Fundamental mode of freely decaying laminar swirling flows

• It has been shown that there is a fundamental swirling mode.
• It has been shown that there is a fundamental tangential velocity profile.
• It is shown that the swirl decay is exponential and linked to the Reynolds number.
• A new swirl number has been introduced, referred to as the torque swirl number.
• The torque swirl number of the fundamental tangential velocity profile is 1.083.

A detailed study of a swirling flow in a tube is presented in the first part of the paper. A simplified analytical solution of the governing equations indicates specific modes of the tangential velocity and that the decay of the swirl effect is exponential. The problem is then solved in three dimensions using computational fluid dynamics (CFD) and a comparison with analytical expressions shows that the CFD code is reliable in terms of accuracy. The CFD results confirm that a fundamental swirling mode is reached within a short distance from the inlet. The torque swirl number is introduced to physically estimate the intensity of the swirl. A companion value is given: it is the average deviation.