Coefficients Of Seals Research Articles

Leakage and rotordynamic coefficients of labyrinth-scallop seals

Reducing leakages and improving the rotor-dynamic damping characteristics of annular seals is an essential problem of sealing technology. A whole range of damping seals are used to seal the shafts of turbomachines, such as honeycomb, hole pattern, pocket, and scallop seals. To reduce the cost and production time, the scallop seals are increasingly used. They showed quite good dynamic and leakage characteristics in the modernization of compressors in the chemical industry. Some designs of scallop seals are able not only to increase dynamic performance (additional use of swirl brakes in the form of semi-open scallops at the inlet) but also thanks to the hybrid design of the scallop and labyrinth seal made of PEEK material, which ensures a minimum clearance between the seal and the shaft, reduce leakages of pumped fluid. This paper presents the results of calculating the rotordynamic and flow rate characteristics of scallop and labyrinth-scallop seals depending on the operating parameters using computational fluid dynamics (CFD) methods. The CFD was used to calculate the hydrodynamic and rotordynamic characteristics of the seal with shaft whirl. The rotordynamic coefficients were obtained using the frequency excitation method. The obtained characteristics were compared with experimental data available from the literature for annular and labyrinth seals. The study confirmed the relatively low leakages, the high dynamic characteristics of the labyrinth-scallop seals, and the frequency dependence of the stiffness and damping coefficients. It has been confirmed that sickle-shaped scallops create obstacles to the circumferential flow of the working medium. Reducing the circumferential gas flow increases the hydraulic resistance in the grooves and simultaneously minimizes the circulation forces that create shaft whirl, increasing vibration

Studies on Improving Seals for Enhancing the Vibration and Environmental Safety of Rotary Machines

There is a constant demand for higher equipment parameters, such as the pressure of a sealing medium and shaft rotation speed. However, as the parameters increase, it becomes more difficult to ensure hermetization efficiency. The rotor of a multi-stage machine rotates in non-contact seals. Seals’ parameters have a great influence on vibration characteristics. Non-contact seals are considered to be hydrostatodynamic supports that can effectively dampen rotor oscillations. The force coefficients of gap seals are determined by geometric and operational parameters. A purposeful choice of these parameters can influence the vibration state of the rotor. It is shown for the first time that the initially dynamically flexible rotor, in combination with properly designed seals, can become dynamically rigid. Analytical dependencies for the computation of the dynamic characteristics are obtained. The resulting equations make it possible to calculate the radial-angular vibrations of the rotor of a centrifugal machine in the seals and construct the amplitude–frequency characteristics. By purposefully changing the parameters of non-contact seals, an initially flexible rotor can be made rigid, and its vibration resistance increases. Due to this, the environmental safety of critical pumping equipment increases.

Contribution to the estimation of force coefficients of plain gas seals with high preswirl considering rotor-foundation dynamics

Rotor dynamic force coefficients of gas seals strongly depend on the machine operational conditions. These force coefficients influence the overall dynamical response and modal properties of machines, consequently defining the machine vibration levels. Accurate estimations of the rotor dynamic coefficients are required for designing machines with low vibration amplifications and well-defined stability margins throughout the operational range. Experimental methods applied to test benches are used to validate such force coefficients and they normally rely on (i) the quality of the measurements and (ii) the assumption that the mathematical model is able to capture the whole system dynamics. If relevant dynamical contributions in a system are neglected by the mathematical model, the contribution will erroneously be concluded to originate from the seal being tested. The theoretical and experimental investigation in this paper focuses on quantifying and qualifying the effect of neglected system dynamics modelling on the estimation of seals force coefficients and stability margins. The in-situ identification of seal forces shows that the direct stiffness, cross-coupling stiffness, and direct damping coefficient estimations for a gas seal with high preswirl are statistically significantly affected by the baseline model. Nevertheless, the baseline model leads to small deviations of the seal force coefficient estimations. The prediction accuracy of stability margins is found to be more influenced by the baseline model describing the system dynamics than by the deviations between the seal force coefficient estimations.

The Effect of Inflow Distortion on the Rotordynamic Characteristics of a 1400-MW Reactor Coolant Pump Annular Seal

The annular seal between stator and rotor substantively acts as a bearing that affects the rotordynamic characteristic of the turbomachinery rotor system. The rotor wake turbulence in a canned motor Reactor Coolant Pump (RCP) will lead to inflow pressure distortion at the annular seal entrance, thus further affecting the seal rotordynamic characteristics and threatening the stable operation of RCP. In order to obtain the seal rotordynamic coefficients, a transient numerical method applies the mesh deformation technique to simulate the multiple-frequency elliptical rotor whirling orbit model. The transient solutions were proposed to solve the unsteady reaction forces of annular seals at five excitation frequencies for each case. The inflow pressure distortion patterns were simplified as harmonic functions, including two important influence parameters that are impeller blades number m and pressure fluctuation ratio λ. The numerical results showed that with nonuniform time-averaged pressure distribution at the entrance of the annular seal in Case 2, the inflow distortion significantly affects the seal rotordynamic coefficients, while the rotational spinning speed in Case 3 can weaken the time-averaged nonuniformity and accordingly make a dent in the influence. Increasing impeller blades number m and pressure fluctuation λ both result in a sharp diminution of the negative stiffness Keff, as well as an obvious increase in the effective damping Ceff, which will strengthen rotor misalignment and system stability. In addition, the larger impeller blades number m and higher pressure fluctuation λ will make the effective damping Ceff more independent of the whirling frequency. These results provide theoretical guidance for the operation safety of RCP.

A Nonhomogeneous Bulk Flow Model for Gas in Liquid Flow Annular Seals: An Effort to Produce Engineering Results

Abstract Seals in multiple-phase rotordynamic pumps must operate without compromising system efficiency and stability. Both field operation and laboratory experiments show that seals supplied with a gas in liquid mixture (bubbly flow) can produce rotordynamic instability and excessive rotor vibrations. This paper advances a nonhomogeneous bulk flow model (NHBFM) for the prediction of the leakage and dynamic force coefficients of uniform clearance annular seals lubricated with gas in liquid mixtures. Compared to a homogeneous bulk flow model (HBFM), the current model includes diffusion coefficients in the momentum transport equations and a field equation for the transport of the gas volume fraction (GVF). Published experimental leakage and dynamic force coefficients for two seals supplied with an air in oil mixture whose GVF varies from 0% (pure liquid) to 20% serve to validate the novel model as well as to benchmark it against predictions from a HBFM. The first seal withstands a large pressure drop (∼38 bar) and the shaft speed equals 7.5 krpm. The second seal restricts a small pressure drop (1.6 bar) as the shaft turns at 3.5 krpm. The first seal is typical as a balance piston whereas the second seal is found as a neck-ring seal in an impeller. For the high pressure seal and inlet GVF = 0.1, the flow is mostly homogeneous as the maximum diffusion velocity at the seal exit plane is just ∼0.1% of the liquid flow velocity. Thus, both the NHBFM and HBFM predict similar flow fields, leakage (mass flow rate), and drag torque. The difference between the predicted leakage and measurement is less than 5%. The NHBFM direct stiffness (K) agrees with the experimental results and reduces faster with inlet GVF than the HBFM K. Both direct damping (C) and cross-coupled stiffness (k) increase with inlet GVF < 0.1. Compared to the test data, the two models generally under predict C and k by ∼25%. Both models deliver a whirl frequency ratio (fw) ∼ 0.3 for the pure liquid seal, hence closely matching the test data. fw raises to ∼0.35 as the GVF approaches 0.1. For the low-pressure seal, the flow is laminar; the experimental results and both NHBFM and HBFM predict a null direct stiffness (K). At an inlet GVF = 0.2, the NHBFM predicted added mass (M) is ∼30% below the experimental result while the HBFM predicts a null M. C and k predicted by both models are within the uncertainty of the experimental results. For operation with either a pure liquid or a mixture (GVF = 0.2), both models deliver fw = 0.5 and equal to the experimental finding. The comparisons of predictions against experimental data demonstrate that the NHBFM offers a marked improvement, in particular for the direct stiffness (K). The predictions reveal that the fluid flow maintains the homogeneous character known at the inlet condition.

An Analytical Two-Phase Flow Model for Prediction of Leakage in Wet Gas Labyrinth Seals and Pocket Damper Seals. Is Simplicity Still Desired?

Abstract Current and upcoming two-phase pump and compression systems in subsea production facilities must demonstrate long-term operation and continuous availability. Annular pressure seals, limiting secondary flow, also influence the dynamic stability of turbomachinery. Hence, it becomes paramount to quantify the leakage and dynamic force coefficients of annular seals operating with two-phase flow, a liquid in gas mixture or wet gas. Until now, a simple model for labyrinth seals (LSs) and the more modern pocket damper seals (PDSs) is not available, though these seal types find wide applications in subsea machinery. The paper develops a simple analytical model predicting the leakage and cavity pressures for LSs and PDSs operating with two-phase flow. The model adapts Neumann’s leakage equation for use with the physical properties of a homogeneous two-phase flow mixture. Predictions of leakage for a four-blade, eight-pocket, fully partitioned PDS operating under a low supply pressure (PS = 2.3 bar and 3.2 bar) and a low rotor speed equal to 5250 rpm (surface speed = 35 m/s) agree well with experimental results procured for both a pure gas and a wet gas conditions (2.2% in liquid volume). Predicted leakage and cavity pressures also agree with those found by a multimillion node computational fluid dynamics (CFD) model. For an eight-blade, sixteen-pocket PDS supplied with air at PS = 62.1 bar, discharge pressure Pa = 31.1 bar, and rotor speed of 15 krpm (surface speed = 91 m/s), the analytical model predicts leakage that is just 2% larger than a published CFD prediction. For the PDS supplied with an oil in gas mixture having gas volume fraction βS = 0.92–0.98, the simple model delivers leakage that is up to ∼6% lower than published CFD results. An analysis of the two-phase leakage predictions via a modified flow factor reveals a loss coefficient (cd) impervious to the range of supply and discharge pressures considered and growing in proportion to the liquid volume fraction (LVF). Throughout the life of an oil well that sees radical changes in gas and liquid composition as well as pressure conditions, the expedient model, quick and accurate to estimate leakage in wet gases seals, can be readily integrated into an engineering routine or practice.

Orbit Decomposition Method for Rotordynamic Coefficients Identification of Annular Seals

The elliptical orbit whirl model is widely used to identify the frequency-dependent rotordynamic coefficients of annular seals. The existing solution technique of an elliptical orbit whirl model is the transient computational fluid dynamics (CFD) method. Its computational time is very long. For rapid computation, this paper proposes the orbit decomposition method. The elliptical whirl orbit is decomposed into the forward and backward circular whirl orbits. Under small perturbation circumstances, the fluid-induced forces of the elliptical orbit model can be obtained by the linear superposition of the fluid-induced forces arising from the two decomposed circular orbit models. Due to that the fluid-induced forces of circular orbit, the model can be calculated with the steady CFD method, and the transient computations can be replaced with steady ones when calculating the elliptical orbit whirl model. The computational time is significantly reduced. To validate the present method, its rotordynamic results are compared with those of the transient CFD method and experimental data. Comparisons show that the present method can accurately calculate the rotordynamic coefficients. Elliptical orbit parameter analysis reveals that the present method is valid when the whirl amplitude is less than 20% of seal clearance. The effect of ellipticity on rotordynamic coefficients can be ignored.

Test Results for the Static and Rotordynamic Characteristics of a Long (L/D = 0.75) Smooth Seal in Two-Phase (Mainly Gas) Conditions With a 62-Bar Inlet Pressure

Abstract Recent multiphase-pump developments encountered several rotordynamic issues with smooth balance-piston seals, creating a need to better understand the performance of annular seals under multiphase-flow operation. This paper presents measurements of static and dynamic characteristics of a long smooth seal (L/D = 0.75, D = 114.686 mm, and Cr = 0.200 mm) operating under pure- and mainly air condition in which air is mixed with silicone oil (PSF-5cSt). Tests are performed at a supply pressure of 62.1 bars-g, three rotation speeds (5, 10, and 15 krpm), three pressure ratios (PRs) (0.6, 0.5, 0.4), for a range of inlet liquid volume fraction (LVFi) from 0% to 8%. The results are then compared to: (1) the previous test reported by Zhang et al. (2017, “Experimental Study of the Static and Dynamic Characteristics of a Long Smooth Seal with Two-Phase, Mainly-air Mixtures,” ASME J. Eng. Gas Turbines Power, 139(12), p. 122504) with similar testing condition but a different seal geometry (L/D = 0.65, D = 89.306 mm, and Cr = 0.188 mm) and (2) the predictions from a bulk-flow model developed by San Andrés (2012, “Rotordynamic Force Coefficients of Bubbly Mixture Annular Pressure Seals,” ASME J. Eng. Gas Turbines Power, 134(2), p. 022503). Results show a significant increase of direct dynamic stiffness KΩ as LVFi increases, especially at low PR. Test results reported by Zhang et al. (2017, “Experimental Study of the Static and Dynamic Characteristics of a Long Smooth Seal with Two-Phase, Mainly-air Mixtures,” ASME J. Eng. Gas Turbines Power, 139(12), p. 122504) has an opposite tendency of KΩ as an impact of increasing LVFi values. Concerning cross-coupled dynamic stiffness kΩ and cross-coupled damping c, the results from Zhang et al. (2017) and the present results agree to the effects of changing speed, PR, and LVFi under pure- and mainly air conditions. As LVFi increases, direct damping C increases while test results reported by Zhang et al. (2017, “Experimental Study of the Static and Dynamic Characteristics of a Long Smooth Seal with Two-Phase, Mainly-air Mixtures,” ASME J. Eng. Gas Turbines Power, 139(12), p. 122504) showed no significant increase. A steady-state computational fluid dynamics (CFD) result for a testing case suggests a significant difference happening inside the two seals (present seal and Zhang et al.'s (2017, “Experimental Study of the Static and Dynamic Characteristics of a Long Smooth Seal with Two-Phase, Mainly-air Mixtures,” ASME J. Eng. Gas Turbines Power, 139(12), p. 122504) seal). A full investigation in CFD is needed. Except for the direct dynamic stiffness and the impact of changing LVFi on the cross-coupled dynamic stiffness, the bulk-flow model of San Andrés (2012, “Rotordynamic Force Coefficients of Bubbly Mixture Annular Pressure Seals,” ASME J. Eng. Gas Turbines Power, 134(2), p. 022503) predicts decently the tendencies and magnitudes of the rotordynamic coefficients.

Effects of tooth bending damage on the leakage performance and rotordynamic coefficients of labyrinth seals

Tooth bending damage resulting from an intense impact by the rotor sometimes occurs in the transient operation. To investigate the influence of after-damage clearance and tooth bending length on the leakage performance and rotordynamic coefficients of labyrinth seals, three tooth bending damages were taken into consideration, including the unbent tooth damage (abbreviated as Unbent), the partial tooth bending damage (abbreviated as Pbent) and the complete tooth bending damage (abbreviated as Cbent). The transient CFD solution was utilized to calculate the leakage flow rates and rotordynamic coefficients of labyrinth seals with clearances of 0.3, 0.4, 0.5, 0.6 mm for three tooth bending damages. The obtained result shows that the Unbent tooth damage leaks least while the Pbent tooth bending damage leaks most, and an increase of 6.1% for Cbent tooth bending damage and an increase of 19.4% for Pbent tooth bending damage are discovered at the tooth clearance of 0.6 mm in comparison with the Unbent tooth damage. Compared to the Unbent tooth damage, the effective damping for Pbent tooth bending damage and Cbent tooth bending damage is lower and drops by 9.7%–33.6% and 8.5%–22.6% respectively at the tooth clearance of 0.6 mm, suggesting that Pbent tooth bending damage or Cbent tooth bending damage tends to weaken the seal stability when compared to the Unbent tooth damage.

Impact of damper seal coefficients uncertainties in rotor dynamics

Damper seals might have a great impact on rotordynamics, but the values of their coefficients are difficult to be determined and have a significant uncertainty. In the present paper, a probabilistic model is proposed to model damper seal coefficients, which are frequency dependent. A stochastic process (frequency indexed) is constructed such that modeling errors are taken into account. The impact of these uncertainties on the rotordynamic behavior of a compressor is analyzed. The deterministic seal coefficients are determined considering a bulk-flow model, and values are calculated by a compressor manufacturer based on experimental data. The results obtained show that uncertainties in these coefficients have a considerable impact on the compressor Campbell diagram, stability, and unbalance response.

Experimental Study of the Leakage and Rotordynamic Coefficients of a Long-Smooth Seal With Two-Phase, Mainly Oil Mixtures

This paper experimentally studies the leakage and rotordynamic performance of a long-smooth seal with air–oil mixtures. Tests are performed with inlet gas-volume-fraction gas volume fraction (GVF) = 0%, 2%, 4%, 6%, and 10%, rotor speed ω = 5, 7.5, 10, and 15 krpm, inlet temperature Ti = 39.4 °C, exit pressure Pe = 6.9 bars, and pressure drop (PD) = 31, 37.9, and 48.3 bars. Test results show that adding air into the oil flow does not change the seal's mass flow leakage m˙ discernibly but significantly impacts the seal's rotordynamic characteristics. For all PDs and speeds, K increases as inlet GVF increases from zero to 10% except for 6% ≤ inlet GVF ≤ 10% when PD = 48.3 bars, where K decreases as inlet GVF increases. The K increment will increase a pump rotor's natural frequency and critical speed. Increasing the rotor's natural frequency would also increase the onset speed of instability (OSI) and improve the stability of the rotor. Adding air into the oil flow has little impact on cross-coupled stiffness k, direct damping C, and effective damping Ceff. Ceff = C − k/ω + mqω, where mq is the cross-coupled virtual-mass. Test results are compared to predictions from San Andrés's (San Andrés, 2011, “Rotordynamic Force Coefficients of Bubbly Mixture Annular Pressure Seals,” ASME J. Eng. Gas Turbines Power, 134(2), p. 022503.) bulk-flow model, which assumes that the liquid–gas mixture is isothermal and homogenous. The model reasonably predicts m˙, C, and Ceff. All predicted K values are positive, while measured K values are negative for some test cases. Predicted k values are close to measurements when ω = 5 krpm and are larger than measurements when 7.5 ≤ ω ≤ 15 krpm.

Experimental Investigation on Rotordynamic Characteristics and Rotor System Stability of a Novel Negative Dislocated Seal

Air‐induced force generated in seals is one key factor on the stability of the rotor system. In this paper, a novel negative dislocated seal (NDS) was developed in respect of dislocated bearing theory, to reduce hydrodynamic pressure effect and air‐induced force and improve rotor stability as well. A test rig was built to test rotordynamic characteristics and rotor stability of the NDS. The rotordynamic characteristics of seals were investigated based on the unbalanced synchronous excitation method, and seal‐rotor system stability was evaluated by the identification method with an electromagnetic bearing exciter. The effects of both rotating speed and inlet/outlet pressure ratio on the rotordynamic characteristics and rotor stability of both NDS and conventional cylindrical labyrinth seal were experimentally investigated. The results show that with the increasing rotating speed, inlet/outlet pressure ratio is promising to reduce the direct stiffness coefficients of seals and the logarithmic decrement rate of seal‐rotor system and enhance both cross stiffness and damping coefficient as well. Besides, the developed NDS effectively reduces cross‐stiffness coefficients and increases direct damping coefficients and the logarithmic decrement rate of the seal‐rotor system, relative to the conventional cylindrical seal. The proposed seal can effectively improve seal stability of turbomachinery.

Clearance Effects on Rotordynamic Performance of a Long Smooth Seal With Two-Phase, Mainly-Air Mixtures

This paper experimentally studies the effects of changing radial clearance Cr on the performance of a long (length-to-diameter ratio L/D = 0.65) smooth seal under mainly-air (wet-gas) conditions. The test fluid is a mixture of air and silicone oil. Tests are conducted with Cr = 0.188, 0.163, and 0.140 mm, inlet pressure Pi = 62.1 bars, exit pressure Pe = 31 bars, inlet liquid volume fraction LVF = 0%, 2%, 5%, and 8%, and shaft speed ω = 10, 15, and 20 krpm. The seal's complex dynamic stiffness coefficients Hij are measured. The real parts of Hij cannot be fitted by frequency-independent stiffness and virtual-mass coefficients. Therefore, frequency-dependent direct KΩ and cross-coupled kΩ stiffness coefficients are used. The imaginary parts of direct Hij produce frequency-independent direct damping C. Test results show that, for all pure- and mainly-air conditions, decreasing Cr decreases (as expected) the leakage mass flow rate m˙. Under mainly-air conditions, decreasing Cr decreases KΩ. This outcome is contrary to the test results at pure-air conditions, where KΩ increases as Cr decreases. Since an unstable centrifugal compressor rotor may precess at approximately 0.5ω, the effective damping Ceff at about 0.5ω is used as an indicator of the impact a seal would have on its associated compressor. For pure-air conditions, when Ω ≈ 0.5ω, decreasing Cr increases Ceff and makes the seal more stabilizing. This trend continues after the oil is added. A bulk-flow model developed by San Andrés (2011, “Rotordynamic Force Coefficients of Bubbly Mixture Annular Pressure Seals,” ASME J. Eng. Gas Turbines Power, 134(2), p. 022503) produces predictions to compare with test results. m˙ predictions correlate with measurements. Under pure-air conditions, the model correctly predicts the effects of changing Cr on KΩ and the Ceff value near 0.5ω. After the oil is added, as Cr decreases, predicted KΩ increases while measured KΩ decreases. Also, for mainly-air cases and Ω ≈ 0.5ω, decreasing Cr does not discernibly change predicted Ceff but increases the measured value.

Dynamic analysis of a planar multi-stage centrifugal pump rotor system based on a novel coupled model

The coupled rotor-dynamics issue is always one of the most important and difficult research for multi-stage pump system due to the complexity of multiple fluid-induced forces and multi-degree of freedom rotor model. In this paper, the Reynolds equation of journal bearing is solved by the finite difference method and corresponding fluid-induced force is obtained by small parameter method. In addition, the dynamic coefficients of annular seal are calculated according to bulk-flow model and perturbation method. Furthermore, a novel rotor system model fully considering the coupled effects of bearing and seal is proposed by matrix manipulation method. Then the coupled rotor-dynamics for multi-stage pump system is investigated subsequently based on the novel model. Finally, the Lomakin effect of annular seal is studied in detail. The calculated results indicate that the fluid-induced force of seal exerting on the rotor system should not be ignored in the calculation of coupled dynamic characteristics. Smaller length and clearance of annular seal are good for the stability of coupled rotor system. Compared with asymmetric structure, the symmetric sealing structure has a larger stability margin on condition of ‘rigid rotor’ status. Moreover, the Lomakin effect on stability presents linear superposition property. The proposed method can provide valuable reference for the design and modeling of multi-dimensional matrix system.

Experimental and Theoretical Rotordynamic Coefficients of Smooth and Round-Hole Pattern Water-Fed Annular Seals

This work presents the comparison between experimental and theoretical results obtained for three straight annular seals. One of the annular seals has smooth rotor and stator while the others have a textured stator; the textures are equally spaced shallow round holes, with two different depths. The experimental results were obtained on a test rig dedicated to the identification of the dynamic coefficients of high Reynolds bearings and annular seals. The test rig uses hot water (<50 °C) as a working fluid. Dynamic excitations imposed by piezoelectric shakers to the rotor enable the identification of dynamic coefficients via complex impedances. Theoretical results compared with experimental findings were obtained by numerically solving the “bulk flow” equations (film thickness averaged equations dominated by inertia effects). The numerical model was extensively validated for smooth annular seals but is less confident for textured surfaces. The present comparisons between experimental and numerical results enable to estimate the accuracy of the numerical model employed for the textured seals.

Dynamic analysis of liquid annular seals with herringbone grooves on the rotor based on the perturbation method.

Annular seals have significant effects on the hydraulic and rotordynamic performances of turbomachinery. In this paper, an analysis method for calculating the leakage flow rates and dynamic characteristics of liquid annular seals with herringbone grooves on the rotor is proposed and verified. Leakage flow rates and dynamic characteristics of the model seals under different operating conditions are theoretically analysed and compared with those of plain and spiral-grooved seals of the same size. In addition, the influence of geometric parameters such as spiral angle and the lengths of the constituent parts on the sealing and rotordynamic coefficients of seals with herringbone grooves are also discussed. The results show that seals with herringbone grooves have better sealing performance, while providing better support actions and damping characteristics than the other two seal types under the same operating conditions. The seal geometric parameters including spiral angle, the lengths of the constituent parts and the clearance value have a significant influence on the dynamic characteristics of seals with herringbone grooves.

Design of Active Magnetic Bearing Controllers for Rotors Subjected to Gas Seal Forces

Proper design of feedback controllers is crucial for ensuring high performance of active magnetic bearing (AMB) supported rotor dynamic systems. Annular seals in those systems can contribute significant forces, which, in many cases, are hard to model in advance due to complex geometries of the seal and multiphase fluids. Hence, it can be challenging to design AMB controllers that will guarantee robust performance for these kinds of systems. This paper demonstrates the design, simulation, and experimental results of model-based controllers for AMB systems, subjected to dynamic seal forces. The controllers are found using H∞ and μ synthesis and are based on a global rotor dynamic model in which the seal coefficients are identified in situ. The controllers are implemented in a rotor-dynamic test facility with two radial AMBs and one annular seal with an adjustable inlet pressure. The seal is a smooth annular type, with large clearance (worn seal) and with high preswirl, which generates significant cross-coupled forces. The H∞ controller is designed to compensate for the seal forces and the μ controller is furthermore designed to be robust against a range of pressures across the seal. In this study, the rotor is nonrotating. Experimental and simulation results show that significant performance can be achieved using the model-based controllers compared to a reference decentralized proportional-integral-derivative (PID) controller and robustness against large variations of pressure across the seal can be improved by the use of robust synthesized controllers.

On-Site Identification of Dynamic Annular Seal Forces in Turbo Machinery Using Active Magnetic Bearings: An Experimental Investigation

Significant dynamic forces can be generated by annular seals in rotordynamics and can under certain conditions destabilize the system leading to a machine failure. Mathematical modeling of dynamic seal forces are still challenging, especially for multiphase fluids and for seals with complex geometries. This results in much uncertainty in the estimation of the dynamic seal forces, which often leads to unexpected system behavior. This paper presents the results of a method suitable for on-site identification of uncertain dynamic annular seal forces in rotordynamic systems supported by active magnetic bearings (AMB). An excitation current is applied through the AMBs to obtain perturbation forces and a system response, from which the seal coefficients are extracted by utilizing optimization and a priori information about the mathematical model structure and its known system dynamics. As a study case, the method is applied to a full-scale test facility supported by two radial AMBs interacting with one annular center-mounted test seal. Specifically, the dynamic behavior of a smooth annular seal with high preswirl and large clearance (worn seal) is investigated in this study for different excitation frequencies and differential pressures across the seal. The seal coefficients are extracted and a global model on reduced state-space modal form is obtained using the identification process. The global model can be used to update the model-based controller to improve the performance of the overall system. This could potentially be implemented in all rotordynamic systems supported by AMBs and subjected to seal forces or other fluid film forces.

Design and Analysis of CFD Experiments for the Development of Bulk-Flow Model for Staggered Labyrinth Seal

Nowadays, bulk-flow models are the most time-efficient approaches to estimate the rotor dynamic coefficients of labyrinth seals. Dealing with the one-control volume bulk-flow model developed by Iwatsubo and improved by Childs, the “leakage correlation” allows the leakage mass-flow rate to be estimated, which directly affects the calculation of the rotor dynamic coefficients. This paper aims at filling the lack of the numerical modelling for staggered labyrinth seals: a one-control volume bulk-flow model has been developed and, furthermore, a new leakage correlation has been defined using CFD analysis. Design and analysis of computer experiments have been performed to investigate the leakage mass-flow rate, static pressure, circumferential velocity, and temperature distribution along the seal cavities. Four design factors have been chosen, which are the geometry, pressure drop, inlet preswirl, and rotor peripheral speed. Finally, dynamic forces, estimated by the bulk-flow model, are compared with experimental measurements available in the literature.

On the Thermodynamic Process in the Bulk-Flow Model for the Estimation of the Dynamic Coefficients of Labyrinth Seals

The impact of sealing equipment on the stability of turbomachineries is a crucial topic because the power generation market is continuously requiring high rotational speed and high performance, leading to the clearance reduction in the seals. The accurate characterization of the rotordynamic coefficients generated by the seals is pivotal to mitigate instability issues. In the paper, the authors propose an improvement of the state-of-the-art one-control volume (1CV) bulk-flow model (Childs and Scharrer, 1986, “An Iwatsubo-Based Solution for Labyrinth Seals: Comparison to Experimental Results,” ASME J. Eng. Gas Turbines Power, 108(2), pp. 325–331) by considering the energy equation in the steady-state problem. Thus, real gas properties can be evaluated in a more accurate way because the enthalpy variation, expected through the seal cavities, is evaluated in the model. The authors assume that the enthalpy is not a function of the clearance perturbation; therefore, the energy equation is considered only in the steady-state problem. The results of experimental tests of a 14 teeth-on-stator (TOS) labyrinth seal, performed in the high-pressure seal test rig owned by GE Oil&Gas, are presented in the paper. Positive and negative preswirl ratios are used in the experimental tests to investigate the effect of the preswirl on the rotordynamic coefficients. Overall, by considering the energy equation, a better numerical estimation of the rotordynamic coefficients for the tests with the negative preswirl ratio has been obtained (as it results from the comparison with the experiments). Finally, the numerical results are compared with a reference bulk-flow model proposed by Thorat and Childs (2010, “Predicted Rotordynamic Behavior of a Labyrinth Seal as Rotor Surface Speed Approaches Mach 1,” ASME J. Eng. Gas Turbines Power, 132(11), p. 112504), highlighting the improvement obtained.