Séverine Millet

Temporal Stability of Carreau Fluid Flow down an Incline

This paper deals with the temporal stability of a Carreau fluid flow down an inclined plane. As a first step, a weakly non-Newtonian behavior is considered in the limit of very long waves. It is found that the critical Reynolds number is lower for shear-thinning fluids than for Newtonian fluids, while the celerity is larger. In a second step the general case is studied numerically. Particular attention is paid to small angles of inclination for which either surface or shear modes can arise. It is shown that shear-dependency can change the nature of instability.

Oscillating acoustic streaming jet

The present paper provides the first experimental investigation of an oscillating acoustic streaming jet. The observations are performed in the far field of a 2 MHz circular plane ultrasound transducer introduced in a rectangular cavity filled with water. Measurements are made by Particle Image Velocimetry (PIV) in horizontal and vertical planes near the end of the cavity. Oscillations of the jet appear in this zone, for a sufficiently high Reynolds number, as an intermittent phenomenon on an otherwise straight jet fluctuating in intensity. The observed perturbation pattern is similar to that of former theoretical studies. This intermittently oscillatory behavior is the first step to the transition to turbulence.

Stability of a flow down an incline with respect to two-dimensional and three-dimensional disturbances for Newtonian and non-Newtonian fluids.

Squires theorem, which states that the two-dimensional instabilities are more dangerous than the three-dimensional instabilities, is revisited here for a flow down an incline, making use of numerical stability analysis and Squire relationships when available. For flows down inclined planes, one of these Squire relationships involves the slopes of the inclines. This means that the Reynolds number associated with a two-dimensional wave can be shown to be smaller than that for an oblique wave, but this oblique wave being obtained for a larger slope. Physically speaking, this prevents the possibility to directly compare the thresholds at a given slope. The goal of the paper is then to reach a conclusion about the predominance or not of two-dimensional instabilities at a given slope, which is of practical interest for industrial or environmental applications. For a Newtonian fluid, it is shown that, for a given slope, oblique wave instabilities are never the dominant instabilities. Both the Squire relationships and the particular variations of the two-dimensional wave critical curve with regard to the inclination angle are involved in the proof of this result. For a generalized Newtonian fluid, a similar result can only be obtained for a reduced stability problem where some term connected to the perturbation of viscosity is neglected. For the general stability problem, however, no Squire relationships can be derived and the numerical stability results show that the thresholds for oblique waves can be smaller than the thresholds for two-dimensional waves at a given slope, particularly for large obliquity angles and strong shear-thinning behaviors. The conclusion is then completely different in that case: the dominant instability for a generalized Newtonian fluid flowing down an inclined plane with a given slope can be three dimensional.

Y-shaped jets driven by an ultrasonic beam reflecting on a wall.

This paper presents an original experimental and numerical investigation of acoustic streaming driven by an acoustic beam reflecting on a wall. The water experiment features a 2 MHz acoustic beam totally reflecting on one of the tank glass walls. The velocity field in the plane containing the incident and reflected beam axes is investigated using Particle Image Velocimetry (PIV). It exhibits an original y-shaped structure: the impinging jet driven by the incident beam is continued by a wall jet, and a second jet is driven by the reflected beam, making an angle with the impinging jet. The flow is also numerically modeled as that of an incompressible fluid undergoing a volumetric acoustic force. This is a classical approach, but the complexity of the acoustic field in the reflection zone, however, makes it difficult to derive an exact force field in this area. Several approximations are thus tested; we show that the observed velocity field only weakly depends on the approximation used in this small region. The numerical model results are in good agreement with the experimental results. The spreading of the jets around their impingement points and the creeping of the wall jets along the walls are observed to allow the interaction of the flow with a large wall surface, which can even extend to the corners of the tank; this could be an interesting feature for applications requiring efficient heat and mass transfer at the wall. More fundamentally, the velocity field is shown to have both similarities and differences with the velocity field in a classical centered acoustic streaming jet. In particular its magnitude exhibits a fairly good agreement with a formerly derived scaling law based on the balance of the acoustic forcing with the inertia due to the flow acceleration along the beam axis.