Conceptual Flutter Analysis of Labyrinth Seals Using Analytical Models—Part I: Theoretical Support

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Roque Corral ◽  
Almudena Vega
Keyword(s):  
Gas Turbines ◽  
Control Volume ◽  
Pressure Ratio ◽  
Analytical Models ◽  
Propagation Time ◽  
Labyrinth Seals ◽  
Acoustic Frequency ◽  
Aeroelastic Instability ◽  
Prediction And Prevention ◽  
The Stability

A simple nondimensional model to describe the flutter onset of labyrinth seals is presented. The linearized mass and momentum integral equations for a control volume which represents the interfin seal cavity, retaining the circumferential unsteady flow perturbations created by the seal vibration, are used. First, the downstream fin is assumed to be choked, whereas in a second step the model is generalized for unchoked exit conditions. An analytical expression for the nondimensional work-per-cycle is derived. It is concluded that the stability of a two-fin seal depends on three nondimensional parameters, which allow explaining seal flutter behavior in a comprehensive fashion. These parameters account for the effect of the pressure ratio, the cavity geometry, the fin clearance, the nodal diameter (ND), the fluid swirl velocity, the vibration frequency, and the torsion center location in a compact and interrelated form. A number of conclusions have been drawn by means of a thorough examination of the work-per-cycle expression, also known as the stability parameter by other authors. It was found that the physics of the problem strongly depends on the nondimensional acoustic frequency. When the discharge time of the seal cavity is much greater than the acoustic propagation time, the damping of the system is very small and the amplitude of the response at the resonance conditions is very high. The model not only provides a unified framework for the stability criteria derived by Ehrich (1968, “Aeroelastic Instability in Labyrinth Seals,” ASME J. Eng. Gas Turbines Power, 90(4), pp. 369–374) and Abbot (1981, “Advances in Labyrinth Seal Aeroelastic Instability Prediction and Prevention,” ASME J. Eng. Gas Turbines Power, 103(2), pp. 308–312), but delivers an explicit expression for the work-per-cycle of a two-fin rotating seal. All the existing and well-established engineering trends are contained in the model, despite its simplicity. Finally, the effect of swirl in the fluid is included. It is found that the swirl of the fluid in the interfin cavity gives rise to a correction of the resonance frequency and shifts the stability region. The nondimensionalization of the governing equations is an essential part of the method and it groups physical effects in a very compact form. Part I of the paper details the derivation of the theoretical model and draws some preliminary conclusions. Part II of the corresponding paper analyzes in depth the implications of the model and outlines the extension to multiple cavity seals.

Conceptual Flutter Analysis of Labyrinth Seals Using Analytical Models: Part I — Theoretical Support

2018 ◽  
Author(s):  
Roque Corral ◽  
Almudena Vega
Keyword(s):  
Control Volume ◽  
Pressure Ratio ◽  
Analytical Models ◽  
Propagation Time ◽  
Unified Framework ◽  
Labyrinth Seals ◽  
Acoustic Frequency ◽  
Dimensional Parameters ◽  
The Stability ◽  
And Shifts

A simple non-dimensional model to describe the flutter onset of labyrinth seals is presented. The linearized equations for a control volume which represents the inter-fin seal cavity, retaining the circumferential unsteady flow perturbations created by the seal vibration, are used. Firstly, the downstream fin is assumed to be choked, whereas in a second step the model is generalized for unchocked exit conditions. An analytical expression for the non-dimensional work-per-cycle is derived. It is concluded that the stability of a two-fin seal, depends on three non-dimensional parameters, which allow explaining seal flutter behaviour in a comprehensive fashion. These parameters account for the effect of the pressure ratio, the cavity geometry, the fin clearance, the nodal diameter, the fluid swirl velocity, the vibration frequency and the torsion center location in a compact and interrelated form. A number of conclusions have been drawn by means of a thorough examination of the work-per-cycle expression, also known as the stability parameter by other authors. It was found that the physics of the problem strongly depends on the non-dimensional acoustic frequency. When the discharge time of the seal cavity is much greater than the acoustic propagation time, the damping of the system is very small and the amplitude of the response at the resonance conditions is very high. The model not only provides a unified framework for the stability criteria derived by Ehrich [1] and Abbot [2], but delivers an explicit expression for the work-per-cycle of a two-fin rotating seal. All the existing and well established engineering trends are contained in the model, despite its simplicity. Finally, the effect of swirl in the fluid is included. It is found that the swirl of the fluid in the inter-fin cavity gives rise to a correction of the resonance frequency and shifts the stability region. The non-dimensionalization of the governing equations is an essential part of the method and it groups physical effects in a very compact form. Part I of the paper details the derivation of the theoretical model and draws some preliminary conclusions. Part II of the corresponding paper analyzes in depth the implications of the model and outlines the extension to multiple cavity seals.

Conceptual Flutter Analysis of Labyrinth Seals Using Analytical Models: Part II — Physical Interpretation

2018 ◽  
Author(s):  
Almudena Vega ◽  
Roque Corral
Keyword(s):  
Control Volume ◽  
Pressure Ratio ◽  
Analytical Models ◽  
Propagation Time ◽  
Unified Framework ◽  
Labyrinth Seals ◽  
Acoustic Frequency ◽  
Dimensional Parameters ◽  
The Stability ◽  
And Shifts

A simple non-dimensional model to describe the flutter onset of labyrinth seals is presented. The linearized equations for a control volume which represents the inter-fin seal cavity, retaining the circumferential unsteady flow perturbations created by the seal vibration, are used. Firstly, the downstream fin is assumed to be choked, whereas in a second step the model is generalized for unchocked exit conditions. An analytical expression for the non-dimensional work-per-cycle is derived. It is concluded that the stability of a two-fin seal, depends on three non-dimensional parameters, which allow explaining seal flutter behaviour in a comprehensive fashion. These parameters account for the effect of the pressure ratio, the cavity geometry, the fin clearance, the nodal diameter, the fluid swirl velocity, the vibration frequency and the torsion center location in a compact and interrelated form. A number of conclusions have been drawn by means of a thorough examination of the work-per-cycle expression, also known as the stability parameter by other authors. It was found that the physics of the problem strongly depends on the non-dimensional acoustic frequency. When the discharge time of the seal cavity is much greater than the acoustic propagation time, the damping of the system is very small and the amplitude of the response at the resonance conditions is very high. The model not only provides a unified framework for the stability criteria derived by Ehrich [1] and Abbot [2], but delivers an explicit expression for the work-per-cycle of a two-fin rotating seal. All the existing and well established engineering trends are contained in the model, despite its simplicity. Finally, the effect of swirl in the fluid is included. It is found that the swirl of the fluid in the inter-fin cavity gives rise to a correction of the resonance frequency and shifts the stability region. The non-dimensionalization of the governing equations is an essential part of the method and it groups physical effects in a very compact form. Part I of the paper[3] detailed the derivation of the theoretical model and drew some preliminary conclusions. Part II analyzes in depth the implications of the model and outlines the extension to multiple cavity seals.

Conceptual Flutter Analysis of Stepped Labyrinth Seals

2020 ◽  
Vol 142 (7) ◽  
Author(s):  
Roque Corral ◽  
Almudena Vega ◽  
Michele Greco
Keyword(s):  
Natural Frequency ◽  
Fundamental Mode ◽  
Theoretical Background ◽  
Analytical Models ◽  
Second Step ◽  
Pressure Side ◽  
Labyrinth Seals ◽  
Acoustic Frequency ◽  
Flutter Analysis ◽  
The Stability

Abstract A simple nondimensional model to describe the flutter onset of two-fin straight labyrinth seals (Corral and Vega, 2018, “Conceptual Flutter Analysis of Labyrinth Seals Using Analytical Models—Part I: Theoretical Background,” ASME J. Turbomach., 140(10), p. 121006) is extended to stepped seals. The effect of the axial displacement of the seal is analyzed first in isolation. It is shown that this fundamental mode is always stable. In a second step, the combination of axial and torsion displacements is used to determine the damping of modes with arbitrary torsion centers. It is concluded that the classical Abbot's criterion stating that seals supported on the low-pressure side of the seal are stable provided that natural frequency of the mode is greater than the acoustic frequency breaks down under certain conditions. An analytical expression for the nondimensional work-per-cycle is derived and new nondimensional parameters controlling the seal stability identified. It is finally concluded that the stability of stepped seals can be assimilated to that of a straight through seal if the appropriate distance of the torsion center to the seal is chosen.

Conceptual Flutter Analysis of Stepped Labyrinth Seals

2019 ◽  
Author(s):  
Roque Corral ◽  
Almudena Vega ◽  
Michele Greco
Keyword(s):  
Natural Frequency ◽  
Fundamental Mode ◽  
Second Step ◽  
Pressure Side ◽  
Dimensional Model ◽  
Labyrinth Seals ◽  
Acoustic Frequency ◽  
Flutter Analysis ◽  
Dimensional Parameters ◽  
The Stability

Abstract A simple non-dimensional model to describe the flutter onset of two-fin straight labyrinth seals [1] is extended to stepped seals. The effect of the axial displacement of the seal is analyzed first in isolation. It is shown that this fundamental mode is always stable. In a second step, the combination of axial and torsion displacements is used to determine the damping of modes with arbitrary torsion centers. It is concluded that the classical Abbot’s criterion stating that seals supported in the low-pressure side of the seal are stable provided that natural frequency of the mode is greater than the acoustic frequency breaks down under certain conditions. An analytical expression for the non-dimensional work-per-cycle is derived and new non-dimensional parameters controlling the seal stability identified. It is finally concluded the stability of stepped seals can be assimilated to that of a straight through seal if the appropriate distance of the torsion center to the seal is chosen.

A Comparison of Experimental Results and Theoretical Predictions for the Rotordynamic Coefficients of Short (L/D = 1/6) Labyrinth Seals

1991 ◽  
Author(s):  
Joseph M. Pelletti ◽  
Dara W. Childs
Keyword(s):  
Flow Model ◽  
Control Volume ◽  
Pressure Ratio ◽  
Experimental Results ◽  
Rotor Speed ◽  
Labyrinth Seals ◽  
Rotordynamic Coefficients ◽  
Supply Pressure ◽  
Test Conditions ◽  
Theoretical Predictions

Abstract Experimental results for the rotordynamic coefficients of short (L/D = 1/6) teeth-on-stator and teeth-on-rotor labyrinth seals are presented. The effects that pressure ratio (fluid density), rotor speed, fluid pre-swirl and seal clearance have on these coefficients are studied. Tests were run out to speeds of 16000 rpm with a supply pressure of 17.3 bar and seal clearances ranging from 0.229–0.419 mm. The experimental results are compared with theoretical predictions of a two control volume compressible flow model. The experimental results show that decreases in pressure ratio and increases in rotor speed are stabilizing while increases in fluid pre-swirl and seal clearance are destabilizing for both seal configurations. The theoretical model correctly predicts the effects of pressure ratio, rotor speed and fluid pre-swirl on the cross-coupled stiffness. It also predicts reasonable values for direct damping for all test conditions. However, the theory incorrectly predicts the effect of seal clearance on these coefficients. Consequently the theoretical predictions are much better for the large clearance seals.

Rotordynamic Characterization of a Staggered Labyrinth Seal: Experimental Test Data and Comparison With Predictions

2018 ◽  
Author(s):  
Filippo Cangioli ◽  
Giuseppe Vannini ◽  
Paolo Pennacchi ◽  
Lorenzo Ciuchicchi ◽  
Leonardo Nettis ◽  
...  
Keyword(s):  
Gas Turbines ◽  
Flow Model ◽  
Labyrinth Seal ◽  
Accurate Estimation ◽  
Stability Assessment ◽  
Labyrinth Seals ◽  
Rotordynamic Coefficients ◽  
Working Principle ◽  
The Stability

As well known, the stability assessment of turbomachines is strongly related to internal sealing components. For instance, labyrinth seals are widely used in compressors, steam and gas turbines and pumps to control the clearance leakage between rotating and stationary parts, owing to their simplicity, reliability and tolerance to large thermal and pressure variations. Labyrinth seals working principle consists in reducing the leakage by imposing tortuous passages to the fluid that are effective on dissipating the kinetic energy of the fluid from high-pressure regions to low-pressure regions. Conversely, labyrinth seals could lead to dynamics issues. Therefore, an accurate estimation of their dynamic behavior is very important. In this paper, the experimental results of a long-staggered labyrinth seal will be presented. The results in terms of rotordynamic coefficients and leakage will be discussed as well as the critical assessment of the experimental measurements. Eventually, the experimental data are compared to numerical results obtained with the new bulk-flow model (BFM) introduced in this paper.

Conceptual Flutter Analysis of Labyrinth Seals Using Analytical Models—Part II: Physical Interpretation

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Almudena Vega ◽  
Roque Corral
Keyword(s):  
Pressure Ratio ◽  
Analytical Models ◽  
Design Parameters ◽  
Physical Parameters ◽  
Labyrinth Seals ◽  
Simple Method ◽  
Nodal Diameter ◽  
Swirl Velocity ◽  
Flutter Analysis ◽  
Unsteady Interaction

The dimensionless model presented in part I of the corresponding paper to describe the flutter onset of two-fin rotating seals is exploited to extract valuable engineering trends with the design parameters. The analytical expression for the nondimensional work-per-cycle depends on three dimensionless parameters of which two of them are new. These parameters are simple but interrelate the effect of the pressure ratio, the height, and length of the interfin geometry, the seal clearance, the nodal diameter (ND), the fluid swirl velocity, the vibration frequency, and the torsion center location in a compact and intricate manner. It is shown that nonrelated physical parameters can actually have an equivalent impact on seal stability. It is concluded that the pressure ratio can be stabilizing or destabilizing depending on the case, whereas the swirl of the flow is always destabilizing. Finally, a simple method to extend the model to multiple interfin cavities, neglecting the unsteady interaction among them, is described.

The Evolution of Compressor and Turbine Bladings in Gas Turbine Design

1967 ◽  
Vol 89 (2) ◽  
pp. 199-205 ◽  
Author(s):  
C. Seippel
Keyword(s):  
Steam Turbine ◽  
Gas Turbine ◽  
Gas Turbines ◽  
Pressure Ratio ◽  
Parallel Evolution ◽  
Axial Compressor ◽  
Expansion Turbine ◽  
The Stability ◽  
Turbine Design ◽  
The City

The author, having been associated with the construction of gas turbines from the first 4000-kw unit delivered in 1939 to the city of Neuchaˆtel to the present time, gives some personal views on the evolution of the axial compressor and turbine bladings which are the key elements to the gas turbines. The axial compressor was created to supply air efficiently for the supercharged “Velox” boiler. It made the evolution to the modern gas turbine possible. The main problems encountered were related to the stability of flow. An enormous increase of volume capacity was achieved in the course of time. The increase of pressure ratio made special measures necessary to overcome instability at starting. The expansion turbine started on the basis of steam turbine practice and underwent a parallel evolution to large capacities. Its particular problems are related to the high temperatures of the gases.

Experimental Identification for Seals Rotordynamic Coefficients Based on Double Plane Balance Method

2011 ◽  
Vol 291-294 ◽  
pp. 1965-1969
Author(s):  
Hao Cao ◽  
Jian Gang Yang ◽  
Wan Fu Zhang ◽  
Rui Guo
Keyword(s):  
Pressure Ratio ◽  
Eccentricity Ratio ◽  
Labyrinth Seals ◽  
Rotordynamic Coefficients ◽  
Domain Identification ◽  
Air Inlet ◽  
Double Plane ◽  
Set Up ◽  
The Stability ◽  
Stiffness And Damping

This paper presents a new rotordynamic measurements conducted on a test rig for evaluation of multiple rings of labyrinth seals. Considering the tilting motion of cylinder occurs in experiments, the impedance matrix of cylinder system is obtained first. An equivalent seal force identification model is set up for multiple seals based on double plane balance theory of rotor dynamics. The resultant seal forces are calculated on two end planes of the cylinder, and resolved to multiple sections that seals located. A frequency domain identification method delivers the test seals stiffness and damping coefficients. Compressed air inlet tests were run from 1000 rpm-2200rpm, 0.1-0.6Mpa supply pressures were used. For each ΔP test condition, the static eccentricity ratio ε=e/Cr is range from zero to approximately 0.6. Results show that 8 rotordynamic coefficients increase almost linearly with inlet/outlet pressure ratio. Increasing eccentricity ratio weakens the stability of seal-rotor system obviously.

Experimental and Numerical Investigation on Leakage Characteristic of Stepped Labyrinth Seal

2016 ◽  
Author(s):  
Li Zhang ◽  
Hui-ren Zhu ◽  
Cun-liang Liu ◽  
Fei Tong
Keyword(s):  
Gas Turbines ◽  
Pressure Ratio ◽  
Labyrinth Seal ◽  
Scaling Effects ◽  
Labyrinth Seals ◽  
Maximal Deviation ◽  
Tooth Number ◽  
Leakage Coefficient ◽  
Secondary Air ◽  
Aero Engines

Labyrinth seals represent an important flow element in the secondary air system of aero engines. The influence of seal clearance and teeth parameters on the leakage characteristic of a real size stepped labyrinth seal was experimentally and numerically analyzed in a stationary state. Two kinds of labyrinth seals were studied in this investigation that are generally used in gas turbines, namely downward stepped labyrinth and upward stepped labyrinth. The differences of seal flow leakage mechanisms between the two types of the labyrinth were investigated. In order to eliminate the scaling effects on leakage losses in labyrinth seals, the experimental labyrinth seal model took the size of the real one in an aero engine. The experiments covered a range of pressure ratio from 1.1 to 3.5. The experimental and numerical results show that in the range of the studied parameters the main teeth parameters affecting leakage coefficient are seal clearance, tooth tip thickness, tooth number and tooth front inclination. The influence of tooth height, pith and rear inclination angle on leakage coefficient of downward stepped labyrinth seal can almost be neglected in this research. And when the step height is more than twice the width of seal clearance, its effect on seal performance can be ignored. An empirical formula express of leakage coefficient with pressure ratio, seal clearance and teeth parameters of downward stepped labyrinth seal was organized which fits the experimental data with a maximal deviation of 8%. With similar pressure ratios and seal clearances, the downward stepped labyrinth seal displays lower leakage rates and provides the best sealing efficiency.

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