The effect of pulsation frequency on transition in pulsatile pipe flow

TL;DR

This study uses direct numerical simulations to investigate how pulsation frequency and amplitude affect flow stability and transition to turbulence in pulsatile pipe flow, clarifying previous conflicting experimental results.

Contribution

It provides a quantitative analysis of pulsation effects on flow stability, confirming that higher amplitude and lower frequency delay transition, and introduces an equation for transition threshold reduction.

Findings

Increasing pulsation amplitude delays transition.

Lower pulsation frequency enhances flow stability.

High-frequency pulsation recovers steady flow behavior.

Abstract

Pulsatile flows are common in nature and in applications, but their stability and transition to turbulence are still poorly understood. Even in the simple case of pipe flow subject to harmonic pulsation, there is no consensus among experimental studies on whether pulsation delays or enhances transition. We here report direct numerical simulations of pulsatile pipe flow at low pulsation amplitude A<0.4. We use a spatially localized impulsive disturbance to generate a single turbulent puff and track its dynamics as it travels downstream. The computed relaminarization statistics are in quantitative agreement with the experiments of Xu et al. (J. Fluid Mech., vol. 831, 2017, pp. 418-432) and support the conclusion that increasing the pulsation amplitude and lowering the frequency enhance the stability of the flow. In the high-frequency regime, the behaviour of steady pipe flow is recovered. In addition, we show that when the pipe length does not permit the observation of a full cycle, a reduction of the transition threshold is observed. We obtain an equation quantifying this effect and compare it favourably with the measurements of Stettler & Hussain (J. Fluid Mech., vol. 170, 1986, pp. 169-197). Our results resolve previous discrepancies, which are due to different pipe lengths, perturbation methods and criteria chosen to quantify transition in experiments.