Arabian Journal for Science and Engineering

, Volume 44, Issue 2, pp 1293–1303 | Cite as

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

  • Wenjie Zhou
  • Guangkuan WuEmail author
  • Ning Qiu
  • Shengzhu Liu
  • Zhounian Lai
Research Article - Mechanical Engineering


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.


Annular seal Exit-recovery coefficient Leakage performance Dynamic coefficients Whirl-frequency ratio 

List of symbols


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


Dimensionless principle damping of seal


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


Dimensionless cross-coupled damping of seal


Fluid-induced force (N)


Clearance of radial seal (m)


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


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


Dimensionless principal stiffness of seal


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


Dimensionless cross-coupled stiffness of seal


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


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


Dimensionless principal mass of seal


Dimensionless pressure

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

Inlet and outlet pressure (MPa)


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


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

\({\bar{r_0 }}\)

Dimensionless whirl amplitude


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

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

Dimensionless zero-order velocity in axial and circumferential direction


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


Dimensionless pre-whirl velocity


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


Dimensionless axes

\(\Delta {p}\)

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

\(\varepsilon \)


\(\zeta \)

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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Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  • Wenjie Zhou
    • 1
    • 2
  • Guangkuan Wu
    • 3
    Email author
  • Ning Qiu
    • 4
  • Shengzhu Liu
    • 2
  • Zhounian Lai
    • 5
  1. 1.School of Energy and Power EngineeringJiangsu UniversityZhenjiangPeople’s Republic of China
  2. 2.Zhejiang Fuchunjiang Hydropower Equipment Co., Ltd.HangzhouPeople’s Republic of China
  3. 3.Institute of Water Resources and Hydro-electric EngineeringXi’an University of TechnologyXi’anPeople’s Republic of China
  4. 4.Research Center of Fluid Machinery Engineering and TechnologyJiangsu UniversityZhenjiangPeople’s Republic of China
  5. 5.Department of Civil and Environmental EngineeringThe Hong Kong University of Science and TechnologyHong KongPeople’s Republic of China

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