The efficiency of modern axial turbomachinery is strongly driven by the secondary flows within the vane or blade passages. The secondary flows are characterized by a complex pattern of vortical structures that origin, interact and dissipate along the turbine gas path. The endwall flows are responsible for the generation of a significant part of the overall turbine loss because of the dissipation of secondary kinetic energy and mixing-out of non-uniform momentum flows. The understanding and analysis of secondary flows requires a reliable vortex identification technique to predict and analyse the impact of specific turbine designs on the turbine performance. However, literature shows a remarkable lack of general methods to detect vortices and to determine the location of their cores and to quantify their strength.
This paper presents a novel technique for the identification of vortical structures in a general 3D flow field. The method operates on the local flow field and it is based on a triple decomposition of motion proposed by Kolář. In contrast to a decomposition of velocity gradient into the strain and vorticity tensors, this method considers a third, pure shear component. The subtraction of the pure shear tensor from the velocity gradient remedies the inherent flaw of vorticity-based techniques which cannot distinguish between rigid rotation and shear. The triple decomposition of motion serves to obtain a 3D field of residual vorticity whose magnitude is used to define vortex regions.
The present method allows to locate automatically the core of each vortex, quantify its strength and determine the vortex bounding surface. The output may be used to visualize the turbine vortical structures for the purpose of interpreting the complex three-dimensional viscous flow field, as well as to highlight any case-to-case variations by quantifying the vortex strength and location.
The vortex identification method is applied to a high-pressure turbine with three optimized blade tip geometries. The 3D flow-field is obtained by CFD computations performed with Numeca FINE/Open. The computational model uses steady-state RANS equations closed by the Spalart-Allmaras turbulence model. Although developed for turbomachinery applications, the vortex identification method proposed in this work is of general applicability to any three-dimensional flow-field.