Application of a Novel Rotordynamic Identification Method for Annular Seals With Arbitrary Elliptical Orbits and Eccentricities

2019 ◽  
Vol 141 (9) ◽  
Author(s):  
Wanfu Zhang ◽  
Qianlei Gu ◽  
Jiangang Yang ◽  
Chun Li
Keyword(s):  
Fluid Velocity ◽  
Reaction Force ◽  
Grid Method ◽  
Labyrinth Seal ◽  
Damping Coefficient ◽  
Eccentricity Ratio ◽  
Rotordynamic Coefficients ◽  
Identification Method ◽  
Gas Seals ◽  
Annular Seals

The identification method using infinitesimal theory is proposed to predict rotordynamic coefficients of annular gas seals. The transient solution combined with moving grid method was unitized to obtain the fluid reaction force at a specific position under different whirling frequencies. The infinitesimal method is then applied to obtain the rotordynamic coefficients, which agrees well with published experimental results for both labyrinth seals and eccentric smooth annular seals. Particularly, the stability parameter of the effective damping coefficient can be solved precisely. Results show that the whirling frequency has little influence on direct damping coefficient, effective damping coefficient, and cross-coupled stiffness coefficient for the labyrinth seal. And the effective damping coefficients decrease as the eccentricity ratio increases. A higher eccentricity ratio tends to destabilize the seal system, especially at a low whirling frequency. Results also show that the fluid velocity in the maximum clearance in the seal leakage path is less than that in the minimum clearance. The inertial effect dominates the flow field. Then it results in higher pressure appearing in maximum clearances. The pressure difference aggravates the eccentricity of rotor and results in static instabilities of the seal system.

Theory Versus Experiment for the Rotordynamic Coefficients of Labyrinth Gas Seals: Part I—A Two Control Volume Model

1988 ◽  
Vol 110 (3) ◽  
pp. 270-280 ◽  
Author(s):  
Joseph K. Scharrer
Keyword(s):  
Pressure Distribution ◽  
Control Volume ◽  
Reaction Force ◽  
Labyrinth Seal ◽  
Wall Friction ◽  
Small Motion ◽  
First Order ◽  
Rotordynamic Coefficients ◽  
Volume Model ◽  
Gas Seals

The basic equations are derived for a two-control-volume model for compressible flow in a labyrinth seal. The recirculation velocity in the cavity is incorporated into the model for the first time. The flow is assumed to be completely turbulent and isoenergetic. The wall friction factors are determined using the Blasius formula. Jet flow theory is used for the calculation of the recirculation velocity in the cavity. Linearized zeroth and first-order perturbation equations are developed for small motion about a centered position by an expansion in the eccentricity ratio. The zeroth-order pressure distribution is found by satisfying the leakage equation while the circumferential velocity distribution is determined by satisfying the momentum equations. The first-order equations are solved by a separation of variable solution. Integration of the resultant pressure distribution along and around the seal defines the reaction force developed by the seal and the corresponding dynamic coefficients.

scholarly journals Rotordynamic Coefficient and Leakage Test Results for Interlock and Tooth-on-Stator Labyrinth Seals

1988 ◽  
Author(s):  
Dara W. Childs ◽  
David A. Elrod ◽  
Keith Hale
Keyword(s):  
Labyrinth Seal ◽  
Damping Coefficient ◽  
Test Results ◽  
Labyrinth Seals ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
Leakage Test ◽  
Stiffness And Damping ◽  
Rotordynamic Coefficient

Test results (leakage and rotordynamic coefficients) are presented for an interlock and tooth-on-stator labyrinth seals. Tests were carried out with air at speeds out to 16,000 cpm and supply pressures up to 7.5 bars. The rotordynamic coefficients consist of direct and cross-coupled stiffness and damping coefficients. Damping-coefficient data have not previously been presented for interlock seals. The test results support the following conclusions: (a) The interlock seal leaks substantially less than labyrinth seals. (b) Destabilizing forces are lower for the interlock seal. (c) The labyrinth seal has substantially greater direct damping values than the interlock seal. A complete rotordynamics analysis is needed to determine which type of seal would yield the best stability predictions for a given turbomachinery unit.

A CFD Based Approach for Estimation of Rotor Dynamic Coefficients for Liquid Annular Seals in Turbomachinery

2018 ◽  
Author(s):  
Bachanti Krishna ◽  
B. Premachandran ◽  
Ashish K. Darpe
Keyword(s):  
High Speed ◽  
Reaction Force ◽  
Physical And Mechanical Properties ◽  
Working Fluid ◽  
Complex Geometries ◽  
Experimental Conditions ◽  
Rotordynamic Coefficients ◽  
Dynamic Coefficients ◽  
Rotor Dynamic ◽  
Annular Seals

Seals are used to control leakage across stages in pumps and other rotating machinery such as turbomachines. However, while acting to control leakage, the seals generate a reaction force on the rotating members. The rotordynamic forces produced by fluid impact the stability behaviour of the high-speed turbomachinery, therefore precise estimation of rotordynamic parameters is important to ensure vibrational stability and desired dynamic performance of rotors having annular seals. Studies on seals have so far mainly focused on bulk flow model based on Hirs turbulent lubrication theory for calculating leakage flow rate and rotordynamic coefficients. However, it is incapable to deal complex geometries and is less efficient in predicting precise rotor dynamic parameters for high speed rotating systems due to its basic assumptions. The experiments performed for calculating rotordynamic coefficients show their dependence on many physical and mechanical properties such as working fluid properties, pressure drop, seal clearance, rotor speed, eccentricity and misalignments. With the latest high performance computing facilities it is now relatively easy to simulate the flow in seal and evaluate the dynamic coefficients at high rotational speeds and with complex geometries. This paper proposes a 3-D CFD based transient stimulation method to capture the experimental conditions in virtual environment. The fluid force is calculated by integrating pressure to the rotor surface and the stiffness and damping coefficients are evaluated by appropriate curve fitting of fluid forces for various eccentricity values. The coefficients obtained from the present method show better correlation with experimental data compared to the existing steady state CFD and theoretical models. Variation of these rotordynamic coefficients with eccentricity helps in assessing the safe design of turbomachinery.

A Generalized Prediction Method for Rotordynamic Coefficients of Annular Gas Seals

2015 ◽  
Vol 137 (9) ◽  
Author(s):  
Xin Yan ◽  
Kun He ◽  
Jun Li ◽  
Zhenping Feng
Keyword(s):  
Reaction Force ◽  
Excitation Frequency ◽  
Prediction Method ◽  
Experimental Tests ◽  
Computational Time ◽  
Transform Method ◽  
Rotordynamic Coefficients ◽  
The Laplace Transform ◽  
Computational Fluid Dynamics Cfd ◽  
Gas Seals

The improvement in rotordynamic performance of the annular gas seal requires efficient and accurate prediction methods of rotordynamic coefficients. Although the existed transient computational fluid dynamics (CFD) methods in published literature have excellent numerical accuracy, most of them face the challenge due to rotordynamic coefficients at every excitation frequency to be solved by a separate transient CFD prediction thus much time-consuming. In this paper, a generalized prediction method is proposed to address this difficulty. Based on the Laplace transform method, the solution procedures for the reaction force/motion equation of the annular gas seal are deduced. With the specified excitations (rotor motion), the rotordynamic coefficients at all excitation frequencies can be solved by only one or two transient CFD solutions. To verify the present generalized method, the rotordynamic coefficients of two typical hole-pattern seals are computed and compared to the available experimental data. The results show that the predicted rotordynamic coefficients are in good agreement with the experimental tests. Compared to the previous transient CFD methods, the computational time of the present generalized method is reduced significantly while the accuracy is still maintained.

Theory Versus Experiment for the Rotordynamic Coefficient of Labyrinth Gas Seals: Part II—A Comparison to Experiment

1988 ◽  
Vol 110 (3) ◽  
pp. 281-287 ◽  
Author(s):  
D. W. Childs ◽  
J. K. Scharrer
Keyword(s):  
Experimental Test ◽  
Damping Coefficient ◽  
Test Facility ◽  
Radial Clearance ◽  
Test Results ◽  
Rotordynamic Coefficients ◽  
Theory Versus ◽  
Gas Seals ◽  
Predicted Values ◽  
Rotordynamic Coefficient

An experimental test facility is used to measure the leakage and rotordynamic coefficients of teeth-on-rotor and teeth-on-stator labyrinth gas seals. The test results are presented along with the theoretically predicted values for the two seal configurations at three different radial clearances and shaft speeds to 16,000 cpm. The test results show that the theory accurately predicts the cross-coupled stiffness for both seal configurations and shows improvement in the prediction of the direct damping for the teeth-on-rotor seal. The theory fails to predict a decrease in the direct damping coefficient for an increase in the radial clearance for the teeth-on-stator seal.

Finite-Length Solutions for Rotordynamic Coefficients of Turbulent Annular Seals

1983 ◽  
Vol 105 (3) ◽  
pp. 437-444 ◽  
Author(s):  
D. W. Childs
Keyword(s):  
Pressure Distribution ◽  
Finite Length ◽  
Reaction Force ◽  
Centrifugal Pumps ◽  
First Order ◽  
Rotordynamic Coefficients ◽  
Dynamic Coefficients ◽  
Continuity Equations ◽  
Complex Differential Equations ◽  
Annular Seals

Expressions are derived which define dynamic coefficients for high-pressure annular seals typical of wear-ring and interstage seals employed in multistage centrifugal pumps. Completely developed turbulent flow is assumed in both the circumferential and axial directions, and is modeled by Hirs’ turbulent lubrication equations. Linear zeroth and first-order perturbation equations are developed by an expansion in the eccentricity ratio. The influence of inlet swirl is accounted for in the development of the circumferential flow. The zeroth-order momentum and continuity equations are solved exactly, while their first-order counterparts are reduced to three ordinary, complex, differential equations in the axial coordinate Z. The equations are integrated to satisfy the boundary conditions and define the pressure distribution due to seal motion. Integration of the pressure distribution defines the reaction force developed by the seal and the corresponding dynamic coefficients. Finite-length solutions for the coefficients are compared to two “short-seal” solutions.

CFD Prediction and Test Results of Stiffness and Damping Coefficients for Brush-Labyrinth Gas Seals

2010 ◽  
Author(s):  
Alexander O. Pugachev ◽  
Martin Deckner
Keyword(s):  
Porous Medium ◽  
Three Dimensional ◽  
Great Influence ◽  
Dynamic Test ◽  
Labyrinth Seal ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
Brush Seal ◽  
Gas Seals ◽  
Stiffness And Damping

This paper presents ongoing investigations on calculation and measurement of rotordynamic coefficients for brush-labyrinth gas seals. The seals are tested on static and dynamic test rigs to measure leakage, pressure distribution, and seal specific forces. To predict seal performance a full three-dimensional eccentric CFD model is considered. Rotordynamic coefficients are calculated using the whirling rotor method. The bristle pack of the brush seal is modeled using the porous medium approach. The prediction results show some deviations in absolute values of stiffness and damping coefficients in comparison with the experimental values, but the trends are similar. Comparing with a staggered labyrinth seal, the brush seal improves rotordynamic characteristics in most cases. Position of the brush seal in sealing configuration has a great influence on the stiffness and damping coefficients, while leakage performance remains relatively unaffected. The capability of the brush seal model based on the porous medium approach to predict rotordynamic coefficients is discussed.

scholarly journals Rotordynamic Coefficients for Stepped Labyrinth Gas Seals

1989 ◽  
Vol 111 (1) ◽  
pp. 101-107 ◽  
Author(s):  
J. K. Scharrer
Keyword(s):  
Pressure Distribution ◽  
Parametric Study ◽  
Separation Of Variables ◽  
Reaction Force ◽  
Zeroth Order ◽  
Small Motion ◽  
First Order ◽  
Rotordynamic Coefficients ◽  
Gas Seals ◽  
Basic Equations

The basic equations are derived for compressible flow in a stepped labyrinth gas seal. The flow is assumed to be completely turbulent in the circumferential direction where the friction factor is determined by the Blasius relation. Linearized zeroth and first-order perturbation equations are developed for small motion about a centered position by an expansion in the eccentricity ratio. The zeroth-order pressure distribution is found by satisfying the leakage equation while the circumferential velocity distribution is determined by satisfying the momentum equations. The first order equations are solved by a separation of variables solution. Integration of the resultant pressure distribution along and around the seal defines the reaction force developed by the seal and the corresponding dynamic coefficients. The results of this analysis are presented in the form of a parametric study, since there are no known experimental data for the rotordynamic coefficients of stepped labyrinth gas seals. The parametric study investigates the relative rotordynamic stability of convergent, straight and divergent stepped labyrinth gas seals. The results show that, generally, the divergent seal is more stable, rotordynamically, than the straight or convergent seals. The results also show that the teeth-on-stator seals are not always more stable, rotordynamically, then the teeth-on-rotor seals as was shown by experiment by Childs and Scharrer (1986b) for a 15 tooth seal.

Static Destabilizing Behavior for Gas Annular Seals at High Eccentricity Ratios

2013 ◽  
Author(s):  
Dara W. Childs ◽  
Stephen P. Arthur
Keyword(s):  
Reaction Force ◽  
Negative Stiffness ◽  
Negative Slope ◽  
Test Fluid ◽  
Test Results ◽  
Force Magnitude ◽  
Piston Seal ◽  
Annular Seal ◽  
Gas Seals ◽  
Annular Seals

The centering force of a plain, annular, liquid seal in a centered position has a pronounced effect on the rotordynamic behavior of pumps due to the Lomakin Effect. In centrifugal injection compressors, the centering force for a hole-pattern-stator/smooth-rotor for a balance-piston seal in a straight-through design or a division-wall seal in a back-to-back design has an impact on the rotordynamic behavior of high-pressure injection compressors. Annular seals for pumps and compressors are designed to operate in a nominally centered position. Previous test results show that the direct (centering) stiffness for liquid seals and hole-pattern-stator seals remain relatively constant out to eccentricity ratios of 0.5. For liquid seals, tests have shown positive centering capability at eccentricity ratios on the order of 0.7. New test results are presented for annular gas seals with smooth and hole-pattern stators, moving from centered to fully eccentric (contact) positions. The test fluid is air. The tests are for non-rotating conditions with a supply pressure up to 70 bars and pressure rations (PRs) of 0.4, 0.5, and 0.6. The exit Mach numbers for the tests are on the order of 0.33, so compressibility effects are not pronounced. Test results are presented for the net reaction force for a smooth seal and a hole-pattern-stator gas annular seal in moving from centered to fully eccentric positions. Comparisons are made between measurements and predictions from a bulk-flow code. The smooth seal creates significantly larger de-centering forces than the HP seal. Its measured de-centering force increases steadily as the stator approaches the wall. The negative slope of the reaction force also increases, indicating a steadily increasing negative stiffness. The de-centering force increased with decreasing PR, increasing ΔP, and is much larger than predicted. The HP seal de-centering reaction force is bi-linear with an approximate constant slope out to ε0 ≅ 0.5, and then a much steeper slope out to wall contact. The model does not predict the bilinear behavior but does a reasonable job of predicting the force magnitude at contact. The de-centering forces measured here have not previously been reported and emphasize the importance of concentric assembly of annular seals in pumps and compressors. Unanticipated eccentricities that create negative stiffness will lead to over prediction of critical speeds and overly optimistic stability calculations.

Rotordynamic Stability Predictions for Centrifugal Compressors Using a Bulk-Flow Model to Predict Impeller Shroud Force and Moment Coefficients

2010 ◽  
Vol 132 (9) ◽  
Author(s):  
Manoj K. Gupta ◽  
Dara W. Childs
Keyword(s):  
Gas Turbines ◽  
Flow Model ◽  
Reaction Force ◽  
Labyrinth Seal ◽  
Bulk Flow ◽  
Hole Injection ◽  
Pump Impeller ◽  
Stability Margins ◽  
Rotordynamic Coefficients ◽  
Model Predictions

An analysis is developed for a compressible bulk-flow model of the leakage path between a centrifugal-compressor impeller’s shroud and its housing along the impeller’s front and back sides. This development is an extension of analyses performed first by Childs (1989, ASME J. Vib. Acoust., Stress, Reliab. Des., 111, pp. 216–225) for pump impellers. The bulk-flow model is used to predict reaction force and moment coefficients for the impeller shroud. A labyrinth seal code developed by Childs and Scharrer ( 1986, ASME Trans. J. Eng. Gas Turbines Power, 108, pp. 325–331) is used to calculate the rotordynamic coefficients developed by the labyrinth seals in the compressor stage and also provides a boundary condition for the shroud calculations. Comparisons between the measured shroud moment coefficients by Yoshida et al. (1996, Proceedings of the 6th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, 2, pp. 151–160) and model predictions show reasonable agreements for the clearance flow and reaction moments. For the conditions considered, low Mach number flow existed in the shroud clearance areas and compressible-flow and incompressible-flow models produced similar predictions. Childs’ model predictions for the direct damping and cross-coupled stiffness coefficients of a pump impeller produced reasonable agreement; hence the present model was validated to the extent possible. A rotor model consisting of an overhung impeller stage supported by a nominally cantilevered rotor was analyzed for stability using the present bulk-flow model and an API standard Wachel–von Nimitz formula model (1981, J. Petrol. Technol., pp. 2252–2260). The bulk-flow model predicted significantly higher onset speeds of instability. Given that some compressors have been predicted to be comfortably stable using API standard Wachel–von Nimitz formula but have been unstable on the test stand, these results suggest that unidentified destabilizing forces and or moments are present in compressors. Seal rub conditions that arise from surge events and increase the seal clearances are simulated, showing that enlarged clearances increase the preswirl at the seals, thus increasing these seal’s destabilizing forces and reducing stability margins. These results are consistent with field experience. Predictions concerning the back shroud indicate that shunt-hole injection mainly acts to enhance stability by changing the flow field of the division wall or balance piston seals, not by influencing the back-shroud’s forces or moments. Effective swirl brakes at these seals also serve this purpose.

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