Analytical and Numerical Investigations of Steady and Unsteady Turbulent Swirling Flow in Diffusers
Swirling flows are found in many technical applications, e.g. turbines, pumps, fans, compressors and combustors. The objective of the present work is to acquire an understanding of the physics of swirling flow in general and unsteady swirling flow in draft tubes of water turbines in particular. Analytical studies of axisymmetric swirling flow were carried out using a quasi-cylindrical approximation of the Navier-Stokes equations. It is shown that there are no quasi-cylindrical solutions to the Navier-Stokes equations for certain critical levels of swirl. It is argued that this property of the equations is related to a vortex breakdown phenomenon. In draft tubes of hydraulic power plants, the vortex breakdown phenomenon gives rise to a highly unsteady, oscillating pressure field that can endanger the machine. Numerical three-dimensional and unsteady simulations of swirling flows in simplified draft tube geometries were carried out to investigate this dynamic behaviour. The numerical methods include both LES (large eddy simulations) and RANS (Reynolds averaged Navier-Stokes) simulations. An LES is not an option for a full-scale draft tube simulation but provides valuable information for simplified cases. The RANS simulations in combination with the standard two-equation turbulence models are more applicable for industrial purposes but do not provide enough information about the unsteadiness of the flow. A dynamic filtering procedure of the turbulent length and time scales is generalised, employed and evaluated in order to remedy this shortcoming in the two-equation models. It is shown that the filtering procedure can yield solutions that contain more information about the flow dynamics as well as better time-averaged results compared to an ordinary RANS simulation.