Greitzer Model Research Articles

Robust active finite-time control of gas compressor system surge in the presence of unmatched disturbance and uncertainty

Active and robust control of surge instability is a special necessity for optimal and safe operation of centrifugal compressors, and for the purpose, this article presents a new hybrid scheme based on fuzzy and terminal sliding mode methods. The Greitzer model is used to design a novel controller when the disturbance instability in the flow and pressure alike the uncertainity in the compressor characteristic curve and throttle valve are embedded in it. The fuzzy approximator is used to estimate the effects of parametric uncertainty and the nonlinear terms, and the robustness of the proposed method is guaranteed using the terminal sliding mode control method. The Lyapunov criterion is utilized to verify the finite-time stability of the closed-loop system. The performance of the presented method is compared with other methods in the literature through simulations in MATLAB software. The results suggest that our designed controller outperforms the existing ones in terms of surge prevention and robustness against unmatched uncertainties and disturbances.

Development and Validation of a Model for Centrifugal Compressors in Reversed Flow Regimes

Abstract Turbochargers are widely used to help reduce the environmental impact of automotive engines. However, a limiting factor for turbochargers is compressor surge. Surge is an instability that induces pressure and flow oscillations that often damages the turbocharger and its installation. Most predictions of the surge limit are based on low-order models, such as the Moore–Greitzer model. These models tend to rely on a characteristic curve for the compressor created by extrapolating the constant speed lines of a steady-state compressor map into the negative mass flow region. However, there is little validation of these assumptions in the public literature. In this article, we develop further the first-principles model for a compressor characteristic presented in Powers, K., Brace, C., Budd, C., Copeland, C., & Milewski, P., 2020, “Modeling Axisymmetric Centrifugal Compressor Characteristics From First Principles,” J. Turbomachinery, 142(9), with a particular emphasis on reverse flow. We then perform experiments using a 58 mm diameter centrifugal compressor provided by Cummins Turbo Technologies, where we feed air in the reverse direction though the compressor while the impeller is spinning in the forward direction to obtain data in the negative mass flow region of the compressor map. This demonstrated experimentally that there is a stable operating region in the reverse flow regime. The recorded data showed a good match with the theoretical model developed in this article. We also identified a change in characteristic behavior as the impeller speed is increased, which, to the authors’ knowledge, has not been observed in any previously published experimental work.

Study of the Greitzer Model for Centrifugal Compressors: Variable Lc Parameter and Two Types of Surge

In this paper, the Greitzer surge model was systematically analysed with the model compressor duct length Lc as the tuning parameter. The surge phenomenon is known to induce a serious risk to centrifugal compressor operation. The two-dimensional Greitzer model is a well-established way of modelling this dangerous instability, but the determination and changes of the model parameters are still being discussed. In this paper an automated procedure determines the Lc value providing the best fit with the experimental data has been presented. The algorithm was tested on five valve positions and revealed that the best fit was obtained for different Lc values following a linear trend against the mass flow rate. The study has also shown that the Greitzer model has two solutions for a given pressure oscillation amplitude: one similar to the deep surge (low Lc) and one similar to the mild surge (low Lc). This suggests that this model can be used to simulate both types of the phenomenon known from the experimental analyses. The study proposes the dimensionless average pressure as the parameter allowing to distinguish which surge cycle was observed at a given instance. Past papers were analysed to observe the surge type that appeared in different experiments. It was found that most researchers obtained low Lc surge. The results show that both deep and mild surge could be simulated with the Greitzer model. It also revealed that the Lc should not be treated as a constant value for a given machine and that it changes with the mass flow rate.

Sensitivity Study of Greitzer Model Based on Physical System Parameters of Radial Compressing Units

Centrifugal compressors are key elements of energy systems and industrial installations including fluid flow. Their operating range is strictly limited by the surge phenomenon. The Greitzer model is a known way of simulating the compressor’s behaviour at the surge. In this paper, the parametric study of different versions of the Greitzer model is conducted. There are several versions of this model that include 4 to 2 equation models. The system behaviour depends on the features of the compressor itself as well as of the plenum. In this paper, all terms connected with the compressor were grouped into the “Co” parameter, while those associated with the plenum were grouped into the “Pl” parameter. The study shows how each component influences the system stability. The comparison of analytical data with experimental results allowed to draw conclusions regarding the way of choosing the model parameters that provide the best simulation of the real system behaviour. The study shows that the system is well simulated by a model with relatively large values of the Lc parameter. The length of the compressor parameter Lc=3.57 m was performing well for the machine with impeller radius 0.33 m. Possible explanations of this finding are presented and compared to the state of the art. This result may provide possible help in adjusting the model parameters for other machines and designing reliable anti-surge systems based on the Greitzer model suited to energy conversion systems.

Influence of different operating conditions on centrifugal compressor surge control with active magnetic bearings

ABSTRACTThe purpose of this paper is to study the surge control effects of centrifugal compressors with active magnetic bearings (AMBs) under several operating conditions. First, the working principle of the magnetic thrust bearing is introduced, and the tracking performance of the rotor under the low frequency is verified by experiments. Then, the Greitzer model of centrifugal compressor is established. The relationship between tip clearance and the performance of compressor is derived, and the proportional-integral-derivative surge controller is designed based on the mass flow feedback. Finally, the surge control platform of the centrifugal compressor with active magnetic bearings is set up, and the surge control experiment of the magnetic bearing system is carried out. The influence of different speeds and different throttle valve openings on surge control performance is analyzed. The experimental results illustrate that speed has little effect on surge control, and the different throttle valve opening sizes have a certain influence on surge. The surge controller designed in this paper has a good control effect on different throttle valve opening sizes. Thus, the magnetic thrust bearing is effective in surge control by adjusting the tip clearance of the compressor.

Surge explicit nonlinear model predictive control using extended Greitzer model for a CCV supported compressor

ABSTRACTThis paper indicates the use of explicit nonlinear model predictive control method to prevent and control of compressor surge using extended Greitzer model. To encompass the effects of fast transients, nonlinear extended Greitzer model is considered for modelling and control of the compressor system. This model covers the effects of different parts, especially the compressor system pipeline, as the most important factor in the occurrence and acceleration of the surge. Also, the mathematical description of the flow dynamic of compression system is derived in the presence of close-coupled valve (CCV) as the most commonly used actuator. For controlling the compressor system surge instability, explicit nonlinear model predictive control (NMPC) is applied, whose allows efficient online implementation, significantly enlarges the operating region of the compressor and enhances the authority of the control system. Numerical simulations show that the proposed control system is able to meet the desired specifications in avoiding and active control of surge, in the presence of different types of disturbances occurring along the pipeline.Ovo je primjer sažetka. Ovo je primjer sažetka. Ovo je primjer sažetka. Ovo je primjer sažetka. Ovo je primjer sažetka. Ovo je primjer sažetka. Ovo je primjer sažetka. Ovo je primjer sažetka. Ovo je primjer sažetka. Ovo je primjer sažetka. Ovo je primjer sažetka. Ovo je primjer sažetka. Ovo je primjer sažetka. Ovo je primjer sažetka. Ovo je primjer sažetka.

Influence of Fouling on Compressor Dynamics: Experimental and Modeling Approach

The effect of compressor fouling on the performance of a gas turbine has been the subject of several papers; however, the goal of this paper is to address a more fundamental question of the effect of fouling, which is the onset of unstable operation of the compressor. Compressor fouling experiments have been carried out on a test rig refitted with TJ100 small jet engine with centrifugal compressor. Fouling on the compressor blade was simulated with texturized paint with average roughness value of 6 μm. Compressor characteristic was measured for both the clean (baseline) and fouled compressor blades at several rotational speeds by throttling the engine with variable exhaust nozzle. A Greitzer-type compression system model has been applied based on the geometric and performance parameters of the TJ100 small jet engine test rig. Frequency of plenum pressure fluctuation, the mean disturbance flow coefficient, and pressure-rise coefficient at the onset of plenum flow field disturbance predicted by the model was compared with the measurement for both the baseline and fouled engine. Model prediction of the flow field parameters at inception of unstable operation in the compressor showed good agreement with the experimental data. The results proved that used simple Greitzer model is suitable for prediction of the engine compressor unstable behavior and prediction of the mild surge inception point for both the clean and the fouled compressor.

Detecting Rotating Stall Precursors in Axial Compressors via Perturbations Part 2: Experiments

In Part 1 of this paper by Dong and Wang (“Detection of Rotating Stall Precursors in Axial Compressors via Periodic Perturbation Part 1: General Theory of Nonlinear Dynamics,” Journal of Propulsion and Power.), a general theoretic framework is established for prediction of the imminence of a subcritical Hopf bifurcation by using the properties of the dynamic response to periodic and small-amplitude random disturbances. In this paper (Part 2), experiments are carried out on a single-stage low-speed high hub-to-tip ratio compressor by using different levels of static circumferential inlet distortions. Based on the experimental data, a modified Moore–Greitzer model is proposed to accommodate the effects of the distortions on both the mean flow and the first spatial mode. The general theory is then applied to the model, and it is found that the theoretical formula for the sensitivity of amplitude of the first spatial mode to the variation of the bifurcation parameter predicts qualitatively well when compared with numerical simulations and the experiments. By using the sensitivity as the criterion, the imminence of rotating stall can be identified well before its inception, whereas without inlet distortion, the amplification of the first spatial model cannot be detected until at stall inception.

LINEAR STATE FEEDBACK DESIGN FOR SURGE CONTROL OF AXIAL FLOW COMPRESSOR DYNAMICS

Based on Moore and Greitzer's model [15], the surge behavior of axial flow compression system was found to be attributed to the appearance of Andronov-Hopf bifurcationin [12]. In this paper, we focus on the design of control law to prevent and/or delay the occurrence of the bifurcations, which will then suppress the surge behavior. Both types of linear dynamic state feedback and linear washout filter controllers are proposed. The proposed washout design does not require the explicit knowledge of the operating point and keep the original equilibrium characteristic while the dynamic feedback design will change the equilibrium operating points for pre-surge and post-surge regime. In addition, the washout type control scheme can relax the implementation of the control law in the practical applications. Numerical results demonstrate the effectiveness of the proposed designs and the superiority of the washout filter scheme.

Stable and Efficient Operation of Gas Compressor With Improving of Surge Detection System

This paper investigates the application of fault diagnosis (FD) approach for improving performance of compressors within exact operating point determination. Detecting of sensor fault or failure status is more important in the compressor for safety-critical application. No work has previously been reported on the use of the FD system within a compressor surge-suppressing system. Therefore, the main contribution of this paper is presenting different and complementary techniques for surge-suppressing studies via sensor FD. By data acquisition from a nonlinear Moore–Greitzer model, a neural network (NN) and innovation complex decision logic provide residual generation and evaluation blocks in an analytical redundancy FD system, respectively. The proposed FD deals with the most-common sensor faults and failures in seven different scenarios according to their nature, such as bias, cutoff, loss of efficiency, and freeze.

Surge Onset in Turbo Heat Pumps

A typical turbo heat pump system consists of a centrifugal compressor, expansion valve, and two heat exchangers—a condenser and evaporator. Compared to a gas turbine, a turbo heat pump introduces additional complexities because it is a two-phase closed-loop system with heat exchange using a real gas/liquid (refrigerant) as the working fluid. For the first time, surge onset in such systems has been physically, analytically, and experimentally investigated. This study analytically investigates the physical mechanisms of surge onset in turbo heat pumps. From an existing nonlinear turbo heat pump surge model, the turbo heat pump is viewed as a mass-spring-damper system with two inertias, two dampers, and four springs which is then further simplified to a single degree-of-freedom system. Surge onset occurs when the system damping becomes zero and depends not only the compressor but also on the ducts, heat exchangers, and expansion valve. Alternatively, a new stability model has been developed by applying a linearized small perturbation method to the nonlinear turbo heat pump surge model. When the new linear stability model is applied to a conventional open loop compression system (e.g., a turbocharger), predictions identical to those of Greitzer's model are obtained. In addition, surge onset has been experimentally measured in two turbo heat pumps. A comparison of the predictions and measurements shows that the mass-spring-damper model and the linearized stability model can accurately predict the turbo heat pump surge onset and the mass-spring-damper model can explain the turbo heat pump surge onset mechanisms and parametric trends in turbo heat pumps.

A Hybrid Approach for the Modelling of Axial Compressor Surge

This paper discusses the results of a hybrid approach, which couples the Moore–Greitzer potential flow model and the Navier–Stokes solution to predict the viscous effects on the axial compressor surge. The viscous effects are accounted by the inclusion of a duct between the compressor exit and the plenum inlet. The unsteady mass flow solution from the Moore–Greitzer model is supplied as an inlet boundary condition, to the duct, to solve the Navier–Stokes equation. The viscosity is seen to damp the surge oscillations and alter the character of oscillations significantly. A shortcoming of the Moore–Greitzer model in predicting proper phase relationship between the compressor flow and the plenum pressure is pointed out and the proposed hybrid approach is shown to overcome this flaw to a greater extent. It is depicted that this hybrid approach captures the existence of rotating stall disturbances in the combustor, during a typical classic surge cycle, as reported in the literatures. Thus this hybrid model is more physically appropriate in describing the plenum pressure oscillations than the Moore–Greitzer model. The combustor pressure oscillations from the hybrid approach shows two distinct time scales that can influence the combustor efficiency.

A Simple Feedback Control Strategy for Controlling the Axial Compressor Surge

This paper presents the results of a feedback technique for controlling low frequency surge oscillations in an axial compressor. To simulate surge a hybrid model is developed, by coupling the Moore - Greitzer potential flow model and the Navier - Stokes solution, to result in more realistic flow predictions. This hybrid model incorporates the viscous effect on the flow behaviour, which is neglected in the Moore - Greitzer model. The present model is shown to capture the existence of rotating stall disturbances in the combustor during a typical classic surge cycle as has been reported in the experiments. After modelling the surge we propose a steady feedback control scheme to minimise the adverse effect of the surge oscillations on the combustor operation. The results for a four hole and six hole feedback control mechanisms are reported and it is seen that the existing high frequency fluctuations in the unsteady variation of plenum pressure before control are virtually eliminated in the presence of a stead...

Theoretical analysis of the effect of water and ethanol injection on axial compressor instabilities

Two types of instabilities that occur in compression systems rotating stall and surge have an adverse effect on the compressor performance. Several techniques have been explored to minimize the effect of these instabilities. It has been observed that injection of a liquid into the compressor not only improves thermodynamic efficiencies but also results in stabilizing the system. Therefore, water and ethanol injection has been investigated as an effective tool for controlling these compressor instabilities. In the present paper a modified Moore–Greitzer model has been proposed for wet compression-based system using water and ethanol. Under this work the effect of injection of water (1) at various stages of compressor, (2) at different altitudes and (3) by varying amounts has also been presented. The effect of various parameters on wet compression such as (a) Optimum stage for liquid injection (b) Optimum amount of liquid injection and (c) Effect of altitude on liquid injection is also examined in the present work which shows that the liquid injection helps in improving the performance of compression systems in terms of increase in the stall margin and pressure rise coefficient. ► We model the effect of liquid injection on the performance of axial flow compressors. ► The basic Moore–Grietzer’s model has been appropriately modified. ► Injection of liquid in the later stages of the compressor resulted in improved stall margin and pressure rise. ► Use of ethanol was found to give better performance than water.

DYNAMICS OF LOSS OF GASDYNAMIC STABILITY OF TURBO-ENGINE

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. A bifurcation analysis was carried out to determine the system stability.

USE BIFURCATION THEORY TO ASSESS THE STABILITY OF CURRENTS IN THE AXIAL COMPRESSOR

In the paper surge is considered as self-oscillation phenomenon. Possibility of surge prediction and effect on its development with the help of feedback controllers is investigated. Solving of a problem of non-linear control using the bifurcation theory is considered in the article. The Moore—Greitzer model (MG86) is used for research of processes in the compressor after loss gasdynamic stability. The model takes into account non-linear features of compressor characteristics and property of the compressor system. The model allows to determine what type of phenomena (rotating stall or surge) can appear, to establish distinctions in character surge oscillations and to estimate influence of various factors on area surge modes, to determine area of steady modes.

Variable structure surge control for constant speed centrifugal compressors

This paper presents the application of active control of surge in constant speed centrifugal compressors based on the Moore–Greitzer (MG) model. Different controllers are developed for a compression system equipped with a close-coupled valve (CCV) and a throttle control valve (TCV). The combination of the two valves helps suppress surge and assists in overcoming the drawbacks of each valve when it is used individually. The presented controllers are evaluated based on many performance indices. Accordingly, a case-based variable structure controller is developed that succeeds to stabilize the system for various operating conditions and to extend the stable range well beyond the surge line. A flow extension of 76% and a stable throttle level of 0.1, with substantially decreased pressure settling times, are reported. The developed controller performs significantly better compared to other nonlinear controllers, such as the backstepping controller.

Quantitative Characteristic of Rotating Stall and Surge for Moore–Greitzer PDE Model of an Axial Flow Compressor

A commonly used mathematical model for axial flow compressors that captures the flow behavior of a compression system, known as the Moore–Greitzer model, consists of a PDE and two ODEs. The PDE describes the dynamical behavior of disturbances in the inlet region of the compression system, and the two ODEs describe the coupling of the disturbances with the mean flow. In this paper, we obtain a quantitative characteristic $\Delta$, depending on the compressor geometry, to identify the type of oscillations of the system. More specifically, the sign of $\Delta$ indicates the physical oscillations predominated by rotating stall or by surge. In mathematical terminology, these three types of oscillations are distinctive Hopf bifurcations occurring in the system as the throttle coefficient decreases, and they present quite different dynamical behaviors in axial engine compressors. Estimations of oscillation frequencies corresponding to surge and rotating stall, respectively, are also given in the paper. Numerical simulations are provided to demonstrate different types of flow oscillation of the system.

ACTIVE SUPPRESSION OF AERODYNAMIC INSTABILITIES IN THE AXIAL FLOW COMPRESSORS

Aerodynamic instabilities due to rotating stall initiation and surge trigger in the axial flow compressors were investigated using different mathematical models. Limit of stability of the rotating stall was detected using simple model that considers transport of energy by the rotor wakes passing through the stator. Active suppression of the aerodynamic instabilities in the axial flow compressors were demonstrated using mechanical compensated system with controlled plenum simultaneously with air injection through reed valve. A nonlinear controller based on a bifurcation theory was used to design feedback control system for eliminating surge and rotating stall as well hysteresis. The bifurcation analysis was performed to determine the effect of throttle gain on the compressor limit of stability and then modifying the throttle characteristic to eliminate hysteresis and suppresses surge. The Moore–Greitzer model was extended to include the influences of the air injection on the axial flow compressors performance characteristics and to enhance the limit of stabilities of both the stall and the surge. Comparisons of the present theoretical results with the available previous experimental and theoretical results were carried out.

LPV model identification for gain scheduling control: An application to rotating stall and surge control problem

We approach the problem of identifying a nonlinear plant by parameterizing its dynamics as a linear parameter varying (LPV) model. The system under consideration is the Moore–Greitzer model which captures surge and stall phenomena in compressors. The control task is formulated as a problem of output regulation at various set points (stable and unstable) of the system under inputs and states constraints. We assume that inputs, outputs and scheduling parameters are measurable. It is worth pointing out that the adopted technique allows for identification of an LPV model's coefficients without the requirements of slow variations amongst set points. An example of combined identification, feedback control design and subsequent validation is presented.