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.Fil: Tuerke, F.. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Ingeniería Mecánica. Laboratorio de Fluidodinámica; ArgentinaFil: Lusseyran, F.. Centre National de la Recherche Scientifique; FranciaFil: Sciamarella, Denisse. Centre National de la Recherche Scientifique; Francia. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Pastur, L.. Centre National de la Recherche Scientifique; FranciaFil: Artana, Guillermo Osvaldo. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Ingeniería Mecánica. Laboratorio de Fluidodinámica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Frequency-selection mechanism in incompressible open-cavity flows via reflected instability waves

We present an alternative perspective on nonharmonic mode coexistence, commonly found in the shear layer spectrum of open-cavity flows. Modes obtained by a local linear stability analysis of perturbations to a two-dimensional, incompressible, and inviscid sheared flow over a cavity of finite length and depth were conditioned by a so-called coincidence condition first proposed by Kulikowskii [J. Appl. Math. Mech. 30, 180 (1966)JAMMAR0021-892810.1016/0021-8928(66)90066-9] which takes into account instability wave reflection within the cavity. The analysis yields a set of discrete, nonharmonic frequencies, which compare well with experimental results [Phys. Fluids 20, 114101 (2008)PHFLE61070-663110.1063/1.3005435; Exp. Fluids 50, 905 (2010)EXFLDU0723-486410.1007/s00348-010-0942-9].Fil: Tuerke, F.. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Ingeniería Mecánica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Université Paris Sud; FranciaFil: Sciamarella, Denisse. Centre National de la Recherche Scientifique; FranciaFil: Pastur, L.R.. Université Paris Sud; Francia. Centre National de la Recherche Scientifique; FranciaFil: Lusseyran, F.. Université Paris Sud; Francia. Centre National de la Recherche Scientifique; FranciaFil: Artana, Guillermo Osvaldo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Ingeniería Mecánica; Argentin