Abstract
A comprehensive analytical work to estimate the leakage rate is presented for compressible fluid flow across shaft seals. The sealing gap for this study includes geometric terms such as eccentricity, misaligned shaft, and sinusoidal waviness of the mating surfaces. A temperature distribution across the sealing gap is developed using a temperature dependent viscosity. A pressure distribution in polynomial form is solved based on the simplified nonlinear Reynolds equation using the approximate power series expansion. It was found that the seal performance is largely influenced by the eccentricity and width of the seal at high speeds (greater than about 150m/s).
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Abbreviations
- a :
-
Velocity of sound
- C i :
-
Wave velocity of the lower body
- C u :
-
Wave velocity of the upper body
- e :
-
Eccentricity\(( = \overline {O_1 O_2 } )\)
- e o :
-
Shaft eccentricity at\(z = 0( = \overline {O_1 N} )\)
- k :
-
Specific heat ratio
- K :
-
Thermal conductivity
- L :
-
Half of the seal width
- \(\dot m\) :
-
Mass flow rate
- \(\dot M\) :
-
Dimensionless mass flow rate
- N :
-
Center at the midplane, i.e.,z=0
- O1 :
-
Center of the seal
- O2 :
-
Center of the shaft at any plane
- p :
-
Pressure
- \(\tilde R\) :
-
r/r 1
- R g :
-
Gas constant
- t :
-
Time
- T :
-
Temperature
- U :
-
r 2ω, velocity of the shaft
- v π :
-
Tangential velocity component of fluid
- V z :
-
Axial velocity component of fluid
- z :
-
Axial coordinate
- γ:
-
Angle of tilt
- ε:
-
\(\gamma L/\bar h\) tilt parameter of the shaft seal
- ε0 :
-
\(e_0 /\bar h\) eccentricity ratio atz=0
- η:
-
Viscosity of fluid
- χ:
-
2π/λ, wave number
- λ:
-
Wavelength
- Λι :
-
T l /T r
- μ:
-
Coefficient of friction
- ξ l :
-
\(\left| {\bar h_g } \right|/\bar h\)
- ξ u :
-
\(\left| {\overline {h_u } } \right|/\bar h\)
- σ:
-
Density
- Ω:
-
Angular speed
- Ω l :
-
X l C l
- Ω u :
-
x u (C u +U)
- ω:
-
Angular speed of the moving surface
- 1:
-
Seal
- 2:
-
Shaft
- r :
-
Reference conditions
- l :
-
Lower
- u :
-
Upper
References
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Bryant, M.D. and Kim, C.K., 1987, “Estimating the Leakage of Compressible Gases through Face Seals Rotating at High Speeds, Part I-Geometric Effect on Sealing Gap,” Submitted to the Journal of Tribology.
Chen, W.C. and Jackson, E.D., “Eccentricity and Misalignment Effects on the Performance of High-Pressure Annular Seals,” ASLE Trans., Vol. 28, No. 1, pp. 104–110.
Constantinescu, V.N., 1969, “Gas Lubrication,” Pub. by ASME.
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Dhagat, S.K., Sinhasan, R. and Singh, D.V., “Dynamic Analysis of Wedge-Type Shaft Seal, ASLE Trans., Vol. 24, No. 3, pp. 387–397.
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Kim, C.K. Estimation of the leakage for compressible gases in high-speed shaft seals. KSME Journal 2, 3–8 (1988). https://doi.org/10.1007/BF02944070
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DOI: https://doi.org/10.1007/BF02944070