On transition of the pulsatile pipe flow

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Abstract
Transition in a pipe flow with a superimposed sinusoidal modulation has been studied in a straight circular water pipe using laser-Doppler anemometer (LDA) techniques. This study has determined the stability–transition boundary in the three-dimensional parameter space defined by the mean and modulation Reynolds numbers Rem, Remω and the frequency parameter λ. Furthermore, it documents the mean passage frequency Fp of ‘turbulent plugs’ as functions of Rem’ Remω and λ. This study also delineates the conditions when plugs occur randomly in time (as in the steady flow) or phase-locked with the excitation. The periodic flow requires a new definition of the transitional Reynolds number Rer, identified on the basis of the rate of change of Fp with Rem. The extent of increase or decrease in Rer from the corresponding steady flow value depends on λ and Remω. At any Rem and Remω, maximum stabilization occurs at λ ≈ 5. With increasing Remω, the ‘stabilization bandwidth’ of modulation frequencies increases and then abruptly decreases after levelling off. The maximum stabilization bandwidth depends strongly on Rem, decreasing with increasing Rem. Previously reported observations of turbulence during deceleration, followed by a relaminarization during acceleration, can be explained in terms of a new phenomenon: namely, periodic modulation produces longitudinally periodic cells of turbulent fluid ‘plugs’ which differ in structural details from ‘puffs’ or ‘slugs’ in steady transitional pipe flows and are called patches. The length of a patch could be increased continuously from zero to the entire pipe length by increasing Rem. This tends to question the concept that all turbulent plugs (and even the fully-turbulent pipe flow) consists of many identical elementary plugs as basic ‘building blocks’.

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