Harmonic and Broadband Separation of Noise from a Small Ducted Fan

Abstract

In the study of noise from propellers and ducted fans, rigorous signal decomposition into harmonic and broadband components is essential for the development of high-fidelity predictive models. Current spectral methods and phase averaging techniques lack the temporal resolution to compensate for fluctuations in operating condition intrinsic to real world experiments. In this paper we use a Vold-Kalman filter to extract the tonal and broadband content of noise from a small ducted fan simulating the conditions of an ultrahigh-bypass turbofan engine. The fan operated at pressure ratio of 1.15 and tip Mach number of 0.61. The investigation includes time traces, narrowband spectra, one-third octave spectra, and overall sound pressure level. The energies of the tonal and broadband components are similar at low frequency, while the broadband component dominates at high frequency. In addition, there are distinct differences in the directivities of the two components. The trends are in general agreement with NASA large-scale fan tests at transonic conditions. NomenclatureA = structural equation matrix BPF = blade passing frequency C k = complex phasor matrix f (t) = instantaneous frequency FPR = fan pressure ratio i = imaginary unit = √ −1 I = identity matrix J(x) = cost function r = weighting factor SPL = sound pressure level t = time x k (t) = time-varying (complex) envelope of order k y(t) = total measured acoustic signal ε(t) = error in structural equation fit η(t) = broadband or shaft-uncorrelated noise θ = polar angle relative to downstream axis φ = azimuthal angle ∇ p x k [n] = structural equation of order p () = round brackets denote continuous signals [] = square brackets denote discrete signals Subscripts and Superscripts H = Hermitian k = harmonic or order of signal T = transpose Downloaded by CARLETON UNIVERSITY LIBRARY on July 22, 2015 | http://arc.aiaa.org |

Standalone Extraction of Tonal Components from Aeroacoustic Signals

“…Assuming that the model is identifiable, the next question concerns the estimation of the time-varying Fourier coefficients. Although least square estimation is conceivable [20,21,29], it would rapidly become intractable as the number of tones becomes large. Besides, the classical Fourier transform cannot be used because the Fourier coefficients are functions of time, whereas the phasors are functions of angle.…”

“…with F the cardinal of K and I 0 eff the effective number of snapshots as returned by Eq. (20). Clearly, this defines a cost function Cγ that depends on the spectral bandwidth γ through the computation of the residual signal et.…”

“…Tracking algorithms can be seen as generalizations of the combfilters [17] and conditioned filters that adapt themselves to nonstationary evolutions of the signal. The Kalman filter [18,19], the RLS filter, the Vold-Kalman filter [20,21], etc., are popular examples. They pertain to model-based methods, where the dynamics of the tones is explicitly modeled.…”

Stand-Alone Extraction of Cyclostationary Broadband Components from Aeroacoustic Signals

“…Several methods have been proposed in the literature to do so, with various degrees of refinement [1][2][3]. Once removed from the signals, they leave the place to the broadband content of the signals [4][5][6][7]. Far fewer works have attempted to further decompose broadband signals into more constituents that originate from distinct physical phenomena or sound sources, at least without explicit knowledge of the propagation mechanisms.…”

“…As far as the authors know, this topic has rarely been reported in the literature. The aforementioned works [1,2,[4][5][6][7] have contented themselves with the total broadband part left after removal of tonal components, yet without further decomposing it. A notable exception is Ref.…”