scholarly journals Flow-Excited Turbine Rotor Instability

1994 ◽  
Vol 1 (1) ◽  
pp. 37-51 ◽  
Author(s):  
Andrew D. Dimarogonas ◽  
Julio C. Gomez-Mancilla
Keyword(s):  
Limit Cycles ◽  
High Amplitude ◽  
Turbine Rotor ◽  
Design Stage ◽  
Stable Limit ◽  
Element Analysis ◽  
Tilting Pad ◽  
Linearized System ◽  
The Stability ◽  
Analytical Expressions

The problem of steam whirl is one of the technological limits that now prohibit the development of power-generating turbomachinery substantially above GW. Due to steam flow, self-excited vibrations develop at high loads in the form of stable limit cycles that, at even higher loads, deteriorate to chaotic vibration of high amplitude.A mathematical model is developed for stability analysis and for the development of a rational stability criterion to be used at the design stage. The bearing nonlinearity is introduced in the form of high-order coefficients of a Taylor expansion of the perturbation forces for fixed-arc slider bearings and employing nonlinear pad functions for the tilting pad bearings. The flow excitation is introduced in the form of follower force gradients related to the flow and the power generated.The study of the stable and unstable limit cycles, and the stability of the system in the large, beyond the linear analysis currently utilized, is done analytically for the De Laval rotor and numerically with finite element analysis of typical turbomachinery rotors.The range of loads for which limit cycles exist was found to be substantial. This is important for the operation of large machinery because such cycles permit the operation at loads much higher than the ones that correspond to the onset of instability of the linearized system. The conditions for the limit cycle deterioration into chaotic orbit are investigated. Analytical expressions have been obtained for the different stability thresholds for the De Laval rotor.

On the Behaviour of Steamwhirl and Nonlinear Rotor-Bearing Systems

1993 ◽  
Author(s):  
Julio C. Gómez-Mancilla ◽  
Andrew D. Dimarogonas
Keyword(s):  
Limit Cycles ◽  
Tangential Force ◽  
Stable Limit ◽  
Slider Bearing ◽  
Chaotic Orbit ◽  
Element Analysis ◽  
Tilting Pad ◽  
Linearized System ◽  
Analytical Expressions ◽  
Stable Limit Cycles

Abstract The problem of steamwhirl is the technological limit which now prohibits the development of power generating turbomachinery substantially above 1 GW. Due to the steam flow, self excited vibrations develop at high loads, above the onset of instability of the linearized system, in the form of stable limit cycles which, at even higher loads, deteriorate to chaotic vibration. The bearing nonlinearity is introduced in the form of high order coefficients of a Taylor expansion of the perturbation forces for fixed-arc slider bearing and employing non-linear pad functions for the tilting pad bearings. The flow excitation is introduced in the form of radial and tangential force gradients related to the flow and power generated. The study of stable and unstable limit cycles and stability of the system in the large, beyond the linear analysis currently utilized, is done analytically for the DeLaval rotor and numerically with Finite Element analysis of typical turbomachinery rotors. The range of loads for which limit cycles exist was found to be substantial. This is important for the operation of large machinery because such limit cycles permit the operation at loads much higher than the ones which correspond to the onset of instability of the linearized system. The conditions for the limit cycle deterioration into chaotic orbit is studied. Analytical expressions have been obtained for the different thresholds for the DeLaval rotor.

Turbine Rotor Tooth Head and Stress Analysis of Wedge

2013 ◽  
Vol 395-396 ◽  
pp. 856-861
Author(s):  
Li Li Zhao
Keyword(s):  
Structural Design ◽  
Turbine Rotor ◽  
Structure Modification ◽  
Ansys Software ◽  
Turbine Generator ◽  
Element Analysis ◽  
Generator Rotor ◽  
The Stability ◽  
Rotor Tooth ◽  
Rotor Structure

The turbine generator rotor and the wedge is an important part of the turbogenerator. In order to ensure the stability and reliability of the steam turbine during operation, it needs to calculate and analyze the strength of the generator rotor and the wedge. In this paper, we did the study of the turbine generator rotor and the strength of the wedge by finite element analysis. by using ANSYS software, when in operating speed and speeding, we compared to the results of the calculation of plane and solid elements, and found that the safety factor of the plane was lower. Based on the results of two calculations, we got the generator rotor structure modification and optimization of the structural design, which improve the strength of the generator rotor tooth head and wedge.

scholarly journals An analysis of instabilities and limit cycles in glacier-dammed reservoirs

2019 ◽  
Author(s):  
Christian Schoof
Keyword(s):  
Limit Cycle ◽  
Limit Cycles ◽  
Water Storage ◽  
Drainage System ◽  
Stable Limit Cycle ◽  
Stable Limit ◽  
Outburst Floods ◽  
The World ◽  
The Stability ◽  
Glacial Hazards

Abstract. Glacier lake outburst floods are common glacial hazards around the world. How big such floods can become (either in terms of peak discharge or in terms of total volume released) depends on how they are initiated: what causes the runaway enlargement of a subglacial or other conduit to start, and how big can the lake get before that point is reached? Here we investigate how the spontaneous channelization of a linked-cavity drainage system controls the onset of floods. In agreement with previous work, we show that floods only occur in a band of water throughput rates, and identify stabilizing mechanisms that allow steady drainage of an ice-dammed reservoir. We also show how stable limit cycle solutions emerge from the instability, a show how and why the stability properties of a drainage system with spatially spread-out water storage differ from those where storage is localized in a single reservoir or lake.

Optimization of Seepage Prevention of Ma Erdang Hydropower Station

2014 ◽  
Vol 1065-1069 ◽  
pp. 619-624
Author(s):  
Li Ting Qiu ◽  
Zhen Zhong Shen ◽  
Xiao Hu Tao
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Seepage Flow ◽  
Design Stage ◽  
Seepage Discharge ◽  
Element Analysis ◽  
Seepage Control ◽  
Calculation Results ◽  
Dam Site ◽  
The Stability

Base on the design of seepage control, the three-dimensional non-steady saturated - unsaturated seepage finite element analysis program CNPM3D is used to establish the three-dimentional finite element seepage model of junction area during operating period. The seepage field of dam site area is studied under the different anti-seepage curtain arrangement scheme. Specifically, the seepage gradient and the seepage discharge of the panel, major material zone, foundation curtains and two sides abutment curtains are analyzed to evaluate the stability of the major district of dam area, in order to provide suggestions for choosing the seepage control standard in the next deepen design stage.The calculation results show that the panel and the impervious curtain anti-seepage effect is remarkable.Impervious curtain can greatly reduce the total seepage flow of the dam and its foundation.However the curtain deepened to 1Lu has little effect on seepage discharge. It is showed that the seepage prevention standards of 3 lu should be proposed in the deepen design stage for both security and economic benefit. The achievement and experience of this seepage prevention design should be taken into consideration for other similar projects.

Non-linear stability analysis of floating ring bearings using Hopf bifurcation theory

2011 ◽  
Vol 225 (12) ◽  
pp. 2804-2818 ◽  
Author(s):  
A Amamou ◽  
M Chouchane
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Limit Cycles ◽  
Critical Speed ◽  
Design Parameters ◽  
Stable Limit ◽  
Non Linear ◽  
The Stability

Floating ring bearings are used to support and guide rotors in several high-speed rotating machinery applications. They are usually credited for lower heat generation and higher vibration suppressing ability. Similar to conventional hydrodynamic bearings, floating ring bearings may exhibit unstable behaviour above a certain stability critical speed. Linear stability analysis is usually applied to predict the stability threshold speed. Non-linear stability analysis, however, is needed to predict the presence and the size of stable limit cycles above the stability threshold speed or unstable limit cycles below the stability critical speed. The prediction of limit cycles is an important step in bearing stability analysis. In this article, a non-linear dynamic model is derived and used to investigate the stability of a perfectly balanced symmetric rigid rotor supported by two identical floating ring bearings near the critical stability boundaries. The fluid film hydrodynamic reactions of the floating ring bearings are modelled by applying the short bearing theory and the half Sommerfeld solution. Hopf bifurcation theory is then utilized to determine the existence and the approximate size of stable and unstable limit cycles in the neighbourhood of the stability critical speed depending on the bearing design parameters. Numerical integration of the non-linear equations of motion is then carried out in order to compare the trajectories obtained by numerical integration to those obtained analytically using Hopf bifurcation analysis. Stability boundary curves for typical bearing design parameters have been decomposed into boundaries with supercritical stable limit cycles and boundaries with subcritical unstable limit cycles. The shape and size of the limit cycles for selected bearing parameters are presented using both analytical and numerical approaches. This article shows that floating ring stability boundaries may exhibit either stable supercritical limit cycles or unstable subcritical limit cycles predictable by Hopf bifurcation.

The Effect of Tilting Pad Journal Bearing Dynamic Models on the Linear Stability Analysis of an 8-Stage Compressor

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Timothy W. Dimond ◽  
Amir A. Younan ◽  
Paul Allaire
Keyword(s):  
Dynamic Models ◽  
Stability Margin ◽  
Design Stage ◽  
Stability Estimates ◽  
Flexible Rotors ◽  
Excited Vibration ◽  
Tilting Pad ◽  
Equipment Failures ◽  
The Stability ◽  
Tilting Pad Journal Bearing

Rotordynamic instability, a self-excited vibration phenomenon, can lead to equipment failures, reduced production rates, and expensive redesign. Properly characterizing the stability response of flexible rotors on tilting pad bearings is therefore vital. Typically, this must be first considered during the design stage with computer modeling. Previous studies have demonstrated that non-synchronous bearing coefficients give a lower estimate of bearing stability than the eight synchronously reduced tiling pad bearing coefficients. However, a study of a reduced order non-synchronous stiffness-damping-mass (KCM) model and the effect on stability estimates has not been done previously for the same rotor model. In this paper, four load-between-pad tilting pad bearing designs, two four-pad and two five-pad, are considered. The stability margin for an eight-stage gas reinjection compressor is estimated for the four bearings, using a full KC representation, the KCM representation, and synchronously reduced bearing coefficients. The full KC representation gave the lowest estimate of stability margin, with up to 18% difference between full KC and KCM and up to 109% difference between full KC and synchronously reduced bearing coefficients. The results indicate that the KCM bearing representation does not necessarily result in the lowest estimate of rotordynamic stability margin, which is of significant interest to rotating machinery designers.

scholarly journals Bifurcations of Finite-Time Stable Limit Cycles from Focus Boundary Equilibria in Impacting Systems, Filippov Systems, and Sweeping Processes

2018 ◽  
Vol 28 (10) ◽  
pp. 1850126 ◽  
Author(s):  
Oleg Makarenkov ◽  
Lakmi Niwanthi Wadippuli Achchige
Keyword(s):  
Limit Cycles ◽  
Finite Time ◽  
Stable Limit Cycle ◽  
Piecewise Smooth ◽  
Stable Limit ◽  
Bifurcation Of Limit Cycles ◽  
Filippov Systems ◽  
Boundary Equilibrium ◽  
Sweeping Processes ◽  
Linearized System

We establish a theorem on bifurcation of limit cycles from a focus boundary equilibrium of an impacting system, which is universally applicable to prove the bifurcation of limit cycles from focus boundary equilibria in other types of piecewise-smooth systems, such as Filippov systems and sweeping processes. Specifically, we assume that one of the subsystems of the piecewise-smooth system under consideration admits a focus equilibrium that lie on the switching manifold at the bifurcation value of the parameter. In each of the three cases, we derive a linearized system which is capable of concluding the occurrence of a finite-time stable limit cycle from the above-mentioned focus equilibrium when the parameter crosses the bifurcation value. Examples illustrate how conditions of our theorems lead to closed-form formulas for the coefficients of the linearized system.

Complex Dynamics Due to Multiple Limit Cycle Bifurcations in a Tritrophic Food Chain Model

2019 ◽  
Vol 29 (14) ◽  
pp. 1950193
Author(s):  
Xiangyu Wang ◽  
Pei Yu
Keyword(s):  
Food Chain ◽  
Limit Cycles ◽  
Complex Dynamics ◽  
Chain Model ◽  
Stable Limit ◽  
Normal Form Theory ◽  
Bistable Phenomenon ◽  
Multiple Limit Cycle ◽  
The Stability ◽  
Food Chain Model

In this paper, we consider a tritrophic food chain model with Holling functional response types III and IV for the predator and superpredator, respectively. The main attention is focused on the stability and bifurcation of equilibria when the prey has a linear growth. Coexistence of different species is shown in the food chain, demonstrating bistable phenomenon. Hopf bifurcation is studied to show complex dynamics due to multiple limit cycles bifurcation. In particular, normal form theory is applied to prove that three limit cycles can bifurcate from an equilibrium in the vicinity of a Hopf critical point, yielding a new bistable phenomenon which involves two stable limit cycles.

Prediction of the nonlinear hysteresis loop for fluid-film bearings by numerical continuation

2014 ◽  
Vol 229 (4) ◽  
pp. 651-662 ◽  
Author(s):  
Radhouane Sghir ◽  
Mnaouar Chouchane
Keyword(s):  
Hysteresis Loop ◽  
Limit Cycles ◽  
Limit Point ◽  
Stability Domain ◽  
Numerical Continuation ◽  
Stable Limit ◽  
Nonlinear Dynamic Model ◽  
Nonlinear Hysteresis ◽  
The Stability ◽  
Loop Motion

A nonlinear dynamic model of a short journal bearing is used to predict the steady-state motion of the journal and its successive bifurcations in the neighbourhood of the stability critical speed. Numerical continuation is applied to determine the branch of equilibrium point and its bifurcation into stable or unstable limit cycles. It has been found that the unstable limit cycles undergo a single limit point bifurcation whereas the stable limit cycles undergo two successive limit point bifurcations. Thus, the bi-stability domain, the potential jumping from small to large motion and the hysteresis loop motion are predicted.

A Simplified Design Model for Modular Steel Buildings Subject to Vapor Cloud Explosions (VCEs)

2020 ◽  
Vol 14 ◽  
Author(s):  
Osama Bedair
Keyword(s):  
Dynamic Response ◽  
Minimum Cost ◽  
Design Parameters ◽  
Front Wall ◽  
Steel Buildings ◽  
Element Analysis ◽  
Analysis And Design ◽  
Vapor Cloud ◽  
Building Components ◽  
Analytical Expressions

Background: Modular steel buildings (MSB) are extensively used in petrochemical plants and refineries. Limited guidelines are available in the industry for analysis and design of (MSB) subject to accidental vapor cloud explosions (VCEs). Objectives: The paper presents simplified engineering model for modular steel buildings (MSB) subject to accidental vapor cloud explosions (VCEs) that are extensively used in petrochemical plants and refineries. Method: A Single degree of freedom (SDOF) dynamic model is utilized to simulate the dynamic response of primary building components. Analytical expressions are then provided to compute the dynamic load factors (DLF) for critical building elements. Recommended foundation systems are also proposed to install the modular building with minimum cost. Results: Numerical results are presented to illustrate the dynamic response of (MSB) subject to blast loading. It is shown that (DLF)=1.6 is attained at (td/t)=0.4 for front wall (W1) with (td/T)=1.25. For side walls (DLF)=1.41 and is attained at (td/t)=0.6. Conclusions: The paper presented simplified tools for analysis and design of (MSB) subject accidental vapor cloud blast explosions (VCEs). The analytical expressions can be utilized by practitioners to compute the (MSB) response and identify the design parameters. They are simple to use compared to Finite Element Analysis.

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