Hostname: page-component-7f64f4797f-vhqbp Total loading time: 0 Render date: 2025-11-04T06:18:40.999Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  30 October 2018

T. Nagata Open the ORCID record for T. Nagata [Opens in a new window] ,
T. Nonomura Open the ORCID record for T. Nonomura [Opens in a new window] ,
S. Takahashi ,
Y. Mizuno  and
K. Fukuda
T. Nagata*
Affiliation:
Department of Aerospace Engineering, Tohoku University, 6-6-01, Aramaki, Aoba-ku, Sendai, Miyagi, 980-8579, Japan
T. Nonomura
Affiliation:
Department of Aerospace Engineering, Tohoku University, 6-6-01, Aramaki, Aoba-ku, Sendai, Miyagi, 980-8579, Japan
S. Takahashi
Affiliation:
Department of Prime Mover Engineering, Tokai University, 4-4-1, Kita-kaname, Hiratsuka, Kanagawa, 259-1292, Japan
Y. Mizuno
Affiliation:
Course of Science and Technology, Tokai University, 4-4-1, Kita-kaname, Hiratsuka, Kanagawa, 259-1292, Japan
K. Fukuda
Affiliation:
Department of Aeronautics and Astronautics, Tokai University, 4-4-1, Kita-kaname, Hiratsuka, Kanagawa, 259-1292, Japan
*
†Email address for correspondence: nagata.takayuki@aero.mech.tohoku.ac.jp
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

JFM classification

Aerodynamics: Aerodynamics Aerodynamics: High-speed flow Low-Reynolds-number flows: Low-Reynolds-number flows

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 857 , 25 December 2018 , pp. 878 - 906
Check for updates
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

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, 27–31.Google Scholar
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, 269–291.Google Scholar
Dobson, J., Ooi, A. & Poon, E. K. W. 2014 The flow structures of a transversely rotating sphere at high rotation rates. Comput. Fluids 102, 170–181.Google Scholar
Eldred, K. M.1971 Acoustic loads generated by the propulsion system. NASA Special Publication. NASA SP-8072.Google Scholar
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.Google Scholar
Giacobello, M., Ooi, A. & Balachandar, S. 2009 Wake structure of a transversely rotating sphere at moderate Reynolds numbers. J. Fluid Mech. 621, 103–130.Google Scholar
Gottlieb, S. & Shu, C.-W. 1998 Total variation diminishing Runge–Kutta schemes. Math. Comput. 67 (221), 73–85.Google Scholar
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), 235–245.Google Scholar
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.Google Scholar
Johnson, T. A. & Patel, V. C. 1999 Flow past a sphere up to a Reynolds number of 300. J. Fluid Mech. 378, 19–70.Google Scholar
Kajishima, T. 2004 Influence of particle rotation on the interaction between particle clusters and particle-induced turbulence. Intl J. Heat Fluid Flow 25 (5), 721–728.Google Scholar
Kurose, R. & Komori, S. 1999 Drag and lift forces on a rotating sphere in a linear shear flow. J. Fluid Mech. 384, 183–206.Google Scholar
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.Google Scholar
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.Google Scholar
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, 284–299.Google Scholar
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.Google Scholar
Niazmand, H. & Renksizbulut, M. 2003 Surface effects on transient three-dimensional flows around rotating spheres at moderate Reynolds numbers. Comput. Fluids 32 (10), 1405–1433.Google Scholar
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.Google Scholar
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, 242–255.Google Scholar
Pirozzoli, S. 2011 Stabilized non-dissipative approximations of Euler equations in generalized curvilinear coordinates. J. Comput. Phys. 230 (8), 2997–3014.Google Scholar
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, 751–781.Google Scholar
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, 361–383.Google Scholar
Rubinow, S. I. & Keller, J. B. 1961 The transverse force on a spinning sphere moving in a viscous fluid. J. Fluid Mech. 44, 447–459.Google Scholar
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, 62–86.Google Scholar
Shimada, T., Daimon, Y. & Sekino, N.2006 Computational fluid dynamics of multiphase flows in solid rocket motors. JAXA Special Publication. JAXA-SP-05-035E.Google Scholar
Sutherland, W. 1893 The viscosity of gases and molecular force. Phil. Mag. Series 5 36, 507–531.Google Scholar
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. 366–369. The Korean Society of Mechanical Engineers.Google Scholar
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.Google Scholar
Teymourtash, A. R. & Salimipour, S. E. 2017 Compressibility effects on the flow past a rotating cylinder. Phys. Fluids 29 (1), 016101.Google Scholar
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), 350–361.Google Scholar
Volkov, A. N. 2011 Transitional flow of a rarefied gas over a spinning sphere. J. Fluid Mech. 683, 320–345.Google Scholar
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), 199–238.Google Scholar
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), 300–307.Google Scholar