A simple model for obstructed two-dimensional turbulent channel flow

We have investigated obstructed two-dimensional turbulent channel flow. The objective is to provide a simple building block for design models and to gain physical insight in this type of flow. We have designed a simple model with some unknown parameters to be calibrated against a CFD model. The model divides the domain between an area of main flow and recirculation areas. The model approximates these areas by polygonal shapes. The locations of the vertices of these polygons are the parameters in the model. This way, we can evaluate the simple model using the Schwarz-Christoffel integral. As a consequence, the model can be evaluated much more quickly than CFD models. The main flow is modeled to be irrotational. The recirculation area behind the obstacle is modeled as a stretched monopolar vortex and this requires 4 extra parameters. The other areas of separated flow are simply modeled to be stationary. By calibrating the simple model we have demonstrated that this physical description works reasonably well. Using only 9 parameters, the simple model reaches an error of 22\% of the inflow velocity.