Density measurements via background-oriented schlieren and parallel-ray omnidirectional integration

Abstract

Most measurements of density via background-oriented schlieren (BOS) numerically integrate the Poisson equation to calculate the density field from density gradients, which is susceptible to errors in measurements and uncertainties in boundary values. An alternative method, parallel-ray omnidirectional integration (ODI), was implemented and found to be significantly more accurate and precise. To compare the performance of the integration algorithms, a BOS displacement field was synthesized for the Taylor–Maccoll solution for inviscid, supersonic, conical flow. The impact of measurement error was simulated by adding noise to the synthetic displacement field. Density was reconstructed from 200 statistically independent displacement fields for two noise levels. The ODI algorithm resulted in higher accuracy and precision for all cases analyzed. In fact, the mean error for ODI at the highest noise level was found to be lower than that of Poisson integration, even when Poisson is evaluated without any input noise. These algorithms were also used to reconstruct density from experimental BOS measurements on a cone-flare model in hypersonic flow and zero angle of attack. This geometry exhibits a shock-wave/boundary-layer interaction which consists of bow, separation, and reattachment shocks and a recirculation bubble. The reconstructed density agreed excellently with the inviscid solution outside the boundary layer and recirculation bubble. The ODI-derived density field provided a closer match to the anticipated result than the Poisson-derived density, and is thus the recommended method. This work emphasizes the exceptional capability of ODI in reconstructing accurate and precise density fields from BOS measurements, thereby advancing the high spatial resolution, non-intrusive, and quantitative measurement technique used to deepen the understanding of complex fluid flows.