Analogy between Developing Laminar Flows in Curved Pipes and Orthogonally Rotating Pipes

Abstract

This paper describes a quantitative analogy between developing laminar flows in the inlet regions of curved pipes and orthogonally rotating straight pipes through similarity arguments and computational studies. Three-dimensional developments of these flows are characterized by secondary flows due to the centrifugal or the Coriolis force. Similarity considerations with taking the secondary flow into account result in a pair of governing parameters and a dimensionless axial distance for each flow. When the second parameter is large enough in each flow, we have a quantitative analogy between them ; the computed results for the two flows show strong similarity regarding the developments of flow structure, wall friction, and velocity profile of primary and secondary flows.