Nonlinear delayed feedback model for incompressible open cavity flow

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.

Figure 1

Sketch of open cavity flow. Flow is from left to right, as indicated by the arrows. See the text for details.

Figure 2

Results for all cases in Table 1. (a)–(f) Time series of LDV velocity measurements in the real flow. (g)–(l) Time series from the nonlinear delayed feedback model. (m)–(r) Comparison of experimental power spectra (black curve), computed from the time series in (a)–(f), and power spectra from the delayed feedback model (gray curve), computed from the time series in (g)–(l), for all cases in Table 1. Horizontally dashed lines in (g)–(l) indicate the value of the stable fixed point.