Running a feedback control simulation of the flow around a cylinder
 

Hi all,

This is my very first post on this forum, so feel free to move this thread somewhere else if this is not the appropriate section.

I do not have a specific problem right now, but I wanted to pose a few general questions to understand where are the difficult points in what I want to achieve. In this post I will raise a few issue that I reckon are relevant or not straightforward due to my limited skills with OpenFoam. I will be glad if you could provide some hint for those and/or to point me in the right point in the docs.

Basically, I am working on a problem where we develop feedback controllers for fluid flows and we selected the 2D cylinder flow at low Reynolds number as a benchmark problem. Simulation of this flow is relatively straightforwrad. However, I aim at suppressing the wake instability and reduce the drag by implementing a feeback controller tha appropriately varies the angular speed of the cylinder in order to control the two separating shear layers. The angular speed of the cylinder will be determined by the controller, running in parallel with the simulation and it is not known a priori, but comes along with the solution. So the issue number (1) will be to vary the boundary conditions at run time.

Issue number (2) is related to the fact that the controller works on a state space model of the flow where the states a_i will have to be computed at run time from the projection of the current velocity field onto a set of basis functions, i.e. velocity vector field that are known before hand. Thus, for each basis function I will have to compute the integral over the domain of the inner product between the current solution and the basis function. For this issue I will require to a) load these basis function from a field file, b) perform the multiplication and c) perform the integral.

Any help or indication on this would be much appreciated.

Regards,

Davide