Nonlinear delayed feedback model for incompressible open cavity flow
Résumé
The dynamics of an oscillating shear layer when confined is enriched by retarded actions
whose physical modeling is not trivial.We present a nonlinear delayed saturation feedback
model, which allows us to correctly reproduce the complex shear layer spectra observed
experimentally in open cavity flows in the incompressible limit. The model describes the
evolution of the amplitude of the shear layer instabilities and considers two hydrodynamic
feedback mechanisms directly related to the confinement introduced by the walls. One is
associated with reflections of instability waves on the vertical cavity walls and the other to
intracavity recirculation flow. These feedback mechanisms provide retarded actions with
time lags that are used in the delay differential equation and allow the computation of the
model parameters on physical grounds. The frequency components of six experimental
cases in different flow regimes are well recovered by the dynamical model. The results
show that the model with a single feedback mechanism produces monoperiodic oscillations
of the amplitude, while the interplay of two purely hydrodynamic feedback mechanisms
allow quasiperiodicity to develop.