Investigation of the noise emitting zones of a cold jet via causality correlations

Within the framework of lighthill's acoustic analogy the causality method proposed by Ribner and Siddon is used to identify equivalent noise sources inside a cold jet. An exploration of a few cross-sections shows that a two-dimensional investigation suffices in a first approach for integrating the source function provided the upper frequency limit does not exceed a Strouhal number approximately equal to 0·5. Furthermore the transverse distribution of the source term shows the jet region located on the microphone side to be dominant; the effective diameter of the source region is comparable with that of the nozzle. It is shown that in a direction with an angle of 30° to the jet axis, the “shear noise” is dominant (about 70% of the noise measured in the same frequency range). The noise emanates essentially from the transition region and from layers located between $\text{r}\text{D}\text{= ±0·25}$ and $\text{r}\text{D}\text{= ±0·375}$. This analysis is suitable for frequency range bounded above by St = 0·54. For the direction with an angle of 45° to the jet axis comparable results are obtained in a frequency range also limited at St = 0·54. However, this range contains only 40% of the total acoustic energy. The source region of the “shear noise” (near 70% of the total energy) and that of the “self-noise” remain always in the transition region located at 4–11 D. Radially the main part of the noise originates from the layers located on the microphone side between $\text{r}\text{D}\text{= 0·25}$ and 0·375. For the direction with an angle of 60° to the jet axis the “shear noise” is no longer measurable and the calculated “self-noise” represents only a few percent of the noise measured. For an acoustically excited jet (white noise filtered between St = 0·39 and St = 0·52, 320 Pa at the nozzle) another type of correlation appears which is believed to be related to a coherent structure travelling inside the jet at 0·75 v_j. The study of the source term shows that this structure must be related to noise originating from the nozzle outlet.