Low-frequency sound sources in high-speed turbulent jets

Abstract

An analysis of the sound radiated by three turbulent, high-speed jets is conducted using Lighthill's acoustic analogy (Proc. R. Soc. Lond. A, vol. 211, 1952, p. 564). Computed by large eddy simulation the three jets operate at different conditions: a Mach 0.9 cold jet, a Mach 2.0 cold jet and a Mach 1.0 heated jet. The last two jets have the same jet velocity and differ only by temperature. None of the jets exhibit Mach wave characteristics. For these jets the comparison between the Lighthill-predicted sound and the directly computed sound is favourable for all jets and for the two angles (30° and 90°, measured from the downstream jet axis) considered. The momentum (ρuiuj) and the so-called entropy [p − p∞ − a∞2(ρ − ρ∞)] contributions are examined in the acoustic far field. It is found that significant phase cancellation exists between the momentum and entropy components. It is observed that for high-speed jets one cannot consider ρuiuj and (p′ − a∞2ρ′)δij as independent sources. In particular the ρ′ūxūx component of ρuiuj is strongly coupled with the entropy term as a consequence of compressibility and the high jet velocity and not because of a linear sound-generation mechanism. Further, in more usefully decoupling the momentum and entropic contributions, the decomposition of Tij due to Lilley (Tech. Rep. AGARD CP-131 1974) is preferred. Connections are made between the present results and the quieting of high-speed jets with heating.