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.

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.

Effects of Pressure Ratio and Sealing Clearance on Leakage Flow Characteristics in the Rotating Honeycomb Labyrinth Seal

2007 ◽  
Author(s):  
Jun Li ◽  
Xin Yan ◽  
Guojun Li ◽  
Zhenping Feng
Keyword(s):  
Pressure Ratio ◽  
Flow Characteristics ◽  
Labyrinth Seal ◽  
Navier Stokes ◽  
Leakage Flow ◽  
Labyrinth Seals ◽  
Aerodynamic Efficiency ◽  
Flow Losses ◽  
Leakage Flow Rate ◽  
Swirl Velocity

Honeycomb stepped labyrinth seals in turbomachinery enhance aerodynamic efficiency by reducing leakage flow losses through the clearance between rotating and stationary components. The influence of pressure ratio and sealing clearance on the leakage flow characteristics in the honeycomb stepped labyrinth seal is numerically determined. The geometries investigated represent designs of the honeycomb labyrinth seal typical for modern turbomachinery. The leakage flow fields in the honeycomb and smooth stepped labyrinth seals are obtained by the Reynolds-Averaged Navier-Stokes solution using the commercial software FLUENT. Numerical simulations covered a range of pressure ratio and three sizes of sealing clearance for the honeycomb and smooth stepped labyrinth seals. The numerical discharge coefficients of the non-rotating honeycomb and smooth stepped labyrinth seals are in good agreement with previous experimental data. In addition rotational effects are also taken into account in numerical computations. The numerical results show that the leakage flow rate increases with the increasing pressure ratio at the fixed sealing clearance for the rotating and non-rotating honeycomb labyrinth seal. The influence of the sealing clearance on the leakage flow pattern for the rotating and non-rotating honeycomb labyrinth seal are observed. Moreover, the similar leakage flow rates are obtained at the same flow condition between the rotating and non-rotating honeycomb labyrinth seal due to the honeycomb acts to kill swirl velocity development for the rotating honeycomb labyrinth seal.

Effective Clearance And Differential Gapping Impact on Seal Flutter Modelling and Validation

2021 ◽  
Author(s):  
Roque Corral ◽  
Michele Greco ◽  
Almudena Vega
Keyword(s):  
Labyrinth Seal ◽  
Analytical Models ◽  
Navier Stokes ◽  
Labyrinth Seals ◽  
Theoretical Support ◽  
Gap Ratio ◽  
Flutter Analysis ◽  
The Impact ◽  
Cv Model ◽  
Additional Loss

Abstract This paper presents an update of the model derived by Corral and Vega (2018, “Conceptual Flutter Analysis of Labyrinth Seal Using Analytical Models. Part I - Theoretical Support”, ASME J. of Turbomach., 140 (12), pp. 121006) for labyrinth seal flutter stability, providing a method of accounting for the effect of dissimilar gaps. The original CV model was intended as a conceptual model for understanding the effect of different geometric parameters on the seal stability comprehensively, providing qualitative trends for seal flutter stability. However, the quantitative evaluation of seal flutter, and the comparison of the CV model with detailed unsteady numerical simulations or experimental data, require including additional physics. The kinetic energy generated in the inlet gap is not dissipated entirely in the inter-fin cavity of straight-through labyrinth seals, and part is recovered in the downstream knife. This mechanism needs to be retained in the seal flutter model. It is concluded that when the theoretical gaps are identical, the impact of the recovery factor on the seal stability can be high. The sensitivity of the seal stability to large changes in the outlet to inlet gap ratio is high as well. It is concluded that fin variations due to rubbing or wearing inducing inlet gaps more open than the exit gaps lead to an additional loss of stability concerning the case of identical gaps. The agreement between the updated model and 3D linearized Navier-Stokes simulations is excellent when the model is informed with data coming from steady RANS simulations of the seal.

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

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.

Interdependence of Discharge Behavior, Swirl Development and Total Temperature Increase in Rotating Labyrinth Seals

2008 ◽  
Author(s):  
J. Denecke ◽  
J. Fa¨rber ◽  
K. Dullenkopf ◽  
H.-J. Bauer
Keyword(s):  
Gas Turbines ◽  
Temperature Increase ◽  
Computational Effort ◽  
Analytical Models ◽  
Labyrinth Seals ◽  
Simple Method ◽  
Air System ◽  
Total Temperature ◽  
Discharge Behavior ◽  
Secondary Air

Leakage flows between stationary and rotating components are one of the main sources for losses in turbo machines. Therefore, their reduction is a main goal in the design of modern aircraft engines. Contactless seals, mainly labyrinth seals are key elements either to seal rotating parts or to control the amount of leakage flow for internal use in the secondary air system. Even though new seal types like, brush seals, carbon seals etc. will be seen more often in advanced gas turbines, labyrinth seals will continue to play an important role in the primary and secondary air system and thus improved design tools are a necessity for more efficient and reliable engines. In the design process but also during the life time of the engine the characterization of contactless seals e.g. their discharge behavior, the development of the circumferential velocity (swirl) and the loss induced total temperature increase (windage heating) are of special interest for designers and operators. Despite of today’s efficient CFD methods, analytical models remain a valuable tool as they provide for reasonably estimates fast with small computational effort. Additionally, analytical models are especially suited to improve the understanding of the complex interdependency of the aforementioned parameters. As one limit of the swirl in rotating seals, the equilibrium swirl is defined in this paper and a simple method to determine its value is presented. In this context, the influences of the rotor-stator area ratio and the stator roughness on the equilibrium swirl are taken into account. In the case the inlet swirl is known or can be estimated with reasonable confidence an analytical approach to determine the swirl development from chamber to chamber is proposed. Given this swirl development along the seal axis, the overall total temperature increase can be calculated. Based on the final dimensionless equation for the total temperature change the interdependent influences of discharge behavior, swirl development and the total temperature increase on each other are discussed.

Higher Order Conceptual Model for Labyrinth Seal Flutter

2021 ◽  
Vol 143 (7) ◽  
Author(s):  
Roque Corral ◽  
Michele Greco ◽  
Almudena Vega
Keyword(s):  
High Pressure ◽  
Frequency Domain ◽  
Theoretical Background ◽  
The Body ◽  
Previous Model ◽  
Analytical Models ◽  
Pressure Side ◽  
Labyrinth Seals ◽  
Numerical Work ◽  
Flutter Analysis

Abstract A simple nondimensional model to describe the flutter onset of two-fin straight labyrinth seals (Corral, R., and Vega, A., 2018, “Conceptual Flutter Analysis of Labyrinth Seals Using Analytical Models. Part I: Theoretical Background,” ASME J. Turbomach., 140(10), p. 121006) is extended to account for nonisentropic flow perturbations. The isentropic relationship is replaced by the more general integral energy equation of the inter-fin cavity. A new expression for the Corral and Vega stability criterion is derived, which is very consistent with the previous model in the whole design space of the seal but for torsion centers located in the high-pressure side close to the seal. The new model formally depends on more dimensionless parameters since the existing parameter grouping of the previous model does not hold anymore, but this dependency is weak in relative terms. The model blends the limit where the discharge time of the inter-fin cavity is much longer than the vibration period, and the flow is nearly isentropic, and the opposite limit, where the perturbations are isothermic, gracefully. A few numerical examples obtained using a three-dimensional linearized frequency domain solver are included to support the model and show that the trends are correct, but the body of the numerical work will be presented in a separated article. The matching between the work-per-cycle obtained with the model and frequency domain solver is good. It is shown that some weird trends obtained using linearized unsteady simulations are qualitatively consistent with the current model but not with the previous one (Corral, R., and Vega, A., 2018, “Conceptual Flutter Analysis of Labyrinth Seals Using Analytical Models. Part I: Theoretical Background,” ASME J. Turbomach., 140(10), p. 121006). The largest differences between the new and the previous model are seen when the seal is supported at the high-pressure side.

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.

EFFECTIVE CLEARANCE AND DIFFERENTIAL GAPPING IMPACT ON SEAL FLUTTER MODELLING AND VALIDATION

2021 ◽  
pp. 1-16
Author(s):  
Roque Corral ◽  
Michele Greco ◽  
Almudena Vega
Keyword(s):  
Labyrinth Seal ◽  
Analytical Models ◽  
Navier Stokes ◽  
Labyrinth Seals ◽  
Theoretical Support ◽  
Gap Ratio ◽  
Flutter Analysis ◽  
The Impact ◽  
Cv Model ◽  
Additional Loss

Abstract This paper presents an update of the model derived by Corral and Vega (2018, “Conceptual Flutter Analysis of Labyrinth Seal Using Analytical Models. Part I - Theoretical Support”, ASME J. of Turbomach., 140 (12), pp. 121006) for labyrinth seal flutter stability, providing a method of accounting for the effect of dissimilar gaps. The original CV model was intended as a conceptual model for understanding the effect of different parameters on the seal stability comprehensively, providing qualitative trends for seal flutter stability. However, the quantitative evaluation of seal flutter, and the comparison of the CV model with detailed unsteady numerical simulations or experimental data, require including additional physics. The kinetic energy generated in the inlet gap is not dissipated entirely in the inter-fin cavity of straight-through labyrinth seals, and part is recovered in the downstream knife. This mechanism needs to be retained in the model. It is concluded that when the theoretical gaps are identical, the impact of the recovery factor on the seal stability can be high. The sensitivity of the seal stability to large changes in the outlet to inlet gap ratio is high as well. It is concluded that fin variations due to rubbing or wearing inducing inlet gaps more open than the exit gaps lead to an additional loss of stability concerning the case of identical gaps. The agreement between the updated model and 3D linearized Navier-Stokes simulations is excellent when the model is informed with data coming from steady RANS simulations of the seal.

Automatic Three-Dimensional Optimisation of a Modern Tandem Compressor Vane

2014 ◽  
Author(s):  
R. C. Schlaps ◽  
S. Shahpar ◽  
V. Gümmer
Keyword(s):  
Pressure Ratio ◽  
Three Dimensional ◽  
Trust Region ◽  
Automatic Generation ◽  
Navier Stokes ◽  
Design Parameters ◽  
High Fidelity ◽  
Stall Margin ◽  
Design Choice ◽  
Multipoint Approximation

In order to increase the performance of a modern gas turbine, compressors are required to provide higher pressure ratio and avoid incurring higher losses. The tandem aerofoil has the potential to achieve a higher blade loading in combination with lower losses compared to single vanes. The main reason for this is due to the fact that a new boundary layer is generated on the second blade surface and the turning can be achieved with smaller separation occurring. The lift split between the two vanes with respect to the overall turning is an important design choice. In this paper an automated three-dimensional optimisation of a highly loaded compressor stator is presented. For optimisation a novel methodology based on the Multipoint Approximation Method (MAM) is used. MAM makes use of an automatic design of experiments, response surface modelling and a trust region to represent the design space. The CFD solutions are obtained with the high-fidelity 3D Navier-Stokes solver HYDRA. In order to increase the stage performance the 3D shape of the tandem vane is modified changing both the front and rear aerofoils. Moreover the relative location of the two aerofoils is controlled modifying the axial and tangential relative positions. It is shown that the novel optimisation methodology is able to cope with a large number of design parameters and produce designs which performs better than its single vane counterpart in terms of efficiency and numerical stall margin. One of the key challenges in producing an automatic optimisation process has been the automatic generation of high-fidelity computational meshes. The multi block-structured, high-fidelity meshing tool PADRAM is enhanced to cope with the tandem blade topologies. The wakes of each aerofoil is properly resolved and the interaction and the mixing of the front aerofoil wake and the second tandem vane are adequately resolved.

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