Aeolian tone level as a consequence of distance to the onset of unsteadiness: influence of bluff-body shape on the critical Reynolds number

Wagner Gonçalves Pinto (1) , Florent Margnat (1) , Camille Nous

1 PPrime [Poitiers] - Institut Pprime [UPR 3346]

<latex> In order to interpret recent results of shape optimization for the aeolian tone problem in 2D, laminar flows, the Reynolds number of the onset of unsteadiness in a flow over a bluff body is estimated for a set shapes : five canonical shapes (the ellipse, the rectangle, the losenge and two triangles) are studied, as well as the influence of their aspect ratio that is varied from 0.2 to 2. The critical Reynolds number (Reₓ) is obtained by binary search within direct numerical solutions of the Navier-Stokes equations obtained from Incompact3D solver with an immersed boundary method. A criterion is designed on purpose to discriminate between steady and unsteady solutions. This methodology yields Reₓ values in good agreement with literature results. For all of the shapes, Reₓ increases exponentially with the aspect ratio. When the latter tends to zero, the evolution merges around Reₓ ≈ 31, which is that of a flat plate normal to the flow. The ranking of shapes using their Reₓ provides insight of the different levels of unsteadiness, and thus of radiated noise, that are noticed between bluff-body flows when analysed at a fixed Reynolds number. </latex>

Mots clés: Aeolian tone; Bluff body noise; Critical Reynolds number

Domaines: Acoustique [physics.class-ph]; Vibrations [physics.class-ph]

Wagner Gonçalves Pinto, Florent Margnat, Camille Nous. Aeolian tone level as a consequence of distance to the onset of unsteadiness: influence of bluff-body shape on the critical Reynolds number. Forum Acusticum, Dec 2020, Lyon, France. pp.2619-2626, ⟨10.48465/fa.2020.0761⟩. ⟨hal-03242471⟩