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Uncertainty-based weighted least squares density integration for background-oriented schlieren

Abstract

We propose an improved density integration methodology for Background-Oriented Schlieren (BOS) measurements that overcomes the noise sensitivity of the commonly used Poisson solver. The method employs a weighted least-squares (WLS) optimization of the 2D integration of the density gradient field by solving an over-determined system of equations. Weights are assigned to the grid points based on density gradient uncertainties to ensure that a less reliable measurement point has less effect on the integration procedure. Synthetic image analysis with a Gaussian density field shows that WLS constrains the propagation of random error and reduces it by 80% in comparison to Poisson for the highest noise level. Using WLS with experimental BOS measurements of flow induced by a spark plasma discharge shows a 30% reduction in density uncertainty in comparison to Poisson, thereby increasing the overall precision of the BOS density measurements.

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Acknowledgements

Bhavini Singh is acknowledged for help in conducting the spark discharge experiment. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences under Award Number DE-SC0018156. This work was also supported by NSF 1706474.

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Correspondence to Pavlos Vlachos.

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Rajendran, L., Zhang, J., Bane, S. et al. Uncertainty-based weighted least squares density integration for background-oriented schlieren. Exp Fluids 61, 239 (2020). https://doi.org/10.1007/s00348-020-03071-w

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  • DOI: https://doi.org/10.1007/s00348-020-03071-w