Abstract
Starting jet is commonly defined as the transient motion produced when a viscous incompressible fluid is forced from an initial state of rest Cantwell (Journal of Fluid Mechanics, 173, 159–189 [6]). The applied force can be time dependent in the form of an impulsive, step or ramp function acting at a point or along a line. Starting jet can be used in fundamental study of vortex ring dynamics, synthetic jets, mixing enhancement, and vortex-enhanced unsteady propulsion systems. Researches related to starting jets have been carried out broadly in two directions. The first direction is focused on the underlying mechanism for the vortex ring pinch-off, which is defined as the process whereby a forming vortex ring is no longer able to absorb vorticity flux from the jet source via the separated shear layer . Several theoretical models are proposed to predict a critical time scale for the pinch-off process, dubbed as the formation number F, for different flow conditions. The second direction is focused on its practical applications in entrainment enhancement as well as pulsed-jet propulsion systems. Specifically, due to the restricted vortex ring formation in starting jet , the propulsive efficiency can be effectively improved over the steady jet propulsion by increasing the generated thrust via the vortex over-pressure in the near-wake and by decreasing the kinetic energy loss in the wake via vortex entrainment. In this chapter, we intend to provide the readers with some basic ideas on the dynamic process of vortex ring formation in a starting jet , and its practical application in nature and engineering fields. This chapter is divided into four parts. The first part provides a brief introduction of the starting jet and the phenomenon of vortex ring pinch-off. The discussion of the underlying mechanisms and its theoretical explanation are provided in part two. In the third part, the practical application of starting jets in engineering systems will be explained and discussed. This chapter ends with a summary and an outlook for future study on the starting jet.
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References
Allen, J. J. & Naitoh, T. (2005). Experimental study of the production of vortex rings using a variable diameter orifice. Physics of Fluids, 17(6), 061701.
Auerbach, D. (1991). Stirring properties of vortex rings. Phys Fluids A-Fluid, 3, 1351–1355.
Bartol, I. K., Krueger, P. S., Stewart, W. J., & Thompson, J. T. (2009). Hydrodynamics of pulsed jetting in juvenile and adult brief squid Lolliguncula brevis: Evidence of multiple jet ‘modes’ and their implications for propulsive efficiency. Journal of Experimental Biology, 212, 1889–1903.
Bartol, I. K., Krueger, P. S., Thompson, J. T., & Stewart, W. J. (2008). Swimming dynamics and propulsive efficiency of squids throughout ontogeny. Integrative and Comparative Biology, 48, 720–733.
Bremhorst, K., & Watson, R. D. (1981). Velocity-field and entrainment of a pulsed core jet. Journal of Fluids Engineering T ASME, 103, 605–608.
Cantwell, B. J. (1986). Viscous starting jets. Journal of Fluid Mechanics, 173, 159–189.
Cossali, G. E., Coghe, A., & Araneo, L. (2001). Near-field entrainment in an impulsively started turbulent gas jet. AIAA Journal, 39, 1113–1122.
Dabiri, J. O. (2009). Optimal vortex formation as a unifying principle in biological propulsion. Annual Review of Fluid Mechanics, 41, 17–33.
Dabiri, J. O., & Gharib, M. (2004). Delay of vortex ring pinchoff by an imposed bulk counterflow. Physics of Fluids, 16, L28–L30.
Dabiri, J. O., & Gharib, M. (2004). Fluid entrainment by isolated vortex rings. Journal of Fluid Mechanics, 511, 311–331.
Dabiri, J. O., & Gharib, M. (2005). Starting flow through nozzles with temporally variable exit diameter. Journal of Fluid Mechanics, 538, 111–136.
Didden, N. (1979). Formation of vortex rings—Rolling-up and production of circulation. Zeitschrift fur Angewandte Mathematik und Physik, 30, 101–116.
Fraenkel, L. E. (1972). Examples of steady vortex rings of small cross-section in an ideal fluid. Journal of Fluid Mechanics, 51, 119–135.
Gao, L., & Yu, S. C. M. (2010). A model for the pinch-off process of the leading vortex ring in a starting jet. Journal of Fluid Mechanics, 656, 205–222.
Gao, L., & Yu, S. C. M. (2012). Development of the trailing shear layer in a starting jet during pinch-off. Journal of Fluid Mechanics, 700, 382–405.
Gharib, M., Rambod, E., & Shariff, K. (1998). A universal time scale for vortex ring formation. Journal of Fluid Mechanics, 360, 121–140.
Glezer, A. (1988). The formation of vortex rings. Physics of Fluids, 31, 3532–3542.
Heeg, R. S., & Riley, N. (1997). Simulations of the formation of an axisymmetric vortex ring. Journal of Fluid Mechanics, 339, 199–211.
Hettel, M., Wetzel, F., Habisreuther, P., & Bockhorn, H. (2007). Numerical verification of the similarity laws for the formation of laminar vortex rings. Journal of Fluid Mechanics, 590, 35–60.
Hill, M. J. M. (1894). On a spherical vortex. Proceedings of the Royal Society of London, A185, 213–245.
James, S., & Madnia, C. K. (1996). Direct numerical simulation of a laminar vortex ring. Physics of Fluids, 8, 2400–2414.
Kaden, H. (1931). Aufwicklung einer unstabilen Unstetigkeitsfläche. Ingenieur Archiv, 2, 140–168.
Krieg, M., & Mohseni, K. (2008). Thrust characterization of a bioinspired vortex ring thruster for locomotion of underwater robots. IEEE Journal of Oceanic Engineering, 33, 123–132.
Krueger, P. S., Dabiri, J. O., & Gharib, M. (2006). The formation number of vortex rings formed in uniform background co-flow. Journal of Fluid Mechanics, 556, 147–166.
Krueger, P. S., & Gharib, A. (2005). Thrust augmentation and vortex ring evolution in a fully pulsed jet. AIAA Journal, 43, 792–801.
Krueger, P. S., & Gharib, M. (2003). The significance of vortex ring formation to the impulse and thrust of a starting jet. Physics of Fluids, 15, 1271–1281.
Lawson, J. M., & Dawson, J. R. (2013). The formation of turbulent vortex rings by synthetic jets. Physics of Fluids, 25(10), 105113.
Leweke, T., & Williamson, C. H. K. (1998). Cooperative elliptic instability of a vortex pair. Journal of Fluid Mechanics, 360, 85–119.
Lim, T. T., Nickels, T. B. (1995). Vortex rings. In S. Green (Ed.), Fluid Vortices (pp. 95–153). Netherlands: Springer.
Linden, P. F., & Turner, J. S. (2001). The formation of ‘optimal’ vortex rings, and the efficiency of propulsion devices. Journal of Fluid Mechanics, 427, 61–72.
List, E. J. (1982). Turbulent jets and plumes. Annual Review of Fluid Mechanics, 14, 189–212.
Maxworthy, T. (1972). Structure and stability of vortex rings. Journal of Fluid Mechanics, 51, 15–32.
Maxworthy, T. (1977). Some experimental studies of vortex rings. Journal of Fluid Mechanics, 81, 465–495.
Mohseni, K., & Gharib, M. (1998). A model for universal time scale of vortex ring formation. Physics of Fluids, 10, 2436–2438.
Mohseni, K., Ran, H. Y., & Colonius, T. (2001). Numerical experiments on vortex ring formation. Journal of Fluid Mechanics, 430, 267–282.
Moore, D. W., & Saffman, P. G. (1973). Axial-flow in laminar trailing vortices. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 333, 491–508.
Moslemi, A. A., Krueger, P. S. (2010). Propulsive efficiency of a biomorphic pulsed-jet underwater vehicle. Bioinspiration and Biomimetics, 5(3), 036003.
Nitsche, M. (1993) Numerical simulation of axisymmetric vortex sheet roll-up. Vortex flows and related numerical methods. In: Proceedings NATO Advanced Res. Workshop. (eds. Beale, J. T., Collet, G. H. and Hubersou, S.) Kluwer Acad. Publishers.
Nitsche, M., & Krasny, R. (1994). A numerical study of vortex ring formation at the edge of a circular tube. Journal of Fluid Mechanics, 276, 139–161.
Norbury, J. (1973). Family of steady vortex rings. Journal of Fluid Mechanics, 57, 417–431.
O’farrell, C., & Dabiri, J. O. (2010). A Lagrangian approach to identifying vortex pinch-off. Chaos, 20, 017513.
O’farrell, C., & Dabiri, J. O. (2012). Perturbation response and pinch-off of vortex rings and dipoles. Journal of Fluid Mechanics, 704, 280–300.
Olcay, A. B., & Krueger, P. S. (2008). Measurement of ambient fluid entrainment during laminar vortex ring formation. Experiments in Fluids, 44, 235–247.
Olcay, A. B., & Krueger, P. S. (2010). Momentum evolution of ejected and entrained fluid during laminar vortex ring formation. Theoretical and Computational Fluid Dynamics, 24, 465–482.
Pawlak, G., Marugan-Cruz, C., Martinez-Bazan, C., & Garcia-Hrdy, P. (2007). Experimental characterization of starting jet dynamics. Fluid Dynamics Research, 39, 711–730.
Ricou, F. P., & Spalding, D. B. (1961). Measurements of entrainment by axisymmetrical turbulent jets. Journal of Fluid Mechanics, 11, 21–32.
Rosenfeld, M., Rambod, E., & Gharib, M. (1998). Circulation and formation number of laminar vortex rings. Journal of Fluid Mechanics, 376, 297–318.
Ruiz, L. A., Whittlesey, R. W. & Dabiri, J. O. (2011). Vortex-enhanced propulsion. Journal of Fluid Mechanics, 668, 5–32.
Saffman, P. G. (1978). Number of waves on unstable vortex rings. Journal of Fluid Mechanics, 84, 625–639.
Schram, C., & Riethmuller, M. L. (2001). Vortex ring evolution in an impulsively started jet using digital particle image velocimetry and continuous wavelet analysis. Measurement Science and Technology, 12, 1413–1421.
Shadden, S. C., Dabiri, J. O., & Marsden, J. E. (2006). Lagrangian analysis of fluid transport in empirical flows. Physics of Fluids, 18.
Shadden, S. C., Lekien, F., & Marsden, J. E. (2005). Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows. Physica D: Nonlinear Phenomena, 212, 271–304.
Shariff, K., & Leonard, A. (1992). Vortex rings. Annual Review of Fluid Mechanics, 24, 235–279.
Shusser, M., & Gharib, M. (2000). Energy and velocity of a forming vortex ring. Physics of Fluids, 12, 618–621.
Shusser, M., Gharib, M., Rosenfeld, M., & Mohseni, K. (2002). On the effect of pipe boundary layer growth on the formation of a laminar vortex ring generated by a piston/cylinder arrangement. Theoretical and computational fluid dynamics, 15, 303–316.
Weigand, A., & Gharib, M. (1997). On the evolution of laminar vortex rings. Experiments in Fluids, 22, 447–457.
Zhao, W., Frankel, S. H., & Mongeau, L. G. (2000). Effects of trailing jet instability on vortex ring formation. Physics of Fluids, 12, 589–596.
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Gao, L., Yu, S.C.M. (2015). Starting Jets and Vortex Ring Pinch-Off. In: New, D., Yu, S. (eds) Vortex Rings and Jets. Fluid Mechanics and Its Applications, vol 111. Springer, Singapore. https://doi.org/10.1007/978-981-287-396-5_1
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