Large-scale flow phenomena in axial compressors: Modeling, analysis, and control with air injectors

This thesis presents a large scale model of axial compressor flows that is detailed enough to describe the modal and spike stall inception processes, and is also amenable to dynamical systems analysis and control design. The research presented here is based on the model derived by Mezić, which shows that the flows are dominated by the competition between the blade forcing of the compressor and the overall pressure differential created by the compressor. This model describes the modal stall inception process in a similar manner as the Moore-Greitzer model, but also describes the cross sectional flow velocities, and exhibits full span and part span stall. All of these flow patterns described by the model agree with experimental data. Furthermore, the initial model is altered in order to describe the effects of three dimensional spike disturbances, which can destabilize the compressor at otherwise stable operating points. The three dimensional model exhibits flow patterns during spike stall inception that also appear in experiments.; The second part of this research focuses on the dynamical systems analysis of, and control design with, the PDE model of the axial flow in the compressor. We show that the axial flow model can be written as a gradient system and illustrate some stability properties of the stalled flow. This also reveals that flows with multiple stall cells correspond to higher energy states in the compressor. The model is derived with air injection actuation, and globally stabilizing distributed controls are designed. We first present a locally optimal controller for the linearized system, and then use Lyapunov analysis to show sufficient conditions for global stability. The concept of sector nonlinearities is applied to the problem of distributed parameter systems, and by analyzing the sector property of the compressor characteristic function, completely decentralized controllers are derived. Finally, the modal decomposition and Lyapunov analysis used in constructing the distributed controllers are combined to present a new formulation for the finite-dimensional control of semilinear dissipative PDEs. The design technique can also be applied to a finite-dimensional observation problem, and the controller and observer designs can be directly combined to yield a globally stabilizing compensator with a finite number of inputs and outputs, thus exhibiting a separation principle.