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¯ are 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−0.15γMj2, where Ls*¯ is the average shock-cell length normalized by nozzle throat diameter Dth, AR is the nozzle aspect ratio, γ 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−0.11γMj2, where Lc* is the nozzle throat diameter normalized supersonic core length. The scaling laws Ls*¯AR0.2e−0.15γMj2 and Lc*AR0.5e−0.11γMj2 are valid across a wide range of parameters, such as γ 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.