The present paper is the first part of a two-part report on a detailed investigation of periodic turbulent pipe flow. In this investigation, experimental data on instantaneous velocity and wall shear stress were obtained at a mean Reynolds number of 50000 in a fully developed turbulent pipe flow in which the volumetric flow rate was varied sinusoidally with time around the mean. Two oscillation frequencies at significant levels of flow modulation were studied in detail. The higher of these frequencies was of the order of the turbulent bursting frequency in the flow, and the other can be regarded as an intermediate frequency at which the flow still departed significantly from quasi-steady behaviour. While a few similar experiments have been reported in the recent literature, the present study stands out from the others in respect of the flow regimes investigated, the magnitude of flow modulation, the detailed nature of the measurements and most importantly the identification of a relevant parameter to characterize unsteady shear flows. The present paper contains the main experimental results and comparisons of these results with the results of a numerical calculation procedure which employs a well-known quasi-steady turbulence closure model. The experimental data are used to study the manner in which the time-mean, the ensemble-averaged and the random flow properties are influenced by flow oscillation at moderate to high frequencies. In addition, the data are also used to bring out the capability and limitations of quasi-steady turbulence modelling in the prediction of unsteady shear flows. A further and more detailed analysis of the experimental data, results of some additional experiments and a discussion on the characterization of turbulent shear flows are provided in Part 2 (Ramaprian & Tu 1983).

The main experimental results of the study of periodic turbulent pipe flow have been described in Part 1 of this report. In this second part, these experimental data are examined in greater detail to understand the effect of imposed oscillation on the flow structure, at moderate to large oscillation frequencies. Data on phase and amplitude and energy spectrum are used to study the effect of the imposed oscillation on the turbulence structure at these interactive frequencies of oscillation. Additional experiments which were performed to study the effect of oscillation frequency on the flow structure are also reported. Based on the present observations as well as on the data from other sources, it is inferred that turbulent shear flows respond very differently from laminar shear flows to imposed unsteadiness. A turbulent Stokes number relevant for characterizing the unsteady turbulent shear flows is identified and used to classify such flows.

Fully developed oil flow in a smooth circular pipe at a mean Reynolds number of about 2100 was subjected to a nominally sinusoidal flow modulation at frequencies ranging from 0·05−1·75 Hz. It was observed that flow oscillation increased the critical Reynolds number and, under certain conditions, even brought about laminarization of the flow, which would be intermittently turbulent at the mean Reynolds number under quasi-steady (infinitely small oscillation frequency) conditions. The occurrence and extent of laminarization was, however, found to depend on factors such as the intermittency of turbulent puffs in the mean quasi-steady flow, frequency of oscillation, etc. Two series of experiments were performed. In one series, the oscillatory flow was almost completely laminarized. In the other series, the oscillatory flow was fully turbulent. In both the cases, instantaneous velocities in the flow were measured using laser-Doppler anemometry (LDA). The instantaneous velocity was decomposed into time-mean, periodic and random components employing ensemble-averaging techniques. The experiments indicated that the laminarized oscillatory flow behaves very similarly to laminar oscillatory flow at either end of the Strouhal-number range studied. The oscillatory turbulent flow was found to depend on both the Strouhal number and the ratio of the oscillation frequency (f) to some characteristic frequency (ft) of turbulence in the flow. The design of the present experimental facility made it possible to study the flow at f/ft ≈ 1 (‘high’ oscillation frequency), a condition that could not be attained in most previous investigations. Another unique feature of the present experiment was that the viscous sublayer and Stokes layer were both large enough (several millimetres in thickness) to allow detailed measurements to be made in these regions. It was found, that at this high frequency of oscillation, the Reynolds stresses generally remained frozen at an average state during the entire oscillation cycle. The turbulent structure showed significant departures from equilibrium at all times during the oscillation cycle. As a result, there was a net change in the time-mean velocity profile near the wall and a net increase in the time-mean wall shear stress and power loss due to friction. The observation that unsteadiness can indeed affect the mean flow behaviour in a significant way is new and contradicts the view presently held by many researchers (based on their studies at relatively low oscillation frequencies, i.e. f/ft [Lt ] 1). The data also indicated that the direct interaction between oscillation and the turbulent structure was essentially confined to the Stokes layer. The study suggests that (again contrary to the existing belief) quasi-steady turbulence models may not be adequate to describe unsteady flows when the time scale of unsteadiness is comparable to that of dominant turbulent eddies.

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