Skip to main content
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
1.K. M. Eldred, “Acoustic loads generated by the propulsion system,” NASA Special Publication NASA SP-8072, 1971.
2.T. Ishii, S. Tsutsumi, K. Ui, S. Tokudome, Y. Ishii, K. Wada, and S. Nakamura, “Acoustic measurement of 1:42 scale booster and launch pad,” Proc. Meet. Acoust. 18(1), 040009 (2014).
3.S. Tsutsumi, R. Takaki, E. Shima, and K. Fujii, “Generation and propagation of pressure waves from H-IIA launch vehicle at lift-off,” in Conference Proceedings of the 46th AIAA Aerospace Sciences Meeting and Exhibit, Nevada, USA, 7-10 January 2008 (American Institute of Aeronautics and Astronautics, 2008).
4.S. Tsutsumi, T. Ishii, K. Ui, S. Tokudome, and K. Wada, “Study on acoustic prediction and reduction of epsilon launch vehicle at liftoff,” J. Spacecr. Rockets 52(2), 350361 (2015).
5.T. Nonomura, S. Morizawa, S. Obayashi, and K. Fujii, “Computational prediction of acoustic waves from a subscale rocket motor,” Transac. Jpn. Soc. Aeronaut. Space Sci., Aerosp. Technol. Jpn. 12(29), Pe_11Pe_17 (2014).
6.K. Fukuda, S. Tsutsumi, T. Shimizu, R. Takaki, and K. Ui, “Examination of sound suppression by water injection at lift-off of launch vehicles,” AIAA Paper 2011–2814,2011.
7.J. K. Ignatius, S. Sathiyavageeswaran, and S. R. Chakravarthy, “Hot-flow simulation of aeroacoustics and suppression by water injection during rocket liftoff,” AIAA J. 53(1), 235245 (2014).
8.T. Shimada, Y. Daimon, and N. Sekino, “Computational fluid dynamics of multiphase flows in solid rocket motors,” JAXA Special Publication, JAXA-SP-05–035E, 2006.
9.T. Saito, M. Marumoto, and K. Takayama, “Numerical investigations of shock waves in gas-particle mixtures,” Shock Waves 13(4), 299322 (2003).
10.D. J. Carlson and R. F. Hoglund, “Particle drag and heat transfer in rocket nozzles,” AIAA J. 2(11), 19801984 (1964).
11.C. T. Crowe, “Drag coefficient of particles in a rocket nozzle,” AIAA J. 5(5), 10211022 (1967).
12.C. B. Henderson, “Drag coefficients of spheres in continuum and rarefied flows,” AIAA J. 14(6), 707708 (1976).
13.C. T. Crowe, W. R. Babcock, P. G. Willoughby, and R. L. Carlson, “Measurement of particle drag coefficients in flow regimes encountered by particles in a rocket nozzle,” Final Technical Report for the Period 1 September 1967 through 28 February 1969, UTC 2296-FR, United Technology Center, 1969.
14.A. B. Bailey and J. Hiatt, “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 No. AEDC-TR-70–291, 1971.
15.T. A. Johnson and V. C. Patel, “Flow past a sphere up to a Reynolds number of 300,” J. Fluid Mech. 378, 1970 (1999).
16.S. Gottlieb and C.-W. Shu, “Total variation diminishing Runge–Kutta schemes,” Math. Comput. 67(221), 7385 (1998).
17.T. Nonomura, D. Terakado, Y. Abe, and K. Fujii, “A new technique for freestream preservation of finite-difference WENO on curvilinear grid,” Comput. Fluids 107(31), 242255 (2015).
18.S. Pirozzoli, “Stabilized non-dissipative approximations of euler equations in generalized curvilinear coordinates,” J. Comput. Phys. 230(8), 29973014 (2011).
19.K. Hida, “An approximate study on the detached shock wave in front of a circular cylinder and a sphere,” J. Phys. Soc. Jpn. 8(6), 740745 (1953).
20.J. W. Heberle, G. P. Wood, and P. B. Gooderum, “Data on sphere and location of detached shock waves on cones and spheres,” NACA Technical Note 2000, 1950.
21.A. Ambrosio and A. Wortman, “Stagnation point shock detachment distance for flow around spheres and cylinders,” ARS J. 32(2), 281 (1962).
22.D. Destarac and J. van der vooren, “Drag/thrust analysis of jet-propelled transonic transport aircraft; definition of physical drag components,” Aerosp. Sci. Technol. 8(6), 545556 (2004).
23.K. Kusunose, “A wake integration method for airplane drag prediction,” in The 21st Century COE Program International COE of Flow Dynamics Lecture Series (Tohoku University Press, 2005), Vol. 3.
24.T. Nagata, T. Nonomura, S. Takahashi, Y. Mizuno, and K. Fukuda, “Analysis of the temperature ratio effect on the flow properties of the low Reynolds and high Mach number flow around a sphere,” in Conference Proceedings of the 54th AIAA Aerospace Sciences Meeting, California, USA, 4-8 January 2016 (American Institute of Aeronautics and Astronautics, 2016).

Data & Media loading...


Article metrics loading...



In this study, analysis of flow properties around a sphere and its aerodynamic coefficients in the high-Mach-and-low-Reynolds-numbers conditions is carried out by direct numerical simulations solving the three-dimensional compressible Navier–Stokes equations. The calculation is performed on a boundary-fitted coordinate system with a high-order scheme of sufficient accuracy. The analysis is conducted by assuming a rigid sphere with a Reynolds number of between 50 and 300, based on the diameter of the sphere and the freestream velocity and a freestream Mach number of between 0.3 and 2.0, together with the adiabatic wall boundary condition. The calculation shows the following yields: (1) unsteady fluctuation of hydrodynamic forces become smaller as the Mach number increases under the same Reynolds number condition, (2) the drag coefficient increases with the Mach number due to an increase in the pressure drag by the shock wave, and (3) an accurate prediction of the drag coefficient in the supersonic regime using traditional models might be difficult.


Full text loading...


Access Key

  • FFree Content
  • OAOpen Access Content
  • SSubscribed Content
  • TFree Trial Content
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd