Modeling the transient and steady-state flow over a stationary cylinder

A reduced-order model for the two-dimensional flow over a stationary circular cylinder is examined. The lift is modeled with the van der Pol equation with three parameters; it models self-excited self-limiting systems. The drag is modeled as the sum of a mean term and a time-varying term proportional to the product of the lift and its time derivative. The transient and steady-state flows are calculated using a CFD code based on the unsteady Reynolds-averaged Navier-Stokes equations. The steady-state lift and drag CFD results are used to identify the three parameters in the lift model using a combination of higher-order spectral techniques and perturbation methods. The model is validated using steady-state numerical simulations for three cases describing low, moderate, and high Reynolds number flows. Then, the model is shown to reproduce the transient lift and drag calculated with the CFD code.