Laminar flow in rotating curved pipes

Abstract

When a curved pipe rotates about the centre of curvature, the fluid flowing in it is subjected to both Coriolis and centrifugal forces. Based on the analogy between laminar flows in stationary curved pipes and in orthogonally rotating pipes, the flow characteristics of fully developed laminar flow in rotating curved pipes are made clear and definite by similarity arguments, computational studies and using experimental data. Similarity arguments clarify that the flow characteristics in loosely coiled rotating pipes are governed by three parameters: the Dean number KLC, a body force ratio F and the Rossby number Ro. As the effect of Ro is negligible when Ro is large, computational results are presented for this case first, and then the effect of Ro is studied. Flow structure and friction factor are studied in detail. Variations of flow structure show secondary flow reversal at F ≈ −1, where the two body forces are of the same order but in opposite directions. It is also shown how the Taylor–Proudman effect dominates the flow structure when Ro is small. Computed curves of the friction factor for constant Dean number have their minimum at F ≈ −1. A composite parameter KL is introduced as a convenient governing parameter and used to correlate the characteristics. By applying KL to the analogy formula previously derived for two limiting flows, a semi-empirical formula for the friction factor is presented, which shows good agreement with the experimental data for a wide range of the parameters.