Revisiting the stability of pulsatile pipe flow

Fedele, Francesco; Hitt, Darren L.; Prabhu, R. D.

doi:10.1016/j.euromechflu.2004.07.005

Cited by 21 publications

(15 citation statements)

References 34 publications

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“…where B j is the amplitude of the radial eigenfunctions φ j that satisfy the Boundary Value Problem (BVP) (see [16]) L 2 φ j = −λ 2 j Lφ j , with 1 r φ j and 1 r ∂ r φ j bounded at r → +0, and φ j = ∂ r φ j = 0 at r = 1. Since φ j satisfies the pipe flow boundary conditions a priori, so does ψ of (2.2).…”

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confidence: 99%

Vortexons in axisymmetric Poiseuille pipe flows

Fedele¹,

Dutykh²

2013

EPL

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Abstract. We present a study on the nonlinear dynamics of small long-wave disturbances to the laminar state in non-rotating axisymmetric Poiseuille pipe flows. At high Reynolds numbers, the associated Navier-Stokes equations can be reduced to a set of coupled Korteweg-de Vries-type (KdV) equations that support inviscid and smooth travelling waves numerically computed using the Petviashvili method. In physical space they correspond to localized toroidal vortices concentrated near the pipe boundaries (wall vortexons) or that wrap around the pipe axis (centre vortexons), in agreement with the analytical soliton solutions derived by Fedele (2012) [12]. The KdV dynamics of a perturbation is also investigated by means of an high accurate Fourier-based numerical scheme. We observe that an initial vortical patch splits into a centre vortexon radiating patches of vorticity near the wall. These can undergo further splitting leading to a proliferation of centre vortexons that eventually decay due to viscous effects. The splitting process originates from a radial flux of azimuthal vorticity from the wall to the pipe axis in agreement with the inverse cascade of cross-stream vorticity identified in channel flows by Eyink (2008) [10]. The inviscid vortexon most likely is unstable to non-axisymmetric disturbances and may be a precursor to puffs and slug flow formation.

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confidence: 99%

Vortexons in axisymmetric Poiseuille pipe flows

Fedele¹,

Dutykh²

2013

EPL

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“…All configurations for which calculations have been carried out are found to be stable. Later, Fedele et al (2005) also claim that axisymmetric modes in pulsatile pipe flow are stable, while, more recently, Thomas et al (2011) were able to obtain unstable axisymmetric modes and to establish critical conditions for this flow.…”

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confidence: 99%

Linear and nonlinear dynamics of pulsatile channel flow

Pier

Schmid

2017

J. Fluid Mech.

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The dynamics of small-amplitude perturbations as well as the regime of fully developed nonlinear propagating waves is investigated for pulsatile channel flows. The timeperiodic base flows are known analytically and completely determined by the Reynolds number Re (based on the mean flowrate), the Womersley number Wo (a dimensionless expression of the frequency) and the flowrate waveform. This paper considers pulsatile flows with a single oscillating component and hence only three non-dimensional control parameters are present. Linear stability characteristics are obtained both by Floquet analyses and by linearized direct numerical simulations. In particular, the long-term growth or decay rates and the intracyclic modulation amplitudes are systematically computed. At large frequencies (mainly Wo 14), increasing the amplitude of the oscillating component is found to have a stabilizing effect, while it is destabilizing at lower frequencies; strongest destabilization is found for Wo ≃ 7. Whether stable or unstable, perturbations may undergo large-amplitude intracyclic modulations; these intracyclic modulation amplitudes reach huge values at low pulsation frequencies. For linearly unstable configurations, the resulting saturated fully developed finite-amplitude solutions are computed by direct numerical simulations of the complete Navier-Stokes equations. Essentially two types of nonlinear dynamics have been identified: "cruising" regimes for which nonlinearities are sustained throughout the entire pulsation cycle and which may be interpreted as modulated Tollmien-Schlichting waves, and "ballistic" regimes that are propelled into a nonlinear phase before subsiding again to small amplitudes within every pulsation cycle. Cruising regimes are found to prevail for weak baseflow pulsation amplitudes, while ballistic regimes are selected at larger pulsation amplitudes; at larger pulsation frequencies, however, the ballistic regime may be bypassed due to the stabilizing effect of the base-flow pulsating component. By investigating extended regions of a multi-dimensional parameter space and considering both two-dimensional and threedimensional perturbations, the linear and nonlinear dynamics are systematically explored and characterized.

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“…These conclusions, however, contradict the experimental observation on transition of pulsatile pipe flows (Stettler and Hussain, 1986). Several investigations were carried out and are still being conducted in order to find out the reason for apparent contradiction (see for example, Tozzi and von Kerczek, 1986;Straatman et al, 2002;Fedele et al, 2005;Nebauer and Blackburn, 2010;Smith and Blackburn, 2010). Although these detailed studies included non-linear stability analysis and also considered the effect of non-axi-symmetric disturbances, exact quantification of Recrit still remains largely inclusive.…”

Section: Governing Equations Boundary and Initial Conditionsmentioning

confidence: 81%