Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-30T14:59:00.146Z Has data issue: false hasContentIssue false

Compressible starting jet: pinch-off and vortex ring–trailing jet interaction

Published online by Cambridge University Press:  27 March 2017

Juan José Peña Fernández*
Affiliation:
Institut für Strömungsmechanik und Technische Akustik, Technische Universität Berlin, 10623, Berlin, Germany
Jörn Sesterhenn
Affiliation:
Institut für Strömungsmechanik und Technische Akustik, Technische Universität Berlin, 10623, Berlin, Germany
*
Email address for correspondence: [email protected]

Abstract

The dominant feature of the compressible starting jet is the interaction between the emerging vortex ring and the trailing jet. There are two types of interaction: the shock–shear layer–vortex interaction and the shear layer–vortex interaction. The former is clearly not present in the incompressible case, since there are no shocks. The shear layer–vortex interaction has been reported in the literature in the incompressible case and it was found that compressibility reduces the critical Reynolds number for the interaction. Four governing parameters describe the compressible starting jet: the non-dimensional mass supply, the Reynolds number, the reservoir to unbounded chamber temperature ratio and the reservoir to unbounded chamber pressure ratio. The latter parameter does not exist in the incompressible case. For large Reynolds numbers, the vortex pinch-off takes place in a multiple way. We studied the compressible starting jet numerically and found that the interaction strongly links the vortex ring and the trailing jet. The shear layer–vortex interaction leads to a rapid breakdown of the head vortex ring when the flow impacted by the Kelvin–Helmholtz instabilities is ingested into the head vortex ring. The shock–shear layer–vortex interaction is similar to the noise generation mechanism of broadband shock noise in a continuously blowing jet and results in similar sound pressure amplitudes in the far field.

Type
Papers
Copyright
© 2017 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.)

References

Adams, N. A. & Shariff, K. 1996 A high-resolution hybrid compact scheme for shock-turbulence interaction problems. J. Comput. Phys. 127, 2751.Google Scholar
Anderson, D., Tannehill, J. & Pletcher, R. 1984 Computational Fluid Mechanics and Heat Transfer. Hemisphere Publishing.Google Scholar
Archer, P. J., Thomas, T. G. & Coleman, G. N. 2008 Direct numerical simulation of vortex ring evolution from the laminar to the early turbulent regime. J. Fluid Mech. 598, 201226.Google Scholar
Ball, C. G., Fellouah, H. & Pollard, A. 2012 The flow field in turbulent round free jets. Prog. Aerosp. Sci. 50, 126.Google Scholar
Becker, E. 1968 Gas Dynamics. Academic.Google Scholar
Bogey, C., de Caqueray, N. & Bailly, C. 2009 A shock-capturing methodology based on adaptative spatial filtering for high-order non-linear computations. J. Comput. Phys. 228 (5), 14471465.CrossRefGoogle Scholar
Bremhorst, K. & Hollis, P. G. 1990 Velocity field of an axisymmetric pulsed, subsonic air jet. AIAA J. 28 (12), 20432049.CrossRefGoogle Scholar
Cimarelli, C., Alatorre-Ibargengoitia, M. A., Kueppers, U., Scheu, B. & Dingwell, D. B. 2014 Experimental generation of volcanic lightning. Geology 42, 7982.Google Scholar
Didden, N. 1979 On the formation of vortex rings: rolling-up and production of circulation. Z. Angew. Math. Phys. 30 (1), 101116.CrossRefGoogle Scholar
Dimotakis, P. E. 2000 The mixing transition in turbulent flows. J. Fluid Mech. 409, 6998.CrossRefGoogle Scholar
Freund, J. B., Lele, S. K. & Moin, P. 2000 Numerical simulation of a Mach 1.92 turbulent jet and its sound field. AIAA J. 38 (11), 20232031.Google Scholar
Gao, L. & Yu, S. C. M. 2010 A model for the pinch-off process of the leading vortex ring in a starting jet. J. Fluid Mech. 656, 205222.Google Scholar
Gao, L. & Yu, S. C. M. 2015 Starting jets and vortex ring pinch-off. In Vortex Rings and Jets (ed. New, D. T. H. & Yu, S. C. M.), Fluid Mechanics and Its Applications, vol. 111, pp. 131. Springer.Google Scholar
Gharib, M., Rambod, E. & Shariff, K. 1998 A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121140.Google Scholar
Glezer, A. 1988 The formation of vortex rings. Phys. Fluids 31 (12), 35323542.CrossRefGoogle Scholar
Glezer, A. & Amitay, M. 2002 Synthetic jets. Annu. Rev. Fluid Mech. 34 (1), 503529.Google Scholar
Hermanson, J. C., Dugnani, R. & Johari, H. 2000 Structure and flame length of fully-modulated, turbulent diffusion flames. Combust. Sci. Technol. 155 (1), 203225.CrossRefGoogle Scholar
Ishii, R., Fujimoto, H., Hatta, N. & Umeda, Y. 1999 Experimental and numerical analysis of circular pulse jets. J. Fluid Mech. 392, 129153.CrossRefGoogle Scholar
James, S. & Madnia, C. K. 1996 Direct numerical simulation of a laminar vortex ring. Phys. Fluids 8 (9), 24002414.Google Scholar
Kelvin, Lord 1867 The traslatory velocity of a circular vortex ring. Phil. Mag. 33, 511512.Google Scholar
Kim, C. M., Krejsa, E. A. & Khavaran, A. 1994 Significance of shock structure on supersonic jet mixing noise of axisymmetric nozzles. AIAA J. 32 (9), 19201923.Google Scholar
Kleine, H., Le, C. V., Takehara, K. & Etoh, T. G. 2010 Time-resolved visualization of shock-vortex systems emitted from an open shock tube. J. Vis. 13 (1), 3340.CrossRefGoogle Scholar
Kuethe, A. M. 1935 Investigations of the turbulent mixing regions formed by jets. Trans. ASME J. Appl. Mech. 11 (3), 8795.CrossRefGoogle Scholar
Lim, T. T. & Nickels, T. B. 1995 Vortex rings. In Fluid Vortices (ed. Green, S. I.), Fluid Mechanics and its Applications, vol. 30, pp. 95153. Springer.CrossRefGoogle Scholar
Maxworthy, T. 1972 The structure and stability of vortex rings. J. Fluid Mech. 51, 1532.Google Scholar
Norum, T. D. & Seiner, J. M. 1982 Broadband shock noise from supersonic jets. AIAA J. 20, 6873.Google Scholar
Panda, J. 1998 Shock oscillation in underexpanded screeching jets. J. Fluid Mech. 363, 173198.Google Scholar
Pawlak, G., Marugan Cruz, C., Martinez Bazan, C. & Garcia Hrdy, P. 2007 Experimental characterization of starting jet dynamics. Fluid Dyn. Res. 39 (11–12), 711730.Google Scholar
Powell, A. 1953 On the mechanism of chocked jet noise. Proc. Phys. Soc. Lond. B 66, 10391056.Google Scholar
Ran, H. & Colonius, T. 2009 Numerical simulation of the sound radiated from a turbulent vortex ring. Intl J. Aeroacoust. 8 (4), 317336.Google Scholar
Ricou, F. & Spalding, D. B. 1961 Measurements of entrainment by axisymmetric turbulent jets. J. Fluid Mech. 11, 2132.Google Scholar
Rosenfeld, M., Rambod, E. & Gharib, M. 1998 Circulation and formation number of laminar vortex rings. J. Fluid Mech. 376, 297318.CrossRefGoogle Scholar
Ruden, P. 1933 Turbulente Ausbreitungsvorgänge im Freistrahl. Naturwissenschaften 21 (21–23), 375378.Google Scholar
Ryhming, I. L. 1973 Analysis of unsteady incompressible jet nozzle flow. Z. Angew. Math. Phys. 24 (2), 149164.Google Scholar
Saad, M. A. 1985 Compressible Fluid Flow. Prentice-Hall.Google Scholar
Saffman, P. G. 1970 The velocity of viscous vortex rings (small cross section viscous vortex ring velocity in ideal fluid with arbitrary vorticity distribution in core). Stud. Appl. Maths 49, 371380.CrossRefGoogle Scholar
Salas, M. D. & Iollo, A. 1996 Entropy jump across an inviscid shock wave. Theor. Comput. Fluid Dyn. 8 (5), 365375.Google Scholar
Schulze, J.2011 Adjoint based jet-noise minimization PhD thesis, Technische Universität, Berlin.Google Scholar
Seiner, J. M. & Yu, J. C. 1984 Acoustic near-field properties associated with broadband shock noise. AIAA J. 22, 12071215.CrossRefGoogle Scholar
Sesterhenn, J. 2000 A characteristic-type formulation of the Navier–Stokes equations for high order upwind schemes. Comput. Fluids 30 (1), 3767.Google Scholar
Shariff, K. & Leonard, A. 1992 Vortex rings. Annu. Rev. Fluid Mech. 24 (1), 235279.Google Scholar
Tam, C. K. W. 1991 Jet noise generated by large-scale coherent motion. In Aeroacoustics of Flight Vehicles: Theory and Practice, vol 1, chap. 6. NASA RP 4258.Google Scholar
Tam, C. K. W. 1995 Supersonic jet noise. Annu. Rev. Fluid Mech. 27 (1), 1743.Google Scholar
Tam, C. K. W., Golebiowski, M. & Seiner, J. M. 1996 On the two components of the turbulent mixing noise from supersonic jets. 2nd AIAA/CEAS Aeroacoustics Conference.Google Scholar
Tam, C. K. W. & Tanna, H. K. 1982 Shock associated noise of supersonic jets from convergent-divergent nozzles. J. Sound Vib. 81 (3), 337358.Google Scholar
Tam, C. K. W., Viswanathan, K., Ahuja, K. K. & Panda, J. 2008 The sources of jet noise: experimental evidence. J. Fluid Mech. 615, 253292.Google Scholar
Tanna, H. K. 1977a An experimental study of jet noise part i: turbulent mixing noise. J. Sound Vib. 50 (3), 405428.CrossRefGoogle Scholar
Tanna, H. K. 1977b An experimental study of jet noise part ii: shock associated noise. J. Sound Vib. 50 (3), 429444.Google Scholar
Taylor, G. 1950 The formation of a blast wave by a very intense explosion. i. Theoretical discussion. Proc. R. Soc. Lond. A 201 (1065), 159174.Google Scholar
Tollmien, W. 1926 Berechnung turbulenter Ausbreitungsvorgänge. Z. Angew. Math. Mech. 6, 468478.Google Scholar
Turner, J. 1962 The starting plume in neutral surroundings. J. Fluid Mech. 13, 356368.CrossRefGoogle Scholar
Witze, P. O.1980 The impulsively started incompressible turbulent jet. Sandia Laboratories Rep., SAND80-8617.Google Scholar
Witze, P. O. 1983 Hot-film anemometer measurements in a starting turbulent jet. AIAA J. 21, 308309.CrossRefGoogle Scholar
Zaitsev, M. Y., Kopiev, V. F. & Kotova, A. N. 2001 Representation of the sound field of a turbulent vortex ring as a superposition of quadrupoles. Acoust. Phys. 47 (6), 699706.Google Scholar
Zhao, W., Frankel, S. H. & Mongeau, L. G. 2000 Effects of trailing jet instability on vortex ring formation. Phys. Fluids 12 (3), 589596.Google Scholar