Data assimilation of mean velocity from 2D PIV measurements of flow over an idealized airfoil
Data assimilation can be used to combine experimental and numerical realizations of the same flow to produce hybrid flow fields. These have the advantages of less noise contamination and higher resolution while simultaneously reproducing the main physical features of the measured flow. This study investigates data assimilation of the mean flow around an idealized airfoil (Re = 13,500) obtained from time-averaged two-dimensional particle image velocimetry (PIV) data. The experimental data, which constitute a low-dimensional representation of the full flow field due to resolution and field-of-view limitations, are incorporated into a simulation governed by the two-dimensional, incompressible Reynolds-averaged Navier–Stokes (RANS) equations with an unknown momentum forcing. This forcing, which corresponds to the divergence of the Reynolds stress tensor, is calculated from a direct-adjoint optimization procedure to match the experimental and numerical mean velocity fields. The simulation is projected onto the low-dimensional subspace of the experiment to calculate the discrepancy and a smoothing procedure is used to recover adjoint solutions on the higher dimensional subspace of the simulation. The study quantifies how well data assimilation can reconstruct the mean flow and the minimum experimental measurements needed by altering the resolution and domain size of the time-averaged PIV.
KeywordsParticle Image Velocimetry Data Assimilation Particle Image Velocimetry Measurement Particle Image Velocimetry Data Variational Data Assimilation
Support from a National Science Foundation Graduate Fellowship (S.S.) is gratefully acknowledged. The authors would also like to thank Professors Tim Colonius and Anthony Leonard for discussions about the direct-adjoint optimization framework as well as Kevin Rosenberg for his assistance in implementing the optimization procedure on a cluster. Finally, the authors wish to thank the referees for their suggestions which improved the clarity of the paper.
- Flemming J (2011) Generalized Tikhonov regularization: Basic theory and comprehensive results on convergence rates. PhD thesis, Techn Univ ChemnitzGoogle Scholar
- Gharib M (1983) The effect of flow oscillations on cavity drag, and a technique for their control. PhD thesis, California Institute of TechnologyGoogle Scholar
- Gonzalez C, Bruhat JF, Wainfan B, McKeon BJ (2010) Control of laminar separation on an idealized airfoil using periodic dynamic roughness actuation. In 63rd Meeting of the American Physical Society Division of Fluid Dynamics. Gallery of Fluid Motion, Poster 26Google Scholar
- Kompenhans J, Raffel M, Willert C (2007) Particle image velocimetry—a pratical guide. Springer, BerlinGoogle Scholar
- Lewis JM, Lakshmivarahan S, Dhall S (2006) Dynamic data assimilation: a least squares approach. In: Encyclopedia of mathematics and its application 104, vol 13. Cambridge University PressGoogle Scholar
- Wallace RD, McKeon BJ (2012) Laminar separation bubble manipulation with dynamic roughness. In: Proceedings of the 6th AIAA flow control conference. AIAA 2012–2680Google Scholar
- Wilson BM, Smith BL (2013) Uncertainty on PIV mean and fluctuating velocity due to bias and random errors. Meas Sci Technol 24(3):1–15Google Scholar