Preswirl Ratio Research Articles

Rotordynamic characteristics of a novel labyrinth seal with partition walls and helical groove teeth

To improve the stability of the conventional labyrinth seal (LS), in this paper, four novel fully partitioned helically labyrinth seals (FPHGLS) were designed and they were in comparison with one FPPGLS. The influences of the preswirl ratio and the helical groove pitch on the leakage flow and rotordynamic characteristics were numerically investigated, using the transient computational fluid dynamics (CFD) method based on the multi-frequency elliptical whirling orbit model. The accuracy and availability of the present transient numerical method were demonstrated based on the experiment data. The results show that the partition walls design can significantly increase the direct damping and cross-coupling stiffness for labyrinth seals and the helical teeth design can significantly decrease the cross-coupling stiffness and tangential force. When the helical groove pitch is equal to the seal length, the leakage nearly remains unchanged. Compared to the baseline design (LS), the FPPGLS and the FPHGLS have similar and significantly larger direct stiffness and direct damping. The two designs possess positive direct stiffness throughout the frequency range. The FPPGLS and FPHGLS possess significantly higher direct damping (∼323.7% larger than LS). But the FPPGLS possesses the largest cross-coupling stiffness among three seals at two preswirl ratios. From preswirl ratio = 0.13–0.84, the cross-coupling stiffness of the FPHGLS decreases by 53.4-310.1% compared with the FPPGLS. Increasing the helical groove pitch increases both direct stiffness and direct damping and reduces cross-coupling stiffness, but it also leads to greater leakage losses. In general, the novel FPHGLS whose helical groove pitch is equal to seal length possesses superior rotordynamic characteristics and similar leakage characteristic. This work provides the reference of the seal design and safety operation for the turbomachinery.

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.

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.

Inlet preswirl dependence research on three different labyrinth seals

In this paper, an angular velocity is proposed to calculate the air inlet preswirl condition. The potential influences on rotordynamic and leakage performance of inlet preswirl ratios ranging from −1–1 are considered in the traditional labyrinth seal (LS), diaphragm labyrinth seal (DLS) and hole diaphragm labyrinth seal (HDLS). The simulation results show that the inlet preswirl of the LS has little influence under low rotation speeds, while the negative influence on the higher rotation speed for the positive preswirl is clear. The maximum improvement of effective damping under the −1 preswirl ratio compared to zero preswirl conditions for LS, DLS and HDLS can reach 132.1%, 240.6% and 385.1%, respectively, when that of effective stiffness for DLS and HDLS can improve 14.8% and 90.1%, respectively, and that of leakage reduction for DLS and HDLS can reach 4.12% and 4.5%, respectively. Meanwhile, the average leakage under different conditions of HDLS can obtain 5.70% reduction than that of LS and 1.78% than DLS, which is better than another new seal, which was proposed by other scholars. Further discussions on detailed flow areas show that the existence of holes brings more energy dissipation for HDLS, which brings lower leakage among the three different seals. Comparing DLS and HDLS also shows a potential combination to obtain a new type of seal with higher stability for rotor-seal systems and lower leakage.

Static Force Characteristic of Annular Gaps – Experimental and Simulation Results

AbstractWe discuss the static characteristics, i.e., the induced force on the rotor, the attitude angle and the pressure difference, of off-centered annular gaps with an axial flow component without cavitation. The paper focuses on turbulent flow inside the annulus. Instead of modeling the inertia effects using the bulk-flow approach, the presented model uses an integro-differential approach in combination with power-law ansatz functions for the velocity profiles and a Hirs’ model to calculate the resulting pressure field. For an experimental validation of the model and comparison to the bulk-flow approach, an annular gap test rig is presented using magnetic bearings to inherently measure the position as well as the force on the rotor induced by the flow field inside the gap. The experimental investigations are performed using three different annuli with three different lengths. The impact of a variation of a modified Reynolds number, the flow number and the preswirl ratio on the resulting force on the rotor, the attitude angle and the pressure difference across the annulus is investigated and compared to the presented model and the bulk-flow approach.

Effect of hole arrangement patterns on the leakage and rotordynamic characteristics of the honeycomb seal

The honeycomb seal is a vital component to reduce the leakage flow and improve the system stability for the turbomachines. In this work, a three-dimensional model is established for the interlaced hole honeycomb seal (IHHCS) and the non-interlaced hole honeycomb seal (NIHHCS) to investigate its leakage and rotordynamic characteristics by adopting computational fluid dynamics (CFD). Results show that the hole arrangement patterns have little impact on the pressure drop and turbulence kinetic energy distribution for the seals, and the IHHCS possesses a slightly lower leakage flow rate than the NIHHCS. Moreover, the numerical results also show that the NIHHCS possesses a better rotordynamic performance than the IHHCS at all investigated conditions. Both seals show a larger k and a lower Ceff with the increase of the positive preswirl ratios and rotational speeds, while the negative preswirl ratios would reduce the k and improve the Ceff. The NIHHCS possesses a higher absolute value of Ft for all operating conditions, this could explain the distinction of Ceff for both seals at different working 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.

Research on the inlet preswirl effect of clearance flow in canned motor reactor coolant pump

For a pressurized water reactor power plant, the reactor coolant pump (RCP) is a kernel component. And for a canned motor RCP, the rotor system's properties determines its safety. The liquid coolant inside the canned motor RCP fills clearance between the metal shields of rotor and stator, forming a lengthy clearance flow. The influence of inlet preswirl on rotordynamic coefficients of clearance flow in canned motor RCP and their effects on the rotordynamic characteristics of the pump are numerically and experimentally investigated in this work. A quasi-steady state computational fluid dynamics (CFD) method has been used to investigate the influence of inlet preswirl. A vertical experiment rig has also been established for this purpose. Rotordynamic coefficients on different inlet preswirl ratios (IR) are obtained through CFD and experiment. Results show that the cross-coupled stiffness of the clearance flow would change significantly with inlet preswirl, but other rotordynamic coefficients would not change significantly with inlet preswirl. For the case of clearance flow between the stator and rotor cans, influence of inlet preswirl is not so significant as the IR is not large enough.

Making Better Swirl Brakes Using Computational Fluid Dynamics: Performance Enhancement From Geometry Variation

Abstract A fluid with a large swirl (circumferential) velocity entering an annular pressure seal influences the seal cross-coupled dynamic stiffness coefficients, and hence it affects system stability. Typically comprising a large number of angled vanes around the seal circumference, a swirl brake (SB) is a mechanical element installed to reduce (even reverse) the swirl velocity entering an annular seal. SB design guidelines are not readily available, and existing configurations appear to reproduce a single source. By using a computational fluid dynamics (CFD) model, the paper details a process to engineer a SB upstream of a 16-tooth labyrinth seal (LS) with tip clearance Cr = 0.203 mm. The process begins with a known nominal SB* geometry and considers variations in vane length (LV* = 3.25 mm) and width (WV* = 1.02 mm), and stagger angle (θ* = 0 deg). The vane number NV* = 72 and vane height HV* = 2.01 mm remain unchanged. The SB–LS operates with air supplied at pressure PS = 70 bar, a pressure ratio PR = exit pressure Pa/PS = 0.5, and rotor speed Ω = 10.2 krpm (surface speed ΩR = 61 m/s). Just before the SB, the preswirl velocity ratio = average circumferential velocity U/shaft surface speed (ΩR) equals α = 0.5. For the given conditions, an increase in LV allows more space for the development of vortexes between two adjacent vanes. These are significant to the dissipation of fluid kinetic energy and thus control the reduction of α. A 42% increase in vane length (LV = 4.6 mm) produces a ∼43% drop in swirl ratio at the entrance of the LS (exit of the SB), from αE = 0.23 to 0.13. Based on the SB with LV = 4.6 mm, the stagger angle θ varies from 0 deg to 50 deg. The growth in angle amplifies a vortex at ∼70% of the vane height, while it weakens a vortex at 30% of HV. For θ = 40 deg, the influence of the two vortexes on the flow produces the smallest swirl ratio at the LS entrance, αE = −0.03. For a SB with LV = 4.6 mm and θ = 40 deg, the vane width WV varies from 0.51 mm to 1.52 mm (±50% of WV*). A reduction in WV provides more space for the strengthening of the vortex between adjacent vanes. Therefore, a SB with greater spacing of vanes also reduces the inlet circumferential velocity. For WV = 0.51 mm, αE further decreases to −0.07. Besides the design condition (α = 0.5), the engineered SB having LV = 4.6 mm, θ = 40 deg, and WV = 0.51 mm effectively reduces the circumferential velocity at the LS entrance for other inlet preswirl ratios equaling α = 0 and 1.3. Rather than relying on extensive experiments, the CFD analysis proves effective to quickly engineer a best SB configuration from the quantification of performance while varying the SB geometry and inlet swirl condition.

Rotordynamic Characteristics of the Straight-Through Labyrinth Seal Based on the Applicability Analysis of Leakage Models Using Bulk-Flow Method

Abstract Labyrinth seals are widely applied in the turbomachinery to control the leakage flow through the clearance between stationary and rotating components. The fluid excitation induced by the labyrinth seal would deteriorate the stability of turbomachinery shaft. Developing an accurate and rapid prediction approach is crucial to the analysis of the fluid excitation rotordynamics of labyrinth seals. The objective of this study is to analyze the applicability of leakage models using Bulk-Flow method and investigate the factors affecting the rotordynamic characteristics of the labyrinth seal. An elliptical orbit for rotor whirling was assumed in the one-control-volume Bulk-Flow model considering an isentropic process to predict the frequency-dependent rotordynamic coefficients of the labyrinth seal. The optimal leakage model was determined by comprehensively analyzing the applicability of seventy-two leakage models. Employing the optimal leakage model in the Bulk-Flow method, the effects of sealing clearance, pressure ratio, preswirl ratio and rotational speed on the rotordynamic characteristics of the labyrinth seal were investigated. The conclusions show that the Bulk-Flow method has an average prediction error of around 10% for the leakage flow rate, cross-coupled stiffness and direct damping when equipped with the optimal leakage model. Increasing preswirl ratio has a significantly destabilizing effect on the rotor stability, while the influence of increasing rotational speed is strongly related to preswirl direction. The effective damping of the labyrinth seal is sensitive to the inlet pressure, but insensitive to the outlet pressure and sealing clearance. The crossover frequency is almost impervious to the inlet pressure, outlet pressure and sealing clearance.

Rotordynamic characteristics prediction for scallop damper seals using computational fluid dynamics

Enhancing damping characteristic is one of the effective methods to solve the instability problem of the rotor system. The three-dimensional numerical analysis model of scallop damper seal was established, and the effects of inlet pressures, preswirl ratios, rotational speeds, interlaced angles and seal cavity depths on the rotordynamic characteristics of scallop damper seal were studied based on dynamic mesh method and multi-frequencies elliptic whirling model. Results show that the direct stiffness of the scallop damper seal increases with decreasing inlet pressure and increasing rotational speed and cavity depth. When the seal cavity is interlaced by a certain angle, which shows positive direct stiffness. The effective damping of the scallop damper seal increases with the increasing inlet pressure, the decreasing preswirl ratio and the rotational speed and cavity depth. There exists an optimal interlaced angle to maximize the effective damping and the system stability. The leakage of the scallop damper seal is significantly reduced with decreasing inlet pressure. The preswirl will reduce the leakage flowrate, and the rotational speed has a slight effect on the leakage performance. The leakage of the scallop damper seal decreases with increasing seal cavity depth.

Swirl brakes optimization for rotordynamic performance improvement of labyrinth seals using computational fluid dynamics method

The various lengths, clearances, numbers, and rotation angles of swirl brakes are investigated to evaluate their effects on the static and rotordynamic performance of the labyrinth seal using Computational Fluid Dynamics. With increasing number, length and decreasing clearance, the efficiency of the straight swirl brake can be improved. The negative stagger angle could reverse the forward flow. The lean angle has relatively slight effects on the swirl brake. Increasing preswirl ratios tends to increase the circumferential velocity. Compared with the no-brake labyrinth seal, the labyrinth seal with swirl brakes shows lower cross-coupled stiffness and resultant larger effective damping. The effective damping with negative stagger angles is increased about 100%–200% compared to the straight swirl brakes.

Effects of swirl brake axial arrangement on the leakage performance and rotor stability of labyrinth seals

Swirl brakes are usually introduced at the seal entrance in industry to improve the seal stability, especially for labyrinth seals suffering low seal clearance and high inlet preswirl ratio. However, how to arrange swirl brakes at the seal entrance to obtain better seal stability retains unknown, such as the axial distance between the brake trailing edge and the first tooth. To this end, the effects of the distance between brakes and the first tooth on the leakage flow rate and seal rotordynamic coefficients were numerically investigated at typical inlet preswirl ratios of 0.45 and 0.8, and the predicted results were in comparison with the results for no-brake configuration. The obtained results disclose that the brake configuration arranged against the first tooth produces lower circumferential velocity in the downstream of the brakes as a result of the larger counter-clockwise vortex moving from the brake trailing edge to the brake leading edge when compared to the brake configuration away from the first tooth. Besides, the dropped circumferential velocity in the downstream of brakes will cause larger pressure fluctuation in the circumferential direction and thus generates larger tangential force to restrain the rotor forward whirl. On the other hand, the effective damping is further increased when the distance between brakes and the first tooth decreases to zero, that is, the crossover frequency is even disappeared at the inlet preswirl ratio of 0.45 and successfully drops from 69.9 Hz to 32.7 Hz at the preswirl ratio of 0.8.

Improving the rotordynamic stability of short labyrinth seals using positive preswirl

Introducing a negative preswirl at the upstream of annular gas seals has been considered as an effective way to improve the system stability. This paper demonstrates a stability enhancement approach for a short labyrinth seal using positive preswirls. The static and dynamic characteristics of the labyrinth seal with various blade numbers (5, 10, 15), inlet preswirl ratios (–0.3, –0.15, 0, 0.15, 0.3) were studied. Results show that the inlet preswirl ratio has a dramatic effect on the circumferential location of the high-pressure spot for each seal cavity, particularly for the first cavity. The inlet preswirl ratio has opposite effects on the system stability due to the difference of high-pressure spot locations between the first cavity and the others. An increasing positive inlet preswirl could improve the system stability for the labyrinth seal with fewer blades (e.g. 5 blades). Its characteristics is mainly dominated by the first seal cavity. For the labyrinth seal with 10 blades, the system characteristics shows slight dependency on the inlet preswirl ratio. For the labyrinth seal with more blades (e.g. 15 blades), the negative inlet preswirl still increases the system stability, which agrees with the conventional conclusion. The paper provides a deeper understanding on the stability improvement of the labyrinth seal.

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.

Preswirl and Mixed-Flow (Mainly Liquid) Effects on Rotordynamic Performance of a Long (L/D = 0.75) Smooth Seal

Abstract Measured results are presented for rotordynamic coefficients and mass leakage rates of a long smooth annular seal (length-to-diameter ratio L/D = 0.75, diameter D = 114.686 mm, and radial clearance Cr = 0.200 mm) tested with a mixture of silicone oil (PSF-5cSt) and air. The test seal is centered, the seal exit pressure is maintained at 6.9 bars-g while the fluid inlet temperature is controlled within 37.8–40.6 °C. It is tested with three inlet-preswirl inserts, namely, zero, medium, and high (the preswirl ratios (PSRs), i.e., the ratio between the fluid's circumferential velocity and the shaft surface's velocity, are in ranges of 0.10–0.18, 0.30–0.65, and 0.65–1.40 for zero, medium, and high preswirls, respectively), six inlet gas-volume fractions GVFi (0%, 2%, 4%, 6%, 8%, and 10%), four pressure drops PDs (20.7, 27.6, 34.5, and 41.4 bars), and three speeds ω (3, 4, and 5 krpm). The targeted test matrix could not be achieved for the medium- and high-preswirl inserts at PD ≥ 27.6 bars due to the test-rig stator's dynamic instability issues. Spargers were used to inject air into the oil, and GVFi values higher than 0.10 could not be consistently achieved because of unsteady surging flow downstream from the sparger mixing section. Leakage mass flow rate m˙ and rotordynamic coefficients are measured, and the effect of changing inlet preswirl and GVFi is studied. The test results are then compared with predictions from a two-phase, homogeneous-mixture, bulk-flow model developed in 2011. Generally, both measurements and predictions show little change in m˙ as inlet preswirl changes. Measured m˙ remains unchanged or slightly increases with increasing GVFi, but predicted m˙ decreases. Measured m˙ is comparable to predicted values but consistently lower. Dynamic-stiffness coefficients are measured using an ensemble of excitation frequencies and curve-fitted well by frequency-independent stiffness Kij, damping Cij, and virtual mass Mij coefficients. Planned tests with the medium- and high-preswirl inserts could not be accomplished at PD = 34.5 and 41.4 bars because the seal stator became unstable with any finite injection of air. The test results show that the instability arose because the seal's direct stiffness K became negative and increased in magnitude with increasing GVFi. The model predicts a drop in K as GVFi increases, but the test results dropped substantially more rapidly than predicted. Also, the model does not predict the observed strong tendency for K to drop with an increase in preswirl in moving from the zero-to-medium and medium-to-high preswirl inserts. The authors believe that the observed drop in K due to increasing GVFi is not explained by either (a) a reverse Lomakin effect from operating in the transition flow regime or (b) the predicted drop in K at higher GVFi values from the model. A separate and as yet unidentified two-phase flow phenomenon probably causes the observed results. The negative K results due to increasing GVFi and moving from the zero to medium, and medium to high preswirl observed here could explain the instability issue (sudden subsynchronous vibration) on a high-differential-pressure helico-axial multiphase pump (MPP), reported in 2013. Effective damping Ceff combines the stabilizing effect of direct damping C, the destabilizing effect of cross-coupled stiffness k, and the influence of cross-coupled mass mq. As predicted and measured, increasing inlet preswirl significantly increases k and decreases Ceff, which decreases the seal's stabilizing properties. Ceff increases with increasing GVFi—becomes more stable.

A Novel Bulk-Flow Model for Pocket Damper Seals

Abstract In this paper, a novel bulk-flow model for pocket damper seals (PDS) is introduced. The model is based on two control volumes (CVs) for each circumferential pocket of the seal. The continuity, circumferential momentum, and energy equations are considered for each control volume. The circumferential recirculating flow within the pocket is modeled for the first time. The boundary layer theory is used to estimate the recirculating flow area, and the Swamee–Jain friction factor correlation allows for defining the dissipation of the circumferential velocity. The perturbation method is used to solve the partial derivative governing equations in the zeroth- and first-order system of equations. The rotordynamic coefficients are evaluated by integrating the dynamic pressure and rotor shear stresses along the circumferential direction. The predictions are compared to the experimental data, which refer to test conditions representative of high-pressure centrifugal compressors. Numerical predictions are accurate for both high positive–negative inlet preswirl ratios. Leakage predictions are also aligned with measurements. Finally, sealing selection approach is introduced in the paper for comparing the dynamic behavior of two different sealing technologies and identifying stable regions as a function of the rotor natural frequency and preswirl ratio.

Gas labyrinth seals: On the effect of clearance and operating conditions on wall friction factors – A CFD investigation

Abstract This paper presents a computational fluid dynamic (CFD) investigation quantifying the effects of labyrinth seal geometry and operating conditions on the rotor and stator circumferential friction factors (frθ, fsθ). These are needed to improve bulk-flow model (BFM) predictions of the evolution of circumferential flow velocity and the seal force coefficients. For a typical labyrinth seal tested by Vannini et al. (2014), the rotor frθ is independent of changes in clearance (0.8–2 × Cr) or the inlet preswirl ratio (αinlet = 0–0.72); whereas an increase in rotor speed (RΩ = 58–173 m/s) or outlet/inlet pressure ratio (PR = Pout/Pin = 0.40–0.85) decreases frθ. On the other hand, an increase in Ω, PR, and αinlet decrease the stator fsθ. Besides, fsθ increases with Cr. Predictions show that frθ and fsθ are mainly sensitive to PR, not to the magnitude of supply and discharge pressures.

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.

Measured Static and Rotordynamic Characteristics of a Smooth-Stator/Grooved-Rotor Liquid Annular Seal

Electric submersible pumps (ESPs) utilize grooved-rotor/smooth-stator (SS/GR) seals to reduce leakage and break up contaminants within the pumped fluid. Additionally, due to their decreased surface area (when compared to a smooth seal), grooved seals decrease the chance of seizure in the case of rotor-stator rubs. Despite their use in industry, the literature does not contain rotordynamic measurements for smooth-stator/circumferentially grooved-rotor liquid annular seals. This paper presents test results consisting of leakage measurements and rotordynamic coefficients for a SS/GR liquid annular sdeal. Both static and dynamic variables are investigated for various imposed preswirl ratios (PSRs), static eccentricity ratios (0–0.8), axial pressure drops (2–8 bars), and running speeds (2–8 krpm). The seals' static and dynamic features are compared to those of a smooth seal with the same length, diameter, and minimum radial clearance. Results show that the grooves reduce leakage at lower speeds (less than 5 krpm) and higher axial pressure drops, but does little at higher speeds. The grooved seal's direct stiffness is generally negative, which would be detrimental to pump rotordynamics. As expected, increasing preswirl increases the magnitude of cross-coupled stiffness and increases the whirl frequency ratio (WFR). When compared to the smooth seal, the grooved seal has smaller effective damping coefficients, indicative of poorer stability characteristics.