Scaling law for shock-cell length and its correlation with shock-associated noise of circular and elliptic supersonic free jets

Abstract

A supersonic core length Lc and an average shock-cell length Ls Lare experimentally investigated for the acoustic properties of supersonic jets. Following Kumar and Rathakrishnan [Scaling law for supersonic core length in circular and elliptic free jets, Phys. Fluids 33(5), 051707 (2021)], a proper scale for the average shock-cell length Ls of circular and elliptic supersonic free jets is found as Ls*AR0.2e-0.15γ M2j, where Ls* is the average shock-cell length normalized by nozzle throat diameter Dth, AR is the nozzle aspect ratio, ? is the specific heat ratio, and Mj is the ideally expanded jet Mach number. The scaling law developed for Ls* exhibits a close similarity with the scaling law for supersonic core length Lc*AR0.5e-0.11γ M2j, where Lc* is the nozzle throat diameter normalized supersonic core length. The scaling laws Ls*AR0.2e-0.15γM2j are valid across a wide range of parameters, such as from 1.28 to 1.6, the nozzle design Mach number Md from 1 to 2, AR from 1 to 6, and Mj corresponds to the absence of Mach reflection. Discussion conducted on the scaling laws provides important insight into the choice of AR. Furthermore, the relationship between Lc*and Ls* with the intensity of shock-associated noise is also discussed; hence, new correlation functions are developed for Lc*and Ls* that provide an analogous measure of the shock-associated noise.