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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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