Labyrinth seals are utilized inside turbomachinery to provide noncontacting control of internal leakage. These seals can also play an important role in determining the rotordynamic stability of the machine. Traditional labyrinth seal models are based on bulk-flow assumptions where the fluid is assumed to behave as a rigid body affected by shear stress at the interfaces. To model the labyrinth seal cavity, a single, driven vortex is assumed and relationships for the shear stress and divergence angle of the through flow jet are developed. These models, while efficient to compute, typically show poor prediction for seals with small clearances, high running speed, and high pressure.* In an effort to improve the prediction of these components, this work utilizes three-dimensional computational fluid dynamics (CFD) to model the labyrinth seal flow path by solving the Reynolds Averaged Navier Stokes equations. Unlike bulk-flow techniques, CFD makes no fundamental assumptions on geometry, shear stress at the walls, as well as internal flow structure. The method allows modeling of any arbitrarily shaped domain including stepped and interlocking labyrinths with straight or angled teeth. When only leakage prediction is required, an axisymmetric model is created. To calculate rotordynamic forces, a full 3D, eccentric model is solved. The results demonstrate improved leakage anti rotordynamic prediction over bulk-flow approaches compared to experimental measurements.

Three-Dimensional CFD Rotordynamic Analysis of Gas Labyrinth Seals

Traditional annular seal models are based on bulk flow theory While these methods are computationally efficient and can predict dynamic properties fairly well for short seals, they lack accuracy in cases of seals with complex geometry or with large aspect ratios (above 10) In this paper, the linearized rotordynamic coefficients for a seal with a large aspect ratio are calculated by means of a three-dimensional CFD analysis performed to predict the fluid-induced forces acting on the rotor For comparison, the dynamic coefficients were also calculated using two other codes: one developed on the bulk flow method and one based on finite difference method These two sets of dynamic coefficients were compared with those obtained from CFD Results show a reasonable correlation for the direct stiffness estimates, with largest value predicted by CFD In terms of cross-coupled stiffness, which is known to be directly related to cross-coupled forces that contribute to rotor instability, the CFD also predicts the highest value; however, a much larger discrepancy can be observed for this term (73% higher than the value predicted by the finite difference method and 79% higher than the bulk flow code prediction) One can see similar large differences in predictions in the estimates for damping and direct mass coefficients, where the highest values are predicted by the bulk flow method These large variations in damping and mass coefficients, and most importantly the large difference in the cross-coupled stiffness predictions, may be attributed to the large difference in seal geometry (ie, the large aspect ratio AR >10 of this seal model versus the short seal configuration the bulk flow code is usually calibrated for using an empirical friction factor) [DOI: 101115/14007341]

Numerical Modeling of Fluid-Induced Rotordynamic Forces in Seals With Large Aspect Ratios

The demand for higher efficiencies and performance of modern centrifugal turbomachinery requires improved knowledge of critical design factors in strength of materials, aerodynamics, and rotordynamics. While tremendous strides in finite element stress analysis and computational fluid dynamics (CFD) have addressed the first two areas, the lack of accurate prediction tools for centrifugal impellers typically leaves rotordynamics out of the design loop. While several authors have analyzed the rotordynamic forces arising from shrouded centrifugal impellers, there has been no study to couple the secondary shroud passage with the three-dimensional primary flow model. The strong interaction between these domains makes this approach advantageous. The current study utilizes CFD techniques to analyze the full three-dimensional viscous, primary/secondary flow field in a centrifugal pump impeller to determine rotordynamic forces. Multiple quasisteady solutions of an eccentric three-dimensional model at different precessional frequency ratios yield the rotordynamic impedance forces. Performing a second order least-squares analysis generates the skew-symmetric stiffness, damping, and mass matrices. The results show good correlation with experiment for both performance and rotordynamic forces.

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Rotordynamic Force Prediction of Whirling Centrifugal Impeller Shroud Passages Using Computational Fluid Dynamic Techniques

This paper deals with modeling of hole-pattern and honeycomb seals. These are frequently used as balance piston seals in high pressure centrifugal compressor applications as they have the potential to facilitate superior rotordynamic damping characteristics while providing good leakage control. On the other hand it is also well-established that the rotordynamic performance of hole-pattern and honeycomb seals is very sensitive to convergence and divergence in the streamwise direction.The ISOTSEAL bulk-flow code has shown difficulties in predicting the rotordynamic coefficients for convergent seal geometries or in cases with negative preswirl. This has lead to increased interest in CFD-based analysis of seal dynamics. CFD-based models generally have less assumptions and are applicable for complex geometries or operating ranges not covered by bulk-flow codes.The CFD-based Instationary Perturbation Model (IPM) is utilized for the analysis of the hole-pattern and honeycomb seals. The rotordynamic forces are obtained by means of a time-dependent perturbation of the rotor position with respect to the stator. A sequence of perturbation frequencies is utilized to obtain the frequency dependence of the rotordynamic seal force coefficients.A strong effort has been put into validating the CFD-based perturbation modeling techniques against published experimental seal test data and the paper describes selected validation cases. A constant-clearance hole-pattern seal and a convergent honeycomb seal are analyzed and the results are compared to experimental results. The frequency dependence of the rotordynamic stiffness and damping characteristics of the seals is very well-captured for both types of seals.Finally the IPM method was applied to a convergent hole-pattern seal to investigate the effects of eccentricity on the rotordynamic coefficients. The results are consistent with available experimental data.Copyright © 2012 by ASME

Hole-Pattern and Honeycomb Seal Rotordynamic Forces: Validation of CFD-Based Prediction Techniques

This paper investigates the dynamics of a TCP system described by a first- order nonlinear delay differential equation. By analyzing the associated characteristic transcendental equation, it is shown that a Hopf bifurcation sequence occurs at the pos- itive equilibrium as the delay passes through a sequence of critical values. The explicit algorithms for determining the Hopf bifurcation direction and the stability of the bifur- cating periodic solutions are derived with the normal form theory and the center manifold theory. The global existence of periodic solutions is also established with the method of Wu (Wu, J. H. Symmetric functional differential equations and neural networks with mem- ory. Transactions of the American Mathematical Society 350(12), 4799-4838 (1998)).

Applied Mathematics and Mechanics

For modelling the turbulent flow in a seal the Navier-Stokes equations in connection with a turbulence (kappa-epsilon) model are solved by a finite-difference method. A motion of the shaft round the centered position is assumed. After calculating the corresponding flow field and the pressure distribution, the rotor-dynamic coefficients of the seal can be determined. These coefficients are compared with results obtained by using the bulk flow theory of Childs and with experimental results.

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F. J. Dietzen

Papers

Calculating Rotordynamic Coefficients of Seals by Finite-Difference Techniques