Skip to main content Accessibility help
×
×
Home

Instability waves in a low-Reynolds-number planar jet investigated with hybrid simulation combining particle tracking velocimetry and direct numerical simulation

  • TAKAO SUZUKI (a1), HUI JI (a2) and FUJIO YAMAMOTO (a2)
Abstract

Instability waves in a laminar planar jet are extracted using hybrid unsteady-flow simulation combining particle tracking velocimetry (PTV) and direct numerical simulation (DNS). Unsteady velocity fields on a laser sheet in a water tunnel are measured with time-resolved PTV; subsequently, PTV velocity fields are rectified in a least squares sense so that the equation of continuity is satisfied, and they are transplanted to a two-dimensional incompressible Navier–Stokes solver by setting a multiple of the computational time step equal to the frame rate of the PTV system. As a result, the unsteady hybrid velocity field approaches that of the measured one over time, and we can simultaneously acquire the unsteady pressure field. The resultant set of flow quantities satisfies the governing equations, and their resolution is comparable to that of numerical simulation with the noise level much lower than the original PTV data. From hybrid unsteady velocity fields, we extract eigenfunctions using bi-orthogonal decomposition as a spatial problem for viscous instability. We also investigate stability/convergence characteristics of the hybrid simulation referring to linear stability analysis.

Copyright
Corresponding author
Email address for correspondence: takao@its.caltech.edu
Footnotes
Hide All

Present address: Powertrain Development Division, Mazda Motor Corporation, Hiroshima 730-8670, Japan

Footnotes
References
Hide All
Ahluwalia, D. S. & Keller, J. B. 1977 Exact and asymptotic representations of the sound field in a stratified ocean. In Wave Propagation and Underwater Acoustics (ed. Keller, J. B. & Papadakis, J. S.), vol. 70, pp. 1485. Springer.
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, 133.
Barone, M. F. & Lele, S. K. 2005 Receptivity of the compressible mixing layer. J. Fluid Mech. 540, 301335.
Bewley, T. R. & Liu, S. 1998 Optimal and robust control and estimation of linear paths to transition. J. Fluid Mech. 365, 305349.
Blumen, W. 1971 Jet flow instability of an inviscid compressible fluid. J. Fluid Mech. 46, 737747.
Bridges, T. J. & Morris, P. J. 1984 Differential eigenvalue problems in which the parameter appears nonlinearly. J. Comput. Phys. 55, 437460.
Brown, G. L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775816.
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, 137166.
Denissen, N. A. & White, E. B. 2009 Continuous spectrum analysis of roughness-induced transient growth. Phys. Fluids 21, 114105.
Drazin, P. G. & Reid, R. H. 1981 Hydrodynamic Stability, 2nd edn. Cambridge University Press.
Gaster, M. 1962 A note on the relation between temporally-increasing and spatially-increasing disturbances in hydrodynamic stability. J. Fluid Mech. 14, 222224.
Herbert, T. 1997 Parabolized stability equations. Annu. Rev. Fluid Mech. 29, 245283.
Hill, D. C. 1995 Adjoint systems and their role in the receptivity problem for boundary layers. J. Fluid Mech. 292, 183204.
Huerre, P. 1980 The nonlinear stability of a free shear layer in the viscous critical layer regime. Phil. Trans. R. Soc. Lond. 293 (1408), 643672.
Huerre, P. & Monkewitz, P. A. 1990 Local and global stabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473537.
Kampanis, N. A. & Ekaterinaris, J. A. 2006 A staggered grid, high-order accurate method for the incompressible Navier–Stokes equations. J. Comput. Phys. 215 (2), 589613.
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308323.
Ma, X., Karniadakis, G. E., Park, H. & Gharib, M. 2003 DPIV-driven flow simulation: a new computational paradigm. Proc. R. Soc. Lond. A 459, 547565.
Mankbadi, R. R. 1985 On the interaction between fundamental and subharmonic instability waves in a turbulent round jet. J. Fluid Mech. 160, 385419.
Maslowe, S. A. 1991 Barotropic instability of the Bickley jet. J. Fluid Mech. 229, 417426.
Mollendorf, J. C. & Gebhart, B. 1973 An experimental and numerical study of the viscous stability of a round laminar vertical jet with and without thermal buoyancy for symmetric and axisymmetric disturbances. J. Fluid Mech. 61, 367399.
Morris, P. J. 1976 The spatial viscous instability of axisymmetric jets. J. Fluid Mech. 77, 511529.
Morse, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics. McGraw-Hill.
Nishino, K., Kasagi, K. & Hirata, M. 1989 Three-dimensional particle tracking velocimetry based on automated digital image processing. Trans. ASME: J. Fluids Engng 111, 384391.
Nisugi, K., Hayase, T. & Shirai, A. 2004 Fundamental study of hybrid wind tunnel integrating numerical simulation and experiment in analysis of flow field. JSME, Int. J. Ser. B 47 (3), 593604.
Orszag, S. A. 1971 Accurate solution of the Orr–Sommerfeld stability equation. J. Fluid Mech. 50, 689703.
Reynolds, W. C. & Hussain, A. K. M. F. 1972 The mechanics of an oroganized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J. Fluid Mech. 54, 263288.
Rogers, M. M. & Moser, R. D. 1992 The three-dimensional evolution of a plane mixing layer: the Kelvin–Helmholtz rollup. J. Fluid Mech. 243, 183226.
Salwen, H. & Grosch, C. E. 1981 The continuous spectrum of the Orr–Sommerfeld equation. Part 2. Eigenfunction expansions. J. Fluid Mech. 104, 445465.
Sato, H. 1960 The stability and transition of a two-dimensional jet. J. Fluid Mech. 7, 5380.
Sfeir, A. A. 1979 Investigation of three-dimensional turbulent rectangular jets. AIAA J. 17 (10), 10551060.
Sirisup, S., Karniadakis, G. E., Yang, Y. & Rockwell, D. 2004 Wave-structure iteraction: simulation driven by quantitative imaging. Proc. R. Soc. Lond. A 460, 729755.
Spalart, P. R., Moser, R. D. & Rogers, M. M. 1991 Spectral methods for the Navier–Stokes equations with one infinite and two periodic directions. J. Comput. Phys. 96, 297324.
Suzuki, T. & Colonius, T. 2003 Inverse-imaging method for detection of a vortex in a channel. AIAA J. 41 (9), 17431751.
Suzuki, T. & Colonius, T. 2006 Instability waves in a subsonic round jet detected using a near-field phased microphone array. J. Fluid Mech. 565, 197226.
Suzuki, T., Ji, H. & Yamamoto, F. 2009 a Unsteady PTV velocity field past an airfoil solved with DNS: Part 1. algorithm of hybrid simulation and hybrid velocity field at Re ≈ 103. Exp. Fluids 47 (6), 957976.
Suzuki, T. & Lele, S. K. 2003 a Green's functions for a source in a boundary layer: direct waves, channelled waves and diffracted waves. J. Fluid Mech. 477, 129173.
Suzuki, T. & Lele, S. K. 2003 b Green's functions for a source in a mixing layer: direct waves, refracted arrival waves and instability waves. J. Fluid Mech. 477, 89128.
Suzuki, T., Sanse, A., Mizushima, T. & Yamamoto, F. 2009 b Unsteady PTV velocity field past an airfoil solved with DNS. Part 2. Validation and application at Reynolds numbers up to Re ≤ 104. Exp. Fluids 47 (6), 977994.
Tam, C. K. W. & Morris, P. J. 1985 Tone excited jets.- Part V. A theoretical-model and comparison with experiment. J. Sound Vib. 102 (1), 119151.
Theofilis, V. 2000 On the structure of global linear instabilities and their experimental identification. Aerosp. Sci. Technol. 4, 249262.
Theofilis, V. 2003 Advances in global linear instability analysis of nonparallel and three-dimensional flows. Prog. Aerosp. Sci. 39, 249315.
Tumin, A. 1996 Receptivity of pipe Poiseuille flow. J. Fluid Mech. 315, 119137.
Tumin, A. 2003 Multimode decomposition of spatially growing perturbations in a two-dimensional boundary layer. Phys. Fluids 15 (9), 25252540.
Tumin, A. 2007 Three-dimensional spatial normal modes in compressible boundary layers. J. Fluid Mech. 586, 295322.
Williamson, C. H. K. 1996 Three-dimensional wake transition. J. Fluid Mech. 328, 345407.
Yamagata, T., Hayase, T. & Higuchi, H. 2008 Effect of feedback data rate in PIV measurement-integrated simulation. J. Fluid Sci. Technol. 3 (4), 477487.
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, 449491.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed