Stability Increase of Aerodynamically Unstable Rotors Using Intentional Mistuning

2006 ◽  
Author(s):  
Carlos Martel ◽  
Roque Corral ◽  
Jose´ Miguel Llorens
Keyword(s):  
Asymptotic Expansion ◽  
Small Parameter ◽  
Structural Dynamics ◽  
Low Pressure ◽  
Vibration Characteristics ◽  
Stability Properties ◽  
First Order ◽  
Low Pressure Turbine ◽  
Turbine Rotors ◽  
The Stability

A new simple asymptotic mistuning model (AMM), which constitutes an extension of the well known Fundamental Mistuning Model for groups of modes belonging to a modal family exhibiting a large variation of the tuned vibration characteristics, is used to analyze the effect of mistuning on the stability properties of aerodynamically unstable rotors. The model assumes that both, the aerodynamics and the structural dynamics of the assembly are linear, and retains the first order terms of a fully consistent asymptotic expansion of the tuned system where the small parameter is the blade mistuning. The simplicity of the model allows the optimization of the blade mistuning pattern to achieve maximum rotor stability. The results of the application of this technique to realistic welded-in-pair and interlock low-pressure-turbine rotors are also presented.

Stability Increase of Aerodynamically Unstable Rotors Using Intentional Mistuning

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
Carlos Martel ◽  
Roque Corral ◽  
José Miguel Llorens
Keyword(s):  
Asymptotic Expansion ◽  
Small Parameter ◽  
Structural Dynamics ◽  
Low Pressure ◽  
Vibration Characteristics ◽  
Stability Properties ◽  
First Order ◽  
Low Pressure Turbine ◽  
Turbine Rotors ◽  
The Stability

A new simple asymptotic mistuning model, which constitutes an extension of the well known fundamental mistuning model for groups of modes belonging to a modal family exhibiting a large variation of the tuned vibration characteristics, is used to analyze the effect of mistuning on the stability properties of aerodynamically unstable rotors. The model assumes that both the aerodynamics and the structural dynamics of the assembly are linear, and retains the first-order terms of a fully consistent asymptotic expansion of the tuned system where the small parameter is the blade mistuning. The simplicity of the model allows the optimization of the blade mistuning pattern to achieve maximum rotor stability. The results of the application of this technique to realistic welded-in-pair and interlock low-pressure-turbine rotors are also presented.

Experimental Study on the Effect of Clocking on the Propagation of Inflow Pressure Distortions in a Low Pressure Turbine Stage

2020 ◽  
Author(s):  
L. Simonassi ◽  
M. Zenz ◽  
P. Bruckner ◽  
S. Pramstrahler ◽  
F. Heitmeir ◽  
...  
Keyword(s):  
Experimental Study ◽  
Flow Field ◽  
Total Pressure ◽  
Low Pressure ◽  
Vibration Characteristics ◽  
Test Facility ◽  
Turbine Stage ◽  
Rotor Vibration ◽  
Low Pressure Turbine ◽  
The Impact

Abstract The design of modern aero engines enhances the interaction between components and facilitates the propagation of circumferential distortions of total pressure and temperature. As a consequence, the inlet conditions of a real turbine have significant spatial non-uniformities, which have direct consequences on both its aerodynamic and vibration characteristics. This work presents the results of an experimental study on the effects of different inlet total pressure distortion-stator clocking positions on the propagation of total pressure inflow disturbances through a low pressure turbine stage, with a particular focus on both the aerodynamic and aeroelastic performance. Measurements at a stable engine relevant operating condition and during transient operation were carried out in a one and a half stage subsonic turbine test facility at the Institute of Thermal Turbomachinery and Machine Dynamics at Graz University of Technology. A localised total pressure distortion was generated upstream of the stage in three different azimuthal positions relative to the stator vanes. The locations were chosen in order to align the distortion directly with a vane leading edge, suction side and pressure side. Additionally, a setup with clean inflow was used as reference. Steady and unsteady aerodynamic measurements were taken downstream of the investigated stage by means of a five-hole-probe (5HP) and a fast response aerodynamic pressure probe (FRAPP) respectively. Strain gauges applied on different blades were used in combination with a telemetry system to acquire the rotor vibration data. The aerodynamic interactions between the stator and rotor rows and the circumferential perturbation were studied through the identification of the main structures constituting the flow field. This showed that the steady and unsteady alterations created by the distortion in the flow field lead to modifications of the rotor vibration characteristics. Moreover, the importance of the impact that the pressure distortion azimuthal position has on the LPT stage aerodynamics and vibrations was highlighted.

Stability and Categoricity of Lattices

1981 ◽  
Vol 33 (6) ◽  
pp. 1380-1419 ◽  
Author(s):  
Kenneth W. Smith
Keyword(s):  
Stability Theory ◽  
Successive Approximations ◽  
Stability Properties ◽  
First Order ◽  
Strong Property ◽  
The Stability

This paper is a contribution to applied stability theory. Our purpose is to investigate the complexity of lattices by determining the stability of their first order theories.Stability measures the complexity of a theory T by counting the number of different “kinds” of elements in models of T. The notion of ω-stability was introduced by Morley [26] in 1965 and generalized by Shelah [31] in 1969. Shelah classified all first order theories according to their stability properties.Stability and -categoricity are closely related (see [26] and [1]). In fact, the notions of stable, superstable and ω-stable can be regarded as successive approximations of -categorical. -categoricity is a very strong property while stability, superstability and ω-stability facilitate the classification of more “complex” theories.

scholarly journals A Design Method to Prevent Low Pressure Turbine Blade Flutter

1998 ◽  
Author(s):  
Josef Panovsky ◽  
Robert E. Kielb
Keyword(s):  
Mode Shape ◽  
Design Method ◽  
Turbine Blades ◽  
Low Pressure ◽  
Stability Parameter ◽  
Influence Coefficient ◽  
Low Pressure Turbine ◽  
Reduced Frequency ◽  
Blade Flutter ◽  
The Stability

A design approach to avoid flutter of low pressure turbine blades in aircraft engines is described. A linearized Euler analysis, previously validated using experimental data, is used for a series of parameter studies. The influence of mode shape and reduced frequency are investigated. Mode shape is identified as the most important contributor to determining the stability of a blade design. A new stability parameter is introduced to gain additional insight into the key contributors to flutter. This stability parameter is derived from the influence coefficient representation of the cascade, and includes only contributions from the reference blade and its immediate neighbors. This has the effect of retaining the most important contributions to aerodynamic damping while filtering out terms of less significance. This parameter is utilized to develop a stability map, which provides the critical reduced frequency as a function of torsion axis location. Rules for preliminary design and procedures for detailed design analysis are defined.

Performance Considerations in Replacement of Low-Pressure Turbine Rotors for Nuclear Power Plants: A Case Study

2005 ◽  
Author(s):  
Komandur S. Sunder Raj
Keyword(s):  
Power Plant ◽  
Nuclear Power Plant ◽  
Nuclear Power ◽  
Low Pressure ◽  
Turbine Rotor ◽  
Modeling Tools ◽  
Low Pressure Turbine ◽  
Turbine Rotors ◽  
The Impact

In recent years, the nuclear power industry has witnessed profound changes in terms of renewal of operating licenses and power uprates. Renewal of operating licenses for an additional 20 years beyond the original licensed period of 40 years entails several considerations relating to aging management, performance, reliability, availability, and maintainability. Power uprates range from a low of up to 2% due to improved techniques in feedwater flow measurement to a high of up to 20% for extended power uprates. Since the limitations of power uprates are generally encountered in design of the turbine cycle, the impact upon the performance, reliability, availability and maintainability of the equipment and components in the turbine cycle may vary from low or moderate to significant. Several nuclear power plant owners have already replaced the low-pressure turbine rotors of their nuclear units with improved designs to mitigate blade failures and forced outages due to stress corrosion cracking, to reduce inspection intervals and maintenance, achieve higher output due to improved efficiency, etc. Others are either embarking upon or planning similar initiatives to confront aging, performance, availability, reliability and maintainability concerns stemming from renewal of operating licenses as well as the need to accommodate higher pressures and flows accompanying the proposed power uprates. Typically, the original low-pressure turbine designs utilizing built-up rotors with shrunk-on disks are being replaced with monoblock rotors with fully integral disks, couplings, blading and shrouds. The last stage blading is also longer resulting in a larger annulus area. Since these replacement programs involve significant expenditures, several factors need to be considered in order to ensure that the objectives of the rotor replacement programs are met. Using a case study, this paper examines the various considerations involved in replacing the low-pressure turbine rotors for a nuclear power plant. Design, performance and test considerations that need to be addressed before and after the low-pressure turbine rotors are replaced are discussed. The use of performance modeling tools in evaluating performance gains from low-pressure turbine rotor replacements is reviewed. Finally, the paper provides recommendations for ensuring that the objectives of a low-pressure turbine rotor replacement program are met.

A Design Method to Prevent Low Pressure Turbine Blade Flutter

1999 ◽  
Vol 122 (1) ◽  
pp. 89-98 ◽  
Author(s):  
J. Panovsky ◽  
R. E. Kielb
Keyword(s):  
Mode Shape ◽  
Design Method ◽  
Turbine Blades ◽  
Low Pressure ◽  
Stability Parameter ◽  
Influence Coefficient ◽  
Low Pressure Turbine ◽  
Reduced Frequency ◽  
Blade Flutter ◽  
The Stability

A design approach to avoid flutter of low pressure turbine blades in aircraft engines is described. A linearized Euler analysis, previously validated using experimental data, is used for a series of parameter studies. The influence of mode shape and reduced frequency are investigated. Mode shape is identified as the most important contributor to determining the stability of a blade design. A new stability parameter is introduced to gain additional insight into the key contributors to flutter. This stability parameter is derived from the influence coefficient representation of the cascade, and includes only contributions from the reference blade and its immediate neighbors. This has the effect of retaining the most important contributions to aerodynamic damping while filtering out terms of less significance. This parameter is utilized to develop a stability map, which provides the critical reduced frequency as a function of torsion axis location. Rules for preliminary design and procedures for detailed design analysis are defined. [S0742-4795(00)01401-0]

scholarly journals On the stability of stationary solutions of a linear integro-differential equation

2001 ◽  
Vol 14 (2) ◽  
pp. 139-150 ◽  
Author(s):  
A. Ya. Dorogovtsev ◽  
O. Yu. Trofimchuk
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Asymptotic Expansion ◽  
Boundary Value Problem ◽  
Small Parameter ◽  
Stationary Solution ◽  
Stationary Process ◽  
Telegraph Equation ◽  
Stationary Solutions ◽  
The Stability

In this paper the following two connected problems are discussed. The problem of the existence of a stationary solution for the abstract equation ϵx″(t)+x′(t)=Ax(t)+∫−∞tE(t−s)x(s)ds+ξ(t),t∈R containing a small parameter ϵ in Banach space B is considered. Here A∈ℒ(B) is a fixed operator, E∈C([0,+∞),ℒ(B)) and ξ is a stationary process. The asymptotic expansion of the stationary solution for equation (1) in the series on degrees of e is given.We have proved also the existence of a stationary with respect to time solution of the boundary value problem in B for a telegraph equation (6) containing the small parameter ϵ. The asymptotic expansion of this solution is also obtained.

ASYMPTOTIC SOLUTION OF FIRST-ORDER EQUATION WITH SMALL PARAMETER UNDER THE DERIVATIVE WITH PERTURBED OPERATOR

2018 ◽  
pp. 784-796
Author(s):  
Vladimir Igorevich Uskov
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Cauchy Problem ◽  
Asymptotic Expansion ◽  
Asymptotic Solution ◽  
Small Parameter ◽  
Decomposition Method ◽  
Order Equation ◽  
First Order ◽  
The Cauchy Problem

The paper is devoted to the Cauchy problem for a differential equation with a small parameter when using a Fredholm operator in a Banach space with a certain method. The investigated effect of this parameter. The solution is in the form of an asymptotic expansion. When solving the problems of using the cascade decomposition method for equations, which allows us to split the equation into equations in subspaces.

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