Determination of compressor in-stall characteristics from engine surge transients

A technique for extracting the in-stall pumping characteristics for an axial flow compressor operating in an engine system environment is developed. The technique utilizes a Hybrid computer simulation of the compressor momentum equation into which actual transient data are used to provide all terms but the desired compressor characteristic. The compressor force characteristic as a function of corrected flow and speed result from the computation. The critical problem of data filtering is addressed. Results for a compressor operating in a turbofan engine are presented and comparison is made with the conventional compressor map. The relationship of the compressor surge characteristic with its rotating stall characteristic is explored. Initial interpretation of the measured results is presented

Active Control of an Axial Flow Compressor via Pulsed Air Injection

This paper presents the use of pulsed air injection to control the onset of rotating stall in a low-speed, axial flow compressor. By measuring the unsteady pressures near the rotor face, a control algorithm determines the magnitude and phase of the first mode of rotating stall and controls the injection of air in the front of the rotor face. Experimental results show that this technique slightly extends the stall point of the compressor and eliminates the hysteresis loop normally associated with rotating stall. A parametric study is used to determine the optimal control parameters for suppression of stall. Analytic results---using a low-dimensional model developed by Moore and Greitzer combined with an unsteady shift in the compressor characteristic to model the injectors---give further insights into the operation of the controller. Based on this model, we show that the behavior of the experiment can be explained as a change in the bifurcation behavior of the system under nonlinear feedback. A higher fidelity simulation model is then used to further verify some of the specific performance characteristics that are observed in experiments

Nonlinear Control and Modeling of Rotating Stall in an Axial Flow Compressor

This thesis focuses on understanding the use of air injection as a means of controlling rotating stall in an axial flow compressor, involving modeling, dynamical systems analysis, and experimental investigations. The first step towards this understanding was the development of a low order model for air injection control, the starting point of which was the Moore and Greitzer model for axial flow compressors. The Moore and Greitzer model was extended to include the effects of air injection and bifurcation analysis was performed to determine how the closed loop system dynamics are different from those of the open loop system. This low order model was then used to determine the optimal placement of the air injection actuators. Experimental work focused on verifying that the low order model, developed for air injection actuation, qualitatively captured the behavior of the Caltech compressor rig. Open loop tests were performed to determine how the placement of the air injectors on the rig affected the performance of the compressor. The positioning of the air injectors that provided the greatest control authority were used in the development of air injection controllers for rotating stall. The controllers resulted in complete elimination of the hysteresis associated with rotating stall. The use of a throttle actuator for the control of the surge dynamics was investigated, and then combined with an air injection controller for rotating stall; the resulting controller performed quite well in throttle disturbance rejection tests. A higher order model was developed to qualitatively match the experimental results with a simulation. The results of this modeling effort compared quite well with the experimental results for the open loop behavior of the Caltech rig. The details of how the air injection actuators affect the compressor flow were included in this model, and the simulation predicted the same optimal controller that was developed through experimentation. The development of the higher order model also included the investigation of systematic methods for determining the simulation parameters. Based on experimental measurements of compression system transients, the open loop simulation parameters were identified, including values for the compressor performance characteristic in regions where direct measurements were not possible. These methods also provided information on parameters used in the modeling of the pressure rise delivered by the compressor under unsteady flow conditions

Model Analysis and Nonlinear Control of Air Compressors

RÉSUMÉ Pendant des décennies, les turbines à gaz ont été des dispositifs importants et fiables dans les domaines de la production d'énergie, de l'industrie pétrochimique, et de l'aéronautique. Ces machines utilisent les compresseurs centrifuges et axiaux qui se dégradent en présence d’instabilités aérodynamiques telles que le pompage et le décrochage tournant. Ces dernières limitent la performance et peuvent causer des sollicitations mécaniques importantes, une réduction de la durée de vie, du bruit et des vibrations. De plus, dans les compresseurs axiaux à vitesse variable (CAVV), les variations de vitesse affectent la stabilité des systèmes et peuvent entraîner le pompage et le décrochage tournant. Cela limite le taux de variation de vitesse et pénalise la performance. Le travail présenté dans cette thèse dresse premièrement l'analyse de bifurcation du modèle des CAVVs afin d’étudier l'impact de la dynamique de la vitesse sur la stabilité de points de fonctionnement efficaces. Ici, le taux de variation de vitesse (accélération) est défini comme un nouveau paramètre du modèle et une analyse détaillée de bifurcation numérique est fournie. Les résultats des simulations dans le domaine temporel valident non seulement l'analyse de bifurcation, mais élargissent aussi nos connaissances sur la réponse transitoire du modèle, qui est d’une importance majeure. L'analyse réalisée révèle que les variations de vitesse peuvent mener à un décrochage tournant entièrement développé ainsi qu’au décrochage temporaire mentionné précédemment. Les résultats montrent que les instabilités développées dépendent fortement du taux d'accélération. L'impact des autres paramètres du modèle, les vitesses initiale et finale, et la contribution des modes du décrochage sont également étudiés. Au niveau du contrôle, malgré toutes les réalisations présentées, la conception d’une commande robuste même pour des systèmes de compression axiaux à vitesse constante demeure encore un problème difficile. Ici, deux méthodes de commande non linéaires: le contrôle par modes glissants et le contrôle par passivité sont proposées pour résoudre ce problème de stabilité. Ces deux approches traitent de tous les aspects difficiles du sujet qui apparaissent dans la littérature : l'impact des perturbations externes, le manque de connaissance précise des paramètres du modèle, et l'absence d’un retour d’état complet.---------- ABSTRACT For decades, gas turbines have been important, widespread, and reliable devices in the field of power generation, petrochemical industry, and aeronautics. They employ centrifugal and axial compressors which suffer from aerodynamic instabilities, namely, surge and rotating stall. These performance limiting instabilities can cause component stress, lifespan reduction, noise, and vibration. Furthermore, in variable speed axial compressors (VSACs), speed variations affect the system stability and can lead to surge and rotating stall. This limits the rate of speed variations and results in important performance penalties. The present work firstly addresses the bifurcation analysis of VSACs’ model to investigate the impact of speed dynamics on the stability of efficient operating points. Here, the rate of speed variations (acceleration rate) is defined as a new parameter of the model and a detailed numerical bifurcation analysis is provided. The results of time-domain simulations not only validate the results of bifurcation analysis, but also broaden our knowledge about the transient response of the model, which is a matter of importance as well. The analysis reveals that speed variations can lead to a fully developed rotating stall as well as the previously reported temporary stall developments. The results show that the developed instabilities depend to a great extent on the acceleration rate. The impact of other key issues such as throttle gain, viscosity factor, initial speed, final speed, and the contribution of stall modes are also explored. From the control point of view, despite reported achievements, robust control design for compression systems remains a challenging problem. In this work, at first, two nonlinear approaches are proposed to tackle the stability problem of constant-speed axial compressors (CSACs). The first approach is a robust passivity-based control and the second one is a second order sliding mode control. The approaches tackle the challenging problems being addressed in the literature such as: the impact of external perturbations, the lack of detailed parameters knowledge, and the absence of full-state feedback. They drive the control from pressure and mass flow measurements and use throttle and close-coupled valve actuations. Finally, this study reports that these methods can be used in the case of VSACs by applying the required modifications to simultaneously control speed and instabilities. This simultaneous control design has been an open problem and the proposed method can improve the performance of VSACs

"Analysis of dynamic responses and instabilities in rotating machinery\u201d

The first task of the present research is to characterize both experimentally and numerically journal bearings with low radial clearances for rotors in small-scale applications (e.g., micro Gas Turbines); their diameter is in the order of ten millimetres, leading to very small dimensional clearances when the typical relative ones (order of 1/1000) are employed; investigating this particular class of journal bearings under static and dynamic loading conditions represents something unexplored. To this goal, a suitable test rig was designed, and the performance of its bearings were investigated under steady load. For the sake of comparison, numerical simulations of the lubrication were also performed by means of a simplified model. The original test rig adopted is a commercial Rotor Kit (RK), but substantial modifications were carried out in order to allow significant measurements. Indeed, the relative radial clearance of RK4 RK bearings is about 2/100, while it is around 1/1000 in industrial bearings. Therefore, the same original RK bearings are employed in this new test rig, but a new shaft was designed to reduce their original clearance. The new custom shaft allows to study bearing behaviour for different clearances, since it is equipped with interchangeable journals. Experimental data obtained by this test rig are then compared with further results of more sophisticated simulations. They were carried out by means of an in-house developed finite element (FEM) code, suitable for ThermoElasto-HydroDynamic (TEHD) analysis of journal bearings both in static and dynamic conditions. In this work, bearing static performances are studied to assess the reliability of the experimental journal location predictions by comparing them with the ones coming from already validated numerical codes. Such comparisons are presented both for large and small clearance bearings of original and modified RK, respectively. Good agreement is found only for the modified RK equipped with small clearance bearings (relative radial clearance 8/1000), as expected. In comparison with two-dimensional lubrication analysis, three-dimensional simulation improves prediction of journal location and correlation with experimental results. The second main task of the present work is the development and the implementation of a suitable analytical model to correctly capture rolling bearing radial stiffness, particularly nearby the critical speeds of the investigated rotor-bearings system. In this work, such bearing non-linear stiffness lumped parameter model is firstly validated on the commercial RK and then it is applied to both air bladeless turbines (or Tesla turbines) and to an innovative microturbine, in order to assess their global rotodynamic behavior when they are mounted on ball bearings. In order to properly investigate all the issues related to critical speeds and stiffness, an adequate number of experimental tests was performed by exploiting an experimental air Tesla turbine prototype located at TPG experimental facility of the University of Genoa. The correlation between measured flexural critical speeds and their numerical predictions is markedly conditioned by the correct identification of ball bearings dynamic characteristics; in particular, bearings stiffness effect may play a significant role in terms of rotor-bearings system natural frequencies and therefore it must be properly assessed. Indeed, Tesla turbine rotor FE model previously employed for numerical modal analysis relies on rigid bearings assumption and therefore it does not account for bearings stiffness overall contribution, which may become crucial in case of \u201chard mounting\u201d of rotor-bearings systems. Subsequently, high-speed air Tesla rotor is investigated by means of an enhanced FE model for numerical modal analysis within Ansys\uae environment, where ball bearings are modelled as non-linear springs whose stiffness is expressed according to the analytic model implemented in Matlab\uae. Two different numerical FE models are devised for microturbine rotor modelling which respectively rely on beam elements and on three-dimensional solid elements for mechanical system spatial discretization. The obtained results in terms of rotor-bearings system modal analysis exhibit an improvement in experimental-numerical results correlation by relying on such ball bearing stiffness model; moreover, beam-based FE model critical speeds predictions are coherent with experimental evidence and with respect to solid elements model it is characterized by lower computational time and it is more easily interpretable. Thus, such experimentally validated numerical model represents a reliable and easily adaptable tool for highspeed rotating machinery critical speeds prediction in practical industrial application cases. Finally In this work, several signal processing techniques performed on vibro-acoustic signals acquired from a T100 Turbec microturbine (which is furnished with a centrifugal compressor) are illustrated. Research activity goal focuses on the investigation different kinds of system response starting from non-intrusive probes signals like accelerometers and microphones; this is made by means of techniques such as HOSA and Wavelet Transform, developed in Matlab\uae environment, for early detection of the onset of unstable phenomena in centrifugal compressors. These new and different methods have been applied to the same set of data to get sufficiently independent information useful to synergistically improve knowledge in the diagnostic system. Data were acquired by means of an experimental facility based on a T100 turbine developed by the Thermochemical Power Group (TPG) at the University of Genoa. Sampling rate and sensor placement were carefully taken into account, basing both on the physical phenomena to be observed and on the sensor dynamic characteristics. In this context, it is meant to study microphones and accelerometers signals not from an isolated centrifugal turbomachine installed in a dedicated line, but from a whole compressor placed in a mGT system for energy generation. Indeed, the investigated machine is not operating in standalone mode, but its working point and angular velocity depend on the coupling with several elements. In particular, compressor working point and then its vibro-acoustic signals are expected to convey vibration and sound contributions coming from all the plant components; thus, they are more representative of machine realistic behavior in the energy system

A new first-principles model to predict mild and deep surge for a centrifugal compressor

Centrifugal compressors are used in many applications, including automotive turbochargers. Surge is an instability that occurs at low mass flow rates that is often damaging. Even mild surge produces noise characteristics that cause problems with customer acceptance. It is therefore important to be able to predict both mild and deep surge onset. In existing literature, models resulting in cubic-shaped compressor characteristics have been developed from first principles. This paper extends these to include diffuser recirculation and show a new quintic-like shape for compressor characteristics which, for the first time, can differentiate between mild and deep surge. These characteristics are incorporated into a model for an experimental facility and resulting simulations show remarkable fit to experimental data. The model allows for variations in both space and time, so simulations can capture wave dynamics in the pipework. The model captures: stable operation, mild surge, transition from mild to deep surge, deep surge, and the potential for a stable quiet period beyond the surge limit. Furthermore, the model can provide physical explanations for the surge dynamics observed. This combined with the model's predictive ability will be of help to turbocharger manufacturers during early design stages, prior to experimental tests or detailed CFD studies.</p

Hopf Bifurcations of Moore-Greitzer PDE Model with Additive Noise

The Moore-Greitzer partial differential equation (PDE) is a commonly used mathematical model for capturing flow and pressure changes in axial-flow jet engine compressors. Determined by compressor geometry, the deterministic model is characterized by three types of Hopf bifurcations as the throttle coefficient decreases, namely surge (mean flow oscillations), stall (inlet flow disturbances) or a combination of both. Instabilities place fundamental limits on jet-engine operating range and thus limit the design space. In contrast to the deterministic PDEs, the Hopf bifurcation in stochastic PDEs is not well understood. The goal of this particular work is to rigorously develop low-dimensional approximations using a multiscale analysis approach near the deterministic stall bifurcation points in the presence of additive noise acting on the fast modes. We also show that the reduced-dimensional approximations (SDEs) contain multiplicative noise. Instability margins in the presence of uncertainties can be thus approximated, which will eventually lead to lighter and more efficient jet engine design