On the Similarity of Pulsating and Accelerating Turbulent Pipe Flows

The near-wall region of an unsteady turbulent pipe flow has been investigated experimentally using hot-film anemometry and two-component particle image velocimetry. The imposed unsteadiness has been pulsating, i.e., when a non-zero mean turbulent flow is perturbed by sinusoidal oscillations, and near-uniformly accelerating in which the mean flow ramped monotonically between two turbulent states. Previous studies of accelerating flows have shown that the time evolution between the two turbulent states occurs in three stages. The first stage is associated with a minimal response of the Reynolds shear stress and the ensemble-averaged mean flow evolves essentially akin to a laminar flow undergoing the same change in flow rate. During the second stage, the turbulence responds rapidly to the new flow conditions set by the acceleration and the laminar-like behavior rapidly disappears. During the final stage, the flow adapts to the conditions set by the final Reynolds number. In here, it is shown that the time-development of the ensemble-averaged wall shear stress and turbulence during the accelerating phase of a pulsating flow bears marked similarity to the first two stages of time-development exhibited by a near-uniformly accelerating flow. The stage-like time-development is observed even for a very low forcing frequency; \(\omega ^{+}=\omega \nu /{\overline {u}}_{\tau }^{2}=0.00073\) (or equivalently, \({l}_{s}^{+}=\sqrt {2/\omega ^{+}}=52\)), at an amplitude of pulsation of 0.5. Some previous studies have considered the flow to be quasi-steady at \({l}_{s}^{+}=52\); however, the forcing amplitude has been smaller in those studies. The importance of the forcing amplitude is reinforced by the time-development of the ensemble-averaged turbulence field. For, the near-wall response of the Reynolds stresses showed a dependence on the amplitude of pulsation. Thus, it appears to exist a need to seek alternative similarity parameters, taking the amplitude of pulsation into account, if the response of different flow quantities in a pulsating flow are to be classified correctly.