A numerical analysis method for identification of three-dimensional vortical structure of spiral vortex in wind turbine with two-dimensional velocity data in parallel planes at plural azimuthal angles

Abstract

An identification method is presented to specify three-dimensional vortical flow topology of a spiral vortex (wing tip vortex) in a wind turbine, from two-dimensional velocity data in planes at different azimuthal angles. This method needs only the two-dimensional velocity field (data) in the parallel planes, and need not change the angle (horizontality) of the planes. The three-dimensional velocity structure is specified by physical properties associated with the velocity gradient tensor, and the formulation of the linear transformation between rotated coordinate systems associated with a spiral vortex derives the unknown components in the three-dimensional velocity gradient tensor. This method specifies the three-dimensional local vortical flow topology in detail including swirl plane, vortical axis and its orthogonality. Swirlity specifies the unidirectionality and intensity of the azimuthal flow, and sourcity does those of the radial flow. It also identifies the vortical flow symmetry that are associated with the important vortical features such as the pressure minimum.

Keywords

• vortical flow
• topology
• spiral vortex
• wind turbine
• swirlity
• sourcity