Similarity solutions for viscous vortex cores

Mayer, Ernst W.; Powell, Kenneth G.

doi:10.1017/s0022112092001794

Cited by 23 publications

(6 citation statements)

References 3 publications

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“…The lack of change in the flow parameters suggests that the new core is very stable. Stability would be expected given the monotonically increasing circulation distribution (Rayleigh's criterion) and low Rossby number U d /V θ1 (see Mayer & Powell 1992). Figure 7 gives a broad view of the turbulence structure of the flow in terms of contours of turbulence kinetic energy k = 1 2 (u 2 + v 2 + w 2 ).…”

Section: Chordlengthmentioning

confidence: 98%

Flow structure produced by the interaction and merger of a pair of co-rotating wing-tip vortices

1999

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Experiments have been performed to study the co-rotating wing-tip vortex pair produced by a pair of rectangular wings in a split-wing configuration. Detailed measurements made in cross-sections upstream and downstream of merger reveal, for the first time, the complex turbulence structure of this flow. The vortices spiral around each other and merge some 20 chordlengths downstream of the wings. As merger is approached the vortices lose their axisymmetry – their cores develop lopsided tangential velocity fields and the mean vorticity field is convected into filaments. The cores also become part of a single turbulence structure dominated by a braid of high turbulence levels that links them together. The braid, which quite closely resembles the structure formed between adjacent spanwise eddies of transitional mixing layers, grows in intensity with downstream distance and extends into the vortex cores. Unlike a single tip vortex, the unmerged cores appear turbulent.The merging of the vortices wraps the cores and the flow structure that surrounds them into a large turbulent region with an intricate double spiral structure. This structure then relaxes to a closely axisymmetric state. The merged core appears stable and develops a structure similar to the laminar core of a vortex shed from a single wing. However, the turbulent region formed around the vortex core during the merger process is much larger and more axisymmetric than that found around a single wing-tip vortex.

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Section: Chordlengthmentioning

confidence: 98%

Flow structure produced by the interaction and merger of a pair of co-rotating wing-tip vortices

1999

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“…In a free vortex such a large ratio of axial velocity deficit to peak tangential velocity would render the vortex unstable to helical disturbances. 5 This instability generates helical turbulent structures and mixing that acts to diffuse the axial velocity deficit. 6 The tip leakage vortex is indeed a center of turbulent activity as evidenced by the turbulence kinetic energy contours of Fig.…”

Section: Background To the Two-point Measurementsmentioning

confidence: 99%

“…We therefore conclude that the blade wakes were not subject to any correlated unsteadiness. All spanwise profiles (1)(2)(3)(4)(5) consisted of 20 to 30 two-point measurements. A minimum probe separation of 3.8 mm (0.027c a ) was used with an increment of 1.3 mm (0.009c a ) for small probe separations.…”

Section: Two-point Profilesmentioning

confidence: 99%

Wake of a Compressor Cascade with Tip Gap, Part 3: Two Point Statistics

et al. 2004

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Velocity spectra and space-time correlations have been measured downstream of a low-speed linear compressor cascade with tip gap. The objective of this work is an improved understanding of the coherent turbulence structures present in fan-tip wakes and of the turbulent source terms responsible for broadband stator noise. The two-point measurements show no correlation between turbulent motions in the wakes or leakage vortices shed by adjacent blades and that the leakage vortex is not subject to low-frequency wandering motions. They also show that the tip leakage vortex turbulence is highly anisotropic and characterized by elongated eddies inclined at about 30 deg to the vortex axis. The presence of such structures, which produce no clearly identifiable footprint in velocity spectra, appears consistent with the helical structures seen in direct numerical simulations of a line vortex with unstably large streamwise velocity defect. This suggests the same mechanism is behind the generation of turbulence in this vortex. Examination of the correlation data from the point of view of a hypothetical stator blade suggests that, because of the anisotropy in turbulence structure, velocity correlations seen by a stator in a real engine are likely to be a strong function of engine geometry and operating point. IntroductionT HIS paper is our third in a series dealing with the flow downstream of a linear compressor cascade. This cascade is designed to reproduce, in an idealized setting, some of the important conditions experienced in the subsonic fan of a large-bypass-ratio aircraft engine, specifically the mechanisms leading to the generation and evolution of the tip leakage vortices that dominate the casing endwall flow, which impinges on the bypass stator. Our first two papers 1,2 focused on single-point velocity measurements of the mean flow and Reynolds-stress fields produced by the blade wakes, the leakage vortices, and the associated endwall flow, as functions of streamwise position, tip gap, and relative motion between the blade tips and endwall. Such measurements provide data and understanding to aid in the development and testing of computational-fluid-dynamics (CFD) prediction tools for calculation of the unsteady aerodynamics and tone noise produced by the stator interaction. In this paper we focus on two-point turbulence measurements. This type of information not only provides insight into the scale and form of the coherent structures that populate the turbulent regions, but is also critical to understanding the generation of broadband noise by the stator row.To predict the broadband rotor/stator interaction noise, it is, in principle, necessary to have a complete description of the rotor wake turbulence in terms of its two-point space-time correlation function and a response model for the blade row. Complete two-point information is rarely available even for relatively simple flows and cannot be provided by performing Reynolds-averaged CFD calculations. Drastic assumptions about the form of the two-point cor-

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“…The same experience has been reported in and the reader is referred to this paper for a discussion of the different criteria. A justification may come from compressible viscous vortex similarity solutions, where the vortex core is shown to possess a strong local pressure minimum (Mayer & Powell 1992). In the current work the coincidence of pressure minima and vortex cores has always been verified by an additional necessary criterion, usually that of a positive discriminant of the characteristic equation of the velocity-gradient tensor (Vollmers…”

Section: Formation Of A-vorticesmentioning

confidence: 99%

Subharmonic transition to turbulence in a flat-plate boundary layer at Mach number 4.5

Adams

Kleiser

1996

J. Fluid Mech.

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The subharmonic transition process of a flat-plate boundary layer at a free-stream Mach number of M∞ = 4.5 and a Reynolds number of 10000 based on free-stream velocity and initial displacement thickness is investigated by direct numerical simulation up to the beginning of turbulence. A second-mode instability superimposed with random noise of low amplitude is forced initially. The secondary subharmonic instability evolves from the noise in accordance with theory and leads to a staggered Λ-vortex pattern. Finite-amplitude Λ-vortices initiate the build-up of detached high-shear layers below and above the critical layer. The detached shear-layer generation and break-up are confined to the relative-subsonic part of the boundary layer. The breakdown to turbulence can be separated into two phases, the first being the break-up of the lower shear layer and the second being the break-up of the upper shear layer. Four levels of subsequent roll-up of the lower, Y-shaped shear layer have been observed, leading to new vortical structures which are unknown from transition at low Mach numbers. The upper shear layer behaviour is similar to that of the well-known high-shear layer in incompressible boundary-layer transition. It is concluded that, as in incompressible flow, turbulence is generated via a cascade of vortices and detached shear layers with successively smaller scales. The different phases of shear-layer break-up are also reflected in the evolution of averaged quantities. A strong decrease of the shape factor, as well as an increase of the skin friction coefficient, and a gradual loss of spanwise symmetry indicate the final breakdown to turbulence, where the mean velocity and temperature profiles approach those measured in fully turbulent flow.

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Similarity solutions for viscous vortex cores

Cited by 23 publications

References 3 publications

Flow structure produced by the interaction and merger of a pair of co-rotating wing-tip vortices

Flow structure produced by the interaction and merger of a pair of co-rotating wing-tip vortices

Wake of a Compressor Cascade with Tip Gap, Part 3: Two Point Statistics

Subharmonic transition to turbulence in a flat-plate boundary layer at Mach number 4.5

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