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.

Effects of heating on noise radiation from a two-dimensional mixing layer: direct computation and acoustic analogy predictions

“…Analysis of sound source terms in the acoustic analogy suggest that although the source term fluctuations become stronger in the near field with heating, the mutually cancelling effects of individual sources lead to a weaker sound field. This result is consistent with the finding of 11 using LES data for turbulent heated jets that the enthalpy flux source terms cancel partially with the momentum flux source terms in Lighthill's acoustic analogy. Alternative form of Lighthill's stress tensor was also derived by Bodony (2009) 9 that decoupled various components of Lighthill's tensor to study the effect of heating.…”

Educing the source mechanism associated with downstream radiation in subsonic jets

“…The source is a non-compact axial distribution of axially aligned longitudinal quadrupoles that form a subsonically convected wavepacket. Only the linear component is modelled, as this has been shown in a number of studies to dominate low-angle radiation (Freund 2003;Bodony & Lele 2008;Sinayoko, Agarwal & Hu 2011). The radial integral, which allows the source to be concentrated on a line, is justified because of the radial acoustic compactness of the flow for the frequencies considered (St ∼ 0.3).…”

Identifying turbulent jet sound sources

“…Predictions of the noise characteristics of hot jets based on the Lighthill theory become more justified when calculating an entropic source. It has been shown [15,28,29] that to predict the noise characteristics of nonisothermal jets, in the acoustic analogy it is necessary to take into account sources resulting from flow temperature or enthalpy pulsations. If we represent the second term in the right hand side of the wave equation related to the change in entropy in the form then clea rly changes in enthalpy h = c p T condition the change in the source structure; here, c p is the spe cific heat capacity at a constant pressure, T is abso lute temperature, γ = c p / is the specific heat capacity at a constant volume, h 0 = c p T 0 , T 0 is the absolute temperature of the environment (i, j, k = 1, 2, 3) [29,30].…”