Flow Visualization of a Wave Packet on a Rotating Disk

Wilkinson, Stephen; Blanchard, A.; Selby, G. V.; Gaster, M.; Tritz, T.; Gad‐el‐Hak, Mohamed

doi:10.1007/978-1-4612-3430-2_37

Cited by 3 publications

(6 citation statements)

References 4 publications

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“…We can observe evidence of traveling modes that develop higher wave angles than those of stationary modes in flow visualization by Wilkinson et al [22]. An example is shown in Fig.…”

Section: Dispersion Relation-traveling Modesmentioning

confidence: 88%

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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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“…We can observe evidence of traveling modes that develop higher wave angles than those of stationary modes in flow visualization by Wilkinson et al [22]. An example is shown in Fig.…”

Section: Dispersion Relation-traveling Modesmentioning

confidence: 88%

“…11 Visualization of flow over disk surface with a surface hole used to introduce an unsteady disturbance. From Wilkinson et al [22] (with permission) and 5 list the wave-number vectors for the respective frequencies f 2 and f 1 , in columns 1 and 2. The wave number of the n = 4 stationary mode, κ 3 , is listed in column 6.…”

Section: Triad Wavenumber Resonancementioning

confidence: 99%

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

2006

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“…The disturbance generated by the pulse is sharp and impulse-like, as required to excite a broad spectrum of frequencies, and there is very little overshoot, i.e. negative disturbances around the main pulse, as was the case with the acoustic forcing of the rotating-disk boundary layer performed by Wilkinson et al (1989). Figure 12(b) shows the power spectrum P(w1) calculated from the time series shown in figure 12(a).…”

Section: The Excited Flowmentioning

confidence: 96%

“…Because of such visualization experiments, with few exceptions (e.g. Bassom & Gajjar 1988;Wilkinson et al 1989;Balakumar & Malik 1990;Bassom & Hall 1991;Faller 1991), previous studies of the rotating-disk boundary layer have concentrated on the stationary waves. However, the boundary layer is also susceptible to excitation from free-stream turbulence and some of the resulting travelling waves are more unstable than the stationary waves.…”

Section: Introductionmentioning

confidence: 99%

An experimental study of absolute instability of the rotating-disk boundary-layer flow

1996

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In this paper, the results of experiments on unsteady disturbances in the boundary-layer flow over a disk rotating in otherwise still air are presented. The flow was perturbed impulsively at a point corresponding to a Reynolds numberRbelow the value at which transition from laminar to turbulent flow is observed. Among the frequencies excited are convectively unstable modes, which form a three-dimensional wave packet that initially convects away from the source. The wave packet consists of two families of travelling convectively unstable waves that propagate together as one packet. These two families are predicted by linear-stability theory: branch-2 modes dominate close to the source but, as the packet moves outwards into regions with higher Reynolds numbers, branch-1 modes grow preferentially and this behaviour was found in the experiment. However, the radial propagation of the trailing edge of the wave packet was observed to tend towards zero as it approaches the critical Reynolds number (about 510) for the onset of radial absolute instability. The wave packet remains convectively unstable in the circumferential direction up to this critical Reynolds number, but it is suggested that the accumulation of energy at a well-defined radius, due to the flow becoming radially absolutely unstable, causes the onset of laminar–turbulent transition. The onset of transition has been consistently observed by previous authors at an average value of 513, with only a small scatter around this value. Here, transition is also observed at about this average value, with and without artificial excitation of the boundary layer. This lack of sensitivity to the exact form of the disturbance environment is characteristic of an absolutely unstable flow, because absolute growth of disturbances can start from either noise or artificial sources to reach the same final state, which is determined by nonlinear effects.

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“…The first is the introduction of the temporal disturbances through a hole in the disk surface. A similar approach was used by Wilkinson et al (1989). Their flow visualization revealed that the hole produced a stationary disturbance wedge that swept outward on a logarithmic arc.…”

Section: Introductionmentioning

confidence: 93%

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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Flow Visualization of a Wave Packet on a Rotating Disk

Cited by 3 publications

References 4 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

An experimental study of absolute instability of the rotating-disk boundary-layer flow

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

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