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Modeling, Simulation, and Control of Cavity Flow Oscillations


Rowley, Clarence Worth, III (2002) Modeling, Simulation, and Control of Cavity Flow Oscillations. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/G4ZX-KH73.


This thesis involves the modeling of self-sustained oscillations in the flow past a rectangular cavity. The emphasis is on developing low-dimensional models that are suitable for analysis using tools from dynamical systems and control theory. Two-dimensional direct numerical simulations are performed, and indicate the presence of a “wake mode,” which has been observed previously in experiments, but which is much less well understood than the “shear-layer mode” usually observed. We characterize the flow in both shear-layer mode and wake mode, and provide a criterion for predicting the onset of wake mode, as a function of the various geometrical and flow-related parameters. We focus on the modeling of shear-layer mode, and employ two distinct modeling approaches: first, we use the method of Proper Orthogonal Decomposition (POD) and Galerkin projection to reduce the Navier-Stokes equations to a lowdimensional system of ordinary differential equations (ODEs). We extend the method to compressible flows, using approximations that are valid for cold flows at moderate Mach number. In a compressible flow, both the kinematic and thermodynamic variables contribute to the total energy, and an inner product is introduced which respects this, and allows one to use vector-valued POD modes for the Galerkin projection. We obtain models in the form of ODEs with between 2 and 60 states, and compare models based on scalar-valued and vector-valued POD modes. All of the models work well for short times (a few periods of oscillation), but the models based on scalar-valued modes deviate for longer times, while in general the models based on vector-valued modes retain qualitatively correct dynamical behavior. In the second modeling approach, we model the underlying physical mechanisms separately (shear-layer amplification, acoustic scattering, acoustic propagation), and obtain linear models that are suitable for control design and analysis. We design a controller which stabilizes the model, and implement a similar control law on an experiment, demonstrating significant reduction in the amplitude of the oscillations, but revealing some limitations of feedback control.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:compressible flow; galerkin projection; proper orthogonal decomposition
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Mechanical Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Colonius, Tim
Thesis Committee:
  • Colonius, Tim (chair)
  • Leonard, Anthony
  • Marsden, Jerrold E.
  • Murray, Richard M.
  • Brennen, Christopher E.
Defense Date:8 August 2001
Record Number:CaltechETD:etd-12032004-075012
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4742
Deposited By: Imported from ETD-db
Deposited On:03 Dec 2004
Last Modified:25 Oct 2023 20:47

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