Abstract
The aerodynamic analysis of a non-contacting finger seal is performed on the basis of an equivalent 2-DOF model of a padded finger. Gas loads acting on flexible fingers are nonlinearly dependent on the radial clearance and are evaluated by calculations based on the 2D Reynolds equation for a thin gas layer. The computations are conducted by using of the in-house nonlinear FEA program. Finger stiffness coefficients are calculated by using the previously developed finger “beam” model. The dynamic response of the fingers to rotor’s radial excursions of model type is evaluated. The stability of the fingers in the gas flow is also assessed. The obtained results allow us to conclude that the radial adjustment of the seal to the rotor’s radial excursion is possible in case of a circumferentially convergent operating gap under the pads. Otherwise the developing suction force can drop the fingers towards the rotor surface and cause an undesired contact between the seal and the rotor.
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Abbreviations
- \(D_{\text{inv}}\) :
-
Region of flow calculation
- \(E_{s}\) :
-
Finger material elastic modulus
- \(i,j\) :
-
Indexes of bending moments
- \(I^{*}\) :
-
Finger equivalent mass inertia moment
- \(J_{s}\) :
-
Stick cross-section inertia moment
- \(g_{\updelta} ,\,g_{\uptheta} ,\,g\) :
-
Finger compliances
- \(k_{\updelta} ,\,k_{\uptheta} ,\,k\) :
-
Finger stiffness coefficients
- \(h(z,s)\) :
-
Gap (clearance) thickness
- \(h^{*}\) :
-
Dimensionless gap (clearance) thickness
- \(h_{1} (t),\,h_{2} (t)\) :
-
Inlet, outlet gap values
- \(L\) :
-
Gas moment acting on finger pad
- \(\vec{L}^{0}\) :
-
Equivalent total moment of gas forces
- \(m^{*}\) :
-
Finger equivalent mass
- \(M_{1}^{i,j} \left( \varphi \right)\) :
-
Internal bending moments
- \(\vec{n}_{g}\) :
-
Unit normal vector to pad surface
- \(p(z,s)\) :
-
Gas pressure distribution on pad
- \(p_{H} ,\,p_{L}\) :
-
High, low pressure
- \(R\) :
-
Gas force acting on finger pad
- \(R_{g}\) :
-
Total gas lifting force
- \(R_{s}\) :
-
Finger stick radius
- \(R_{\text{sh}}\) :
-
Rotor shaft radius
- \(\vec{R}^{0}\) :
-
Equivalent total gas force
- \(s\) :
-
Circumferential coordinate
- \(t,\,\tau\) :
-
Time, dimensionless time
- \(T_{\text{sim}}\) :
-
Total time used in dynamic simulations
- \(V(s)\) :
-
Relative radial velocity distribution of lifting pad and rotor shaft surface
- \(y(t),\,\dot{y}(t)\) :
-
Radial displacement and velocity of the rotor shaft surface
- \(y^{*}\) :
-
Dimensionless rotor radial displacement
- \(y_{\hbox{max} }\) :
-
Maximum value of rotor deflection
- \(z\) :
-
Axial coordinate
- \(\updelta,{ \dot{\updelta }},\;\mathop\updelta\limits^{..};\;\uptheta,{\dot{\uptheta}},\;\mathop\uptheta\limits^{..}\) :
-
Generalized displacements, velocities and accelerations corresponding to degrees of freedom of finger equivalent dynamic model
- \(\Delta_{1}^{ij}\) :
-
Displacements of finger stick end
- \(\Delta_{\text{root}}^{ij}\) :
-
Compliances of finger stick root
- \(\Delta p\) :
-
Pressure drop across seal
- \(\varphi\) :
-
Angular parameter of finger stick
- \(\upeta\) :
-
Gas dynamic viscosity
- \(< \vec{\tau },\vec{\nu },\text{ }\vec{\beta } >\) :
-
Stick coordinates system
- \(\upomega\) :
-
Rotor rotation velocity
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Temis, J., Selivanov, A., Dzeva, I. (2015). Dynamic Analysis of a Non-contacting Finger Seal. In: Pennacchi, P. (eds) Proceedings of the 9th IFToMM International Conference on Rotor Dynamics. Mechanisms and Machine Science, vol 21. Springer, Cham. https://doi.org/10.1007/978-3-319-06590-8_168
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DOI: https://doi.org/10.1007/978-3-319-06590-8_168
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