Non-modal transient growth of disturbances in pulsatile and oscillatory pipe flows

Xu, Duo; Song, Baofang; Avila, Marc

doi:10.1017/jfm.2020.940

Cited by 31 publications

(43 citation statements)

References 31 publications

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“…The fact that different geometric disturbances can trigger different structures is consistent with the non-modal stability analysis of Xu et al. [ 20 ]. The analysis showed that the instantaneous Sexl–Womersley profile is linearly unstable (in the quasi-steady limit) during most of the DC phase.…”

Section: Resultssupporting

confidence: 86%

“…Next, we followed Xu et al. [ 20 ] and performed a linear non-modal stability analysis to identify the optimal perturbation for the parameter values of interest (

, and several A ). This method produces the geometry (radial shape and axial/azimuthal wavenumbers) and the initial time (

) of the perturbation achieving the maximum energy amplification.…”

Section: Resultsmentioning

confidence: 99%

“…Motivated by this finding, Xu et al. [ 20 ] carried out a comprehensive non-modal stability analysis of pulsatile pipe flow. They showed that certain helical perturbations exploit an Orr-like mechanism to grow by several orders of magnitude in energy.…”

Section: Introductionmentioning

confidence: 99%

“…However, as the Womersley number is reduced, the velocity profile becomes increasingly parabolic and, hence, loses its inflection points. The amplification of helical disturbances is most efficient for

[ 20 ], exactly in the regime where the helical instability was observed experimentally [ 17 ].…”

Section: Introductionmentioning

confidence: 99%

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Spatiotemporal Intermittency in Pulsatile Pipe Flow

Feldmann¹,

Morón²,

Avila³

2020

Entropy

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Despite its importance in cardiovascular diseases and engineering applications, turbulence in pulsatile pipe flow remains little comprehended. Important advances have been made in the recent years in understanding the transition to turbulence in such flows, but the question remains of how turbulence behaves once triggered. In this paper, we explore the spatiotemporal intermittency of turbulence in pulsatile pipe flows at fixed Reynolds and Womersley numbers (Re=2400, Wo=8) and different pulsation amplitudes. Direct numerical simulations (DNS) were performed according to two strategies. First, we performed DNS starting from a statistically steady pipe flow. Second, we performed DNS starting from the laminar Sexl–Womersley flow and disturbed with the optimal helical perturbation according to a non-modal stability analysis. Our results show that the optimal perturbation is unable to sustain turbulence after the first pulsation period. Spatiotemporally intermittent turbulence only survives for multiple periods if puffs are triggered. We find that puffs in pulsatile pipe flow do not only take advantage of the self-sustaining lift-up mechanism, but also of the intermittent stability of the mean velocity profile.

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Section: Resultssupporting

confidence: 86%

“…Next, we followed Xu et al. [ 20 ] and performed a linear non-modal stability analysis to identify the optimal perturbation for the parameter values of interest (

, and several A ). This method produces the geometry (radial shape and axial/azimuthal wavenumbers) and the initial time (

) of the perturbation achieving the maximum energy amplification.…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

[ 20 ], exactly in the regime where the helical instability was observed experimentally [ 17 ].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Spatiotemporal Intermittency in Pulsatile Pipe Flow

Feldmann¹,

Morón²,

Avila³

2020

Entropy

Self Cite

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“…Complementary nonlinear simulations further verified that triggering by these mechanisms can yield subcritical transition to turbulence. A similar technique has been applied in a recent study by Xu, Song & Avila (2021) for oscillatory and pulsating pipe flow. Among others, they have reported that pulsating pipe flows are generally dominated by helical perturbations.…”

Section: Introductionmentioning

confidence: 99%

Optimal energy growth in pulsatile channel and pipe flows

Pier

Schmid

2021

J. Fluid Mech.

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Pulsatile channel and pipe flows constitute a fundamental flow configuration with significant bearing on many applications in the engineering and medical sciences. Rotating machinery, hydraulic pumps or cardiovascular systems are dominated by time-periodic flows, and their stability characteristics play an important role in their efficient and proper operation. While previous work has mainly concentrated on the modal, harmonic response to an oscillatory or pulsatile base flow, this study employs a direct–adjoint optimisation technique to assess short-term instabilities, identify transient energy-amplification mechanisms and determine their prevalence within a wide parameter space. At low pulsation amplitudes, the transient dynamics is found to be similar to that resulting from the equivalent steady parabolic flow profile, and the oscillating flow component appears to have only a weak effect. After a critical pulsation amplitude is surpassed, linear transient growth is shown to increase exponentially with the pulsation amplitude and to occur mainly during the slow part of the pulsation cycle. In this latter regime, a detailed analysis of the energy transfer mechanisms demonstrates that the huge linear transient growth factors are the result of an optimal combination of Orr mechanism and intracyclic normal-mode growth during half a pulsation cycle. Two-dimensional sinuous perturbations are favoured in channel flow, while pipe flow is dominated by helical perturbations. An extensive parameter study is presented that tracks these flow features across variations in the pulsation amplitude, Reynolds and Womersley numbers, perturbation wavenumbers and imposed time horizon.

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