Pulsating flow in a pipe

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Abstract
Turbulent and laminar pulsating flows in a straight smooth pipe are compared at identical frequencies and Reynolds numbers. Most measurements were made at a mean Reynolds number of 4000, but the influence of Re was checked for 2900 < Re < 7500. The period of forcing ranged from 0.5 to 5 s, with corresponding change in the non-dimensional frequency parameter α = R √(ω/ν) from 4.5 to 15. The amplitude of the imposed oscillations did not exceed 35% of the mean in order to avoid flow reversal or relaminarization. Velocities at the exit plane of the pipe and pressure drop along the pipe were measured simultaneously; velocity measurements were made with arrays of normal hot wires. The introduction of the periodic surging had no significant effect on the time-averaged quantities, regardless of the flow regime (i.e. in both laminar and turbulent flows). The time-dependent components at the forcing frequency, represented by a radial distribution of amplitudes and phases, are qualitatively different in laminar and turbulent flows. The ensemble-averaged turbulent quantities may also be represented by an amplitude and a phase; however, the non-harmonic content of these intensities increases with increasing amplitude of the imposed oscillations. A normalization procedure is proposed which relates phase-locked turbulent flow parameters in unsteady flow to similar time-averaged quantities. An integral momentum equation in a time-dependent flow requires that a triad of forces (pressure, inertia and shear) will be in equilibrium at any instant of time. All the terms in the force-balance equation were measured independently, providing a good check of data. The analysis of the experimental results suggests that turbulence adjusts rather slowly to the local mean-flow conditions. A simple eddy-viscosity model described by a complex function can account for ‘memory’ of turbulence and explain the different phase distribution in laminar and turbulent flows.