On transition of the pulsatile pipe flow

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 Re m , Re mω and the frequency parameter λ. Furthermore, it documents the mean passage frequency F p of ‘turbulent plugs’ as functions of Re m ’ Re mω 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 Re r , identified on the basis of the rate of change of F p with Re m . The extent of increase or decrease in Re r from the corresponding steady flow value depends on λ and Re mω . At any Re m and Re mω , maximum stabilization occurs at λ ≈ 5. With increasing Re mω , the ‘stabilization bandwidth’ of modulation frequencies increases and then abruptly decreases after levelling off. The maximum stabilization bandwidth depends strongly on Re m , decreasing with increasing Re m . 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 Re m . 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’.