Scaling and dimensional analysis of acoustic streaming jets.

Brahim Moudjed (1) , Valéry Botton (1) , Daniel Henry (1) , Hamda Ben-Hadid (1) , Jean-Paul Garandet (2, 3)

1 LMFA - Laboratoire de Mecanique des Fluides et d'Acoustique
2 DTS - Département des Technologies Solaires
3 INES - Institut National de L'Energie Solaire

The present paper focuses on acoustic streaming free jets. This is to say that progressive acoustic waves are used to generate a steady flow far from any wall. The derivation of governing equations under the form of a non-linear hydrodynamics problem coupled with an acoustic propagation problem is revisited. To do so, a time scale discrimination approach is preferred to the usually invoked amplitude perturbations expansion. This is indeed more consistent with experimental observations of acoustic streaming flows featuring hydrodynamic non-linearities and turbulence. Experimental results are also presented together with a review of former experimental investigations concerning the power-to-velocity relationship for plane ultrasonic transducers in water. A comparison of the shape of the acoustic field with the shape of the velocity field shows that diffraction is a key ingredient in the problem though it is rarely accounted for in the literature. A scaling analysis is made and leads to two scaling laws for the typical velocity level in acoustic streaming free jets; these are both observed in our setup and in former studies by other teams. We also perform a dimensional analysis of this problem: a set of seven dimensionless groups is required to describe a typical acoustic experiment. We find that a full similarity is usually not possible between two acoustic streaming experiments featuring different fluids. We then choose to relax the similarity with respect to sound attenuation and to focus on the case of a scaled water experiment representing an acoustic streaming application in liquid metals, in particular in liquid silicon and in liquid sodium. We show that small acoustic powers can yield relatively high Reynolds numbers and velocity levels; this could be a virtue for heat and mass transfer applications but a drawback for ultrasonic velocimetry.

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Brahim Moudjed, Valéry Botton, Daniel Henry, Hamda Ben-Hadid, Jean-Paul Garandet. Scaling and dimensional analysis of acoustic streaming jets.. Physics of Fluids, 2014, 26, pp.093602. ⟨10.1063/1.4895518⟩. ⟨hal-00923712v3⟩