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Research Papers

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

[+] Author and Article Information
Roque Corral

Advanced Engineering Direction,
Industria de Turbopropulsores S.A.U.,
Madrid 28108, Spain;
Department of Fluid Mechanics
and Aerospace Propulsion,
Universidad Politecnica de Madrid,
Madrid 28040, Spain
e-mail: roque.corral@itpaero.es

Almudena Vega

Department of Fluid Mechanics and
Aerospace Propulsion,
Universidad Politécnica de Madrid,
Madrid 28040, Spain
e-mail: almudena.vega@upm.es

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received July 19, 2018; final manuscript received August 29, 2018; published online October 18, 2018. Editor: Kenneth Hall.

J. Turbomach 140(12), 121006 (Oct 18, 2018) (11 pages) Paper No: TURBO-18-1165; doi: 10.1115/1.4041373 History: Received July 19, 2018; Revised August 29, 2018

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.

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References

Alford, J. S. , 1971, “ Labyrinth Seal Designs Have Benefitted From Development and Service Experience,” SAE Paper No. 710435.
Alford, J. S. , 1975, “ Nature, Causes and Prevention of Labyrinth Air Seal Failures,” AIAA J. Aircr., 12(4), pp. 313–318. [CrossRef]
Lewis, D. , Platt, C. , and Smith, E. , 1979, “ Aeroelastic Instability in f100 Labyrinth Air Seals,” AIAA J. Aircr., 16(7), pp. 484–490. [CrossRef]
Alford, J. , 1964, “ Protection of Labyrinth Seals From Flexural Vibration,” ASME J. Eng. Gas Turbines Power, 86(2), pp. 141–147. [CrossRef]
Alford, J. , 1967, “ Protecting Turbomachinery From Unstable and Oscillatory Flows,” ASME J. Eng. Gas Turbines Power, 89(4), pp. 513–528. [CrossRef]
Ehrich, F. , 1968, “ Aeroelastic Instability in Labyrinth Seals,” ASME J. Eng. Gas Turbines Power, 90(4), pp. 369–374. [CrossRef]
Abbot, D. R. , 1981, “ Advances in Labyrinth Seal Aeroelastic Instability Prediction and Prevention,” ASME J. Eng. Gas Turbines Power, 103(2), pp. 308–312. [CrossRef]
Nordmann, R. , and Weiser, P. , 1990, “ Evaluation of Rotor-Dynamic coefficients of look-Through Labyrinths by Means of a Three Volume Bulk Flow Model,” Rotordynamic Instability Problems in High Performance Turbomachinery, College Station, TX, pp. 147–163.
Zhuang, Q. , 2012, “ Parametric Study on the Aeroelastic Stability of Rotor Seals,” M.S. thesis, Royal Institute of Technology, Stockholm, Sweden.
Hirano, T. , Guo, Z. , and Kirk, R. G. , 2005, “ Application of Computational Fluid Dynamics Analysis for Rotating Machinery—Part II: Labyrinth Seal Analysis,” ASME J. Eng. Gas Turbines Power, 127(4), pp. 820–826. [CrossRef]
Mare, L. D. , Imregun, M. , Green, J. , and Sayma, A. I. , 2010, “ A Numerical Study on Labyrinth Seal Flutter,” ASME J. Tribol., 132(2), p. 022201. [CrossRef]
Phibel, R. , Mare, L. D. , and Imregun, J. G. M. , 2009, “ Labyrinth Seal Aeroelastic Stability, a Numerical Investigation,” 12th International Symposium on Unsteady Aerodynamics, Aeroacoustics & Aeroelasticity of Turbomachines, London, UK, Sept. 1–4, Paper No. I12-S2-3.
Phibel, R. , and Mare, L. D. , 2011, “ Comparison Between a Cfd Code and a Three-Control-Volume Model for Labyrinth Seal Flutter Predictions,” ASME Paper No. GT2011-46281.
Sayma, A. I. , Breard, C. , Vahdati, M. , and Imregun, M. , 2002, “ Aeroelastic Analysis of Air-Ridind Seals for Aeroengine Applications,” ASME J. Tribol., 124(3), pp. 607–616. [CrossRef]
Corral, R. , and Vega, A. , 2016, “ The Low Reduced Frequency Limit of Vibrating Airfoils—Part I: Theoretical Analysis,” ASME J. Turbomach, 138(2), p. 021004. [CrossRef]
Corral, R. , and Vega, A. , 2016, “ Physics of Vibrating Turbine Airfoils at Low Reduced Frequency,” AIAA J. Propul. Power, 32(2), pp. 325–336. [CrossRef]
Barbarossa, F. , Parry, A. B. , Green, J. S. , and di Mare, L. , 2016, “ An Aerodynamic Parameter for Low-Pressure Turbine Flutter,” ASME J. Turbomach., 138(5), p. 051001. [CrossRef]
Corral, R. , and Vega, A. , 2017, “ Quantification of the Influence of Unsteady Aerodynamic Loading on the Damping Characteristics of Oscillating Airfoils at Low Reduced Frequency—Part I: Theoretical Support,” ASME J. Turbomach., 139(3), p. 0310009.
Vega, A. , and Corral, R. , 2016, “ The Low Reduced Frequency Limit of Vibrating Airfoils—Part II: Numerical Experiments,” ASME J. Turbomach., 128(2), p. 021005. [CrossRef]
Vega, A. , and Corral, R. , 2017, “ Quantification of the Influence of Unsteady Aerodynamic Loading on the Damping Characteristics of Oscillating Airfoils at Low Reduced Frequency—Part II: Numerical Verification,” ASME J. Turbomach., 139(3), p. 031010. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Sketch of an idealized seal cavity rotating about a torsion center located in the low pressure side

Grahic Jump Location
Fig. 4

Work-per-cycle as a function of the nondimensional frequency for the 2D model

Grahic Jump Location
Fig. 2

Cavity pressure at the steady-state as a function of the total pressure ratio. solid red line: standard seal solution, with choked exit when πT > πT*≃2.3. Dashed blue line: nonphysical solution of Eq. (5)πT > πT*≃2.3.

Grahic Jump Location
Fig. 3

Variation of h′ as a function of the total pressure ratio πT

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Fig. 5

Sketch of the tridimensional seal geometry

Grahic Jump Location
Fig. 6

Scheme of the work-per-cycle of a rotating seal supported in the low-pressure side (a) and in the high-pressure side for different values of ẽh′ ((b) −0.5 < ẽh′ < 0, (c): −1 < ẽh′ < −0.5, and (d) ẽh′ < −1) as a function of Ω̃ and St2

Grahic Jump Location
Fig. 7

(a) Ehrich's stability criterion adapted from Ref. [6]. (b) Abbot's stability criterion interpreted from Ref. [7]. (c) stability criterion derived from Eq. (46).

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