Fully Partitioned Pocket Damper Seal Research Articles

Leakage and Rotordynamic Characteristics for Three Types of Annular Gas Seals Operating in Supercritical CO2 Turbomachinery

Abstract The balance piston seal in multiple-stage centrifugal compressors and axial turbines sustains the largest pressure drop through the machines and therefore plays an important role in successful full load operation at high rotational speed. This is especially true for power dense turbomachines in supercritical CO2 power cycles that generate or expend higher fluid pressures (above the critical value 7.3 MPa) and density (close to water 1000 kg/m3), because the fluid forces generated by the balance piston seals are directly proportional to the fluid density and the pressure drop across the seal. This paper presents a comprehensive assessment and comparison on the leakage and rotordynamic performance of three types of annular gas seals for application in a 14 MW supercritical CO2 turbine. These three seals represent the main seal types used in high-speed rotating machines at the balance piston location in efforts to limit internal leakage flow and achieve rotordynamic stability, including a labyrinth seal (LABY), a fully partitioned pocket damper seal (FPDS), and a hole-pattern damper seal (HPS). These three seals were designed to have the same sealing clearance and similar axial lengths. To enhance the seal net damping capability at high inlet preswirl condition, a straight swirl brake was also designed and employed at seal entrance for each type seal to reduce the seal inlet preswirl velocity. Numerical results of leakage flow rates, rotordynamic force coefficients, cavity dynamic pressure, and swirl velocity developments were analyzed and compared for three seal designs at high positive inlet preswirl (in the direction of shaft rotation), using a proposed transient computational fluid dynamic (CFD)-based perturbation method based on the multiple-frequency elliptical-orbit rotor whirling model and the mesh deformation technique. To take into account of real gas effect with high accuracy, a table look-up procedure based on the National Institute of Standards and Technology reference fluid properties database was implemented, using an in-house code, for the fluid properties of CO2 in both supercritical and subcritical conditions. Results show that the inlet swirl brake can significantly reduce the preswirl velocity at seal entrance, lowering the effective damping crossover frequency fco (or even fco = 0) to maximize the full operational frequency range of the machines. In stability analysis phase of a MW-scale supercritical CO2 turbine/compressor, the seal stiffness effects on the rotor mode shape must be evaluated carefully, where the seal stiffness is sufficiently large (comparable to the bearing stiffness). From a rotordynamic viewpoint, the HPS seal with entrance swirl brake is a better seal concept for the balance piston seal in supercritical CO2 turbomachinery, which possesses the largest positive effective damping throughout the entire subsynchronous frequency range.

Impact Analysis of Pocket Damper Seal Geometry Variations on Leakage Performance and Rotordynamic Force Coefficients Using Computational Fluid Dynamics

In this paper, different notch and partition wall arrangements of a fully partitioned pocket damper seal (FPDS) are investigated using computational fluid dynamics (CFD). The CFD model is derived for a baseline FPDS design reflecting the full sealing configuration with a structured mesh. Steady-state simulations are performed for eccentric rotor position and different operational parameters. The results are validated using experimental cavity pressure measurements. In transient computations, rotor whirl is modeled as a circular motion around an initial eccentricity using a moving mesh technique. Different whirl frequencies are computed to account for the frequency-dependent behavior of damper seals. The stiffness and damping coefficients are evaluated from the impedances in the frequency domain using a fast Fourier transform. The validated model is then transferred to varying designs. In addition to the baseline design, six different notch arrangements with constant clearance ratio were modeled. Moreover, two partition wall design variations were studied based on manufacturability considerations. Predicted leakage as well as frequency-dependent stiffness and damping coefficients are presented and the impact of geometry variations on these parameters is discussed. The results suggest that a single centered notch is favorable and indicate considerably higher effective damping for a design with staggered partition walls. A rounded partition wall design with significantly eased manufacturing reveals good performance.

Numerical Investigation on the Leakage and Rotordynamic Characteristics for Three Types of Annular Gas Seals in Wet Gas Conditions

The modern compressor operation is challenged by the liquid presence in wet gas operating conditions. The liquid phase may affect the compressor stability by partially flooding the internal annular gas seals and inducing subsynchronous vibration (SSV). To improve the annular seal behavior and increase the rotor stability, high-precision results of leakage flow rates and rotordynamic force coefficients are needed for annular gas seals in wet gas conditions. In order to better understand the leakage and rotordynamic characteristics of the annular gas seal in wet gas conditions, a 3D transient CFD-based perturbation method was proposed for computations of leakage flow rates and rotordynamic force coefficients of annular gas seals with liquid phase in main gas phase, based on inhomogeneous Eulerian-Eulerian multiphase flow model, mesh deformation technique, and the multifrequency rotor whirling orbit model. Numerical results of frequency-dependent rotordynamic force coefficients and leakage flow rates were presented and compared for three types of noncontact annular gas seals, which include a smooth plain annular seal (SPAS), a labyrinth (LABY) seal, and a fully partitioned pocket damper seal (FPDS). These three seals were designed to have the identical rotor diameter, sealing clearance, and axial length. The accuracy and the availability of the present transient CFD numerical method were demonstrated with the experiment data of leakage flow rates and frequency-dependent rotordynamic force coefficients of the smooth plain seal with four inlet liquid volume fractions (LVFs) of 0%, 2%, 5%, and 8%. Steady and transient numerical simulations were conducted at inlet air pressure of 62.1 bar, pressure ratio of 0.5, rotational speed of 15,000 rpm, and inlet preswirl ratio of 0.3 for four inlet LVFs varying from 0% to 8% and 14 subsynchronous and synchronous whirling frequencies up to 280 Hz. The numerical results show that the inlet liquid phase has a significant influence on the leakage and rotordynamic coefficients for all three types of annular gas seals. The mixture leakage flow rate increases with the increasing inlet LVF, combining the decreasing gas-phase and linearly increasing liquid-phase leakage flow rates. The smooth plain seal leaks the most gas phase and liquid phase, followed by the pocket damper seal (PDS) and then the labyrinth seal. Increasing inlet LVF significantly decreases the direct stiffness and slightly increases the effective damping of the smooth plain seal. The labyrinth seal possesses evident negative direct stiffness and shows a noticeable decreasing effective damping with the increasing inlet LVF at the subsynchronous frequency range. Increasing inlet LVF obviously increases all the force coefficients of the pocket damper seal including the positive effective damping. From a rotordynamic viewpoint, the FPDS possesses a better liquid tolerant capability and so is a better sealing scheme for the balance piston seals and center seals of the centrifugal compressor in wet gas operating condition.

Numerical Investigation on the Leakage and Static Stability Characteristics of Pocket Damper Seals at High Eccentricity Ratios

Annular gas seals for compressors and turbines are designed to operate in a nominally centered position in which the rotor and stator are at concentric condition, but due to the rotor–stator misalignment or flexible rotor deflection, many seals usually are suffering from high eccentricity. The centering force (represented by static stiffness) of an annular gas seal at eccentricity plays a pronounced effect on the rotordynamic and static stability behavior of rotating machines. The paper deals with the leakage and static stability behavior of a fully partitioned pocket damper seal (FPDS) at high eccentricity ratios. The present work introduces a novel mesh generation method for the full 360 deg mesh of annular gas seals with eccentric rotor, based on the mesh deformation technique. The leakage flow rates, static fluid-induced response forces, and static stiffness coefficients were solved for the FPDS at high eccentricity ratios, using the steady Reynolds-averaged Navier–Stokes solution approach. The calculations were performed at typical operating conditions including seven rotor eccentricity ratios up to 0.9 for four rotational speeds (0 rpm, 7000 rpm, 11,000 rpm, and 15,000 rpm) including the nonrotating condition, three pressure ratios (0.17, 0.35, and 0.50) including the choked exit flow condition, two inlet preswirl velocities (0 m/s, 60 m/s). The numerical method was validated by comparisons to the experiment data of static stiffness coefficients at choked exit flow conditions. The static direct and cross-coupling stiffness coefficients are in reasonable agreement with the experiment data. An interesting observation stemming from these numerical results is that the FPDS has a positive direct stiffness as long as it operates at subsonic exit flow conditions; no matter the eccentricity ratio and rotational speed are high or low. For the choked exit condition, the FPDS shows negative direct stiffness at low eccentricity ratio and then crosses over to positive value at the crossover eccentricity ratio (0.5–0.7) following a trend indicative of a parabola. Therefore, the negative static direct stiffness is limited to the specific operating conditions: choked exit flow condition and low eccentricity ratio less than the crossover eccentricity ratio, where the pocket damper seal (PDS) would be statically unstable.

Numerical Comparison of Rotordynamic Characteristics for a Fully Partitioned Pocket Damper Seal and a Labyrinth Seal With High Positive and Negative Inlet Preswirl

Pocket damper seals (PDSs) are used as replacements for labyrinth seals in high-pressure centrifugal compressors at the balance-piston location or center seal location to enhance rotordynamic stability. A concern exists that this enhanced stability will be lost at high positive inlet preswirl. Numerical results of frequency-dependent rotordynamic force coefficients and leakage flow rates were presented and compared for a fully partitioned PDS (FPDS) and a labyrinth seal at high positive and negative inlet preswirl, using a proposed transient computational fluid dynamics (CFD) method based on the multifrequency elliptical orbit whirling model. The negative preswirl indicates a fluid swirl in a direction opposite to rotor rotation at seal inlet. Both seals have identical diameter and sealing clearance. The full 3D concentric CFD model and mesh were built for the labyrinth seal and FPDS, respectively. The accuracy and availability of the present transient CFD numerical method were demonstrated with the experiment data of frequency-dependent rotordynamic coefficients of the labyrinth seal and FPDS at zero and high positive preswirl conditions. The numerical boundary conditions include two high positive preswirl, two high negative preswirl, and a zero preswirl. Numerical results show that the effect of inlet preswirl on the direct force coefficients is weak, but the effect on the cross-coupling stiffness and effective damping is dramatic. Both seals possess negative effective damping at lower excitation frequencies due to positive preswirl, and the crossover frequency of effective damping term increases with increasing positive preswirl. Negative preswirl produces negative cross-coupling stiffness and positive effective damping over the whole excitation frequency range. Increasing negative preswirl is a stabilizing factor for annular gas seals, which results in a significant increase in the effective damping and a decrease in the crossover frequency. It is desirable to reduce the inlet preswirl to zero or even negative through applications of negative-swirl brakes and negative injection devices.

Comparisons of Rotordynamic Characteristics Predictions for Annular Gas Seals Using the Transient Computational Fluid Dynamic Method Based on Different Single-Frequency and Multifrequency Rotor Whirling Models

The three-dimensional (3D) transient computational fluid dynamic (CFD) method was proposed to predict rotordynamic coefficients for annular gas seals. This transient CFD method uses unsteady Reynolds-Averaged Navier–Stokes (RANS) solution technique and mesh deformation theory, which requires a rotor whirling model as the rotor excitation signal to solve the transient leakage flow field in seal and obtain the transient fluid response forces on the rotor surface. A fully partitioned pocket damper seal (FPDS) was taken as the test object to validate the present numerical method. Comparisons were made between experimental data and rotordynamic coefficient predictions using the three variations of the single-frequency and multiple-frequency rotor whirling models: (1) one-dimensional whirling model, (2) circular orbit whirling model, and (3) elliptical orbit whirling model. The numerical results show that the rotordynamic coefficients predicted by the present CFD method and six different rotor whirling models all agree well with the experiment data, and nearly coincide for all rotor whirling models. The proposed transient CFD method can be used to perform a reasonably accurate prediction of the frequency-dependent rotordynamic coefficients for annular gas seals based on any one of the present six rotor whirling models, as long as ensuring the combination of these whirling model parameters captures the small perturbation theory. The rotor whirling parameters such as whirling orbit, amplitude, and frequency number are important in predicting rotor whirling motion and fluid response forces, but have almost no effect on the computed rotordynamic coefficients. The benefit of the multiple-frequency rotor whirling models is the ability to calculate accurate rotordynamic coefficients of annular gas seals in a wide frequency range with a simulation time on the order of one-tenth the cost of the single-frequency whirling models.

Numerical Investigations on the Leakage and Rotordynamic Characteristics of Pocket Damper Seals—Part II: Effects of Partition Wall Type, Partition Wall Number, and Cavity Depth

Effects of partition wall type, partition wall number and cavity depth on the leakage and rotordynamic characteristics of the pocket damper seal (PDS) were numerically investigated using a presented 3D transient computational fluid dynamics (CFD) method based on the multifrequency elliptical whirling orbit model. The accuracy and availability of this transient CFD method and the multifrequency elliptical whirling orbit model were demonstrated with the experimental data of the experimental eight-bladed fully partitioned pocket damper seal (FPDS). The leakage flow rates and frequency-dependent rotordynamic coefficients of PDS were computed for two types of partition wall (namely conventional PDS and fully partitioned PDS), four partition wall numbers including the labyrinth seal (no partition wall) and six cavity depths including the plain smooth seal (zero cavity depth) at operational conditions with or without inlet preswirl and 15,000 rpm rotational speed. The numerical results show that the FPDS has the similar leakage performance and more superior stability capacity than the conventional PDS. The FPDS possesses slightly larger leakage flow rate (∼2.6–4.0% larger) compared to the labyrinth seal. Eight is a preferable value for the partition wall number to gain the best leakage performance of the FPDS with the least manufacturing cost. The FPDS possesses significantly larger stiffness and damping than the labyrinth seal. Increasing partition wall number results in a significant increase in the direct stiffness but limited desirable effect on the effective damping. The FPDS possesses the lowest leakage flow rate when the cavity depth is about 2.0 mm. Compared to the plain smooth seal, the FPDS possesses larger positive direct stiffness and significantly less direct damping and effective damping. Increasing cavity depth results in a significant decrease in the stabilizing direct damping and the magnitude of the destabilizing cross-coupling stiffness. H= 3.175 mm is a preferable value of the cavity depth for which the effective damping of the FPDS is largest, especially for the concerned frequencies (80–120 Hz) where most multistage high-pressure centrifugal compressors have stability problem.

Numerical Investigations on the Leakage and Rotordynamic Characteristics of Pocket Damper Seals—Part I: Effects of Pressure Ratio, Rotational Speed, and Inlet Preswirl

Effects of pressure ratio, rotational speed and inlet preswirl on the leakage and rotordynamic characteristics of a eight-bladed fully partitioned pocket damper seal (FPDS) were numerically investigated using proposed three-dimensional (3D) transient computational fluid dynamics (CFD) methods based on the multifrequency elliptical whirling orbit model. The accuracy and availability of the multifrequency elliptical whirling orbit model and the transient CFD numerical methods were demonstrated with the experimental data of frequency-dependent rotordynamic coefficients of the FPDS at two rotational speeds with high preswirl conditions. The frequency-dependent rotordynamic coefficients of the FPDS at three pressure ratios (three inlet pressures and three outlet pressures), three rotational speeds, three inlet preswirls were computed. The numerical results show that changes in outlet pressure have only weak effects on most rotordynamic coefficients. The direct damping and effective damping slightly increase in magnitude with decreasing outlet pressure at the frequency range of 20–200 Hz. The effect of inlet pressure is most prominent, and increasing inlet pressure for the FPDS results in a significant increase in the magnitudes of all rotordynamic coefficients. The magnitudes of the seal response force and effective damping are proportional to pressure drop through the seal. Increasing rotational speed and increasing inlet preswirl velocity both result in a significant decrease in the effective damping term due to the obvious increase in the magnitude of the destabilizing cross-coupling stiffness with increasing rotational speed or increasing preswirl velocity. The crossover frequency of effective damping significantly increases and the peak magnitude of effective damping decreases with increasing rotational speed or increasing preswirl velocity. The destabilizing cross-coupling stiffness is mainly caused by the circumferential swirl velocity generating from high rotational speed and inlet preswirl. Reducing swirl velocity (such as swirl brake) can greatly enhance the stabilizing capacity of the FPDS.