Numerical analysis of the flow pattern in convergent vortex tubes for cyclone cooling applications

The use of swirling flows in cyclone cooling systems is a promising method for internal cooling applications for instance in the leading edge of gas turbine blades. However, vortex breakdown can occur in such flows, which is associated with an axial flow reversal. Within the scope of this investigation a numerical parameter study was conducted in order to explore the impact of convergent tube geometries on the flow pattern. For this purpose, Delayed Detached Eddy Simulations (DDES) were conducted for a Reynolds number of 10,000 and a swirl number of 5.3. First of all, the numerically obtained velocity field was compared to experimental data for a reference tube with a constant cross-section. This validation showed overall good agreement. Subsequently, the same reference tube was compared to four convergent tubes. The latter ones comprised three geometries with linearly decreasing diameters reaching convergence angles of 0.42 deg., 0.61 deg. and 0.72 deg., respectively. Furthermore, an additional tube featuring a hyperbolic diameter decrease was considered. The current investigation demonstrates that convergent vortex tubes impose a flow acceleration that sup-presses the vortex breakdown phenomenon. Moreover, the axial velocity can be associated to different flow regimes with supercritical and subcritical character. These regimes indicate that the flow field within convergent tubes is less affected by the outlet conditions. Moreover, a physical reason is given that explains the formation of different flow regimes and their associated backflow as pressure-driven phenomenon. Furthermore, a modified Q-criterion illustrates two double helix vortex systems that can both be stabilized by choosing an appropriate geometry.