Just enough jitter for jet noise?

Abstract

We use model problems to explore the mechanisms that underpin jitter and coherence decay-related phenomena, both of which are important for wavepacket sound generation from subsonic jets. The inquiry is motivated by the incapacity of linear models to capture these important dynamic traits explicitly, and the need to understand how to distill a non-linear system down to some simplified form in which they are preserved.We first consider solutions of the non-linear Burgers' equation subject to periodic and stochastic upstream forcing; from these we obtain time-invariant and time-varying base flows about which linearisation is performed. The linearised systems are driven with upstream conditions similar to the non-linear case and the solutions analysed in terms of jitter and coherence decay; both can be preserved when linearisation is performed about a time-varying base flow.A similar investigation is then undertaken using the Linearised Euler Equations (LEE). Solutions are obtained using a previously studied, experimentally obtained, base flow, on which low-frequency, deterministic and stochastic, time variations are imposed. This introduction of time variations in the base flow amounts to a constrained permission of non-linear dynamics and additional, associated, degrees of freedom in what remains a linear model. The axial and radial hydrodynamic structures and radiated sound fields of the resulting wavepackets are compared with those obtained using a steady base flow. It is shown that many of the discrepancies observed between classical linear models (stability theory or LEE for instance) and experiment can be reduced: the wavepackets jitter, their axial coherence decays, the axial evolution of their fluctuation energy downstream of the end of the potential core shows qualitative agreement with experiment; and, most importantly, sound levels are boosted by many orders of magnitude.

A coherence-matched linear source mechanism for subsonic jet noise

“…This underscores the importance of determining the flow features related to the decaying coherence profiles for a more complete understanding of jet noise in subsonic turbulent jets. Some work in this direction has been done by and Zhang et al (2014), who have related coherence decay with nonlinearity. In order to obtain predictions of the radiated sound by subsonic jets, reduced-order linear wavepacket models such as LPSE or LEE should be extended in order to account for coherence decay in some way.…”

Jet-noise control by fluidic injection from a rotating plug: linear and nonlinear sound-source mechanisms

“…The control mechanism demonstrated in the case of the louder jet may also be of interest where noise control is concerned: forcing a jet at unstable ω-m combinations can produce strong deterministic dynamics. While producing a louder jet in the present study, this kind of forcing is what is necessary for closed-loop control strategies, and, accompanied by a reduced-order model for the wavepacket dynamics (such as linear PSE), may allow for the real-time manipulation of the acoustic efficiency of sound-source dynamics, for the problem of jittering wavepackets for instance (Cavalieri et al 2011b;Zhang et al 2012). normalisation proposed in Herbert (1997), ∞ 0q ∂q * ∂x r dr = 0.…”

Experimental study of turbulent-jet wave packets and their acoustic efficiency

“…For example, even a full linearized Euler equation solution of the near-field fluctuations has been shown to be insufficient to capture these sound-generating dynamics [41]. For these reasons, attempts to further improve the near-field representation have not been made here.…”