Cross-Flow Instability with Periodic Distributed Roughness

Corke, Thomas; Knasiak, Keith F.

doi:10.1007/978-94-011-1032-7_4

Cited by 6 publications

(16 citation statements)

References 7 publications

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“…Dashed line is from linear simulation of Davies and Carpenter [14] to excite the mode with n = 19 at its most unstable radius just beyond R c I . Other cases designed to excite n = 27 at its most amplified radius [23], and "clean" disks [9,10], have also been studied in this regard. Even when care is taken to wipe the disk surface, the "clean" disk is not necessarily controlled since the cross-flow instability is exceedingly sensitive to even minute dust particles, which of course is the basis behind adding dots on the surface.…”

Section: Discussionmentioning

confidence: 99%

“…In the study of the triad resonance mechanism, we followed the lead of Corke and Knasiak [9,10] and applied an array of roughness "dots" onto the surface of the disk to prescribe a repeatable initial condition on amplitude and wave number while otherwise not altering the mean flow. The case reported was designed [17].…”

Section: Discussionmentioning

confidence: 99%

“…Corke and Knasiak [9,10] had documented the growth of a low-wavenumber (n = 3) stationary mode during the later stages of transition to turbulence on the disk, and speculated that it was due to a triad resonance with a pair of traveling modes. For this, they demonstrated a triple phase-locking through a cross-bicoherence (CBC) analysis, which is the first condition of proof of a triad resonance.…”

Section: Mode-triad Resonancementioning

confidence: 98%

“…In an effort to better control the initial conditions, and owing to the sensitivity of this instability to surface roughness, we used an earlier technique [9,10] and applied an array of roughness "dots" to the surface of the disk. The diameter and height of the dots were very reproducible.…”

Section: Mode-resonance Setupmentioning

confidence: 99%

“…For example, when the initial amplitudes of the traveling and the stationary modes were the same, the traveling modes, owing to their larger growth rates, would dominate most of the flow development. With this in mind, Corke and Knasiak [9,10] documented a triple phase-locking between traveling and stationary cross-flow modes through cross-bicoherence (CBC) analysis of velocity time series that was the first experimental evidence of a triad resonance mechanism in this flow.…”

Section: Introductionmentioning

confidence: 96%

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Transition to turbulence in rotating-disk boundary layers—convective and absolute instabilities

2006

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This work is an experimental study of mechanisms for transition to turbulence in the boundary layer on a rotating disk. In one case, the focus was on a triad resonance between pairs of traveling cross-flow modes and a stationary cross-flow mode. The other was on the temporal growth of traveling modes through a linear absolute instability mechanism first discovered by Lingwood (1995, J Fluid Mech 314:373-405). Both research directions made use of methods for introducing controlled initial disturbances. One used a distributed array of ink dots placed on the disk surface to enhance a narrow band of azimuthal and radial wave numbers of both stationary and traveling modes. The size of the dots was small so that the disturbances they produce were linear. Another approach introduced temporal disturbances by a shortduration air pulse from a hypodermic tube located above the disk and outside the boundary layer. Hot-wire sensors primarily sensitive to the azimuthal velocity component, were positioned at different spatial (r, θ ) locations on the disk to document the growth of disturbances. Spatial correlation measurements were used with two simultaneous sensors to obtain wavenumber vectors. Cross-bicoherence was used to identify three-frequency phase locking. Ensemble averages conditioned on the air pulses revealed wave packets that evolved in time and space. The space-time evolution of the leading and trailing edges of the wave packets were followed past the critical radius for the absolute instability, r c A . With documented linear amplitudes, the spreading of the disturbance wave packets did not continue to grow in time as r c A was approached. Rather, the spreading of the trailing edge of the wave packet decelerated and asymptotically approached a constant. This result supports the linear DNS simulations of Davies and Carpenter (2003, J Fluid Mech 486:287-329) who concluded that the absolute instability mechanism does not result in a global mode, and that linear-disturbance wave packets are dominated by the convective instability. In contrast, wave-number matching between traveling cross-flow modes confirmed a triad resonance that lead to the growth of a low azimuthal number (n = 4) stationary mode. At transition, this mode had the largest amplitude. Signs of this mechanism can be found in past flow visualization of transition to turbulence in rotating disk flows.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Mode-triad Resonancementioning

confidence: 98%

Section: Mode-resonance Setupmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

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Transition to turbulence in rotating-disk boundary layers—convective and absolute instabilities

2006

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Upper branch nonstationary modes of the boundary layer due to a rotating disk

Türkyılmazoğlu

Gajjar

2001

Applied Mathematics Letters

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Experimental investigation of absolute instability of a rotating-disk boundary layer

Othman

Corke

2006

J. Fluid Mech.

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A series of experiments were performed to study the absolute instability of Type I travelling crossflow modes in the boundary layer on a smooth disk rotating at constant speed. The basic flow agreed with analytic theory, and the growth of natural disturbances matched linear theory predictions. Controlled temporal disturbances were introduced by a short-duration air pulse from a hypodermic tube located above the disk and outside the boundary layer. The air pulse was positioned just outboard of the linear-theory critical radius for Type I crossflow modes. A hot-wire sensor primarily sensitive to the azimuthal velocity component, was positioned at different spatial ($r,\theta$) locations on the disk to document the growth of disturbances produced by the air pulses. Ensemble averages conditioned on the air pulses revealed wave packets that evolved in time and space. Two amplitudes of air pulses were used. The lower amplitude was verified to produced wave packets with linear amplitude characteristics. The space–time evolution of the leading and trailing edges of the wave packets were followed past the critical radius for the absolute instability, $r_{c_{A}}$. With the lower amplitudes, the spreading of the disturbance wave packets did not continue to grow in time as $r_{c_{A}}$ was approached. Rather, the spreading of the trailing edge of the wave packet decelerated and asymptotically approached a constant. This result supports previous linear DNS simulations where it was concluded that the absolute instability does not produce a global mode and that linear disturbance wave packets are dominated by the convective instability. The larger-amplitude disturbances were found to produce larger temporal spreading of the wave packets. This was accompanied by a sharp growth in the wave packet amplitude past $r_{c_{A}}$. Explanations for this are discussed.

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Cross-Flow Instability with Periodic Distributed Roughness

Cited by 6 publications

References 7 publications

Transition to turbulence in rotating-disk boundary layers—convective and absolute instabilities

Transition to turbulence in rotating-disk boundary layers—convective and absolute instabilities

Upper branch nonstationary modes of the boundary layer due to a rotating disk

Experimental investigation of absolute instability of a rotating-disk boundary layer

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