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1
Doerffer, Piotr, Pawel Flaszynski, and Franco Magagnato. "Streamwise vortex interaction with a horseshoe vortex." Journal of Thermal Science 12, no. 4 (November 2003): 304–9. http://dx.doi.org/10.1007/s11630-003-0035-7.
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Hamilton, James M., and Frederick H. Abernathy. "Streamwise vortices and transition to turbulence." Journal of Fluid Mechanics 264 (April 10, 1994): 185–212. http://dx.doi.org/10.1017/s0022112094000637.
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A series of experiments was conducted to determine the conditions under which streamwise vortices can cause transition to turbulence in shear flows. A specially designed obstacle was used to produce a single vortex in a water-table flow, and the design of this obstacle is discussed. Laser-Doppler velocimetry measurements of the streamwise and crossflow velocity fields were made in transitional and non-transitional flows, and flow visualization was also used. It was found that strong vortices (vortices with large circulation) lead to turbulence while weaker vortices do not. Determination of a critical value of vortex strength for transition, however, was complicated by ambiguities in calculating the vortex circulation. The profiles of streamwise velocity were found to be inflexional for both transitional and non-transitional flows. Transition in single-vortex and multi-vortex flows was compared, and no qualitative differences were observed, suggesting no significant vortex interactions affecting transition.
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McKenna, C., M. Bross, and D. Rockwell. "Structure of a streamwise-oriented vortex incident upon a wing." Journal of Fluid Mechanics 816 (March 6, 2017): 306–30. http://dx.doi.org/10.1017/jfm.2017.87.
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Impingement of a streamwise-oriented vortex upon a fin, tail, blade or wing represents a fundamental class of flow–structure interaction that extends across a range of applications. It can give rise to unsteady loading known as buffeting and to changes of the lift to drag ratio. These consequences are sensitive to parameters of the incident vortex as well as the location of vortex impingement on the downstream aerodynamic surface, generically designated as a wing. Particle image velocimetry is employed to determine patterns of velocity and vorticity on successive cross-flow planes along the vortex, which lead to volume representations and thereby characterization of the streamwise evolution of the vortex structure as it approaches the downstream wing. This evolution of the incident vortex is affected by the upstream influence of the downstream wing, and is highly dependent on the spanwise location of vortex impingement. Even at spanwise locations of impingement well outboard of the wing tip, a substantial influence on the structure of the incident vortex at locations significantly upstream of the leading edge of the wing was observed. For spanwise locations close to or intersecting the vortex core, the effects of upstream influence of the wing on the vortex are to: decrease the swirl ratio; increase the streamwise velocity deficit; decrease the streamwise vorticity; increase the azimuthal vorticity; increase the upwash; decrease the downwash; and increase the root-mean-square fluctuations of both streamwise velocity and vorticity. The interrelationship between these effects is addressed, including the rapid attenuation of axial vorticity in presence of an enhanced defect of axial velocity in the central region of the vortex. When the incident vortex is aligned with, or inboard of, the tip of the wing, the swirl ratio decreases to values associated with instability of the vortex, thereby giving rise to enhanced values of azimuthal vorticity relative to the streamwise (axial) vorticity, as well as relatively large root-mean-square values of streamwise velocity and vorticity.
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Namgyal, Lhendup, and Joseph W. Hall. "Coherent Streamwise Vortex Structure of a Three-Dimensional Wall Jet." Fluids 6, no. 1 (January 11, 2021): 35. http://dx.doi.org/10.3390/fluids6010035.
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The dynamics of the coherent structures in a turbulent three-dimensional wall jet with an exit Reynolds number of 250,000 were investigated using the Snapshot Proper Orthogonal Decomposition (POD). A low-dimensional reconstruction using the first 10 POD modes indicates that the turbulent flow is dominated by streamwise vortex structures that grow in size and relative strength, and that are often accompanied by strong lateral sweeps of fluid across the wall. This causes an increase in the bulging and distortions of streamwise velocity contours as the flow evolves downstream. The instantaneous streamwise vorticity computed from the reconstructed instantaneous velocities has a high level of vorticity associated with these outer streamwise vortex structures, but often has a persistent pair of counter-rotating regions located close to the wall on either side of the jet centerline. A model of the coherent structures in the wall jet is presented. In this model, streamwise vortex structures are produced in the near-field by the breakdown of vortex rings formed at the jet outlet. Separate structures are associated with the near-wall streamwise vorticity. As the flow evolves downstream, the inner near-wall structures tilt outward, while the outer streamwise structures amalgamate to form larger streamwise asymmetric structures. In all cases, these streamwise vortex structures tend to cause large lateral velocity sweeps in the intermediate and far-field regions of the three-dimensional wall jet. Further, these structures meander laterally across the jet, causing a strongly intermittent jet flow.
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Namgyal, Lhendup, and Joseph W. Hall. "Coherent Streamwise Vortex Structure of a Three-Dimensional Wall Jet." Fluids 6, no. 1 (January 11, 2021): 35. http://dx.doi.org/10.3390/fluids6010035.
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The dynamics of the coherent structures in a turbulent three-dimensional wall jet with an exit Reynolds number of 250,000 were investigated using the Snapshot Proper Orthogonal Decomposition (POD). A low-dimensional reconstruction using the first 10 POD modes indicates that the turbulent flow is dominated by streamwise vortex structures that grow in size and relative strength, and that are often accompanied by strong lateral sweeps of fluid across the wall. This causes an increase in the bulging and distortions of streamwise velocity contours as the flow evolves downstream. The instantaneous streamwise vorticity computed from the reconstructed instantaneous velocities has a high level of vorticity associated with these outer streamwise vortex structures, but often has a persistent pair of counter-rotating regions located close to the wall on either side of the jet centerline. A model of the coherent structures in the wall jet is presented. In this model, streamwise vortex structures are produced in the near-field by the breakdown of vortex rings formed at the jet outlet. Separate structures are associated with the near-wall streamwise vorticity. As the flow evolves downstream, the inner near-wall structures tilt outward, while the outer streamwise structures amalgamate to form larger streamwise asymmetric structures. In all cases, these streamwise vortex structures tend to cause large lateral velocity sweeps in the intermediate and far-field regions of the three-dimensional wall jet. Further, these structures meander laterally across the jet, causing a strongly intermittent jet flow.
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Carlson, Bailey, Al Habib Ullah, and Jordi Estevadeordal. "Experimental Investigation of Vortex-Tube Streamwise-Vorticity Characteristics and Interaction Effects with a Finite-Aspect-Ratio Wing." Fluids 5, no. 3 (July 24, 2020): 122. http://dx.doi.org/10.3390/fluids5030122.
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An experimental study is conducted to analyze a streamwise-oriented vortex and investigate the unsteady interaction with a finite-aspect-ratio wing. A pressurized vortex tube is used to generate streamwise vortices in a wind tunnel and the resulting flow behavior is analyzed. The vortex tube, operated at various pressures, yields flows that evolve downstream under several freestream wind tunnel speeds. Flow measurements are performed using two- and three- dimensional (2D and 3D) particle image velocimetry to observe vortices and their freestream interactions from which velocity and vorticity data are comparatively analyzed. Results indicate that vortex velocity greater than freestream flow velocity is a primary factor in maintaining vortex structures further downstream, while increased supply pressure and reduced freestream velocity also reduce vortex dissipation rate. The generated streamwise-oriented vortex is also impinged on a finite-aspect-ratio airfoil wing with a cross-section of standard NACA0012 airfoil. The wingtip-aligned vortex is shown to investigate the interaction of the streamwise vortex and the wingtip vortex region. The results indicate that the vorticity at the high vortex-tube pressure has a significant effect on the boundary layer of airfoil.
7
Younis, Md Yamin, Hua Zhang, Reiwei Zhu, and Zaka Muhammad. "Horseshoe Vortex Control Using Streamwise Vortices." Procedia Engineering 126 (2015): 139–44. http://dx.doi.org/10.1016/j.proeng.2015.11.196.
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Hiejima, Toshihiko. "Streamwise vortex breakdown in supersonic flows." Physics of Fluids 29, no. 5 (May 2017): 054102. http://dx.doi.org/10.1063/1.4982901.
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SZWABA, Ryszard, Pawel FLASZYNSKI, and Piotr DOERFFER. "Streamwise vortex generation by the rod." Chinese Journal of Aeronautics 32, no. 8 (August 2019): 1903–11. http://dx.doi.org/10.1016/j.cja.2019.03.033.
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Yaras, M. I. "Measurements of Surface-Roughness Effects on the Development of a Vortex Produced by an Inclined Jet in Cross-Flow." Journal of Fluids Engineering 126, no. 3 (May 1, 2004): 346–54. http://dx.doi.org/10.1115/1.1758260.
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This study examines the effects of surface roughness on the streamwise development of a vortex created by an isolated circular jet injected at 45 deg pitch and 90 deg skew into a crossflow. The study is motivated by the typical surface conditions encountered on in-service turbine blades of gas-turbine engines. Detailed measurements of the velocity field have been performed with a miniature four-wire probe at the jet exit plane, in the oncoming cross-stream boundary layer, and in a series of planes that capture the streamwise development of the vortex in the crossflow boundary layer up to about 15 jet-discharge diameters downstream of the jet. The paper presents the effects of surface roughness on the structure of the dominant streamwise vortex created by the interaction of the inclined jet with the mainstream, and documents the changes in the location, streamwise rate of change of circulation, and streamwise rate of diffusion of this vortex. Through these results, the change in the effectiveness of the vortex in energizing the boundary layer in the presence of surface roughness can be quantified.
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MIRONOV, S. G., and A. A. MASLOV. "Experimental study of secondary instability in a hypersonic shock layer on a flat plate." Journal of Fluid Mechanics 412 (June 10, 2000): 259–77. http://dx.doi.org/10.1017/s0022112000008387.
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The development of secondary instability on streamwise vortex structures generated in a hypersonic shock layer on a flat plate is experimentally studied for the flow with Mach number M∞ = 21 and unit Reynolds number Re1 = 6 × 105 m−1. The study is performed using the electron-beam method. The generation of weak unsteady vortices and steady streamwise vortex structures with finite-amplitude perturbations imposed onto them is studied in detail. Complex data on the characteristics of density fluctuations developed on quasi-steady and unsteady streamwise vortex structures are obtained. It is shown that the characteristics of the natural fluctuations of density developing in the shock layer on a flat plate are qualitatively similar to density fluctuations induced by weak unsteady vortex perturbations introduced into the shock layer. The possibility of existence of parametric resonance between the fundamental frequency and its harmonic and between harmonics for steady streamwise vortex structure is shown.
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McLelland, Grant, David MacManus, and Chris Sheaf. "A semi-empirical model for streamwise vortex intensification." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 233, no. 12 (April 2019): 4396–409. http://dx.doi.org/10.1177/0954410019838421.
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Vortex intensification plays an important role in a wide range of flows of engineering interest. One scenario of interest is when a streamwise vortex passes through the contracting streamtube of an aircraft intake. There is, however, limited experimental data of flows of this type to reveal the dominant flow physics and to guide the development of vortex models. To this end, the evolution of wing-tip vortices inside a range of streamtube contractions has been measured using stereoscopic particle image velocimetry. A semi-empirical model has been applied to provide new insight on the role of vorticity diffusion during the intensification process. The analysis demonstrates that for mild flow contractions, vorticity diffusion has a negligible influence due to the low rates of diffusion in the vortex flow prior to intensification and the short convective times associated with the streamtube contraction. As the contraction levels increase, there is a substantial increase in the rates of diffusion which is driven by the greater levels of vorticity in the vortex core. A new semi-empirical relationship, as a function of the local streamtube contraction levels and vortex Reynolds number, has been developed. The model comprises a simple correction to vortex filament theory and provides a significant improvement in the estimation of vortex characteristics in contracting flows. For the range of contractions investigated, errors in the estimation of vortex core radius, peak tangential velocity and vorticity are reduced by an order of magnitude. The model can be applied to estimate the change in vortex characteristics for a range of flows with intense axial strain, such as contracting intake streamtubes and swirling flows in turbomachinery.
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Hall, Philip. "Streamwise vortices in heated boundary layers." Journal of Fluid Mechanics 252 (July 1993): 301–24. http://dx.doi.org/10.1017/s0022112093003775.
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The nonlinear instability of the boundary layer on a heated flat plate placed in an oncoming flow is investigated. Such flows are unstable to stationary vortex instabilities and inviscid travelling wave disturbances governed by the Taylor-Goldstein equation. For small temperature differences the Taylor-Goldstein equation reduces to Rayleigh's equation. When the temperature difference between the wall and free stream is small the preferred mode of instability is a streamwise vortex. It is shown in this case that the vortex, assumed to be of small wavelength, restructures the underlying mean flow to produce a profile which can be massively unstable to inviscid travelling waves. The mean state is shown to be destabilized if the Prandtl number is less than unity.
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Bernal, L. P., and A. Roshko. "Streamwise vortex structure in plane mixing layers." Journal of Fluid Mechanics 170 (September 1986): 499–525. http://dx.doi.org/10.1017/s002211208600099x.
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The development of three-dimensional motions in a plane mixing layer was investigated experimentally. It is shown that superimposed on the primary, spanwise vortex structure there is a secondary, steamwise vortex structure. Three aspects of this secondary structure were studied. First, the spanwise vortex instability that generates the secondary structure was characterized by measurements of the critical Reynolds number and the spanwise wavelength at several flow conditions. While the critical Reynolds number was found to depend on the velocity ratio, density ratio and initial shear-layer-profile shape, the mean normalized wavelength is independent of these parameters. Secondly, flow visualization in water was used to obtain cross-sectional views of the secondary structure associated with the streamwise counter-rotating vortices. A model is proposed in which those vortices are part of a single vortex line winding back and forth between the high-speed side of a primary vortex and the low-speed side of the following one. Finally, the effect of the secondary structure on the spanwise concentration field was measured in a helium–nitrogen mixing layer. The spatial organization of the secondary structure produces a well-defined spanwise entrainment pattern in which fluid from each stream is preferentially entrained at different spanwise locations. These measurements show that the spanwise scale of the secondary structure increases with downstream distance.
15
Lee, T., and Y. Adukesem. "Interaction of a Streamwise Vortex with a Blade Tip Vortex." Journal of Aircraft 43, no. 6 (November 2006): 1956–58. http://dx.doi.org/10.2514/1.26324.
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Wang, Peng, Chen, and Fan. "Analysis of the Interconnections between Classic Vortex Models of Coherent Structures Based on DNS Data." Water 11, no. 10 (September 26, 2019): 2005. http://dx.doi.org/10.3390/w11102005.
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Low- and high-speed streaks (ejection, Q2, and sweep, Q4, events in quadrant analysis) are significant features of coherent structures in turbulent flow. Streak formation is closely related to turbulent structures in several vortex models, such as attached eddy models, streamwise vortex analysis models, and hairpin vortex models, which are all standard models. Vortex models are complex, whereby the relationships among the different vortex models are unclear; thus, further studies are still needed to complete our understanding of vortices. In this study, 30 sets of direct numerical simulation (DNS) data were obtained to analyze the mechanics of the formation of coherent structures. Image processing techniques and statistical analysis were used to identify and quantify streak characteristics. We used a method of vortex recognition to extract spanwise vortices in the x–z plane. Analysis of the interactions among coherent structures showed that the three standard vortex models all gave reasonably close results. The attached eddy vortex model provides a good explanation of the linear dimensions of streaky structures with respect to the water depth and Q2 and Q4 events, whereby it can be augmented to form the quasi-streamwise vortex model. The legs of a hairpin vortex envelop low-speed streaky structures and so move in the streamwise direction; lower-velocity vortex legs also gradually accumulate into a streamwise vortex. Statistical analysis allowed us to combine our present results with some previous research results to propose a mechanism for the formation of streaky structures. This study provides a deeper understanding of the interrelationships among different vortex models.
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Fishman, G., and D. Rockwell. "Onset of orbital motion in a trailing vortex from an oscillating wing." Journal of Fluid Mechanics 856 (October 2, 2018): 257–87. http://dx.doi.org/10.1017/jfm.2018.697.
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The onset and development of orbital motion of a trailing vortex from a wing undergoing small amplitude heaving motion is investigated using stereo particle image velocimetry in conjunction with three-dimensional reconstruction techniques. The effect of Strouhal number is examined via space–time representations of axial and azimuthal vorticity, axial velocity deficit and swirl ratio. At low Strouhal number, the undulation of the vortex remains unidirectional with no amplification in the streamwise direction. In contrast, at high Strouhal number, the amplitude of vortex undulation can increase by up to a factor of ten in the streamwise direction. These large amplitudes occur during orbital motion of the vortex. Irrespective of the value of either the Strouhal number of excitation or the streamwise location along the undulating vortex, generic physical mechanisms occur. Changes in curvature along the vortex are closely related to changes in the axial velocity deficit, extreme values of axial vorticity and swirl ratio and the onset and attenuation of pronounced azimuthal vorticity.
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Garmann, D. J., and M. R. Visbal. "Interactions of a streamwise-oriented vortex with a finite wing." Journal of Fluid Mechanics 767 (February 24, 2015): 782–810. http://dx.doi.org/10.1017/jfm.2015.51.
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AbstractA canonical study is developed to investigate the unsteady interactions of a streamwise-oriented vortex impinging upon a finite surface using high-fidelity simulation. As a model problem, an analytically defined vortex superimposed on a free stream is convected towards an aspect-ratio-six ($\mathit{AR}=6$) plate oriented at an angle of ${\it\alpha}=4^{\circ }$ and Reynolds number of $\mathit{Re}=20\,000$ in order to characterize the unsteady modes of interaction resulting from different spanwise positions of the incoming vortex. Outboard, tip-aligned and inboard positioning are shown to produce three distinct flow regimes: when the vortex is positioned outboard of, but in close proximity to, the wingtip, it pairs with the tip vortex to form a dipole that propels itself away from the plate through mutual induction, and also leads to an enhancement of the tip vortex. When the incoming vortex is aligned with the wingtip, the tip vortex is initially strengthened by the proximity of the incident vortex, but both structures attenuate into the wake as instabilities arise in the pair’s feeding sheets from the entrainment of opposite-signed vorticity into either structure. Finally, when the incident vortex is positioned inboard of the wingtip, the vortex bifurcates in the time-mean sense with portions convecting above and below the wing, and the tip vortex is mostly suppressed. The time-mean bifurcation is actually a result of an unsteady spiralling instability in the vortex core that reorients the vortex as it impacts the leading edge, pinches off, and alternately attaches to either side of the wing. The increased effective angle of attack inboard of impingement enhances the three-dimensional recirculation region created by the separated boundary layer off the leading edge which draws fluid from the incident vortex inboard and diminishes its impact on the outboard section of the wing. The slight but remaining downwash present outboard of impingement reduces the effective angle of attack in that region, resulting in a small separation bubble on either side of the wing in the time-mean solution, effectively unloading the tip outboard of impingement and suppressing the tip vortex. All incident vortex positions provide substantial increases in the wing’s lift-to-drag ratio; however, significant sustained rolling moments also result. As the vortex is brought inboard, the rolling moment diminishes and eventually switches sign as the reduced outboard loading balances the augmented sectional lift inboard of impingement.
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Chadwick, Edmund. "The vortex line in steady, incompressible Oseen flow." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2066 (November 29, 2005): 391–401. http://dx.doi.org/10.1098/rspa.2005.1593.
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The horseshoe vortex is given in Oseen flow as a constant spanwise distribution of lift Oseenlets. From this, the vortex line is represented in steady, incompressible Oseen flow. The velocity near to the vortex line is determined, as well as near to and far from the far field wake. The velocity field in the transverse plane near to the vortex line is shown to approximate to the two-dimensional Lamb–Oseen vortex, and the velocity field in the streamwise direction is generated by the bound vortex line of the horseshoe vortex giving a streamwise decay much faster than that of the Batchelor vortex. The far field wake description is shown to be consistent with laminar wake theory.
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Kim, Lina, and Jeff Moehlis. "Transient growth for streak-streamwise vortex interactions." Physics Letters A 358, no. 5-6 (October 2006): 431–37. http://dx.doi.org/10.1016/j.physleta.2006.05.052.
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GOTODA, Hiroshi, Yu HASHIBA, Toshihiko HIEJIMA, Kazumichi MATSUTANI, and Michio NISHIOKA. "Instability of a Hollow-Type Streamwise Vortex." TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series B 78, no. 787 (2012): 531–40. http://dx.doi.org/10.1299/kikaib.78.531.
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Schowalter, David G., Charles W. Van Van Atta, and Juan C. Lasheras. "A study of streamwise vortex structure in a stratified shear layer." Journal of Fluid Mechanics 281 (December 25, 1994): 247–91. http://dx.doi.org/10.1017/s0022112094003101.
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The existence of an organized streamwise vortical structure, which is superimposed on the well known coherent spanwise vorticity in nominally two-dimensional free shear layers, has been studied extensively. In the presence of stratification, however, buoyancy forces contribute to an additional mechanism for the generation of streamwise vorticity. As the spanwise vorticity layer rolls up and pulls high-density fluid above low-density fluid, a local instability results. The purpose of the current investigation is to force the three-dimensional instability in the stratified shear layer. In this manner, we experimentally observe the effect of buoyancy on the streamwise vortex tube evolution, the evolution of the buoyancy-induced instability, and the interaction between these two vortical structures. A simple numerical model is proposed which captures the relevant physics of the flow evolution. It is found that, depending on the location, streamwise vortices resulting from vortex stretching may be weakened or enhanced by the stratification. Buoyancy-induced vortex structures are shown to form where the unstable part of the interface is tilted by the streamwise vortex tubes. These vortices strengthen initially, then weaken downstream, the timescale for this process depending upon the degree of stratification. For initial Richardson numbers larger than about 0.03, the baroclinically weakened vortex tubes eventually disappear as the flow evolves downstream and the baroclinically generated vortices dominate the three-dimensional flow structure.
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Jukes, Timothy N., and Kwing-So Choi. "On the formation of streamwise vortices by plasma vortex generators." Journal of Fluid Mechanics 733 (September 23, 2013): 370–93. http://dx.doi.org/10.1017/jfm.2013.418.
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AbstractThe streamwise vortices generated by dielectric-barrier-discharge plasma actuators in the laminar boundary layer were investigated using particle image velocimetry to understand the vortex-formation mechanisms. The plasma vortex generator was oriented along the primary flow direction to produce a body force in the spanwise direction. This created a spanwise-directed wall jet which interacted with the oncoming boundary layer to form a coherent streamwise vortex. It was found that the streamwise vortices were formed by the twisting and folding of the spanwise vorticity in the oncoming boundary layer into the outer shear layer of the spanwise wall jet, which added its own vorticity to increase the circulation along the actuator length. This is similar to the delta-shaped, vane-type vortex generator, except that the circulation was enhanced by the addition of the vorticity in the plasma jet. It was also observed that the plasma vortex was formed close to the wall with an enhanced wall-ward entrainment, which created strong downwash above the actuator.
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Liu, J. T. C. "An extended Reynolds analogy for excited wavy instabilities of developing streamwise vortices with applications to scalar mixing intensification." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2083 (May 16, 2007): 1791–813. http://dx.doi.org/10.1098/rspa.2007.1848.
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Studies are presented to elucidate the role of steady streamwise vortex structures, initiated upstream from weak Görtler vortices in the absence of explicit vortex generators, and their excited nonlinear wavy instabilities in the intensification of scalar mixing in a spatially developing mixing region. While steady streamwise vortex flow gives rise to significant mixing enhancement, the excited nonlinear wavy instabilities, which in turn modify the basic three-dimensional streamwise vortices, give rise to further mixing intensification which is quantitatively assessed by a mixedness parameter. Possibility of similarity between the dimensionless streamwise momentum and scalar transport problems leading to an extended Reynolds analogy is sought. This similarity is shown earlier to hold for the steady streamwise vortex flow in the absence of nonlinear wavy instabilities (Liu & Sabry 1991 Proc. R. Soc. A 432 , 1–12). In this paper, the momentum conservation equations for the nonlinear wavy or secondary instabilities together with the advected fluctuation scalar problems are examined in detail. The presence of the streamwise fluctuation pressure gradient, which prevents the similarity, is estimated in terms of the fluctuation dynamical pressure and its relative importance to advective transport. It is found from scaling that the fluctuating streamwise pressure gradient, though not completely negligible, is sufficiently unimportant so as to render similarity between fluctuation streamwise velocity and fluctuation temperature and concentration a distinct possibility. The scalar fluctuations are then inferable from the fluctuation streamwise velocity and that the Reynolds stresses of the nonlinear fluctuations and the scalar fluxes are also similar. The nonlinear instability-modified mean streamwise momentum and the modified mean heat and mass transport problems are also similar, thus providing a complete ‘Reynolds analogy’, rendering possible the interpretation of the scalar mixedness for a gaseous medium for which the Prandtl and Schmidt numbers are near unity. It is found that the nonlinearity of the wavy instability, which induces scalar fluxes modifying the mean scalar transport, further intensifies scalar mixedness over a significant streamwise region which is well above that achieved by the steady, unmodified streamwise vortices alone for the numerical example corresponding to the most amplified wavy-sinuous mode.
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Lee, T., and Y. Aboelkassem. "Erratum: Interaction of a Streamwise Vortex with a Blade Tip Vortex." Journal of Aircraft 44, no. 2 (March 2007): 702. http://dx.doi.org/10.2514/1.30574.
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Fan, Dong, and Chao Zhou. "Streamwise vortex transportation and loss generation in an intermediate turbine duct." Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 234, no. 6 (October 3, 2019): 766–76. http://dx.doi.org/10.1177/0957650919879309.
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Annular S-shaped intermediate turbine ducts are used in modern turbofan engines with large by-pass ratios. To reduce the weight of an engine, the intermediate turbine ducts should be as short as possible, while keeping the loss at an acceptable level. Understanding the flow physics within the intermediate turbine ducts is the key to improve the intermediate turbine duct design. This paper aims to understand the transportation of the inlet streamwise vortices and loss generation in intermediate turbine ducts. First, cases with isolate incoming streamwise vortices at different spanwise locations and different axial velocities are investigated. The transportation of isolated vortex and loss generation are highly related to the interaction between vortex and boundary layer, which are mainly determined by the streamwise pressure gradient. When the axial velocity of the streamwise vortex is different to the main flow, the radial pressure gradient also has an effect. Then, the inlet condition of the intermediate turbine ducts is setup based on the flow field at the exit of a cascade, which contains the flow structures such as the tip leakage vortex, hub secondary vortex and the wake. The flow physics and the loss mechanism are analysed in detail. The formation mechanism of counter-rotating vortices pair and the influence of inlet vortex on loss generation within the intermediate turbine ducts are also presented.
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SHAH, P. N., P. ATSAVAPRANEE, T. Y. HSU, T. WEI, and J. McHUGH. "Turbulent transport in the core of a trailing half-delta-wing vortex." Journal of Fluid Mechanics 387 (May 25, 1999): 151–75. http://dx.doi.org/10.1017/s0022112099004553.
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The development of a turbulent streamwise vortex core in the wake of a half delta wing has been examined using high-resolution DPIV. The objective of this work was to gain understanding of the transport processes at work a short distance downstream of the wing trailing edge as the wake vortex developed. Experiments were conducted in the Rutgers Free Surface Water Tunnel using an in-house DPIV system. A turbulent streamwise vortex was generated by a half delta wing, with 44 cm chord length and 60° sweep angle, mounted at 30° angle of attack. Reynolds number based on chord length was 65 000. Laser sheets oriented perpendicular to the flow direction were positioned 1, 3.5, and 7 chord lengths downstream of the wing trailing edge. Instantaneous vortex centres were identified in order to track vortex meandering as well as for better quantification of turbulence levels in the vortex core. Mean and fluctuating turbulence terms in the mean streamwise vorticity transport equation along with turbulent kinetic energy dissipation and production were evaluated relative to an inertial reference frame as well as relative to a vortex-centred frame. The results of this analysis highlight the importance of this near-wake region to the downstream evolution of the trailing vortices. There is a high degree of dissipation as well as streamwise vorticity convection in the very near wake which decreases rapidly with increasing distance from the trailing edge.
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Martin, J. E., and E. Meiburg. "Numerical investigation of three-dimensionally evolving jets subject to axisymmetric and azimuthal perturbations." Journal of Fluid Mechanics 230 (September 1991): 271–318. http://dx.doi.org/10.1017/s0022112091000794.
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We study the inviscid mechanisms governing the three-dimensional evolution of an axisymmetric jet by means of vortex filament simulations. The spatially periodic calculations provide a detailed picture of the processes leading to the concentration, reorientation, and stretching of the vorticity. In the purely axisymmetric case, a wavy perturbation in the streamwise direction leads to the formation of vortex rings connected by braid regions, which become depleted of vorticity. The curvature of the jet shear layer leads to a loss of symmetry as compared to a plane shear layer, and the position of the free stagnation point forming in the braid region is shifted towards the jet axis. As a result, the upstream neighbourhood of a vortex ring is depleted of vorticity at a faster rate than the downstream side. When the jet is also subjected to a sinusoidal perturbation in the azimuthal direction, it develops regions of counter-rotating streamwise vorticity, whose sign is determined by a competition between global and local induction effects. In a way very similar to plane shear layers, the streamwise braid vorticity collapses into counter-rotating round vortex tubes under the influence of the extensional strain. In addition, the cores of the vortex rings develop a wavy dislocation. As expected, the vortex ring evolution depends on the ratio R/θ of the jet radius and the jet shear-layer thickness. When forced with a certain azimuthal wavenumber, a jet corresponding to R/θ = 22.6 develops vortex rings that slowly rotate around their unperturbed centreline, thus preventing a vortex ring instability from growing. For R/θ = 11.3, on the other hand, we observe an exponentially growing ring waviness, indicating a vortex ring instability. Comparison with stability theory yields poor agreement for the wavenumber, but better agreement for the growth rate. The growth of the momentum thickness is much more dramatic in the second case. Furthermore, it is found that the rate at which streamwise vorticity develops is strongly affected by the ratio of the streamwise and azimuthal perturbation amplitudes.
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Angele, K. P., and F. Grewe. "Instantaneous Behavior of Streamwise Vortices for Turbulent Boundary Layer Separation Control." Journal of Fluids Engineering 129, no. 2 (June 6, 2006): 226–35. http://dx.doi.org/10.1115/1.2409327.
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The present study investigates turbulent boundary layer separation control by means of streamwise vortices with focus on the instantaneous vortex behavior. A turbulent boundary layer is exposed to a pressure gradient that generates a separation bubble with substantial backflow. The separation bubble is controlled by conventional passive vortex generators creating pairs of counterrotating vortices. Quantitative information is achieved by applying Particle Image Velocimetry (PIV) to the cross-stream plane of the vortices. The characteristics of a pair of counter-rotating vortices shed from a vortex generator is investigated in the near-field downstream of the vortex generator. The vortices were found to grow with the boundary layer in the downstream direction, and the maximum vorticity decreases as the circulation is conserved. The vortices are nonstationary, and the movements in the spanwise direction are larger than those in the wall-normal direction, due to the presence of the wall. The vortices fluctuate substantially and move over a spanwise distance, which is approximately equal to their size. The most probable instantaneous separation between the two vortices shed from one vortex generator equals the difference between their mean positions. The unsteadiness of the vortices contributes to the observed maxima in the Reynolds stresses around the mean vortex centers. The instantaneous vortex size and the instantaneous maximum vorticity are also fluctuating properties, and the instantaneous vortex is generally smaller and stronger than the mean vortex. A correlation was found between a large instantaneous vortex size and a low instantaneous maximum vorticity (and vice versa), suggesting that the vortices are subjected to vortex stretching.
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Vergine, Fabrizio, Cody Ground, and Luca Maddalena. "Turbulent kinetic energy decay in supersonic streamwise interacting vortices." Journal of Fluid Mechanics 807 (October 19, 2016): 353–85. http://dx.doi.org/10.1017/jfm.2016.611.
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Only a few fundamental studies on the dynamics and interactions of supersonic streamwise vortices have been conducted so far despite the recognized potential of these structures to enhance supersonic mixing. In an effort to shed light on this largely unexplored field, multiple experimental campaigns were conducted in a Mach 2.5 flow to probe the dynamics of turbulence decay in complex flows originating from selected modes of supersonic streamwise vortex interaction. The first part of the manuscript presents the detailed study of two vortex interaction scenarios: one selected to obtain merging of co-rotating vortices and the other to prevent vorticity amalgamation. In the second part, data from three additional vortex merging cases are used to substantiate the findings of the first part of the study and characterize the decay of turbulence. Stereoscopic particle image velocimetry was employed to probe the resulting flow fields at different downstream stations. It was found that these complex vortex interactions measurably affect both the morphology and the magnitude of the streamwise vorticity and turbulent kinetic energy as well as the associated decays. Particularly, while the turbulent kinetic energy across each vorticity patch undergoes an initial production before decreasing monotonically in both scenarios, its content in the coalesced structure is roughly double that of the isolated vortices. The manuscript also presents the analysis of the turbulence data from 27 supersonic vortical structures differing in shape, strength and modes of interaction, acquired within a range of vortex Reynolds numbers of almost one order of magnitude. Dimensional analysis was then used to correlate the spatial decay of turbulent kinetic energy with the vortex Reynolds number. For all the cases considered here, where the fluctuating Mach number was found to be subsonic, the form of the resulting law was similar to that reported in previous scholarly publications, despite the complexity of the vortex dynamics considered in this work.
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LÖGDBERG, OLA, JENS H. M. FRANSSON, and P. HENRIK ALFREDSSON. "Streamwise evolution of longitudinal vortices in a turbulent boundary layer." Journal of Fluid Mechanics 623 (March 6, 2009): 27–58. http://dx.doi.org/10.1017/s0022112008004825.
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In this experimental study both smoke visualization and three-component hot-wire measurements have been performed in order to characterize the streamwise evolution of longitudinal counter-rotating vortices in a turbulent boundary layer. The vortices were generated by means of vortex generators (VGs) in different configurations. Both single pairs and arrays in a natural setting as well as in yaw have been considered. Moreover three different vortex blade heights h, with the spacing d and the distance to the neighbouring vortex pair D for the array configuration, were studied keeping the same d/h and D/h ratios. It is shown that the vortex core paths scale with h in the streamwise direction and with D and h in the spanwise and wall-normal directions, respectively. A new peculiar ‘hooklike’ vortex core motion, seen in the cross-flow plane, has been identified in the far region, starting around 200h and 50h for the pair and the array configuration, respectively. This behaviour is explained in the paper. Furthermore the experimental data indicate that the vortex paths asymptote to a prescribed location in the cross-flow plane, which first was stated as a hypothesis and later verified. This observation goes against previously reported numerical results based on inviscid theory. An account for the important viscous effects is taken in a pseudo-viscous vortex model which is able to capture the streamwise core evolution throughout the measurement region down to 450h. Finally, the effect of yawing is reported, and it is shown that spanwise-averaged quantities such as the shape factor and the circulation are hardly perceptible. However, the evolution of the vortex cores are different both between the pair and the array configuration and in the natural setting versus the case with yaw. From a general point of view the present paper reports on fundamental results concerning the vortex evolution in a fully developed turbulent boundary layer.
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Lee, InSub, Hong Sun Ryou, Seong Hyuk Lee, Ki Bae Hong, and Soo Chae. "A Numerical Investigation on the Development of an Embedded Streamwise Vortex in a Turbulent Boundary Layer With Spanwise Pressure Gradient." Journal of Fluids Engineering 123, no. 3 (March 12, 2001): 551–58. http://dx.doi.org/10.1115/1.1378022.
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It is the aim of this article to investigate numerically the effects of spanwise pressure gradient on an embedded streamwise vortex in a turbulent boundary layer. The governing equations were discretized by the finite volume method and SIMPLE algorithm was used to couple between pressure and velocity. The LRR model for Reynolds stresses was utilized to predict the anisotropy of turbulence effectively. The validation was done for two cases: one is the development of a streamwise vortex embedded in a pressure-driven, three-dimensional turbulent boundary layer. The other involves streamwise vortex pairs embedded in a turbulent boundary layer without the spanwise pressure gradient. In the case of the former, the predicted results were compared with Shizawa and Eaton’s experimental data. In the latter case, the calculated results were compared against the experimental data of Pauley and Eaton. We performed numerical simulations for three cases with different values of spanwise pressure gradient. As a result, the primary streamwise vortex with spanwise pressure gradients decays more rapidly than the case with no pressure gradients, as the spanwise pressure gradient increases. This indicates that the spanwise pressure gradient may play an important role on mean and turbulent structures. In particular, it can be seen that the increase of pressure gradient enhances a level of turbulent normal stresses.
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Shrivastava, Shaurya, and Theresa Saxton-Fox. "Correlation between Large-Scale Streamwise Velocity Features and the Height of Coherent Vortices in a Turbulent Boundary Layer." Fluids 6, no. 8 (August 16, 2021): 286. http://dx.doi.org/10.3390/fluids6080286.
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The preferential organisation of coherent vortices in a turbulent boundary layer in relation to local large-scale streamwise velocity features was investigated. Coherent vortices were identified in the wake region using the Triple Decomposition Method (originally proposed by Kolář) from 2D particle image velocimetry (PIV) data of a canonical turbulent boundary layer. Two different approaches, based on conditional averaging and quantitative statistical analysis, were used to analyze the data. The large-scale streamwise velocity field was first conditionally averaged on the height of the detected coherent vortices and a change in the sign of the average large scale streamwise fluctuating velocity was seen depending on the height of the vortex core. A correlation coefficient was then defined to quantify this relationship between the height of coherent vortices and local large-scale streamwise fluctuating velocity. Both of these results indicated a strong negative correlation in the wake region of the boundary layer between vortex height and large-scale velocity. The relationship between vortex height and full large-scale velocity isocontours was also studied and a conceptual model based on the findings of the study was proposed. The results served to relate the hairpin vortex model of Adrian et al. to the scale interaction results reported by Mathis et al., and Chung and McKeon.
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LeBoeuf, Richard L., and Rabindra D. Mehta. "Streamwise vortex meander in a plane mixing layer." Physics of Fluids A: Fluid Dynamics 5, no. 8 (August 1993): 1983–91. http://dx.doi.org/10.1063/1.858825.
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Cagney, N., and S. Balabani. "Mode competition in streamwise-only vortex induced vibrations." Journal of Fluids and Structures 41 (August 2013): 156–65. http://dx.doi.org/10.1016/j.jfluidstructs.2013.02.009.
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Sun, Zhijun, Yunsong Gu, and Hang Zhao. "Experimental investigation on the streamwise vortex–surface interaction." Journal of Visualization 22, no. 3 (January 30, 2019): 477–88. http://dx.doi.org/10.1007/s12650-018-00544-3.
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Smart, M. K., I. M. Kalkhoran, and S. Popovic. "Some aspects of streamwise vortex behavior during oblique shock wave/vortex interaction." Shock Waves 8, no. 4 (August 1, 1998): 243–55. http://dx.doi.org/10.1007/s001930050117.
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Ye, Qingqing, Ferry F. J. Schrijer, and Fulvio Scarano. "Boundary layer transition mechanisms behind a micro-ramp." Journal of Fluid Mechanics 793 (March 14, 2016): 132–61. http://dx.doi.org/10.1017/jfm.2016.120.
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The early stage of three-dimensional laminar-to-turbulent transition behind a micro-ramp is studied in the incompressible regime using tomographic particle image velocimetry. Experiments are conducted at supercritical micro-ramp height $h$ based Reynolds number $Re_{h}=1170$. The measurement domain encompasses 6 ramp widths spanwise and 73 ramp heights streamwise. The mean flow topology reveals the underlying vortex structure of the wake flow with multiple pairs of streamwise counter-rotating vortices visualized by streamwise vorticity. The primary pair generates a vigorous upwash motion in the symmetry plane with a pronounced momentum deficit. A secondary vortex pair is induced closer to the wall. The tertiary and even further vortices maintain a streamwise orientation, but are produced progressively outwards of the secondary pair and follow a wedge-type pattern. The instantaneous flow pattern reveals that the earliest unstable mode of the wake features arc-like Kelvin–Helmholtz (K–H) vortices in the separated shear layer. Under the influence of the K–H vortices, the wake exhibits a high level of fluctuations with a pulsatile mode for the streamwise momentum deficit. The K–H vortices are lifted up due to the upwash induced by the quasi-streamwise vortex pair, while they appear to undergo pairing, distortion and finally breakdown. Immediately downstream, a streamwise interval of relatively low vortical activity separates the end of the K–H region from the formation of new hairpin vortices close to the wall. The latter vortex structures originate from the region of maximum wall shear, induced by the secondary vortex pair causing strong ejection events which transport low-speed flow upwards. The whole pattern features a cascade of hairpin vortices along a turbulent/non-turbulent interface. The wedge-shaped cascade signifies the formation of a turbulent wedge. The turbulent properties of the wake are inspected with the spatial distribution of the velocity fluctuations and turbulence production in the developing boundary layer. Inside the wedge region, the velocity fluctuations approach quasi-spanwise homogeneity, indicating the development towards a turbulent boundary layer. The wedge interface is characterized by a localized higher level of velocity fluctuations and turbulence production, associated to the deflection of the shear layer close to the wall and the onset of coherent hairpin vortices inducing localized large-scale ejections.
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Luo, Yuxi, Fengbo Wen, Rui Hou, Shuai Wang, Songtao Wang, and Zhongqi Wang. "Modal analysis of trailing edge cutback film cooling." International Journal of Numerical Methods for Heat & Fluid Flow 30, no. 8 (November 23, 2019): 3957–83. http://dx.doi.org/10.1108/hff-09-2019-0673.
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Purpose The purpose of this paper devoted to the application of modal analysis to analyze the flow structure of trailing edge cutback film cooling and the effects of vortex structure on the film cooling effectiveness of the cutback surface. Design/methodology/approach Large eddy simulation (LES) is used to simulate the trailing edge cutback film cooling. The results of LES are analyzed by proper orthogonal decomposition (POD) method and dynamic mode decomposition (DMD) method. The POD method is used to determine the dominated vortex structure and the energy level of these structures. The DMD method is used to analyze the relationship between vortex structures and wall temperature. Findings The POD method shows that the flow field consists of three main vortices – streamwise vortex, lip vortex and coolant vortex. The DMD results show that the lip vortex mainly acts on the middle section of the cutback surface, while the streamwise vortex mainly acts on the back section of the cutback surface. Research limitations/implications The modal analysis is only based on numerical simulation but the modal analysis of experimental results will be further studied in the future. Practical implications This paper presents the powerful ability of the modal analysis method to study complex flows in trailing edge cutback film cooling. Establishing the relationship between vortex and wall temperature by modal analysis method can provide a new idea for studying convective heat transfer problems. Originality/value The role of streamwise vortex in the flow of the trailing edge cutback cooling and its effect on the cooling effectiveness of the cutback surface is found.
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Doro, Emmanuel O., and Cyrus K. Aidun. "Interfacial waves and the dynamics of backflow in falling liquid films." Journal of Fluid Mechanics 726 (May 31, 2013): 261–84. http://dx.doi.org/10.1017/jfm.2013.172.
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AbstractBy studying the dynamics of the streamwise pressure gradient at the wavefront of travelling interfacial waves, we investigate the formation and evolution of backflow regions for the sinusoidal and teardrop-shaped surface wave regimes of laminar falling liquid films. The magnitude of the wavefront streamwise pressure gradient grows as the flow inlet disturbance increases in amplitude and steepness. At large enough values, the adverse pressure gradient induces flow separation and subsequently backflow at the large-amplitude wavefront. The backflow region evolves from a closed circulation to an open vortex as the wave grows to saturation. The dynamics of the streamwise pressure gradient at the sinusoidal wavefront approaches a stable fixed point at saturation. Thus, the open vortex retains its structure as the wave continues downstream. The streamwise pressure gradient at the wavefront of the teardrop-shaped pulse evolves similarly to a time-periodic function with multiple minima/maxima. This phenomenon is a consequence of the interaction between the teardrop-shaped wave and newly formed preceding capillary waves. The nature of the teardrop pulse–capillary wave interaction is such that a decrease in magnitude of the streamwise pressure gradient at the teardrop-shaped wavefront is followed by an increase at the capillary wavefront and vice versa. The increased adverse pressure gradient at the capillary wavefront induces a second open vortex backflow, while the teardrop-shaped wavefront’s open vortex reverts to a closed circulation. This interaction between the waves continues as the teardrop pulse–capillary wavetrain travels downstream, leading to multiple capillary waves and backflow regions.
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Chang, Chau-Lyan, and Mujeeb R. Malik. "Oblique-mode breakdown and secondary instability in supersonic boundary layers." Journal of Fluid Mechanics 273 (August 25, 1994): 323–60. http://dx.doi.org/10.1017/s0022112094001965.
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Laminar–turbulent transition mechanisms for a supersonic boundary layer are examined by numerically solving the governing partial differential equations. It is shown that the dominant mechanism for transition at low supersonic Mach numbers is associated with the breakdown of oblique first-mode waves. The first stage in this breakdown process involves nonlinear interaction of a pair of oblique waves with equal but opposite angles resulting in the evolution of a streamwise vortex. This stage can be described by a wave–vortex triad consisting of the oblique waves and a streamwise vortex whereby the oblique waves grow linearly while nonlinear forcing results in the rapid growth of the vortex mode. In the second stage, the mutual and self-interaction of the streamwise vortex and the oblique modes results in the rapid growth of other harmonic waves and transition soon follows. Our calculations are carried all the way into the transition region which is characterized by rapid spectrum broadening, localized (unsteady) flow separation and the emergence of small-scale streamwise structures. The r.m.s. amplitude of the streamwise velocity component is found to be on the order of 4–5 % at the transition onset location marked by the rise in mean wall shear. When the boundary-layer flow is initially forced with multiple (frequency) oblique modes, transition occurs earlier than for a single (frequency) pair of oblique modes. Depending upon the disturbance frequencies, the oblique mode breakdown can occur for very low initial disturbance amplitudes (on the order of 0.001% or even lower) near the lower branch. In contrast, the subharmonic secondary instability mechanism for a two-dimensional primary disturbance requires an initial amplitude on the order of about 0.5% for the primary wave. An in-depth discussion of the oblique-mode breakdown as well as the secondary instability mechanism (both subharmonic and fundamental) is given for a Mach 1.6 flat-plate boundary layer.
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KALKHORAN, I. M., M. K. SMART, and F. Y. WANG. "Supersonic vortex breakdown during vortex/cylinder interaction." Journal of Fluid Mechanics 369 (August 25, 1998): 351–80. http://dx.doi.org/10.1017/s0022112098001566.
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The head-one interaction of a supersonic streamwise vortex with a circular cylinder reveals a vortex breakdown similar in many ways to that of incompressible vortex breakdown. In particular, the dramatic flow reorganization observed during the interaction resembles the conical vortex breakdown reported by Sarpkaya (1995) at high Reynolds number. In the present study, vortex breakdown is brought about when moderate and strong streamwise vortices encounter the bow shock in front of a circular cylinder at Mach 2.49. The main features of the vortex/cylinder interaction are the formation of a blunt-nosed conical shock with apex far upstream of the undisturbed shock stand-off distance, and a vortex core which responds to passage through the apex of the conical shock by expanding into a turbulent conical flow structure. The geometry of the expanding vortex core as well as the location of the conical shock apex are seen to be strong functions of the incoming vortex strength and the cylinder diameter. A salient feature of the supersonic vortex breakdown is the formation of an entropy-shear layer, which separates an interior subsonic zone containing the burst vortex from the surrounding supersonic flow. In keeping with the well-established characteristics of the low-speed vortex breakdown, a region of reversed flow is observed inside the turbulent subsonic zone. The steady vortex/cylinder interaction flow fields generated in the current study exhibit many characteristics of the unsteady vortex distortion patterns previously observed during normal shock wave/vortex interactions. This similarity of the instantaneous flow structure indicates that the phenomenon previously called vortex distortion by Kalkhoran et al. (1996) is a form of supersonic vortex breakdown.
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Cohen, Jacob, Michael Karp, and Vyomesh Mehta. "A minimal flow-elements model for the generation of packets of hairpin vortices in shear flows." Journal of Fluid Mechanics 747 (April 10, 2014): 30–43. http://dx.doi.org/10.1017/jfm.2014.140.
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AbstractPackets of hairpin-shaped vortices and streamwise counter-rotating vortex pairs (CVPs) appear to be key structures during the late stages of the transition process as well as in low-Reynolds-number turbulence in wall-bounded flows. In this work we propose a robust model consisting of minimal flow elements that can produce packets of hairpins. Its three components are: simple shear, a CVP having finite streamwise vorticity magnitude and a two-dimensional (2D) wavy (in the streamwise direction) spanwise vortex sheet. This combination is inherently unstable: the CVP modifies the base flow due to the induced velocity forming an inflection point in the base-flow velocity profile. Consequently, the 2D wavy vortex sheet is amplified, causing undulation of the CVP. The undulation is further enhanced as the wave continues to be amplified and eventually the CVP breaks down into several segments. The induced velocity generates highly localized patches of spanwise vorticity above the regions connecting two consecutive streamwise elements of the CVP. These patches widen with time and join with the streamwise vortical elements situated beneath them forming a packet of hairpins. The results of the unbounded (having no walls) model are compared with pipe and channel flow experiments and with a direct numerical simulation of a transition process in Couette flow. The good agreement in all cases demonstrates the universality and robustness of the model.
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CAULFIELD, C. P., and W. R. PELTIER. "The anatomy of the mixing transition in homogeneous and stratified free shear layers." Journal of Fluid Mechanics 413 (June 25, 2000): 1–47. http://dx.doi.org/10.1017/s0022112000008284.
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We investigate the detailed nature of the ‘mixing transition’ through which turbulence may develop in both homogeneous and stratified free shear layers. Our focus is upon the fundamental role in transition, and in particular the associated ‘mixing’ (i.e. small-scale motions which lead to an irreversible increase in the total potential energy of the flow) that is played by streamwise vortex streaks, which develop once the primary and typically two-dimensional Kelvin–Helmholtz (KH) billow saturates at finite amplitude.Saturated KH billows are susceptible to a family of three-dimensional secondary instabilities. In homogeneous fluid, secondary stability analyses predict that the stream-wise vortex streaks originate through a ‘hyperbolic’ instability that is localized in the vorticity braids that develop between billow cores. In sufficiently strongly stratified fluid, the secondary instability mechanism is fundamentally different, and is associated with convective destabilization of the statically unstable sublayers that are created as the KH billows roll up.We test the validity of these theoretical predictions by performing a sequence of three-dimensional direct numerical simulations of shear layer evolution, with the flow Reynolds number (defined on the basis of shear layer half-depth and half the velocity difference) Re = 750, the Prandtl number of the fluid Pr = 1, and the minimum gradient Richardson number Ri(0) varying between 0 and 0.1. These simulations quantitatively verify the predictions of our stability analysis, both as to the spanwise wavelength and the spatial localization of the streamwise vortex streaks. We track the nonlinear amplification of these secondary coherent structures, and investigate the nature of the process which actually triggers mixing. Both in stratified and unstratified shear layers, the subsequent nonlinear amplification of the initially localized streamwise vortex streaks is driven by the vertical shear in the evolving mean flow. The two-dimensional flow associated with the primary KH billow plays an essentially catalytic role. Vortex stretching causes the streamwise vortices to extend beyond their initially localized regions, and leads eventually to a streamwise-aligned collision between the streamwise vortices that are initially associated with adjacent cores.It is through this collision of neighbouring streamwise vortex streaks that a final and violent finite-amplitude subcritical transition occurs in both stratified and unstratified shear layers, which drives the mixing process. In a stratified flow with appropriate initial characteristics, the irreversible small-scale mixing of the density which is triggered by this transition leads to the development of a third layer within the flow of relatively well-mixed fluid that is of an intermediate density, bounded by narrow regions of strong density gradient.
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Davies-Jones, Robert. "Roles of Streamwise and Transverse Partial-Vorticity Components in Steady Inviscid Isentropic Supercell-Like Flows." Journal of the Atmospheric Sciences 74, no. 9 (August 31, 2017): 3021–41. http://dx.doi.org/10.1175/jas-d-16-0332.1.
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Abstract Investigations of tornadogenesis in supercells attempt to find the origin of the tornado’s large vorticity by determining vorticity generation and amplification along trajectories that enter the tornado from a horizontally uniform unstable environment. Insights into tornadogenesis are provided by finding analytical formulas for vorticity variations along streamlines in idealized, steady, inviscid, isentropic inflows of dry air imported from the environment. The streamlines and vortex lines lie in the stationary isentropic surfaces so the vorticity is 2D. The transverse vorticity component (positive leftward of the streamlines) arises from imported transverse vorticity and from baroclinic vorticity accumulated in streamwise temperature gradients. The streamwise component stems from imported streamwise vorticity, from baroclinic vorticity accrued in transverse temperature gradients, and from positive transverse vorticity that is turned streamwise in cyclonically curved flow by a “river-bend process.” It is amplified in subsiding air as it approaches the ground. Streamwise stretching propagates a parcel’s streamwise vorticity forward in time. In steady flow, vorticity decomposes into baroclinic vorticity and two barotropic parts ωBTIS and ωBTIC arising from imported storm-relative streamwise vorticity (directional shear) and storm-relative crosswise vorticity (speed shear), respectively. The Beltrami vorticity ωBTIS is purely streamwise. It explains why abundant environmental storm-relative streamwise vorticity close to ground favors tornadic supercells. It flows directly into the updraft base unmodified apart from streamwise stretching, establishing mesocyclonic rotation and strong vortex suction at low altitudes. Increase (decrease) in storm-relative environmental wind speed with height near the ground accelerates (delays) tornadogenesis as positive (negative) ωBTIC is turned into streamwise (antistreamwise) vorticity within cyclonically curved flow around the mesocyclone.
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Lee, S., and E. Loth. "Supersonic boundary-layer interactions with various micro-vortex generator geometries." Aeronautical Journal 113, no. 1149 (November 2009): 683–97. http://dx.doi.org/10.1017/s0001924000003353.
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Abstract Various types of micro-vortex generators (μVGs) are investigated for control of a supersonic turbulent boundary layer subject to an oblique shock impingement, which causes flow separation. The micro-vortex generators are embedded in the boundary layer to avoid excessive wave drag while still creating strong streamwise vortices to energise the boundary layer. Several different types of µVGs were considered including micro-ramps and micro-vanes. These were investigated computationally in a supersonic boundary layer at Mach 3 using monotone integrated large eddy simulations (MILES). The results showed that vortices generated from μVGs can partially eliminate shock induced flow separation and can continue to entrain high momentum flux for boundary-layer recovery downstream. The micro-ramps resulted in thinner downstream displacement thickness in comparison to the micro-vanes. However, the strength of the streamwise vorticity for the micro-ramps decayed faster due to dissipation especially after the shock interaction. In addition, the close spanwise distance between each vortex for the ramp geometry causes the vortex cores to move upwards from the wall due to induced upwash effects. Micro-vanes, on the other hand, yielded an increased spanwise spacing of the streamwise vortices at the point of formation. This resulted in streamwise vortices staying closer to the floor with less circulation decay, and the reduction in overall flow separation is attributed to these effects. Two hybrid concepts, named ‘thick-vane’ and ‘split-ramp’, were also studied where the former is a vane with side supports and the latter has a uniform spacing along the centreline of the baseline ramp. These geometries behaved similar to the micro-vanes in terms of the streamwise vorticity and the ability to reduce flow separation, but are more physically robust than the thin vanes.
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YAMADA, Seiji, Shinsuke MOCHIZUKI, and Hideo OSAKA. "Management of Stronger Wall Jet by a Streamwise Vortex with Periodic Perterbation : Evolution of a Streamwise Vortex and Mean Velocity Field." Proceedings of Conference of Chugoku-Shikoku Branch 2002.40 (2002): 261–62. http://dx.doi.org/10.1299/jsmecs.2002.40.261.
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Barnes, C. J., M. R. Visbal, and P. G. Huang. "On the effects of vertical offset and core structure in streamwise-oriented vortex–wing interactions." Journal of Fluid Mechanics 799 (June 21, 2016): 128–58. http://dx.doi.org/10.1017/jfm.2016.320.
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This article explores the three-dimensional flow structure of a streamwise-oriented vortex incident on a finite aspect-ratio wing. The vertical positioning of the incident vortex relative to the wing is shown to have a significant impact on the unsteady flow structure. A direct impingement of the streamwise vortex produces a spiralling instability in the vortex just upstream of the leading edge, reminiscent of the helical instability modes of a Batchelor vortex. A small negative vertical offset develops a more pronounced instability while a positive vertical offset removes the instability altogether. These differences in vertical position are a consequence of the upstream influence of pressure gradients provided by the wing. Direct impingement or a negative vertical offset subject the vortex to an adverse pressure gradient that leads to a reduced axial velocity and diminished swirl conducive to hydrodynamic instability. Conversely, a positive vertical offset removes instability by placing the streamwise vortex in line with a favourable pressure gradient, thereby enhancing swirl and inhibiting the growth of unstable modes. In every case, the helical instability only occurs when the properties of the incident vortex fall within the instability threshold predicted by linear stability theory. The influence of pressure gradients associated with separation and stall downstream also have the potential to introduce suction-side instabilities for a positive vertical offset. The influence of the wing is more severe for larger vortices and diminishes with vortex size due to weaker interaction and increased viscous stability. Helical instability is not the only possible outcome in a direct impingement. Jet-like vortices and a higher swirl ratio in wake-like vortices can retain stability upon impact, resulting in the laminar vortex splitting over either side of the wing.
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Cagney, N., and S. Balabani. "Streamwise vortex-induced vibrations of cylinders with one and two degrees of freedom." Journal of Fluid Mechanics 758 (October 13, 2014): 702–27. http://dx.doi.org/10.1017/jfm.2014.521.
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AbstractMeasurements are presented of the structural response and wake of a two-degree-of-freedom (2-DOF) pivoted cylinder undergoing streamwise vortex-induced vibrations (VIV), which were carried out using particle-image velocimetry (PIV). The results are compared with those of previous studies performed in the same experimental facility examining a cylinder free to move only in the streamwise direction (1-DOF). The aim of this study is to examine to what extent the results of previous work on streamwise-only VIV can be extrapolated to the more practical, multi-DOF case. The response regimes measured for the 1- and 2-DOF cases are similar, containing two response branches separated by a low-amplitude region. The first branch is characterised by negligible transverse motion and the appearance of both alternate and symmetric vortex shedding. The two wake modes compete in an unsteady manner; however, the competition does not appear to have a significant effect on either the streamwise or transverse motion. Comparison of the phase-averaged vorticity fields acquired in the second response branch also indicates that the additional DOF does not alter the vortex-shedding process. However, the additional DOF affects the cylinder-wake system in other ways; for the 1-DOF case the second branch can appear in three different forms (each associated with a different wake mode), while for the 2-DOF case the second branch only exists in one form, and does not exhibit hysteresis. The cylinder follows a figure-of-eight trajectory throughout the lock-in range. The phase angle between the streamwise and transverse motion decreases linearly with reduced velocity. This work highlights the similarities and differences between the fluid–structure interaction and wake dynamics associated with 1- and 2-DOF cylinders throughout the streamwise response regime, which has not received attention to date.
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Sarpkaya, Turgut, and Donald E. Neubert. "Interaction of a streamwise vortex with a free surface." AIAA Journal 32, no. 3 (March 1994): 594–600. http://dx.doi.org/10.2514/3.12026.
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