Skip to main content Accessibility help

Direct numerical simulation of flow past a transversely rotating sphere up to a Reynolds number of 300 in compressible flow

  • T. Nagata (a1), T. Nonomura (a1), S. Takahashi (a2), Y. Mizuno (a3) and K. Fukuda (a4)...


In this study, direct numerical simulation of the flow around a rotating sphere at high Mach and low Reynolds numbers is conducted to investigate the effects of rotation rate and Mach number upon aerodynamic force coefficients and wake structures. The simulation is carried out by solving the three-dimensional compressible Navier–Stokes equations. A free-stream Reynolds number (based on the free-stream velocity, density and viscosity coefficient and the diameter of the sphere) is set to be between 100 and 300, the free-stream Mach number is set to be between 0.2 and 2.0, and the dimensionless rotation rate defined by the ratio of the free-stream and surface velocities above the equator is set between 0.0 and 1.0. Thus, we have clarified the following points: (1) as free-stream Mach number increased, the increment of the lift coefficient due to rotation was reduced; (2) under subsonic conditions, the drag coefficient increased with increase of the rotation rate, whereas under supersonic conditions, the increment of the drag coefficient was reduced with increasing Mach number; and (3) the mode of the wake structure becomes low-Reynolds-number-like as the Mach number is increased.


Corresponding author

Email address for correspondence:


Hide All
Bui Dinh, T., Oesterle, B. & Deneu, F. 1990 Premiers résultats sur la portance d’une sphère en rotation aux nombres de Reynolds intermédiaires. C. R. Acad. Sci. Paris II 311, 2731.
Das, P., Sen, O., Jacobs, G. & Udaykumar, H. S. 2017 A sharp interface Cartesian grid method for viscous simulation of shocked particle-laden flows. Intl J. Comput. Fluid Dyn. 31, 269291.
Dobson, J., Ooi, A. & Poon, E. K. W. 2014 The flow structures of a transversely rotating sphere at high rotation rates. Comput. Fluids 102, 170181.
Eldred, K. M.1971 Acoustic loads generated by the propulsion system. NASA Special Publication. NASA SP-8072.
Fukuda, K., Tsutsumi, S., Shimizu, T., Takaki, R. & Ui, K.2011 Examination of sound suppression by water injection at lift-off of launch vehicles. AIAA Paper 2011–2814.
Giacobello, M., Ooi, A. & Balachandar, S. 2009 Wake structure of a transversely rotating sphere at moderate Reynolds numbers. J. Fluid Mech. 621, 103130.
Gottlieb, S. & Shu, C.-W. 1998 Total variation diminishing Runge–Kutta schemes. Math. Comput. 67 (221), 7385.
Ignatius, J. K., Sathiyavageeswaran, S. & Chakravarthy, S. R. 2014 Hot-flow simulation of aeroacoustics and suppression by water injection during rocket liftoff. AIAA J. 53 (1), 235245.
Ishii, T., Tsutsumi, S., Ui, K., Tokudome, S., Ishii, Y., Wada, K. & Nakamura, S. 2012 Acoustic measurement of 1 : 42 scale booster and launch pad. In Proceedings of Meetings on Acoustics, vol. 18, 040009. Acoustical Society of America.
Johnson, T. A. & Patel, V. C. 1999 Flow past a sphere up to a Reynolds number of 300. J. Fluid Mech. 378, 1970.
Kajishima, T. 2004 Influence of particle rotation on the interaction between particle clusters and particle-induced turbulence. Intl J. Heat Fluid Flow 25 (5), 721728.
Kurose, R. & Komori, S. 1999 Drag and lift forces on a rotating sphere in a linear shear flow. J. Fluid Mech. 384, 183206.
Mizuno, Y., Takahashi, S., Nonomura, T., Nagata, T. & Fukuda, K. 2015 A simple immersed boundary method for compressible flow simulation around a stationary and moving sphere. Math. Problems Engng 2015, 438086.
Nagata, T., Nonomura, T., Takahashi, S., Mizuno, Y. & Fukuda, K. 2016 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 (5), 056101.
Nagata, T., Nonomura, T., Takahashi, S., Mizuno, Y. & Fukuda, K. 2018a Direct numerical simulation of flow around a heated/cooled isolated sphere up to a Reynolds number of 300 under subsonic to supersonic conditions. Intl J. Heat Mass Transfer 120, 284299.
Nagata, T., Nonomura, T., Takahashi, S., Mizuno, Y. & Fukuda, K. 2018b Direct numerical simulation of flow past a sphere at a Reynolds number between 500 and 1000 in compressible flows. In Proceedings of 2018 AIAA Aerospace Science Meeting. AIAA Paper 2018-0381. American Institute of Aeronautics and Astronautics.
Niazmand, H. & Renksizbulut, M. 2003 Surface effects on transient three-dimensional flows around rotating spheres at moderate Reynolds numbers. Comput. Fluids 32 (10), 14051433.
Nonomura, T., Morizawa, S., Obayashi, S. & Fujii, K. 2014 Computational prediction of acoustic waves from a subscale rocket motor. Trans. JSASS Aerospace Tech. Japan 12 (ists29), Pe_11–Pe_17.
Nonomura, T., Terakado, D., Abe, Y. & Fujii, K. 2015 A new technique for freestream preservation of finite-difference WENO on curvilinear grid. Comput. Fluids 107, 242255.
Pirozzoli, S. 2011 Stabilized non-dissipative approximations of Euler equations in generalized curvilinear coordinates. J. Comput. Phys. 230 (8), 29973014.
Poon, E. K. W., Ooi, A. S. H., Giacobello, M., Iaccarino, G. & Chung, D. 2014 Flow past a transversely rotating sphere at Reynolds numbers above the laminar regime. J. Fluid Mech. 759, 751781.
Riahi, H., Meldi, M., Favier, J., Serre, E. & Goncalves, E. 2018 A pressure-corrected immersed boundary method for the numerical simulation of compressible flows. J. Comput. Phys. 374, 361383.
Rubinow, S. I. & Keller, J. B. 1961 The transverse force on a spinning sphere moving in a viscous fluid. J. Fluid Mech. 44, 447459.
Schneiders, L., Günther, C., Meinke, M. & Schröder, W. 2016 An efficient conservative cut-cell method for rigid bodies interacting with viscous compressible flows. J. Comput. Phys. 311, 6286.
Shimada, T., Daimon, Y. & Sekino, N.2006 Computational fluid dynamics of multiphase flows in solid rocket motors. JAXA Special Publication. JAXA-SP-05-035E.
Sutherland, W. 1893 The viscosity of gases and molecular force. Phil. Mag. Series 5 36, 507531.
Tanaka, T., Yamagata, K. & Tsuji, Y. 1990 Experiment on fluid forces on a rotating sphere and spheroid. In Proceedings of the 2nd KSME–JSME Fluids Engineering Conference, pp. 366369. The Korean Society of Mechanical Engineers.
Terakado, D., Nagata, Y., Nonomura, T., Fujii, K. & Yamamoto, M. 2016 Computational analysis of compressible gas-particle-multiphase turbulent mixing layer in Euler–Euler formulation. Trans. JSASS Aerospace Tech. Japan 14 (ists30), Po_2_25–Po_2_31.
Teymourtash, A. R. & Salimipour, S. E. 2017 Compressibility effects on the flow past a rotating cylinder. Phys. Fluids 29 (1), 016101.
Tsutsumi, S., Ishii, T., Ui, K., Tokudome, S. & Wada, K. 2015 Study on acoustic prediction and reduction of Epsilon launch vehicle at liftoff. J. Spacecr. Rockets 52 (2), 350361.
Volkov, A. N. 2011 Transitional flow of a rarefied gas over a spinning sphere. J. Fluid Mech. 683, 320345.
Yee, H. C., Sandham, N. D. & Djomehri, M. J. 1999 Low-dissipative high-order shock-capturing methods using characteristic-based filters. J. Comput. Phys 150 (1), 199238.
You, C. F., Qi, H. Y. & Xu, X. C. 2003 Lift force on rotating sphere at low Reynolds numbers and high rotational speeds. Acta Mechanica Sin. 19 (4), 300307.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed