Helmholtz decomposition of velocity field of a mixing layer: Application to the analysis of acoustic sources

2006 ◽  
pp. 513-520 ◽  
Author(s):  
M. Cabana ◽  
V. Fortuné ◽  
P. Jordan ◽  
F. Golanski ◽  
Eric Lamballais ◽  
...  
Keyword(s):  
Velocity Field ◽  
Mixing Layer ◽  
Helmholtz Decomposition ◽  
Acoustic Sources

scholarly journals Examination of large-scale structures in a turbulent plane mixing layer. Part 2. Dynamical systems model

2001 ◽  
Vol 441 ◽  
pp. 67-108 ◽  
Author(s):  
L. UKEILEY ◽  
L. CORDIER ◽  
R. MANCEAU ◽  
J. DELVILLE ◽  
M. GLAUSER ◽  
...  
Keyword(s):  
Dynamical System ◽  
Velocity Field ◽  
Large Scale ◽  
Stokes Equations ◽  
Temporal Dynamics ◽  
Mixing Layer ◽  
Basis Set ◽  
Large Scale Structures ◽  
Scale Structures ◽  
Low Order

The temporal dynamics of large-scale structures in a plane turbulent mixing layer are studied through the development of a low-order dynamical system of ordinary differential equations (ODEs). This model is derived by projecting Navier–Stokes equations onto an empirical basis set from the proper orthogonal decomposition (POD) using a Galerkin method. To obtain this low-dimensional set of equations, a truncation is performed that only includes the first POD mode for selected streamwise/spanwise (k1/k3) modes. The initial truncations are for k3 = 0; however, once these truncations are evaluated, non-zero spanwise wavenumbers are added. These truncated systems of equations are then examined in the pseudo-Fourier space in which they are solved and by reconstructing the velocity field. Two different methods for closing the mean streamwise velocity are evaluated that show the importance of introducing, into the low-order dynamical system, a term allowing feedback between the turbulent and mean flows. The results of the numerical simulations show a strongly periodic flow indicative of the spanwise vorticity. The simulated flow had the correct energy distributions in the cross-stream direction. These models also indicated that the events associated with the centre of the mixing layer lead the temporal dynamics. For truncations involving both spanwise and streamwise wavenumbers, the reconstructed velocity field exhibits the main spanwise and streamwise vortical structures known to exist in this flow. The streamwise aligned vorticity is shown to connect spanwise vortex tubes.

scholarly journals Sound generation in a mixing layer

1997 ◽  
Vol 330 ◽  
pp. 375-409 ◽  
Author(s):  
TIM COLONIUS ◽  
SANJIVA K. LELE ◽  
PARVIZ MOIN
Keyword(s):  
Acoustic Field ◽  
Stokes Equations ◽  
Near Field ◽  
Mixing Layer ◽  
Navier Stokes ◽  
Far Field ◽  
Source Terms ◽  
Acoustic Analogy ◽  
Navier Stokes Equations ◽  
Acoustic Sources

The sound generated by vortex pairing in a two-dimensional compressible mixing layer is investigated. Direct numerical simulations (DNS) of the Navier–Stokes equations are used to compute both the near-field region and a portion of the acoustic field. The acoustic analogy due to Lilley (1974) is also solved with acoustic sources determined from the near-field data of the DNS. It is shown that several commonly made simplifications to the acoustic sources can lead to erroneous predictions for the acoustic field. Predictions based on the quadrupole form of the source terms derived by Goldstein (1976a, 1984) are in excellent agreement with the acoustic field from the DNS. However, despite the low Mach number of the flow, the acoustic far field generated by the vortex pairings cannot be described by considering compact quadrupole sources. The acoustic sources have the form of modulated wave packets and the acoustic far field is described by a superdirective model (Crighton & Huerre 1990). The presence of flow–acoustic interactions in the computed source terms causes the acoustic field predicted by the acoustic analogy to be very sensitive to small changes in the description of the source.

scholarly journals Velocity field analysis in an experimental cavitating mixing layer

2011 ◽  
Vol 23 (5) ◽  
pp. 055105 ◽  
Author(s):  
Vincent Aeschlimann ◽  
Stéphane Barre ◽  
Henda Djeridi
Keyword(s):  
Velocity Field ◽  
Mixing Layer ◽  
Field Analysis

Three-dimensional velocity field in a compressible mixing layer

AIAA Journal ◽  
1993 ◽  
Vol 31 (11) ◽  
pp. 2061-2067 ◽  
Author(s):  
Mark R. Gruber ◽  
Nathan L. Messersmith ◽  
J. Craig Dutton
Keyword(s):  
Velocity Field ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Compressible Mixing Layer

An Experimental Investigation of the Pressure-Velocity Cross-Correlation in an Axisymmetric Jet

2005 ◽  
Author(s):  
Andre´ M. Hall ◽  
Mark N. Glauser ◽  
Charles E. Tinney
Keyword(s):  
Velocity Field ◽  
Shear Layer ◽  
Cross Correlation ◽  
Near Field ◽  
Mixing Layer ◽  
Ambient Conditions ◽  
Potential Core ◽  
Axisymmetric Jet ◽  
Exit Nozzle ◽  
The Cross

This study investigates the strength of the pressure-velocity correlations of a Mach 0.6, axisymmetric jet, with an exit nozzle diameter of 50.8mm. Experiments are conducted at a constant exit temperature of 25°C, and exit pressure and temperature are balanced with ambient conditions. The instantaneous velocity measurements are acquired using a multi-component LDA system who’s measurement volume is traversed along several radial and streamwise locations within the potential core, and mixing layer regions of the flow. The fluctuating lip pressure is simultaneously sampled by an azimuthal array of (15) dynamic transducers, evenly spaced at 24°. These are positioned just outside the shear layer near the jet exit at z/D = 0.875, and 1.75R from the centerline, where the pressure field has been shown to be hydrodynamic. From this multi-point evaluation, the cross-correlations between the near-field pressure array (fixed), and streamwise component of the velocity field (traversed) are examined as a function of radial, streamwise, and also azimuthal separation. The results illustrate a remarkable coherence between the near field pressure and the velocity field, on the order of 25%. Streamwise convection velocities of 0.77Uj and 0.73Uj are calculated within the potential core and shear layer, respectively. Analysis of the coherency spectra illustrates the frequency band of the correlations and suggest that the potential core and mixing layer regions of the flow are, in general, governed by the high and low frequency motions of the flow, respectively. The azimuthal modal distribution of the cross-correlation shows the dominance of the column mode of the jet, with no higher modes exhibited within the potential core region, and only modes 1 & 2 within the shear layer.

scholarly journals Wavepackets in the velocity field of turbulent jets

2013 ◽  
Vol 730 ◽  
pp. 559-592 ◽  
Author(s):  
André V. G. Cavalieri ◽  
Daniel Rodríguez ◽  
Peter Jordan ◽  
Tim Colonius ◽  
Yves Gervais
Keyword(s):  
Velocity Field ◽  
Acoustic Pressure ◽  
Mixing Layer ◽  
Turbulent Jets ◽  
Velocity Spectrum ◽  
Time Resolved ◽  
Potential Core ◽  
Axisymmetric Mode ◽  
Pressure Fields ◽  
High Reynolds

AbstractWe study the velocity fields of unforced, high Reynolds number, subsonic jets, issuing from round nozzles with turbulent boundary layers. The objective of the study is to educe wavepackets in such flows and to explore their relationship with the radiated sound. The velocity field is measured using a hot-wire anemometer and a stereoscopic, time-resolved PIV system. The field can be decomposed into frequency and azimuthal Fourier modes. The low-angle sound radiation is measured synchronously with a microphone ring array. Consistent with previous observations, the azimuthal wavenumber spectra of the velocity and acoustic pressure fields are distinct. The velocity spectrum of the initial mixing layer exhibits a peak at azimuthal wavenumbers $m$ ranging from 4 to 11, and the peak is found to scale with the local momentum thickness of the mixing layer. The acoustic pressure field is, on the other hand, predominantly axisymmetric, suggesting an increased relative acoustic efficiency of the axisymmetric mode of the velocity field, a characteristic that can be shown theoretically to be caused by the radial compactness of the sound source. This is confirmed by significant correlations, as high as 10 %, between the axisymmetric modes of the velocity and acoustic pressure fields, these values being significantly higher than those reported for two-point flow–acoustic correlations in subsonic jets. The axisymmetric and first helical modes of the velocity field are then compared with solutions of linear parabolized stability equations (PSE) to ascertain if these modes correspond to linear wavepackets. For all but the lowest frequencies close agreement is obtained for the spatial amplification, up to the end of the potential core. The radial shapes of the linear PSE solutions also agree with the experimental results over the same region. The results suggests that, despite the broadband character of the turbulence, the evolution of Strouhal numbers $0. 3\leq St\leq 0. 9$ and azimuthal modes 0 and 1 can be modelled as linear wavepackets, and these are associated with the sound radiated to low polar angles.

scholarly journals Simultaneous concentration and velocity field measurements in a shock-accelerated mixing layer

2014 ◽  
Vol 55 (10) ◽  
Author(s):  
Daniel Reese ◽  
Jason Oakley ◽  
Alonso Navarro-Nunez ◽  
David Rothamer ◽  
Chris Weber ◽  
...  
Keyword(s):  
Velocity Field ◽  
Mixing Layer ◽  
Field Measurements
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