Sequential least-square reconstruction of instantaneous pressure field around a body from TR-PIV
A procedure is introduced to obtain an instantaneous pressure field around a wing from time-resolved particle image velocimetry (TR-PIV) and particle image accelerometry (PIA). The instantaneous fields of velocity and material acceleration are provided by the recently introduced multi-frame PIV method, fluid trajectory evaluation based on ensemble-averaged cross-correlation (FTEE). The integration domain is divided into several subdomains in accordance with the local reliability. The near-edge and near-body regions are determined based on the recorded image of the wing. The instantaneous wake region is assigned by a combination of a self-defined criterion and binary morphological processes. The pressure is reconstructed from a minimization process of the difference between measured and reconstructed pressure gradients in a least-square sense. This is solved sequentially according to a decreasing order of reliability of each subdomain to prevent a propagation of error from the less reliable near-body region to the free-stream. The present procedure is numerically assessed by synthetically generated 2D particle images based on a numerical simulation. Volumetric pressure fields are then evaluated from tomographic TR-PIV of a flow around a 30-degree-inclined NACA0015 airfoil. A possibility of using a different scheme to evaluate material acceleration for a specific subdomain is presented. Moreover, this 3D application allows the investigation of the effect of the third component of the pressure gradient by which the wake region seems to be affected.
The current work has been conducted as part of the NIOPLEX project, Non-intrusive Optical Pressure and Loads Extraction for Aerodynamic Analysis, funded by the European Commission program FP7, Grant No. 605151 and as part of the EVAPOR Astrid project, funded by the Agence Nationale de la Recherche and the DGA, Grant No. NR-16-ASTR-0005-01.
- Harker M, O’Leary P (2008) Least squares surface reconstruction from measured gradient fields. IEEE Computer Vision and Pattern Recognition, AnchorageGoogle Scholar
- Jeon YJ, Chatellier L, Beaudoin A, David L (2015) Least-square reconstruction of instantaneous pressure field around a body based on a directly acquired material acceleration in time-resolved PIV. In: 11th International Symposium on Particle Image Velocimetry-PIV15. Santa Barbara, California, September 14–16Google Scholar
- Lecordier B, Westerweel J (2004) The EUROPIV synthetic image generator. In: Stanislas M, Westerweel J, Kompenhans J (eds) Particle image velocimetry: recent improvements. Springer, HeidelbergGoogle Scholar
- Liu X, Katz J (2003) Measurements of pressure distribution by integrating the material acceleration. In: Cav03-GS-14-001. In: Fifth international symposium on cavitation (CAV2003), Osaka, Japan, 1–4 November, 2003Google Scholar
- Liu X, Moreto JR, Siddle-Mitchell S (2016) Instantaneous Pressure Reconstruction from Measured Pressure Gradient using Rotating Parallel Ray Method. In: 54th AIAA Aerospace Sciences Meeting, 4–8 January 2016, San DiegoGoogle Scholar
- Press WH, Teukolsky SA, Vetterling WT, Flannery BP (2002) Numerical recipes in C/C++. The Press Syndicate of the University of Cambridge, CambridgeGoogle Scholar
- Scarano F, Riethmuller ML (2000) Advances in iterative multigrid PIV image processing. Exp Fluids 29(1):S051–S060Google Scholar
- Schneiders JFG, Scarano F (2016) Dense velocity reconstruction from tomographic PTV with material derivatives. Exp Fluids 57(9)Google Scholar
- Tronchin T, David L, Farcy A (2015) Loads and pressure evaluation of the flow around a flapping wing from instantaneous 3D velocity measurements. Exp Fluids 56(7):1–16Google Scholar