A parametric study of the broadband shock-associated noise in supersonic jets via semi-empirical modeling

A semi-empirical model is developed in this paper to predict the broadband shock-associated noise (BBSAN) generated by shock-instability interaction (SII) in imperfectly expanded supersonic jets. The model makes use of a semi-empirically modified Pack's model that accounts for the decay in both shock amplitude and shock spacing and a Gaussian wave-packet model for the instability waves. The near-field pressure perturbation due to the SII is treated as a boundary value for the Helmholtz equation, which is subsequently solved to predict the far-field acoustic spectra and directivity patterns. A comprehensive parametric study is conducted to reveal the effects of the key parameters on the acoustic spectral and directivity features. It is found that decreasing the instability-wave decay rate narrows the spectral bandwidth and the major lobes in directivity patterns, while variations in shock spacing shift the spectral peak frequency and the major radiation angle. Mechanisms of such changes are discussed based on the model. Further validation against multiple experimental datasets demonstrates that incorporating more realistic parameters in the model-particularly those accounting for the shock spacing and amplitude decays-considerably improves its prediction accuracy and physical consistency. The improved model successfully reproduces several key spectral features observed in experiments; these include, for example, the peak frequency and the tendency of bandwidth contradiction as the observer angle increases. Moreover, the predicted directivity patterns closely match the experiments outside the shallow-angle region dominated by jet mixing noise. In particular, it captures the major radiation lobes and their frequency-dependent amplitude and shape variations.