HYDRODYNAMICS AND ACOUSTICS

2022 ◊ Volume 2 (92) ◊ Issue 3 ◊ p. 273-299

T. P. Konovalyuk^*

^* Institute of Hydromechanics of NAS of Ukraine, Kyiv, Ukraine

Effect of vortex model complication on estimation of sound fields resulting from vortex interaction

Gidrodin. akust. 2022, 2(3):273-299

https://doi.org/10.15407/jha2022.03.273

TEXT LANGUAGE: Ukrainian

ABSTRACT

The paper deals with estimating the acoustic effects generated by the interaction of several coherent vortex structures within the framework of the moment MZS-model of the first and second orders. The vortices are described by point vortices in the first-order MZS model, and by Kirchhoff vortices in the second-order model. The resulting sound fields are calculated within the Lighthill acoustic analogy in Powell's formulation. Their characteristics are shown to depend significantly on the order of the moment model describing the vortex structures. The only elastic interactions are studied here. This enables distinguishing the fragments in the acoustic spectrum arising as a result of the complication of the moment model. When describing coherent structures with the point vortices, the spectrum of the sound field is characterized by one frequency band reproducing the motion of vorticity centers (large-scale vortex motion). The allowance for the internal dynamics of vortices when switching to an elliptical model leads to expansion of the spectrum. As a result, the level of the calculated sound field generated by the interaction of the given vortex structures increases. At the same time, the lower-frequency band reproduces the motion of the spots' vorticity centers, and the high-frequency band reproduces the internal dynamics of the vorticity. The large-scale motions of vortex spots can be modeled by the point vortices under the condition that the sound spectrum of distributed vortices is clearly divided into bands, and the low-frequency ones have a similar width. In the case of the appearance of a high-frequency component in the sound field, the interacting vortex spots cannot be described by point vortices. Such a simplification of the modeled sound source leads to a significant underestimation of the sound level.

KEY WORDS

coherent vortex structure, MZS-model, point vortex, Kirchhoff vortex, Lighthill acoustic analogy, sound pressure fluctuations, amplitude-frequency spectrum

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