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Local stability analysis of an inviscid transverse jet

Published online by Cambridge University Press:  22 May 2007

LEONARDO S. de B. ALVES ,
ROBERT E. KELLY  and
ANN R. KARAGOZIAN
LEONARDO S. de B. ALVES
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, Los Angeles, CA 90095-1597, USA
ROBERT E. KELLY
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, Los Angeles, CA 90095-1597, USA
ANN R. KARAGOZIAN
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, Los Angeles, CA 90095-1597, USA
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Abstract

A local linear stability analysis is performed for a round inviscid jet with constant density that is injected into a uniform crossflow of the same density. The baseflow is obtained from a modified version of the inviscid transverse jet near-field solution of Coelho & Hunt (J. Fluid Mech. vol. 200, 1989, p. 95) which is valid for small values of the crossflow-to-jet velocity ratio λ. A Fourier expansion in the azimuthal direction is used to couple the disturbances with the three-dimensional crossflow. The spatial growth rates of the modes corresponding to the axisymmetric and first helical modes of the free jet as λ → 0 increase as λ increases. The diagonal dominance of the dispersion relation matrix is used as a quantitative criterion to estimate the range of velocity ratios (0 < λ < λc) within which the transverse jet instability can be considered to have a structure similar to that of the free jet. Further, we show that for λ>0 positive and negative helical modes have different growth rates, suggesting an inherent weak asymmetry in the transverse jet.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 581 , 25 June 2007 , pp. 401 - 418
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

de B. Alves, L. S. 2006 Transverse jet shear-layer instabilities: Linear stability analysis and numerical simulations. PhD thesis, University of California at Los Angeles, Los Angeles, USA.Google Scholar
de B. Alves, L. S., Kelly, R. E. & Karagozian, A. R. 2006 Transverse jet shear-layer instabilities. Part 2. Linear analysis for large jet-to-crossflow velocity ratio. J. Fluid Mech. (submitted).Google Scholar
Batchelor, G. K. & Gill, A. E. 1962 Analysis of the stability of axisymmetric jets. J. Fluid Mech. 14, 529–551.CrossRefGoogle Scholar
Blanchard, J. N., Brunet, Y. & Merlen, A. 1999 Influence of a counter rotating vortex pair on the stability on a jet in cross flow: An experimental study by flow visualizations. Exps. Fluids. 26, 63–74.CrossRefGoogle Scholar
Blossey, P. N. & Schmid, P. J. 2002 Global stability analysis of a jet in cross flow. Bull. Am. Phys. Soc. 47 (10), 92.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.Google Scholar
Coelho, S. L. V. 1988 The dynamics of the near field of entraining jets in cross flows. PhD thesis, University of Cambridge.Google Scholar
Coelho, S. L. V. & Hunt, J. C. R. 1989 The dynamics of the near field of strong jets in cross flow. J. Fluid Mech. 200, 95–120.CrossRefGoogle Scholar
Corke, T. C. & Kusek, S. M. 1993 Resonance in axisymmetric jets with controlled helical-mode input. J. Fluid Mech. 249, 307–336.CrossRefGoogle Scholar
Corke, T. C., Shakib, F. & Nagib, H. M. 1991 Mode selection and resonant phase locking untable axisymmetric jets. J. Fluid Mech. 223, 253–311.CrossRefGoogle Scholar
Cortelezzi, L. & Karagozian, A. R. 2001 On the formation of the counter-rotating vortex pair in transverse jets. J. Fluid Mech. 446, 347–373.CrossRefGoogle Scholar
Crow, S. C. & Champagne, F. M. 1971 Orderly structure in jet turbulence. J. Fluid Mech. 48, 547–591.CrossRefGoogle Scholar
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.Google Scholar
Fric, T. F. & Roshko, A 1994 Vortical structure in the wake of a transverse jet. J. Fluid Mech. 279, 1–47.CrossRefGoogle Scholar
Godrèche, C. & Manneville, P. 1998 Hydrodynamics and Nonlinear Instabilities. Cambridge University Press.CrossRefGoogle Scholar
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473–537.CrossRefGoogle Scholar
Huq, P. & Dhanak, M. R. 1996 The bifurcation of circular jets in cross flow. Phys. Fluids 8 (3), 754–763.CrossRefGoogle Scholar
Kamotani, Y. & Greber, I. 1974 Experiments on confined turbulent jets in a cross flow. Tech. Rep. CR - 2392. NASA.CrossRefGoogle Scholar
Karagozian, A. R., Cortelezzi, L. & Soldati, A. 2003 Manipulation and Control of Transverse Jets. CISM Courses and Lectures, vol. 439. Springer.Google Scholar
Kelso, R. M., Lim, T.T. & Perry, A. E. 1996 An experimental study of round jets in cross flow. J. Fluid Mech. 306, 111–144.CrossRefGoogle Scholar
Kuzo, D. M. 1995 An experimental study of the turbulent transverse jet. PhD thesis, California Institute of Technology.Google Scholar
Lin, S. P. 2003 Breakup of Liquid Sheets and Jets. Cambridge University Press.CrossRefGoogle Scholar
Margason, R. J. 1993 Fifty years of jet in cross flow research. AGARD-CP-534 1, 1–141.Google Scholar
Megerian, S., Davitian, J., de B. Alves, L. S. & Karagozian, A. R. 2006 Transverse jet shear-layer instabilities. protect Part I) experimental studies. J. Fluid Mech. (submitted).CrossRefGoogle Scholar
Michalke, A. 1971 Instabilität eines kompressiblen runden freistrahls unter beräcksichtigung des einflusses der strahlgrenzschichtdicke. Z. Flugwiss. 19 (8–9), 319–328, English translation: NASA TM 75190 (1977).Google Scholar
Needham, D. J., Riley, N. & Smith, J. H. B. 1988 A jet in cross flow. J. Fluid Mech. 188, 159–184.CrossRefGoogle Scholar
Smith, S. H. & Mungal, M. G. 1998 Mixing, structure and scaling of the jet in cross flow. J. Fluid Mech. 357, 83–122.CrossRefGoogle Scholar
Wolfram, S. 1999 The Mathematica Book, 4th edn. Cambridge: Wolfram Media.Google Scholar