Weighted divergence correction scheme and its fast implementation
- 388 Downloads
Forcing the experimental volumetric velocity fields to satisfy mass conversation principles has been proved beneficial for improving the quality of measured data. A number of correction methods including the divergence correction scheme (DCS) have been proposed to remove divergence errors from measurement velocity fields. For tomographic particle image velocimetry (TPIV) data, the measurement uncertainty for the velocity component along the light thickness direction is typically much larger than for the other two components. Such biased measurement errors would weaken the performance of traditional correction methods. The paper proposes a variant for the existing DCS by adding weighting coefficients to the three velocity components, named as the weighting DCS (WDCS). The generalized cross validation (GCV) method is employed to choose the suitable weighting coefficients. A fast algorithm for DCS or WDCS is developed, making the correction process significantly low-cost to implement. WDCS has strong advantages when correcting velocity components with biased noise levels. Numerical tests validate the accuracy and efficiency of the fast algorithm, the effectiveness of GCV method, and the advantages of WDCS. Lastly, DCS and WDCS are employed to process experimental velocity fields from the TPIV measurement of a turbulent boundary layer. This shows that WDCS achieves a better performance than DCS in improving some flow statistics.
KeywordsDirect Numerical Simulation Weighting Coefficient Correlate Noise Noise Strength Generalize Cross Validation
This work is supported by the National Natural Science Foundation of China (11327202, 11472030, 11490552) and the Fundamental Research Funds for Central Universities (YWF-16-JCTD-A-05).
- Chong M, Perry AE, Cantwell B (1990) A general classification of three-dimensional flow fields. Physics of Fluids A: Fluid Dynamics (1989–1993) 2(5):765–777Google Scholar
- Clark TH (2012) Measurement of three-dimensional coherent fluid structure in high reynolds number turbulent boundary layers. PhD thesis. Trinity hall, CambridgeGoogle Scholar
- Graham J, Lee M, Malaya N, Moser R, Eyink G, Meneveau C, Kanov K, Burns R, Szalay A (2013) Turbulent channel flow data set. http://turbulence.pha.jhu.edu/docs/README-CHANNEL.pdfGoogle Scholar
- Lee M, Malaya N, Moser RD (2013) Petascale direct numerical simulation of turbulent channel flow on up to 786k cores. In: Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis, ACM, p 61Google Scholar
- Schneiders J, Dwight RP, Scarano F (2013) Vortex-in-cell method for time-supersampling of PIV data. In: PIV13; 10th International Symposium on Particle Image Velocimetry, Delft, The Netherlands, July 1-3, 2013, Delft University of Technology, Faculty of Mechanical, Maritime and Materials Engineering, and Faculty of Aerospace EngineeringGoogle Scholar
- Sillero JA, Jiménez J, Moser RD (2013) One-point statistics for turbulent wall-bounded flows at reynolds numbers up to \(\delta ^+\approx 2000\). Physics of Fluids (1994-present) 25(10)Google Scholar
- Vennell R, Beatson R (2009) A divergence-free spatial interpolator for large sparse velocity data sets. Journal of Geophysical Research: Oceans 114(C10)Google Scholar
- Wang H, Gao Q, Wei R, Wang J (2016b) Intensity-enhanced mart for tomographic PIV. Exp Fluids 57(5):1–19Google Scholar
- Yang G, Kilner P, Firmin D, Underwood S, Burger P, Longmore D (1993) 3D cine velocity reconstruction using the method of convex projections. Computers in Cardiology 1993. Proceedings, IEEE, pp 361–364Google Scholar