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Rotordynamic analysis for stepped-labyrinth gas seals using Moody’s friction-factor model

  • Materials & Fracture · Solids & Structures · Dynamics & Control · Production & Design
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Abstract

The governing equations are derived for the analysis of a stepped labyrinth gas seal generally used in high performance compressors, gas turbines, and steam turbines. The bulk-flow is assumed for a single cavity control volume set up in a stepped labyrinth cavity and the flow is assumed to be completely turbulent in the circumferential direction. The Moody’s wall-friction-factor model is used for the calculation of wall shear stresses in the single cavity control volume. For the reaction force developed by the stepped labyrinth gas seal, linearized zeroth-order and first-order perturbation equations are developed for small motion about a centered position. Integration of the resultant first-order pressure distribution along and around the seal defines the rotordynamic coefficients of the stepped labyrinth gas seal. The resulting leakage and rotordynamic characteristics of the stepped labyrinth gas seal are presented and compared with Scharrer’s theoretical analysis using Blasius’ wall-friction-factor model. The present analysis shows a good qualitative agreement of leakage characteristics with Scharrer’s analysis, but underpredicts by about 20 %. For the rotordynamic coefficients, the present analysis generally yields smaller predictied values compared with Scharrer’s analysis.

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Abbreviations

A :

Circumferential cross-sectional area of control volume(m2)

B :

Height of labyrinth tooth(m)

C, c :

Direct and cross-coupled damping coefficients(N·s/m)

C r :

Nominal clearance of seal(m)

D :

Diameter of pipe(m)

d :

Step height(m)

e :

Absolute surface roughness(m)

f :

Frequency ratio(Ω/ω)

f B ,f M :

Fanning friction factors defined by Blasius’ and Moody’s model

Fx, Fy :

Components of seal reaction force in x−y coordinate system(N)

H :

Local seal clearance(m)

K, k :

Direct and cross-coupled stiffness coefficients(N/m)

L :

Pitch of labyrinth tooth(m)

\(\dot m\) :

Mass flowrate per circumferential length (kg/(s·m))

m, n :

Coefficients for Blasius’s friction model

P :

Pressure(bar)

R :

Gas constant(N·m/kg·K)

R s :

Inlet radius of seal rotor(m)

t :

Time(s)

T :

Temperature(K)

t p :

Labyrinth tooth width(m)

V :

Average circumferential velocity in a labyrinth cavity(m/s)

Z c :

Compressibility factor

x,\(\dot x\):

Displacement and velocity of x-direction in rectangular coordinate(m, m/s)

y,\(\dot y\):

Displacement and velocity of y-direction in rectangular coordinate(m, m/s)

ɛ:

Eccentricity ratio

θ:

Angular coordinate

ϱ:

Fluid density (kg/m3)

τ:

Shear stress(N/m2)

ν:

Kinematic viscosity(m2/s)

ω:

Rotor angular velocity (rad/s)

0, 1:

Zeroth and first-order perturbations

s, r :

Stator, rotor

i :

i-th cavity

References

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Authors and Affiliations

  1. Mechanical Engineering Department, Kyungwon University, 461-701, Kyunggi-do, Korea

    Tae Woong Ha (Associate professor)

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  1. Tae Woong Ha
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Correspondence to Tae Woong Ha.

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Ha, T.W. Rotordynamic analysis for stepped-labyrinth gas seals using Moody’s friction-factor model. KSME International Journal 15, 1217–1225 (2001). https://doi.org/10.1007/BF03185662

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  • DOI: https://doi.org/10.1007/BF03185662

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