PERIODICALLY OSCILLATING TURBULENT FLOW IN A PIPE.

A fluctuating eddy viscosity model for Reynolds stress is proposed. The validity of this model is verified for all frequencies tested through comparisons between the calculations and measurements. The analysis yields three properly-modified Strouhal numbers: the first of them is adequate to illustrate similarly the velocity distributions in turbulent region over a wide range of frequencies and the time-mean Reynolds numbers, the second is adequate in the vicinity of wall, the last is for the instantaneous friction factor. The following results are obtained: at low frequencies the amplitude of the wall shear stress is proportional to the amplitude of the velocity. At high frequencies it is proportional to both the velocity amplitude and the square root of the frequency. The predicted magnitude of the instantaneous friction factor exceeds that of steady state during accelerating flow and it is smaller than that during decelerating flow.