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Experimental study on the instability of wake of axisymmetric streamlined body

Published online by Cambridge University Press:  29 March 2011

MASAHITO ASAI*
Affiliation:
Department of Aerospace Engineering, Tokyo Metropolitan University, 6-6 Asahigaoka, Hino, Tokyo 191-0065, Japan
AYUMU INASAWA
Affiliation:
Department of Aerospace Engineering, Tokyo Metropolitan University, 6-6 Asahigaoka, Hino, Tokyo 191-0065, Japan
YASUFUMI KONISHI
Affiliation:
Department of Aerospace Engineering, Tokyo Metropolitan University, 6-6 Asahigaoka, Hino, Tokyo 191-0065, Japan
SHINICHI HOSHINO
Affiliation:
Department of Aerospace Engineering, Tokyo Metropolitan University, 6-6 Asahigaoka, Hino, Tokyo 191-0065, Japan
SHOHEI TAKAGI
Affiliation:
Aerospace Plane Research Center, Muroran Institute of Technology, 27-1 Mizumoto-cho, Muroran 050-8585, Japan
*
Email address for correspondence: masai@sd.tmu.ac.jp

Abstract

The instability of wake of an axisymmetric body with the NACA aerofoil section was experimentally studied under low background turbulence. The body was suspended using a magnetic suspension and balance system to avoid undesirable influences of mechanical supports on the disturbance development. The Reynolds number based on the chord length of the aerofoil section ranged from 5.3 × 104 to 2.1 × 105. For the body with a NACA0015 aerofoil section where there is no boundary-layer separation on the body surface, the wake was convectively unstable, even at the highest Reynolds number examined. Although the wake maintained axisymmetry of mean flow, the instability waves often took a planar-symmetric form, indicating that the occurrence of disturbance can be influenced by minute variations in the position and orientation of the suspended body. For bodies with thicker NACA0018 and NACA0024 aerofoil sections where the flow involved a region of absolute instability immediately downstream of the trailing edge, the global mode could grow rapidly and attain saturation amplitude within a very short distance from the trailing edge despite that the region of absolute instability was limited only to small streamwise distance, about one tenth of the instability wavelength. The predominant frequency of vortex shedding was found to be very close to the absolute frequency near the trailing edge, especially at the upstream boundary of the region of absolute instability. This is consistent with the theoretical model for the development of a nonlinear global mode. It was also found that the mean flow axisymmetry was broken around the critical Reynolds number for global instability, which led to the appearance and growth of a planar-symmetric global mode.

Type
Papers
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Batchelor, G. K. & Gill, A. E. 1962 Analysis of the stability of axisymmetric jets. J. Fluid Mech. 14, 529551.CrossRefGoogle Scholar
Chomaz, J. M. 2005 Global instability in spatially developing flows: Non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37, 357392.CrossRefGoogle Scholar
Chomaz, J. M., Huerre, P. & Redekopp, L. G. 1991 A frequency selection criterion in spatially developing flows. Stud. Appl. Maths 84, 119144.CrossRefGoogle Scholar
Ghidersa, B. & Ducek, J. 2000 Breaking of axisymmetry and onset of unsteadiness in the wake of sphere. J. Fluid Mech. 423, 3369.CrossRefGoogle Scholar
Higuchi, H., Sawada, H. & Kato, H. 2008 Sting-free measurements on a magnetically supported right circular cylinder aligned with the free stream. J. Fluid Mech. 596, 4972.CrossRefGoogle Scholar
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473537.CrossRefGoogle Scholar
Jackson, C. P. 1987 A finite-element study of the onset of vortex shedding in flow past variously shaped bodies. J. Fluid Mech. 182, 2345.CrossRefGoogle Scholar
Johnson, A. & Patel, V. C. 1999 Flow past a sphere up to a Reynolds number of 300. J. Fluid Mech. 378, 1970.CrossRefGoogle Scholar
Meliga, P., Chomaz, J.-M. & Sipp, D. 2009 Global mode interaction and pattern selection in the wake of a disk: A weakly nonlinear expansion. J. Fluid Mech. 633, 159189.CrossRefGoogle Scholar
Monkewitz, P. A. 1988 a The absolute and convective nature of instability in two-dimensional wakes at low Reynolds numbers. Phys. Fluids 31, 9991006.CrossRefGoogle Scholar
Monkewitz, P. A. 1988 b A note on vortex shedding from axisymmetric bluff bodies. J. Fluid Mech. 192, 561575.CrossRefGoogle Scholar
Monkewitz, P. A., Huerre, P. & Chomaz, J.-M. 1993 Global linear stability analysis of weakly non-parallel shear-flows. J. Fluid Mech. 251, 120.CrossRefGoogle Scholar
Natarajan, R. & Acrivos, A. 1993 The instability of the steady flow past spheres and disks. J. Fluid Mech. 254, 323344.CrossRefGoogle Scholar
Nishioka, M. & Sato, H. 1978 Mechanism of determination of the shedding frequency of vortices behind a cylinder at low Reynolds number. J. Fluid Mech. 89, 4960.CrossRefGoogle Scholar
Oertel, H. Jr. 1990 Wakes behind blunt bodies. Annu. Rev. Fluid Mech. 24, 539564.CrossRefGoogle Scholar
Peterson, L. F. & Hama, F. R. 1978 Instability and transition of the axisymmetric wake of a slender body of revolution. J. Fluid Mech. 88, 7196.CrossRefGoogle Scholar
Pier, B. 2002 On the frequency selection of finite-amplitude vortex shedding in the cylinder wake. J. Fluid Mech. 438, 407417.CrossRefGoogle Scholar
Pier, B. 2008 Local and global instabilities in the wake of a sphere. J. Fluid Mech. 603, 3961.CrossRefGoogle Scholar
Pier, B. & Huerre, P. 2001 Nonlinear self-sustained structures and fronts in spatially developing wake flows. J. Fluid Mech. 435, 145174.CrossRefGoogle Scholar
Pier, B. & Huerre, P., Chomaz, J.-M. & Couairon, A. 1998 Steep nonlinear global modes in spatially developing media. Phys. Fluids 10, 24332435.CrossRefGoogle Scholar
Sakamoto, H. & Haniu, H. 1990 A study on vortex shedding from spheres in a uniform flow. Trans. ASME: J. Fluids Engng 112, 3861–392.Google Scholar
Sakamoto, H. & Haniu, H. 1995 The formation mechanism and shedding frequency of vortices from a sphere in uniform shear flow. J. Fluid Mech. 287, 151171.CrossRefGoogle Scholar
Sato, H. & Okada, O. 1966 The stability and transition of an axisymmetric wake. J. Fluid Mech. 26, 237253.CrossRefGoogle Scholar
Sawada, H. & Kunimasu, T. 2001 Status of MSBS study at NAL. In Proceedings of the Sixth International Symposium on Magnetic Suspension Technology (ed. Genta, G., Schneider-Muntau, H., di Gloria, L. & Green, W.), pp. 163–168.Google Scholar
Tomboulides, A. G. & Orszag, S. A. 2000 Numerical investigation of transitional and weak turbulent flow past a sphere. J. Fluid Mech. 416, 4573.CrossRefGoogle Scholar