Supersonic jets that are subject to off-design operating conditions are marked by three distinct regions in their far-field spectra: mixing noise, screech and Broadband Shock Associated Noise (BBSAN). BBSAN is conspicuous by the prominent multiple peaks. The Morris and Miller BBSAN model that is based on an acoustic analogy, offering a straightforward implementation for RANS, forms the foundation of the present work. The analogy model robustly captures the peak frequency noise, that occurs near Strouhal number of about 1, based on the nozzle exit diameter but leads to major sound under prediction for higher frequencies. In the jet mixing noise literature, it has been shown that an inclusion of frequency dependence into the characteristic length and temporal scales of the effective noise sources improves the far-field noise predictions. In the present paper, several modifications of the original Morris and Miller model are considered that incorporate the frequency dependent scales as recommended in the jet mixing noise literature. In addition to these, a new mixed scale model is proposed that incorporates a correlation scale that depends both on the mean-flow velocity gradient and the standard mixing noise-type scaling based on the dissipation of turbulent kinetic energy. In comparison with the original Morris and Miller model, the mixed scale model shows considerable improvements in the noise predictions for the benchmark axisymmetric convergent-divergent and convergent jets. Further to this validation, the new model has been applied for improved predictions for elliptic jets of various eccentricity. It has been shown that,

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The acoustic analogy provides a general framework for predicting broadband jet noise. The accuracy of the noise predictions are strongly dependent on the second-and fourth-order integral time and length scales of the turbulence quantities in the jet. Two low-order models for the second-and fourth-order integral length scales are examined. The low-order models are defined by locally isotropic scales estimated from 2D particle image velocimetry measurements. These measurements are of screeching underexpanded unheated round jets issuing from a purely converging nozzle at conditions, which corresponds to ideally expanded Mach numbers of 1.45 and 1.59. The jets are dominated by the helical C instability screech mode, which is associated with large-scale coherent periodic fluctuations. These fluctuations are filtered using a proper orthogonal decomposition method to assess low-order models that approximate the length scales associated with the broadband noise mechanisms. The length scale model parameters are shown to be insensitive for the two Mach numbers considered. The root-mean-square error associated with the low-order models indicates that either is sufficient for approximating the integral length scales required to model equivalent sources of broadband jet noise.

This paper investigates the broadband shock-associated noise (BBSAN) radiated from supersonic jets at the root source level. The sources are modelled according to an acoustic analogy. The acoustic analogy model is informed by high spatial resolution 2D-2C particle image velocimetry (PIV) data and solutions to the Reynolds-Averaged Navier-Stokes (RANS) equations for the reconstruction of the equivalent BBSAN sources. The measurements are of screeching underexpanded jets issuing from a purely converging nozzle at ideally expanded Mach numbers of 1.45 and 1.59. The jet conditions are simulated using a RANS solver with a k − ω shear stress transport turbulence model. The RANS scales are modelled using formulations of a two-time scale model based on the turbulence dissipation and large eddy convection time. The large eddy convection based scale is recommended as a replacement for the standard turbulence dissipation scale in low-order BBSAN models. The equivalent BBSAN sources are reconstructed from the PIV measurements and RANS solutions at the peak Strouhal number. The equivalent BBSAN sources extracted from the PIV and RANS data are shown to have favourable agreement.

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