OH* Chemiluminescence in a Multipoint Combustion System: Steady State and Limit Cycle Behavior

2013 ◽  
Author(s):  
Brian Dolan ◽  
Rodrigo Villalva Gomez ◽  
David Munday ◽  
Ephraim Gutmark ◽  
Gregory Zink ◽  
...  
Keyword(s):  
Steady State ◽  
Limit Cycle ◽  
Combustion System ◽  
Limit Cycle Behavior

Limit-Cycle Analysis of Planar Rotor/Autobalancer System Supported on Hydrodynamic Journal Bearing

2011 ◽  
Author(s):  
DaeYi Jung ◽  
Hans DeSmidt
Keyword(s):  
Steady State ◽  
Limit Cycle ◽  
Journal Bearing ◽  
Cross Coupling ◽  
Numerical Continuation ◽  
Radial Clearance ◽  
Oil Viscosity ◽  
Rotor Systems ◽  
Automatic Balancing ◽  
Limit Cycle Behavior

In recent years, there has been much interest in the use of so-called automatic balancing devices (ABD) in rotating machinery. Essentially, ABDs or “autobalancers” consists of several freely moving eccentric balancing masses mounted on the rotor, which, at certain operating speeds, act to cancel rotor imbalance at steady-state. This “automatic balancing” phenomena occurs as a result of nonlinear dynamic interactions between the balancer and rotor wherein the balancer masses naturally synchronize with the rotor with appropriate phase and cancel the imbalance. However, due to inherent nonlinearity of the autobalancer, the potential for other, undesirable, non-synchronous limit-cycle behavior exists. In such situations, the balancer masses do not reach their desired synchronous balanced steady-state positions resulting in increased rotor vibration. Such automatic behavior has been widely studied and is well understood for rotor systems on idealized bearings with symmetric supports. This paper presents a comprehensive study into automatic balancing behavior of an imbalanced planar rigid rotor/ABD system mounted in two different widely-used types of hydrodynamic bearings; i) the short journal bearing with asymmetric stiffness, damping and cross-coupling terms and ii) a so-called tilting-pad bearing. In this study the non-dimensional characteristic curves of stiffness and damping of these two fluid film bearings are employed and the rotor/bearing/ABD system autobalancing behavior is studied as a function of rotor speed, bearing eccentricity and bearing journal radial clearance. These two essential bearing parameters in turn are directly determined by the rotor static loading, bearing structure, and oil viscosity. Consequently, this research focuses on the connectivity between the bearing parameters and the corresponding synchronous balancing and non-synchronous limit-cycle behavior of the system. Here, solutions for rotor limit-cycle amplitudes and corresponding autobalancer ball speeds are obtained via a harmonic balance and numerical continuation solution approach. Furthermore, an exact solution for the limit-cycle is obtained for the special case of symmetric support stiffness together with a so-called Alford’s force cross-coupling term. In each case, the limit-cycle stability is assessed via a perturbation and Floquet analysis and the coexistence of the stable balanced synchronous limit-cycle and undesired non-synchronous limit-cycle is studied. It is found that for certain combinations of bearing parameters and operating speeds, the non-synchronous limit-cycle can be made unstable thus guaranteeing global asymptotic stability of the synchronous balanced condition. Finally, the analysis is validated through numerical time-domain simulation. The findings in this paper yield important insights for researchers wishing to utilize automatic balancing devices in practical rotor systems.

Modeling Unsteady Flow of a Lean Partially Premixed Flame on a Dry Low NOx Combustion System

2013 ◽  
Author(s):  
Salvatore Matarazzo ◽  
Hannes Laget ◽  
Evert Vanderhaegen ◽  
Jim B. W. Kok
Keyword(s):  
Gas Turbine ◽  
Limit Cycle ◽  
Gas Turbines ◽  
Premixed Flame ◽  
Computational Domain ◽  
Pressure Oscillations ◽  
Combustion Dynamics ◽  
Partially Premixed ◽  
Partially Premixed Flame ◽  
Limit Cycle Behavior

The phenomenon of combustion dynamics (CD) is one of the most important operational challenges facing the gas turbine (GT) industry today. The Limousine project, a Marie Curie Initial Training network funded by the European Commission, focuses on the understanding of the limit cycle behavior of unstable pressure oscillations in gas turbines, and on the resulting mechanical vibrations and materials fatigue. In the framework of this project, a full transient CFD analysis for a Dry Low NOx combustor in a heavy duty gas turbine has been performed. The goal is to gain insight on the thermo-acoustic instability development mechanisms and limit cycle oscillations. The possibility to use numerical codes for complex industrial cases involving fuel staging, fluid-structure interaction, fuel quality variation and flexible operations has been also addressed. The unsteady U-RANS approach used to describe the high-swirled lean partially premixed flame is presented and the results on the flow characteristics as vortex core generation, vortex shedding, flame pulsation are commented on with respect to monitored parameters during operations of the GT units at Electrabel/GDF-SUEZ sites. The time domain pressure oscillations show limit cycle behavior. By means of Fourier analysis, the coupling frequencies caused by the thermo-acoustic feedback between the acoustic resonances of the chamber and the flame heat release has been detected. The possibility to reduce the computational domain to speed up computations, as done in other works in literature, has been investigated.

Limit-Cycle Analysis of Three-Dimensional Flexible Shaft/Rigid Rotor/Autobalancer System With Symmetric Rigid Supports

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
DaeYi Jung ◽  
H. A. DeSmidt
Keyword(s):  
Limit Cycle ◽  
Three Dimensional ◽  
Design Parameters ◽  
Rigid Rotor ◽  
Modal Shape ◽  
Flexible Shaft ◽  
Flexible Mode ◽  
Automatic Balancing ◽  
Rigid Supports ◽  
Limit Cycle Behavior

In recent years, there has been much interest in the use of automatic balancing devices (ABD) in rotating machinery. Autobalancers consist of several freely moving eccentric balancing masses mounted on the rotor, which, at certain operating speeds, act to cancel rotor imbalance. This “automatic balancing” phenomenon occurs as a result of nonlinear dynamic interactions between the balancer and rotor wherein the balancer masses naturally synchronize with the rotor with appropriate phase to cancel the imbalance. However, due to inherent nonlinearity of the autobalancer, the potential for other undesirable nonsynchronous limit-cycle behavior exists. In such situations, the balancer masses do not reach their desired synchronous balanced positions resulting in increased rotor vibration. To explore this nonsynchronous behavior of ABD, the unstable limit-cycle analysis of three-dimensional (3D) flexible shaft/rigid rotor/ABD/rigid supports described by the modal coordinates has been investigated here. Essentially, this paper presents an approximate harmonic analytical solution to describe the limit-cycle behavior of ABD–rotor system interacting with flexible shaft, which has not been fully considered by ABD researchers. The modal shape of flexible shaft is determined by using well-known fixed–fixed boundary condition due to symmetric rigid supports. Here, the whirl speed of the ABD balancer masses is determined via the solution of a nonlinear characteristic equation. Also, based upon the analytical limit-cycle solutions, the limit-cycle stability of three primary design parameters for ABD is assessed via a perturbation and Floquet analysis: the size of ABD balancer mass, the ABD viscous damping, and the relative axial location of ABD to the imbalance rotor along the shaft. The coexistence of the stable balanced synchronous condition and undesirable nonsynchronous limit-cycle is also studied. It is found that for certain combinations of ABD parameters and rotor speeds, the nonsynchronous limit-cycle can be made unstable, thus guaranteeing asymptotic stability of the synchronous balanced condition at the supercritical shaft speeds between each flexible mode. Finally, the analysis is validated through numerical simulation. The findings in this paper yield important insights for researchers wishing to utilize ABD in flexible shaft/rigid rotor systems and limit-cycle mitigation.

A modified Oregonator model exhibiting complicated limit cycle behavior in a flow system

1978 ◽  
Vol 69 (6) ◽  
pp. 2514 ◽  
Author(s):  
Kenneth Showalter ◽  
Richard M. Noyes ◽  
Kedma Bar-Eli
Keyword(s):  
Limit Cycle ◽  
Flow System ◽  
Oregonator Model ◽  
Limit Cycle Behavior

scholarly journals An intermittent control model of flexible human gait using a stable manifold of saddle-type unstable limit cycle dynamics

2014 ◽  
Vol 11 (101) ◽  
pp. 20140958 ◽  
Author(s):  
Chunjiang Fu ◽  
Yasuyuki Suzuki ◽  
Ken Kiyono ◽  
Pietro Morasso ◽  
Taishin Nomura
Keyword(s):  
Steady State ◽  
Limit Cycle ◽  
Unstable Manifold ◽  
Control Strategy ◽  
Stable Manifold ◽  
Joint Angle ◽  
Feedback Controller ◽  
Human Gait ◽  
Intermittent Control ◽  
Saddle Type

Stability of human gait is the ability to maintain upright posture during walking against external perturbations. It is a complex process determined by a number of cross-related factors, including gait trajectory, joint impedance and neural control strategies. Here, we consider a control strategy that can achieve stable steady-state periodic gait while maintaining joint flexibility with the lowest possible joint impedance. To this end, we carried out a simulation study of a heel-toe footed biped model with hip, knee and ankle joints and a heavy head-arms-trunk element, working in the sagittal plane. For simplicity, the model assumes a periodic desired joint angle trajectory and joint torques generated by a set of feed-forward and proportional-derivative feedback controllers, whereby the joint impedance is parametrized by the feedback gains. We could show that a desired steady-state gait accompanied by the desired joint angle trajectory can be established as a stable limit cycle (LC) for the feedback controller with an appropriate set of large feedback gains. Moreover, as the feedback gains are decreased for lowering the joint stiffness, stability of the LC is lost only in a few dimensions, while leaving the remaining large number of dimensions quite stable: this means that the LC becomes saddle-type, with a low-dimensional unstable manifold and a high-dimensional stable manifold. Remarkably, the unstable manifold remains of low dimensionality even when the feedback gains are decreased far below the instability point. We then developed an intermittent neural feedback controller that is activated only for short periods of time at an optimal phase of each gait stride. We characterized the robustness of this design by showing that it can better stabilize the unstable LC with small feedback gains, leading to a flexible gait, and in particular we demonstrated that such an intermittent controller performs better if it drives the state point to the stable manifold, rather than directly to the LC. The proposed intermittent control strategy might have a high affinity for the inverted pendulum analogy of biped gait, providing a dynamic view of how the step-to-step transition from one pendular stance to the next can be achieved stably in a robust manner by a well-timed neural intervention that exploits the stable modes embedded in the unstable dynamics.

Limit cycle behavior of the bump-on-tail instability

1981 ◽  
Vol 24 (2) ◽  
pp. 268 ◽  
Author(s):  
Peter A. E. M. Janssen
Keyword(s):  
Limit Cycle ◽  
Limit Cycle Behavior
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