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Experimental investigation of transonic and supersonic flow over a sphere for Reynolds numbers of 103–105 by free-flight tests with schlieren visualization

Abstract

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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References

  1. 1.

    Taneda, S.: Experimental investigation of the wake behind a sphere at low Reynolds numbers. J. Phys. Soc. Jpn 11(11), 1104–1108 (1956). https://doi.org/10.1143/JPSJ.11.1104

  2. 2.

    Taneda, S.: Visual observations of the flow past a sphere at Reynolds numbers between 104 and 106. J. Fluid Mech. 85(1), 187–192 (1978). https://doi.org/10.1017/S0022112078000580

  3. 3.

    Sakamoto, H., Haniu, H.: A study on vortex shedding from spheres in a uniform flow. ASME Trans. J. Fluids Eng. 112, 386–392 (1990). https://doi.org/10.1115/1.2909415

  4. 4.

    Magarvey, R.H., Bishop, R.L.: Transition ranges for three-dimensional wakes. Can. J. Phys. 39(10), 1418–1422 (1961). https://doi.org/10.1139/p61-169

  5. 5.

    Johnson, T.A., Patel, V.C.: Flow past a sphere up to a Reynolds number of 300. J. Fluid Mech. 378(10), 19–70 (1999). https://doi.org/10.1017/S0022112098003206

  6. 6.

    Rodriguez, I., Borell, R., Lehmkuhl, O., Segarra, C.D.P., Oliva, A.: Direct numerical simulation of the flow over a sphere at Re = 3700. J. Fluid Mech. 679(10), 263–287 (2011). https://doi.org/10.1017/jfm.2011.136

  7. 7.

    Schlichting, H.: Boundary Layer Theory. McGraw-Hill Inc., New York City (1958)

  8. 8.

    Clift, R., Gauvin, W.H.: The motion of particles in turbulent gas stream, Proceedings of CHEMECA’ 70, vol. 1, pp. 14–28 (1970)

  9. 9.

    Kajishima, T.: Influence of particle rotation on the interaction between particle clusters and particle-induced turbulence. Int. J. Heat and Fluid Flow 25(5), 721–728 (2004). https://doi.org/10.1016/j.ijheatfluidflow.2004.05.007

  10. 10.

    Crowe, T.C., Babcock, R.W., Willoughby, G.P., Carlson, L.R.: Measurement of particle drag coefficients in flow regimes encountered by particles in a rocket nozzle. UTC 2296-FR, United Technology Center (1969). https://apps.dtic.mil/dtic/tr/fulltext/u2/850098.pdf

  11. 11.

    Bailey, A.B., Hiatt, J.: Free-flight measurements of sphere drag at subsonic, transonic, supersonic, and hypersonic speeds for continuum, transition, and near-free-molecular flow conditions. AEDC Technical Report, AEDC-TR-70-291 (1971). https://apps.dtic.mil/dtic/tr/fulltext/u2/721208.pdf

  12. 12.

    Zarin, N.A., Nicholls, J.A.: Sphere drag in solid rockets—non-continuum and turbulence effects. Combust. Sci. Technol. 3(6), 273–285 (1971). https://doi.org/10.1080/00102207108952295

  13. 13.

    Handa, T., Koike, S., Imabayashi, K.: Estimation of the particle drag coefficients for compressible and rarefied flows using PIV and MTV data. 31st International Symposium on Shock Waves (2017). https://doi.org/10.1007/978-3-319-91017-8_143

  14. 14.

    Macrossan, M.: Scaling parameters in rarefied flow: breakdown of the Navier–Stokes equations. Department of Mechanical Engineering, University of Queensland, Departmental Report (2006)

  15. 15.

    Nagata, T., Nonomura, T., Takahashi, S., Mizuno, Y., Fukuda, K.: Investigation on subsonic to supersonic flow around a sphere at low Reynolds number of between 50 and 300 by direct numerical simulation. Phys. Fluids 28, 056101 (2016). https://doi.org/10.1063/1.4947244

  16. 16.

    Nagata, T., Nonomura, T., Takahashi, S., Mizuno, Y., Fukuda, K.: Direct numerical simulation of flow around a heated/cooled isolated sphere up to a Reynolds number of 300 under subsonic to supersonic conditions. Int. J. Heat Mass Transf. 120, 284–299 (2018). https://doi.org/10.1016/j.ijheatmasstransfer.2017.12.042

  17. 17.

    Nagata, T., Nonomura, T., Takahashi, S., Mizuno, Y., Fukuda, K.: Direct numerical simulation of flow past a sphere at a Reynolds number between 500 and 1000 in compressible flows. 56th AIAA Aerospace Sciences Meeting, Kissimmee, FL, AIAA Paper 2018-0381 (2018). https://doi.org/10.2514/6.2018-0381

  18. 18.

    Nagata, T., Nonomura, T., Takahashi, S., Mizuno, Y., Fukuda, K.: Direct numerical simulation of flow past a transversely rotating sphere up to a Reynolds number of 300 in compressible flow. J. Fluid Mech. 857, 878–906 (2018). https://doi.org/10.1017/jfm.2018.756

  19. 19.

    Sansica, A., Robinet, J.-Ch., Alizard, F., Goncalves, E.: Three-dimensional instability of the flow past a sphere: Mach evolution of the regular and Hopf bifurcations. J. Fluid Mech. 855, 1088–1115 (2018). https://doi.org/10.1017/jfm.2018.664

  20. 20.

    Riahi, H., Meldi, M., Favier, J., Serre, E., Goncalves, E.: A pressure-corrected immersed boundary method for the numerical simulation of compressible flows. J. Compt. Phys. 374, 361–383 (2018). https://doi.org/10.1016/j.jcp.2018.07.033

  21. 21.

    Golub, G.H., Van Loan, C.F.: Matrix Computations. The Johns Hopkins University Press, Baltimore (2013)

  22. 22.

    Keys, R.: Cubic convolution interpolation for digital image processing. IEEE Trans. Acoust. Speech Signal Process. (ASSP) 29(6), 1153–1160 (1981). https://doi.org/10.1109/TASSP.1981.1163711

  23. 23.

    Makita, H.: Forefront of wind-tunnel experiment on turbulence structure. J. Fluid Sci. Technol. 2(3), 525–534 (2007). https://doi.org/10.1299/jfst.2.525

  24. 24.

    Ambrosio, A., Wortman, A.: Stagnation point shock detachment distance for flow around spheres and cylinders. ARS J. 32(2), 281 (1962). https://doi.org/10.2514/8.5988

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Acknowledgments

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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Correspondence to T. Nagata.

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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.

Fig. 18
figure18

Effect of data length in the time direction on the extracted fluctuating modes by SVD (M = 1.39 and Re = 1.0 × 105)

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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

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Keywords

  • Sphere
  • Compressible low-Reynolds-number flow
  • Schlieren visualization
  • Ballistic range