A time-resolved estimate of the turbulence and sound source mechanisms in a subsonic jet flow

A dynamical estimate of the axial component of a Mach 0.60 axisymmetric jet's turbulent velocity field is presented here using spectral linear stochastic estimation. The pressure field surrounding the exit of the jet is employed as the unconditional parameter in the estimation technique. A sub-grid interpolation method is used to improve the spatial resolution of the estimate. The model estimate is time-resolved and reconstructed using a purely experimental database. A decomposition of the model estimate using POD and Fourier-azimuthal techniques identifies the turbulent velocity modes that are responsible for driving the near-field pressure when compared with direct measurements of the jet's modal features. In effect, the signatures left in the near pressure field by the turbulence are a result of the low-order structure, the higher azimuthal modes being inefficient in driving the hydrodynamic pressure. A direct calculation of the source field using a Lighthill approach is performed, from which the low-dimensional features of the sound source mechanisms are illustrated.

Acknowledgments

February 2006

Notes

¹ r _s is taken from r/R = 1 and is positive in the direction away from the jet.

²Processing of the LDA data is described in Hall et al. [14] and employed a zero-order substitution algorithm discussed by Adrian and Yao [17].

³This includes a certain degree of user bias and may be different in other applications where threshold filtering is employed.

⁴This is an interesting artifact that was pointed out by a reviewer.

⁵Only in this instance will we use a ‘tilde’ to denote instantaneous functions.

⁶The term ‘turbulence model’ will now refer to an empirically derived model estimate of the flow using the SLSE techniques, rather than what may normally be interpreted, e.g k-epsilon, algebraic stress.

⁷The azimuthal symmetry of the jet reduced the computation from 15 azimuthal separations to eight (k = 0° to 180°, Δθ = 24°).

⁸The same model approach has been investigated [7] using stereo (u,v & w) PIV measurements of a Mach 0.85 axisymmetric jet, the results of which promises a calculation of the full Lighthill source term, from which the acoustic far-field can be estimated more accurately.