Rotordynamic Force Coefficients Research Articles

A comparison of static and rotordynamic characteristics for two types of liquid annular seals with and without helical grooved stator

Less leakage is a benefit of parallel grooved liquid seals (labyrinth seals). But researches show that the liquid seal with parallel grooves on the rotor harms the rotor stability. The seal with helical grooves on stator performs well in terms of rotordynamics, and its leakage is sensitive to the rotating speed. To make use of the advantages of both seals and improve seal stability, based on the Smooth-stator/Parallel Grooved-rotor (SPG) liquid seal, a Helical Grooved-stator/Parallel Grooved-rotor (HGPG) liquid seal is designed. To evaluate two liquid seals’ leakage, rotordynamic characteristics and drag power loss, a transient computational fluid dynamics-based method is employed. This method is based on the multi-frequency elliptical-orbit rotor whirling model and the mesh deformation technique. The published experimental data of the leakage and rotordynamic force coefficients for an SPG liquid seal are used to validate the accuracy and dependability of the current method. Seal leakage and force coefficients are presented and compared for the SPG liquid seal and the HGPG liquid seal at various pressure drops. The influences of parallel groove depth on the leakage and rotordynamic properties for the HGPG liquid seals at two rotational speeds (2000, 6000 r/min) are analyzed. The numerical findings demonstrate that the novel HGPG liquid seal has a lower leakage flow rate (by ∼22.3%) than the traditional SPG liquid seal. There is an optimal parallel groove depth that minimizes leakage. The presented novel HGPG liquid seal significantly improves rotordynamic stability, due to the similar effective stiffness and the obviously larger positive effective damping. Reducing parallel groove depth can increase the positive effective damping. In terms of leakage and rotordynamic characteristics, the novel HGPG liquid seal is a better seal design for liquid turbomachinery.

Leakage and Rotordynamic Force Coefficients of a Labyrinth Seal and a Pocket Damper Seal Operating With Wet Gas

Abstract Subsea centrifugal compressors commonly using labyrinth seals (LS) and pocket damper seals (PDS) must withstand the flow of oil in gas mixtures with a liquid volume fraction (LVF) up to 5%. This paper presents experimental results for the leakage and rotordynamic coefficients of a uniform clearance PDS and a similar size LS both supplied with wet gas. The shaft diameter D = 127 mm and the seal axial length L = 48 mm. In the tests, the seals' pressure ratio (inlet/exit) = 2.5, and the shaft speed reaches 5.25 krpm (surface speed = 35 m/s). The LS has a 17% larger radial clearance (Cr,LS = 0.230 mm > Cr,PDS = 0.196 mm) due to a manufacturing error. This paper extends prior work by Torres et al. (2022, “A Stepped Shaft Labyrinth Seal versus a Pocket Damper Seal: Leakage and Dynamic Force Coefficients Under Wet Gas Operation,” ASME J. Eng. Gas Turbines Power, 145(1), p. 011006) for the same two seal types with a stepped clearance configuration that promotes damping. When supplied with a dry gas, the LS leaks more because of its larger clearance. A loss coefficient (cd) is a fraction of the physical clearance that characterizes a seal's effectiveness in reducing leakage. The cd of both seals is nearly identical for operation with pure gas; the small differences are well within the experimental uncertainty. For operation with wet gas, the PDS cd decreases as the LVF increases whereas the LS cd increases, thus indicating the PDS is more effective to restrict wet gas leakage. When operating with pure gas, the direct stiffness (K) and effective damping (Ceff) of both seals are small in magnitude (K < 0.5 MN/m, Ceff < 2 kN-s/m) and often less than the experimental uncertainty. For wet gas operation and with shaft speed = 3 krpm and 5.25 krpm, the PDS produces Ceff < 0 for whirl frequencies below 50 Hz. In contrast, the LS Ceff > 0, although small in magnitude. The experimental results under wet gas operation are similar for operation with LVF equal to 3% and 5%. Unexpected low-frequency broadband motions appear when supplying the PDS with a wet gas. Although small in amplitude (<5 μm), the motions increase in severity as the mixture inlet LVF and shaft speed increase. The motions are entirely absent for tests with the LS. Experiments in which the mixture is drawn from the PDS cavities rule out liquid accumulation as the cause of the observed motions. The current test results serve as a reference for turbomachinery design engineers and aid in the validation of analytical predictive tools.

Numerical Investigation on the Leakage and Rotordynamic Characteristics for a Hole-Pattern Seal in Wet-Gas Conditions

Abstract For turbomachinery working in wet-gas conditions, liquid-phase fluid may worsen the rotordynamic characteristic of an annular seal, which induces a subsynchronous vibration problem and destabilizes the rotor-bearing system. The hole-pattern seal, demonstrated as effective to eliminate synchronous or subsynchronous vibrations for gas turbomachinery, is an ideal seal scheme to increase rotor stability and liquid tolerance capability of wet-gas turbomachinery. In this paper, the leakage and rotordynamic characteristics of a hole-pattern seal are numerically investigated under wet-gas conditions, using a three-dimensional transient CFD-based perturbation method. The accuracy and reliability of the present numerical method are demonstrated based on published experimental data. The rotordynamic force coefficients are presented and compared for the wet-gas hole-pattern seal with various inlet liquid volume fractions (LVF = 0%–20%), rotor speeds (ω = 0–20 krpm), inlet preswirl ratios (Sr = −0.2–0.5), and pressure ratios (Pr = 0.3–0.7). Numerical results show that the hole-pattern seal possesses desired tolerance capability for high inlet liquid volume fraction (LVF) of up to 20%. With inlet LVF increasing from 0 to 20%, the effective damping of the hole-pattern seal increases by about 50%, suggesting an improvement in rotor stability. The leakage flow rate of the oil-air mixture increases by 97.5%, combined with the sharply increasing oil leakage flow rate (by 636%) and decreasing air leakage flow rate (by 40%). The increasing rotor speed and inlet preswirl ratio both result in an obvious increase (by 50%) in the cross-coupled stiffness, yielding a smaller effective damping and worse rotor stability. With the increase in pressure ratio, all the rotordynamic force coefficients show a weaker frequency dependency and smaller magnitudes. The swirl velocity in the seal clearance can cause an accumulation of the liquid component in the hole cavities. With the increase of swirl velocity, more liquid component accumulates in the hole cavities, and the main accumulation position gradually moves upstream.

Experimental Force Coefficients for a Fully-Partitioned Pocket Damper Seal and Comparison to Other Two Seal Types

Abstract Labyrinth seals (LSs), honeycomb seals (HCSs) and hole-pattern seals, pocket damper seals (PDSs), and fully-partitioned damper seals (FPDSs) serve as balance pistons on the discharge side of barrel-type centrifugal compressors. These seals, facing large pressure differentials along with significant changes in gas density, produce sizeable lateral forces that impact compressor stability and rotordynamic performance. There is extensive archival data on the dynamic forced performance of LS and textured surface seals. However, the experimental database for a FPDS is insufficient, thus a comprehensive comparison of their dynamic force performance against that of textured surface seals is missing. The paper presents experimentally derived rotordynamic force coefficients for a FPDS along with a direct comparison to published data for a HCS and a LS, both similar in size and in operating conditions. The dynamic load tests with the FPDS include operation at a shaft speed (Ω) of 10 krpm (rotor surface speed of 60 m/s) while supplied with air at Pin = 70 bar and Tin =10 °C, and a discharge at Pout = 0.25, 0.5, and 0.65 of Pin. The preswirl circumferential velocity at the seal inlet is low, approximately 6% of rotor surface speed. The FPDS having eight pockets × eight axial blades produces a direct stiffness (K) increasing with excitation frequency (ω), though K < 0 for the lowest pressure ratio PR = (Pout/Pin) = 0.25. The cross-coupled stiffness (k) is invariant to frequency whereas the direct damping (C) steadily decreases as ω/Ω → 1, and then increases for larger frequencies. Hence, the effective damping coefficient (Ceff = C − k/ω) is approximately constant for ω < Ω, while increasing for higher frequencies. For the three PRs, the FPDS leakage is roughly up to 26% larger than the HCS leakage, while the 20-blade LS leaks in between both. The comparison of results shows the LS has insignificant forces compared to those from the HCS and FPDS, both producing a comparable Ceff and similar crossover frequencies (Ceff > 0). The HCS produces a large direct stiffness (K), three to four times that of the FPDS. Comparison of computational fluid dynamics (CFD) predictions for the FPDS against the experimental force coefficients shows significant differences, in particular an overestimation of direct stiffness as the frequency grows along with a lower direct damping for frequencies equal and above the shaft speed. Besides manufacturing considerations, a FPDS is a better alternative to a HCS whose large centering stiffness (K) may affect the compressor's critical speed, hence shortening the separation margin with respect to the operating speed.

Measured Leakage and Rotordynamic Force Coefficients for Two Liquid Annular Seal Configurations: Smooth-Rotor/Grooved-Stator Versus Grooved-Rotor/Smooth-Stator

Abstract This paper reports and compares the experimental results of leakage and dynamic force coefficients for two liquid annular pressure seals, one having a smooth-rotor/circumferentially grooved stator (SR/GS), the other one with a circumferentially grooved rotor/smooth-stator (GR/SS). Differing only in the grooves’ location, the GR/SS seal’s geometry and operating conditions are representative of those in electrical submersible pumps (ESPs) used for oil recovery. Supplied with an ISO VG2 oil at 46 °C, both seals have the same diameter D = 102 mm, length-to-diameter ratio L/D = 0.5, and nominal land clearance Cr = 0.203 mm. The seals have 15 circumferential grooves with grooves and land lengths equal to 1.52 mm. Test variable ranges include (a) shaft speeds (ω) ranging from 2 to 8 krpm (shaft surface speed ∼ 43 m/s), and (b) pressure differences (ΔP) from 2 to 8 bar. Upstream of the test seals, three separate prerotation rings generate a range of inlet circumferential velocities (entrance swirl). Under all conditions, the GR/SS seal leaks about 10% less than the SR/GS seal. For both seals, the direct stiffnesses (KXX, KYY) have low magnitudes that drop with increasing ω; in some cases, they turn negative at 6 krpm. The GR/SS seal produces cross-coupled stiffnesses (KXY, KYX) that are ∼1.5 times larger than those for the SR/GS seal. Under the same conditions, the SR/GS seal is more stabilizing as its direct damping, and added mass coefficients are ∼ 20% larger than those for the GR/SS seal. Instability issues are likely to arise with either seal geometry because negative KXX and KYY drop a pump critical speed, aggravating the well-known destabilizing coefficients KXY and KYX. The whirl frequency ratio (WFR) combines the effects of the cross-coupled stiffness, direct damping and cross-coupled mass terms, thus providing a good basis for comparing two seals’ stability characteristics. Overall, the WFR magnitudes for the GR/SS seal are about three times higher than those for the SR/GS seal. Note that, irrespective of the inlet swirl condition, the GR/SS approaches a WFR ∼ 0.50 for operating shaft speeds greater than 4 krpm. At the lowest shaft speed (2 krpm), the WFR ≪ 0.5 for the low inlet preswirl ring, whereas WFR > 0.8 for the medium and high preswirl rings. For the SR/GS seal, the WFR ∼ 0.2 at the highest shaft speed of 6 krpm, and not affected by the inlet preswirl condition. On the other hand, at the lowest shaft speed, the WFR ranges from 0.5 to 0.75 for the SR/GS seal with medium and high preswirl rings. At this speed, the WFR = 0 with the low inlet preswirl ring. Hence, to enhance the operational stability, an effective swirl brake that could drop the inlet preswirl ratio upstream of a seal is helpful for the GR/SS seal out to 4 krpm and for the SR/GS seal out to 6 krpm.

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.

Static and Rotordynamic Characteristics for Supercritical Carbon Dioxide Spiral Groove Dry Gas Seal With the Tilted Seal Ring

Abstract Supercritical carbon dioxide (SCO2) Brayton cycle has been widely used as a substitute for traditional steam cycles. As one of the key components of power-dense turbomachines, dry gas seal (DGS) has been considered one of the most suitable dynamic seal options due to its superior sealing performance. In this paper, considering the installation errors and external disturbances of the shaft end seal in a 14 MW supercritical carbon dioxide turbine, a comprehensive numerical study was conducted on the seal static and rotordynamic characteristics for four dry gas seal designs with different coning displacements. To account for the real gas effect of SCO2, a table lookup program was used to obtain the physics properties of CO2 under supercritical conditions based on the database of the National Institute of Standards and Technology (NIST). A frequency-dependent rotordynamic coefficients stiffness damping model (KC model) for SCO2 DGS and the mesh deformation technique were adapted to analyze the rotordynamic performance of the designed DGS. Steady-state numerical results of leakage rate, opening force, and steady film stiffness were analyzed and compared under four coning displacements. Transient numerical results of rotordynamic force coefficients were analyzed and studied under four coning displacement ratios and 10 vibration frequencies. Results show that the increase in coning displacement causes a 20% rise in leakage rate and a 2.4% increase in opening force. The tilted seal ring results in a maximum 30%–84% variation of the dynamic stiffness and greatly influences the damping coefficient. From a comprehensive view, the tilt of the seal rings brings undesired influences on both the static and rotor dynamic performance of SCO2 DGS. The distortion of the seal rings due to installation errors and other disturbances should be avoided as far as possible in SCO2 DGSs.

Computational Fluid Dynamics Analysis of the Influence of Gas Content on the Rotordynamic Force Coefficients for a Circumferentially Grooved Annular Seal for Multiple Phase Pumps

Abstract Pumping efficiency and rotordynamic stability are paramount to subsea multiphase pump operation since, during the life of a well, the process fluid transitions from a pure liquid to a mixture of gas in the liquid to just gas. Circumferentially grooved seals commonly serve as balance pistons in pumps while also restricting secondary flow. Prior experimental results obtained with a grooved seal operating with a mixture of air and mineral oil show the seal rotordynamic force coefficients vary significantly with the gas volume fraction (GVF). This paper, complementing an exhaustive experimental program, presents a computational fluid dynamics (CFD) analysis to predict the leakage and dynamic force coefficients of a circumferentially grooved seal supplied with air in an oil mixture with a GVF varying from 0 to 0.7. The test seal has 14 grooves, an overall axial length of 43.6 mm, and radial clearance of 0.211 mm. The 127 mm diameter rotor spins at constant angular speed (Ω = 3500 rpm). The mixture enters the seal at a supply pressure (Pin) of 2.9 bar(a), and the seal exit pressure (Pout) is 1 bar(a). The CFD two-phase flow simulations utilize the Euler–Euler multiphase model to predict the mass flowrate and the pressure field as a function of the operating conditions. Using a multi-frequency shaft orbit motion method, the CFD simulations deliver the variations of reaction force on the rotor with respect to the excitation frequency. For a pure liquid condition (GVF = 0), both the CFD and experimental results produce constant stiffness, damping, and added mass coefficients. The experimental and CFD results demonstrate the seal rotordynamic force coefficients are quite sensitive to the GVF. When introducing a small amount of air into the oil (GVF = 0.1), the direct damping coefficient increases by approximately 10%. For operation with a mixture with inlet GVF > 0.1, the cross-coupled stiffness coefficients develop strong frequency-dependent characteristics. In contrast, the direct damping coefficient has a negligible variation with excitation frequency. The CFD predictions, as well as the experimental results, evidence that air injection in a liquid stream can significantly change the seal rotordynamic characteristics, and thus can affect the rotordynamic stability of a pump. An accurate CFD analysis provides engineers to design reliable grooved seals operating under two-phase flow conditions.

Static and Rotordynamic Characteristics for Two Types of Novel Hole-Pattern Seals Operating in Supercritical CO2 Turbomachinery

Abstract In this paper, two novel hole-pattern seals were assessed for applications at the balance piston in a 14 MW supercritical CO2 turbine, focusing on the improvement of the seal leakage and rotordynamic performances. These two novel hole-pattern seals were derived from the conventional straight-through hole-pattern seal (HPS) with the same sealing clearance, diameter, axial length, hole diameter and depth, including a stepped hole-pattern damper seal (SHPS) and a grooved hole-pattern damper seal (GHPS). To enhance the seal net damping capability at high inlet preswirl condition, a straight swirl brake also was designed and employed at seal entrance for each type seal. A comprehensive assessment and comparison was conducted on the conventional HPS and the present two novel hole-pattern seals (SHPS and GHPS) with a static concentric rotor. The leakage flow rates, rotordynamic force coefficients, cavity pressure, and swirl velocity developments were analyzed for three hole-pattern seal designs with/without swirl brakes at two inlet preswirl ratios (0.1, 0.5), using a transient computational fluid dynamics (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 (NIST) database was implemented, using an in-house code, for the fluid properties of CO2 in both supercritical and subcritical conditions. Results show that the present two novel hole-pattern seals have better sealing capability, especially for the GHPS seal which leaks less by a factor of 44%. In general, the GHPS seal possesses the lowest positive effective stiffness, highest effective damping, and the lowest crossover frequency of 60–70 Hz, especially at high inlet preswirl case. From a viewpoint of the rotor stability and unbalance sensitivity analysis, the GHPS seal without entrance swirl brake is a better seal design scheme for the balance piston seal in sCO2 turbine.

Influence of Ambient Pressure on Measured Stiffness and Damping of Radial Gas Foil Bearings

Abstract As gas bearings have gained popularity, they have been used in a diverse range of applications. In many cases these bearings are used in various process gases at a range of pressures. Although numerous analytical tools exist to predict the behavior of gas bearings in these environments, these tools are challenging to validate. The current work describes a test loop that is capable of measuring rotordynamic force coefficients in a hermetically sealed environment. To the author's knowledge, this capability is the first of its kind. To illustrate operation of the test rig, an industrial 3-lobe gas-foil bearing was installed in the test fixture, and operated at pressures from 0.5 to 3.5 bara at speeds ranging from 25 to 65 krpm. The tests show that dynamic coefficients increase with speed and pressure; however, a slight reduction in coefficients were observed at the highest speed under ambient conditions. In addition, subambient pressure tests showed higher than ambient stiffness, but comparably low damping in comparison to the other test cases. It is believed that this is the first publication of gas foil bearing coefficients at subambient pressure.

Numerical Investigations on Static and Rotordynamic Characteristics for Two Types of Liquid Hole-Pattern Seals With Tilted Cavities

Abstract Two types of liquid hole-pattern seals with axially oblique (A-HPS) or circumferentially oblique (C-HPS) hole cavities are designed. To evaluate the leakage and rotordynamic characteristics of the liquid hole-pattern seals, a 3D transient perturbation method is employed, which based on the multifrequency one-dimensional rotor whirling model and the mesh deformation technique. The accuracy and reliability of the proposed numerical approach is demonstrated based on the published experimental data of the leakage and rotordynamic force coefficients for a hole-pattern seal (HPS). Seal leakage and force coefficients are presented and compared for the A-HPS (axially oblique angle α=−30degto30deg), C-HPS (circumferentially oblique angle β=−30degto30deg), and HPS (α = 0, β = 0) at various rotational speeds (n = 0.05, 2.0, 4.0, and 6.0 krpm). Results reveal that the tilted hole cavity with positive α or β can reduce the seal effective clearance and strengthen the kinetic dissipation in hole cavities, yielding less leakage by 5–10%, especially at higher rotational speeds. The tilted hole cavity with a positive oblique angle (α=30deg,β=30deg) results in a moderate growth (by ∼6% for the A-HPS, by ∼15% for C-HPS) in the effective stiffness. Furthermore, the tilted hole cavity shows a very weak influence (<4.0%) on the effective damping, particularly for higher rotational speeds and vibration frequencies. Considering the decreasing leakage and nonworse rotordynamic characteristics, a tilted hole cavity with suitable positive oblique angles (10deg–30deg) is beneficial for the liquid hole-pattern seal.

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.

Rotordynamic Behavior of Leaf Seals: Measurement of Frequency-Dependent Force Coefficients for Varying Inlet Parameters

Abstract While brush seals can be found in various applications for turbomachines today, leaf seals are a further development in compliant seal technology and have a lower level of maturity. Among the purported advantages are greater axial rigidity when subject to higher pressure differences and the potential for noncontacting operation due to lift-up. However, especially their rotordynamic behavior is little investigated in the literature so far. In this paper, measured rotordynamic force coefficients of a leaf seal are presented for varying inlet pressures, preswirl velocities, and excitation frequencies. The leaf pack of the tested leaf seal has zero rotor cold clearance, and its coverplates are designed for facilitating a lift-up effect when pressurizing the seal. Experiments were performed on a dynamic test rig with whirling rotor using active magnetic bearing (AMB) technology and evaluated in the frequency domain based on the impedance method. Test results for the leaf seal reveal positive direct stiffness and an advantageous rotordynamic behavior due to significant levels of direct damping and negative cross-coupled stiffness throughout the operating parameter range. Leaf seal results are compared to brush and labyrinth seal data from previous studies for varying inlet pressures and preswirl velocities. Additional computational fluid dynamics (CFD) simulations were carried out to predict the leaf deflection moment, which supports the findings regarding hydrostatic lift-up from the experimental results.

Static and Rotordynamic Characteristics for Two Types of Novel Mixed Liquid Damper Seals With Hole-Pattern/Pocket-Textured Stator and Helically Grooved Rotor

Abstract Noncontacting liquid annular seals, such as helical groove seals, are widely used at the impeller interstage and shaft end in the liquid turbomachinery to reduce the fluid leakage and stabilize the rotor-bearing system. However, previous literatures have expounded that the helical groove seal possesses the poor sealing property at low rotational speed condition and suffers the rotor instability problem inducing by negative stiffness and damping, which is undesirable for the liquid turbomachinery. In this paper, to obtain the high sealing performance and the reliable rotordynamic capability throughout full operational conditions of machines, two novel mixed liquid damper seals, which possess a hole-pattern/pocket-textured stator matching with a helically grooved rotor, were designed and assessed for the balance piston location in a multiple-stage high-pressure centrifugal liquid pump. To assess the static and rotordynamic characteristics of these two types of mixed liquid damper seals, a three-dimensional (3D) steady computational fluid dynamics (CFD)-based method with the multiple reference frame theory was used to predict the seal leakage and drag power loss. Moreover, a novel 3D transient CFD-based perturbation method, based on the multifrequency one-dimensional stator whirling model, the multiple reference frame theory, and the mesh deformation technique, was proposed for the predictions of liquid seal rotordynamic characteristics. The reliability and accuracy of the present numerical methods were demonstrated based on the published experiment data of leakage and rotordynamic force coefficients of a helical groove liquid annular seal and a hole-pattern liquid annular seal. The leakage and rotordynamic force coefficients of these two mixed liquid damper seals were presented at five rotational speeds (0.5 krpm, 2.0 krpm, 4.0 krpm, 6.0 krpm, and 8.0 kpm) with large pressure drop of 25 MPa, and compared with three types of conventional helical groove seals (helical grooves on rotor, stator or both), two typical damper seals (hole-pattern seal, pocket damper seal with smooth rotor), and a mixed helical groove seal. Numerical results show that two novel mixed liquid damper seals both possess generally better sealing capacity than the conventional helical groove seals, especially at lower rotational speeds. The circumferentially isolated cavities (hole/pocket types) on the stator can enhance the “pumping effect” of the helical grooves for mixed helical groove seals, by weakening the swirl flow in seal clearance (which results in the increase of the fluid velocity gradient near the helically grooved rotor). What is more, the helical grooves on rotor also strengthen the dissipation of fluid kinetic energy in the isolated cavities, so the mixed liquid damper seals offer less leakage. Although the mixed liquid damper seals possess a slightly larger (less than 40%) drag power loss, it is acceptable in consideration of the reduced (∼60%) leakage for the high-power turbomachinery, such as the multiple-stage high-pressure centrifugal liquid pump. The present novel mixed liquid damper seals have pronounced rotordynamic stability advantages over the conventional helical groove seals, due to the obviously larger positive stiffness and damping. The mixed liquid damper seal with the hole-pattern stator and the helically grooved rotor (HPS/GR) possesses the lowest leakage and the largest effective damping, especially for higher rotational speeds. From the viewpoint of sealing capacity and rotor stability, the present two novel mixed liquid damper seals have the potential to become the attractive alternative seal designs for the future liquid turbomachinery.

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.

Rotordynamic force estimation of turbulent, annular seals using OpenFOAM®

3D CFD simulations are performed to resolve the leakage rates, axial pressure drops, and dynamic force coefficients of smooth annular seals. Simulations are performed for several, simple annular seal geometries subject to water and gas flows in order to verify and validate the open-source CFD library OpenFOAM for such applications. Rotordynamic force coefficients are determined using the whirling-rotor method. Accuracy of CFD-predicted results is assessed through direct comparison with published experimental data and bulk-flow model predictions. For the three water seals analyzed, the open-source, CFD-predicted dynamic coefficients closely agree with their experimental counterparts. The k- $$\omega $$ family of turbulence models is shown to outperform the k- $$\epsilon $$ models. For the gas seals, the open-source CFD solver is shown to be unsatisfactory in predicting damping coefficients and simulations are alternatively performed with ANSYS Fluent.

Gas Labyrinth Seals: Improved Prediction of Leakage in Gas Labyrinth Seals Using an Updated Kinetic Energy Carry-Over Coefficient

Abstract Though simple and fast, bulk-flow models (BFMs) for gas labyrinth seals (LSs) often predict the mass flow inaccurately. The BFM models rely on classical Neumann's equation model to characterize the flow through a labyrinth tooth. Presently, a computational fluid dynamics (CFD) analysis quantifies the effects of tip clearance (Cr) and operating conditions on the prediction of LS mass flow, and then derives an updated kinetic energy carry-over coefficient (μ1i) to improve the accuracy of Neumann's leakage equation. μ1i is a function of the seal tip clearance (Cr), the tooth pitch, and the total teeth number; but it does not depend on the seal supply or discharge pressures. The analysis selects a 14-teeth on stator LS (length/diameter = L/D = 0.29) with clearance Cr = (1/733)D and operating at nominal supply (Pin) and discharge (Pout) pressures equal to 73 bar and 51 bar, respectively, and at a rotor speed of 12 krpm (surface speed = 138 m/s). The CFD produces flow fields for LSs with a clearance varying from 80% to 200% of the nominal Cr, a gas supply pressure from 60 bar to 100 bar, and with various discharge pressures giving a pressure ratio (PR = Pout/Pin) ranging from 0.40 to 0.85. The numerous predictions deliver the mass flow as well as the bulk-flow velocities and cavity pressures within the seals. The kinetic energy carry-over coefficient (μ1i) increases with respect to the seal radial clearance (Cr). μ1i shows a parabolic correlation with PR; at first, μ1i increases with a rise in PR from a low value; and then, a further increase in PR leads to a decrease in μ1i. The coefficient μ1i is only sensitive to the PR and not to the magnitude of either the supply or discharge pressures. Lastly, for use with Neumann's leakage model, the CFD predictions produce an updated μ1i, a function of the seal geometry and the PR condition. Integration of the new μ1i correlation into a BFM code improves its accuracy to predict LS mass flow rate, a 19% difference against test data reduces to within 6%. A TOS LS tested by Ertas et al. (2012, Rotordynamic Force Coefficients for Three Types of Annular Gas Seals With Inlet Preswirl and High Differential Pressure Ratio,” ASME J. Eng. Gas Turbine Power, 134(4), p. 4250301) serves to further validate the accuracy of the modified leakage model.

A Comparison of Static and Rotordynamic Characteristics for Two Types of Liquid Annular Seals With Parallelly Grooved Stator/Rotor

Abstract Liquid annular seals with parallelly grooved stator or rotor are used as replacements for smooth plain seals in centrifugal pumps to reduce leakage and break up contaminants within the working fluid. Parallelly grooved liquid annular seals have advantages of less leakage and smaller possibility of abrasion when the seal rotor–stator rubs in comparison to smooth plain seals. This paper deals with the static and rotordynamic characteristics of parallelly grooved liquid annular seals, which are limited in the literature. Numerical results of leakage flow rates, drag powers, and rotordynamic force coefficients were presented and compared for a grooved-stator/smooth-rotor (GS-SR) liquid annular seal and a smooth-stator/grooved-rotor (SS-GR) liquid annular seal, utilizing a modified transient computational fluid dynamics-based perturbation approach based on the multiple-frequency elliptical-orbit rotor whirling model. Both liquid annular seals have identical seal axial length, rotor diameter, sealing clearance, groove number, and geometry. The present transient computational fluid dynamics-based perturbation method was adequately validated based on the published experiment data of leakage flow rates and frequency-independent rotordynamic force coefficients for the GS-SR and SS-GR liquid annular seals at various pressure drops with differential inlet preswirl ratios. Simulations were performed at three pressure drops (4.14 bar, 6.21 bar, and 8.27 bar), three rotational speeds (2 krpm, 4 krpm, and 6 krpm) and three inlet preswirl ratios (0, 0.5, and 1.0), applying a wide rotor whirling frequency range up to 200 Hz, to analyze and compare the influences of operation conditions on the static and rotordynamic characteristics for both the GS-SR and SS-GR liquid annular seals. Results show that the present two liquid annular seals possess similar sealing capability, and the SS-GR seal produces a slightly larger (∼2–10%) drag power loss than the GS-SR seal. For small rotor whirling motion around a centered position, both seals have the identical direct force coefficients and the equal-magnitude opposite-sign cross-coupling force coefficients in the orthogonal directions x and y. For all operation conditions, both the GS-SR and SS-GR liquid annular seals possess negative direct stiffness K and positive direct damping C. The GS-SR seal produces purely positive Ceff throughout the whirling frequency range for all operation conditions, while Ceff for the SS-GR seal shows a significant decrease and transitions to negative value at the crossover frequency fco with increasing rotational speed and inlet preswirl. From a rotordynamic viewpoint, the GS-SR liquid annular seal is a better seal concept for pumps.

Influence of Annular/Pocket Groove on the Static and Rotordynamic Characteristics of Hole-Pattern Seals

Abstract Annular damper seals, such as hole-pattern seals, are widely used to control leakage and enhance rotordynamic stability in turbomachinery, especially, for the balance-piston seal in the straight-through multistage centrifugal compressor, and the center seal in the back-to-back compressor. To avoid negative static stiffness (zero frequency), annular grooves on seal stator have been used to increase the direct static stiffness of hole-pattern seals by dividing a long seal to several shorter seal sections. However, few literatures are available for understanding the influences of grooves on seal static and rotordynamic characteristics. To comprehensively understand the effects of grooves on the static and rotordynamic characteristics of annular damper seals, a proposed three-dimensional (3D) transient CFD-based method was used to predict the rotordynamic characteristics of annular damper seals, based on the multifrequency one-dimensional rotor whirling model and mesh deformation technique. Moreover, a 3D steady CFD-based method based on the mesh deformation technique was also proposed to predict the static characteristics of annular damper seals. The accuracy and reliability of the present transient CFD-based method were demonstrated with the experimental data of frequency-dependent rotordynamic force coefficients for an experimental hole-pattern seal at three inlet preswirl conditions (μ0 = −0.244, 0, 0.598). Numerical results such as leakage flowrates, static and rotordynamic force coefficients were presented and compared for a conventional straight-through hole-pattern seal (without grooves, HPS) and two types of grooved hole-pattern seals (one with annular groove on stator, HPS-AG; one with pocket groove on stator, HPS-PG) with three groove positions (20%, 40%, 60% of seal axial length), at zero (μ0 = 0) and positive (μ0 = 0.598) inlet preswirl conditions. These seals are long (L/D = 0.75), with a diameter of 114.5 mm and a radial clearance of 0.2 mm. The effects of groove types (annular and pocket) and groove positions on seal's static and rotordynamic force coefficients were numerically discussed. Results show that compared to the conventional HPS seal, two types of grooves (annular and pocket) both produce a significant increase (20–150%, especially for the larger rotor eccentric ratios) in static direct stiffness, and the HPS-PG seal possesses the relatively optimal static stability. Two types of grooves (annular and pocket) both result in a slight increase (less than 5%) in seal leakage. The annular groove will significantly weaken the seal dynamic stiffness capability, however, the pocket groove shows only very weak influences. Compared to the conventional HPS seal, the HPS-PG seal possesses the similar increasing effective damping and decreasing crossover frequency with the HPS-AG seal. This suggests that the pocket groove is a more suitable design to improve the seal static and rotordynamic characteristics. The rotordynamic force coefficients show a strong dependence on the groove location for the HPS-AG seal, but which is insensitive for the HPS-PG seal. The optimal location of annular groove is strongly related to the inlet preswirl conditions.

Numerical Modeling of Static and Rotordynamic Characteristics for Three Types of Helically Grooved Liquid Annular Seals

Abstract This paper deals with numerical predictions of the leakage flowrates, drag power, and rotordynamic force coefficients for three types of helically grooved liquid annular seals, which include a liquid annular seal with helically grooved stator (GS/SR seal), one with helically grooved rotor (SS/GR seal), and one with helical grooves on stator and rotor (GS/GR seal). A novel transient computational fluid dynamics (CFD)-based perturbation method was proposed for the predictions of the leakage flowrates, drag power, and rotordynamic force coefficients of helically grooved liquid annular seals. This method is based on the unsteady Reynolds-averaged Navier–Stokes (RANS) solution with the mesh-deformation technique and the multiple reference frame theory. The time-varying fluid-induced forces acting on the rotor/stator surface were obtained as a response to the time-dependent perturbation of the seal stator surface with the periodic motion, based on the multiple-frequency elliptical-orbit stator whirling model. The frequency-independent rotordynamic force coefficients were determined using curve fit and fast Fourier transform (FFT) in the frequency domain. The CFD-based method was adequately validated by comparisons with the published experiment data of leakage flowrates and fluid response forces for three types of helically grooved liquid annular seals. Based on the transient CFD-based perturbation method, numerical results of the leakage flowrates, drag powers, and rotordynamic force coefficients were presented and compared for three types of helically grooved liquid annular seals at five rotational speeds (n = 0.5 krpm, 1.0 krpm, 2.0 krpm, 3.0 krpm, and 4.0 krpm), paying special attention to the effective stiffness coefficient and effective damping coefficient.