Modeling, simulation, and control of cavity flow oscillations

compressible flow;galerkin projection;proper orthogonal decomposition

Rowley, Clarence Worth ; Colonius, Timothy E. (advisor)

University:California Institute of Technology

Department:Engineering and Applied Science

关键词: compressible flow;    galerkin projection;    proper orthogonal decomposition;   

Others  :  https://thesis.library.caltech.edu/4742/1/cwr_thesis.pdf

美国|英语

来源: Caltech THESIS

【 摘 要 】

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.