Item Details

Analysis and Computational Fluid Dynamics for the Stabilization and Control of 3-Dimensional Navier-Stokes Fluid Channel Flows by a Wall-Normal Boundary Controller

ReMine, Daniel
Format
Thesis/Dissertation; Online
Author
ReMine, Daniel
Advisor
Triggiani, Roberto
Abstract
The field of fluid control seeks to analyze our ability to control fluid-mechanical systems and stabilize their flows towards desired outcomes. This work considers the extension of exponential stability enhancement results from a previously analyzed 2-D linear Navier-Stokes channel flow case to that of 3-D. We consider a 3-D, linear Navier-Stokes channel flow with periodic boundary conditions in the streamwise direction and subject to a wall-normal control on the top wall. There exists an infinite-dimensional subspace E, where the normal component v of the velocity vector, as well as the vorticity omega, are not influenced by the control. The corresponding control-free dynamics for $v$ and omega on E are inherently exponentially stable, though with limited decay rate. In the case of the linear 3-D channel, the stability margin of the component v on the complementary space Z can be enhanced by a prescribed decay rate, by means of an explicit, 3-D wall-normal controller acting on the top wall, whose space component is subject to algebraic rank conditions. Moreover, its support may be arbitrarily small. Corresponding optimal decays, by the same 3-D wall-normal controller, of the tangential component u of the velocity vector; of the pressure p; and of the vorticity omega over Z are also obtained, to complete the optimal analysis. Incompressible computational fluid dynamics methods are used to simulate the analysis of the 2-D channel flow case. Computational fluid dynamics methods and control simulation algorithms are presented.
Language
English
Date Received
20140730
Published
University of Virginia, Department of Mathematics, PHD (Doctor of Philosophy), 2014
Published Date
2014-07-25
Degree
PHD (Doctor of Philosophy)
Collection
Libra ETD Repository
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