OPTIMAL PROPERTIES OF INCOMPRESSIBLE SWIRLING FLOW IN A RECTILINEAR CIRCULAR PIPE

Swirling flows are frequently encountered in technical devices, particularly in hydraulic and pneumatic systems. Optimal performance of these devices cannot be achieved without a thorough understanding of the physics governing these flows—physics that, as it turns out, is characterized by optimality. It is precisely these optimality properties that prove useful in situations where existing models fail to accurately describe the flow on their own. This paper provides an overview of contemporary research and achievements regarding swirling flows and highlights the challenge of describing them adequately. Based on this, the study's objective is formulated: to consolidate and systematize existing knowledge while deriving new insights–specifically, the optimality properties of swirling flows. The results demonstrate that swirling flows in a rectilinear circular pipe possess optimality properties; for instance, a flow with extremal helicity exhibits zero helicity at every point. Swirling flow where the velocity field depends solely on the radial coordinate is also optimal. For laminar flow, this entails the property of maximum flow rate, whereas for turbulent flow, the condition of maximum vorticity is also satisfied. The obtained results are compared with existing theoretical and experimental data.