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 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 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 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.

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.

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.

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.

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.

scholarly journals Numerical validation of an analytical seal flutter model

2021 ◽  
Vol 5 ◽  
pp. 191-201
Author(s):  
Michele Greco ◽  
Roque Corral
Keyword(s):  
Analytical Model ◽  
Fluid Dynamic ◽  
Stability Limit ◽  
Labyrinth Seal ◽  
Analytical Models ◽  
Mode Shapes ◽  
Labyrinth Seals ◽  
Low Frequencies ◽  
Wide Range ◽  
The Stability

An analytical model to describe the flutter onset of straight-through labyrinth seals has been numerically validated using a frequency domain linearized Navier-Stokes solver. A comprehensive set of simulations has been conducted to assess the stability criterion of the analytical model originally derived by Corral and Vega (2018), “Conceptual Flutter Analysis of Labyrinth Seals Using Analytical Models - Part I: Theoretical Support,” ASME J. Turbomach., 140 (12), pp. 121006. The accuracy of the model has been assessed by using a simplified geometry consisting of a two-fin straight-through labyrinth seal with identical gaps. The effective gaps and the kinetic energy carried over are retained and their effects on stability are evaluated. It turns out that is important to inform the model with the correct values of both parameters to allow a proper comparison with the numerical simulations. Moreover, the non-isentropic perturbations included in the formulations are observed in the simulations at relatively low frequencies whose characteristic time is of the same order as the discharge time of the seal. This effect is responsible for the bending of the stability limit in the <inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mn>0</mml:mn><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> ND stability map obtained both in the model and the simulations. It turns out that the analytical model can predict accurately the stability of the seal in a wide range of pressure ratios, vibration mode-shapes, and frequencies provided that this is informed with the fluid dynamic gaps and the energy carried over to the downstream fin from a steady RANS simulation. The numerical calculations show for the first time that the model can be used to predict accurately not only the trends of the work-per-cycle of the seal but also quantitative results.

scholarly journals Reliability Estimation of Reinforced Slopes to Prioritize Maintenance Actions

2021 ◽  
Vol 18 (2) ◽  
pp. 373
Author(s):  
Farshad BahooToroody ◽  
Saeed Khalaj ◽  
Leonardo Leoni ◽  
Filippo De Carlo ◽  
Gianpaolo Di Bona ◽  
...  
Keyword(s):  
Urban Areas ◽  
Evaluation Method ◽  
Likelihood Function ◽  
Reliability Estimation ◽  
Analytical Models ◽  
Geotechnical Structures ◽  
Reinforced Slopes ◽  
The Stability ◽  
Methods Analytical ◽  
Asset Managers

Geosynthetics are extensively utilized to improve the stability of geotechnical structures and slopes in urban areas. Among all existing geosynthetics, geotextiles are widely used to reinforce unstable slopes due to their capabilities in facilitating reinforcement and drainage. To reduce settlement and increase the bearing capacity and slope stability, the classical use of geotextiles in embankments has been suggested. However, several catastrophic events have been reported, including failures in slopes in the absence of geotextiles. Many researchers have studied the stability of geotextile-reinforced slopes (GRSs) by employing different methods (analytical models, numerical simulation, etc.). The presence of source-to-source uncertainty in the gathered data increases the complexity of evaluating the failure risk in GRSs since the uncertainty varies among them. Consequently, developing a sound methodology is necessary to alleviate the risk complexity. Our study sought to develop an advanced risk-based maintenance (RBM) methodology for prioritizing maintenance operations by addressing fluctuations that accompany event data. For this purpose, a hierarchical Bayesian approach (HBA) was applied to estimate the failure probabilities of GRSs. Using Markov chain Monte Carlo simulations of likelihood function and prior distribution, the HBA can incorporate the aforementioned uncertainties. The proposed method can be exploited by urban designers, asset managers, and policymakers to predict the mean time to failures, thus directly avoiding unnecessary maintenance and safety consequences. To demonstrate the application of the proposed methodology, the performance of nine reinforced slopes was considered. The results indicate that the average failure probability of the system in an hour is 2.8×10−5 during its lifespan, which shows that the proposed evaluation method is more realistic than the traditional methods.

Roles of vanes in diffuser on stability of centrifugal compressor

2019 ◽  
Vol 233 (14) ◽  
pp. 5380-5392
Author(s):  
Wangzhi Zou ◽  
Xiao He ◽  
Wenchao Zhang ◽  
Zitian Niu ◽  
Xinqian Zheng
Keyword(s):  
High Pressure ◽  
Centrifugal Compressor ◽  
Dynamic Pressure ◽  
Pressure Ratio ◽  
Pressure Rise ◽  
Rotating Stall ◽  
Centrifugal Compressors ◽  
Compression System ◽  
The Stability ◽  
Rotating Instability

The stability considerations of centrifugal compressors become increasingly severe with the high pressure ratios, especially in aero-engines. Diffuser is the major subcomponent of centrifugal compressor, and its performance greatly influences the stability of compressor. This paper experimentally investigates the roles of vanes in diffuser on component instability and compression system instability. High pressure ratio centrifugal compressors with and without vanes in diffuser are tested and analyzed. Rig tests are carried out to obtain the compressor performance map. Dynamic pressure measurements and relevant Fourier analysis are performed to identify complex instability phenomena in the time domain and frequency domain, including rotating instability, stall, and surge. For component instability, vanes in diffuser are capable of suppressing the emergence of rotating stall in the diffuser at full speeds, but barely affect the characteristics of rotating instability in the impeller at low and middle speeds. For compression system instability, it is shown that the use of vanes in diffuser can effectively postpone the occurrence of compression system surge at full speeds. According to the experimental results and the one-dimensional flow theory, vanes in diffuser turn the diffuser pressure rise slope more negative and thus improve the stability of compressor stage, which means lower surge mass flow rate.

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