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The stability of countercurrent mixing layers in circular jets

Published online by Cambridge University Press:  26 April 2006

P. J. Strykowski  and
D. L. Niccum
P. J. Strykowski
Affiliation:
Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455, USA
D. L. Niccum
Affiliation:
Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455, USA
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Abstract

A spatially developing countercurrent mixing layer was established experimentally by applying suction to the periphery of an axisymmetric jet. A laminar mixing region was studied in detail for a velocity ratio R = ΔU/2U between 1 and 1.5, where ΔU describes the intensity of the shear across the layer and U is the average speed of the two streams. Above a critical velocity ratio Rr = 1.32 the shear layer displays energetic oscillations at a discrete frequency which are the result of very organized axisymmetric vortex structures in the mixing layer. The spatial order of the primary vortices inhibits the pairing process and dramatically alters the spatial development of the shear layer downstream. Consequently, the turbulence level in the jet core is significantly reduced, as is the decay rate of the mean velocity on the jet centreline. The response of the shear layer to controlled external forcing indicates that the shear layer oscillations at supercritical velocity ratios are self-excited. The experimentally determined critical velocity ratio of 1.32, established for very thin axisymmetric shear layers, compares favourably with the theoretically predicted value of 1.315 for the transition from convective to absolute instability in plane mixing layers (Huerre & Monkewitz 1985).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 227 , June 1991 , pp. 309 - 343
Copyright
© 1991 Cambridge University Press

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References

Bechert, D. W. 1985 Excitation of instability waves. Z. Flugwiss. Weltraumforsch. 9, 356–361.Google Scholar
Becker, H. A. & Massaro, T. A. 1968 Vortex evolution in a round jet. J. Fluid Mech. 31, 435–448.Google Scholar
Bradshaw, P. 1966 The effect of initial conditions on the development of a free shear layer. J. Fluid Mech. 26, 225–236.Google Scholar
Brown, G. L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775–816.Google Scholar
Chomaz, J. M., Huerre, P. & Redekopp, L. G. 1988 Bifurcations to local and global modes in spatially-developing flows. Phys. Rev. Lett. 60, 25–28.Google Scholar
Corke, T., Koga, D., Drubka, R. & Nagib, H. 1977 A new technique for introducing controlled sheets of smoke streaklines in wind tunnels. Proc. ICIASF, IEEE 77CH1251–8 AES, pp. 74–80.
Crow, S. C. & Champagne, F. H. 1971 Orderly structure in jet turbulence. J. Fluid Mech. 48, 547–591.Google Scholar
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic stability. Cambridge University Press.
Drubka, R. E. & Nagib, H. M. 1981 Instabilities in near field of turbulent jets and their dependence on initial conditions and Reynolds number. Tech. Rep. AFOSR-TR-82. Illinois Institute of Technology, Chicago.Google Scholar
Drubka, R. E., Reisenthel, P. & Nagib, H. M. 1989 The dynamics of low initial disturbance turbulent jets.. Phys. Fluids A 1, 1723–1735.Google Scholar
Freymuth, P. 1966 On the transition in a separated laminar boundary layer. J. Fluid Mech. 25, 683–704.Google Scholar
Hannemann, K. & Oertel, H. 1989 Numerical simulation of the absolutely and convectively unstable wake. J. Fluid Mech. 199, 55–88.Google Scholar
Ho, C.-M. & Huang, L.-S. 1982 Subharmonics and vortex merging in mixing layers. J. Fluid Mech. 119, 443–473.Google Scholar
Ho, C.-M. & Huerre, P. 1984 Perturbed free shear layers. Ann. Rev. Fluid Mech. 16, 365–424.Google Scholar
Huerre, P. & Monkewitz, P. A. 1985 Absolute and convective instabilities in free shear layers. J. Fluid Mech. 159, 151–168.Google Scholar
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Ann. Rev. Fluid Mech. 22, 473–537.Google Scholar
Humphrey, J. A. C. & Li, S. 1981 Tilting, stretching, pairing and collapse of vortex structures in confined counter-current flows. Trans. ASME I: J. Fluids Engng 101, 466–470.Google Scholar
Husain, Z. D. & Hussain, A. K. M. F. 1979 Axisymmetric mixing layer: influence of the initial and boundary conditions. AIAA J. 17, 48–55.Google Scholar
Hussain, A. K. M. F. & Zaman, K. B. M. Q. 1978 The free shear layer tone phenomenon and probe interference. J. Fluid Mech. 87, 349–383.Google Scholar
Jackson, C. P. 1987 A finite-element study of the onset of vortex shedding in flow past variously shaped bodies. J. Fluid Mech. 182, 23–45.Google Scholar
Karniadakis, G. E. & Triantafyllou, G. S. 1989 Frequency selection and asymptotic states in laminar wakes. J. Fluid Mech. 199, 441–469.Google Scholar
Kelly, R. E. 1967 On the stability of an inviscid shear layer which is periodic in space and time. J. Fluid Mech. 27, 657–689.Google Scholar
Kibens, V. 1989 Jet flows and turbulence control. McDonnell Douglas Research Laboratories Rep. MDRL 89–106.Google Scholar
Koch, W. 1985 Local instability characteristics and frequency determination of self-excited wake flows. J. Sound Vib. 99, 53–83.Google Scholar
Kyle, D. & Sreenivasan, K. R. 1989 Stability properties of He/air jets. Proc. ASME Fluids Engng Spring. Conf., La Jolla.
Mathis, C., Provansal, M. & Boyer, L. 1984 The Bénard—von Kármán instability: an experimental study near the threshold. J. Phys. Lett. 45, 483–491.Google Scholar
Michalke, A. 1964 On the inviscid instability of the hyperbolic tangent velocity profile. J. Fluid Mech. 19, 543–556.Google Scholar
Michalke, A. 1965 On spatially growing disturbances in an inviscid shear layer. J. Fluid Mech. 23, 521–544.Google Scholar
Michalke, A. 1971 Instabilität eines kompressiblen runden Freistrahls under Berücksichtigung des Einflusses der Strahlgrenzschichtdicke. Z. Flugwiss. 19, 319–328.Google Scholar
Miksad, R. W. 1972 Experiments on the nonlinear stages of free shear layer transition. J. Fluid Mech. 56, 695–719.Google Scholar
Monkewitz, P. A. 1988 The absolute and convective nature of instability in two-dimensional wakes at low Reynolds numbers. Phys. Fluids 31, 999–1006.Google Scholar
Monkewitz, P. A., Bechert, D. W., Barsikow, B. & Lehmann, B. 1990 Self-excited oscillations and mixing in a heated round jet. J. Fluid Mech. 213, 611–639.Google Scholar
Monkewitz, P. A. & Huerre, P. 1982 The influence of the velocity ratio on the spatial instability of mixing layers. Phys. Fluids 25, 1137–1143.Google Scholar
Monkewitz, P. A. & Nguyen, L. N. 1987 Absolute instability in the near wake of two-dimensional bluff bodies. J. Fluids Struct. 1, 165–184.Google Scholar
Monkewitz, P. A. & Sohn, K. D. 1988 Absolute instability in hot jets. AIAA J. 26, 911–916.Google Scholar
Morkovin, M. & Paranjape, S. V. 1971 Acoustic excitation of shear layers. Z. Flugwiss. 19, 328–335.Google Scholar
Niccum, D. L. 1990 The influence of velocity ratio on a counterflowing circular jet. M.S. thesis, University of Minnesota.
Perry, A. E. & Lim, T. T. 1978 Coherent structures in coflowing jets and wakes. J. Fluid Mech. 88, 451–463.Google Scholar
Perry, A. E., Lim, T. T. & Chong, M. S. 1980 The instantaneous velocity fields of coherent structures in coflowing jets and wakes. J. Fluid Mech. 101, 243–256.Google Scholar
Petersen, R. A. 1978 Influence of wave dispersion on vortex pairing in a jet. J. Fluid Mech. 89, 469–495.Google Scholar
Provansal, M., Mathis, C. & Boyer, L. 1987 Bénard—von Kármán instability: transient and forced regimes. J. Fluid Mech. 182, 1–22.Google Scholar
Raman, G., Zaman, K. B. M. Q. & Rice, E. J. 1989 Initial turbulence effect on jet evolution with and without tonal excitation.. Phys. Fluids A 1, 1240–1248.Google Scholar
Ramshankar, R. 1988 The dynamics of countercurrent mixing layers. Ph.D. thesis, Yale University.
Sreenivasan, K. R., Raghu, S. & Kyle, D. 1989 Absolute instability in variable density round jets. Exp. Fluids 7, 309–317.Google Scholar
Sreenivasan, K. R., Strykowski, P. J. & Olinger, D. J. 1987 Hopf bifurcation, Landau equation and vortex shedding behind circular cylinders. In Proc. Forum Unsteady Flow Sep. (ed. K. Ghia), vol. 52, pp. 1–13 ASME.
Strykowski, P. J. & Niccum, D. L. 1989 Turbulence suppression in axisymmetric counterflowing jets by self-excitation. Bull. Am. Phys. Soc. 34, 2326 (abstract only).Google Scholar
Strykowski, P. J. & Sreenivasan, K. R. 1990 On the formation and suppression of vortex ‘shedding’ at low Reynolds numbers. J. Fluid Mech. 218, 71–107.Google Scholar
Stuart, J. T. 1958 On the nonlinear mechanics of hydrodynamic stability. J. Fluid Mech. 4, 1–21.Google Scholar
Tan-Atichat, J. 1980 Effects of axisymmetric contractions of various scales. Ph.D. thesis, Illinois Institute of Technology.
Thorpe, A. S. 1968 A method of producing a shear flow in a stratified fluid. J. Fluid Mech. 32, 693–704.Google Scholar
Thorpe, A. S. 1971 Experiments on instability and turbulence in a stratified shear flow: miscible fluids. J. Fluid Mech. 46, 299–319.Google Scholar
Wille, R. 1963 Beiträge zur Phänomenologie der Freistrahlen. Z. Flugwiss. 11, 222–233.Google Scholar
Winant, C. D. & Browand, F. K. 1974 Vortex pairing, the mechanism of turbulent mixing-layer growth at moderate Reynolds number. J. Fluid Mech. 63, 237–255.Google Scholar
Zaman, K. B. M. Q. & Hussain, A. K. M. F. 1980 Vortex pairing in a circular jet under controlled excitation. Part 1. General jet response. J. Fluid Mech. 101, 449–491.Google Scholar
Zaman, K. B. M. Q. & Hussain, A. K. M. F. 1981 Turbulence suppression in free shear flows by controlled excitation. J. Fluid Mech. 103, 133–159.Google Scholar
Zebib, A. 1987 Stability of viscous flow past a circular cylinder. J. Engng Maths 21, 155–165.Google Scholar