A Solid Body Model for Swirl Flow in Cylindrical Ducts

Tangential velocity in the cross-section of a cylindrical duct is a linear function of radius in many cases. This gives rise to the analogy of a Solid Body Model for swirl flow in ducts because of the similarity with a stiff rotating shaft. The generation of swirling flow by profiled ducts is described. Helically profiled lobate duct walls generate a twisting torque in an annular region at the outside periphery of the core flow. By contrast, wall friction in simple circular ducts causes swirl to decay. In the liquid counterpart of the solid body the torque is transmitted by duct walls rather than by shaft stiffness as in the solid case. The effect of the polar moment of inertia, J, of the rotating and twisting cylinder is unchanged from its solid counterpart and the damping coefficient, c, is directly related to the viscosity of the liquid acting in a narrow ring within the annulus between the rotating liquid cylinder and the duct wall. The system presents as a first order system with time constant J/c. The paper explores the behaviour of the “solid-body” in a cylindrical tube following a swirl- inducing duct using a 50mm bore duct conveying clean water as an example.