Spatiotemporal Intermittency in Pulsatile Pipe Flow

Abstract

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.

Effect of waveform on turbulence transition in pulsatile pipe flow

“…2017; Xu & Avila 2018; Feldmann et al. 2021). At higher , the dynamics of turbulence are similar to those observed in steady pipe flow and the waveform is not expected to have much influence on them.…”

“…The computational domain is long and, following Feldmann et al. (2021), the simulations are initialised at with the corresponding SW velocity profile disturbed with the optimal helical perturbation obtained from our TGA. In numerical simulations with global initial perturbations (not shown here), the perturbations grow and trigger turbulence in the whole domain.…”

“…(2012), Xu et al. (2017), direct numerical simulations (DNS) of Xu & Avila (2018) and Feldmann, Morón & Avila (2021) and linear stability analysis (LSA) of Thomas et al. (2011), to name just a few.…”

“…a n = b n = 0 for all n in (1.1) except for b 1 = A. There are experiments of Sarpkaya (1966), Stettler & Hussain (1986) Trip et al (2012), Xu et al (2017), direct numerical simulations (DNS) of Xu & Avila (2018) and Feldmann, Morón & Avila (2021) and linear stability analysis (LSA) of Thomas et al (2011), to name just a few. In those cases, the shape of the waveform is given by the amplitude A = max(u b )/u s − 1 and the transition depends on three control parameters (Re, Wo and A).…”

Taylor rolls on tour

“…The highest friction Reynolds number (Re τ = uτ d /ν) measured in all DNS is 408 (Tab. I) and the spatial resolution in terms of viscous units (i. e. based on Re τ ) is at least 0.07 ≤ ∆r + ≤ 4.03 and ∆z + = 4.89, which is state of the art in DNS of wall-bounded turbulence [11,15,27].…”