Greitzer Model Research Articles

Dynamic of gas turbine engine gasdynamic stability loss

Dynamic of rotating stall and surge development in axial compressor after loss of gasdynamic stability is considered in the article. The Moore – Greitzer model is used for research. The model takes into account non-linear features of compressor characteristics and property of the compressor system. To determine system stabile state bifurcation analyze is carried out.

Slope seeking: a generalization of extremum seeking

AbstractThis work introduces slope seeking, a new idea for non‐model based adaptive control. It involves driving the output of a plant to a value corresponding to a commanded slope of its reference‐to‐output map. To achieve this objective, we introduce a slope reference input into a sinusoidal perturbation‐based extremum seeking scheme; derive a stability test for single parameter slope seeking, and then develop a systematic design algorithm based on standard linear SISO control methods to satisfy the stability test. We then extend the results to the multivariable case of gradient seeking. Finally, we illustrate near‐optimal compressor operation under slope seeking feedback through a simulation study upon the well‐known Moore–Greitzer model of compressor instability. Copyright © 2003 John Wiley & Sons, Ltd.

Control of self-oscillating systems

In order to obtain a mathematical model of a self-sustained oscillation, a Van der Pol oscillator can be enhanced upstream and downstream with transfer functions identified from measurements. Using a specific engineering control technique, the above model has been used to define a control law aimed at suppressing the oscillation. The method has been applied to a two-dimensional buffet observed on an airfoil in a wind tunnel. The results obtained by applying this law confirmed the authors theory, thus, validating the principles of this type of modelling and design. The same method was successfully applied to the Greitzer model of a compressor surge.

Bifurcation analysis of surge and rotating stall in the Moore-Greitzer compression system

A simple compression system model, described by a set of three ordinary nonlinear differential equations (the Moore–Greitzer model) is studied using bifurcation analysis to give a qualitative understanding of the presence of surge and rotating stall. First, three parameter values are chosen and a reduced planar system is studied to detect the local bifurcations of pure surge modes. The global bifurcation diagrams are then completed with the help of the continuation software AUTO. A special feature of this 2D system is a set of parameter values where two Takens–Bogdanov points merge. As a next step, the interaction of surge and rotating stall modes is analysed using the same branch tracking technique. Several novel bifurcation scenarios are described. Two‐parameter bifurcation maps are computed and a satisfactory agreement with experimental results is found. An explanation is given for the onset of deep surge, rotating stall, classic surge and the hysteresis effects experienced in measurements.

Linear Versus Quadratic Amplitude Feedback in Active Control of Compressor Rotating Stall

Several issues that have been overlooked or only partially addressed in previous literature related to the active control of compressor rotating stall are clarie ed. This is accomplished via a detailed local stability analysis of the rotating stall inception point and the locally branched unstalled and stalled equilibria. The analysis is based on the e rst-term Galerkin approximation of the Moore ‐Greitzer model (Moore, F. K., and Greitzer, E. M., “ A Theory of Post-StallTransientsinAxialCompressorSystems,Part1,DevelopmentofEquations,”JournalofTurbomachinery , 1986), and it is valid for an arbitrary compressor map and a parabolic throttle characteristic. It is generically performed for a rather large class of throttle feedback control laws. Each such law is proportional to the rotating stall amplitude, raised to a strictly positive exponent. The proportionality constant is a nonnegative feedback gain. It is shown that linear feedback renders the rotating stall inception point and the neighboring stalled branch locally asymptotically stable for any value of the feedback gain. Quadratic feedback on the other hand represents a limiting case of control effectiveness and can at best lead to conditional local stability; that is, it can render the stall inception point and the neighboring stalled branch locally asymptotically stable only for sufe ciently high values of the feedback gain. Finally, sublinear feedback, namely, feedback with an exponent less than unity, not only unconditionally stabilizes the stall inception point and the neighboring stalled branch, but also completely smooths out any transition to rotating stall. These results extend and in some places contrast previous work on the subject that has dismissed such linear or sublinear feedback and concentrated mainly on quadratic feedback as a viable means of controlling compressor rotating stall.

Surging Behavior of Gas Turbines.

Using the lumped-parameter Greitzer model, most compressor surging behavior (for classic or deep surge) can be estimated. However, this model is too simple, since, in general, the rotor flow passage length is longer for high-pressure compressors than that for low-pressure ones, and modern high-pressure compressors have a strong axial pressure gradient distribution in the flow passage. Dealing with the above, this paper aims to suggest a multielement model to which a Greitzer model is applied for each element, and explain relationships between the surging behavior and compressor flow field time constant, by comparing the results from the Greitzer model and the experiments of the aircraft gas turbine with a relatively high-pressure compressor.

Surge Behavior of Gas Turbines.

Using the lumped parameter Greitzer model, most compressor surge behaviors (for classic or deep surge) can be estimated. However this model is too simple, since, in general, the rotor flow passage length is longer for high-pressure compressors than that for low-pressure ones, and modern high-pressure compressors have a strong axial pressure gradient distribution in the flow passage. Dealing with the above, this paper is aimed towards suggesting a multielement model to which is applied Greitzer model for each element, and explaining the relations between the surge behavior and compressor flow field time constant, by comparing the results of Greitzer model and the experiments of the aircraft gas turbine with a relatively high-pressure compressor.

Surge Behavior of Compressor with Decompression Suction System.

A decompression suction system is often installed in front of a compressor to reduce the compressor drive power in the case of large compressor test rigs. In such cases the surge behavior is different from that in the absence of a decompression facility. This paper reports numerical results by an extended analysis based on Greitzer's model and compares to surge experimental results of an axial compressor with the decompression chamber, and shows that a critical resistance coefficient dependent on the suction throttle setting divides the surge patterns into two groups: one is limited to the maximum period with rather high frequency. and the other is similar to the relaxation type with low frequency. Further, an explanation is given for the difference in behavior between the surge in the installation with a decompression chamber and the one with no chamber.

Bifurcation Analysis of Axial Flow Compressor Stability

With a one-mode truncation it is possible to reduce the Moore–Greitzer model for compressor instability to a set of three ordinary differential equations. These are approached from the point of view of bifurcation theory. Most of the bifurcations emerge from a degenerate Takens–Bogdanov bifurcation point. The bifurcation sets are completed using the numerical branch tracking scheme AUTO. Despite the severity of the truncation, the agreement with experimental results is excellent.

Numerical Results for Axial Flow Compressor Instability

Using Cornell’s supercomputing facilities, we have carried out an extensive study of the Moore–Greitzer model, which gives accurate and reliable information about compressor instability. The bifurcation analysis in the companion paper shows the dependence of the mode of compressor response on the shape of the rotating stall characteristic. The numerical results verify and extend this with a more accurate representation of the characteristic. The effect of the parameters on the shape of the rotating stall characteristic is investigated, and it is found that the parameters with the strongest effects are the inlet length, and the shape of the compressor pressure rise versus mass flow diagram (i.e., tall diagrams versus shallow diagrams). We also discuss the effects of inlet guide vane loss on the characteristic. An evaluation is made of the h′ = −g approximation, and a spectral analysis of the rotating stall cell given by the full model suggests why this breaks down.

Experimental and Theoretical Study of Surge in a Small Centrifugal Compressor

Experimental results for deep surge in a small single-stage centrifugal compressor are compared to predictions based on the lumped parameter Greitzer model developed for axial compressors. Both negative and positive flow branches of the steady characteristic, being essential for the model, were measured. Predictions are in fair agreement with data when using a relaxation time smaller than the one proposed for axial compressors. The stability limit of the model equations have been studied for finite amplitude disturbances.