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Influence of Exit-Recovery Coefficient on the Leakage and Dynamic Characteristics of Annular Seal

  • Research Article - Mechanical Engineering
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Abstract

In order to study the effect of exit-recovery coefficient on leakage performance and dynamic characteristics of finite-length annular seal, a new boundary condition including exit-recovery coefficient is applied to the solution of the first-order perturbation equations according to bulk-flow model and small disturbance hypothesis. The theoretical results are validated by the experimental results with the minimum and maximum error percentage being 0.22% and 4.33%, respectively. On the basis of the accurate model, the influences of exit-recovery coefficient on leakage performance, dynamic coefficients and stability are investigated in detail. The calculated results imply that the exit-recovery coefficient needs to be considered in the characteristic research of annular seal. The exit-recovery coefficient is proportional to principle stiffness, while it is inversely proportional to leakage, principle damping, cross-coupled stiffness and damping. In addition, the exit-recovery coefficient has little effect on the stability of annular seal. The theoretical model including the exit-recovery coefficient is closer to actual condition and the results can provide references for the design of annular seal and multistage pump rotor system.

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Abbreviations

C :

Principle damping of seal (\(\hbox {N}\,\hbox {s/m}\))

\({\bar{C}}\) :

Dimensionless principle damping of seal

c :

Cross-coupled damping of seal (\(\hbox {N}\,\hbox {s/m}\))

\({\bar{c}}\) :

Dimensionless cross-coupled damping of seal

\(F_{s}\) :

Fluid-induced force (N)

\(H_{0}\) :

Clearance of radial seal (m)

i :

Imaginary unit (\(i^{2} = -1\))

K :

Principal stiffness of seal (\(\hbox {N/m}\))

\({\bar{K}}\) :

Dimensionless principal stiffness of seal

k :

Cross-coupled stiffness of seal (\(\hbox {N/m}\))

\({\bar{k}}\) :

Dimensionless cross-coupled stiffness of seal

\(L_{c}\) :

Length of seal (\(\hbox {m}\))

M :

Principal mass of seal (\(\hbox {kg}\))

\({\bar{M}}\) :

Dimensionless principal mass of seal

\({\bar{p}}\) :

Dimensionless pressure

\(P_\mathrm{in}, p_\mathrm{out}\) :

Inlet and outlet pressure (MPa)

Q :

Leakage flow (\(\hbox {m}^{3}/\hbox {s}\))

R :

Radius of rotor (\(\hbox {m}\))

\({\bar{r_0 }}\) :

Dimensionless whirl amplitude

T :

Time passed through seal (\(\hbox {s}\))

\(\bar{u}_{{\mathrm{z}}0}, {\bar{u}}_{\phi {0}}\) :

Dimensionless zero-order velocity in axial and circumferential direction

V :

Axial velocity (\(\hbox {m/s}\))

v :

Dimensionless pre-whirl velocity

x, y, z :

Axes (\(\hbox {m}\))

\({\bar{x}},{\bar{y}},{\bar{z}}\) :

Dimensionless axes

\(\Delta {p}\) :

Differential pressure (\(\hbox {MPa}\))

\(\varepsilon \) :

Eccentricity

\(\zeta \) :

Dimensionless eccentricity ratio of seal

\(\xi _{i}\) :

Inlet-loss coefficient

\(\xi _\mathrm{e}\) :

Exit-recovery coefficient

\(\varOmega \) :

Whirl speed (\(\hbox {r/min}\))

\(\omega \) :

Rotating speed (\(\hbox {r/min}\))

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Authors and Affiliations

  1. School of Energy and Power Engineering, Jiangsu University, Zhenjiang, 212013, People’s Republic of China

    Wenjie Zhou

  2. Zhejiang Fuchunjiang Hydropower Equipment Co., Ltd., Hangzhou, 311501, People’s Republic of China

    Wenjie Zhou & Shengzhu Liu

  3. Institute of Water Resources and Hydro-electric Engineering, Xi’an University of Technology, Xi’an, 710048, People’s Republic of China

    Guangkuan Wu

  4. Research Center of Fluid Machinery Engineering and Technology, Jiangsu University, Zhenjiang, 212013, People’s Republic of China

    Ning Qiu

  5. Department of Civil and Environmental Engineering, The Hong Kong University of Science and Technology, Hong Kong, People’s Republic of China

    Zhounian Lai

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  1. Wenjie Zhou
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  2. Guangkuan Wu
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  3. Ning Qiu
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  4. Shengzhu Liu
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  5. Zhounian Lai
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Correspondence to Guangkuan Wu.

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Zhou, W., Wu, G., Qiu, N. et al. Influence of Exit-Recovery Coefficient on the Leakage and Dynamic Characteristics of Annular Seal. Arab J Sci Eng 44, 1293–1303 (2019). https://doi.org/10.1007/s13369-018-3495-5

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  • DOI: https://doi.org/10.1007/s13369-018-3495-5

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