Advertisement

Smoke streak visualization of steady flows over a spinning cone at angle of attack in flight

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

  • 62 Accesses

Abstract

A smoke streak visualization technique is employed to observe the steady flow field over a cone of a half angle of \(\theta _c = 30^\circ \), spinning at an angular speed of \(\varOmega = 5 \text { revs/s}\), at angles of attack of \(0 \le \alpha \le 36^\circ \), in an axial flow of \(U_\infty = 1 \text { m/s}\). The Reynolds number is \({\sim }10^4\) based on the generator of the cone. Streaklines highlight increasing asymmetry of the flow and formation of vortices at increasing angles of attack. The rotation direction of the cone shapes the streaklines ingested into the boundary layers. Good agreement in streakline patterns between potential flow theory and experiment is observed over the cone at \(\alpha = 0\), the agreement getting better near the tip of the cone. No signs of boundary layer instabilities are noted as the Reynolds number is not sufficiently high, except at the highest angle of attack \(\alpha =36^\circ \) where a wave pattern is observed on the rolled-up streamwise vortex.

Graphic abstract

Streaklines over a \(60^\circ \) cone at angle of attack \(\alpha \) in an axial flow of 1 m/s.

This is a preview of subscription content, log in to check access.

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

Subscribe to journal

Immediate online access to all issues from 2019. Subscription will auto renew annually.

US$ 99

This is the net price. Taxes to be calculated in checkout.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

References

  1. Calvert JR (1967) Experiments on the low-speed flow past cones. J Fluid Mech 27(2):273–289. https://doi.org/10.1017/s002211206700031x

  2. Dol SS, Nor MAM, Kamaruzaman MK (2006) An improved smoke-wire flow visualization technique. In: Proceedings of the 4th WSEAS International Conference on Fluid Mechanics and Aerodynamics, pp 231–236

  3. Garrett S, Peake N (2007) The absolute instability of the boundary layer on a rotating cone. Eur J Mech B Fluids 26(3):344–353. https://doi.org/10.1016/j.euromechflu.2006.08.002

  4. Gregory N, Stuart JT, Walker WS (1955) On the stability of three-dimensional boundary layers with application to the flow due to a rotating disk. Philos Trans R Soc A: Math Phys Eng Sci 248(943):155–199. https://doi.org/10.1098/rsta.1955.0013

  5. Hussain Z, Stephen SO, Garrett SJ (2012) The centrifugal instability of a slender rotating cone. J Algorithms Comput Technol 6(1):113–128. https://doi.org/10.1260/1748-3018.6.1.113

  6. Hussain Z, Garrett SJ, Stephen SO (2014) The centrifugal instability of the boundary-layer flow over slender rotating cones. J Fluid Mech 755(274):293. https://doi.org/10.1017/jfm.2014.417

  7. Hussain Z, Garrett SJ, Stephen SO, Griffiths PT (2016) The centrifugal instability of the boundary-layer flow over a slender rotating cone in an enforced axial free stream. J Fluid Mech 788(70):94. https://doi.org/10.1017/jfm.2015.671

  8. Illingworth C (1953) XLII. The laminar boundary layer of a rotating body of revolution. Lond Edinb Dublin Philos Mag J Sci 44(351):389–403. https://doi.org/10.1080/14786440408520323

  9. ImageJ (2019) Imagej. https://imagej.nih.gov/ij/

  10. Keisan (2019) High precision calculator - keisan.casio.com. https://keisan.casio.com/calculator?_escaped_fragment_=#!

  11. Kim JW, Morris PJ (2002) Computation of subsonic inviscid flow past a cone using high-order schemes. AIAA J 40(10):1961–1968. https://doi.org/10.2514/2.1557

  12. Kobayashi R (1981) Linear stability theory of boundary layer along a cone rotating in axial flow. Bull JSME 24(192):934–940. https://doi.org/10.1299/jsme1958.24.934

  13. Kobayashi R, Izumi H (1983) Boundary-layer transition on a rotating cone in still fluid. J Fluid Mech 127(–1):353. https://doi.org/10.1017/s0022112083002761

  14. Kobayashi R, Kohama Y, Kurosawa M (1983) Boundary-layer transition on a rotating cone in axial flow. J Fluid Mech 127(–1):341. https://doi.org/10.1017/s002211208300275x

  15. Kohama Y, Kobayashi R (1983) Boundary-layer transition and the behaviour of spiral vortices on rotating spheres. J Fluid Mech 137(153):164. https://doi.org/10.1017/s0022112083002335

  16. Rosenhead L (1988) Laminar boundary layers. Dover, NY

  17. Savaş Ö (1987) Stability of Bödewadt flow. J Fluid Mech 183(77):94. https://doi.org/10.1017/s0022112087002532

  18. Schlichting H, Kestin J (1979) Boundary- layer theory. McGraw-Hill, NY

  19. Tien CL, Tsuji IJ (1965) A theoretical analysis of laminar forced flow and heat transfer about a rotating cone. J Heat Transf 87(2):184. https://doi.org/10.1115/1.3689069

  20. Van Dyke M (1982) An album of fluid motion. Parabolic Press, California

  21. Whitehead L, Canetti G (1950) XCI. The laminar boundary layer on solids of revolution. Lond Edinb Dublin Philos Mag J Sci 41(321):988–1000. https://doi.org/10.1080/14786445008561034

Download references

Acknowledgements

A. M. Kuraan thanks the National Science Foundation for their generous support through the Graduate Research Fellowship Program. Seed funding is provided by Powley Funds of the Department of Mechanical Engineering. We thank Brandon Sauw for his excellent design of the cone mounting mechanism. Discussions with Eric Ibarra have been very fruitful.

Author information

Correspondence to Ömer Savaş.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kuraan, A.M., Savaş, Ö. Smoke streak visualization of steady flows over a spinning cone at angle of attack in flight. J Vis (2019). https://doi.org/10.1007/s12650-019-00621-1

Download citation

Keywords

  • Smoke visualization
  • Spinning cone
  • Vortex formation