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Research Papers

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

[+] Author and Article Information
Almudena Vega

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

Roque Corral

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

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received July 25, 2018; final manuscript received August 21, 2018; published online October 18, 2018. Editor: Kenneth Hall.

J. Turbomach 140(12), 121007 (Oct 18, 2018) (8 pages) Paper No: TURBO-18-1171; doi: 10.1115/1.4041377 History: Received July 25, 2018; Revised August 21, 2018

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.

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References

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]
Lewis, D. , Platt, C. , and Smith, E. , 1979, “ Aeroelastic Instability in F100 Labyrinth Air Seals,” AIAA J. Aircr., 16(7), pp. 484–490. [CrossRef]
Waschka, W. , Witting, S. , and Kim, S. , 1992, “ Influence of High Rotational Speeds on the Heat Transfer and Discharge Coefficients in Labyrinth Seals,” ASME J. Turbomach., 114(2), pp. 462–468. [CrossRef]
Willenborg, K. , Kim, S. , and Witting, S. , 2001, “ Effect of Reynolds Number and Pressure Ratio on Leakage Flow and Heat Transfer in a Stepped Labyrinth Seal,” ASME J. Turbomach., 123(4), pp. 815–822. [CrossRef]
Alford, J. , 1964, “ Protection of Labyrinth Seals From Flexural Vibration,” ASME J. Eng. Gas Turbines Power, 86(2), pp. 141–147. [CrossRef]
Ehrich, F. , 1968, “ Aeroelastic Instability in Labyrinth Seals,” ASME J. Eng. Gas Turbines Power, 90(4), pp. 369–374. [CrossRef]
Alford, J. S. , 1975, “ Nature, Causes and Prevention of Labyrinth Air Seal Failures,” AIAA J. Aircr., 12(4), pp. 313–318. [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]
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.
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.
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]
Corral, R. , and Vega, A. , 2018, “ Conceptual Flutter Analysis of Labyrinth Seals Using Analytical Models—Part I: Theoretical Support,” ASME J. Turbomach. (accepted).
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, Sept. 1–4, Paper No. I12-S2-3.

Figures

Grahic Jump Location
Fig. 3

Work-per-cycle for a seal rotating around a torsion center located on the high pressure side (r < 0) (a) and on the LPS (r > 0) (b) as a function of the nondimensional frequency and the damping quality factor q (ẽh′ = ±0.1)

Grahic Jump Location
Fig. 2

Nondimensional work-per-cycle as a function of Ω̃, St, and ẽh′: (a) ẽh′ = 0, (b) ẽh′ = 0.1, (c) ẽh′ = 1.0, (d) ẽh′ = 10

Grahic Jump Location
Fig. 1

Sketch of an idealized seal cavity rotating about a torsion center located in the LPS

Grahic Jump Location
Fig. 4

Stability parameter of the seal as a function of the torsion center location, for a choked seal supported in the LPS (a) and the HPS (b) (q = 10, h′ = 2.25)

Grahic Jump Location
Fig. 5

Stability characteristics of a seal rotating around a center located at the LPS,  = 0.082, for different values of seal pressure ratio, as a function of St (q = 10)

Grahic Jump Location
Fig. 6

Stability parameter for the seal rotating about a center located at the LPS, for different values of St, as a function of the pressure ratio of the seal ( = 0.082, q = 10)

Grahic Jump Location
Fig. 7

Stability characteristics of a seal rotating about a center located at the LPS, q = 10, β = 0.5, ẽh′ = 0.21), for different values of the circumferential Mach number Mθ, as a function of the St

Grahic Jump Location
Fig. 8

Schematics of a multiple-cavity seal model supported in the LPS

Grahic Jump Location
Fig. 9

Stability characteristics of the seal rotating around a center located at the LPS, for a pressure ratio πT = 1.5. Number of cavities effect (ẽh′ = 0.1, q = 10).

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