On the Theory of Viscous Swirl

Abstract

To analyse the flow in the swirl injection nozzles used for the gas turbines, we have attempted to calculate the properties of the viscous swirling flow solving the Navier-Stokes' equation. The integration constants appeared in the solutions are obtained from the consideration of the energy loss between two consecutive layers of viscous fluid, thus enabling the determination of the size of the cavity or the core, which rotates like a solid cylindrical column. The effects of viscosities of the fuels on the discharge coefficients and spray angles are also calculated with various actual examples. As a special case, the mathematical conditions for the generation of 'the eye of the swirl' is also explained, where the cavity or the core ceases its rotation and forms a cylindrical column of fluid at rest similar to that happens in the swirling wind such as in the Typhoon, the Cyclone or the Hurricane.