Identification of an initial non-linear transition in reciprocating finite-length pipe flow

We present an experimental study of reciprocating pipe flow with free-end effects, specifically, oscillations of a column of water trapped inside an open vertical cylinder under the action of regular linear waves. The aims were to identify parameters where an initial transition to non-linearity in reciprocating flow might occur and to quantify energy losses in the non-linear regime. Reciprocating flows are a subclass of oscillatory flows that are characterized by a zero-mean flux. The investigation may provide a deeper fundamental understanding of the characteristics of reciprocating flows, which differ significantly from the properties of well-studied unidirectional flows. From measured amplitudes of the incoming and excited oscillations inside the column, we draw the dependence of the amount of the absorbed kinetic power on the amplitude and frequency of the incident waves. Quantifications were made of the balance between the energy absorbed by the column and dissipated due to the radiation of waves and wall friction, which are usually considered linear, as well as non-linear losses of energy due to flow separation at the walls and vortex shedding and turbulence at the bottom free end of the cylinder. It is found that the non-linear effects become significant at incident wave amplitudes much smaller than expected, thus affecting the energy balance. We suggest that the initial transition from linear to non-linear behavior in reciprocating finite pipe flow has been identified and the critical oscillatory Reynolds number at which it occurs has been estimated as Reos = 4400 ± 1250.