Sound source characteristics generated by shocklets in isotropic compressible turbulence

This study analyzes the effects of shocklets on sound source characteristics using direct numerical simulations. The sound sources are obtained from the source terms of the Lighthill equation. The highest initial turbulent Mach number Mt0 is set to be 1.0, and the strong effects of shocklets on sound sources are investigated. Results show that the occurrence of shocklets in high turbulent Mach numbers Mt0 0.7 affects the sound generation mechanism in addition to vortical motions which are well-known sound sources in low Mach number turbulent flows. The change in mechanism influences the relationship between the Reynolds stress and entropy terms. For low turbulent Mach number flows without shocklets, the Reynolds stress and entropy terms partially show the same signs around and on vortices. However, for high turbulent Mach numbers with shocklets, the terms exhibit opposite signs across shocklets. The behaviors of the Reynolds stress and entropy terms across shocklets are explained analytically by using a one-dimensional shock relation. The change in sound source characteristics keeps velocity dependence on total sound source strength almost unchanged independent of the turbulent Mach number, though each term's sound source strength (normalized by the total sound source strength) becomes larger for the higher turbulent Mach numbers Mt0 0.9 than those for low turbulent Mach numbers Mt0 0.4. Besides, the applicability of the present study to predict far-field acoustic wave characteristics is discussed. The source terms based on Lilley's decomposition show that the sound sources derived by shocklets have quadruple characteristics. Also, it is shown that the given knowledge in the present study, especially for the relation between the Reynolds stress and entropy terms across shocklets, can be used to improve the source modeling for a nonlinear acoustic analogy based on the Lighthill's acoustic analogy and Burgers' equation. In addition, the paper provides a possible explanation of the contributions of the shocklets for a mechanism of crackle noise that the generated acoustic waves by shocklets propagates to the acoustic field and show high-frequency spectral characteristics.