Section: New Results

Visual servoing approach for fluid flow control

Fully exploitation of the controlled degrees of freedom of the 2D plane Poiseuille flow

Participants : Christophe Collewet, Xuan Quy Dao.

This works concerns the Phd of Xuan-Quy Dao and can be seen as an extension of the works carried out by Roméo Tatsambon. Since visual measurements are used, we propose here to use advanced visual servoing techniques to fully exploit the controlled degrees of freedom of the 2D plane Poiseuille flow. To achieve this goal we propose to design a control law based on partitioned visual servo control (this approach has been first proposed in the robotics community by [46] but in a very different context). Therefore, we have shown that, following this way and contrary to the literature concerning drag reduction, it becomes easy to simultaneously reduce the drag and the kinetic energy density of the flow. That is of great importance since the controlled flow is in an unstable state and may become turbulent when the kinetic energy density is growing. This key problem is not well taken into account in the literature. Indeed, either the drag or the kinetic energy density is reduced, but never booth of them. Moreover, we have shown that in practice, the way the drag is reduced does not influence the way the kinetic energy density is reduced. In addition, since dense visual measurements are used, our approach is very robust against measurement noise.

Visual servoing for the 3D plane Poiseuille flow

Participant : Christophe Collewet.

We focus here on the 3D plane Poiseuille flow which is much more realistic than the 2D case. In that case, it can be shown that the reduced linearized flow is in a stable configuration. However, it is possible to find some bad initial conditions which causes the flow to present high transient energy growths. Indeed, a small perturbation velocity value in the reduced linearized system leads to a transient effect which is characterized by a growth in a short-time behaviour of the kinetic density energy, before a decay occurs. Practically, this transient effect, if not controlled, can cause transition to turbulence. Usually, the streamwise shear stress component at a point belonging to the wall is used as the output of the system in order to control it in a closed-loop fashion. We have proposed a vision-based approach to control this flow (see section  3.4 ). Our approach has revealed to be the most efficient approach in comparison to existing ones. Indeed, the transient energy is highly reduced. In addition, as in the 2D plane Poiseuille flow, the initialization problem is not of concerned in the vision-base approach. In addition, our approach is robust to measurement noise when a large number of flow measurements is available, which is possible in real practical situations. This work has been published in several conferences [33] , [20] , [32] and has been recently accepted for publication in the International Journal of Flow Control [19] .