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A modeling of pump impeller shroud and wear-ring seal as a whole, and its application to the pump rotordynamics

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Abstract

A modeling methodology of pump impeller shroud and wear-ring seal as a whole has been developed to give its rotordynamic coefficients. In this work the governing equations are derived for the continuous flow path of the impeller shroud and wear-ring seal. Pressure loss at the discontinuity of the connecting point between the impeller shroud and the wear-ring seal is defined by utilizing a pressure loss coefficient obtained from experimental measurements. The governing equations are solved directly by using the known conditions at the inlet of the impeller shroud and the outlet of the wear-ring seal. A detailed rotordynamic analysis has been carried out on a 750 m-head fourteen-stage centrifugal pump system with the effects of the hydrodynamic forces of such as impeller shroud and wear-ring seals, balance piston, and interstage seals. Results have shown that the first critical speed obtained with all the seal effects is much higher than that obtained without those effects, and moreover that the system under consideration is unstable. Large cross coupled stiffness (k) of the impeller shroud and wear-ring seal has been suspected as the source of the problem. Design modifications of the impeller shroud and wear-ring seal geometry have been performed to decrease k and increase the direct damping(C). Finally, the design modifications have yielded a stable and well damped system.

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Abbreviations

C, c :

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

C i :

Inlet clearance of impeller shroud (mm)

C p :

Pressure loss coefficient in Eq. (8)

f :

Frequency ratio in Eq. (10)

f s ,f r :

Fanning friction factor of stator and rotor surface in Eq. (4)

F W ,F Y :

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

F r ,F θ :

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

H :

Local clearance(mm)

K, k :

Direct and cross-coupled stiffness(N/m)

Ls :

Impeller shroud surface length in path coordinate(m)

P :

Pressure(bar)

R :

Local radius(m)

R i :

Inlet radius of impeller shroud(m)

S :

Path coordinate

s :

Nondimensionalized path coordinate

f :

time(s)

U s ,U r :

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

W s ,U s :

Fluid velocity in the path and circumferential direction (m/s)

V :

Fluid velocity(m/s)

V r :

Fluid velocity at impeller shroud entrance(m/s)

X, Y :

Rotor displacements from its static position(m)

Z :

Axial coordinate

ε:

Eccentricity ratio

ρ:

Fluid density (kg/m3)

ξ:

Inlet loss coefficient in Eq. (7)

γ:

Slope of impeller shroud in Fig. 2

ω:

Rotor angular velocity (rad/s)

a :

Reservoir

0, 1:

Zeroth and first-order perturbations

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Authors and Affiliations

  1. Architectural Equipment Engineering Department, Kyung-won University, Sungnam, Korea

    Tae Woong Ha (Assistant professor)

  2. Rotor Dynamics Group Korea Institute of Machinery and Materials, 305 600, Daejeon, Republic of Korea

    An Sung Lee (Senior Researcher)

Authors
  1. Tae Woong Ha
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  2. An Sung Lee
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Ha, T.W., Lee, A.S. A modeling of pump impeller shroud and wear-ring seal as a whole, and its application to the pump rotordynamics. KSME International Journal 12, 441–450 (1998). https://doi.org/10.1007/BF02946359

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