KSME International Journal

, Volume 14, Issue 3, pp 261–271 | Cite as

A rotordynamic analysis of circumferentially-grooved pump seals based on a three-control-volume theory

  • Tae Woong HaEmail author
  • An Sung Lee
Materials & Fracture · Solids & Structures · Dynamics & Control · Production & Design


In this paper the leakage prediction and rotordynamic analysis of an annular seal with a smooth rotor and circumferentially grooved stator are performed based on a three-control-volume theory. The present analysis is validated by comparing with the experimental data of Iwatsubo and Sheng and theoretical results suggested by Marquette and Childs. For the leakage prediction the present analysis shows a good agreement with Marquette and Childs’ result and a qualitation agreement with Iwatsubo and Shengs’ experimental data. Direct and cross-coupled stiffness coefficients show closer agreement with the experimental values than those of Marquette and Childs. However, direct damping coefficient shows greater discrepancy from the experimental value than Marquette and Childs’.

Key Words

Rotordynamic Analysis Grooved pump seal Control-Volume Analysis Friction-Factor Model Leakage Rotordynamic Coefficients 



Depth of groove

C, c

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


Grooved seal clearance (mm)


Frequency ratio (Ω/ω) in Eq. (17)


Fanning friction factors of stator and rotor surface


Components of seal reaction force in X-Y coordinate system (N)

Fr, Fθ

Components of seal reaction force in r-θ coordinate system (N)


Local seal clearance (mm)

K, k

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


Seal length (mm)

M, m

Added mass and cross-coupled added mass coefficients (N · s2/m)


Pressure (bar)


Seal entrance pressure and exit pressure (bar)


Radius of rotor (mm)




Fluid velocity in the circumferential direction (m/s)

Us, Ur

Bulk-flow velocities relative to stator and rotor of Eq. (4)


Radial velocity of the flow at the inteface between control volume II and III


Fluid velocity in the axial direction (m/s)


Average axial fluid velocity in a land part (m/s)

x, y

Rotor displacements from its static position (m)


Axial coordinate


Groove penetration angle (rad)


Eccentricity ratio


Fluid density (kg/m3)


Angular coordinate


Rotor angular velocity (rad/s)



Relative to control volume I, II, or III

0, 1

Zeroth and first-order perturbations


Groove part

Land part

s, r

Stator, rotor


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  1. Black, H. F., and Cochran, E. A., 1973, “Leakage and Hybrid Bearing Properties of Serrated Seals in Centrifugal Pumps,”presented at the 6th International Confernece on Fluid Sealing, Munich, Germany, G5-61–G5-70.Google Scholar
  2. Childs, D. W., and Kim, C. H., 1986, “Testing for Rotordynamic Coefficients and Leakage: Circumferentially-Grooved Turbulent Annular Seals,”in Proceedings of the Second IFToMM International Conference on Rotordynamics, Tokyo, Japan, pp. 609–618.Google Scholar
  3. Florjancic, S., 1990, “Annular Seals of High Energy Centrifugal Pumps: A New Theory and Full Scale Measurement of Rotordynamic Coefficients and Hydraulic Friction Factors,” Ph. D. Dissertation, Swiss Federal Institute of Technology, Zurich, Switzerland.Google Scholar
  4. Ha, T. W., 1998, “Hydrodynamic Forces of Impeller Shroud and Wear-ring Seal on Centrifugal Pump,”KSME Journal Vol. A, No. 22, pp. 102–110.Google Scholar
  5. Hirs, G., 1973, “A Bulk-Flow Theory for Turbulence in Lubrication Films,”ASME Journal of Lubrication Technology, pp. 137–146.Google Scholar
  6. Iwatsubo, T., and Sheng, B., 1990, “Evaluation of Dynamic Characteristics of Parallel Grooved Seals by Theory and Experiment,”in Proceedings of the Third IFToMM International Conference on Rotordynamics, Lyon, France, pp. 313–318.Google Scholar
  7. Iwatsubo, T., Sheng, B., and Ono, M., 1990, “Experiment of Static and Dynamic Characteristics of Spiral Grooved Seals,”Rotordynamic Instability Problems in High-Performance Turbomachinery, NASA CP No. 3122, Proceedings of a workshop held at Texas A&M University, pp. 223–234.Google Scholar
  8. Kilgore, J. J., and Childs, D. W., 1990, “Rotor-dynamic Coefficients and Leakage Flow of Circumferentially Grooved Liquid-Seals,”ASME Journal of Fluids Engineering, Vol. 112, pp. 250–256.CrossRefGoogle Scholar
  9. Kim, C. H., and Childs, D. W., 1987, “Analysis for Rotordynamic Coefficients of Helically-Grooved Turbulent Annular Seals,”ASME Journal of Tribology, Vol. 109 (1), pp. 136–143CrossRefGoogle Scholar
  10. Marquette, O. R., and Childs D. W., 1996, “An Extended Three-Control-Volume Theory for Circumferentially-Grooved Liquid Seals,”ASME Journal of Tribology, Vol. 118, pp. 276–285.CrossRefGoogle Scholar
  11. Meirovitch, L., 1985,Introduction to Dynamics and Control, Wiley Interscience, New York.Google Scholar
  12. Nordmann, R., Dietzen, F. J., Janson, W., Frei, A., and Florjancic, S., 1986, “Rotordynamic Coefficients and Leakage Flow of Parallel Grooved Seals and Smooth Seals,”Rotordynamic Instability Problems in High-Performance Turbomachinery, NASA CP No. 2338, Proceedings of a workshop held at Texas A&M University, pp. 129–153.Google Scholar
  13. Wyssman, H., Pham, T., and Jenny, R., 1984, “Prediction of Stiffness and Damping Coefficients for Centrifugal Compressor Labyrinth Seals,”ASME Journal of Engineering for Gas Turbines and Power, Vol. 106, pp. 920–926.CrossRefGoogle Scholar

Copyright information

© The Korean Society of Mechanical Engineers (KSME) 2000

Authors and Affiliations

  1. 1.Rotor Dynamics GroupKorea Institute of Machinery and MaterialsKorea
  2. 2.Mechanical Design & Production Engineering DepartmentKyung-won UniversitySungnam, Kyunggi-doKorea

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