Broad band shock associated noise predictions in axisymmetric and asymmetric jets using an improved turbulence scale model

Abstract

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,

Equivalent Shock-Associated Noise Source Reconstruction of Screeching Underexpanded Unheated Round Jets

“…The contribution ofτ 1 to the time scale associated with the generation of BBSAN dominates for the LTRAC jets [22]. In the framework of the mixed- scale model [24], this suggests that contributions to the time scale from the random turbulence dominates over the shock cell effects for the LTRAC jets. Importantly, the same conclusion follows from either using the standard turbulence dissipation scale or the large eddy convection scale model.…”

“…A two-time scale approach for modelling the source scales was implemented by Kalyan and Karabasov [24] to explicitly take into account the dependence of the BBSAN generation mechanism on the strength of the shock cells. The generation mechanism is described by two random processes with functional time scalesτ 1 andτ 2 .…”

“…The upper limit of integration is chosen to minimise the low-correlation noise. The proportionality coefficients that relate the models to the integral scales are assumed to be fixed for a range of jet conditions [12,24,32].…”

“…The length scale proportionality coefficients are based on a linear fit between the functional scales and the integral length scales along the nozzle lip line [22]. The integral length scales were evaluated with an upper limit of integration defined by r v (x, η = Λ, τ = 0) = 0.1 (24) where Λ is the axial separation distance corresponding to a correlation of 0.1. A cut-off criteria of 0.1 was used to avoid the low-correlation noise and contributions from negative correlations that are observed in screeching jets.…”

“…All of the coefficients were determined by matching predictions to far-field acoustic mea-surements for a single jet condition and observer location [12,24]. There is considerable variation with the values in Table 5.…”