Variational second order flow estimation for PIV sequences
- 157 Downloads
We present in this paper a variational approach to accurately estimate simultaneously the velocity field and its derivatives directly from PIV image sequences. Our method differs from other techniques that have been presented in the literature in the fact that the energy minimization used to estimate the particles motion depends on a second order Taylor development of the flow. In this way, we are not only able to compute the motion vector field, but we also obtain an accurate estimation of their derivatives. Hence, we avoid the use of numerical schemes to compute the derivatives from the estimated flow that usually yield to numerical amplification of the inherent uncertainty on the estimated flow. The performance of our approach is illustrated with the estimation of the motion vector field and the vorticity on both synthetic and real PIV datasets.
KeywordsVorticity Particle Image Velocimetry Particle Image Velocimetry Image Motion Vector Field Average Angular Error
This work has been funded by the European Commission under the Specific Targeted Research Project FLUID (contract no. FP6-513663). We acknowledge the Research Institute CEMAGREF (Rennes, France) for providing to us the synthetic PIV image and the real PIV sequence we have used in the experiments.
- Adrian R (1988) Statistical properties of particle image velocimetry measurements in turbulent flow. Laser Anemometry Fluid Mech 1:115–129Google Scholar
- Alemßn M, Alvarez L, Gonzßlez E, Mazorra L, Sßnchez J (2005) Optic flow estimation in fluid images i. Cuadernos Instituto Universitario de Ciencias y Tecnologfas CibernTticas 31:1–25Google Scholar
- Hunt J (1987) Vorticity and vortex dynamics in complex turbulent flows. In: Transactions Canadian Society for Mechanical Engineering (ISSN 0315-8977), vol 11, pp 21–35Google Scholar
- Parnaudeau P, Carlier J, Heitz D, Lamballais E (2006) Experimental and numerical studies of the flow over a circular cylinder at reynolds number 3900. Phys Fluids (submitted)Google Scholar
- Press W, Teukolsky S, Vetterling W, Flannery B (1992) Numerical recipes in C: The Art of Scientific Computing. Cambridge University Press, New York, NY, USAGoogle Scholar
- Raffel M, Willert C, Kompenhans J (1998) Particle image velocimetry. A practical guide. Springer, HeidelbergGoogle Scholar
- Westerweel J (1993) Digital particle image velocimetry. Theory and application. Delft University Press, DelftGoogle Scholar