Control of stationary convective instabilities in the rotating disk boundary layer via time-periodic modulation

Morgan, Scott; Davies, Christopher; Thomas, Christian

doi:10.1017/jfm.2021.679

Cited by 3 publications

(36 citation statements)

References 41 publications

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“…The approach for formulating and computing the unsteady base flow is described fully in Morgan et al. (2021). Accordingly, only an outline of the scheme is presented here.…”

Section: Base Flowmentioning

confidence: 99%

“…In the subsequent derivation of the non-dimensional unsteady base flow, all quantities are defined in a non-rotating frame of reference to facilitate the numerical solution via Chebyshev methods (Morgan et al. 2021).…”

Section: Base Flowmentioning

confidence: 99%

“…In keeping with the earlier study by Morgan et al. (2021), modulation parameter settings were chosen carefully to ensure that the time-periodic modulation did not establish any new forms of instability, other than the convective and absolute instabilities already found in the steady von Kármán flow (Malik 1986; Balakumar & Malik 1990; Lingwood 1995). The modulation amplitude was limited to the interval , while, following the observations of Morgan et al.…”

Section: Base Flowmentioning

confidence: 99%

“…The modulation amplitude was limited to the interval , while, following the observations of Morgan et al. (2021), much of the subsequent investigation was based on modulation frequencies . (The earlier Floquet analysis of Morgan and co-workers showed that the optimal frequency for controlling the stationary cross-flow instability was in the interval , while smaller and larger frequencies had a negligible effect on the growth of the disturbance.…”

Section: Base Flowmentioning

confidence: 99%

“…A novel approach for controlling the stationary cross-flow instability was implemented by Morgan, Davies & Thomas (2021), whereby a time-periodic modulation of the disk rotation rate was modelled. The application of modulation to the steady rotating disk was motivated by Thomas et al.…”

Section: Introductionmentioning

confidence: 99%

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Linear impulse response in three-dimensional oscillatory boundary layers formed by periodic modulation of a rotating disk

Morgan

Davies²,

Thomas³

2022

J. Fluid Mech.

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A numerical investigation is undertaken on the development of linear disturbances in the rotating disk boundary layer, in which a time-periodic modulation is applied to the disk rotation rate. The model gives a prototypical example of a three-dimensional oscillatory boundary layer, by adding a Stokes layer to the von Kármán flow that develops on a steady disk. The study extends the Floquet analysis of Morgan et al. (J. Fluid Mech., vol. 925, 2021, A20), who showed that disk modulation stabilises the stationary convective instabilities found on the steady rotating disk. Using a radial homogeneous flow approximation, whereby the radial dependence of the basic state is ignored, disturbance development is simulated for several modulation settings, with flow conditions matched to both convective and absolute forms of linear instability. Disturbances excited via a stationary periodic wall forcing display behaviour consistent with that found using Floquet theory; time-periodic modulation stabilises the cross-flow instability by reducing the radial growth rate. In addition, convective and absolute instabilities, generated by an impulsive wall forcing, are both stabilised by the introduction of modulation to the disk rotation rate. Modulation establishes a significant reduction in both the temporal growth rate and the disturbance amplitude as it propagates away from the impulse origin. Moreover, greater stabilising control benefits are realised as the modulation amplitude increases.

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“…The approach for formulating and computing the unsteady base flow is described fully in Morgan et al. (2021). Accordingly, only an outline of the scheme is presented here.…”

Section: Base Flowmentioning

confidence: 99%

Section: Base Flowmentioning

confidence: 99%

Section: Base Flowmentioning

confidence: 99%

Section: Base Flowmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Linear impulse response in three-dimensional oscillatory boundary layers formed by periodic modulation of a rotating disk

Morgan

Davies²,

Thomas³

2022

J. Fluid Mech.

Self Cite

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Linear instability of a supersonic boundary layer over a rotating cone

Song

Dong

2023

J. Fluid Mech.

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In this paper, we conduct a systematic study of the instability of a boundary layer over a rotating cone that is inserting into a supersonic stream with zero angle of attack. The base flow is obtained by solving the compressible boundary-layer equations using a marching scheme, whose accuracy is confirmed by comparing with the full Navier–Stokes solution. Setting the oncoming Mach number and the semi-apex angle to be 3 and 7 $^\circ$ , respectively, the instability characteristics for different rotating rates ( $\bar \varOmega$ , defined as the ratio of the rotating speed of the cone to the axial velocity) and Reynolds numbers ( $R$ ) are revealed. For a rather weak rotation, $\bar \varOmega \ll 1$ , only the modified Mack mode (MMM) exists, which is an extension of the supersonic Mack mode in a quasi-two-dimensional boundary layer to a rotation configuration. Further increase of $\bar \varOmega$ leads to the appearance of a cross-flow mode (CFM), coexisting with the MMM but in the quasi-zero frequency band. The unstable zones of the MMM and CFM merge together, and so they are referred to as the type-I instability. When $\bar \varOmega$ is increased to an $O(1)$ level, an additional unstable zone emerges, which is referred to as the type-II instability to be distinguished from the aforementioned type-I instability. The type-II instability appears as a centrifugal mode (CM) when $R$ is less than a certain value, but appears as a new CFM for higher Reynolds numbers. The unstable zone of the type-II CM enlarges as $\bar \varOmega$ increases. The vortex structures of these types of instability modes are compared, and their large- $R$ behaviours are also discussed.

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Effect of slip on the linear stability of the rotating disk boundary layer

et al. 2023

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The linear stability of the rotating disk boundary layer with surface roughness is investigated. Surface roughness is modeled using slip boundary conditions [M. Miklavčič and C. Y. Wang, Z. Angew. Math. Phys. 55, 235–246 (2004)], which establish concentric grooves, radial grooves, and isotropic roughness. The effect on the stationary crossflow and Coriolis instabilities is analyzed by applying slip conditions to the undisturbed flow and linear disturbances. This analysis builds on the work of Cooper et al. [Phys. Fluids 27, 014107 (2015)], who modeled slip effects on the base flow but applied the no-slip condition to the linear perturbations. Neutral stability curves and critical parameter settings for linearly unstable behavior are computed for several radial and azimuthal slip length settings. The application of slip on the linear disturbances has a significant impact on the flow stability. In particular, the Coriolis instability undergoes considerable destabilization in the instance of concentric grooves (i.e., radial slip) and radial grooves with sufficiently large azimuthal slip lengths. In addition, concentric grooves destabilize the crossflow instability when the radial slip length is small. Moreover, in the instance of isotropic roughness, the stabilizing effect is markedly less than the observations of Cooper et al. [Phys. Fluids 27, 014107 (2015)]. Finally, an energy analysis is undertaken to ascertain the physical mechanisms brought about by surface roughness.

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Control of stationary convective instabilities in the rotating disk boundary layer via time-periodic modulation

Abstract: Abstract

Cited by 3 publications

References 41 publications

Linear impulse response in three-dimensional oscillatory boundary layers formed by periodic modulation of a rotating disk

Linear impulse response in three-dimensional oscillatory boundary layers formed by periodic modulation of a rotating disk

Linear instability of a supersonic boundary layer over a rotating cone

Effect of slip on the linear stability of the rotating disk boundary layer

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