Interrelated Rotordynamic Effects of Cylindrical and Conical Whirl of Annular Seal Rotors

1991 ◽  
Vol 113 (3) ◽  
pp. 470-480 ◽  
Author(s):  
E. A. Baskharone ◽  
S. J. Hensel
Keyword(s):  
Finite Element ◽  
Flow Model ◽  
Computational Procedure ◽  
Rotordynamic Coefficients ◽  
Conical Whirl ◽  
Conical Rotor ◽  
Annular Seal ◽  
Rotor Surface ◽  
Flow Variables ◽  
Sample Case

A comprehensive approach for computing the dynamic coefficients of an annular seal is presented. The coefficients are partly those associated with a uniform lateral eccentricity mode of the rotor (known as the cylindrical whirl mode) and with an angular eccentricity (which gives rise to a conical whirl type). The rotor excitation effects in both cases are treated as interrelated by recognizing the fluid-exerted moments resulting from the lateral eccentricity and the net fluid force resulting from the angular eccentricity. In all cases, the rotor is assumed to undergo a whirling motion around the housing centerline. The computational procedure is a finite-element perturbation model in which the zeroth-order undisplaced-rotor flow solution in the clearance gap is obtained through a Petrov-Galerkin approach. Next, the rotor translational and angular eccentricities, considered to be infinitesimally small, are perceived to cause virtual distortions of varied magnitudes in the finite element assembly which occupies the clearance gap. Perturbations in the flow variables including, in particular, the rotor surface pressure, are then obtained by expanding the finite-element equations in terms of the rotor eccentricity components. The fluid-exerted forces and moments are in this case computed by integration over the rotor surface, and the full matrix of rotordynamic coefficients, in the end, obtained. The computational model is verified against a bulk-flow model for a sample case involving a straight annular seal. Choice of this sample model for validation was made on the basis that no other existing model has yet been expanded to account for the mutual interaction between the cylindrical and conical rotor whirl, which is under focus in this study.

A Finite-Element Perturbation Approach to Fluid/Rotor Interaction in Turbomachinery Elements. Part 2: Application

1991 ◽  
Vol 113 (3) ◽  
pp. 362-367 ◽  
Author(s):  
E. A. Baskharone ◽  
S. J. Hensel
Keyword(s):  
Finite Element ◽  
Computational Models ◽  
Operation Mode ◽  
Analytical Data ◽  
Perturbation Approach ◽  
Rotordynamic Coefficients ◽  
Eccentric Rotor ◽  
Annular Seal ◽  
Circumferential Distribution ◽  
Flow Variables

A newly devised perturbation model for the fluid-induced vibration of turbomachinery rotating elements is used to compute the rotordynamic coefficients of an annular seal. First, the finite element-based solution of the flow field in the centered-rotor operation mode is verified and its grid dependency tested for different seal configurations. The rotordynamic behavior of a hydraulic seal with a clearance gap depth/length ratio of 0.01, as a representative case, is then analyzed under a cylindrical type of rotor whirl and several running speeds. The direct and cross-coupled rotordynamic coefficients dictating the rotor instability mechanism in this case are compared to experimental and analytical data, and the outcome is favorable. The numerical results are also used to discuss the validity of a common assumption in existing computational models in regard to the circumferential distribution of the perturbed flow variables in the eccentric rotor operation mode.

Development of Scallop Cut Type Damper Seal for Centrifugal Compressors

2014 ◽  
Author(s):  
Naohiko Takahashi ◽  
Haruo Miura ◽  
Mitsuhiro Narita ◽  
Noriyo Nishijima ◽  
Yohei Magara
Keyword(s):  
High Pressure ◽  
Perturbation Analysis ◽  
Flow Model ◽  
Frame Of Reference ◽  
Bulk Flow ◽  
Rotating Frame ◽  
Rotordynamic Coefficients ◽  
Neighboring Region ◽  
Rotor Surface ◽  
Honeycomb Seals

This paper deals with a new type of damper seal developed for a high-pressure centrifugal compressor. Honeycomb seals and hole-pattern seals are popularly used as damper seals and provide superior rotordynamic damping characteristics. Honeycomb seals are expensive because the manufacturing process is complex. Hole-pattern seals are easier to manufacture, but they are still expensive. Use of a scallop pattern is one way to reduce manufacturing cost and time. A new seal that has a scallop pattern and small teeth on the stator surface is proposed. This pattern is cut on the stator surface using a disc type tool. To estimate the rotordynamic coefficients of this new seal, a bulk flow model code that is based on a two-control-volume model developed by Matsuda for labyrinth seals was newly developed. This model uses the Hirs model for the viscous shear stresses. The friction factor coefficients for the rotor surface, the stator surface and the surface between the two control volumes were determined by CFD steady analysis. The rotordynamic coefficients can also be obtained by using CFD perturbation analysis. The high accuracy of the bulk flow model was demonstrated by comparing its results with CFD perturbation analysis results. In the perturbation analysis, the whirling motion was treated as a steady state problem by using a rotating frame of reference. For the damper seal, the rotor surface and its neighboring region were treated with a rotating frame of reference and the neighboring region of the stator was treated with a stationary frame of reference. The damping property of the new seal was evaluated by conducting rotor stability tests using a high-pressure compressor with an electromagnetic exciter. The new seal equipped with swirl brakes was used for the balance piston of the compressor. Stability was evaluated by exciting the rotor during operation and identifying the eigenvalues of the rotor. The experimental results showed that the new seal increases damping. Comparison of the damping effect with calculations based on the bulk flow analysis showed good agreement.

Development of Scallop Cut Type Damper Seal for Centrifugal Compressors

2014 ◽  
Vol 137 (3) ◽  
Author(s):  
Naohiko Takahashi ◽  
Haruo Miura ◽  
Mitsuhiro Narita ◽  
Noriyo Nishijima ◽  
Yohei Magara
Keyword(s):  
High Pressure ◽  
Perturbation Analysis ◽  
Flow Model ◽  
Frame Of Reference ◽  
Bulk Flow ◽  
Rotating Frame ◽  
Rotordynamic Coefficients ◽  
Neighboring Region ◽  
Rotor Surface ◽  
Honeycomb Seals

This paper deals with a new type of damper seal developed for a high-pressure centrifugal compressor. Honeycomb seals and hole pattern seals are popularly used as damper seals and provide superior rotordynamic damping characteristics. Honeycomb seals are expensive because the manufacturing process is complex. Hole pattern seals are easier to manufacture, but they are still expensive. Use of a scallop pattern is one way to reduce manufacturing cost and time. A new seal that has a scallop pattern and small teeth on the stator surface is proposed. This pattern is cut on the stator surface using a disk type tool. To estimate the rotordynamic coefficients of this new seal, a bulk flow model code that is based on a two-control-volume model developed by Matsuda for labyrinth seals was newly developed. This model uses the Hirs model for the viscous shear stresses. The friction factor coefficients for the rotor surface, the stator surface, and the surface between the two-control-volumes were determined by computational fluid dynamics (CFD) steady analysis. The rotordynamic coefficients can also be obtained by using CFD perturbation analysis. The high accuracy of the bulk flow model was demonstrated by comparing its results with CFD perturbation analysis results. In the perturbation analysis, the whirling motion was treated as a steady-state problem by using a rotating frame of reference. For the damper seal, the rotor surface and its neighboring region were treated with a rotating frame of reference and the neighboring region of the stator was treated with a stationary frame of reference. The damping property of the new seal was evaluated by conducting rotor stability tests using a high-pressure compressor with an electromagnetic exciter. The new seal equipped with swirl brakes was used for the balance piston of the compressor. Stability was evaluated by exciting the rotor during operation and identifying the eigenvalues of the rotor. The experimental results showed that the new seal increases damping. Comparison of the damping effect with calculations based on the bulk flow analysis showed good agreement.

Lock-up characteristics of floating ring seals considering rotor whirling motion

2017 ◽  
Vol 232 (4) ◽  
pp. 437-452
Author(s):  
Peng Xia ◽  
Zhan-sheng Liu ◽  
Jia-jia Yan ◽  
Guang-hui Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Friction Force ◽  
Nonlinear Model ◽  
Flow Model ◽  
Bulk Flow ◽  
Circular Trajectory ◽  
Rotordynamic Coefficients ◽  
Whirling Motion ◽  
Ring Seal

This paper presents a lock-up condition with rotor whirling motion to predict the lock-up area for floating ring seals in liquid turbopumps. To calculate the hydrodynamic forces with arbitrary rotor motion, bulk flow model is modified with explicitly considering the squeeze velocity and temporal inertia. Finite element method is implemented to solve the transient nonlinear model. The effect of lock-up position on leakage and rotordynamic coefficients of floating ring seals is studied and shows insensitivity to eccentricity within moderate eccentric area (<0.5), which indicates that predicting lock-up area with the lock-up condition is feasible for application. With circular trajectory of rotors, the effects of rotor whirling radius and friction force on lock-up area are investigated. The results show that the lock-up area shrinks toward rotor whirling center, with the increase in the rotor whirling radius and decrease in the friction force. Further, a coupled method of rotor trajectory and floating ring seal lock-up area is presented to consider the interaction between rotors and floating ring seals. The results show that the effect of the interaction on the lock-up area is almost negligible, as lock-up position of floating ring seals has little effect on rotor trajectory. In addition, the effect of the seal configuration on the lock-up area is studied.

Numerical Modeling of Rotordynamic Coefficients for Deliberately Roughened Stator Gas Annular Seals

2006 ◽  
Vol 129 (2) ◽  
pp. 424-429 ◽  
Author(s):  
Gocha Chochua ◽  
Thomas A. Soulas
Keyword(s):  
Transient Analysis ◽  
Test Rig ◽  
One Dimensional ◽  
Design And Optimization ◽  
Rotordynamic Coefficients ◽  
Seal Design ◽  
Annular Seal ◽  
Rotor Surface ◽  
Good Agreement ◽  
Annular Seals

A method is proposed for computations of rotordynamic coefficients of deliberately roughened stator gas annular seals using computational fluid dynamics. The method is based on a transient analysis with deforming mesh. Frequency-dependent direct and cross-coupled rotordynamic coefficients are determined as a response to an assigned rotor surface periodic motion. The obtained numerical results are found to be in good agreement with the available test data and one-dimensional tool predictions. The method can be used as a research tool or as a virtual annular seal test rig for seal design and optimization.

Rotordynamic Coefficients for Compressible Flow in Tapered Annular Seals

1985 ◽  
Vol 107 (3) ◽  
pp. 318-325 ◽  
Author(s):  
C. C. Nelson
Keyword(s):  
Compressible Flow ◽  
Flow Model ◽  
Space Shuttle ◽  
Governing Equations ◽  
First Order ◽  
Rotordynamic Coefficients ◽  
Annular Seal ◽  
Direct Stiffness ◽  
Stiffness And Damping ◽  
Main Engine

Derivation of the governing equations for compressible flow in a tapered annular seal is based on Hirs’ turbulent bulk-flow model. Zeroth and first-order perturbation equations are developed by an expansion in the eccentricity ratio. These equations are numerically integrated to obtain the leakage, and the direct and cross-coupled stiffness and damping coefficients. Seal parameters similar to the Space Shuttle Main Engine High Pressure Oxidizer Turbopump are used to demonstrate output from the analysis procedure. The effects of preswirl and seal taper are shown for three different length-to-diameter ratios. Generally the results indicate that prerotating the fluid significantly increases the cross-coupled stiffness but has little effect on the other coefficients, and increasing the convergent taper increases the direct stiffness while decreasing the direct damping and cross-coupled stiffness.

Analysis of Eccentric Annular Incompressible Seals: Part 2—Effects of Eccentricity on Rotordynamic Coefficients

1988 ◽  
Vol 110 (2) ◽  
pp. 361-366 ◽  
Author(s):  
C. C. Nelson ◽  
D. T. Nguyen
Keyword(s):  
Flow Model ◽  
Element Model ◽  
Analysis Procedure ◽  
Governing Equations ◽  
Zeroth Order ◽  
Static Displacement ◽  
First Order ◽  
Rotordynamic Coefficients ◽  
Flow Variables ◽  
Factor Equation

In Part 1 of this paper, a new analysis procedure is presented which solves for the flow variables of an annular pressure seal in which the rotor has a large static displacement (eccentricity) from the centered position. This part of the paper (Part 2) incorporates the solutions from Part 1 to investigate the effect of eccentricity on the rotordynamic coefficients. The analysis begins with a set of governing equations based on a turbulent bulk-flow model and Moody’s friction factor equation. Perturbations of the flow variables yields a set of zeroth- and first-order equations. After integration of the zeroth-order equations by means of the method described in Part 1, the resulting zeroth-order flow variables are used as input in the solution of the first-order equations. Further integration of the first order pressures yields the eccentric rotordynamic coefficients. The results from this procedure compare very well with available experimental data, and are clearly more accurate than the predictions based on a Finite Element model.

Impact of Frequency Dependence of Gas Labyrinth Seal Rotordynamic Coefficients on Centrifugal Compressor Stability

2010 ◽  
Author(s):  
Giuseppe Vannini ◽  
Manish R. Thorat ◽  
Dara W. Childs ◽  
Mirko Libraschi
Keyword(s):  
Molecular Weight ◽  
Numerical Model ◽  
Control Volume ◽  
Labyrinth Seal ◽  
Labyrinth Seals ◽  
Frequency Dependent ◽  
Rotordynamic Coefficients ◽  
Frequency Independent ◽  
Rotor Surface ◽  
Independent Model

A numerical model developed by Thorat & Childs [1] has indicated that the conventional frequency independent model for labyrinth seals is invalid for rotor surface velocities reaching a significant fraction of Mach 1. A theoretical one-control-volume (1CV) model based on a leakage equation that yields a reasonably good comparison with experimental results is considered in the present analysis. The numerical model yields frequency-dependent rotordynamic coefficients for the seal. Three real centrifugal compressors are analyzed to compare stability predictions with and without frequency-dependent labyrinth seal model. Three different compressor services are selected to have a comprehensive scenario in terms of pressure and molecular weight (MW). The molecular weight is very important for Mach number calculation and consequently for the frequency dependent nature of the coefficients. A hydrogen recycle application with MW around 8, a natural gas application with MW around 18, and finally a propane application with molecular weight around 44 are selected for this comparison. Useful indications on the applicability range of frequency dependent coefficients are given.

A Comparison of Rotordynamic-Coefficient Predictions for Annular Honeycomb Gas Seals Using Three Different Friction-Factor Models

2002 ◽  
Vol 124 (3) ◽  
pp. 524-529 ◽  
Author(s):  
Rohan J. D’Souza ◽  
Dara W. Childs
Keyword(s):  
Friction Factor ◽  
Flow Model ◽  
Factor Model ◽  
Control Volume ◽  
Bulk Flow ◽  
Shear Stresses ◽  
Steam Turbines ◽  
Frequency Range ◽  
Rotordynamic Coefficients ◽  
Rotordynamic Coefficient

A two-control-volume bulk-flow model is used to predict rotordynamic coefficients for an annular, honeycomb-stator/smooth-rotor gas seal. The bulk-flow model uses Hirs’ turbulent-lubrication model, which requires a friction factor model to define the shear stresses at the rotor and stator wall. Rotordynamic coefficients predictions are compared for the following three variations of the Blasius pipe-friction model: (i) a basic model where the Reynolds number is a linear function of the local clearance, fs=ns Rems (ii) a model where the coefficient is a function of the local clearance, and (iii) a model where both the coefficient and exponent are functions of the local clearance. The latter models are based on data that shows the friction factor increasing with increasing clearances. Rotordynamic-coefficient predictions shows that the friction-factor-model choice is important in predicting the effective-damping coefficients at a lower frequency range (60∼70 Hz) where industrial centrifugal compressors and steam turbines tend to become unstable. At a higher frequency range, irrespective of the friction-factor model, the rotordynamic-coefficient predictions tend to coincide. Blasius-based Models which directly account for the observed increase in stator friction factors with increasing clearance predict significantly lower values for the destabilizing cross-coupled stiffness coefficients.

scholarly journals A system of conservative regridding for ice/atmosphere coupling in a GCM

2013 ◽  
Vol 6 (4) ◽  
pp. 6493-6568 ◽  
Author(s):  
R. Fischer ◽  
S. Nowicki ◽  
M. Kelley ◽  
G. A. Schmidt
Keyword(s):  
Finite Element ◽  
General Circulation ◽  
Flow Model ◽  
Source Code ◽  
Circulation Model ◽  
Surface Mass Balance ◽  
Ice Flow ◽  
Surface Mass ◽  
Flow Models ◽  
Ice Model

Abstract. The method of elevation classes has proven to be a useful way for a low-resolution general circulation model (GCM) to produce high-resolution downscaled surface mass balance fields, for use in one-way studies coupling GCMs and ice flow models. Past uses of elevation classes have been a cause of non-conservation of mass and energy, caused by inconsistency in regridding schemes chosen to regrid to the atmosphere vs. downscaling to the ice model. This causes problems for two-way coupling. A strategy that resolves this conservation issue has been designed and is presented here. The approach identifies three grids between which data must be regridded, and five transformations between those grids required by a typical coupled GCM–ice flow model. This paper shows how each of those transformations may be achieved in a consistent, conservative manner. These transformations are implemented in GLINT2, a library used to couple GCMs with ice models. Source code and documentation are available for download. Confounding real-world issues are discussed, including the use of projections for ice modeling, how to handle dynamically changing ice geometry, and modifications required for finite element ice models.

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