Analytic representations of dissipation in partially-submerged reciprocating pipe flow

Abstract

Abstract A series of analytic models are presented of a partially-submerged, straight circular cross-section pipe subjected to reciprocating flow, incorporating viscous and turbulent boundary-layer dissipation. This pipe is the most elementary paradigm for a fixed-type Oscillating Water Column (OWC), and its analysis more generally addresses one aspect of reciprocating pipe flow. The derivation of the dissipation terms in the momentum conservation equations from their origin in the Navier–Stokes equation are explicitly identified. The contribution of different damping sources to the overall energy loss is compared. The flow inside the pipe is assumed fully developed along the entire length, neglecting the effect of the flow development region. For relevance to engineering applications, a power take-off system is modelled assuming that the air compresses and expands isentropically in an air chamber at the top of the pipe. Existing theory is adapted into the current models for computing the hydrodynamic coefficients related to the scattered wave and radiation wave. A novel contribution of this paper is the inclusion of damping due to the wall shear stress, modelled for the reciprocating flow system inside the pipe. Comparison between the damping factors in relatively short OWCs confirms the findings in the literature that the major part of the damping is due to the radiation wave. However, it is found that with the increase of the draft length, the wall shear stress damping may also become an important factor in the resulting dynamics.