Water droplet deformation and breakup in the vicinity of the leading edge of an incoming airfoil

Resumo

The problem of droplet breakup in the vicinity of the leading edge of an airfoil has been addressed. The aim of this thesis was to study the problem of the deformation and breakup of a droplet that is immersed in a flow field where the velocity and the acceleration that the droplet senses increases continuously. This is a problem that has not been addressed before. Droplet aerobreakup has mainly been studied in shock-tube or wind tunnels facilities, where droplet suddenly experiences a high constant air speed. This is in contrast with the problem studied in this thesis, where droplet are initially in a quiescent flow and then the air velocity starts to increase gradually with an acceleration also increasing, until the acceleration and the velocity have reached values that allow for droplet breakup. The problem is then a non-stationary problem and transient effects need to be considered. Accelerating and decelerated non-uniform flow field have only been studied for non-deformable spheres, or droplets that are small enough to neglect deformation and it has proved to be a very complex problem since there still are contradictory results. Therefore, the novelty of this work is to study the aerobreakup of droplets in a non-stationary flow. The problem of a droplet being approached by an airfoil is of special interest in aerospace applications. In particular, when a plane flies through a cloud, the water droplets inside the cloud will experience this flow field velocity when any lift surface such as the wing of the plane approaches. The interest in studying this problem is that these water droplets, when they are supercooled and impinge on lift surfaces of a plane, can create ice on them changing its aerodynamic lift and drag forces and resulting in a change in the performances of the plane, which in turn could cause accidents and the loss of the plane. An experimental investigation has been conducted in the rotating arm facility at INTA covering droplets diameter from 0.3 mm to 3.6 mm. Droplets were generated and allow to fall in the path of an incoming airfoil. Three airfoil sizes (leading edge radius of 0.103 mm, 0.070 mm, and 0.029 mm) and five airfoil velocities (50 m/s, 60 m/s, 70 m/s, 80 m/s and 90 m/s) were used during the test. By means of shadowgraph technique, video images of the deformation and the breakup of the droplets were recorded. The flow field generated by these airfoils was characterized in advance using PIV technique. A tracking software was developed to obtain quantitative data on the droplet deformation and the breakup from the images. During the thesis, first, a characterization of the specific flow field that droplets actually senses when an airfoil is approaching is made and the principal flow parameters involved in the problem of deformation and breakup of droplets are obtained. Then, a data reduction method, the so-called HOSVD, was applied to the problem aiming to provide insight in the underlying physics. Two tensors were constructed: one containing the deformation information and the other containing the breakup time. These tensors were used to extrapolate outside the tensor and to interpolate inside. And finally, the definitions of the onset of the breakup for each mode have been discussed and a breakup criterion equation has been proposed. It was found that in the most of the cases that were addressed during the experimental campaigns, the breakup type was `bag and stamen'. In a few cases `bag' and `shear' breakup were also identified. Unsteady effects due to unsteady slip velocity and acceleration profiles play a critical role in the droplet deformation and breakup processes. In the cases addressed in this thesis (continuously accelerating flow) the effect was to anticipate significantly the onset of breakup. It was found that if the flow acceleration profile times the square of the droplet residence time is constant, droplet deformation (its instant aspect ratio) depends on the slip velocity only. This suggests that the problem is, at least, governed by a parameter that involves two characteristic times: the characteristic time of the flowfield variation and the droplet residence time. This thesis has been the first step, only, in a long term development process aiming to generate reliable engineering methods to predict droplet behavior in the vicinity of aircraft wings. This required the availability of reliable databases that can be used for algorithm development purposes. Because of their own nature, the experiments involved are complex and expensive. Then, in this context, it has been found that High Order Singular Value Decomposition is a rather adequate data reduction method for this problem. The reason is that it allows for the generation of clean and densified databases (that are obtained after a limited set of experiments) that can readily be used for model development purposes. A new breakup criterion has been proposed to predict breakup in the `bag and stamen' mode that has proved to be prevailing one in the majority of experimental cases that were addressed in this thesis. Again, the breakup criterion depends on a dimensionless time that is the ratio of the characteristic droplet deformation time to the flow field typical variation time.