In this study, free-flight tests of a sphere for Reynolds numbers between 3.9 × 103 and 3.8 × 105 and free-flight Mach numbers between 0.9 and 1.6 were conducted using a ballistic range, and compressible low-Reynolds-number flows over an isolated sphere were investigated with the schlieren technique. The flow visualization was carried out under low-pressure conditions with a small sphere (minimum diameter of 1.5 mm) to produce compressible low-Reynolds-number flow. Also, time-averaged images of the flow near the sphere were obtained and compared to previous numerical results for Reynolds numbers between 50 and 1000. The experimental results clarified the structure of shock waves, recirculation region, and wake structures at the Reynolds number of 103–105 under transonic and supersonic flows. As a result, the following characteristics were clarified: (1) the amplitude of the wake oscillation was attenuated as the free-flight Mach number increased; (2) use of singular value decomposition permitted extraction of the mode of the wake structure even when schlieren images were unclear due to severe condition, and different modes in the wake structure were identified; (3) the Reynolds number had little effect on the separation point, but the length of the recirculation region increased as the Reynolds number decreased; and (4) the wake diameter at the end of the recirculation region decreased as the Mach number increased.
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This work was supported by the Japan Society for the Promotion of Science, KAKENHI Grants 18J11205 and 18K18818. The authors express their gratitude to Toshihiro Ogawa for his collaboration in the preparation and execution of the experiments.
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Communicated by G. Jagadeesh and A. Higgins.
Appendix: Effect of data length in the time direction on extracted SVD modes
Appendix: Effect of data length in the time direction on extracted SVD modes
Figure 18 illustrates the effect of data length in the time direction on the extracted fluctuating modes by SVD. The flow condition is M = 1.39 and Re = 1.0 × 105 (P/Patm = 1.0), which represents the same case as in Figs. 10c and 11a. In this case, the acquired number of frames for extracting the SVD modes was 61, and this dataset includes four periods of large-scale wake oscillation. The mode corresponding to the large-scale wake oscillation can be extracted even with 25% (including one period of the large-scale wake oscillation) of the original data. On the other hand, the mode corresponding to the large-scale wake oscillation could not be extracted from the 10% data subset of the original data. However, finer-scale wake structure is extracted in lower modes, because the long-period phenomena are not extracted due to short-time data. In the case of the original data, these finer modes were extracted in the higher mode.
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Nagata, T., Noguchi, A., Nonomura, T. et al. Experimental investigation of transonic and supersonic flow over a sphere for Reynolds numbers of 103–105 by free-flight tests with schlieren visualization. Shock Waves 30, 139–151 (2020). https://doi.org/10.1007/s00193-019-00924-0
- Compressible low-Reynolds-number flow
- Schlieren visualization
- Ballistic range