### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 107-141 |

Number of pages | 35 |

Journal | Journal of Fluid Mechanics |

Volume | 612 |

DOIs | |

State | Published - 2008 |

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### ASJC Scopus subject areas

- Mechanical Engineering
- Mechanics of Materials
- Condensed Matter Physics

### Cite this

*Journal of Fluid Mechanics*,

*612*, 107-141. https://doi.org/10.1017/S0022112008002978

**Low-dimensional characteristics of a transonic jet. Part 1. Proper orthogonal decomposition.** / Tinney, C. E.; Glauser, Mark N; Ukeiley, L. S.

Research output: Contribution to journal › Article

*Journal of Fluid Mechanics*, vol. 612, pp. 107-141. https://doi.org/10.1017/S0022112008002978

}

TY - JOUR

T1 - Low-dimensional characteristics of a transonic jet. Part 1. Proper orthogonal decomposition

AU - Tinney, C. E.

AU - Glauser, Mark N

AU - Ukeiley, L. S.

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=52949083953&partnerID=8YFLogxK

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U2 - 10.1017/S0022112008002978

DO - 10.1017/S0022112008002978

M3 - Article

VL - 612

SP - 107

EP - 141

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -