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.

scholarly journals Higher-Order Conceptual Model for Labyrinth Seal Flutter

2020 ◽  
Author(s):  
Roque Corral ◽  
Michele Greco ◽  
Almudena Vega
Keyword(s):  
High Pressure ◽  
Frequency Domain ◽  
Current Model ◽  
Three Dimensional ◽  
Labyrinth Seal ◽  
The Body ◽  
Previous Model ◽  
Pressure Side ◽  
Numerical Work ◽  
Vibration Period

Abstract A simple non-dimensional model to describe the flutter onset of two-fin straight labyrinth seals [1] is extended to account for non-isentropic 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 & 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 [1]. 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 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.

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.

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.

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.

Plumpness Analysis of Indicator Diagram for Vehicle Damper

2013 ◽  
Vol 415 ◽  
pp. 582-585
Author(s):  
Xing Xu ◽  
Zhen Cui ◽  
Jin Chao Zhang
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Dynamic Load ◽  
Performance Indicators ◽  
Load Distribution ◽  
The Body ◽  
Quantitative Index ◽  
Indicator Diagram ◽  
Vehicle Demand ◽  
Mathematical Relationships

According to the indicator diagram of damper, the indicator diagram plumpness was proposed as a quantitative index, and its mathematical relationships with the sprung mass acceleration, suspension dynamic travel and tire dynamic load were built. Moreover, the influence of the total area on suspension characteristics was analyzed in time domain and frequency domain. The results show that, the increase of the indicator diagram plumpness can effectively restrain the variation of suspension dynamic travel and tire dynamic load, meanwhile, the body acceleration will be enlarged. Excessive indicator diagram plumpness also affects the dynamic tire load distribution in frequency domain, and it will decrease the driving security. Therefore, it should be reasonably selected from the performance indicators, which is based on the requirement of vehicle demand in the design process.

Ciało poza Człowiekiem, czyli Ciało Wyemancypowane w ujęciu Elizabeth Grosz

2012 ◽  
Author(s):  
Monika Rogowska-Stangret
Keyword(s):  
Women's Movement ◽  
Ways Of Knowing ◽  
Theoretical Background ◽  
The Body ◽  
Human Being ◽  
Biological Aspect ◽  
Theory Of Evolution

The article presents the philosophy of Elizabeth Grosz, its theoretical background and methods. It concentrates mainly on the category of the body which is present in her thought from the very beginning. The author pays particular attention to the problem of materiality of the body raised in The Nick of Time and Time Travels: why is the body docile? What makes it so vulnerable? What precedes social inscriptions? Those questions underline the problem of the biological aspect of the body as a part of nature which comes together with Grosz's interpretation of Darwin. The theory of evolution shows the temporality of human being and its culture and introduces future possibilities of overcoming the humankind and creating new ways of knowing, new sexes, new forms of living etc. The author suggests that this understanding of the body takes us beyond the human being and beyond subjectivity, it faces us with the process of becoming different which is perceived as emancipating. The author also suggests that Grosz's idea of the politics of imperceptibility is close to Foucault's recognition of the value of women's movement which, in his opinion, lies not in identity struggles but above all in struggles concentrating on broader cultural, social etc. changes. Both Foucault and Grosz aim at potential practices that involve giving up the question of our identities.

MULTIBODY DYNAMIC MODELING AND FLUTTER ANALYSIS OF A FLEXIBLE SLENDER VEHICLE

2012 ◽  
Vol 12 (06) ◽  
pp. 1250049 ◽  
Author(s):  
A. RASTI ◽  
S. A. FAZELZADEH
Keyword(s):  
Differential Equations ◽  
Rigid Body ◽  
Dynamic Modeling ◽  
Equations Of Motion ◽  
The Body ◽  
Elastic Deformations ◽  
Strip Theory ◽  
Multibody Dynamic ◽  
Flutter Analysis ◽  
Rigid Body Motions

In this paper, multibody dynamic modeling and flutter analysis of a flexible slender vehicle are investigated. The method is a comprehensive procedure based on the hybrid equations of motion in terms of quasi-coordinates. The equations consist of ordinary differential equations for the rigid body motions of the vehicle and partial differential equations for the elastic deformations of the flexible components of the vehicle. These equations are naturally nonlinear, but to avoid high nonlinearity of equations the elastic displacements are assumed to be small so that the equations of motion can be linearized. For the aeroelastic analysis a perturbation approach is used, by which the problem is divided into a nonlinear flight dynamics problem for quasi-rigid flight vehicle and a linear extended aeroelasticity problem for the elastic deformations and perturbations in the rigid body motions. In this manner, the trim values that are obtained from the first problem are used as an input to the second problem. The body of the vehicle is modeled with a uniform free–free beam and the aeroelastic forces are derived from the strip theory. The effect of some crucial geometric and physical parameters and the acting forces on the flutter speed and frequency of the vehicle are investigated.

Investigation of Trailing Edge Cooling Concepts in a High Pressure Turbine Cascade—Aerodynamic Experiments and Loss Analysis

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Hans-Ju¨rgen Rehder
Keyword(s):  
Boundary Layer ◽  
High Pressure ◽  
Coolant Flow ◽  
Coolant Fluid ◽  
Pressure Side ◽  
Turbine Cascade ◽  
High Pressure Turbine ◽  
Trailing Edge ◽  
Number Range ◽  
Mixing Losses

As part of a European research project, the aerodynamic and thermodynamic performance of a high pressure turbine cascade with different trailing edge cooling configurations was investigated in the wind tunnel for linear cascades at DLR in Go¨ttingen. A transonic rotor profile with a relative thick trailing edge was chosen for the experiments. Three trailing edge cooling configurations were applied, first central trailing edge ejection, second a trailing edge shape with a pressure side cut-back and slot equipped with a diffuser rib array, and third pressure side film cooling through a row of cylindrical holes. For comparison, aerodynamic investigations on a reference cascade with solid blades (no cooling holes or slots) were performed. The experiments covered the subsonic, transonic and supersonic exit Mach number range of the cascade while varying cooling mass flow ratios up to 2 %. This paper analyzes the effect of coolant ejection on the airfoil losses. Emphasis was given on separating the different loss contributions due to shocks, pressure, and suction side boundary layer, trailing edge, and mixing of the coolant flow. Employed measurement techniques are schlieren visualization, blade surface pressure measurements, and traverses by pneumatic probes in the cascade exit flow field and around the trailing edge. The results show that central trailing edge ejection significantly reduces the mixing losses and therefore decreases the overall loss. Higher loss levels are obtained when applying the configurations with pressure side blowing. In particular, the cut-back geometry reveals strong mixing losses due to the low momentum coolant fluid, which is decelerated by the diffuser rib array inside the slot. The influence of coolant flow rate on the trailing edge loss is tremendous, too. Shock and boundary layer losses are major contributions to the overall loss but are less affected by the coolant. Finally a parameter variation changing the temperature ratio of coolant to main flow was performed, resulting in increasing losses with decreasing coolant temperature.

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