A Theoretical Basis for the Scaling Law of Broadband Shock Noise Intensity in Supersonic Jets

Abstract

A theoretical basis for the scaling of broadband shock noise intensity in supersonic jets was formulated considering linear shockshear wave interaction. Modeling of broadband shock noise with the aid of shock-turbulence interaction with special reference to linear theories is briefly reviewed. A hypothesis has been postulated that the peak angle of incidence (closer to the critical angle) for the shear wave primarily governs the generation of sound in the interaction process with the noise generation contribution from off-peak incident angles being relatively unimportant. The proposed hypothesis satisfactorily explains the well-known scaling law for the broadband shock-associated noise in supersonic jets.

Sound Produced by Large Area-Ratio Nozzles During Fixed and Transient Operations

“…Figure 8a reveals the two essential features that are typical of imperfectly expanded supersonic jets. That is, BBSN from the constructive interference of turbulence-shock interactions [36][37][38] and turbulent mixing noise from Mach waves [1,6]. BBSN signatures are expected to dominate over turbulent mixing noise at steep angles due to the weak convective amplification for mixing noise in this direction.…”

“…Despite these observations, many of the working models that have been developed to predict the behavior of BBSN are confined to low values of the shock parameter β M 2 j − 1 0.5 , in which it has been shown to scale with I ∝ β 4 for 0.5 < β < 1.2 by Harper-Bourne and Fisher [37] or with I ∝ β 4.2 for 0.2 < β < 2.0 by Kandula [38]. The failure of this scaling to exhibit a linear relationship at higher values of β is known to be caused by the large portion of subsonic flow that forms downstream of the Mach disk.…”