On the computation of farfield cross-spectra and coherences from reduced parameter models of high speed jet noise

Abstract

Reduced parameter models of jet noise mechanisms serve as computational vehicles to estimate sound pressure and directivies at arbitrary locations in the farfield. The customary formulations have been successful at predicting autospectra and directivities, but the calculation of crossspectra and coherences has not been attempted. The authors will present a procedure for calculating crossspectra and coherences from the simple source model, i.e., an equivalent monopole density over a volume enclosing the jet noise sources. It will be shown that realistic coherences and crossspectra are only well defined when several mutually incoherent noise sources are being considered, and both convergence and spatial aliasing phenomena will be defined and investigated.

Axisymmetry and azimuthal modes in jet noise

“…The relative error in the solution for the azimuthal modes are plotted on a logarithmic scale in figure 16. The relative error is defined as the norm of the true solution of equation (13) divided into the norm of the numerical minus the true solution.…”

“…This composite field also has swirl, since only the positive polarity azimuthal modes have nonzero magnitude; examine the phase of the crossspectrum on figure 15(b). Now, we form the and solve equation (13) in 64 bit IEEE floating point arithmetic for azimuthal sector sizes Φ ∈ [15 • . .…”

“…Partial fields may be used directly as quantitative expressions of the traveling wavepackets or may be used to fit physics-based reduced order models. 12,13,14 Organized turbulence structures have been detected at model-scale by a number of researchers ( 15,16,17 ) using near-field measurement arrays in the linear hydrodynamic regime. The detection technique involves fitting the eigenfunctions of the instability wave model to measured data in the jet near-field.…”