A Parabolised Stability Equation based Broadband Shock-Associated Noise Model

Abstract

Wavepacket models have been used extensively to predict the noise produced from turbulent subsonic and supersonic jets. Such wavepackets, which represent the organised structures of the flow, are solutions to the linearised Navier-Stokes equations. Using a kinematic two-point model, Wong et al. [1] have indicated the importance of incorporating coherence decay in modelling broadband shock-associated noise (BBSAN) in supersonic jets. In this work, we aim to improve the model by using solutions from linear parabolised stability equations (PSE) to model the wavepacket part of the BBSAN source. The two-point coherence of the wavepackets is obtained from large-eddy simulation (LES) data of a M j = 1.5 fully-expanded isothermal supersonic jet [2]. The aim is to build a dynamic sound-source model for BBSAN that would improve on the simplified line-source model proposed by Wong et al. [3]. We find that a frequency dependent coherence decay length scale is important in order to suppress the higherorder harmonic peaks [4] and to obtain the correct BBSAN peak shape. Moderate agreement up to St = 1 was found between the current noise predictions and those from experimental data.

Characteristics of acoustic and hydrodynamic waves in under-expanded supersonic impinging jets

“…(The red circles are the Strouhal number of the maximum growth rate obtained from linear spatial instability analysis.) the linear parabolised stability equations (PSE), where the assumption of parallel flow is relaxed, is expected to deliver a better agreement with LES results(Sinha et al 2016;Kim et al 2019;Towne, Rigas & Colonius 2019;Wong et al 2019).…”

Wavepacket modelling of broadband shock-associated noise in supersonic jets

“…The use of PSE to model wavepackets has been well studied in both subsonic (Gudmundsson & Colonius 2011;Cavalieri et al 2013) and supersonic (Sinha et al 2014;Rodríguez et al 2015;Kleine et al 2017) turbulent jets where the mean flow is assumed to be slowly diverging. The PSE approach has also been used to model the turbulent component in previous BBSAN models (Ray & Lele 2007;Wong et al 2019a).…”

“…The inclusion of coherence decay removed the 'dips' observed in the predicted acoustic spectra. In Wong et al (2019a), an equivalent BBSAN source was constructed using parabolised stability equations (PSE) to model the wavepackets, along with two-point coherence information derived from an large-eddy simulation (LES) database. While a single amplitude scaling coefficient was required to match experimental data, recovery of the spectral shape at high frequencies was encouraging.…”