ERCOFTAC Bulletin - Centre Acoustique

for 0.3 ≤ St ≤ 0.5. Results are shown in Figure (7),
taken from [5], and are compared to the axisymmetric
mode of the pressure for the same frequency range. The
agreement found at low angles (high x1 in Figure (7))
between the models with “unsteady envelope”, i.e. when
temporal changes of A and L follow the simulation data,
is reasonable for both computations.
(a)
SPL (dB)
(b)
SPL (dB)
125
120
115
110
105
100
95
90
DNS
Steady envelope
Unsteady envelope (analytical)
Unsteady envelope (numerical)
85
0 2 4 6 8 10 12 14
125
120
115
110
105
100
95
90
x1/D
LES
Steady envelope
Unsteady envelope (analytical)
Unsteady envelope (numerical)
85
2 4 6 8 10 12 14 16 18 20
x1/D
Figure 7: Comparison between jittering wave-packet
models and numerical data of Mach 0.9 jets: (a) DNS
(Freund[14]) and (b) LES (Daviller[12]). SPL taken
for the axisymmetric mode of the acoustic pressure for
0.3 ≤ St ≤ 0.5. Taken from [5].
6 Conclusions
The results reviewed in the present paper show that the
sound field at low axial angles from subsonic jets can
be calculated using source models consisting of a train
of axisymmetric structures that undergo an amplitude
modulation. This has been accomplished both using experimental
data, for which the source is modelled as linear
instability waves, or numerical simulations that allow
the use of full volume data for the velocity field.
The current progress in both numerical simulations
and measurement techniques can guide us further
into the nature of the low azimuthal modes in free
jets. Although a detailed characterisation of the full
turbulent field seems to be a hard task, focus on
the axisymmetric and on other low azimuthal modes
allows considerable simplifications. Such modes have a
relatively low energy level if compared to the overall
turbulent fluctuations[30], but their higher acoustic
efficiency can lead to significant sound radiation.
The present work was supported by CNPq, National
Council of Scientific and Technological Development –
Brazil. The authors thank Daniel Rodríguez and Tim
Colonius for the helpful discussions and for the PSE calculations.
References
[1] G. K. Batchelor and A. E. Gill. Analysis of the
stability of axisymmetric jets. Journal of Fluid Mechanics,
14(04):529–551, 1962.
[2] C. Brown and J. Bridges. Acoustic efficiency of azimuthal
modes in jet noise using chevron nozzles.
Technical report, National Aeronautics and Space
Administration, 2006.
[3] G. L. Brown and A. Roshko. On density effects and
large structure in turbulent mixing layers. Journal
of Fluid Mechanics, 64(4):775–816, 1974.
[4] G. Broze and F. Hussain. Nonlinear dynamics of
forced transitional jets: periodic and chaotic attractors.
Journal of Fluid Mechanics, 263:93–132, 1994.
[5] A. V. G. Cavalieri, P. Jordan, A. Agarwal, and
Y. Gervais. Jittering wave-packet models for subsonic
jet noise. Journal of Sound and Vibration,
330(18-19):4474–4492, 2011.
[6] A. V. G. Cavalieri, P. Jordan, T. Colonius, and
Y. Gervais. Axisymmetric superdirectivity in subsonic
jets. In 17th AIAA/CEAS Aeroacoustics Conference
and Exhibit, Portland, OR, USA, June 5-8
2011.
[7] D. G. Crighton. Basic principles of aerodynamic
noise generation. Progress in Aerospace Sciences,
16(1):31–96, 1975.
[8] D. G. Crighton and M. Gaster. Stability of slowly
diverging jet flow. Journal of Fluid Mechanics,
77(2):397–413, 1976.
[9] D. G. Crighton and P. Huerre. Shear-layer pressure
fluctuations and superdirective acoustic sources.
Journal of Fluid Mechanics, 220:355–368, 1990.
[10] S. C. Crow. Acoustic gain of a turbulent jet. In
Phys. Soc. Meeting, Univ. Colorado, Boulder, paper
IE, volume 6, 1972.
[11] S. C. Crow and F. H. Champagne. Orderly structure
in jet turbulence. Journal of Fluid Mechanics,
48(3):547–591, 1971.
[12] G. Daviller. Etude numérique des effets de temperature
dans les jets simples et coaxiaux. PhD
thesis, Ecole Nationale Supérieure de Mécanique et
d’Aérotechnique, Poitiers, France (in French), 2010.
[13] J. E. Ffowcs Williams and A. J. Kempton. The
noise from the large-scale structure of a jet. Journal
of Fluid Mechanics, 84(4):673–694, 1978.
[14] J. B. Freund. Noise sources in a low-Reynoldsnumber
turbulent jet at Mach 0.9. Journal of Fluid
Mechanics, 438:277–305, 2001.
38 ERCOFTAC Bulletin 90