A topological evaluation procedure to assess the integrity of a PIV vector field
Abstract
Particle image velocimetry (PIV) provides a field of discrete vectors to represent a continuum velocity field. Various methods have been adopted to evaluate the integrity of the discrete vectors. In contrast, the present communication provides a systematic technique whereby the integrity of the measured field can be assessed using basic topological principles. Starting with the recognition that PIV provides a vector field overlaid on a planar surface, the analyst can identify the holes (to be punched through the surface of a sphere) and the handles (to be added to the sphere’s surface) that will represent the appropriate surface for the topological analysis. These operations define the a priori Euler characteristic (χ A ) for the subject PIV image. The experimental Euler characteristic (χ E ) will be known from the properties of the measured vector field: nodes, saddles, etc. A necessary condition for the integrity of the measured vector field is that χ E = χ A . The topological bases for the integrity evaluation, including the important constraint of ensuring a smooth collapsed sphere, are carefully explained and described with examples.
- Publication:
-
Measurement Science and Technology
- Pub Date:
- September 2016
- DOI:
- 10.1088/0957-0233/27/9/094007
- Bibcode:
- 2016MeScT..27i4007F