Institute for Systems Research

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Author: search.filters.author.Adomaitis, Raymond A.Subject: search.filters.subject.nonlinear systems

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Now showing 1 - 7 of 7
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    Spatially Resolved Compressor Characteristics for Modeling and Control of Blade-Scale Flow Instabilities
    (1995) Adomaitis, Raymond A.; ISR
    A numerical techniques cable of simulating blade-scale compression system flow instabilities over times scales spanning tens of rotor revolutions is presented. Simulations of stall inception, growth to fully-developed rotating stall, and evidence for hysteresis, secondary instabilities, and other nonlinear phenomena are presented. signal processing techniques for flow asymmetry characterization are discussed in the context of obtaining low-order representations of the flow disturbances with the ultimate goal of active stall suppression.
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    Local Nonlinear Control of Stall Inception in Axial Flow Compressors
    (1993) Adomaitis, Raymond A.; Abed, Eyad H.; ISR
    A combination of theoretical and computational nonlinear analysis techniques are used to study the scenario of bifurcations responsible for the initiation of rotating stall in an axial flow compressor model. It is found that viscosity tends to damp higher-frequency modes and so results in a sequence of bifurcations along the uniform-flow solution branch to stall cells of different mode number. Lower-mode stalled flow solutions are born in subcritical bifurcations, meaning that these equilibria will be unstable for small amplitudes. Secondary bifurcations, however, can render them stable, leading to hysteresis. Using throttle position as a control, we find that while the stall bifurcations are not linearly stabilizable, nonlinear state feedback of the first mode amplitude will reduce the hysteresis. This improves the nonlinear stability of the compression system near the stall margin.
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    Bifurcation Analysis of Nonuniform Flow Patterns in Axial-Flow Gas Compressors
    (1992) Adomaitis, Raymond A.; Abed, Eyad H.; ISR
    We study the transition from steady, spatially uniform-flow to nonuniform and time-dependent gas axial velocity profiles in an axial flow compression system. Local bifurcation analysis of the uniform-flow solution reveals a series of bifurcations to traveling waves of different mode number as a function of throttle opening. The number of bifurcating modes is found to depend on the gas viscosity parameter, an effect introduced in this work. Using the local approximations of the bifurcating solutions as starting points of our numerical analysis, we uncover a complicated scenario of secondary bifurcations ultimately resulting in parameter ranges where locally asymptotically stable stalled-flow solutions of different mode number coexist.
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    Nonlinear Dynamics of Axial-Flow Compressors: A Parametric Study
    (1992) Adomaitis, Raymond A.; Liaw, Der-Cherng; Abed, Eyad H.; ISR
    Analysis of the post-instability dynamical behavior of an axial- flow compression system model is carried out in a bifurcation- theoretic setting. Using global analysis techniques, we uncover the sequence of bifurcations in parameter space which allows us to rigorously determine whether the compressor stalls or surges when the throttle is slowly closed beyond the instability margin. Using these computational techniques, we also determine the conditions under which stalled and/or surging flow solutions coexist with the desired uniform-flow operating point and quantify the perturbations which destabilize this operating point.
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    On the Dynamics and Global Stability Characteristics of Adaptive Systems
    (1991) Adomaitis, Raymond A.; Frouzakis, Christos E.; Kevrekidis, Ioannis G.; ISR
    We consider the dynamics of some representative adaptively- controlled systems and focus on situations where the desired operating point is locally, but not globally, stable. Perturbations which drive the system from the set point are quantified by computing the boundaries separating the basin of attraction of the set point from the basins of attraction of the other, undesirable attractors. The basins are found to sometimes consist of complicated, disconnected structures in phase space. This results from the nonunique reverse-time dynamics often exhibited by these systems and can be studied by considering the behavior of the reverse-time map along the basin boundaries. The effect of noninvertibility on the forward-time dynamical behavior is also explored.
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    Predicting the Complexity of Disconnected Basins of Attraction for a Noninvertible System
    (1991) Adomaitis, Raymond A.; Kevrekidis, Ioannis G.; Llave, Rafael de la; ISR
    A noninvertible, two-dimensional, discrete-time system featuring multistability is presented. Because the preimage behavior of this system is a function of location in phase space, the boundary separating the basins of attraction can be disconnected. These "polka-dot" basins of attraction have either a finite number of preimages (giving a finitely-complicated basin) or infinitely many (giving infinite complexity). A complexity criterion based on following the noninvertible region forward in time is presented and a fixed-point algorithm for computing the boundary of the "complete" noninvertible region is discussed.
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    Nonlinear Dynamics of Axial Flow Compressors: A Parametric Study
    (1991) Liaw, Der-Cherng; Adomaitis, Raymond A.; Abed, Eyad H.; ISR
    This paper presents the analysis of the dynamics of a representative axial flow compressor model, emphasizing the influence of two important control parameters. These are a nondimensional parameter B (previously introduced by Greitzer (1976) as a primary determinant of post-stall behavior) and the setting of the throttle line. Greitzer's lumped-parameter model is employed in this study, with a specific choice of compressor and throttle characteristics. Our analysis shows the presence of a rich variety of global as well as local bifurcations as the two control parameters are varied. The analysis leads to a characterization of compressor operation into three major zones: the stalled zone, the pre-stall zone, and the normal (unstalled) zone. Simulation results demonstrate the qualitatively different dynamical behaviors within each regime of parameter space.