The significance of vortex ring formation to the impulse and thrust of a starting jet

Physics of Fluids

Volumn 15, Issue 5, 2003, Pages 1271-1281

  Krueger, Paul S ^a   Gharib, M ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACCELERATION; NOZZLES; PISTONS; VELOCITY; VORTEX FLOW;

VORTEX RINGS;

JETS;

CYLINDER; EXPERIMENTAL STUDY; FLUID MECHANICS; JET FLOW; PISTON; PROPULSION UNIT; SHEAR FLOW; THRUST; VORTEX RING;

EID: 0037594125     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1564600     Document Type: Article

References (31)

1. N. Didden, "On the formation of vortex rings: Rolling-up and production of circulation," Z. Angew. Math. Phys. 30, 101 (1979).
2. M. Nitsche and R. Krasny, "A numerical study of vortex ring formation at the edge of a circular tube," J. Fluid Mech. 276, 139 (1994).
3. T. Maxworthy, "Some experimental studies of vortex rings," J. Fluid Mech. 81, 465 (1977).
4. D. Auerbach, "Experiments on the trajectory and circulation of the starting vortex," J. Fluid Mech. 183, 185 (1987).
5. A. Glezer, "The formation of vortex rings," Phys. Fluids 31, 3532 (1988).
6. A. Glezer and D. Coles, "An experimental study of a turbulent vortex ring." J. Fluid Mech. 221, 243 (1990).
7. S. James and C. K. Madnia, "Direct numerical simulation of a laminar vortex ring." Phys. Fluids 8, 2400 (1996).
8. K. Shariff and A. Leonard, "Vortex rings," Annu. Rev. Fluid Mech. 24. 235 (1992).
9. M. Gharib, E. Rambod, and K. Shariff, "A universal time scale for vortex ring formation," J. Fluid Mech. 360, 121 (1998).
10. M. Rosenfeld, E. Rambod, and M. Gharib, "Circulation and formation number of laminar vortex rings," J. Fluid Mech. 376, 297 (1998).
11. K. Mohseni, H. Ran, and T. Colonius, "Numerical experiments on vortex ring formation," J. Fluid Mech. 430. 267 (2001).
12. K. Mohseni and M. Gharib, "A model for universal time scale of vortex ring formation," Phys. Fluids 10, 2436 (1998).
13. C. E. Willert and M. Gharib, "Digital particle image velocimetry," Exp. Fluids 10, 181 (1991).
14. M. Raffel, C. E. Willert, and J. Kompenhans. Particle Image Velocimetry: A Practical Guide (Springer, Berlin, 1998).
15. J. Westerweel, D. Dabiri, and M. Gharib, "The effect of a discrete window offset on the accuracy of cross-correlation analysis of digital PIV recordings," Exp. Fluids 23, 20 (1997).
16. H. B. Atabek and C. C. Chang, "Oscillatory flow near the entry of a circular tube," Z. Angew. Math. Phys. 12, 185 (1961).
17. The convention used throughout this paper is that I (without reference to time dependence) refers to the total impulse per pulse.
18. L. Prandtl and O. G. Tietjens, Applied Hydro- and Aeromechanics (Dover, New York. 1934).
19. u.
20. P. S. Krueger, "The significance of vortex ring formation and nozzle exit over-pressure to pulsatile jet propulsion," Ph.D. thesis, California Institute of Technology, 2001.
21. M. Shusser and M. Gharib, "Energy and velocity of a forming vortex ring," Phys. Fluids 12, 618 (2000).
22. M. Shusser, M. Gharib, M. Rosenfeld, and K. Mohseni, "On the effect of pipe boundary layer growth on the formation of a laminar vortex ring generated by a piston/cylinder arrangement," Theor. Comput. Fluid Dyn. 15, 303 (2002).
23. T. T. Lim and T. B. Nickels, "Vortex rings," in Fluid Vortices, edited by S. I. Green (Kluwer Academic, New York. 1995).
24. The illustration of the added mass effect in Fig. 10 suggests the added mass of the fluid external to the ring is actually convected with the ring in the sense that the same fluid particles are always in front of and behind the ring. Since the vorticity in the ring generates a velocity field that tends to sweep fluid around the boundary of the ring, this cannot be entirely true. Indeed, when a starting jet is initiated, this effect is manifested as ambient fluid getting pushed out of the way. It is therefore not possible to define this added mass as entrained mass in the traditional sense. The fluid inducted into the body of the ring, however, can be considered entrained mass in that it is convected downstream with the ring.
25. Perhaps a term other than "added mass" should be used to describe the potential flow external to a completely formed vortex ring since it is associated with the steady motion of the ring while added mass is typically related to accelerating bodies. Since, however, it is the acceleration of the forming ring that leads to the motion of this fluid, added mass as used here also refers to the fluid motion external to a completely formed vortex ring.
26. s.
27. P. Saffman, Vortex Dynamics (Cambridge University Press, Cambridge, 1992).
28. J. Z. Wu and J. M. Wu, "Interactions between a solid surface and a viscous compressible flow field," J. Fluid Mech. 254, 183 (1993).
29. If the vortex ring is thin enough that the vortex "bubble" is actually a torus (as assumed by Weihs-Ref. 31 and Miloh et al.-Ref. 32), then an extra term is required in Eq. (22) to correct for the fact that the "bubble" is not simply connected (see Saffman-Ref. 28-pp. 81, 200).
30. D. Weihs, "Periodic jet propulsion of aquatic creatures," Fortschr. Zool. 24, 171 (1977).
31. T. Miloh, G. Waisman, and D. Weihs, "The added-mass coefficients of a torus," J. Eng. Math. 12, 1 (1978).