Oscillatory flow in curved pipes. Part 2. The fully developed case

A theoretical and experimental investigation of oscillatory flow in curved pipes is presented. The equations for fully developed laminar flow are found to depend on an amplitude parameter G and a frequency parameter α. Initially the Navier–Stokes equations are expanded in terms of G and the resulting linearized equations are solved numerically using finite Hankel integral transforms. A further expansion is used for the case α → 0 and closed-form solutions are presented. Laser-Doppler anemometry has been used to obtain velocity information in oscillatory air flow in small-diameter curved glass tubes. Using this technique, low-Reynolds-number experiments were carried out and comparison between theory and experiments is presented. For α [les ] 1 the velocity distributions found are essentially those for steady flow, while for α [ges ] 11·0 the results are not at variance with earlier work. It is for the transition stage between these two regimes that unexpected behaviour is recorded, but a satisfactory explanation is found in terms of general trends within the flow.