Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2025-01-03T17:32:25.339Z Has data issue: false hasContentIssue false
  • English
  • Français

Low-dimensional characteristics of a transonic jet. Part 1. Proper orthogonal decomposition

Published online by Cambridge University Press:  10 October 2008

C. E. TINNEY ,
M. N. GLAUSER  and
L. S. UKEILEY
C. E. TINNEY
Affiliation:
Department of Aerospace Engineering & Engineering Mechanics, University of Texas at Austin, Austin, TX 78712, USA
M. N. GLAUSER
Affiliation:
Department of Mechanical & Aerospace Engineering, Syracuse University, Syracuse, NY 13244, USA
L. S. UKEILEY
Affiliation:
Department of Mechanical & Aerospace Engineering, University of Florida, Shalimar, FL 32579, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

An experimental investigation concerning the most energetic turbulent features of the flow exiting from an axisymmetric converging nozzle at Mach 0.85 and ambient temperature is discussed using planar optical measurement techniques. The arrangement of the particle image velocimetry (PIV) system allows for all three components of the velocity field to be captured along the (r, θ)-plane of the jet at discrete streamwise locations between x/D=3.0 and 8.0 in 0.25 diameter increments. The ensemble-averaged (time-suppressed) two-point full Reynolds stress matrix is constructed from which the integral eigenvalue problem of the proper orthogonal decomposition (POD) is applied using both scalar and vector forms of the technique. A grid sensitivity study indicates that the POD eigenvalues converge safely to within 1% of their expected value when the discretization of the spatial grid is less than 30% of the integral length scale or 10% of the shear-layer width. The first POD eigenvalue from the scalar decomposition of the streamwise component is shown to agree with previous investigations for a range of Reynolds numbers and Mach numbers with a peak in azimuthal mode 5 at x/D=3.0, and a gradual shift to azimuthal mode 2 by x/D=8.0. The eigenvalues from the scalar POD of the radial and azimuthal components are shown to be much lower-dimensional with most of their energy residing in the first few azimuthal modes, that is modes 0, 1 and 2, with little change in the relative energies along the streamwise direction. From the vector decomposition, the azimuthal eigenspectra of the first two POD modes shift from a peak in azimuthal mode 5 at x/D=3.0, followed by a gradual decay to azimuthal mode 2 at x/D=8.0, the differences in the peak energies being very subtle. The conclusion from these findings is that when the Mach number is subsonic and the Reynolds number sufficiently large, the structure of the turbulent jet behaves independently of these factors.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 612 , 10 October 2008 , pp. 107 - 141
Copyright
Copyright © Cambridge University Press 2008

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. 1991 Particle-imaging techniques for experimental fluid mechanics. Annu. Rev. Fluid. Mech. 23, 261–304.Google Scholar
Adrian, R. J. & Yao, C. S. 1986 Power spectra of fluid velocities measured by laser Doppler velocimetry. Exps. Fluids 5, 17–28.CrossRefGoogle Scholar
Agüí, J. C. & Jiménez, J. 1987 On the performance of particle tracking. J. Fluid Mech. 185, 447–468.Google Scholar
Alkislar, M. B., Krothapalli, A. & Butler, G. W. 2007 The effect of streamwise vortices on the aeroacoustics of a Mach 0.9 jet. J. Fluid Mech. 578, 139–169.CrossRefGoogle Scholar
Arakeri, V. H., Krothapalli, A., Siddavaram, V., Alkislar, M. B. & Lourenco, L. M. 2003 On the use of microjets to suppress turbulence in a Mach 0.9 axisymmetric jet. J. Fluid Mech. 490, 75–98.Google Scholar
Aubry, N., Holmes, P., Lumley, J. & Stone, E. 1988 The dynamics of coherent structures in the wall region of a turbulent boundary layer. J. Fluid Mech. 192, 115–173.CrossRefGoogle Scholar
Bastin, F., Lafon, P. & Candel, S. 1997 Computation of jet mixing noise due to coherent structures: the plane jet case. J. Fluid Mech. 335, 261–304.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.Google Scholar
Bonnet, J. P., Delville, J., Glauser, M. N., Antonia, R. A., Bisset, D. K., Cole, D. R., Fiedler, H. E., Garem, J. H., Hilberg, D., Jeong, J., Kevlahan, N. K. R., Ukeiley, L. S. & Vincendeau, E. 1998 Collaborative testing of eddy structure identification methods in free turbulent shear flows. Exps. Fluids 25, 197–225.Google Scholar
Bradshaw, P., Ferriss, D. H. & Johnson, R. F. 1964 Turbulence in the noise-producing region of a circular jet. J. Fluid Mech. 19, 591–624.Google Scholar
Bridges, J. 2006 Effect of heat on space–time correlations in jets. AIAA Paper 2006-2534.Google Scholar
Brown, G. L. & Roshko, A. 1974 Density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775–816.CrossRefGoogle Scholar
Caraballo, E., Samimy, M., Scott, J., Narayanan, S. & DeBonis, J. 2003 Application of proper orthogonal decomposition to a supersonic axisymmetric jet. AIAA J. 41, 1–12.CrossRefGoogle Scholar
Citriniti, J. H. & George, W. K. 1997 The reduction of spatial aliasing by long hot-wire anemometer probes. Exps. Fluids 23, 217–224.Google Scholar
Citriniti, J. H. & George, W. K. 2000 Reconstruction of the global velocity field in the axisymmetric mixing layer utilizing the proper orthogonal decomposition. J. Fluid Mech. 418, 137–166.CrossRefGoogle Scholar
Delville, J. 1994 Characterization of the organization in shear layers via the proper orthogonal decomposition. Appl. Sci. Res. 53, 263–281.CrossRefGoogle Scholar
Delville, J., Ukeiley, L., Cordier, L., Bonnet, J. P. & Glauser, M. N. 1999 Examination of large scale structures in a turbulent plane mixing layer. Part 1. Proper orthogonal decomposition. J. Fluid Mech. 391, 91–122.Google Scholar
Dosanjh, D. S., Bhutiani, P. K. & Ahuja, K. K. 1977 Supersonic jet noise suppression by coaxial multi-nozzle cold/heated jet flows. Dept of Transportation Final Rep., Washington DC, March, 1977.Google Scholar
Ewing, D. & Citriniti, J. 1999 Examination of a LSE/POD complementary technique using single and multi-time information in the axisymmetric shear layer. Proc. IUTAM Symp. Lynby, Denmark, 25–29 May, 1997 (ed. Sorensen, J. N., Hopfinger, E. J. & Aubry, N.), pp. 375–384. Kluwer.CrossRefGoogle Scholar
Ffowcs Williams, J. E. & Kempton, A. J. 1978 The noise from the large scale structure of a jet. J. Fluid Mech. 84, 673–694.Google Scholar
Freund, J. B. 2001 Noise sources in a low-Reynolds-number turbulent jet at Mach 0.9. J. Fluid Mech. 438, 277–305.Google Scholar
Freund, J. B. & Colonius, T. 2002 POD analysis of sound generation by a turbulent jet. AIAA Paper 2002-0072.Google Scholar
Gamard, S., Jung, D. & George, W. K. 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, 205–230.CrossRefGoogle Scholar
George, W. K., Beuther, P. D. & Arndt, R. E. A. 1984 Pressure spectra in turbulent free shear flows. J. Fluid Mech. 148, 155–191.Google Scholar
Glauser, M. N. 1987 Coherent structures in the axisymmetric turbulent jet mixing layer. PhD Dissertation, State University of New York at Buffalo. Amherst.CrossRefGoogle Scholar
Glauser, M. N. & George, W. K. 1987 Orthogonal decomposition of the axisymmetric jet mixing layer including azimuthal dependence. Advances in Turbulence (ed. Comte-Bellot, G. & Mathieu, J.), pp. 357–366. Springer.Google Scholar
Glauser, M. N. & George, W. K. 1992 Application of multipoint measurements for flow characterization. Expl Thermal Fluid Sci. 11, 617–632.Google Scholar
Guitton, A., Tinney, C. E., Jordan, P. & Delville, J. 2007 Measurements in a co-axial subsonic jet. AIAA Paper 2007-0015.CrossRefGoogle Scholar
Hall, A. M., Glauser, M. N. & Tinney, C. E. 2005 Experimental investigation of the pressure–velocity correlation of an M = 0.6 axisymmetric jet. AIAA Paper 2005-5294.Google Scholar
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, 263–294.Google 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. & Thomas, F. O. 2007 Coherent structures in a turbulent jet via a vector implementation of the proper orthogonal decomposition. J. Fluid Mech. 571, 281–326.Google 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
Juve, D., Sunyach, M. & Comte-Bellot, G. 1980 Intermittency of the noise emission in subsonic cold jets. J. Sound Vib. 71:3, 319–332.Google Scholar
Keane, R. D. & Adrian, R. J, 1992 Theory of cross-correlation analysis of PIV images. Appl. Sci. Res. 49, 191–215.Google Scholar
Kerhervé, F., Jordan, P., Gervais, Y., Valière, J. C. & Braud, P. 2004 Two-point laser Doppler velocimetry measurements in a Mach 1.2 cold supersonic jet for statistical aeroacoustic source model. Exps. Fluids 37, 419–437.CrossRefGoogle Scholar
Lau, J. C., Morris, P. J. & Fisher, M. J. 1979 Measurements in subsonic and supersonic free jets using a laser velocimeter. J. Fluid Mech. 93, 1–27.Google Scholar
Lighthill, M. J. 1952 On sound generated aerodynamically: general theory. Proc. R. Soc. Lond. 211, 564–587.Google Scholar
Lumley, J. L. 1967 The structure of inhomogenous turbulent flows In Atmospheric Turbulence and Radio Wave Propagation (ed. Yaglom, A. M. & Tatarski, V. I.), pp. 166–178. Nauka, Moscow.Google Scholar
Meinhart, C. D. & Wereley, S. T. 2003 Theory of diffraction-limited resolution in micro particle image velocimetry. Meas. Sci. Technol. 14, 1047–1053.Google Scholar
Melling, A. 1997 Tracer particles and seeding for particle image velocimetry. Meas. Sci. Technol. 8, 1406–1416.Google Scholar
Meyers, J. F. 1991 Generation of particles and seeding. Von Karman Inst. Fluid Dyn. 8, 1–42.Google Scholar
Michalke, A. & Fuchs, H. V. 1975 On turbulence and noise of an axisymmetric shear flow. J. Fluid Mech. 70, 179–205.Google Scholar
Moin, P. & Moser, R. D. 1989 Characteristic eddy decomposition of turbulence in a channel. J. Fluid Mech. 200, 471–509.Google Scholar
Morris, P. J. 1976 Turbulence measurements in subsonic and supersonic axisymmetric jets in a parallel stream. AIAA J. 14, 1468–1475.Google Scholar
Narayanan, S., Barber, T. J. & Polak, D. R. 2002 High subsonic jet experiments: turbulence and noise generation studies. AIAA J. 40, 430–437.Google Scholar
Noack, B. R., Papas, P. & Monkewitz, P. A. 2005 The need for a pressure-term representation in empirical Galerkin models of incompressible shear flows. J. Fluid Mech. 523, 339–365.CrossRefGoogle Scholar
Raffel, M., Willert, C. & Kompenhans, J. 1998 Particle Image Velocimetry. Springer.Google Scholar
Ribner, H. S. 1969 Quadrupole correlations governing the pattern of jet noise. J. Fluid Mech. 38, 1–24.CrossRefGoogle Scholar
Seiner, J. 1998 A new rational approach to jet noise reduction. Theor. Comput. Fluid Dyn. 10, 373–383.Google Scholar
Sirovich, L. 1987 Turbulence and the dynamics of coherent structures. Part I. Coherent structures. Q. Appl. Maths 45, 561–571.Google Scholar
Stromberg, J. L., McLaughlin, D. K. & Trout, T. R. 1980 Flow field and acoustic properties of a Mach number 0.9 jet at low Reynolds number. J. Sound Vib. 72, 159–176.Google Scholar
Tam, C. K. W. 1998 Jet Noise: Since 1952. Theor. Comput. Fluid Dyn. 10, 393–405.Google Scholar
Taylor, J. A. 2001 Dynamics of large scale structures in turbulent shear layers. PhD Dissertation, Clarkson University Rep. MAE-354, Potsdam, NY.Google Scholar
Taylor, J. T., Ukeiley, L. S. & Glauser, M. N. 2001 A low-dimensional description of the compressible axisymmetric shear layer. AIAA Paper 2001-0292.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.Google Scholar
Tinney, C. E. 2005 Low-dimensional techniques for sound source identification in high speed jets. PhD Dissertation, Syracuse University, Syracuse.Google Scholar
Tinney, C. E. & Jordan, P. 2008 The near-field pressure surrounding co-axial subsonic jets. J. Fluid Mech. 611, 175–204.Google Scholar
Tinney, C. E., Hall, A., Glauser, M. N., Ukeiley, L. S. & Coughlin, T. 2004 Designing an anechoic chamber for the experimental study of high speed heated jets. AIAA Paper 2004-0010.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.Google Scholar
Tinney, C. E., Coiffet, F., Delville, J., Glauser, M., Jordan, P. & Hall, A. 2006 a On spectral linear stochastic estimation. Exps. Fluids 41, 763–775.CrossRefGoogle Scholar
Tinney, C. E., Glauser, M. N., Eaton, E. & Taylor, J. A. 2006 b Low-dimensional azimuthal characteristics of suddenly expanding axisymmetric flows. J. Fluid Mech. 567, 141–155.CrossRefGoogle Scholar
Tinney, C. E., Jordan, P., Delville, J., Hall, A. M. & Glauser, M. N. 2006 c A time-resolved estimate of the turbulence and sound source mechanisms in a subsonic jet flow. J. Turbulence 8, 1–20.Google Scholar
Tinney, C. E., Ukeiley, L. S. & Glauser, M. N. 2008 Low-dimensional characteristics of a transonic jet. Part 2. Estimate and far-field prediction. J. Fluid Mech. (in press).Google Scholar
Townsend, A. A. 1956 The structure of turbulent shear flow, 2nd edn.Cambridge University Press.Google Scholar
Ukeiley, L. S. & Ponton, M. K. 2004 On the near field pressure of a transonic axisymmetric jet. Intl J. Aeroacoust. 3, 43–66.Google Scholar
Ukeiley, L., Seiner, J. & Ponton, M. 1999 Azimuthal structure of an axisymmetric jet mixing layer. ASME FEDSM 99-7252.Google Scholar
Ukeiley, L., 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., Tinney, C. E., Mann, R. & Glauser, M. N. 2007 Spatial correlations in a transonic jet. AIAA J. 45, 1357–1369.Google Scholar
Wänström, M., George, W. K. & Meyer, K. E. 2006 Stereoscopic PIV and POD applied to the far turbulent axisymmetric jet. AIAA Paper 2006-3368.Google Scholar
Westerweel, J. 1998 Effect of sensor geometry on the performance of PIV interrogation. Laser Techniques Applied to Fluid Mech, 9th Intl Symp., Lisbon, Portugal, pp. 37–55. Springer.Google Scholar
Westerweel, J., Dabiri, D. & Gharib, M. 1997 The effect of a discrete window offest on the accuracy of cross-correlation analysis of digital PIV recordings. Exps. Fluids 23, 20–28.CrossRefGoogle Scholar
Willert, C. E. & Gharib, M. 1991 Digital particle image velocimetry. Exps. Fluids 10, 181–193.Google Scholar
Wills, J. A. B. 1964 On convection velocities in turbulent shear flows. J. Fluid Mech. 20, 417–432.CrossRefGoogle 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.CrossRefGoogle Scholar