Dynamic Forces From Single Gland Labyrinth Seals: Part I—Ideal and Viscous Decomposition

A theoretical and experimental investigation on the aerodynamic forces generated by a single gland labyrinth seal executing a spinning/whirling motion has been conducted. A lumped parameter model, which includes the kinetic energy carryover effect, is presented along with a linear perturbation solution technique. The resulting system is nondimensionalized and the physical significance of the reduced parameters is discussed. Closed-form algebraic formulas are given for some simple limiting cases. It is shown that the total cross force predicted by this model can be represented as the sum of an ideal component due to an inviscid flow with entry swirl and a viscous part due to the change in swirl created by friction inside the gland. The frequency-dependent ideal part is solely responsible for the rotordynamic direct damping. The facility designed and built to measure these frequency dependent forces is described. Experimental data confirm the validity and usefulness of this ideal/viscous decomposition. A method for calculating the damping coefficients based on the force decomposition using the static measurements only is presented.

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Dynamic Forces From Single Gland Labyrinth Seals: Part I — Ideal and Viscous Decomposition

Volume 3B: General ◽

10.1115/93-gt-302 ◽

1993 ◽

Author(s):

Knox T. Millsaps ◽

Manuel Martinez-Sanchez

Keyword(s):

Inviscid Flow ◽

Labyrinth Seal ◽

Lumped Parameter Model ◽

Solution Technique ◽

Linear Perturbation ◽

Labyrinth Seals ◽

Frequency Dependent ◽

Lumped Parameter ◽

Reduced Parameters ◽

Carry Over

A theoretical and experimental investigation on the aerodynamic forces generated by a single gland labyrinth seal executing a spinning/whirling motion has been conducted. A lumped parameter model which includes the kinetic energy carry-over effect is presented along with a linear perturbation solution technique. The resulting system is nondimensionalized and the physical significance of the reduced parameters is discussed. Closed form algebraic formulas are given for some simple limiting cases. It is shown that the total cross-force predicted by this model can be represented as the sum of an ideal component due to an inviscid flow with entry swirl and a viscous part due to the change in swirl created by friction inside the gland. The frequency dependent ideal part is solely responsible for the rotordynamic direct damping. The facility designed and built to measure these frequency dependent forces is described. Experimental data confirm the validity and usefulness of this ideal/viscous decomposition. A method for calculating the damping coefficients based on the force decomposition using the static measurements only is presented.

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Synchronous Rotor Vibration Driven by Fluid Forces From a Geometrically Imperfect Labyrinth Seal

Volume 5: Manufacturing Materials and Metallurgy; Ceramics; Structures and Dynamics; Controls, Diagnostics and Instrumentation; Education; IGTI Scholar Award ◽

10.1115/95-gt-362 ◽

1995 ◽

Author(s):

Knox T. Millsaps ◽

William C. Williston

Keyword(s):

Labyrinth Seal ◽

Radial Force ◽

Lumped Parameter Model ◽

Solution Technique ◽

Labyrinth Seals ◽

Fluid Forces ◽

Lumped Parameter ◽

Manufacturing Tolerances ◽

Vibration Problems ◽

Wear Damage

The radial force acting on a rotor, due to an asymmetric pressure distribution inside the seal gland, generated from a slightly non-circular single gland labyrinth seal rotating inside a circular outer casing is investigated theoretically. A fluid mechanical lumped parameter model for the flow in and out of the seal as well as the flow around the gland in the seal is developed. The model includes first and second knife imperfections as well as rotating gland depth variations. Knife non-circularity on the rotor may be due to manufacturing tolerances or defects from in service wear damage. An appropriate solution technique for the coupled one-dimensional equations is presented. Results from this model are presented that indicate these fluid induced forces are comparable in magnitude to those generated by a rotating unbalance under some conditions. Considerations for design are given for avoiding synchronous vibration problems due to non-circular labyrinth seals.

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Impact of Frequency Dependence of Gas Labyrinth Seal Rotordynamic Coefficients on Centrifugal Compressor Stability

Volume 6: Structures and Dynamics, Parts A and B ◽

10.1115/gt2010-22039 ◽

2010 ◽

Cited By ~ 3

Author(s):

Giuseppe Vannini ◽

Manish R. Thorat ◽

Dara W. Childs ◽

Mirko Libraschi

Keyword(s):

Molecular Weight ◽

Numerical Model ◽

Control Volume ◽

Labyrinth Seal ◽

Labyrinth Seals ◽

Frequency Dependent ◽

Rotordynamic Coefficients ◽

Frequency Independent ◽

Rotor Surface ◽

Independent Model

A numerical model developed by Thorat & Childs [1] has indicated that the conventional frequency independent model for labyrinth seals is invalid for rotor surface velocities reaching a significant fraction of Mach 1. A theoretical one-control-volume (1CV) model based on a leakage equation that yields a reasonably good comparison with experimental results is considered in the present analysis. The numerical model yields frequency-dependent rotordynamic coefficients for the seal. Three real centrifugal compressors are analyzed to compare stability predictions with and without frequency-dependent labyrinth seal model. Three different compressor services are selected to have a comprehensive scenario in terms of pressure and molecular weight (MW). The molecular weight is very important for Mach number calculation and consequently for the frequency dependent nature of the coefficients. A hydrogen recycle application with MW around 8, a natural gas application with MW around 18, and finally a propane application with molecular weight around 44 are selected for this comparison. Useful indications on the applicability range of frequency dependent coefficients are given.

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Dynamic Forces From Single Gland Labyrinth Seals: Part II—Upstream Coupling

Journal of Turbomachinery ◽

10.1115/1.2929462 ◽

1994 ◽

Vol 116 (4) ◽

pp. 694-700 ◽

Cited By ~ 1

Author(s):

K. T. Millsaps ◽

M. Martinez-Sanchez

Keyword(s):

Azimuthal Velocity ◽

Labyrinth Seal ◽

Quantitative Agreement ◽

Lumped Parameter Model ◽

Strong Impact ◽

Labyrinth Seals ◽

New Model ◽

Large Pressure ◽

Calculated Effect ◽

The Face

The standard lumped parameter model for flow in an eccentrically offset labyrinth seal, which assumes constant upstream and downstream boundary conditions, has been extended to include the effects of a nonuniform upstream cavity flow due to coupling. This new model predicts that the upstream perturbations in pressure and azimuthal velocity caused by this coupling can have a very strong impact on the pressure distribution in the seal gland itself. Augmentation by a factor of four, over the uniform inlet model, is predicted under some circumstances. Although no precise comparison to the experimental data with this new model was possible, due to the lack of control over the face seal venting the upstream cavity to the center hub plenum, the calculated effect of this coupling was shown to be approximately what was required to restore quantitative agreement between the data and theory. The new theory can explain the anomalously large pressure nonuniformity previously found by other authors in short seals as well as the first few glands of multicavity seals.

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Dynamic Forces From Single Gland Labyrinth Seals: Part II — Upstream Coupling

Volume 3B: General ◽

10.1115/93-gt-322 ◽

1993 ◽

Cited By ~ 1

Author(s):

Knox T. Millsaps ◽

Manuel Martinez-Sanchez

Keyword(s):

Azimuthal Velocity ◽

Labyrinth Seal ◽

Quantitative Agreement ◽

Lumped Parameter Model ◽

Strong Impact ◽

Labyrinth Seals ◽

New Model ◽

Large Pressure ◽

Calculated Effect ◽

The Face

The standard lumped parameter model for flow in an eccentrically offset labyrinth seal, which assumes constant upstream and downstream boundary conditions, has been extended to include the effects of a non-uniform upstream cavity flow due to coupling. This new model predicts that the upstream perturbations in pressure and azimuthal velocity caused by this coupling, can have a very strong impact on the pressure distribution in the seal gland itself. Augmentation by a factor of four, over the uniform inlet model, is predicted under some circumstances. Although no precise comparison to the experimental data with this new model was possible, due to the lack of control over the face seal venting the upstream cavity to the center hub plenum, the calculated effect of this coupling was shown to be approximately what was required to restore quantitative agreement between the data and theory. The new theory can explain the anomalously large pressure non-uniformity previously found by other authors in short seals as well as the first few glands of multi-cavity seals.

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