Abstract
A quantitative rainbow schlieren study was conducted on an over-expanded jet at nozzle pressure ratio of 2.8, based on two different schlieren set-ups: the standard z-type and a single-mirror schlieren set-up. The technique used a single, weak focal-length lens placed in the field of view of the system to provide the calibration information required for the extraction of the quantitative data. In the case of the single-mirror set-up, the calibration image required further post-processing procedures to take into account the double refraction experienced by the light. Density gradients were calculated using Abel transform and compared to validated reference data. Results indicate that the single-mirror set-up is able to improve prediction of the density gradient field as compared to the standard z-type schlieren, due to its inherent property of higher sensitivity. The study has shown that the single-mirror set-up performs on average better than the standard z-type system, yielding an overall averaged error of ± 20%, with localized values as low as ± 5% where the shock cell structure is clearly defined, with respect to the validated reference data. At the same time, both systems perform poorly in regions where the flow structure displays poor image contrast.
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Acknowledgements
The authors gratefully acknowledge support for the study through a Singapore Ministry of Education AcRF Tier-2 grant (Grant number: MOE2014-T2-1-002), support for the second and third authors through NTU Nanyang President Graduate Scholarship and MAE Graduate Research Officer scheme respectively, as well as facility support from Temasek Laboratories at the National University of Singapore.
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Mariani, R., Lim, H.D., Zang, B. et al. On the application of non-standard rainbow schlieren technique upon supersonic jets. J Vis 23, 383–393 (2020). https://doi.org/10.1007/s12650-020-00637-y
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DOI: https://doi.org/10.1007/s12650-020-00637-y