wake into a highly three-dimensional one offers a possible way of alleviating the hazard posed by the vortex wake of transport aircraft.

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14

Forster, Kyle J., Tracie J. Barber, Sammy Diasinos, and Graham Doig. "Interactions of a counter-rotating vortex pair at multiple offsets." Experimental Thermal and Fluid Science 86 (September 2017): 63–74. http://dx.doi.org/10.1016/j.expthermflusci.2017.04.007.

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15

Bearman, P., A. Heyes, C. Lear, and D. Smith. "Natural and forced evolution of a counter rotating vortex pair." Experiments in Fluids 40, no. 1 (October 14, 2005): 98–105. http://dx.doi.org/10.1007/s00348-005-0051-3.

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16

Zheng, Z. C. "Thin-tube vortex simulations for sinusoidal instability in a counter-rotating vortex pair." International Journal for Numerical Methods in Fluids 39, no. 4 (2002): 301–24. http://dx.doi.org/10.1002/fld.327.

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17

Wang, Jinjun, Chong Pan, Kwing-So Choi, Lei Gao, and Qi-Xiang Lian. "Formation, growth and instability of vortex pairs in an axisymmetric stagnation flow." Journal of Fluid Mechanics 725 (May 23, 2013): 681–708. http://dx.doi.org/10.1017/jfm.2013.205.

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AbstractThe formation, growth and instability of a pair of counter-rotating vortices over a circular plate in the downstream of a thin fishing line were studied using particle image velocimetry and flow visualization. Initially, the vortex pair in an axisymmetric stagnation flow was small, but it grew steadily by accumulating the shear-layer vorticity of the wake before going through vortical instability. Two types of vortical development were observed in the present experiment. Type I was a common type of vortical development in an axisymmetric stagnation flow over a circular plate. Here, the circulation of the vortex pair increased linearly with time reflecting a constant flux of vorticity impinging on the plate wall. After the growth, the counter-rotating pair of vortices went through an antisymmetric deformation in the wall-normal direction while the vortex deformation was symmetric in the wall-parallel direction. This was remarkably similar to the short-wavelength elliptic instability of counter-rotating vortices in an open system. On the other hand, type II development of a vortex pair was a rare case, where the vortices grew for much longer duration than in type I cases. This initiated a breakdown of vortices before the residual vorticity moved away from the centre of the plate. It is considered that the disturbance due to vortical instability could be partially responsible for the unexpectedly high heat transfer rate in the stagnation region of bluff bodies that has been reported in the last half-century.

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18

Navrose, H. G. Johnson, V. Brion, L. Jacquin, and J. C. Robinet. "Optimal perturbation for two-dimensional vortex systems: route to non-axisymmetric state." Journal of Fluid Mechanics 855 (September 21, 2018): 922–52. http://dx.doi.org/10.1017/jfm.2018.689.

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We investigate perturbations that maximize the gain of disturbance energy in a two-dimensional isolated vortex and a counter-rotating vortex pair. The optimization is carried out using the method of Lagrange multipliers. For low initial energy of the perturbation ( $E(0)$ ), the nonlinear optimal perturbation/gain is found to be the same as the linear optimal perturbation/gain. Beyond a certain threshold $E(0)$ , the optimal perturbation/gain obtained from linear and nonlinear computations are different. There exists a range of $E(0)$ for which the nonlinear optimal gain is higher than the linear optimal gain. For an isolated vortex, the higher value of nonlinear optimal gain is attributed to interaction among different azimuthal components, which is otherwise absent in a linearized system. Spiral dislocations are found in the nonlinear optimal perturbation at the radial location where the most dominant wavenumber changes. Long-time nonlinear evolution of linear and nonlinear optimal perturbations is studied. The evolution shows that, after the initial increment of perturbation energy, the vortex attains a quasi-steady state where the mean perturbation energy decreases on a slow time scale. The quasi-steady vortex state is non-axisymmetric and its shape depends on the initial perturbation. It is observed that the lifetime of a quasi-steady vortex state obtained using the nonlinear optimal perturbation is longer than that obtained using the linear optimal perturbation. For a counter-rotating vortex pair, the mechanism that maximizes the energy gain is found to be similar to that of the isolated vortex. Within the linear framework, the optimal perturbation for a vortex pair can be either symmetric or antisymmetric, whereas the structure of the nonlinear optimal perturbation, beyond the threshold $E(0)$ , is always asymmetric. No quasi-steady state for a counter-rotating vortex pair is observed.

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19

GARTEN, J. F., S. ARENDT, D. C. FRITTS, and J. WERNE. "Dynamics of counter-rotating vortex pairs in stratified and sheared environments." Journal of Fluid Mechanics 361 (April 25, 1998): 189–236. http://dx.doi.org/10.1017/s0022112098008684.

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The evolution of a vertically propagating vortex pair in stratified and sheared environments is studied with a two-dimensional numerical model. We consider a range of Froude (Fr) and Richardson (Ri) numbers, and a limited number of Reynolds numbers (Re). We find that stratification causes the formation of counter-sign vorticity around each of the original vortices through baroclinic production. At higher Fr, this wake vorticity advects the primary vortices closer together, decreasing their separation distance and increasing their vertical propagation speed, as predicted by Crow (1974) and Scorer & Davenport (1970). For these higher values of Fr, the wake vorticity also participates in an instability of the primary vortex pair, with the direction of propagation of the pair oscillating about the vertical. We term this instability the vortex head instability to distinguish it from the jet instabilities to which the wake itself is also susceptible. At lower Fr, internal gravity wave radiation dominates, and the intensity and spatial coherence of each vortex is rapidly reduced.When a mean horizontal flow having constant shear is present in an unstratified fluid, we find that the vortices eventually rotate about one another with the same rotational sense as the background shear flow, as predicted in Lissaman et al. (1973). When stratification is also present, we find that the distribution of baroclinically generated wake vorticity is asymmetric, which sometimes leads to the emergence of a solitary vortex with the same sign as the background shear vorticity (depending on the values of Fr, Ri, and Re). Our limited survey of parameter space indicates that a solitary vortex emerges more rapidly for smaller values of Ri, smaller values of Fr, and/or larger values of Re.

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20

Miller, V. A., D. M. Harris, and Charles H. K. Williamson. "Briefing: Interaction of a counter-rotating vortex pair with the ground." Proceedings of the Institution of Civil Engineers - Engineering and Computational Mechanics 162, no. 4 (December 2009): 181–83. http://dx.doi.org/10.1680/eacm.2009.162.4.181.

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21

Nair, Vedanth, Matthew Sirignano, Benjamin Emerson, Ben Halls, Naibo Jiang, Josef Felver, Sukesh Roy, Jim Gord, and Tim Lieuwen. "Counter rotating vortex pair structure in a reacting jet in crossflow." Proceedings of the Combustion Institute 37, no. 2 (2019): 1489–96. http://dx.doi.org/10.1016/j.proci.2018.06.059.

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22

Kim, Kyung Chun. "3. Development of counter-rotating vortex pair in a crossflow jet." Journal of Visualization 3, no. 2 (June 2000): 97. http://dx.doi.org/10.1007/bf03182399.

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23

Devenport, William J., Jeffrey S. Zsoldos, and Christine M. Vogel. "The structure and development of a counter-rotating wing-tip vortex pair." Journal of Fluid Mechanics 332 (February 1997): 71–104. http://dx.doi.org/10.1017/s0022112096003795.

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Experiments have been performed to examine the turbulence structure and development of a pair of counter-rotating wing-tip vortices. The vortices were generated by two rectangular NACA 0012 half wings placed tip to tip, separated by 0.25 chordlengths. Preliminary studies showed the vortices to be insensitive to the introduction of a probe and subject only to small wandering motions. Meaningful measurements could therefore be made using hot-wire probes. Three-component velocity measurements were made 10 and 30 chordlengths downstream of the wing leading edges for a chord Reynolds number of 260000.At 10 chordlengths the vortex cores are laminar. True turbulence levels within them are low and vary little with radius. The turbulence that surrounds the cores is formed by the roll-up of and interaction of the wing wakes that spiral around them. This turbulence is stretched and organized but apparently not produced by the circulating mean velocity fields of the vortices.At 30 chordlengths the vortex cores have become turbulent. True turbulence levels within them are larger and increase rapidly with radius. The turbulent region surrounding the cores has doubled in size and turbulence levels have not diminished, apparently being sustained by outward diffusion from the core regions. The distribution of the turbulence has also changed, the wake spirals having been replaced by a much more core-centred turbulence field.This change in flow structure contrasts sharply with what is seen in the equivalent isolated tip vortex, produced when one of the wings is removed. Here the vortex core remains laminar and the turbulence surrounding it decays rapidly with downstream distance. This implies that the transition to turbulence in the cores of the vortex pair is stimulated by interaction between the vortices. Spectral measurements at 10 chordlengths suggest that short-wave instability may be the cause.

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CORTELEZZI, L., and A. R. KARAGOZIAN. "On the formation of the counter-rotating vortex pair in transverse jets." Journal of Fluid Mechanics 446 (October 23, 2001): 347–73. http://dx.doi.org/10.1017/s0022112001005894.

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Among the important physical phenomena associated with the jet in crossflow is the formation and evolution of vortical structures in the flow field, in particular the counter-rotating vortex pair (CVP) associated with the jet cross-section. The present computational study focuses on the mechanisms for the dynamical generation and evolution of these vortical structures. Transient numerical simulations of the flow field are performed using three-dimensional vortex elements. Vortex ring rollup, interactions, tilting, and folding are observed in the near field, consistent with the ideas described in the experimental work of Kelso, Lim & Perry (1996), for example. The time-averaged effect of these jet shear layer vortices, even over a single period of their evolution, is seen to result in initiation of the CVP. Further insight into the topology of the flow field, the formation of wake vortices, the entrainment of crossflow, and the effect of upstream boundary layer thickness is also provided in this study.

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Forster, Kyle J., Sammy Diasinos, Graham Doig, and Tracie J. Barber. "Large eddy simulation of transient upstream/downstream vortex interactions." Journal of Fluid Mechanics 862 (January 9, 2019): 227–60. http://dx.doi.org/10.1017/jfm.2018.949.

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Experimentally validated large eddy simulations were performed on two NACA0012 vanes at various lateral offsets to observe the transient effects of the near field interactions between two streamwise vortices. The vanes were separated in the streamwise direction, allowing the upstream vortex to impact on the downstream geometry. These vanes were evaluated at an angle of incidence of $8^{\circ }$ and a Reynolds number of 70 000, with rear vane angle reversed to create a co-rotating or counter-rotating vortex pair. The downstream vortex merged with the upstream in the co-rotating condition, driven by the suppression of one of the tip vortices of the downstream vane. At close proximity to the pressure side, the vane elongated the upstream vortex, resulting in it being the weakened and merging into the downstream vortex. This produced a transient production of bifurcated vortices in the wake region. The downstream vortex of the co-rotating pair experienced faster meandering growth, with position oscillations equalising between the vortices. The position oscillation was determined to be responsible for statistical variance in the merging location, with variation in vortex separation causing the vortices at a single plane to merge and separate in a time-dependent manner. In the counter-rotating condition position oscillations were found to be larger, with higher growth, but less uniform periodicity. It was found that the circulation transfer between the vortices was linked to the magnitude of their separation, with high separation fluctuations weakening the upstream vortex and strengthening the downstream vortex. In the case of upstream vortex impingement on the downstream vane, the upstream vortex was found to bifurcate, with a four vortex system being formed by interactions with the shear layer. This eventually resulted in a single dominant vortex, which did not magnify its oscillation amplitudes as it travelled downstream due to the destruction of the interacting vortices.

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YUAN, LESTER L., ROBERT L. STREET, and JOEL H. FERZIGER. "Large-eddy simulations of a round jet in crossflow." Journal of Fluid Mechanics 379 (January 25, 1999): 71–104. http://dx.doi.org/10.1017/s0022112098003346.

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This paper reports on a series of large-eddy simulations of a round jet issuing normally into a crossflow. Simulations were performed at two jet-to-crossflow velocity ratios, 2.0 and 3.3, and two Reynolds numbers, 1050 and 2100, based on crossflow velocity and jet diameter. Mean and turbulent statistics computed from the simulations match experimental measurements reasonably well. Large-scale coherent structures observed in experimental flow visualizations are reproduced by the simulations, and the mechanisms by which these structures form are described. The effects of coherent structures upon the evolution of mean velocities, resolved Reynolds stresses, and turbulent kinetic energy along the centreplane are discussed. In this paper, the ubiquitous far-field counter-rotating vortex pair is shown to originate from a pair of quasi-steady ‘hanging’ vortices. These vortices form in the skewed mixing layer that develops between jet and crossflow fluid on the lateral edges of the jet. Axial flow through the hanging vortex transports vortical fluid from the near-wall boundary layer of the incoming pipe flow to the back side of the jet. There, the hanging vortex encounters an adverse pressure gradient and breaks down. As this breakdown occurs, the vortex diameter expands dramatically, and a weak counter-rotating vortex pair is formed that is aligned with the jet trajectory.

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27

So, Joine, Kris Ryan, and Gregory J. Sheard. "Linear stability analysis of a counter rotating vortex pair of unequal strength." ANZIAM Journal 49 (October 29, 2008): 137. http://dx.doi.org/10.21914/anziamj.v50i0.1455.

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28

Donnadieu, Claire, Sabine Ortiz, Jean-Marc Chomaz, and Paul Billant. "Three-dimensional instabilities and transient growth of a counter-rotating vortex pair." Physics of Fluids 21, no. 9 (September 2009): 094102. http://dx.doi.org/10.1063/1.3220173.

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29

LEWEKE, T., and C. H. K. WILLIAMSON. "Cooperative elliptic instability of a vortex pair." Journal of Fluid Mechanics 360 (April 10, 1998): 85–119. http://dx.doi.org/10.1017/s0022112097008331.

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In this paper, we investigate the three-dimensional instability of a counter-rotating vortex pair to short waves, which are of the order of the vortex core size, and less than the inter-vortex spacing. Our experiments involve detailed visualizations and velocimetry to reveal the spatial structure of the instability for a vortex pair, which is generated underwater by two rotating plates. We discover, in this work, a symmetry-breaking phase relationship between the two vortices, which we show to be consistent with a kinematic matching condition for the disturbances evolving on each vortex. In this sense, the instabilities in each vortex evolve in a coupled, or ‘cooperative’, manner. Further results demonstrate that this instability is a manifestation of an elliptic instability of the vortex cores, which is here identified clearly for the first time in a real open flow. We establish a relationship between elliptic instability and other theoretical instability studies involving Kelvin modes. In particular, we note that the perturbation shape near the vortex centres is unaffected by the finite size of the cores. We find that the long-term evolution of the flow involves the inception of secondary transverse vortex pairs, which develop near the leading stagnation point of the pair. The interaction of these short-wavelength structures with the long-wavelength Crow instability is studied, and we observe significant modifications in the longevity of large vortical structures.

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30

Zheng, Z. C., and W. Li. "Dependence of radiated sound frequency on vortex core dynamics in multiple vortex interactions." Aeronautical Journal 113, no. 1142 (April 2009): 233–42. http://dx.doi.org/10.1017/s0001924000002906.

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Abstract With both theoretical analysis and measurement data, it has been identified previously that there exists a robust sound emission from a pair of counter-rotating aircraft wake vortices at the frequency of unsteady vortex core rotation. In a vortex system with multiple vortices, the sound emission frequency can be subjected to change because of interactions among the vortices. The behaviour of the influence, indicated by the ratio between the core size and the distance of the vortices and the underlining vortex core dynamic mechanisms, is investigated in this study. A vortex particle method is used to simulate the vortex core dynamics in two-dimensional, inviscid and incompressible flow. The flow field, in the form of vorticity, is employed as the source in the far-field acoustic calculation using a vortex sound formula. Cases of co-rotating vortices and a multiple-vortex system composed of two counter-rotating vortex pairs are studied for applications to aircraft wake vortex sound. The study shows, without vortex merging, individual frequencies can be clearly identified that are due each to core rotation (self induction) and co-rotating motion of a vortex centre around the other (mutual induction). The ratio of the core size and the distance between vortices does not seem to significantly influence the frequency of vortex core rotation. With vortex merging, a single frequency due to the merged vortex core is generated.

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31

Eibeck, P. A. "An Experimental Study of the Flow Downstream of a Circular and Tapered Cylinder." Journal of Fluids Engineering 112, no. 4 (December 1, 1990): 393–401. http://dx.doi.org/10.1115/1.2909416.

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The flow downstream of the intersection of both a circular and a tapered cylinder with a flat plate was examined at ReD = 1.3 × 105 using surface visualization, five-hole-probe anemometry, and flow visualization. A pair of large, counter-rotating swirls with common flow away from the wall and with centers over one diameter away from the wall was present downstream of both obstacles. It is suggested that the large, swirling pair are formed in the near wake of an obstacle that is exposed to symmetrical channel flow. A pair of smaller counter-rotating vortices with common flow toward the wall was observed embedded in the wall-shear flow eight diameters downstream of the tapered cylinder. This implies that the legs of the horseshoe vortex system only propagate downstream behind the streamlined obstacle shape.

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32

CHAN, ANDRE S., PETER A. DEWEY, ANTONY JAMESON, CHUNLEI LIANG, and ALEXANDER J. SMITS. "Vortex suppression and drag reduction in the wake of counter-rotating cylinders." Journal of Fluid Mechanics 679 (May 12, 2011): 343–82. http://dx.doi.org/10.1017/jfm.2011.134.

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The flow over a pair of counter-rotating cylinders is investigated numerically and experimentally. It is demonstrated that it is possible to suppress unsteady vortex shedding for gap sizes from one to five cylinder diameters, at Reynolds numbers from 100 to 200, expanding on the more limited work by Chan & Jameson (Intl J. Numer. Meth. Fluids, vol. 63, 2010, p. 22). The degree of unsteady wake suppression is proportional to the speed and the direction of rotation, and there is a critical rotation rate where a complete suppression of flow unsteadiness can be achieved. In the doublet-like configuration at higher rotational speeds, a virtual elliptic body that resembles a potential doublet is formed, and the drag is reduced to zero. The shape of the elliptic body primarily depends on the gap between the two cylinders and the speed of rotation. Prior to the formation of the elliptic body, a second instability region is observed, similar to that seen in studies of single rotating cylinders. It is also shown that the unsteady wake suppression can be achieved by rotating each cylinder in the opposite direction, that is, in a reverse doublet-like configuration. This tends to minimize the wake interaction of the cylinder pair and the second instability does not make an appearance over the range of speeds investigated here.

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33

Mokry, Miroslav. "The Vortex Merger Factor in Aircraft Wake Turbulence." Aeronautical Journal 109, no. 1091 (January 2005): 1–13. http://dx.doi.org/10.1017/s0001924000000531.

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Abstract Vortex merger is studied within the context of two-dimensional discrete vortex sheets and demonstrated on two equally oriented circular vortices and aircraft tip and flap vortices. It is confirmed that, depending on the wing load distribution, the latter may or may not coalesce into a single counter-rotating pair. The interaction of a vortex with an equally oriented shear layer, governed by the same physical principle, suggests a possible intensification of an aircraft vortex in cross-wind shear.

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34

Pierce, F. J., and I. K. Tree. "The Mean Flow Structure on the Symmetry Plane of a Turbulent Junction Vortex." Journal of Fluids Engineering 112, no. 1 (March 1, 1990): 16–22. http://dx.doi.org/10.1115/1.2909361.

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The mean flow structure on the symmetry plane of a turbulent junction vortex is documented. A two-channel, two-color LDV system allowed nonintrusive measurements of the two velocity components on the symmetry plane. Extensive measurements were made in and around the separation point and within the junction vortex system, both very close to the floor and to the leading edge of the body generating the vortex system. Real-time smoke visualizations confirmed a region of strongly time-variant flow with large changes in the scale and position of the principal vortex structure. The extensive velocity field data are correlated with high quality surface visualizations and surface pressure measurements. The mean velocity measurements show one large well-defined vortex structure and one singular saddle point of separation on the symmetry plane. The transverse vorticity field computed from the extensive velocity field suggests a very strong but small second, counter rotating vortex located in the extreme corner formed by the floor and leading edge of the body. The surface flow visualization suggests only one clear separation line. The single pair of counter rotating vortices revealed by these detailed LDV velocity measurements is in agreement with two independent studies which used multiple orifice pressure probes. This measured two vortex model is not in agreement with the frequently pictured four vortex flow model, inferred from surface flow visualizations, showing two pairs of counter rotating vortices.

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35

Marshall, J. S., and H. Chen. "Stability of a Counter-Rotating Vortex Pair Immersed in Cross-Stream Shear Flow." AIAA Journal 35, no. 2 (February 1997): 295–305. http://dx.doi.org/10.2514/2.91.

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36

Marshall, J. S., and H. Chen. "Stability of a counter-rotating vortex pair immersed in cross-stream shear flow." AIAA Journal 35 (January 1997): 295–305. http://dx.doi.org/10.2514/3.13501.

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37

Bearman, P., A. Heyes, C. Lear, and D. Smith. "Evolution of a forced counter rotating vortex pair for two selected forcing frequencies." Experiments in Fluids 43, no. 4 (August 28, 2007): 501–7. http://dx.doi.org/10.1007/s00348-007-0312-4.

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38

Cunningham, Philip, Scott L. Goodrick, M. Yousuff Hussaini, and Rodman R. Linn. "Coherent vortical structures in numerical simulations of buoyant plumes from wildland fires." International Journal of Wildland Fire 14, no. 1 (2005): 61. http://dx.doi.org/10.1071/wf04044.

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The structure and dynamics of buoyant plumes arising from surface-based heat sources in a vertically sheared ambient atmospheric flow are examined via simulations of a three-dimensional, compressible numerical model. Simple circular heat sources and asymmetric elliptical ring heat sources that are representative of wildland fires of moderate intensity are considered. Several different coherent vortical structures that dominate the plume structure and evolution are evident in the simulations, and these structures correspond well with those observed in plumes from wildland fires. For the circular source, these structures include: (i) a counter-rotating vortex pair aligned with the plume trajectory that is associated with a bifurcation of the plume, (ii) transverse shear-layer vortices on the upstream face of the plume, and (iii) vertically oriented wake vortices that form periodically with alternating sign on either side of the downstream edge of the plume base. For the elliptical ring source, a streamwise counter-rotating vortex pair is apparent on each flank, and a transverse horizontal vortex is observed above the head of the source. In all simulations the plume cross section is represented poorly by a self-similar Gaussian distribution.

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39

Shen, Chun, Jianbing Li, and Hang Gao. "Two Parameter-Retrieval Algorithms of Aircraft Wake Vortex with Doppler Lidar in Clear Air." EPJ Web of Conferences 237 (2020): 08024. http://dx.doi.org/10.1051/epjconf/202023708024.

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Aircraft wake is a pair of strong counter-rotating vortices generated behind an aircraft, which might be very hazardous to a flowing aircraft and the detection of which has attracted much attention in aviation safety field. This conference paper introduces two parameter-retrieval algorithms, i.e., Optimization method and Max-min method. They have been integrated into a toolbox and can retrieve the parameters of wake vortex efficiently and robustly.

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40

Ortiz, Sabine, Claire Donnadieu, and Jean-Marc Chomaz. "Three-dimensional instabilities and optimal perturbations of a counter-rotating vortex pair in stratified flows." Physics of Fluids 27, no. 10 (October 2015): 106603. http://dx.doi.org/10.1063/1.4934350.

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41

Habibah, Ummu, Hironori Nakagawa, and Yasuhide Fukumoto. "Finite-thickness effect on speed of a counter-rotating vortex pair at high Reynolds numbers." Fluid Dynamics Research 50, no. 3 (March 1, 2018): 031401. http://dx.doi.org/10.1088/1873-7005/aaa5c8.

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42

Marcus, Daniel L., and Stanley A. Berger. "The interaction between a counter‐rotating vortex pair in vertical ascent and a free surface." Physics of Fluids A: Fluid Dynamics 1, no. 12 (December 1989): 1988–2000. http://dx.doi.org/10.1063/1.857471.

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43

Muppidi, Suman, and Krishnan Mahesh. "Two-dimensional model problem to explain counter-rotating vortex pair formation in a transverse jet." Physics of Fluids 18, no. 8 (August 2006): 085103. http://dx.doi.org/10.1063/1.2236304.

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44

Tunkeaw, Jiratrakul, and Watchapon Rojanaratanangkule. "Effect of external turbulence on the short-wavelength instability of a counter-rotating vortex pair." Physics of Fluids 30, no. 6 (June 2018): 064105. http://dx.doi.org/10.1063/1.5030748.

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45

Fujisawa, Kei. "Onset and evolution of counter-rotating baroclinic vortex pair in shock induced aerobreakup of droplets." Progress in Nuclear Energy 152 (October 2022): 104343. http://dx.doi.org/10.1016/j.pnucene.2022.104343.

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46

Bidan, G., and D. E. Nikitopoulos. "On steady and pulsed low-blowing-ratio transverse jets." Journal of Fluid Mechanics 714 (January 2, 2013): 393–433. http://dx.doi.org/10.1017/jfm.2012.482.

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AbstractThe present experimental and numerical study focuses on the vortical structures encountered in steady and pulsed low-blowing-ratio transverse jets ($0. 150\leq \mathit{BR}\leq 4. 2$), a configuration hardly discussed in the literature. Under unforced conditions at low blowing ratio, a stable leading-edge shear-layer rollup is identified inside the jet pipe. As the blowing ratio is increased, the destabilization and evolution of this structure sheds light on the formation mechanisms of the well-known transverse jet vortical system. A discussion on the nature of the counter-rotating vortex pair in low-blowing-ratio transverse jets is also provided. Under forced conditions, the experimental observations support and extend numerical results of previous fully modulated jet studies. Large-eddy simulation results provide scaling parameters for the classification of starting vortices for partly modulated jets, as well as information on their three-dimensional dynamics. The counter-rotating vortex pair initiation is observed and detailed in both Mie scattering visualizations and simulations. The observations support a mechanism based on stretching of the starting vortical structures because of inviscid induction and partial leapfrogging. Two modes of cross-flow ingestion inside the jet pipe are described as the pulsed jet cycles from high to low values of blowing ratio.

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47

Liu, Yanming, Hong Zhang, and Pingchao Liu. "Flow control in supersonic flow field based on micro jets." Advances in Mechanical Engineering 11, no. 1 (January 2019): 168781401882152. http://dx.doi.org/10.1177/1687814018821526.

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The flow field around supersonic aircraft is usually accompanied by complex flow phenomena, such as shock wave and shock wave/boundary layer interaction, which cause some adverse effects on aircraft performance. Seeking effective flow control methods has been a hot topic for many researchers. As an important method to improve the flow characteristics in supersonic flows, micro jet technology and its control mechanism have been paid much attention. In this article, we used compression corner calculation model and conducted detailed numerical investigations in the supersonic flow field with different injection pressure ratios, various actuation positions, and different nozzle types. The interaction between the micro jets and supersonic upstream flows generates complex flow structures, which contain bow shocks, barrel shocks, Mach disk, counter-rotating vortex pairs, and so on. The flow characteristics with micro jet schemes are superior to those in the no-control case. The controlling performance of micro jet is mainly determined by the following aspects. First, the downwash effect of counter-rotating vortex pairs can bring high-energy fluid into the bottom of the boundary layer to activate low-energy fluid and then strengthen the ability of resisting the flow separations. Second, the bow shock, which is generated upstream of the micro jet, significantly decelerates the downstream flows. Thus, the shock intensity at the corner is weakened and the characteristic of shock wave/boundary layer interaction is improved. In addition, the effective function range of MJ, that is, the distance between the counter-rotating vortex pair and the wall surface, is also an important factor. When both the counter-rotating vortex pairs and the bow shock are further from the wall, the flow characteristics around the corner in a larger area can be improved. Research shows that the micro jet scheme with Laval nozzle gives better controlling effect on shock wave/boundary layer interaction when the injection pressure radio is set to be 0.6, with the actuation location being 20 times the jet outlet diameter upstream of the corner.

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48

Wu, J., J. Sheridan, and M. C. Welsh. "Velocity Perturbations Induced by the Longitudinal Vortices in a Cylinder Wake." Journal of Fluids Engineering 118, no. 3 (September 1, 1996): 531–36. http://dx.doi.org/10.1115/1.2817791.

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This paper presents data showing the three-dimensional vortical structures in the near wake region of circular cylinders. The in-plane velocity field was measured using a digital Particle Image Velocimetry (PIV) technique. The vortical structures are found to include inclined counter-rotating longitudinal vortices in the braids joining consecutive Ka´rma´n vortices. A simple vortex-pair model is proposed to estimate velocity perturbation induced by the longitudinal vortices in the near wake region. The perturbation resulting from the longitudinal vortices is shown to induce spanwise velocity modulation and a velocity spike of a nominally two-dimensional vortex street.

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49

Song, Kewei, Lu Wang, Yajun Hu, and Qi Liu. "Flow Symmetry and Heat Transfer Characteristics of Winglet Vortex Generators Arranged in Common Flow up Configuration." Symmetry 12, no. 2 (February 5, 2020): 247. http://dx.doi.org/10.3390/sym12020247.

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The generation of longitudinal vortices is an effective method for promoting thermal performance with a relative low-pressure penalty in heat exchangers. The winglet pair can generate symmetrical longitudinal vortices on the cross-section of the channel. The heat transfer and pressure-loss characteristics of a pair of winglet vortex generators with different transverse pitches are numerically studied in this paper. The winglet pair arranged in a common flow up configuration generates a pair of symmetrical longitudinal main vortices with counter-rotating directions. The symmetrical flow structure induces fluid to flow from the bottom towards the top of the channel in the common flow region between the longitudinal vortices. The flow symmetry of the longitudinal vortices and the heat transfer performance are strongly affected by the transverse pitch of the winglet pair owing to the interaction between the longitudinal vortices. The optimal transverse pitch of the studied winglet pair with the best thermal performance is reported. The increments in the vortex intensity and the Nusselt number for the optimal pitch are increased by up to 21.4% and 29.2%, respectively.

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50

Hirsa, A., and W. W. Willmarth. "Measurements of vortex pair interaction with a clean or contaminated free surface." Journal of Fluid Mechanics 259 (January 25, 1994): 25–45. http://dx.doi.org/10.1017/s0022112094000029.

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Laminar vortex pairs with small Froude number were generated by a submerged delta wing at negative angle of attack or by a pair of vertically oriented, counter-rotating flaps. The vortex pairs thus generated rise and interact with the free surface. The surface and subsurface flow field was studied using flow visualization and particle image velocimetry. Initial surface deformations, striations, are shown to be caused by stretching and interaction of cross-stream vortices near the surface. With small amounts of surface contamination, contamination fronts (producing Reynolds ridges) form on the surface and secondary vorticity, generated beneath the surface beyond the fronts, rolls up to form vortices with opposite rotation outboard of the primary vortices. The circulation associated with the secondary vortices is as much as 1/3 that of the primary vortices. The secondary vortices cause the primary vortex pair to rebound from the surface. Slight surface deformations, scars, are caused by the primary and secondary vortices.

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