Laminar flow in rotating curved pipes

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 K-LC, a body force ratio F and the Rossby number R0. As the effect of R0 is negligible when R0 is large, computational results are presented for this case first, and then the effect of R0 is studied. Flow structure and friction factor are studied in detail. Variations of flow structure show secondary flow reversal at F approximate to -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 how structure when R0 is small. Computed curves of the friction factor for constant Dean number have their minimum at F approximate to -1. A composite parameter K-L is introduced as a convenient governing parameter and used to correlate the characteristics. By applying K-L to the analogy formula previously derived for two limiting hows, 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.