Hostname: page-component-76fb5796d-r6qrq Total loading time: 0 Render date: 2024-04-26T19:16:36.769Z Has data issue: false hasContentIssue false
  • English
  • Français

Coherent structure in a turbulent jet via a vector implementation of the proper orthogonal decomposition

Published online by Cambridge University Press:  04 January 2007

M. O. IQBAL  and
F. O. THOMAS
M. O. IQBAL
Affiliation:
Center for Flow Physics and Control, Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA
F. O. THOMAS
Affiliation:
Center for Flow Physics and Control, Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The coherent structure in the near-field of an axisymmetric turbulent jet at a Reynolds number of 3.8 × 105 and Mach number of 0.3 is experimentally characterized by a vector implementation of the proper orthogonal decomposition (POD). The POD eigenfunctions and associated eigenvalues are extracted at several selected streamwise locations in the initial region. The focus on the near-field is motivated by its importance in numerous technical applications. Results show a rapid energy convergence with POD mode number. Examination of the relative energy contained in the combined azimuthal and radial components of the POD modes reveals that it is comparable to that in the streamwise component. The streamwise evolution of the eigenvalue spectra is characterized by a remarkable variation in the azimuthal mode number energy distribution, leading to the dominance of azimuthal mode m = 1 beyond the end of the jet core. In contrast, a scalar implementation using only the streamwise component shows the dominance of mode m = 2 which is consistent with previous scalar implementations of the POD. For a given azimuthal mode number, the eigenvalue spectra exhibit a broad peak which occurs at a constant value of Strouhal number based on local shear layer momentum thickness and local jet maximum velocity. The phase information required for a local reconstruction of the jet structure is obtained by projecting the POD eigenmodes onto instantaneous realizations of the flow at fixed streamwise locations. The instantaneous realizations are obtained by utilizing cross-stream arrays of multi-sensor probes in conjunction with linear stochastic estimation (LSE). Results clearly show the local dynamic behaviour of each component of the jet structure.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 571 , 25 January 2007 , pp. 281 - 326
Copyright
Copyright © Cambridge University Press 2007

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

REFERENCES

Adrian, R. J. 1977 On the role of conditional averages in turbulent theory. In Turbulence in Liquids: Proc, 4th Biennial Symposium on Turbulence in Liquids (ed. Patteson, G. & Zakin, J.), pp. 322–332. Science Press, Princeton.Google Scholar
Adrian, R. J. 1979 Conditional eddies in isotropic turbulence. Phys. Fluids 22, 2065–2070.CrossRefGoogle Scholar
Adrian, R. J. 1994 Stochastic estimation of conditional structure: A review. Appl. Sci. Res. 53, 291–303.CrossRefGoogle Scholar
Arndt, R. E. A., Long, D. F. & Glauser, M. N. 1997 The proper orthogonal decomposition of pressure fluctuations surrounding a turbulent jet. J. Fluid Mech. 340, 1–33.CrossRefGoogle Scholar
Aubry, N., Holmes, P., Lumley, J. L. & Stone, E. 1988 The dynamics of coherent structures in the wall region of the turbulent shear layer. J. Fluid Mech. 192, 115–175.CrossRefGoogle Scholar
Bendat, S. J. & Piersol, A. G. 1986 Random Data, 2nd Edn. Wiley Interscience.Google Scholar
Berkooz, G., Holmes, P. & Lumley, J. L. 1993 The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech., 25, 539–575.CrossRefGoogle Scholar
Bonnet, J. P., Cole, D. R., Delville, J., Glauser, M. N. & Ukeiley, L. S. 1994 Stochastic estimation and proper orthogonal decomposition: complementary techniques for identifying structure. Exps. Fluids 17, 307–314.CrossRefGoogle Scholar
Bonnet, J. P. & Delville, J. 1996 General concepts on structure identification. In Eddy Structure Identification (ed. Bonnet, J. P.). Springer.CrossRefGoogle Scholar
Bonnet, J. P. & Delville, J. 2001 Review of coherent structures in turbulent free shear flows and their possible influence on computational methods. Flow, Turbulence Combust. 66, 333–353.CrossRefGoogle Scholar
Bradshaw, P., Ferriss, D. H. & Johnson, R. F. 1964 Turbulence in the noise-producing region of a circular jet. J. Fluid Mech. 18, 591–624.CrossRefGoogle Scholar
Chu, H. C. 1993 An experimental study of nonlinear wave coupling and energy transfer characterizing the transition of a planar jet shear layer. PhD dissertation, University of Notre Dame.Google Scholar
Citriniti, J. H. & George, W. K. 2000 Reconstruction of the global velocity field in the axisymmetric mixing layer utilizing the POD. J. Fluid Mech. 418, 137–166.CrossRefGoogle Scholar
Cohen, J. & Wygnanski, I. 1987 The evolution of instabilities in the axisymmetric jet. Part 1. The linear growth of the disurbances near the nozzle. J. Fuid Mech. 176, 191–219.CrossRefGoogle Scholar
Crow, S. C. & Champagne, F. H. 1971 Orderly structure in jet turbulence. J. Fluid Mech. 48, 547–591.CrossRefGoogle Scholar
Davies, P. O. A. L., Ko, N. M. W. & Bose, B. 1967 The local pressure field of turbulent jets. Aero. Res. Counc. Paper 989.Google Scholar
Delville, J., Ukeiley, L. S., Cordier, L., Bonnet, J. P. & Glauser, M. N. 1999 Examination of large scale structures in a plane mixing layer. Part 1. Proper orthogonal decmposition. J. Fluid Mech. 391, 91–122.CrossRefGoogle Scholar
Drubka, R. E. 1981 Instabilities in the near field of turbulent jets and their dependence on initial conditions. PhD Dissertation, Illinois Institute of Technology, Chicago.CrossRefGoogle Scholar
Gamard, S., George, W. K. & Jung, D. 2004 Downstream evolution of the most energetic modes in a turbulent axisymmetric jet at high Reynolds number. Part 2. The far-field region. J. Fluid Mech. 514, 173–204.CrossRefGoogle Scholar
Glauser, M. N. 1987 Coherent structures in axisymmetric turbulent jet mixing layer. PhD Dissertation, SUNY, Buffalo.CrossRefGoogle Scholar
Glauser, M. N. & George, W. K. 1987 Orthogonal decomposition of the axisymmetric jet mixing layer including azimuthal dependence. In Advances in Turbulence (ed. Comte-Bellot, J. C. et al. ) Springer.Google Scholar
Glauser, M. N. & George, W. K. 1992 Application of multipoint meassurements for flow characterization. Expl Thermal Fluid Sci. 5, 617–632.CrossRefGoogle Scholar
Glauser, M. N., Leib, S. J. & George, W. K. 1987 Coherent structures in axisymmetric turbulent jet mixing layer. In Turbulent Shear Flows 5 (ed. Durst, J. C. et al. ). Springer.Google Scholar
Gordeyev, S. V. & Thomas, F. O. 2000 Coherent structure in turbulent planar jet. Part 1. Extraction of POD eigenmodes and their self-similarity. J. Fluid Mech. 414, 145–194.CrossRefGoogle Scholar
Gordeyev, S. V. & Thomas, F. O. 2002 Coherent structure in turbulent planar jet. Part 2. Structural topology via POD eigenmode projection. J. Fluid Mech. 460, 349–380.CrossRefGoogle Scholar
Gutmark, E. & Ho, C. M. 1983 Preferred modes and the spreading rates of jets. Phys. Fluids 26, 2932–2938.CrossRefGoogle Scholar
Gutmark, E. & Wygnanski, I. 1976 The planar turbulent jet. J. Fluid Mech. 73, 465–495.CrossRefGoogle Scholar
Ho, C. M. & Huang, L. S. 1982 Subharmonics and vortex merging in mixing layers. J. Fluid Mech. 119, 443–473.CrossRefGoogle Scholar
Holmes, P., Lumley, J. L. & Berkooz, G. 1996 Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge University Press.CrossRefGoogle Scholar
Hussain, A. K. M. F. 1986 Coherent structures and turbulence. J. Fluid Mech. 173, 303–356.CrossRefGoogle Scholar
Hussein, H. J., Capp, S. P. & George, W. K. 1994 Velocity measurements in a high-Reynolds-number, momentum conserving, axisymmetric, turbulent jet. J. Fluid Mech. 258, 31–75.CrossRefGoogle Scholar
Iqbal, M. O. 2006 Coherent structure in a turbulent axisymmetric jet via a vector implementation of the proper orthogonal decomposition. PhD Dissertation, University of Notre Dame, Notre Dame, IN.Google Scholar
Jeong, J. & Hussain, A. K. M. F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
Jung, D., Gamard, S. & George, W. K. 2004 Downstream evolution of the most energetic modes in a turbulent axisymmetric jet at high Reynolds number. Part 1. The near-field region. J. Fluid Mech. 514, 173–204.CrossRefGoogle Scholar
Karhunen, K. 1946 ‘Zur Spektraltheorie Stochasticher. Prozessa Ann. Acad. Sci. Fennicae 37Google Scholar
Kibens, V. 1981 The limit of initial shear layer influence on jet development. AIAA Paper 81-1960.Google Scholar
Loéve, M. M. 1955 ‘Probability Theory. Van Nostrand.Google Scholar
Lumley, J. 1967 The structure of inhomogeneous turbulent flows. In Proc. Intl Colloq. on Fine Scale Structure of the Atmosphere and its Influence on Radio Waves (ed. Yaglam, A. M. & Tatarsky, V. I.), pp. 166–178. Doklady Akademii Nauk SSSR, Moscow, Nauka.Google Scholar
Lumley, J. 1970 Stochastic Tools in Turbulence. Academic.Google Scholar
Monkewitz, P. A. 1988 Subharmonic resonance, pairing and shredding in the mixing layer. J. Fluid Mech. 188, 223–252.CrossRefGoogle Scholar
Tam, C. K. W. 1986 Excitation of instability waves by sound - A physical interpretation. J. Sound Vib. 105, 169–172.CrossRefGoogle Scholar
Taylor, J. A., Ukeiley, L. S. & Glauser, M. N. 2001 A low-dimensional description of the compressible axisymmetric shear layer. AIAA Paper 2001-0292.CrossRefGoogle Scholar
Thomas, F. O. 1991 Structure of mixing layers and jets. Appl. Mech. Rev. 44 (3), 119–153.CrossRefGoogle Scholar
Tinney, C. E., Glauser, M. N. & Ukeiley, L. S. 2005 The evolution of the most energetic modes in a high subsonic Mach number turbulent jet. AIAA Paper 2005-0417.CrossRefGoogle Scholar
Ukeiley, L. S., Cordier, L., Manceau, R., Delville, J., Glauser, M. N. & Bonnet, J. P. 2001 Examination of large-scale structures in a turbulent plane mixing layer. Part 2. Dynamical systems model. J. Fluid Mech., 441, 67–108.CrossRefGoogle Scholar
Ukeiley, L. S. & Glauser, M. N. 1995 Dynamics of large-scale structures in a plane turbulent mixing layer. Rep. MAE-311. Department of Aerospace and Mechanical Engineering, Clarkson University.Google Scholar
Ukeiley, L. S. & Seiner, J. M. 1998 Examination of large scale structures in transonic jet mixing layer. Proc. ASME FEDSM98-5234.Google Scholar
Ukeiley, L. S., Seiner, J. M. & Ponton, M. K. 1999 Azimuthal structure of an axisymmetric jet mixing layer. Proc. ASME FEDSM99-7252.Google Scholar
Walker, S. H. & Thomas, F. O. 1997 Experiments characterizing nonlinear shear layer dynamics in a supersonic rectangular jet undergoing screech. Phys. Fluids 9, 2562–2579.CrossRefGoogle Scholar
Wänström, M., George, W. K. & Meyer, K.-E. 2005 POD applied to stereo PIV data of the far turbulent axisymmetric jet. Bulletin of the 58th APS DFD meeting., Chicago, IL.CrossRefGoogle Scholar
Wygnanski, I. & Fiedler, H. 1969 Some measurements in the self-preserving jet. J. Fluid Mech. 38, 577–612.CrossRefGoogle Scholar
Zaman, K. B. M. Q. & Hussain, A. K. M. F. 1980 Vortex pairing in circular jet under controlled excitation. Part 1. General jet response. J. Fluid Mech. 101, 449–492.CrossRefGoogle Scholar
Zaman, K. B. M. Q. & Hussain, A. K. M. F. 1981 Turbulence supression in free shear flows by controlled excitation. J. Fluid Mech. 103, 133–159.CrossRefGoogle Scholar