Noise-source turbulence statistics and the noise from a Mach 0.9 jet

Turbulence statistics that are relevant to jet noise modeling but difficult to measure in experiments are computed using a previously validated simulation database of a Mach 0.9 cold jet. Initial focus is on fourth-order statistics that are at the core of acoustic analogy based models built on both the Lilley and Lighthill equations. Common simplifications of fourth-order correlations based on normal statistics are found to be accurate. We see that although two-point correlations are well fitted by exponential functions, as is typical of turbulence at all but the lowest Reynolds numbers, the spatially integrated fourth-order space/retarded-time covariances, which are used in the models, are instead very well fitted by Gaussian functions of different widths for different components, which is counter to conventional modeling practice. We also examine the components of Lighthill’s analogous noise source that are linear and quadratic in velocity fluctuations, as well as components that are deviations from p ′ =a ∞ 2 ρ ′ . The spectrum from the linear components is more peaked and more direction dependent than the spectral shape of the quadratic component’s noise, which is relatively independent of angle. These two components are also correlated, especially at small angles where their mutual correlation coefficient reaches as low as −0.4, which casts doubt on models that treat these so-called shear noise (linear) and self-noise (quadratic) terms as distinct. The p ′ −a ∞ 2 ρ ′ contribution is relatively small, but not negligible as might be expected for this nearly isothermal jet. The total radiated power of the quadratic terms is nearly the same as that of all components combined. It is shown that the standard Lighthill framework does not lead to a straight forward designation of what noise comes from what region of the jet.