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Mode selection and resonant phase locking in unstable axisymmetric jets

  • T. C. Corke (a1), F. Shakib (a1) and H. M. Nagib (a1)

Abstract

This paper presents experimental results on the nonlinear phase locking present in the resonant growth of unstable modes in the shear layer of an axisymmetric jet. The initial instability modes scale with the exiting shear layer and grow convectively with downstream distance. Because of the special condition at the exit lip of the jet, the initial growth of modes is very sensitive to local unsteady pressure fields. A part of the unsteady field is stochastic in nature. To a larger extent, the pressure field at the lip of the jet contains the imprint of the downstream-developing instability modes, in particular the first unstable axisymmetric mode and its subharmonic. These are felt at the lip of the jet as a result of the energetic processes of the first vortex rollup and vortex pairing. As a result, a resonant feedback exists which under special conditions makes the initial region of this flow in some sense absolutely unstable. The features of this process are brought out by the normalized crossbispectrum or cross-bicoherence between the instantaneous unsteady pressure at the lip of the jet and velocity time series measured at the same azimuthal position for different downstream locations. These give a measure of the nonlinear phase locking between the principle modes and their sum and difference modes. Analysis of these show a perfect nonlinear phase locking at the fundamental axisymmetric and subharmonic frequencies between the pressure field at the lip and the velocity field at the downstream locations corresponding to the energy saturations of the fundamental and subharmonic modes. This resonance process can be suppressed or enhanced by low-amplitude axisymmetric mode forcing at the natural preferred frequency of slightly detuned cases. Contrasted to this is the behaviour of the fundamental m = ± 1 helical mode. This mode was found to have the same spatial growth rate as the axisymmetric mode and a streamwise frequency approximately 20 % higher, in agreement with theoretical predictions. However, short-time spectral estimates showed that these two fundamental modes do not exist at the same time or space. This suggests that each is a basin of attraction which suppresses the existence of the other. The apparent non-deterministic switching observed between these modes is probably the result of the response of the jet to stochastic input of axisymmetric or non-axisymmetric disturbances. This scenario may lead to a low-dimensional temporal model based on the interaction between these two modes which captures most of the early random nature seen in our experiments.

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References

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Acton, E.: 1980 A modelling of large eddies in an axisymmetric jet. J. Fluid Mech. 98, 131.
Browand, F. K. & Laufer, J., 1975 The role of large scale structures in the initial development of circular jets. 4th Symp. on Turbulence in Liquids, pp. 333342. Science.
Bruun, H. H.: 1977 A time-domain analysis of the large-scale flow structure in a circular jet. Part 1. Moderate Reynolds number. J. Fluid Mech. 83, 641672.
Corke, T. & Mangano, R., 1987 Transition of a boundary layer: controlled fundamental-subharmonic interactions. In Proc. Symp. on Turbulent Management and Relaminarization, Bangalore, India, pp. 199213. Springer.
Corke, T. & Mangano, R., 1989 Resonant growth of three dimensional modes in transitioning Blasius boundary layers. J. Fluid Mech. 209, 93150.
Corke, T. C., Shakib, F. & Nagib, H. M., 1985 Effects of low amplitude forcing on axisymmetric jet flows. AIAA Shear Flow Control Conference, Boulder, Colorado, AIAA-85–0573.
Drubka, R. E.: 1981 Instability in near field of turbulent jets and their dependence on initial conditions and Reynolds number. Ph.D. thesis, Illinois Institute of Technology.
Drubka, R., Reisenthel, P. & Nagib, H., 1989 The dynamics of low initial disturbance turbulent jets. Phys. Fluids A 1, 17231735.
Williams, J. E. Ffowcs & Kempton, A. J. 1978 The noise from the large-scale structures of a jet. J. Fluid Mech. 84, 673694.
Gutmark, E. & Ho, C.-M. 1983 Preferred modes and the spreading rates of jets. Phys. Fluids 26, 29322938.
Hasselman, K., Munk, W. & McDonald, G., 1963 Bispectrum of ocean waves. In Proc. Symp. on Time Series Analysis (ed. M. Rosenblatt), pp. 125139. John Wiley.
Hinich, M. J. & Clay, C. S., 1968 The application of the discrete Fourier transform in the estimation of power spectra, coherence and bispectra of geophysical data. Rev. Geophys. 6, 347363.
Ho, C.-M.: 1981 Local and global dynamics of free shear layers. In Proc. Symp. on Numerical and Physical Aspects of Aerodynamic Flows, Long Beach, CA, pp. 521533. Springer.
Ho, C-M. & Huang, L.-S. 1982 Subharmonics and vortex merging in mixing layers. J. Fluid Mech. 119, 443473.
Ho, C.-M. & Huerre, P. 1984 Perturbed free shear layers. Ann. Rev. Fluid Mech. 16, 365424.
Hussain, A. K. M. F. & Clark, A. R. 1981 On the coherent structure of the axisymmetric mixing layer: a flow visualization study. J. Fluid Mech. 104, 263295.
Hussain, A. K. M. F. & Zaman, K. B. M. Q. 1981 The preferred mode of the axisymmetric jet. J. Fluid Mech. 110, 3971.
Kelly, R. E.: 1967 On the resonant interaction of neutral disturbances in inviscid shear flows. J. Fluid Mech. 31, 789799.
Kibens, V.: 1979 On the role of vortex pairing in jet noise generation. McDonnel Douglas Research Laboratory Rep.
Knisely, C. & Rockwell, D., 1981 Self-sustained low-frequency components in an impinging shear layer. J. Fluid Mech. 116, 157187.
Kusek, S. M., Corke, T. C. & Reisenthel, P., 1990 Seeding of helical modes in the initial region of an axisymmetric jet. Expts Fluids(to appear).
Laufer, J. & Zhang, J. X., 1983 Unsteady aspects of a low Mach number jet. Phys. Fluids 26, 17401750.
Lii, K. S., Rosenblatt, M. & Van Atta, C. 1976 Bispectral measurements in turbulence, J. Fluid Mech. 77, 4562.
Mattingly, G. E. & Chang, C. C., 1974 Unstable waves on an axisymmetric jet column. J. Fluid Mech. 65, 541560.
Michalke, A.: 1965 On spatially growing disturbance in an inviscid shear layer. J. Fluid Mech. 23, 521544.
Michalke, A.: 1971 Instabilitat eines Kompressiblem Ruden Friestrahls unter Berucksichtingung des Einflusses der Strahlgrenzschichtdicke, Z. Fluzwiss. 9, 319328.
Miksad, R., Jones, F. & Powers, E., 1983 Measurements of nonlinear interactions during natural transition of a symmetric wake. Phys. Fluids 26, 14021409.
Miksad, R. W., Jones, F. L., Powers, E. J., Kim, Y. C. & Khadea, L., 1982 Experiments on the role of amplitude and phase modulations during transition to turbulence. J. Fluid Mech. 123, 129.
Monkewitz, P. A.: 1988 Subharmonic resonance, pairing and shredding in the mixing layer. J. Fluid Mech. 188, 223252.
Peterson, R. A.: 1978 Influence of wave dispersion on vortex pairing in a jet. J. Fluid Mech. 89, 469495.
Pierrehumbert, R. T.: 1980 The structure and stability of large vortices in an inviscid flow. Ph.D. thesis, Massachusetts Institute of Technology.
Reisenthel, P. & Corke, T. C., 1983 Application of spectral entropy methods to non-stationary flow problems. Bull. 36th Am. Phys. Soc. Fluids Division Meeting.
Sarohia, V. & Massier, P. F., 1978 Experimental results of large-scale structure in jet flows and their relation to jet noise production. AIAA J. 16, 831.
Shakib, F.: 1985 Evolution and interaction of instability modes in an axisymmetric jet. M. S. thesis, Illinois Institute of Technology.
Solis, R., Miksad, R. & Powers, E., 1986 Experiments on the influence of mean flow unsteadiness on the laminar-turbulent transition of a wake. Proc. Tenth Symp. on Turbulence in Liquids, Rolla, Missouri. Science.
Wille, R.: 1963 Beitrage Zur Phanomenologie der Freistrahlen. Z. Fluqwiss. 11, 222233.
Winant, C. D. & Browand, F. K., 1974 Vortex pairing: the mechanism of turbulent mixing-layer growth at moderate Reynolds number. J. Fluid Mech. 63, 237255.
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Mode selection and resonant phase locking in unstable axisymmetric jets

  • T. C. Corke (a1), F. Shakib (a1) and H. M. Nagib (a1)

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